A lamp pole with a height of 10 ft casts a shadow of 3 ft. What is the height of a building that casts a shadow of 15 ft at the same time?

[15 + 1/2 ] - [ 2 + 3/4 ] - [6 + 2/3 ]......convertng these to improper fractions, we have

[31 /2 ] - [11 / 4 ] - [ 20 / 3 ] getting a common denominator (12), we have

[186 / 12] - [33 / 12 ] - [ 80 / 12 ] = 73 / 12 inches = about 6.0833 inches left

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{6 \frac{1}{12} \: \: \: inches}}}}} [/tex]

Step-by-step explanation:

Total inches of a green ribbon = [tex] \sf{15 \frac{1}{2} }[/tex]

Finding the total inches of ribbon that she cut off

[tex] \sf{2 \frac{3}{4} + 6 \frac{2}{3} }[/tex]

Convert the mixed number into an improper fraction

[tex] \dashrightarrow{ \sf{ \frac{2 \times 4 + 3}{4} + \frac{3 \times 6 + 2}{3}}} [/tex]

[tex] \dashrightarrow{ \sf{ \frac{8 + 3}{4} + \frac{18 + 2}{3} }}[/tex]

[tex] \dashrightarrow{ \sf{ \frac{11}{4} + \frac{20}{3} }}[/tex]

Take the L.C.M ( Least Common Multiple ) of 4 and 3

L.C.M = 4 and 3 = 12

[tex] \dashrightarrow{ \sf{ \frac{11 \times 3 + 20 \times 4}{12} }}[/tex]

[tex] \dashrightarrow{ \sf{ \frac{33 + 80}{12}}} [/tex]

[tex] \dashrightarrow{ \sf{ \frac{113}{12} }}[/tex]

Total inches of ribbon that she cut off = 113/12

Now, finding the left inches of ribbon

[tex] \sf{15 \frac{1}{2} - \frac{113}{12} }[/tex]

Convert mixed number into improper fraction

[tex] \dashrightarrow{ \sf{ \frac{15 \times 2 + 1}{2} - \frac{113}{12} }}[/tex]

[tex] \dashrightarrow {\sf{ \frac{31}{2} - \frac{113}{12} }}[/tex]

Take the L.C.M of 2 and 12 , you will get 12

[tex] \dashrightarrow{ \sf{ \frac{31 \times 6 - 113}{2} }}[/tex]

[tex] \dashrightarrow{ \sf{ \frac{186 - 113}{12}}} [/tex]

[tex] \dashrightarrow{ \sf{ \frac{73}{12} }}[/tex]

Convert the improper fraction into mixed number

[tex] \dashrightarrow{ \sf{6 \frac{1}{12} }}[/tex] inches

Hope I helped!

Best regards! :D

Answer:

Step-by-step explanation:A function defines one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) means that y varies according to whatever value x takes on. A causal relationship is often implied (i.e. "x causes y"), but does not *necessarily* exist.

Answer:

i have the same question on my worksheet Step-by-step explanation: i need help this is the hardest one

Answer:

x = -2

Step-by-step explanation:

-6x - 29 = 5x - 7​

Add -6x to both sides

-29 = 11x - 7

Add 7 on both sides

-22 = 11x

Divide

[tex]\frac{-22}{11}[/tex] = [tex]\frac{11x}{11}[/tex]

x = -2

Answer:

x = -2

Step-by-step explanation:

move the terms

collect like terms

-11x = 22

divide both sides of the equation by -11

Answer:

I am confused by the question no CAPPPPPP

Step-by-step explanation:

Answer:

3^-5

Step-by-step explanation:

Whenever you multiply exponents, you add the values. Negative two plus negative three results in an answer of negative five. This will be the power. You will end up with 3^-5 as your answer.

Answer:

x = 12.

Step-by-step explanation:

5/2x - 7 = 3/4x + 14.

put the like terms together keeping in mind that when a number crosses the equal sign it changes its sign and it acquires the opposite sign.

5/2x - 3/4x = 14 + 7

7/4x = 21.

divide both sides by the reciprocal of 7/4, the number next to the unknown

so x = 21 ×4/7

x = 12.

Steps to solve:

7x - 6 = 5x + 18

~Add 6 to both sides

7x = 5x + 24

~Subtract 5x to both sides

2x = 24

~Divide 2 to both sides

x = 12

Best of Luck!

Answer:

x = 1/3

Step-by-step explanation:

3(x-1)-2(2x+1)=8(x-1)

Distribute

3x -3  -4x-2  = 8x -8

Combine like terms

-x -5 = 8x -8

Add x to each side

-x-5+x = 8x-8+x

-5 = 9x-8

Add 8 to each side

-5+8 = 9x-8+8

3 = 9x

Divide by 9

3/9 = 9x/8

1/3 =x

3(x-1)-2(2x+1)=8(x-1)

Use distributive property:

3x-3 -4x-2 = 8x-8

Combine like terms:

-x -5 = 8x -8

Add 8 to both sides:

-x +3 = 8x

Add x to both sides:

3 = 9x

Divide both sides by 9:

x = 3/9

x = 1/3

Answer:

y=4x-26

Step-by-step explanation:

First, a parallel equation, ALWAYS has the same slope. Just plug in your x value into 4(x) , then find a number that adds or subtracts to get your y value, and that number you added or subtracted is your y-intercept.

The equation of the line passing through the point (6,-2) that is parallel to the line y=4x-11 is y = 4x - 26

The equation of the linear passes through the point (6, -2) and is parallel to the line y = 4x - 11

Parallel lines have the same slope.

Therefore,

y = 4x - 11

using

y = mx + b

where

m = slope

b= y-intercept

Therefore, the slope of y = 4x - 11 is 4.

And the slope of the other line will be 4 because they are parallel.

Therefore,

y = mx + b

y = 4x + b

it passes through (6, -2)

-2 = 6(4) + b

-2 - 24 = b

b = -26

The equation will be y = 4x - 26

learn more on linear equation here: https://brainly.com/question/19954463

Given:

Area of a circle, A=50.265 sq. units.

Radius of circle, r = 4 units.

To find:

The value of π to the nearest thousandth.

Solution:

Formula for area of a circle is

[tex]A=\pi r^2[/tex]

[tex]\dfrac{A}{r^2}=\pi [/tex]

[tex]Ar^{-2}=\pi [/tex]

Now, using [tex]Ar^{-2}[/tex] expression, we can find the value of π.

[tex]\pi=50.265904(4)^{-2}[/tex]

[tex]\pi=\dfrac{50.265904}{4^2}[/tex]

[tex]\pi=\dfrac{50.265904}{16}[/tex]

[tex]\pi=3.141619[/tex]

Approximate the value to the nearest thousandth (three digits after decimal).

[tex]\pi\approx 3.142[/tex]

Therefore, the approximated value of π is 3.142.

==================================================

Explanation:

The given piecewise function is

[tex]f(x) = \begin{cases}-4x+3 \ \text{ if } \ x < 3\\-x^3 \ \text{ if } \ 3 \le x \le 8\\3x^2+1 \ \text{ if } \ x > 8\end{cases}[/tex]

At first piecewise functions may be strange confusing things, but they aren't so bad. I like to think of it like this: f(x) is a function that changes its identity based on what the input x is. We have three situations

In a sense, we have three different functions but they are combined somehow.

If x is smaller than 3, then we go for the first definition. Or if x is between 3 and 8, then we go for the second definition. Or if x is larger than 8, then we go for the third definition.

-----------------------

f(-5) means f(x) when x = -5. We see that -5 is smaller than 3, so x = -5 makes x < 3 true. We'll use the first definition

f(x) = -4x+3

f(-5) = -4(-5)+3

f(-5) = 20+3

f(-5) = 23

------------------------

Now the input is x = 12. This is larger than 8. In other words, x = 12 makes x > 8 true. We'll use the third definition

f(x) = 3x^2+1

f(12) = 3(12)^2+1

f(12) = 3(144)+1

f(12) = 432+1

f(12) = 433

------------------------

Side notes:

Answer:

yes -2 is the correct answer

Step-by-step explanation:

7x+3=-17-3x

7x+3x=-17-3

10x=-20

x=-20/10

x=-2

Answer:

[tex]\boxed{\bold{\huge{\boxed{\sf Yes.}}}}[/tex]

Step-by-step explanation:

=> [tex]\sf 7x+ 3 = -17-3x[/tex]

Combining like terms

=> [tex]\sf 7x+ 3x = -17-3[/tex]

=> [tex]\sf 10x = -20[/tex]

Dividing both sides by 10

=> [tex]\sf x = -2[/tex]

So, -2 is a solution of the given equation.

==================================================

Explanation:

The given piecewise function basically means we have h(x) defined in two different ways based on what x is

If x is less than 2, then h(x) = 4 - x^3 which is what the first row says

Or

If x = 2 or larger, then h(x) = 2x-3 which is what the second row says.

---------

We want to find h(0). We want to find h(x) when x = 0. We'll use the first definition since x = 0 is less than 2.

h(x) = 4 - x^3

h(0) = 4 - (0)^3

h(0) = 4 - 0

h(0) = 4

Answer:

17 units

Step-by-step explanation:

Answer:

B. 3y + 4

Step-by-step explanation:

Step 1:

3 (y - 1) + 7

Step 2:

3y - 3 + 7

Answer:

3y + 4

Hope This Helps :)

Part 1) The value of x is 5

Part 2) The length of line AB is 5 inches

Part 3) The length of BC is 15 inches

Answer:

5

5

15

Step-by-step explanation:

Answer:

(x+3)(x-3) = x²-9

(a+4)(a-4) = a²-16

(2/3x²y+1/4)(2/3x²y-1/4) = ((4x^4)y²)/9-1/16

(2x²+3y³)(2x²-3y³) = 4x^4-9y^6

(b-2)(b-2)(b-2) = b³-6b²+12b-8

Step-by-step explanation:

(x+3)(x-3) = x²-9

(a+4)(a-4) = a²-16

(2/3x²y+1/4)(2/3x²y-1/4) = ((4x^4)y²)/9-1/16

(2x²+3y³)(2x²-3y³) = 4x^4-9y^6

(b-2)(b-2)(b-2) = b³-6b²+12b-8

Answer:

34:103

Step-by-step explanation:

Add up all the numbers and then put gold then : then the numbers added up

A proportion exists an equation that sets two ratios at the same value.

34 : 103 exists the ratio of gold medals to the total number of medals that the team won 103.

When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. A ratio is a comparison between two values. A ratio is created when two ratios are equal.

If a ratio depicts the same relationship, it is proportionate. Two ratios can be written as fractions and then reduced to determine if they are proportionate to one another. You have proportionate ratios if the reduced fractions are equal.

Use ratios to compare two things.

The formula for the ratio of any two quantities is expressed as

a : b ⇒ a/b.

On the other hand, the proportional formula is

a : b :: c : d ⟶ ab = cd

a : b :: c : d ⟶ ab = cd

Types of proportion

34 : 103 exists the ratio of gold medals to the total number of medals that the team won 34 + 30 + 39 = 103

Add up all the numbers and then put gold then : then the numbers added up

To learn more about ratio and proportions, refer to:

https://brainly.com/question/12024093

#SPJ2

Answer:

Step-by-step explanation:

8x + 23

Step-by-step explanation:

g(x) = f(x) + 4.

This is because g(x) is a translation of f(x) that has been moved up by 4 units. (-2 to 2 when x = 0)

Given the graphs of y = f(x) and y = g(x),

g(x) = f(x)  + 3

expresses g(x) in terms of f(x).

The Answer is 3.

Answer:

B

Step-by-step explanation:

Answer:

P-2L/2= w

P subtract 2L divided by 2 will give u the width

Step-by-step explanation:

Answer:

p

Step-by-step explanation:

p=2w+2l

p -2w=2l

2l=p -2w

divide both sides by 2

l=1/2p-w

Answer:

546

Step-by-step explanation:

Formula: 0.5*[sum of parallel sides] *height

Answer:

636 in.²

Step-by-step explanation:

First divide the shape into three pieces, you will get a triangle and two rectangles, the base of the triangle is 30 in. The height is 8 in. Multiply 30×8 to get 240 and then divide by two to get 120. Next the rectangle on top has sides that are 24 in. and 8 in. You will get 192. Lastly the rectangle on the bottom has sides of 54 in. and 6 in. For this you will get 324. Finally you add up 120+192+324 to get 636 in.²

Answer:

3.888

Step-by-step explanation:

3.24 × 1.2

Using Multiplication method multiply through like normal multiplication, don't

put your decimal yet

= 3.24

× 1.20

_______

000

6480

+32400

_______

38880

_________

Counting the number of decimal places to knowing where to properly place your decimal sign

3.24 = 2 decimal place

1.20 = 2 decimal place

Total = 4 decimal places

3.8880

Therefore, 3.24 × 1.20 = 3.8880 or 3.888

Answer:

Step-by-step explanation:

p(x)= -3+4x

p(-2)=-3+4(-2)

p(5)=-3+4(5)

p(5)=-3+20

Answer:

Your answers may vary slightly. 5.2 Normal Distributions: Finding Probabilities If you are given that a random variable Xhas a normal distribution, nding probabilities corresponds to nding the area between the standard normal curve and the x-axis, using the table of z-scores. The mean (expected value) and standard deviation ˙should be given

Step-by-step explanation:

Answer:

x=19

Step-by-step explanation:

because if you add 6 by 9 and you get 15 and if you plus 9 with 10 uoi get 19

Answer:

d) Root 16 is rational

Step-by-step explanation:

Root 16=4

4 is rational

Therefore root 16 is rational