The initial equation is:
[tex]k^2=47[/tex]Then, we can solve it calculating the square root on both sides:
[tex]\begin{gathered} \sqrt[]{k^2}=\sqrt[]{47} \\ k=6.9 \\ or \\ k=-6.9 \end{gathered}[/tex]Therefore, k is equal to 6.9 or equal to -6.9
Answer: k = 6.9 or k = -6.9
Multiply.-4u? ( – 5u?)Simplify your answer as much as possible.X $
SOLUTION:
Simplify;
[tex]-4u^2(-5u^3)[/tex]Using product rule;
[tex](-\times-)(4\times5)(u^2\times u^3)[/tex]From Indices law;
[tex]a^b\times a^c=a^{b+c}[/tex]Thus;
[tex]\begin{gathered} (-\operatorname{\times}-)(4\times5)(u^2\times u^3)=(+)(20)(u^{2+3}) \\ =20u^5 \end{gathered}[/tex]FINAL ANSWER:
[tex]\begin{equation*} 20u^5 \end{equation*}[/tex]The exponential function that represents an experiment to track the growth of agroup bacterial cells is f(x) = 2200(1.03)*, where f(x) is the number of cells and x isthe time in minutes.• Sketch this scenario, including variables, title, axes and appropriate scales.• How many bacterial cells were there to begin the experiment?• What is the percentage growth of the bacterial cells per minute?• How many bacterial cells are there after one-half hour? Round to the nearestthousand.• How long will it take for there to be 7500 bacterial cells? Round your answerto the nearest whole minute?
For this problem we are going to be working with the function:
[tex]f(x)=2200(1.03)^x[/tex]where x is the time in minutes and f(x) represents the number of bacteria at any given time x.
Part 1.
To sketch the graph we need to determine some points of it; to get them we give values to x and plug them in the expression for the funtion.
If x=0 we have that:
[tex]\begin{gathered} f(0)=2200(1.03)^0 \\ f(0)=2200 \end{gathered}[/tex]Then we have the point (0,2200).
If x=10 we have that:
[tex]\begin{gathered} f(10)=2200(1.03)^{10} \\ f(10)=2956.616 \end{gathered}[/tex]Then we have the point (10,2956.616).
If x=20 we have that:
[tex]\begin{gathered} f(20)=2200(1.03)^{20} \\ f(20)=3973.445 \end{gathered}[/tex]Then we have the point (20,3973.445).
If x=30 we have that:
[tex]\begin{gathered} f(30)=2200(1.03)^{30} \\ f(30)=5339.977 \end{gathered}[/tex]Then we have the point (30,5339.977).
If x=40 we have that:
[tex]\begin{gathered} f(40)=2200(1.03)^{40} \\ f(40)=7176.483 \end{gathered}[/tex]Then we have the point (40,7176.483).
If x=50 we have that:
[tex]\begin{gathered} f(50)=2200(1.03)^{50} \\ f(50)=9644.593 \end{gathered}[/tex]Then we have the point (50,9644.593).
Then we have the points (0,2200), (10,2956.616), (20,3973.445), (30,5339.977), (40,7176.483) and (50,9644.593). Plotting this points on the plane and joining them with a smooth line we have that the grah of the function is:
Part 2.
To determine how many bacteria were at the beginnning of the experiment we plug x=0 in the function describing the population, we did this in the previous question; therefore we conclude that there were 2200 bacteria at the beginning of the experiment.
Part 3.
We notice that the function fgiven has the form:
[tex]f(x)=a(1+r)^x[/tex]where a=2200 and r=0.03; for this type of function the growth rate in decimal form is given by r. Therefore we conclude that the percentage growth in this function is 3%.
Part 4.
To determine how many bacteria were in the experiment after one half hout we plug x=30 in the function give; we did this in part 1 of the proble.Therefore we conclude that after one half hour there were approximately 5340 bacteria cells. (for this part we roun to the neares whole number)
Part 5.
To determine how long it takes to have 7500 cells we plug f(x)=7500 in the expression given and solve the resulting equation for x:
[tex]\begin{gathered} 2200(1.03)^x=7500 \\ 1.03^x=\frac{7500}{2200} \\ 1.03^x=\frac{75}{22} \end{gathered}[/tex]To remove the base we need to remember that:
[tex]b^y=x\Leftrightarrow y=\log _bx[/tex]Then we have:
[tex]\begin{gathered} 1.03^x=\frac{75}{22} \\ x=\log _{1.03}(\frac{75}{22}) \end{gathered}[/tex]Now we use the change of base property for logarithms:
[tex]\log _bx=\frac{\ln x}{\ln b}[/tex]Then we have:
[tex]\begin{gathered} x=\log _{1.03}(\frac{75}{22}) \\ x=\frac{\ln (\frac{75}{22})}{\ln 1.03} \\ x=41.491 \end{gathered}[/tex]Therefore it takes 41 minutes to have 7500 cells.
In a film, a character is criticized for marrying a woman when he is three times her age. He wittily replies, "Ah, but in 21 years time I shall only be twice her age." How old are the man and the
woman?
Write a linear function that models the total monthly costs for each option for x hours of court rental time.
The age of man is 63 years and the age of women is 21 years.
Given that, a character is criticized for marrying a woman when he is three times her age.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let age of man be x and the age of women be y.
Now, x=3y ---------(1)
In 21 years time man will be twice her age.
x+21=2(y+21)
⇒ x+21=2y+42
⇒ x-2y=21 ---------(2)
Substitute equation (1) in (2), we get
3y-2y=21
⇒ y = 21
So, x=3y=63
Therefore, the age of man is 63 years and the age of women is 21 years.
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How would these look graphed ? Look at image attached .
These are two lines intersected ,in one point
One is positive inclined, the other negative.
Then now GRAPH
THEN BOTH LINES INTERSECT AT
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 5 millimeters long, and the height of the equilateral triangle is 4.3 millimeters. The pyramid's slant height is 3 millimeters. What is its surface area?
The surface area of the triangular base pyramid is 19.75 mm².
How to find the surface area of a pyramid?The surface area of a triangular pyramid is the sum of the area of the whole sides of the triangular pyramid.
Therefore,
Surface area of a triangular pyramid = base area + 1 / 2 (perimeter × slant height)
The base of the triangular pyramid is an equilateral triangle. An equilateral triangle has congruent sides.
Therefore,
base area = 1 / 2 × 5 × 4.3
base area = 10.75 mm²
Hence,
perimeter of the base = 5 + 5 + 5 = 15 mm
Surface area of a triangular pyramid = 10.75 + 1 / 2 (15 × 3)
Surface area of a triangular pyramid = 10.75 + 1 / 2(18)
Surface area of a triangular pyramid = 10.75 + 9
Surface area of a triangular pyramid = 19.75 mm²
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Please see image attached. I am not able to solve, even after using the formula
Given:
Total number of cub scouts is 20 and the number of scout is 10 more than 2 times the number of adult leaders.
Required:
We need to find the number of adult leaders.
Explanation:
Lets consider cub scouts as c and adult leaders as a so the
[tex]c=20[/tex]and the formula for adult is
[tex]\begin{gathered} c=2a+10 \\ 20=2a+10 \end{gathered}[/tex]simplify as:
[tex]\begin{gathered} 10=2a \\ a=5 \end{gathered}[/tex]Final answer:
Number of adult leaders is 5
Below, the two-way table is given for a classof students.FreshmenSophomoreJuniorsSeniorsTotalMale4622Female 3463TotalIf a female student is selected at random, find theprobability that the student is a senior.
Conditional Probability
First, we must complete the totals in the table as follows:
The formula for the conditional probability is:
[tex]P(B|A)=\frac{P(B\cap A)}{P(A)}[/tex]Where A is an event we know has already occurred, B is an event we want to calculate its probability of occurrence, and P∩A is the probability of both occurring.
We know a female student has been selected, so that is our known event and:
[tex]P(A)=\frac{16}{30}=\frac{8}{15}[/tex]The probability that a female student is also a senior is:
[tex]P(A\cap B)=\frac{3}{30}=\frac{1}{10}[/tex]Substituting:
[tex]\begin{gathered} P(B|A)=\frac{\frac{1}{10}}{\frac{8}{15}} \\ \\ P(B\lvert\rvert A)=\frac{1}{10}\frac{15}{8}=\frac{3}{16} \end{gathered}[/tex]The required probability is 3/16
There are two machines that produce aluminum cans. The newer machine can produce 5700 cans in 190 minutes. It takesthe older machine 285 minutes to produce that many cans. If the two machines work together, how long will it take them to produce 5700 cans?
114 minutes
Explanation
Step 1
find the rate of production of each machine (cans per minute)
so
a)The newer machine:
[tex]\begin{gathered} rate=\frac{cans\text{ }}{time} \\ rate_1=\frac{5700\text{ cans}}{190\text{ minutes}}=30\text{ }\frac{cans}{minute} \end{gathered}[/tex]b)the older machine:
[tex]\begin{gathered} rate=\frac{cans\text{ }}{time} \\ rate_2=\frac{5700\text{ cans}}{285\text{ minutes}}=20\text{ }\frac{cans}{minute} \end{gathered}[/tex]Step 2
Add the rates together to determine their combined
[tex]\begin{gathered} rate_{total}=rate_1+rate_2 \\ rate_{total}=30\text{ }\frac{cans}{minute}+20\frac{cans}{m\imaginaryI nute} \\ rate_{total}=50\text{ }\frac{cans}{minute} \end{gathered}[/tex]so, the total rate( both machine working ) is 50 cans per minute
Step 3
finally, to find the time to produce 5700 cans, divide the total cans by the rate, so
[tex]\begin{gathered} time=\frac{number\text{ of cans}}{rate} \\ time=\frac{5700\text{ cans}}{50\frac{cans}{minute}}=114minutes \\ time=\text{ 114 minutes} \end{gathered}[/tex]therefore, the answer is 114 minutes
I hope this helps you
An independent third party found the cost of a basic car repair service for a local magazine. The mean cost is $217.00 with a standard deviation of $11.40. Which of the following repair costs would be considered an “unusual” cost?
Given
An independent third party found the cost of a basic car repair service for a local magazine.
The mean cost is $217.00 with a standard deviation of $11.40.
To find: The repair costs which would be considered an “unusual” cost.
Explanation:
It is given that, the mean is 217.00, and the standard deviation is 11.40.
Consider, the distribution as a Normal distribution.
Then, the first range is defined as,
[tex]\begin{gathered} First\text{ }range:mean\pm SD \\ \Rightarrow X_1=mean+SD \\ =217.00+11.40 \\ =228.4 \\ \Rightarrow X_2=mean-SD \\ =217.00-11.40 \\ =205.6 \end{gathered}[/tex]And, the second range is defined as,
[tex]\begin{gathered} Second\text{ }range:mean\pm2SD \\ \Rightarrow X_3=217.00+2(11.40) \\ =217.00+22.8 \\ =239.8 \\ \Rightarrow X_4=217.00-2(11.40) \\ =217.00-22.8 \\ =194.2 \end{gathered}[/tex]Hence, the answer is option a) 192.53 since it does not belongs to the above ranges.
Glven: 3x - 2 = 2(x + 1)Prove: x=4REASONSTATEMENT1. 3x - 2 = 2(x + 1)30.2. 3x - 2 = 2x + 231.3. X-2= 232.4. x= 433.Word Bank:A. Distributive PropE. Transitive PropC. Substituion PropD. Subtraction PropB. GivenF. Addition Prop
you have the following equation:
3x - 2 = 2(x+1)
You have to specify the property used in each step to get the solution of the previous equation. You obtain the following:
1. 3x - 2 = 2(x + 1) given
2. 3x - 2 = 2x + 2 distribution prop
3. 3x - 2x - 2 = 2x - 2x + 2 subtraction 2x both sides - subtraction prop
x - 2 = 2
4. x - 2 + 2 = 2 + 2 summation 2 both sides - addition prop
x = 4
2. The product of two consecutive odd numbers is 143. Find the numbers. (Hint: If the first odd number is x, what is the next odd number?)
Step-by-step explanation:
we have the 2 numbers x and (x+2).
x × (x + 2) = 143
x² + 2x = 143
x² + 2x - 143 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case this is
x = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =
= (-2 ± sqrt(4 + 572))/2 = (-2 ± sqrt(576))/2 =
= (-2 ± 24)/2 = (-1 ± 12)
x1 = -1 + 12 = 11
x2 = -1 - 12 = -13
so, we have 2 solutions : 11 and 13, -13 and -11
11× 13 = 143
-11×-13 = 143
Find the slope of the line passing through the points(-2,6) and (-6, 3).
Answer:
3/4
Step-by-step explanation:
To find the slope (gradient) of the line = change in y / change in x
[tex]slope=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\(x_{1} ,y_{1} ) = (-2,6)\\(x_{2} ,y_{2} ) = (-6,3)[/tex]
insert those coordinates in the equation:
[tex]slope=\frac{3-6}{-6-(-2)} =\frac{-3}{-4} =\frac{3}{4}[/tex]
Eric is a software salesman. His base salary is 2300, and he makes an additional $90 for every copy of History is Fun sells. Let P represent his total pay (in dollars) and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 23 copies of History is Fun.
Equation
P = 2300 + 90(N)
Total payment after selling 23 copies of History is Fun.
P= 2300 + 90(23)
P= 2300 + 2070 (Multiplying)
P= 4370 (Adding)
The answer is $4370
R’S’T’U is a dilation image of RSTU which is the correct description of the dilation?
Statement Problem: R’S’T’U is a dilation image of RSTU which is the correct description of the dilation?
Solution:
R'S'T'U' is a dilation of RSTU by;
[tex]\frac{1}{3}[/tex]because it is reduced by that factor.
CORRECT OPTION: a reduction with scale factor
[tex]\frac{1}{3}[/tex]Write an equation of the line that is parallel to the line y=4x+2 and y-3x=6 are parallel, perpendicular, or neither.
Given:
The point is (-2,3).
The parallel line is y=4x+2.
This is of the form
[tex]y=mx+b_1[/tex]where slope m=4.
We know that the slope of the parallel lines is equal.
Thus we get the slope m =4 for the required line.
Consider the line equaiton
[tex]y=mx+b[/tex]Substitute x= -2,y=3, and m =4 in the equation to find the value of b.
[tex]3=4(-2)+b[/tex][tex]3=-8+b[/tex]Adding 8 on both sides of the equation, we get
[tex]3+8=-8+b+8[/tex][tex]11=b[/tex]We get b=11.
Substitute m=4 and b=11 in the equation, we get
[tex]y=4x+11[/tex]Hence the line equation that passes through the point (-2,3) and parallel to y=4x+2 is
[tex]y=4x+11[/tex]you bought a car for $5000. each year it depreciates by 8.5%. Which equation can be used to find the value, v, of the car, x years after it was purchased?
We have the following:
In this case, we have the following formula:
[tex]v=C\cdot(1-r)^x[/tex]Where C is the original value of the car, r is the depreciation rate and x is the time in years
A basket can hold 40 apples. Justin has 22 apples. He plans to buy 7 more. Each apple costs $1.buys the new ones, how many more apples will the basket hold?The basket can hold 15 more apples after Justin buys more.
Answer
Explanation
The basket can hold a maximum of 40 apples.
Justin currently has 22 apples. He plans to buy
A restaurant has 5 desserts, 3 side dishes and 4 main dishes. A student chooses one side dish, one main dish, and one dessert. How many different meals could he make?
30
Explanation
if the first event occurs in x ways, and the second event occurs in y ways, then two events occur in as sequence of xy ways.
so
event A ; choose (1) dessert , 5 ways
event B , chosen (1) side dish, 3 ways
event C, choose (1) main dish, 2 ways
so
a meal( 1 dessert+1 side dish+main dish) is the product of the 3 ways
[tex]\begin{gathered} \text{ways a meal could be made= (5}\cdot3\cdot2)\text{ ways} \\ \text{ways a meal could be made=}30\text{ ways} \end{gathered}[/tex]therefore, the answer is
30
I hope this helps you
For each quadratic expression below, drag an equivalent expression to its match
1. Given the expression:
[tex]\mleft(x+2\mright)\mleft(x-4\mright)[/tex]You can use the FOIL method to multiply the binomials. Remember that the FOIL method is:
[tex](a+b)\mleft(c+d\mright)=ac+ad+bc+bd[/tex]Then, you get:
[tex]\begin{gathered} =(x)(x)-(x)(4)+(2)(x)-(2)(4) \\ =x^2-4x+2x^{}-8 \end{gathered}[/tex]Adding the like terms, you get:
[tex]=x^2-2x-8[/tex]2. Given:
[tex]x^2-6x+5[/tex]You have to complete the square:
- Identify the coefficient of the x-term". In this case, this is -6.
- Divide -6 by 2 and square the result:
[tex](\frac{-6}{2})^2=(-3)^2=9[/tex]- Now add 9 to the polynomial and also subtract 9 from the polynomial:
[tex]=x^2-6x+(9)+5-(9)[/tex]- Finally, simplifying and completing the square, you get:
[tex]=(x-3)^2-4[/tex]3. Given the expression:
[tex]\mleft(x+3\mright)^2-7[/tex]You can simplify it as follows:
- Apply:
[tex](a+b)^2=a^2+2ab+b^2[/tex]In this case:
[tex]\begin{gathered} a=x \\ b=3 \end{gathered}[/tex]Then:
[tex]\begin{gathered} =\lbrack(x)^2+(2)(x)(3)+(3)^2\rbrack-7 \\ =\lbrack x^2+6x+9\rbrack-7 \end{gathered}[/tex]- Adding the like terms, you get:
[tex]=x^2+6x+2[/tex]4. Given:
[tex]x^2-8x+15[/tex]You need to complete the square by following the procedure used in expression 2.
In this case, the coefficient of the x-term is:
[tex]b=-8[/tex]Then:
[tex](\frac{-8}{2})^2=(-4)^2=16[/tex]By Completing the square, you get:
[tex]\begin{gathered} =x^2-8x+(16)+15-(16) \\ =(x-4)^2-1 \end{gathered}[/tex]Therefore, the answer is:
a. During a basketball practice, Mai attempted 40 free throws and was successful on
25% of them. How many successful free throws did she make?
410
0
free throws
25%
Unit 3, Lesson 11
50%
75% 100% 125% 150%
Answer: 10
1/4 (25%) of 40 is 10, meaning Mai made 10 successful free throws.
Describe the situation and why you think analytical or Euclidean geometry is more applicable need helps with this homework question
EXPLANATION
Since the Euclidean Geometry is the Geometry of the Flat Space, we can affirm that it's in two dimensions, where rotation and similarity make sense.
Although it may be expanded to three-dimensional space and beyond, it is still referred to as flat space. The concept is that all dimensions are equal and that they are equal everywhere in space.
The area of a square created on the diagonal of a rectangle, rectangular parallelepiped, or higher dimensional hyperrectangle is equal to the sum of the areas of the squares built on the mutually perpendicular sides of the rectangle, according to the Pythagorean Theorem.
This is known as Euclidean Geometry. Non-Euclidean Geometry, such as spherical, elliptic, hyperbolic, or relativistic geometry, is distinguished by the fact that the same Pythagorean theorem does not apply (though variations do).
So the true dilemma is when to utilize synthetic geometry instead of analytic geometry. Whenever possible, we could say. The challenge with synthetic geometry is that proofs and constructions frequently need some ingenuity on the prover's side.
If 1 is divided by a number, the quotient is less than the number.If 1 is divided by -2, the result is (enter your response here), which is (your response) -2. A. greater than B. Less thanC. Equal to
Let us revise an important note
Positive numbers are increasing from 0 to positive infinity
Negative numbers are increasing from negative infinity to 0
If we divide 1 by 2, then the answer is 1/2 which is less than 2
That means the quotient is less than the divisor
If we divide 1 by -2, then the answer is -1/2 which is greater than -2
That means the quotient is greater than the divisor
Then the answer is
The result is greater than the number
The answer is A
A set of pool balls contains 15 balls numbered 1-15.
Without replacement: What is the probability that an odd number ball is picked
out of a box twice without the first one being replaced?
With replacement: What is the probability that an even number ball is picked with
the first ball drawn being inserted back into the box?
Step-by-step explanation:
a probability is always
desired cases / totally possible cases
the first case I assume means that we need the probability to pick 2 odd-numbered balls in a row, if we do not put the first drawn ball back into the box.
starting condition :
15 basks in total.
1, 3, 5, 7, 9, 11, 13, 15 = 8 odd numbered balls
2, 4, 6, 8, 10, 12, 14 = 7 even numbered balls
the probability for the first ball to be odd numbered :
8/15
now we have
14 remaining balls in total.
7 remaining odd numbered balls.
the probability of the second ball being odd numbered is
7/14 = 1/2
so, the probability of both as one combined event is
8/15 × 1/2 = 4/15 = 0.266666666...
now back to the starting condition.
the probability to pick an even numbered ball is
7/15
we put the ball back in and pull a second time.
the probability to an even numbered ball is
7/15
so, the probability of both as one combined event is
7/15 × 7/15 = 49/225 = 0.217777777...
Please Help!!
Karen was computing the volume of a rectangular prism where v=lwh. In her case w=h. After she multiplied l and w she realized she made w 1/3 larger than it should have been. Since w=h, she lowered the third number by 1/3 of itself and continued to multiply to get the final answer. Betty, who did the same problem with the correct numbers, showed that Karen was off by 12 cubic yards. The correct volume of the prism is __ cu. yds.
The correct volume of the rectangular prism as calculated by Betty is 108 cubic yards
What is a rectangular prism?A rectangular prism is cuboid and an hexahedron that has 6 faces.
The formula for finding the volume of the rectangular prism is V = l•w•h
Where;
l = Length
w = Width
h = Height
The measurement of the prism, for which Karen is calculating the volume gives;
w = h
The amount larger Karen found that she made the width, which gives;
Width of the cube Karen used = (1 + 1/3) × w
Therefore;
h = (1 + 1/3) × w
The volume becomes;
V' = l × (1 + 1/3) × w × (1 - 1/3) × w = l•w²•(1²-1/3²)
V' = l•w²•(8/9)
The amount by which the volume increased, dV = 12 yd³
Which gives;
l•w²•(8/9) = l•w•h - 12 = l•w² - 12
l•w²•(8/9) - l•w² + 12 = 0
l•w²•(8/9) - l•w² + 12 = 0
l•w²/9 = 12
V = l•w² = 12 × 9 = 108
The correct volume of the prism is 108 cubic yards
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A production applies several layers of a clear acrylic coat to outdoor furniture to help protect it from the weather. If each protective coat is 2/27 inch thick, how many applications will be needed to build up 2/3 inch of clear finish.
We know that
• Each protective coat is 2/27 inches thick.
,• We need to fill 2/3 inches of this protective coat.
To solve this problem, we need to know the total number of the application needed to fill 2/3 inches. We can form the following expression
[tex]\frac{2}{27}x=\frac{2}{3}[/tex]We solve for x
[tex]x=\frac{2\cdot27}{3\cdot2}=\frac{27}{3}=9[/tex]Therefore, we need 9 applications in total.Jina opened a savings account with $600 and was paid simple interest at an annual rate of 3%. When Jina closed the account, she was paid $54 in interest. How long was the account open for, in years?
Answer: The account has been open for 3 years
Step-by-step explanation:
3% of $600 is 18
18*3 = 54
Answer:
3 years
have $600
interest $54
annual rate 3%
600 - 3% = 582 that is the money she has in bank without interest
600-582 = 18
54÷ 18= 3 years
Solve for the missing side of the triangle. Round to the hundredths place if needed.
The Pythagoras theorem gives the relation for the right-angle triangle between the perpendicular, base, and hypotenuse thus the perpendicular x will be 14.70.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
Triangle is a very common figure to deal with in our daily life.
In a triangle, the sum of all three angles is 180°
As per the given right-angle triangle,
Pythagoras' theorem states that in a right-angle triangle →
Hyp² = Perp² + Base²
In the given triangle Hyp = 21 , Base = 15 and Perp = x
So,
21² = x² + 15²
x² = 21² - 15²
x = √216 = 14.6993 ≈ 14.70
Hence "The value of x for the given right-angle triangle is 14.70 units".
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What is the slope of a line perpendicular to the line whose equation is 3x-5y=45. Fully simplify your answer
The slope of a line perpendicular to the line whose equation is 3x-5y=45 is -5/3.
So first of all, we have to find the slope of the given line. Convert it into Slope-Intercept Form.
The Slope - Intercept Form is : y = mx + c
Converting the given equation, we get :
3x - 5y = 45
5y = 3x + 45
y = (3/5)x + 15
Perpendicular Lines
The lines having opposite reciprocal slopes are perpendicular. That means you flip the sign (+/-) and flip the numerator and denominator. The slope of the line perpendicular to this one is -5/3.
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The sum of 5 times a number and 7 equals 8. Find the number
Explanation
Let the number be x. Therefore, we will have
[tex]\begin{gathered} 5x+7=8 \\ 5x=8-7 \\ 5x=1 \\ x=\frac{1}{5} \end{gathered}[/tex]What are the explicit and recursive formulas for the sequence 540, 180, 60, 20, ...?
Here we have a geometric sequence, the recursive formula is:
Aₙ = (1/3)*Aₙ₋₁
And the explicit formula is:
Aₙ = (1/3)*ⁿ⁻¹*540
How to get the recursive formula?
Here we have the following sequence:
540, 180, 60, 20, ...
This seems to be a geometric sequence, to check this, we need to take the quotients between consecutive terms and see if we get the same thing.
180/540 = 1/3
60/180 = 1/3
20/60 = 1/3
So yes, this is a geometric sequence where the common ratio is 1/3, so each term is (1/3) times the previous one, so the recursive formula is:
Aₙ = (1/3)*Aₙ₋₁
And the explicit formula is:
Aₙ = (1/3)*ⁿ⁻¹*A₁
Where A₁ is the first term, in this case 540, so the formula becomes:
Aₙ = (1/3)*ⁿ⁻¹*540
Learn more about geometric sequences:
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