The hypotenuse of a right triangle is 6 inches. if one of the legs is 2 inches, find the degree measure of each angle

Answers

Answer 1

a and b are the 2 smaller sides, and c = hypotenus; only for right triangles,
Pythagorean Theorem states that:
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
given c = 6 in., a = 2 in.
[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {6}^{2} = {2}^{2} + {b}^{2} \\ {b}^{2} = {6}^{2} - {2}^{2} = 36 - 4 \\ \sqrt{ {b}^{2} } = \sqrt{36 - 4} = \sqrt{32} [/tex]
[tex]b = \sqrt{32} = \sqrt{16} \times \sqrt{2} = 4 \sqrt{2} \\ b = 5.66 \: inches[/tex]
So the three side are 2, 6, and 5.66 inches

Answer 2

Answer:

(square root) 30

Step-by-step explanation:

I don't know if that's right I'm taking this test right now it might be wrong sorry if its wrong lol

Related Questions

write the resulting function if the transformation f(x+3)+9 is applied on the function f(x)=x^2+1

a) x^2+13
b)x^2+19
c)x^2+6x+19
d)x^2+3x+13

Answers

We have the following function:
f (x) = x ^ 2 + 1
We apply the transformation f (x + 3) +9:
g (x) = (x + 3) ^ 2 + 1 + 9
Rewriting we have:
g (x) = (x + 3) * (x + 3) + 1 + 9
g (x) = (x ^ 2 + 3x + 3x + 9) + 1 + 9
g (x) = (x ^ 2 + 6x + 9) + 1 + 9
g (x) = x ^ 2 + 6x + 9 + 1 + 9
g (x) = x ^ 2 + 6x + 19
Answer:
the resulting function if the transformation f (x + 3) +9 is applied on the function f (x) = x ^ 2 + 1 is:
c) x ^ 2 + 6x + 19

It costs $3.15 for a pack of 15 pencils.Find the unit price in dollars per pencil.If necessary, round your answer to the nearest cent.

Answers

For this case what you should do is divide the total cost between the number of pencils.
We have then that the unit price is:
P = (3.15) / (15)
P = 0.21 $ / pencil
Answer:
The unit price in dollars per pencil is:
P = 0.21 $ / pencil

30 POINTS + BRAINLIEST! SHOW ALL WORK PLEASE

Answers

Sin(x + 22) = sin(x)*cos(22) + sin(22)*cos(x)

cos(2x - 7) = cos(2x)*cos(7) + sin(2x)*sin(7)
cos(2x - 7) = [cos^2(x) - sin^2(x)]*cos(7) + 2sin(X)*cos(x)*sin(7)

Somebody sure doesn't like you guys very much. A weak joke. I think the best you can do to start with is graph this relationship. The best I can do is get an answer that is somewhere around 145 degrees. - 61 degrees, - 214 degrees and 255 degrees.

If you are intended to solve this any other way by using the double angle formulas as I started to get above and sin(x) or cos(x) I would take the 0 and hope to make it up some other way.

The domain is between -360 and plus 360. The range is between +/- 1.

Answer

Explanation

sin (x + 22)° = cos (2x - 7)°

In trigonometry for any equation where sinθ = cosΦ, θ and Φ are complementary. That is they add up to 90°

sinθ = cosΦ ⇒ θ + Φ = 90

∴ sin (x + 22)° = cos (2x - 7)°

(x + 22) + (2x - 7) = 90

x + 22 + 2x - 7 =90

3x + 15 = 90

3x = 90 - 15

3x = 75

x = 25°

The larger of two numbers is 10 more than three times the smaller number is larger number decreased by the smaller number is 80 what are the two numbers

Answers

One of my old math teachers taught me how to do this, and I'm going to project his words to you. Make two equations, one labeled smaller number, the other labeled larger number, and whatever number has the most detail, the other one is put as X.
Smaller number = x
Larger number = 3x+10
When you have those two equations down, you have another data section that tells you the value of the two numbers. In your case:
Larger number - Smaller number = 80.
Plugging in what we have:
(3x+10)-x=80
3x+10-x=80
2x+10=80
2x=70
2x/2=70/2
x=35...
Plugging back in for the larger number, since we found the smaller one:
3(35)+10=105+10=115
Your numbers are 115 and 35
Hope this helps.

:p

A rectangle has a width of 3 cm and a length of 10 cm. What is the effect on the perimeter when the dimensions are multiplied by 10?

A) The perimeter is increased by a factor of 10.

B) The perimeter is increased by a factor of 40.

C) The perimeter is increased by a factor of 100.

D) The perimeter is increased by a factor of 400.

I think it's 'A'.. but would really appreciate if someone else double checked it cause I'm an idiot and exhausted and can't think.

Answers

Sorry for answering so late but A is correct

HELP PLEASE!

A manufacturer uses a mold to make a part in the shape of a triangular prism The dimensions of this part are shown below.

which estimate is closest to the volume in cubic millimeters of the part

306
768
1,008
2,016

Answers

Hello,

This answer may be wrong.. But I'm trying to make sure it's not!!

C. 1,008 :)

The Volume of the triangular prism is 124.74 cubic mm.

What is Volume?

Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill. Volume is a three-dimensional quantity used to calculate the capacity of a container.

Given:

Base of the triangle (b) = 12.3 mm

Height of the triangle (h) = 8.2 mm

Length of the prism (l) = 20.5 mm

So, the volume of the triangular prism formula:

= 1/2 x b x h x l

= 1/2 x 14.4 x 2.1 x 8.25

= 7.2 x 2.1 x8.25

= 124.74 cubic mm.

Learn more about Volume here:

https://brainly.com/question/14851358

#SPJ3

A spinner has 8 equal sectors with different letters for each sector, as shown below: a spinner with 8 equal sectors is shown. the sectors are labeled b, y, g, p, o, v, m, and r. hamlet spins the spinner 13 times, and it stops at the letter r 9 times. if he spins the spinner a 14th time, what is the theoretical probability that this time it will stop at the letter r? 1 over 14 1 over 13 1 over 9 1 over 8 question 4(multiple choice worth 1 points)

Answers

I THINK 1 over 8 not sure tho

Answer:

The theoretical probability of obtaining letter 'r' at the 14th spin is:

[tex]\dfrac{1}{8}[/tex]

Step-by-step explanation:

It is given that:

A spinner has 8 equal sectors with different letters for each sector.

The sectors are labeled b, y, g, p, o, v, m, and r.

Hamlet spins the spinner 13 times, and it stops at the letter r 9 times.

We are asked to find the theoretical probability that we will get letter r at the 14th spin.

The theoretical Probability is given as the ratio of number of favorable outcomes to the total number of outcomes.

Hence, the theoretical probability of obtaining letter 'r' at the 14th spin is:

[tex]\dfrac{1}{8}[/tex]

( As there are a total of 8 outcomes( or 8 sectors) out of which there is only one sector which is red)

5 . which of the following is NOT considered a low intensity cardiovascular activity ? ( 1point )

A . walking

b. bicycling

c. hiking

d. leisurely paced swimming,

Answers

The answer to this question is bicycling. This is because when you are walking, hiking or leisurely swimming you are going at a specific slower pace. When you are bicycling the act itself is not specific enough to know how fast you are going, or how much energy you are exerting

What is the equation of thr function y=6/x translated 5 units to the left and 4 units up

Answers

If we are given function f(x) vertical translation is done by adding number to end of formula for translation to up or substracting number for translation to down.
f(x) + a OR f(x) - a
Horizontal translation is done by adding number next to x variable for translation to left or substracting number for translation to right.
f(x+a) OR f(x-a)

We need to translate function 5 units to the left and 4 units up. That means that we need to add 5 next to x and add 4 to end of function. The result is:
[tex]f(x)= \frac{6}{x+5} +4[/tex]

If the radius of a circle is 10 feet, how long is the arc subtended by an angle measuring 81°?

A) π
B) 11π
C) 5π
D) 11/45π,

Answers

The length of an arc, L = theta/360 * 2 * pie * r Where theta = 81 and r = 10ft = 3.048m So length = 81/360 * 2 * pie * 3.048 L = * 0.225 * 2 * pie * 3.048 L = 1.37 * pie L = pie. Option A

The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to .

If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?

5n = 3d and n - 2 = 2d - 4
5n = 3d and 2n - 4 = d - 2
3n = 5d and 2n - 4 = d - 2

Answers

You probably missed that when the numerator and denominator are both decreased by 2, the new fraction is now equal to 1/2.

The numerator of the fraction is "n" and the denominator of the fractions is "d". Initially the numerator and denominator are in the ratio 3 to 5. In equation form we can state this as:

[tex]n:d=3:5 \\ \\ \frac{n}{d}= \frac{3}{5} \\ \\ 5n=3d [/tex]

When both numerator and denominator are decreased by 2, the new numerator will be n-2 and denominator will be d-2. These numerator and denominators are in ratio 1 to 2. In equation form we can write this as:

[tex]n-2:d-2=1:2 \\ \\ \frac{n-2}{d-2} = \frac{1}{2} \\ \\ 2(n-2)=1(d-2) \\ \\ 2n-4=d-2 [/tex]

This is our second equation. Thus the two equation which can be used to solve the problem are:

5n = 3d
and
2n - 4 = d - 2

Answer:

A 5n=3d and n-2=2d-4

Step-by-step explanation:

PLEASE HELP A flight across the US takes longer east to west then it does west to east. This is due to the plane having a headwind flying westward (thus slowing it down) and a tailwind flying eastward (thus pushing it along faster). Suppose you are flying from Philadelphia, PA to San Diego, CA. The distance between the cities is 2,400 miles and the plane's speed is 450 mi/hr. What is the speed of the wind?

Complete the chart
Going westward- Distance - Rate- Time
Going Eastward-

Write an equation to represent the total time if the round trip takes 11 hours.

Solve your equation to find the speed of the wind. Round to the nearest mph.
PLEASE HELP!

PLEASE ANSWER CORRECTLY TO GET BRAINLIEST ANSWER

Answers

To solve our questions, we are going to use the kinematic equation for distance: [tex]d=vt[/tex]
where
[tex]d[/tex] is distance
[tex]v[/tex] is speed
[tex]t[/tex] is time

1. Let [tex]v_{w}[/tex] be the speed of the wind, [tex]t_{w}[/tex] be time of the westward trip, and [tex]t_{e}[/tex] the time of the eastward trip. We know from our problem that the distance between the cities is 2,400 miles, so [tex]d=2400[/tex]. We also know that the speed of the plane is 450 mi/hr, so [tex]v=450[/tex]. Now we can use our equation the relate the unknown quantities with the quantities that we know:

Going westward:
The plane is flying against the wind, so we need to subtract the speed of the wind form the speed of the plane:
[tex]d=vt[/tex]
[tex]2400=(450-v_{w})t_{w}[/tex]

Going eastward:
The plane is flying with the wind, so we need to add the speed of the wind to the speed of the plane:
[tex]d=vt[/tex]
[tex]2400=(450+v_{w})t_{e}[/tex]

We can conclude that you should complete the chart as follows:
Going westward -Distance: 2400 Rate:[tex]450-v_w[/tex] Time:[tex]t_w[/tex]
Going eastward -Distance: 2400 Rate:[tex]450+v_w[/tex] Time:[tex]t_e[/tex]

2. Notice that we already have to equations:
Going westward: [tex]2400=(450-v_{w})t_{w}[/tex] equation(1)
Going eastward: [tex]2400=(450+v_{w})t_{e}[/tex] equation (2)

Let [tex]t_{t}[/tex] be the time of the round trip. We know from our problem that the round trip takes 11 hours, so [tex]t_{t}=11[/tex], but we also know that the time round trip is the time of the westward trip plus the time of the eastward trip, so [tex]t_{t}=t_w+t_e [/tex]. Using this equation we can express [tex]t_w[/tex] in terms of [tex]t_e[/tex]:
[tex]t_{t}=t_w+t_e [/tex]
[tex]11=t_w+t_e[/tex] equation
[tex]t_w=11-t_e[/tex] equation (3)
Now, we can replace equation (3) in equation (1) to create a system of equations with two unknowns:
[tex]2400=(450-v_{w})t_{w}[/tex]
[tex]2400=(450-v_{w})(11-t_e)[/tex]

We can conclude that the system of equations that represent the situation if the round trip takes 11 hours is:
[tex]2400=(450-v_{w})(11-t_e)[/tex] equation (1)
[tex]2400=(450+v_{w})t_{e}[/tex] equation (2)

3. Lets solve our system of equations to find the speed of the wind:
[tex]2400=(450-v_{w})(11-t_e)[/tex] equation (1)
[tex]2400=(450+v_{w})t_{e}[/tex] equation (2)

Step 1. Solve for [tex]t_{e}[/tex] in equation (2)
[tex]2400=(450+v_{w})t_{e}[/tex]
[tex]t_{e}= \frac{2400}{450+v_{w}} [/tex] equation (3)

Step 2. Replace equation (3) in equation (1) and solve for [tex]v_w[/tex]:
[tex]2400=(450-v_{w})(11-t_e)[/tex]
[tex]2400=(450-v_{w})(11-\frac{2400}{450+v_{w}} )[/tex]
[tex]2400=(450-v_{w})( \frac{4950+11v_w-2400}{450+v_{w}} )[/tex]
[tex]2400=(450-v_{w})( \frac{255011v_w}{450+v_{w}} ) [/tex]
[tex]2400= \frac{1147500+4950v_w-2550v_w-11(v_w)^2}{450+v_{w}} [/tex]
[tex]2400(450+v_{w})=1147500+2400v_w-11(v_w)^2 [/tex]
[tex]1080000+2400v_w=1147500+2400v_w-11(v_w)^2[/tex]
[tex](11v_w)^2-67500=0[/tex]
[tex]11(v_w)^2=67500[/tex]
[tex](v_w)^2= \frac{67500}{11} [/tex]
[tex]v_w= \sqrt{\frac{67500}{11}} [/tex]
[tex]v_w=78[/tex]

We can conclude that the speed of the wind is 78 mi/hr.

Sean has $65 to spend on CDs. If each CD costs $6.98, about how many CDs can he buy?

Answers

Sean can buy nine CD's at 6.98. plus taxs.

Answer:

9 (did it on college board)

Step-by-step explanation:

X^2/ 100 + Y^2/ 25 =1
(x squared over 100 plus y squared over 25 equals 1)
The y-intercepts are at:

(-10, 0) and (10, 0)
(0, 10) and (0, 5)
(0, -5) and (0, 5)

Answers

The y-intercepts are at (0, 5) and (0, -5).

Every y-intercept has an x-coordinate of 0. Substituting 0 in for x we have:

[tex]\frac{0^2}{100}+\frac{y^2}{25}=1 \\ \\0+\frac{y^2}{25}=1 \\ \\\frac{y^2}{25}=1 \\ \\y^2=25 \\\sqrt{y^2}=\sqrt{25} \\y=\pm5[/tex]

Simplify (6x^2+11x-3) + (2x^2-17x-4)

Answers

Pick out the like terms. 6x^2 (which equals 36x), 11x, 2x^2 (which equals 4x), -17x.

36+11+4= 51, -17= 34x

-3+-4= -7

The simplified expression would be 34x+-7.

(This could be wrong though, I'm sorry if it is ^^)

The simplified expression would be 34x+-7. hope this helps

Identify the polynomial written in descending order. (1 point) 9 − 14x − 7x2+ x3 x3− 7x2− 14x + 9 −7x2+ 9 + x3− 14x −14x + x3+ 9 − 7x2

Answers

B, x3 - 7x2 - 14x + 9

Answer:

Option 2.

Step-by-step explanation:

We need to find a polynomial which is written in descending order.

Polynomial written in descending order: If the terms are written in a manner such that the powers on the variables go from highest to lowest, then it is called polynomial in descending order.

In option 1, the given polynomial is

[tex]9-14x-7x^2+x^3[/tex]

In option 2, the given polynomial is

[tex]x^3-7x^2-14x+9[/tex]

In option 3, the given polynomial is

[tex]-7x^2+9+x^3-14x[/tex]

In option 3, the given polynomial is

[tex]-14x+x^3+9-7x^2[/tex]

Only in option 2, the terms are arranged in descending order of powers.

Therefore, the correct option is 2.

What the answer plz help it dividing

Answers

These are the steps on how to answer your problem

[tex] \frac{9y^{3} - 9y^{2}}{y} \\ \frac{9y^3}{y} - \frac{9y^2}{y} \\ 9y^2 - 9y[/tex]

draw and label an example of two parallel lines that are perpendicular to a third line.

Answers

Euclid used a somewhat different parallel postulate in trying to avoid the notion of the infinite. He observed that when two parallel lines are intersected by a third line, called a transversal, then if you measure two angles formed by these three lines, on the same side of the transversal and between the parallels, they will add to (that is, they will be supplementary). Such angles are called same-side interior angles:

What two numbers add to 2 and multiply to -14

Answers

x^2+2*-14
is your answer

What is 43.29 rounded to the nearest 10th

Answers

Hello,

The answer is "40.30".

Reason:

First you fine the tenths place:

43.29

Then look at the number next to it:

43.29

Its greater than 5 therefore it does round:

=40.30

If you need anymore help feel free to ask me!

Hope this helps!

The number 43.29 rounded to the nearest tenth place is 43.3

Write an expression to represent: The sum of ten and the quotient of a number x and 6.

Answers

Let us break it down. A sum of ten. That is just

+10

Then, we will add that to the quotient (which is the number after dividing) of a number x and 6. We can write that as

+ x/6

The slash means division here. Thus your final answer is

10 + x/6

Using 70 POINTS NEED YOUR HELP NOT SPAMMERS. To make an ice-cream cone, employees at an ice-cream shop completely fill the cone and then add one scoop of ice cream on top. The cone has a height of 6 inches and a diameter of 2 inches.

To the nearest cubic inch, how much ice cream is in the cone before the scoop is added on the top?

6 in³

19 in³

25 in³

75 in³

Answers

19in__________________________________________________________________________________________________________________

Answer:

6in^3

sorry this is late. but i put 19in^3 and got it wrong. the k12 test said the correct answer is 6in^3

if it isnt correct for you, im sorry

30 Points! Please Help!

Please explain your answer.

Answers

Easy sin is opposite over hypotenuse
Cos is adjacent over hypotenuse tangent is sin over cos and cotangent is cos over sin

Find the length of the second base of a trapzoid with one base measuring 12 feet a height of 4 feet and a area of 58 square feet

Answers

equation:
b1+b2 x h / 2 = 58
12+ b2 x 4 / 2 = 58
12+b2 x 4 = 116
12 + b2 = 29
b2 = 17 feet is the length of the second base

Which number is written in scientific notation? A. 6x10^11 B. 12x10^-8 C. 0.2x10^5 D. 8x7^2

Answers

I think the correct answer is C. 0.2*10^5

Answer:

A!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

Algebra 2!..!!!! please help

Answers

We need to multiply the factors (x - 2) and (x^2 + 9x + 10) to see if the product is the original expression given.

(x - 2)(x^2 + 9x + 10)

x^3 + 9x^2 + 10x - 2x^2 - 18x - 20

x^3 + 7x^2 - 8x - 20.

Since the product just found is not the original expression given, Jimmy is wrong.

I will complete the work on paper by synthetic division and post my answer.

After using synthetic division, the correct quotient is x^2 + 9x + 20.

Can someone help fast? I will give 20 points. Thx
1. The Empire State Building in New York CIty is 1,454 feet tall. A model of the building is 24 inches tall. What is the ratio of the height of the model to the height of the actual Empire state Building? A) 727:12 B) 727:1 C: 12/727 D) 1:727
Are the polygons similar? If they are, write a similarity statement and give the scale factor. The figure is not drawn to scale. A) JKML ~ PSRQ; 8:1.5 B) JKML ~ PQRS; 8:4.8 C) JKML ~ PQRS; 2.5:4.8 D) The polygons are not similar.
3. What similarity statement can you write relating the three triangles in the diagram? A) GHF ~ GIH ~ HIF B) HIF ~ GIH ~ GFH C) GFH ~ GHI ~ HIF D) GHF ~ IGH ~ HIF
4. What are the values of x and y? A) x=9/4, y=3/4 B) x=9/4, y=15/4 C) x=15/4, y=5/4 D) x=3/4, y=15/4
5. What is the value of x to the nearest tenth? The figure is not drawn to scale. A) x=15.7 B) x=4.4 C) x=13.9 D) x=1.9
6. Are the two triangles similar? How do you know? A) No B) Yes; by AA ~ C) Yes; by SAS ~ D) Yes; by SSS ~
7. What is the geometric mean of 6 and 13? A) 2_/13 B) 2_/26 C) _/78 D) 78
8. A salsa recipue uses green pepper, onion, and tomato in the extended ratio 3:7:11. How many cups of green pepper are needed to make 189 cups of salsa? A) 9 B) 27 C) 63 D) 99
9. What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale. A) 24 B) _/24 C) 143 D) _/143
10. What is the solution to the proportion? 6/11 = m/121 A) 66 B) 11 C) 1/66 D) 1 11. What is the value of x, given PQ || BC? A) 10 B) 5 C) 7 D) 8

Answers

Answer:This may not help but 1 is 1:727

2is they are not similar

Step-by-step explanation:

Simplify (5y^6u^-7)*(5u^9v^-6)*(3v^5y)

Answers

Greetings!

Simplify the following expression:
[tex](5y^6u^{-7})(5u^9v^{-6})(3v^5y)[/tex]

First, multiply the terms
[tex]=(5y^6u^{-7})(5u^9v^{-6})(3v^5y)[/tex]

[tex]=(25y^6u^{2}v^{-6})(3v^5y)[/tex]

[tex]=(75y^7u^{2}v^{-1})[/tex]

Rearrange the negative exponent:
[tex]=(75y^7u^{2}v^{-1})[/tex]

[tex]= \frac{75y^7u^{2}}{v} [/tex]

Rearrange to follow the correct form:
[tex]= \frac{75u^{2}y^7}{v} [/tex]

This is the most you can simplify this expression:
[tex]\boxed{=\frac{75u^{2}y^7}{v} }[/tex]

I hope this helped!
-Benjamin

A single die is rolled twice. find the probability of rolling an odd number and a number greater than 4 in either order.

Answers

The probability of rolling an odd number and a number greater than 4 in either order is 1/6.

What is probability?

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, a single die is rolled twice,

∴ The 36 outcomes are

(1,1),(1,2)...(1,6),(2,1)...(2,6),(3,1)...(3,6),(4,1)...(4,6)...(5,1)...(5,6)...(6,1)...(6,6).

So, N(S) = 36.

The no of favorable outcomes N(F) an odd number and a number greater than 4 in either order are [{(1,5),(1,6),(3,5)(3,6),(5,5),(5,6)} as given they can occur in either order so (1,5) and (5,1) are one combined.

∴ N(F) = 6.

So, The probability P(F) of rolling an odd number and a number greater than 4 in either order is,

P(F) = N(F)/N(S).

P(F) = 6/36.

P(F) = 1/6.

learn more about probability here :

https://brainly.com/question/795909

#SPJ5

The probability of rolling an odd number and a number greater than 4 in either order when a single die is rolled twice is 1/18.

To find the probability of rolling an odd number and a number greater than 4 in either order when a single die is rolled twice, we need to first identify the possible outcomes. The odd numbers on a die are 1, 3, and 5. Since we are also looking for a number greater than 4, the only possible outcomes that meet both conditions are 5 and 6.

When the die is rolled twice, there are 6 x 6 = 36 possible outcomes. There are two favorable ways to achieve the goal: Roll a 5 (odd) first and then a 6 (greater than 4), or roll a 6 first and then a 5. Thus, there are two successful outcomes: (5, 6) and (6, 5). The probability of each individual outcome is 1/36, so the combined probability is 2/36, which simplifies to 1/18.

Therefore, the probability of rolling an odd number and a number greater than 4 in either order with a single die rolled twice is 1/18.

Which rule can be used to describe the growth of the y-values of the function y=12^x over each interval from x=-1 to x=3?

Answers

"Which rule ..." suggests you have some rules to choose from to describe the growth. Since you refer to "each interval from x=-1 to x=3", we assume your rule is concerned with more than one interval. With no further clues as to what you may be looking for, we can compute the factor by which the function grows from x=-1 to x=3.

The growth factor over that interval is the ratio of final value to initial value:

.. (12^3)/(12^-1) = 12^(3 -(-1)) = 12^4 = 20,736

Answer:

The rule "multiply by 12" describe the growth of the y-values of the function y=12^x over each interval from x=-1 to x=3.

Step-by-step explanation:

The given function is

[tex]y=12^x[/tex]

The initial value is 1 and the growth factor is 12.

It is an exponential function.

At x=-1

[tex]y=12^{-1}=\frac{1}{12}[/tex]

At x=0

[tex]y=12^{0}=12^{-1}\times 12=1[/tex]

At x=1

[tex]y=12^{1}=1 \times 12=12[/tex]

At x=2

[tex]y=12^{2}=12 \times 12=144[/tex]

At x=3

[tex]y=12^{3}=144 \times 12=1728[/tex]

Therefore the rule "multiply by 12" describe the growth of the y-values of the function y=12^x over each interval from x=-1 to x=3.

Other Questions

Yo ____________________ di mis apuntes ayer a mi compaera de clase porque ella est enferma. what is the scale factor if point A(2,22) transforms into A(2,11)? what type of transformation is this? What point did Bartlett make about the British and Czechoslovak armies? The MLA format requires that you use which of the following methods of in-text citation? A. Reference-page method B. Author-page method C. Title-page method D. Citation-page method How many square feet of outdoor carpet will we need for this hole? Iready quiz pic In caves, dripping groundwater containing calcium bicarbonate can form stalactites and stalagmites. When the water is exposed to air, some of the calcium bicarbonate turns into calcium carbonate, which gets deposited on the ground. What makes this process a chemical change? Find the range of 88, 16, 34, 48 and 27 Please answer questions in French. 1) Richard a des problmes physiques. Comment est-il?2) Jean aime planter des fleurs et des plantes dans le jardin public du centre-ville. Que fait-il?3) Brigitte ne veut pas garder les vtements qu'elle n'utilise pas. Que doit-elle faire?Eric aime aller parler le samedi avec les gens qui ont 75 ans. Comment sont ces personnes?4) Adle a beaucoup d'argent. Vit-elle dans la pauvret?5) Quel est un autre mot pour parler de ta maison?6) Si une personne n'a pas de maison, comment dcris-tu a en franais? When cells are metabolically active but not dividing, they are in the ________ phase. when cells are metabolically active but not dividing, they are in the ________ phase. log exponential lag stationary death? In preparation for the Senior Prom, 8 seniors got together and decided to travel in style and rent a limousine. They investigated and found a company that would rent the limousine for a minimum charge of $180 for the first 3 hours and $30 per hour thereafter. They estimated that they needed to be picked up at 8:00 p.m. and be back by 1:00 a.m. How much money would each student have to pay if they planned to leave the limousine driver a $20.00 tip? Each student would have to pay__________. What is the maximum amount of kcl that can dissolve in 200 g of water? (the solubility of kcl is 34 g / 100 g h 2o at 20c.) 6800 g 34 g 68 g 17 g? A group of young people is holding a protest. They argue that their government is oppressing them and unfairly limiting their personal freedoms. Though the protest isn't violent, the mayor of their city decides that they are being too critical of his policies. He orders the police to force them to end their protest. When some protesters resist, the police attack them. Many are killed in the ensuing chaos. This scenario is most A.The Great Leap Forward B.The Cultural Revolution C.The Tiananmen Square Massacre D.The Chinese Civil War similar to which of the following events? How did both the enlightenment and colonized peoples' actions affect political developments after 1750? What does the term demand relationship mean? How does price affect demand? A rectangular field has a diagonal of 360 feet. One of the side of the field is 160 feet long. What is the perimeter of the field? Enter your answer, rounded to the nearest hundredth, in the box. what Amendment addressed the moral issue of alcohol? The sides of a triangle are 7, 4, n. If n is an integer, state the largest and smallest possible values of n.smallest value is-largest value is- Find the area of the regular pentagon if the apothem is 4.9 m and a side is 7.1 m. round to the nearest whole number. 62 m2 34 m2 87 m2 17 m2 Mr. Nelsons Shoes Mr. Nelson manages a shoe store. One day a man came into the store right after it opened and before Mr. Nelson had a lot of change in the register. The man purchased a pair of shoes that cost $80 and gave Mr. Nelson a $100 bill. Mr. Nelson did not have change, so he went next door and exchanged the $100 for five $20 bills. He gave the customer his shoes and $20 in change. Later, the cashier next door heard there were some counterfeit bills being passed, so she asked Mr. Nelson for five $20 bills, which Mr. Nelson now had, in trade for the $100 bill. Shortly after that the police arrived and determined that the $100 bill was counterfeit and confiscated it. Who lost money? How much money? An article in CQ Researcher states, "more than 111 million Americans use mobile phonesmore than one-third of the population."Why is this piece of evidence not appropriate? A. The American statistic is not applicable since the intended audience is Canadian. B. One-third of the American population is not large enough to convince the reader. C. The reader will not believe the author because CQ Researcher is not trustworthy. D. The number of people who use cell phones does not support the author's argument.