GIVEN
The inequality:
[tex]x-8>10[/tex]SOLUTION
The inequality is to be solved.
Add 8 to both sides of the inequality. This follows the Addition Property of Inequalities:
[tex]if\text{ }xTherefore:[tex]\begin{gathered} x-8+8>10+8 \\ x>18 \end{gathered}[/tex]ANSWER
[tex]x>18[/tex]When we use function notation, f(x)=# is asking you to find the input when the output is the given number. We can also consider that an ordered pair can be written as (x,#). With this is mind, explain why f(x)=0 is special.
Notice that f(x)=0 is special because is the intercept of the graph with the x-axis and if f(x) corresponds to a function, the x-intercepts are the roots of the function.
The ordered pair can be written as (x,0), where x is such that f(x)=0.
Transforming the graph of a function by shrinking or stretching
So,
From the graph of the function f(x), we can notice it contains the points:
[tex]\begin{gathered} f(2)=-4\to(2,-4) \\ f(-2)=-2\to(-2,-2) \end{gathered}[/tex]If we use the transformation, we obtain the new points:
[tex]\begin{gathered} f(\frac{1}{2}x)\to f(\frac{1}{2}(2))=f(1)=-\frac{7}{2}\to(2,-\frac{7}{2}) \\ f(\frac{1}{2}x)\to f(\frac{1}{2}(-2))=f(-1)=-\frac{5}{2}\to(-2,-\frac{5}{2}) \end{gathered}[/tex]All we need to do to graph the new line is to plot the points:
[tex](2,-\frac{7}{2})\text{ and }(-2,-\frac{5}{2})[/tex]And form a line that passes through them.
what is the nessecary information you need to know about a cube?
Answer: the width, length and height
Step-by-step explanation: multiply the width length and height of a cube and you get the area
Anna's goal is to raise more than $200 for a
charity. Three of her neighbors donated $15 each, and one of her
friends donated $5. Write an inequality to show how much more
money Anna needs to raise. Explain how you found the answer.
Tell why you chose the inequality symbol that you used.
Answer: 200 < 50 + x
Step-by-step explanation:
Since three of her neighbors donated 15 dollars each, we can find how much she earned from them by doing 3 x 15 = 45.
Including the 5 dollars earned by her friend, we get 50 dollars by doing 45+5 = 50.
Anna needs more than 200 dollars so 200 has to be less than Anna's total earnings. (x) is how much more Anna will need to earn to make the inequality true.
What is the distance from the ball to the base of the building? Round to the nearest foot.*
Given:
[tex]\theta=37^{\circ}\text{ ; height of the building is }60\text{ ft}[/tex][tex]\begin{gathered} \tan 37^{\circ}=\frac{Height\text{ of the building}}{\text{Distance between the ball and foot of the building}} \\ 0.7536=\frac{60}{\text{Distance between the ball and foot of the building}} \\ \text{Distance between the ball and foot of the building}=\frac{60}{0.7536} \\ =80\text{ feet} \end{gathered}[/tex]80 feet is the final answer.
Sand will be placed under the base of a circular pool with a diameter of 14 feet. 1 bag of sand covers about 5 square feet. How many bags of sand are needed? Use 3.14 for pi. Round bags up.
I am getting hung up on the last part of doing this problem.
Any help is greatly appreciated.
Sand will be placed under the base of a circular pool with a diameter of 14 feet. 1 bag of sand covers about 5 square feet. the number of bags of sand required is 30bags.
The area of the pool is
A = πr²
A = 3.14×(7 ft)² = 153.8 ft²
The number of bags of sand required is ...
(153.8 ft²)/(5 ft²/bag) ≈ 30.76bags
bags of sand are needed.
What is diameter?The diameter is defined as twice the length of the radius of the circle. The radius is measured from the centre of the circle to one endpoint on the boundary of the circle, while the diameter is the distance measured from one end of the circle to a point on the other end of the circle that passes through the centre. This is indicated by the letter D. The circumference of a circle has an infinite number of points, which means that the circle has an infinite number of diameters and each diameter of the circle is the same length.
Ø is the symbol used in the design to indicate the diameter. This symbol is often used in technical data and drawings.
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Kayla has $37.99 in her checking account. she uses her debit card to make purchases of $26.29 and $22.98 which overdraws her account. her bank charges her account an overdraft fee of $25.00. She then deposits her paycheck for $55.07 from her part time job. what is the balance in her account?
Aye itz just me, this is the solution:
Initial balance = $ 37.99
Purchase 1 = ($ 26.29)
Purchase 2 = ($ 22.98)
Overdraft fee = ($ 25.00)
Deposit = $ 55.07
______________________
New balance = 37.99 - 26.29 - 22.98 - 25 + 55.07
New balance = $ 18.82
Solve the inequality a < 5 and write the solution using: Inequality Notation:
Answer:
Step-by-step explanation:
Ralph collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25pounds each week. Write an equation in slope-intercept form for the total of pounds, y, ofaluminum cans after x weeks. How long will it take Ralph to collect 400 pounds?
slope intercept form:
y= mx+b
Where:
m= slope
b= y-intercept
total pounds: y
number of weeks: x
the total number of pounds must be equal to the pounds already collected (100) plus the product of the number of weeks (x) and the number of pounds collected per week (25)
y= 100+25x
To collect 400 pounds, replace y by 400 and solve for x ( weeks)
400 = 100+25x
400-100= 25x
300=25x
300/25 = x
12 = x
12 weeks to collect 400 pounds
I need to find two sets of coordinates and graph them. Please help?!
Answer
The two coordinates on the line include
(0, -1.5) and (-4.5, 0)
The graph of the line is presented below
Explanation
We are asked to plot the grap of the given equation of a straight line.
To do that, we will obtainthe coordinates of two points on the line.
These two points will preferrably be the intercepts of the line.
y = (-x/3) - (3/2)
when x = 0
y = 0 - (3/2)
y = -(3/2)
y = -1.5
First coordinate and first point on the line is (0, -1.5)
when y = 0
0 = (-x/3) - (3/2)
(x/3) = -(3/2)
x = (-3) (3/2)
x = -(9/2)
x = -4.5
Second coordinate and second point on the line is thus (-4.5, 0)
So, to plot the line, we just mark these two points and connect them to each other.
The graph of this line is presented under 'Answer' above.
Hope this Helps!!!
The vertex of the parabola below is at the point
SOLUTION
The equation of a parabola in a vertex form is given
since the parabola is on the x-axis.
[tex]\begin{gathered} x=a(y-h)^2+k \\ \text{Where } \\ \text{Vertex}=(h,k) \end{gathered}[/tex]From the diagram given, we have
[tex]\text{vertex}=(-4,-2)[/tex]Substituting into the formula above, we have
[tex]\begin{gathered} x=a(y-h)^2+k \\ h=-4,k=-2 \end{gathered}[/tex]We have
[tex]\begin{gathered} x=(y-(-2)^2-4 \\ x=(y+2)^2-4 \end{gathered}[/tex]Since the parabola is a reflection from the parent function, then
[tex]a=-2[/tex]The equation of the parabola becomes
[tex]x=-2(y+2)^2-4[/tex]Answer; x = -2(y + 2)^2-4
4. (09.01 MC) Let set A = {1, 3, 5, 7) and set B = {1, 2, 3, 4, 5, 6, 7, 8} Which notation shows the relationship between set A and set B? (2 points) O AUB O ASE O Ane OBCA
A set X is said to contain a set Y if every element in Y is an element in X.
[tex]X\supseteq Y\text{ or X}\subseteq Y[/tex]In this case
[tex]1\in B,\text{ 3 }\in B,5\in B,\text{ and 7}\in B[/tex][tex]\in\text{ means: is in}[/tex][tex]so\text{ m}\in N,\text{ means that m is in N}[/tex]Therefore,
[tex]B\supseteq A\text{ or A}\subseteq B[/tex]find the probability of tossing 5 tails, them 5 heads. on the first 10 tosses of a fair coin
When a coin is tossed, the probability iof getting a head or a tail is 1/2.
The probability of tossing 5 tails = (1/2)^5
The probability of tossing 5 heads = (1/2)^5
The probability of tossing 5 talis and 5 heads = (1/2)^5 X (1/2)^5
= (1/2)^10
(If there is more than one answer, use the "or" button.)Round your answer(s) to the nearest hundredth.A ball is thrown from a height of 141 feet with an initial downward velocity of 21 ft/s. The ball's height h (in feet) after t seconds is given by the following.h = 141 - 21t - 16t ^ 2How long after the ball is thrown does it hit the ground?
Solution:
Given:
[tex]h=141-21t-16t^2[/tex]To get the time the ball hit the ground, it hits the ground when the height is zero.
Hence,
[tex]\begin{gathered} At\text{ h = 0;} \\ h=141-21t-16t^2 \\ 0=141-21t-16t^2 \\ 141-21t-16t^2=0 \\ 16t^2+21t-141=0 \end{gathered}[/tex]To solve for t, we use the quadratic formula.
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{where;} \\ a=16,b=21,c=-141 \\ t=\frac{-21\pm\sqrt[]{21^2-(4\times16\times-141)}}{2\times16} \\ t=\frac{-21\pm\sqrt[]{441+9024}}{32} \\ t=\frac{-21\pm\sqrt[]{9465}}{32} \\ t=\frac{-21\pm97.288}{32} \\ t_1=\frac{-21+97.288}{32}=\frac{76.288}{32}=2.384\approx2.38 \\ t_2=\frac{-21-97.288}{32}=\frac{-118.288}{32}=-3.6965\approx-3.70 \end{gathered}[/tex]
Since time can't be a negative value, we pick the positive value of t.
Therefore, to the nearest hundredth, it takes 2.38 seconds for the ball to hit the ground.
1. In the figure, angle CAB is 47. What would prove that angle ACD is also 47?
A A reflection of ABC over AC, such that ABC maps to CDA.
B A rotation of ABC 180 clockwise around C, such that ABC maps to ADC.
C A rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC.
D A translation of ABC to the top right, such that ABC maps to ADC.
The correct option C: A rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC.
What is termed as the rotation?Geometry can be used to determine the meaning of rotation in mathematics. As a result, it is described as the movement of something around a center or an axis. Any rotation is regarded as a specific space motion that freezes at at least one point. In reality, a earth rotates on its axis, which is also an instance of rotation. Because a clockwise rotation has a negative magnitude, a counterclockwise rotation does have a positive magnitude.For the given question;
In triangles ABC angle CAB is 47.
If the triangles ABC and ACD becomes congruent such that angle ACD corresponds to angles ABC.
Then, both angles will be equal.
For, this, a rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC is to be done.
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Hello! Need a little help on parts a,b, and c. The rubric is attached, Thank you!
In this situation, The number of lionfish every year grows by 69%. This means that to the number of lionfish in a year, we need to add the 69% to get the number of fish in the next year.
This is a geometric sequence because the next term of the sequence is obtained by multiplying the previous term by a number.
The explicit formula for a geometric sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]We know that a₁ = 9000 (the number of fish after 1 year)
And the growth rate is 69%, to get the number of lionfish in the next year, we need to multiply by the rate og growth (in decimal) and add to the number of fish. First, let's find the growth rate in decimal, we need to divide by 100:
[tex]\frac{69}{100}=0.69[/tex]Then, if a₁ is the number of lionfish in the year 1, to find the number in the next year:
[tex]a_2=a_1+a_1\cdot0.69[/tex]We can rewrite:
[tex]a_2=a_1(1+0.69)=a_1(1.69)[/tex]With this, we have found the number r = 1.69. And now we can write the equation asked in A:
The answer to A is:
[tex]f(n)=9000\cdot1.69^{n-1}[/tex]Now, to solve B, we need to find the number of lionfish in the bay after 6 years. Then, we can use the equation of item A and evaluate for n = 6:
[tex]f(6)=9000\cdot1.69^{6-1}=9000\cdot1.69^5\approx124072.6427[/tex]To the nearest whole, the number of lionfish after 6 years is 124,072.
For part C, we need to use the recursive form of a geometric sequence:
[tex]a_n=r(a_{n-1})[/tex]We know that the first term of the sequence is 9000. After the first year, the scientists remove 1400 lionfish. We can write this as:
[tex]\begin{gathered} a_1=9000 \\ a_n=r\cdot(a_{n-1}-1400) \end{gathered}[/tex]Because to the number of lionfish in the previous year, we need to subtract the 1400 fish removed by the scientists.
The answer to B is:
[tex][/tex]10 ptQuestion 10A can of soup has a volume of 80 in and mass of 10 ounces. A can of tuna has a volume of 56 in and mass of 8ounces. About how much less is the density of the soup than the tuna (give your answer in ounces/square inch).Round your answer to the nearest 1000th.SOUPSTUNA CHUNKSBrineLENTIL0.0179 ounces per per square inches less0.1429 ounces per per square inches less0.1250 ounces per per square inches less0.0099 ounces per per square inches less
We have that the general formula for the density given the volume and the mass is:
[tex]d=\frac{m}{v}[/tex]in this case, the densities for the can of soup and the can of tuna are:
[tex]\begin{gathered} d_{soup}=\frac{10}{80}=\frac{1}{8} \\ d_{tuna}=\frac{8}{56}=\frac{1}{7} \end{gathered}[/tex]the difference between these two densities is:
[tex]\frac{1}{7}-\frac{1}{8}=\frac{1}{56}=0.0179[/tex]therefore, there is 0.0179 less density of the soup than the tuna
Select the correct product of (x + 3)(x - 5). CX - 15 X5 + 3x - 5x2 - 15 X - 15 C x + 3x - 5x - 15
Distributive property:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]Multiplication of powers with the same base:
[tex]a^m\cdot a^n=a^{m+n}[/tex]For the given expression:
[tex]\begin{gathered} (x^2+3)(x^3-5)=x^2\cdot x^3+x^2\cdot(-5)+3\cdot x^3+3\cdot(-5) \\ \\ =x^{2+3}-5x^2+3x^3-15 \\ =x^5-5x^2+3x^3-15 \\ =x^5+3x^3-5x^2-15 \end{gathered}[/tex]Answer is the second option
Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x.
(x ^4 - 3x^3 + 3x^2 - 3x + 6) / (x - 2)
SOLUTION
We want to perform the following division using synthetic division
[tex]\frac{x^4-3x^3+3x^2-3x+6}{x-2}[/tex]This becomes
First we write the problem in a division format as shown below
Next take the following step to perform the division
Now, we have completed the table and we obtained the following coefficients, 1, -1, 1, -1, 4
Note that the first four ( 1, -1, 1, -1) are coefficients of the quotient, while the last one (4) is the coefficient of the remainder.
Hence the quotient is
[tex]x^3-x^2+x-1[/tex]And the remainder is 4.
Hence
[tex]\frac{x^4-3x^3+3x^2-3x+6}{x-2}=x^3-x^2+x-1+\frac{4}{x-2}[/tex]Which expression is equivalent to (xy)z?A (x+y)+zB 2z(xy)C x(yz)D x(y+z)
The expression (xy)z can be simplified as;
[tex]\begin{gathered} (xy)z=xyz \\ \text{Therefore xyz;} \\ xyz=x(yz) \end{gathered}[/tex]The correct answer is option C
the product of (2-x)and (1-x)is equal to x^2-3x+2
So the product of (2-x) and (1-x) is equal to x^2 - 3x + 2
If tan A = ã and tan B=16calculate and simplify the following:?tan(A - B) = +
SOLUTION
[tex]\begin{gathered} In\text{ Trigonometry} \\ \tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\text{ tan B}}_{} \end{gathered}[/tex]Given:
[tex]\begin{gathered} \tan \text{ A= }\frac{5}{6} \\ \tan \text{ B= }\frac{1}{6} \end{gathered}[/tex]Now substitute these given into the expression above:
[tex]\tan (A-B)=\frac{\frac{5}{6}-\frac{1}{6}}{1+(\frac{5}{6}\times\frac{1}{6})}[/tex]Simplifying further:
[tex]=\frac{\frac{2}{3}}{1+\frac{5}{36}}[/tex][tex]\begin{gathered} =\frac{\frac{2}{3}}{\frac{41}{36}} \\ =\frac{2}{3}\times\frac{36}{41} \\ =\frac{72}{123} \\ =\frac{24}{41} \end{gathered}[/tex]The answer therefore is:
[tex]\frac{24}{41}[/tex]What is 5,435,778 expressed in scientific notation?A.5.435778 x 10*7B.5.435778 x 10*3C.5.435778 x 10*6D.5.435778 x 10*5
Given the number
[tex]5,435,778[/tex]We can express it in scientific notation below;
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.
Therefore, in the given question, we will have;
[tex]5,435,778=5.435778\times10^6[/tex]Answer: Option C
Please help me out here. I really don’t understand
Step-by-step explanation:
you have both points : (1, 1) and (5, 5).
so, we don't need to do any triangle calculations to get the height of the main triangle.
all we need to do is calculate the distance between these 2 points.
2 points in a coordinate grid create a right-angled triangle.
the direct distance is the Hypotenuse (the side opposite of the 90° angle). and the legs are the x- and the y-coordinate differences (one up or down the other left or right).
and we can use Pythagoras
c² = a² + b²
c being the Hypotenuse a and b being the legs.
so, how long are these legs here ?
the x-difference is 5 - 1 = 4.
also the y-difference is 5 - 1 = 4
so,
distance² = 4² + 4² = 16 + 16 = 32
distance = sqrt(32) = sqrt(16×2) = 4×sqrt(2) =
= 5.656854249...
the distance of P to the line RQ is 5.656854249...
the price of a gallon of unleaded gas has risen to $2.92 today. yesterday's price was $2.85. find the percentage increase. round to the nearest 10th of a percent
Given:
[tex]\begin{gathered} P_{\text{today}}=2.92,P_{today}=Price\text{ of a gallon of unleaded gas today} \\ P_{\text{yesterday}}=2.85, \\ P_{yesterday}=Price\text{ of a gallon of unleaded gas today} \end{gathered}[/tex]To Determine: The percentage increase round to the nearest 1oth of a percent
The formula for percentage increase is given below:
[tex]\begin{gathered} P_{in\text{crease}}=\frac{increase}{P_{\text{initial}}}\times100\% \\ In\text{crease}=P_{final}-P_{in\text{itial}} \end{gathered}[/tex]Substitute the given into the formula
[tex]\begin{gathered} P_{\text{yesterday}}=P_{i\text{nitial}}=2.85 \\ P_{\text{today}}=P_{\text{final}}=2.92 \\ \text{Increase}=2.92-2.85=0.07 \end{gathered}[/tex][tex]\begin{gathered} P_{in\text{crease}}=\frac{increase}{P_{\text{initial}}}\times100\% \\ P_{in\text{crease}}=\frac{0.07}{2.85}\times100\% \\ P_{in\text{crease}}=0.02456\times100\% \\ P_{in\text{crease}}=2.456\% \\ P_{in\text{crease}}\approx2.5\%(nearest\text{ 10th)} \end{gathered}[/tex]Hence, the percentage increase to the nearest 10th of a percent is 2.5%
A baker paid $15.05 for flour at a store that sells flour for $0.86 per pound.
Solution:
Given that a store sells flour for $0.86 per pound, this implies that
[tex]1\text{ lb}\Rightarrow\$0.86[/tex]Given that a baker paid $15.05, let y represent the amount of flour the baker bought.
Thus,
[tex]y\text{ lb}\Rightarrow\$15.05[/tex]To solve for y,
[tex]\begin{gathered} 1\text{lb}\operatorname{\Rightarrow}\operatorname{\$}0.86 \\ y\text{ lb}\Rightarrow\$15.05 \\ cross-multiply, \\ y\text{ lb = }\frac{\$\text{15.05}}{\$0.86}\times1\text{ lb} \\ =17.5\text{ lb} \end{gathered}[/tex]Hence, the baker bought 17.5 lb of flour.
The country of Scotstats requires the people in their country to have license tags on their car such that the first 3 characters are English letters but no letter may repeat. The last 3 characters must each be a number 0-9 and again no numbers can be repeated. How many license tags are possible?
Answer
11,232,000 possible license tags.
Explanation
The licenses have space for 6 characters.
We need to note that there are 26 alphabets and 10 numbers to pick from.
So, for the first character, any of the 26 alphabets can take this spot.
For the second character, 25 alphabets are now available for that space. (Since repetition is not allowed)
For the third character, 24 alphabets are available for that.
For the fourth character, any of the 10 numbers can take up that spot.
For the fifth character, only 9 numbers can take this spot now. (No repetition rule too)
For the sixth character, 8 numbers can take that spot.
So, mathematically, the number of license tags possible will be
26 × 25 × 24 × 10 × 9 × 8 = 11,232,000 possible license tags
Hope this Helps!!!
Which of the following correctly represents the movement on the number line for the calculation 21 - (- 15) + (- 30) ?
a- left right left
b-right left left
c- right left right
d-right right left
It is the movement on the number line is right right left
The option (d) is correct .
Given,
The movement on the number line for the calculation
21 - (- 15) + (- 30)
To find the which of the following correctly represents the movement of calculation?
Now, According to the question:
21 - (- 15) + (- 30)
21 + 15 - 30 = 6
right right left
Hence, It is the movement on the number line is right right left
The option (d) is correct.
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12. Find DC.
A
20
54°
B
D
28°
C
The measure of the DC is 30.43 units after applying the trigonometric ratios in the right-angle triangle.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that:
A triangle is shown in the picture.
From the figure:
Applying sin ratio in triangle ADB
sin54 = BD/20
BD = 20sin54
BD = 16.18
Applying the tan ratio in triangle CDB
tan28 = 16.18/DC
DC = 30.43 units
Thus, the measure of the DC is 30.43 units after applying the trigonometric ratios in the right-angle triangle.
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Need help with my math please..
Answer:
i can't read this very well
