The statement that is false is: " lf p q is true, then p is a necessary condition in order that q holds."
In a logical statement "p implies q" (p->q), if p is true, then q must be true as well. However, this doesn't mean that p is necessary for q to hold. A necessary condition means that p is required for q to be true, but it's not sufficient, it may be other conditions that are also needed. In this statement, p is a sufficient condition for q to hold, but it's not necessary. This statement is a logical converse of the second statement "If p q is true, then p is a sufficient condition in order that q holds."
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Roads in Manhattan are called streets and avenues.
Streets run from east to west and avenues run from
north to south.
The distance between streets is around 80 m and the
distance between avenues is around 260 m, as shown
below.
Point X is at the centre of the junction of 15th Street
and 7th Avenue.
Point Y is at the centre of the junction of 21st Street and
4th Avenue.
Using the information above,
a) calculate the straight-line distance between point X
and point Y.
b) calculate the shortest distance along the roads to get
from point X to point Y.
Give your answers to the nearest metre.
The straight-line distance and the shortest distance between point X and point Y will be 2,260 m and 2,361.78, respectively.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The distance between streets is around 80 m and the distance between avenues is around 260 m, as shown below.
The straight-line distance between point X and point Y will be given as,
⇒ (24 - 15) x 260 + (9 - 5) x 80
⇒ 2,340 + 320
⇒ 2,260 m
The shortest distance along the roads to get from point X to point Y will be given as,
D² = (2,340)² + (320)²
D² = 5,475,600 + 102,400
D² = 5,578,000
D = 2,361.78 meters
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The complete question is attached below.
If there are only enough strawberries to produce 2 gallons of strawberry ice cream, how many gallons of chocolate ice cream can the shop efficiently produce? 0 4 12 15
Answer:
15
Step-by-step explanation:
I took the test and got it right
Life expectancy in the U.S. is steadily increasing due to medical advancements and the increased awareness of maintaining a healthy lifestyle. The life expectancies for men and women in the U.S. can be modeled by the following functions: W (x) = 0.126 x + 76.74. M (x) = 0.169 x + 69.11 where W(x) represents the life expectancy for women and M(x) represents the life expectancy for men, and x represents the number of years since 1975. (x = 0 corresponds to the year 1975, x = 5 corresponds to the year 1980 and so on.) Write an inequality to determine the birth years of women whose life expectancy is at least 85. a. 0.126 x + 76.74 less-than-or-equal-to 85 b. 0.126 x + 76.74 greater-than-or-equal-to 85 c. 0.126 x + 76.74 less-than 85 d. 0.126 x + 76.74 = 85 Please select the best answer from the choices provided A B C D
Life expectancy in the U.S. is steadily increasing due to medical advancements and the increased awareness of maintaining a healthy lifestyle. 0.126 x + 76.74 less-than-or-equal-to 85. Option A
What is Life expectancy?Generally, Based on an organism's birth year, present age, and other demographic parameters like sex, life expectancy is a statistical assessment of the typical amount of time that it is predicted to live. Life expectancy at birth, which has two definitions, is the most often used metric.
This inequality states that the life expectancy of women, modeled by the function W(x), is at least 85.
The less-than-or-equal-to symbol is used because the inequality is asking for the minimum birth year required to achieve a life expectancy of at least 85, which means that the value of the function can be equal to 85 as well as greater than 85.
The correct answer is A: 0.126 x + 76.74 less-than-or-equal-to 85.
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How many iterations are required to sort the array 10 23 14 35 17 15 16 using selection sort?
Iterations are required to sort the array 10 23 14 35 17 15 16 using selection sort = 5
The selection sort algorithm sorts an array by repeatedly finding the minimum element (considering ascending order) from the unsorted part and putting it at the beginning.
The algorithm maintains two subarrays in a given array.
The subarray which already sorted.
The remaining subarray was unsorted.
In every iteration of the selection sort, the minimum element (considering ascending order) from the unsorted subarray is picked and moved to the beginning of unsorted subarray.
After every iteration sorted subarray size increase by one and unsorted subarray size decrease by one.
After N (size of array) iteration we will get sorted array.
Lets consider the following array as an example: array[] ={10 23 14 35 17 15 16}
{64, 25, 12, 22, 11}
First pass:
For the first position in the sorted array, the whole array is traversed from index 0 to 6 sequentially. The first position where 10 is stored presently, after traversing whole array it is clear that 10 is the lowest value.
10 23 14 35 17 15 16
Thus, replace10 with 10. After one iteration 10, which happens to be the least value in the array, tends to appear in the first position of the sorted list.
10 23 14 35 17 15 16
Second Pass:
For the second position, where 23 is present, again traverse the rest of the array in a sequential manner.
10 23 14 35 17 15 16
After traversing, we found that 14 is the second lowest value in the array and it should appear at the second place in the array, thus swap these values.
10 14 23 35 17 15 16
Third Pass:
Now, for third place, where 23 is present again traverse the rest of the array and find the third least value present in the array.
10 14 23 35 17 15 16
While traversing, 15 came out to be the third least value and it should appear at the third place in the array, thus swap 15 with element present at third position.
10 14 15 35 17 23 16
Fourth pass:
Now, for fourth place, where 35 is present again traverse the rest of the array and find the fourth least value present in the array.
10 14 15 35 17 23 16
While traversing, 16 came out to be the fourth least value and it should appear at the fourth place in the array, thus swap 16 with element present at fourth position.
10 14 15 16 17 23 35
Fifth Pass:
At last the largest value present in the array automatically get placed at the last position in the array
The resulted array is the sorted array.
10 14 15 16 17 23 35
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How do you find the surface area and volume of a hexagonal prism?
For a Hexagonal Prism , the Surface Area can be calculated by using the formula [tex]3sh+3\sqrt{3}s^{2}[/tex] , and the volume can be calculated by using the formula [tex]\frac{3\sqrt{3}s^{2}}{2} \times s^{2} h[/tex] .
What is a Hexagonal Prism ?
The hexagonal prism is defined as the prism that has a hexagonal base and top. hexagonal prism is a 3D shape and that has 8 faces, 18 edges, and 12 vertices. As it has 8 faces it can also called as Octahedron.
The formula to calculate the Surface Area of the hexagonal prism is written as : [tex]3sh+3\sqrt{3}s^{2}[/tex] ;
The formula to calculate the Volume of hexagonal prism is written as : [tex]\frac{3\sqrt{3}s^{2}}{2} \times s^{2} h[/tex] ;
where h = is the height of hexagonal prism , and
s = is the side of the hexagonal base .
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Zack just got a grade of 93 on his report. However, because he turned it in 4 days late his teacher is going to deduct 5 per day. What will be Zach’s final score?
Answer: 73
Step-by-step explanation:
4 x 5 = 20
93 - 20 = 73
Answer the following
log3(81)=
2^x=1/32 • x
The solutions to the equation are
log₃ ( 81 ) = 4
2ˣ = 1/32 , the value of x = -5
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
A = log₃ ( 81 ) be equation (1)
On simplifying the equation , we get
logₐ ( aᵇ ) = b
From the equation , we get
A = log₃ ( 81 ) = log₃ ( 3⁴ )
So , log₃ ( 3⁴ ) = 4
Therefore , the value of the equation is A = 4
b)
2ˣ = 1/32 be equation (1)
On simplifying the equation , we get
32 = 2⁵
So , 1/32 = ( 1/2⁵ )
( 1/2⁵ ) = 2⁻⁵
Substituting the values in the equation , we get
2ˣ = 2⁻⁵
Therefore , the value of x = -5
Hence , the equations are solved
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x ≤ −9 whats the answer
Answer:
9
Step-by-step explanation:
if you search it up you get the answer your looking for
what is the missing number in the sequence: 4, 6, 10, 18, ___, 66.
Answer:
34
Step-by-step explanation:
Each number is added to by a doubling sequence
4, 4+2=6, 6+4=10, 10+8=18, 18+16=34, 34+32=66
The relative frequency table describes the relationship between students who completed an exam review and their performance on the exam.
Passed exam Did not pass exam Row Totals
Completed exam review 55% 10% 65%
Did not complete exam review 20% 15% 35%
Column Totals 75% 25% 100%
Part A: What is the percentage of students who passed the exam, given that they completed the exam review? Round to the nearest percentage. (2 points)
Part B: What is the percentage of students who passed the exam, given that they did not complete the exam review? Round to the nearest percentage. (2 points)
Part C: Is there an association between passing the exam and completing the exam review? Justify your answer. (2 points
The required percentages are
Part (a): 85% Part (a): 57%There is no association between passing the exam and completing the exam review
The percentage that passes the exam given that they complete the reviewFrom the question, we have the following parameters that can be used in our computation:
The table of values
The required percentage can be calculated as
Percentage = (Pass the exam and complete the review)/Complete the review)
Using the table of values, we have
Percentage = 55%/65%
Evaluate
Percentage = 85%
The percentage that passes the exam given that they did not complete the reviewHere, the required percentage can be calculated as
Percentage = (Pass the exam and did not complete the review)/Did not complete the review)
Using the table of values, we have
Percentage = 20%/35%
Evaluate
Percentage = 57%
The associationFrom (a) and (b), we can see that
85% of students who complete the review passes the exam57% of students who did not complete the review passes the examThese percentages are above 50% and they represent opposite entities
This means that there is no association
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Emma took a taxi from the airport to her house. She paid a flat fee of $$55 plus $$3. 703. 70 per mile. The fare came to $$4242. Complete the equation that can be used to find the correct distance dd in miles and then solve it to determine distance.
Emma traveled 1127.2 miles from the airport to her house.
The equation to calculate the distance traveled by Emma is:
55 + 3.703 * d = 4242
To solve the equation, we need to subtract 55 from both sides of the equation.
4242 - 55 = 4187
Then, we will divide both sides of the equation by 3.703
4187 / 3.703 = 1127.2
Finally, we can calculate the distance traveled by Emma in miles.
d = 1127.2 miles
Therefore, Emma traveled 1127.2 miles from the airport to her house.
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Emma traveled 10 from the airport to her house.
In this question we have been given that Emma took a taxi from the airport to her house.
She paid a flat fee of $5 plus $3. 70 per mile.
The fare came to $42.
We need to find an equation that can be used to find the correct distance d in miles and then solve it to determine distance.
Let c be the total traveling cost.
So, from given information an equation to calculate the distance traveled by Emma would be,
c = 5 + (3.70)d
The fare came to $42.
c = $42
Substiting this value in above equation we get,
42 = 5 + 3.70d
We solve this equation for d
42 - 5 = 3.70d
37 = 3.70d
d = 37 / 3.7
d = 10 miles
Therefore, the distance in miles covered by Emma is 10 miles.
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9p^2q^7-2p^5q^6 ⋅ 4p^7q
Answer:
-8p^12q^7+9p^2q^7
Step-by-step explanation:
Use pemdas
multiply -2p^5q^6 ⋅ 4p^7q
to get -8p^12q^7
add that with the first term
When X 3x² 2x 1 is divided by x 1 The remainder is?
The remainder when X 3x² 2x 1 is divided by x 1 is 2, the last coefficient.
To find the remainder when dividing X 3x² 2x 1 by x 1, we can use the division algorithm. This algorithm states that the remainder is equal to the dividend minus the product of the divisor and the quotient.
To find the quotient, we can use synthetic division, which is a shortcut method that allows us to divide polynomials without needing to use the traditional long division method.
In this case, the divisor is x 1, so we write down x 1 and the coefficients of X 3x² 2x 1 in order from the highest degree to the lowest degree, which is 3x² 2x 1. We then divide the first coefficient, 3, by the divisor, 1, and write this result, 3, as the first number in the quotient.
We then multiply 3 by the divisor, 1, and subtract this from the dividend. The result of this subtraction is 3x² 2x, so we repeat this process until we reach the last coefficient, which is the remainder. In this case, the last coefficient is 2, so this is the remainder when dividing X 3x² 2x 1 by x 1. Therefore, the remainder is 2.
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6. Blake, James and Staunton invested $9,000, $7,000, and $6,000, respectively. Their profits were to be divided according to the ratio of their investments. If James uses his share of the firm's profit of $825 to pay a personal debt of $230, how much will he have left? a. $30.50 b. $32.50 c. $34.50 d. $36.50 e. $37.50
The amount James have left after paying his debt in his profit is $32.50.
How to find the amount James have left?Blake, James and Staunton invested $9,000, $7,000, and $6,000, respectively. Their profits were to be divided according to the ratio of their investments.
James uses his share of the firm's profit of $825 to pay a personal debt of $230. The amount of money James have left can be calculated as follows;
The ratio of the investment is 9000: 7000 : 6000(9:7:6)
Hence,
James share of profit = 7 / 22 × 825
James share of profit = 5775 / 22
James share of profit = 262.5 dollars
Therefore,
amount he has left after paying his debt = 262.5 - 230
amount he has left after paying his debt = 32.50 dollars
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If a building that is 6 stories tall has a shadow that is 24 meters long, how many stories tall is a building with a shadow that is 40 meters long?
To make 40 meters long shadow, building should have 10 stories.
What is multiplication?In arithmetic, the multiplication of two numbers represents the repeated addition of one number with respect to another. These numbers can be whole numbers, natural numbers, integers, fractions, etc. If m is multiplied by n, then it means either m is added to itself ‘n’ number of times or vice versa.
Given,
Stories of building 24 meters long shadow = 6
Stories making 1 meter long shadow = 6/24
Stories in building making 40 meters long shadow = 6/24 × 40
= 240 / 24
Stories in 40 meters long building = 10
Hence, 10 stories tall building will make shadow length of 40 meters.
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Only six players on the tennis team showed up for practice today. If each player plays every other player one game, then how many games the team played total today?
The number of games that the team played today is; 15 games
How to solve combination problems?Let me name of each player be A, B, C, D, E, F.
Now, let's start counting number of matches played by each team one after the other.
1. Player A will play with B, C, D, E, F. So number of matches played by team A is equal to 5.
2. Player B will play with C, D, E & F.( Players B & A have already played match with each other. So we won't count it again.) Thus, number of matches played by player B is equal to 4.
3. Player C will play with D, E, F & as it has already played with B & A, we will not count it again. So, number of matches played by player C is equal to 3.
4. Player D is left to play with E & F as it has already played with rest of the team. So, number of matches played by Player D is equal to 2
5. Player E & F will play with each other;
Add total number of matches played from above which is equal to;
5 + 4 + 3 + 2 + 1 = 15
From here, further matches to be played will be based on how many teams will qualify for next round.
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okay this is the last question for now lol
Answer:
18°
Step-by-step explanation:
We know that, sum of the angles in a straight line are added up to 180°.
Accordingly,
[tex]x - 6 + 8x + 24 = 180[/tex]
Combine like terms.
[tex]9x + 18 =180[/tex]
Subtract 18 from both sides.
[tex]9x = 180 - 18 \\ 9x = 162[/tex]
Divide both sides by 9.
[tex]x = 18 \degree[/tex]
Answer:
x = 18
Step-by-step explanation:
The given angles are,
→ x - 6
→ 8x + 24
We generally know that,
→ Sum of angles in straight line is 180°.
Forming the equation,
→ (8x + 24) + (x - 6) = 180
Now required value of x will be,
→ (8x + 24) + (x - 6) = 180
→ 8x + 24 + x - 6 = 180
→ (8x + x) + (24 - 6) = 180
→ 9x + 18 = 180
→ 9x = 180 - 18
→ 9x = 162
→ x = 162 ÷ 9
→ [ x = 18 ]
Therefore, the value of x is 18.
2
Select the correct answer.
A community center has an L-shaped swimming pool that is 10 feet deep. What is the volume of the pool?
10 ft.
6 ft.
20 ft.
16 ft.
10 ft.
The volume of the pool, if The depth of the pool is 10 feet, is 1040 cubic feet.
What is volume?The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to visualize in any shape, yet it may be compared among shapes. For instance, a compass box has a larger volume than an eraser placed inside of it.
Given:
The depth of the pool is 10 feet,
Calculate the volume of the pool as shown below,
The volume of the pool = the Volume of a rectangular prism with dimensions 20ft. × 10ft. × 4ft. + volume of a rectangular prism has dimensions: 6ft. × 4ft. × 10ft.
The volume of the pool = 20 × 10 × 4 + 6 × 4 × 10
The volume of the pool = 200 × 4 + 24 × 10
The volume of the pool = 800 + 240
The volume of the pool = 1040
Thus, the volume of the pool is 1040 ft³.
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What is the perimeter of △lmn? 8 units 9 units 6 startroot 10 endroot units 8 startroot 10 endroot units
After solving, the perimeter of △lmn is 8 + √10.
In the given question, we have to find the perimeter of △lmn.
The graph of the given question is given below:
From the graph we can see that N(-1, 4), L(2, 4) and M(-2, 1)
Before finding the perimeter we have to find the length of the line.
We can find the length of the line using the formula
L = √[{x(2)-x(1)}^2+{y(2)-y(1)}^2]
We firstly find the length of line NL.
x(1) = -1, y(1) = 4, x(2) = 2 and y(2) = 4
L(NL) = √[(2-(-1))^2+(4-4)^2]
L(NL) = √[(2+1)^2+0^2]
L(NL) = √[(3)^2+0]
L(NL) = 3
Now we find the length of line LM.
x(1) = 2, y(1) = 4, x(2) = -2 and y(2) = 1
L(LM) = √[(-2-2)^2+(1-4)^2]
L(LM) = √[(-4)^2+(-3)^2]
L(LM) = √[16+9]
L(LM) = √25
L(LM) = 5
Now we find the length of line MN.
x(1) = -2, y(1) = 1, x(2) = -1 and y(2) = 4
L(MN) = √[(-1-(-2))^2+(4-1)^2]
L(MN) = √[(-1+2)^2+(3)^2]
L(MN) = √[(1)^2+9]
L(MN) = √[1+9]
L(MN) = √10
Now we finding the perimeter of △lmn
Perimeter of △lmn = length of NL + length of LM + length of MN
Perimeter of △lmn = 3 + 5 + √10
Perimeter of △lmn = 8 + √10
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The perimeter is equal to the sum of the lengths of its three sides. We added 8 units, 9 units, and 10 units to get a total of 27 units, which is the perimeter of △lmn.
The perimeter of a triangle is the sum of the lengths of its three sides. To calculate the perimeter of △lmn, we must first identify the lengths of the three sides. Let's say the length of side lm is 8 units, side mn is 9 units, and side ln is 10 units. We can now use the formula for the perimeter of a triangle to calculate the perimeter of △lmn:
Perimeter of △lmn = 8 + 9 + 10
Perimeter of △lmn = 27 units
To calculate the perimeter of △lmn, we first identified the lengths of its three sides. Then, we used the formula for the perimeter of a triangle, which states that the perimeter is equal to the sum of the lengths of its three sides. We added 8 units, 9 units, and 10 units to get a total of 27 units, which is the perimeter of △lmn.
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At the Planetarium, tickets cost $13.50 for adults and $5.50 for kids under 12. How many total tickets would someone get if they purchased 4 adult tickets and 14 kids tickets? How many total tickets would someone get if they purchased aa adult tickets and kk kids tickets?
If someone bought 4 adult tickets and 14 child tickets, they would get a total of 18 tickets.
If a customer buys aa adult tickets and kk child tickets, they will get a total of aa + kk tickets.
What are tickets?Generally, A ticket is a piece of paper or electronic document that gives you permission to enter an event, travel by a particular mode of transportation, or participate in an activity.
There are many different types of tickets, including tickets to concerts, sporting events, plays, and other performances, airline tickets, train tickets, and tickets to theme parks or other attractions.
Some tickets are sold in advance, while others are available at the door or at a ticket booth.
The number of total tickets someone would get if they purchased 4 adult tickets and 14 kids tickets are
18.
If someone purchases aa adult tickets and kk kids tickets, the total number of tickets they would get is
aa + kk.
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log(3x² + 4x) = log(2x²+12)
To solve this equation, you would need to isolate the logarithm on one side of the equation.
What is a logarithm in simple terms?
A logarithm is the power to which a number must be increased in order to get some other number (see Section 3 of this Math Review for more about exponents) (see Section 3 of this Math Review for more about exponents). For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2, or log 100 = 2.
You can start by using the property of logarithms that states that log(a*b) = log(a) + log(b).
So, you can split the left side of the equation into two logarithms: log(3x²) + log(1 + 4/3x) = log(2x²) + log(1 + 6/x)
Now, you could use the property log(a^b) = b*log(a) to simplify the equation further.
So, you will have: 2log(x) + log(1 + 4/3x) = 2log(x) + log(1 + 6/x)
Then by using log(1+x) ≈ x, you can simplify the equation further to 2log(x) + 4/3x ≈ 2log(x) + 6/x.
Now it's clear that the equation is not true and can't be solved.
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Eating at all you can eat buffet at your favorite restaurant cost $18.50, and increases its cost by 6% each year .
1. Write a function that correctly depicts the scenario.
2. How much will the buffet cost 10 years from now round your answer to the nearest cent
3. How much did the buffet cost 15 years ago ?round your answer to the nearest cent
The function that correctly depicts the scenario is f(x) = 18.50 * (1.06)^x
The cost of the buffet in 10 years is $33.13The cost of the buffet 15 years ago is $7.71How to write a function that correctly depicts the scenario.From the question, we have the following parameters that can be used in our computation:
Value of buffet = $18.50
Rate of increment = 6%
The function that correctly depicts the scenario is represented as
f(x) = Value of buffet * (1 + Rate of increment)^x
Substitute the known values in the above equation, so, we have the following representation
f(x) = 18.50 * (1 + 6%)^x
So, we have
f(x) = 18.50 * (1.06)^x
How much will the buffet cost 10 years from nowThis means that
x = 10
Substitute the known values in the above equation, so, we have the following representation
f(10) = 18.50 * (1.06)^10
Evaluate
f(10) = 33.13
How much did the buffet cost 15 years ago?This means that
x = -15
Substitute the known values in the above equation, so, we have the following representation
f(-15) = 18.50 * (1.06)^(-15)
Evaluate
f(-15) = 7.71
Hence, the amount 15 years ago is $7.71
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A line that includes the points (-6, 2) and (a, 1) has a slope of -1/9. What is the value of a?
Please help!
Step-by-step explanation:
(1 - 2)/(a + 6)= -1/9
-1/a + 6 = -1/9
-a - 6 = -9
-a = -3
a = 3
School work websites
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Compare Functions-Quiz-Level H
The equation and the table show the cost, y, for different sports programs as functions of the number
of classes, z.
Complete the statement.
LOOK AT PHOTO
These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.
What exactly is circumcenter?the triangle's circle's center. It is the point where the "perpendicular bisectors," or lines parallel to the centre of both sides, cross.
The intersection of any two perpendicular bisectors of any two triangle sides is known as the circumcenter of a triangle ABC.
The equation y=1 is the perpendicular bisector of sides B(3,0) and C(3,2). Because AB's midpoint is at 3,1 and its slope is unknown. The perpendicular bisector has zero slope. The equation for such a line is y=y1.
The equation for the perpendicular bisector of A(0,0) and B is also x=1.5 (3,0). The reason is that AB has a midpoint of zero slope and (1.5,0). The perpendicular bisector's slope won't be clearly defined. The equation for such a line is x=x1.
These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.
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find the curvature of r(t) = 5t, t2, t3 at the point (5, 1, 1).
K =
Help with geometry similar triangles.
1. x = (x1+x2)/2
2 .The ratio of DE:AB is DE/AB = √((x2-x1)^2 + (y2-y1)^2) / √((x2-x1)^2 + (y2-y1)^2)
What is the Midpoint?
The midpoint of a line segment is the point that is exactly in the middle of the line segment. It is equidistant from both endpoints of the line segment. It is represented by the coordinates (x, y), where x and y are the averages of the x-coordinates and y-coordinates of the endpoints of the line segment, respectively.
1. To solve for x, we can use the midpoint formula and the fact that D is the midpoint of AC.
The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.
let A(x1,y1) and C(x2,y2) be the coordinates of points A and C respectively
then D(x,y) is the midpoint of AC
x = (x1+x2)/2 and y = (y1+y2)/2
Since we know that AD = 28 and DC = 22, we can use the distance formula to find the coordinates of A and C.
The distance formula states that the distance between two points (x1, y1) and (x2, y2) is √((x2-x1)^2 + (y2-y1)^2)
so we have:
√((x2-x1)^2 + (y2-y1)^2) = √((x2-x1)^2 + (y2-y1)^2) =28
√((x2-x1)^2 + (y2-y1)^2) = √((x2-x1)^2 + (y2-y1)^2) =22
square both equations and we have:
(x2-x1)^2 + (y2-y1)^2 = 28^2
(x2-x1)^2 + (y2-y1)^2 = 22^2
2. To determine the ratio of DE:AB we can use the fact that E is the midpoint of BC.
let B(x1,y1) and C(x2,y2) be the coordinates of points B and C respectively
then E(x,y) is the midpoint of BC
x = (x1+x2)/2 and y = (y1+y2)/2
Since we know that BE = 8x + 3 and EC = 5x + 7.5, we can use the distance formula to find the coordinates of B and C and then find the ratio.
Hence, The ratio of DE:AB is DE/AB = √((x2-x1)^2 + (y2-y1)^2) / √((x2-x1)^2 + (y2-y1)^2)
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10.A ball is thrown upward from a height of 40 m and then falls to the ground. The
relation of its height to time can be written as h(t) = -5t² + 10t + 40, where h
represent the height of the ball above the ground in metres and t represents the
time in seconds.
a. How many seconds does it take the ball to reach the ground?
b. What is the maximum height of the ball?
c. At what time(s) will the ball be at a height of 43.75 m?
On solving the provide question we can say that - the equation, 40 = 10t - 5t^2 = > t^2 - 2t - 8 = 0
Describe equation.An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
u+ 10m/s , a = -10 and s = -40m
-40 = 10t - 5t^2
t^2 - 2t - 8 = 0
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What division calculation does this array describe?
Enter your answer by filling in the boxes.
The array depicted displays the division represented by the equation
20 ÷ 5 = 4
How to show division using arrayDivision is one of the four basic mathematical operators other include
addition
subtraction and
multiplication
Multiplication is the inverse or opposite of division, this means that when reverting the process of division we et to multiplication
In the array the number to be divided is the counting the whole small boxes which is 20.
Division is used to group the numbers in groups of 4 showing 5 divisions in group of four
This may also be 4 divisions in group of 5
Mathematically this written as
20 / 5 = 4
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Please help me pls I need help if you do thank you so much
The solution is
a) The total area of the rectangular grass area is 9600 feet²
b) The number of bags required is 9.6 bags
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the area of the rectangular grass area be = A
Now , the equation will be
The length of the rectangular grass portion = 120 feet
The width of the rectangular grass portion = 80 feet
The area of the rectangular grass portion = Length x Width
Substituting the values in the equation , we get
The area of the rectangular grass portion A = 80 x 120
The area of the rectangular grass portion A = 9600 feet²
Now , each bag of the grass seed covers 1000 feet²
So , the number of bags required for the entire area = area of the rectangular grass portion A / each bag of the grass seed covers 1000 feet²
On simplifying the equation , we get
The number of bags required for the entire area = 9600 / 1000
The number of bags required for the entire area = 9.6 bags
Therefore , the number of bags required is 9.6 bags
Hence , the total area of the rectangular grass area is 9600 feet²
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The floor of a gazebo is in the shape of a regular octagon. The perimeter of the floor is 72 feet. The distance from the center of the octagon to one of the vertices is 11.8 feet. What is the approximate length of the apothem
The approximate length of the apothem is 10.86 feet.
For a regular polygon, the apothem is the perpendicular line drawn from the center to the midpoint of any of its sides.
The formula to find the apothem given its perimeter is:
a = P / (2n tan (180 / n))
where a = length of the apothem
P = perimeter
n = number of sides of the polygon
Plug in the values and solve for the apothem.
a = P / (2n tan (180 / n))
a = 72 feet / (2)(8)(tan (180 / 8))
a = 10.86 feet
Therefore, the approximate length of the apothem is 10.86 feet.
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