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2 years ago

a monument casts a 40-foot shadow. Adam is 6 feet tall and casts a 5-foot shadow. How tall is the monument

2 answers:

4 0

This is a proportion problem. Let the monument me x feet tall.
40/x=5/6
Cross multiply:
240=5x
x=48 ft.
So the monument is 48 ft tall,

Svetllana [295]2 years ago

3 0

Answer:

$48\ ft$

Step-by-step explanation:

we know that

Adam is $6$ feet tall and casts a $5$ -foot shadow

A monument casts a $40$ -foot shadow

by proportion

Find how tall is the monument

Let

x------> the height of the monument

$\frac{6}{5}=\frac{x}{40}\\ \\ x=40*6/5\\\\x=48\ ft$

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Pentagon OPQRS is shown on the coordinate plane below:

sertanlavr [38]

Answer:

Multiply the coordinates of point P by the scale factor 7/4 to get the coordinates of P'.

Given : P(-5,3)

P' (x,y) = P (-5 x 7/4 , 3 x 7/4)

= P(-8.75, 5.25)

Step-by-step explanation:

8 0

2 years ago

What is the length of the segment joining the points at (-6, 8) and (6, 3)?

melisa1 [442]

Answer:

13 units

Step-by-step explanation:

So the length of those 2 points is 6+6 = 12.

The height would be 8-3 =5

Using pythagoras, you can find out the length of the line joining the 2 points so:

$5^2 + 12^2 = 169$

$\sqrt{169} = 13$ units

7 0

1 year ago

The quadratic function g(x) = ax^2 + bx + c has the complex roots (-5+9i) and (-5-9i). (you may assume that a = -1) what is the

gavmur [86]

Answer:

b = -10, c = -106

Step-by-step explanation:

<h3>Given</h3>

<u>Quadratic function </u>

g(x) = ax^2 + bx + c

with the roots:

(-5+9i) and (-5-9i)

b and c if a = -1

<h3>Solution</h3>

<u>As we know the sum of the roots is -b/a and the product of the roots is c/a. Substituting values and solving for b and c:</u>

(-5 + 9i) + (-5 - 9i) = -b/-1
-10 = b
b = -10

And

(-5 + 9i)(-5 - 9i) = c/-1
(-5)² - (9i)² = -c
25 - 81(-1) = -c
- c = 25 + 81
- c = 106
c = -106

g(x) = -x² -10x - 106

4 0

2 years ago

Use each model to predict the life expectancy of residents of a country for which the average annual income is $80,000

Mandarinka [93]

The life expectancies of residents of a country for which the average annual income is $80,000 for the three models are 12309.9352, 172.2436 and 4828.1393

The life expectancies of the models are given as:

$y =69.9352 + 0.1530\times (income)$ --- model 1

$y =4.2436 + 0.0021\times (income)$ --- model 2

$y =4.1393 + 0.0603\times (income)$ --- model 3

Given that the average annual income is $80,000;

We simply substitute 80000 for income in the equations of the three models.

So, we have:

<u>Model 1</u>

$y =69.9352 + 0.1530\times (income)$

$y =69.9352 + 0.1530\times 80000$

$y =12309.9352$

<u>Model 2</u>

$y =4.2436 + 0.0021\times (income)$

$y =4.2436 + 0.0021\times 80000$

$y =172.2436$

<u>Model 3</u>

$y =4.1393 + 0.0603\times (income)$

$y =4.1393 + 0.0603\times 80000$

$y =4828.1393$

Hence, the life expectancies are 12309.9352, 172.2436 and 4828.1393