At the same time of day, a woman who is 78 inches tall casts a 63-inch shadow and her son casts a 21-inch shadow. What is the son's height? *

Answer:

  x = 2

  m = 15/4

  a = 5/4

Step-by-step explanation:

When the "base" lines are parallel, all of the triangles are similar. That means corresponding segments are proportional, including corresponding parts of segments.

We see that x corresponds to a partial segment marked 3. That same top-bottom correspondence has another pair of segments marked 2 and 3. That means x=2.

  x/3 = 2/3   ⇒   x = 2

__

The segments marked 'm' and 'a' are "whole side" segments, so we need to put those in proportions with corresponding whole sides. If we use the bottom side, we find ...

  a/3 = 5/(3+6+3) = 5/12   ⇒   a = 5/4 = 1 1/4 . . . . . multiply by 3

and

  m/(6+3) = 5/12   ⇒   m = 15/4 = 3 3/4 . . . . . multiply by 9

__

  x = 2

  m = 15/4

  a = 5/4

Answer:

Angle 5

Step-by-step explanation:

Answer:

14° and 166°

Step-by-step explanation:

Ok, so a supplementary angle is 180°.

Let's say one angle is x and the other angle is x+152.

We know these angles add up to a supplementary angle (180°) so...

x+(x+152)=180

x+x+152=180

2x+152=180

2x=28

x=14

So now we know one angle is 14°, we also know the other angle is x+152, knowing that x=14 we can plug it in 14+152= 166° for the other angle.

Hope this helps :)

Answer:

The first answer is 21x+22.

Second answer is 36+3x.

Third answer is 29x+6.

Step-by-step explanation:

I just simplified

Answer:

  (p∘q)(5) = 2

  (q∘p)(5) = -1

Step-by-step explanation:

The composition of functions can be written a little differently, perhaps making it easier to understand.

  (p∘q)(x) = p(q(x))

  (p∘q)(5) = p(q(5)) = p(2·5 -5) = p(5) = 5 -3

  (p∘q)(5) = 2

__

  (q∘p)(5) = q(p(5)) = q(2) = 2·2 -5

  (q∘p)(5) = -1

The amount by which the length and width of a shed can be increased to

more than double the area, depends on the initial dimensions.

Reasons:

The given parameters of the shed are;

The length of the shed = 12 m

Width of the shed = 5 m

The amount by which the length and the width are increased = The same amount

The new area after the increase in the length and width of the shed = More than double the initial area

Required:

The amount of increase in the length.

Solution:

Let the amount by which the length and width are increased = x

We have;

Initial area of the shed = 12 m × 5 m = 60 m²

The new area = (12 + x) × (5 + x) > 2 × 60

By multiplication, we get;

(12 + x) × (5 + x) = x² + 17·x + 60 > 2 × 60 = 120

x² + 17·x + 60 - 120 > 120 - 120 = 0

x² + 17·x - 60 > 0

By factorization, we get;

(x + 20)·(x - 3) > 0

x > -20, or x > 3

The increase (positive) amount of the solution is x > 3

Therefore, the amount by which both the length and the width can be increased to more than double the area is x > 3 meters

Learn more about the area of a rectangle here:

https://brainly.com/question/16410706

Answer:

g≤6

Step-by-step explanation:

g≤6 inequality represents the given situation of at most.

" Inequality means an algebraic expression which represents the relation between two situation or values with the sign of > , < , ≥, ≤."

Term used

At most means 'less than to equals to' ( ≤ )

According to the question,

Given'

'g' represents the number of gold fish live in the tank

As per condition of inequality given,

Number of gold fish can live in small tank at most 6

Represent as the  term used we get,

Inequality is

g ≤ 6

Hence, g≤6 inequality represents the given situation of at most.

Learn more about inequality here

https://brainly.com/question/20383699

#SPJ2

Answer:

[tex]\huge\boxed{\sf 1 \ pound \ of \ dough = 1\frac{1}{5} \ cup \ of \ flour}[/tex]

Step-by-step explanation:

[tex]\displaystyle \underline{Given \ that:}\\\\\frac{5}{8} \ pound \ of \ dough = \frac{3}{4} \ cup\ of \ flour\\\\Multiply \ 8 \ to \ both \ sides\\\\5 \ pounds \ of \ dough = \frac{3}{4} \times 8 \ cup \ of \ flour\\\\5 \ pounds \ of \ dough = 3 \times 2 \ cup \ of \ flour\\\\5 \ pounds \ of \ dough = 6 \ cups \ of \ flour\\\\Divide \ both \ sides \ by \ 5\\\\1 \ pound \ of \ dough = \frac{6}{5} \ cup \ of \ flour\\\\\boxed{1 \ pound \ of \ dough = 1\frac{1}{5} \ cup \ of \ flour}\\\\[/tex]

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

a = 11

Step-by-step explanation:

As all angles on a straight line must add up to 180°:

(9a + 6) + 75 = 180

9a + 6 + 75 = 180

9a + 81 = 180

Subtract 81 from both sides of the equation:

9a + 81 - 81 = 180 - 81

9a = 99

Divide both sides by 9 to isolate a:

9a ÷ 9 = 99 ÷ 9

a = 11

Hope this helps!

Answer:

[tex]a=11[/tex]

Step-by-step explanation:

These are supplementary angles, meaning they together make up the whole measure of the angle of a straight line. A straight line is 180°, so the sum of these has to be 180° too:

[tex](9a+6)+75=180[/tex]

Then just solve for a:

[tex]9a+6+75=180\\9a+81=180\\9a=99\\a=11[/tex]

Answer:

You tell me the question properly and i will edit this and put answer

Step-by-step explanation:

Until then bye

Answer:

Read Explanation Below

Step-by-step explanation:

So... I didn't know what you were referencing nor did I see a paper, so I came up with a scenario that I thought would represent this number. (also, if you could send a picture so I know what you're referencing, that would be awesome)

1. When James took a nap at 3pm, he saw that the temperature outside was 70 degrees. However, when he woke up at 8pm, he checked the weather and it was 30 degrees. How much did the temperature change during his nap.  

Answer:

[tex]\frac{4\sqrt{3} }3}[/tex]

Step-by-step explanation:

Since it is an equilaterla triangle, we can see the side opposite to that of side length 4 is 60 degrees. Since the other angle is a right angle (90 degrees), we can find that the other side is 30 degrees (the degrees add up to 180). We can also see that this is a 30-60-90. We can see that the side x, through the identity (you can find 30-60-90 identity online), we see that the side x is [tex]\frac{4}{\sqrt{3}}[/tex]. However, it is also asking us to simplify this, so we multiply the top and bottom by [tex]\sqrt{3}[/tex] and get [tex]\frac{4}{\sqrt{3} } = \frac{4\sqrt{3} }{3}[/tex]

Answer:

A: 16.8

Step-by-step explanation:

4.2 and 16.8 both have decimal place values. If you line up the decimals when you add them, then you get 21.

Answer:

Where's the picture?

Step-by-step explanation:

Answer:

Nooooooo

Step-by-step explanation:

Answer:

$1.20 for one pound of rice

Step-by-step explanation:

$9.60 ÷ 8 = $1.20

I hope this helps!

Answer:

Retainers have been designed to be used as an end of treatment to help retain your teeth in their new position. ... These are removable and fixed retainers. The reason why retainers can't be used to close a gap is because they are fitted at the end of treatment and are made to fit the straight teeth mould.

hope it help u

itz by Riddhi

Answer:

yes

Step-by-step explanation:

Answer:

If your gonna ask it on groups its one group

Answer:

y=7

Step-by-step explanation:

The slope is (7-7)/(3+7) = 0. So, the line is a horizontal line.

The y value of both points is 7.

Answer:

Mode is 58 degrees

Step-by-step explanation:

Answer:

762.24

Step-by-step explanation:

Rounded to the hundredth place

Answer:

(9d+3)

Step-by-step explanation:

(6d+5)-(2-3d)

>(6d+5)+(-2+3d)

>{(6d+3d)+(5-2)}

=(9d+3)

Answer: 68%

Step-by-step explanation:

The best way to do this is add up the number of math and history rooms, and divide that by the total number of rooms.

There are 17 total math and history rooms, and 25 rooms total.

17/25 = .68

Multiply that by 100 to get the percent and the answer is 68%

Answer:

42

Step-by-step explanation:

yeah-ya.......... right?

Answer:

  2.83°

Step-by-step explanation:

The tangent of an angle is the ratio of rise to run.

 θ = arctan(5/101) ≈ 2.83°

_____

We assume the length is referring to the horizontal distance.

If it is the distance along the path, then the angle is ...

  θ = arcsin(5/101) ≈ 2.84°

The exponential function used to predict the number of visitors during month m is [tex]y = 600(2)^m[/tex]

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the factor.

Let y represent the number of visitors during month m.

There were 600 visits to the site the first month and they double each month, hence:

a = 600, b = 2

The exponential function is given by:

[tex]y = 600(2)^m[/tex]

Find out more on exponential function at: brainly.com/question/2456547

Answer:

if it's only translated left 3, then it should be A (-5, -1) B (-1, -1) and C (-1, 2)

Answer:

11

Step-by-step explanation: