Mr. Barnes painted a mural on the office wall.
The rectangular mural is 36 inches long and 24
inches wide. What is the area of the mural?

Answer:

The answer is below

Step-by-step explanation:

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse side is equal to the sum of the square of the remaining sides. The hypotenuse is the longest side (that is side opposite to the 90° angle).

In right angle triangle ABD:

AB² = AD² + BD²     (1)

In right angle triangle ACD:

AC² = AD² + CD²      (2)

Also:

AC² + AB² = BC²       (3)

But BC = BD + CD

AC² + AB² = (BD + CD)²     (4)

Adding equation 1 and 2 gives:

AB² + AC² = (AD² + BD²) + (AD² + CD²)  

AB² + AC² = 2AD² + BD² + CD²

substituting AC² + AB² = (BD + CD)²:

(BD + CD)² = 2AD² + BD² + CD²

BD² + 2(BD)(CD)+ CD² = 2AD² + BD² + CD²

2AD² = 2(BD)(CD)

AD² = BD * CD

Answer:

d = 8

Step-by-step explanation:

V=(π)(r)^2(h/3)

83.7=(π)(r)^2(5/3)

Solve for r

r = 3.9

d = (3.99)(2)

d = 7.98

d = 8

Answer:

5x+17

Step-by-step explanation:

5 times a number, X, can be represented as 5x. If we want to add 5x and 17, we can say 5x+17.

Answer:

Umm lol I don't know why this person and said a weird message

Step-by-step explanation:

okay the answer is ufldnduejndhsjdnshsidmdjdhsoomsbdhdjdjdnd oof lol

Answer:

-4/15

Step-by-step explanation:

-3/5+1/3 = -4/15

Answer:

option a is right cz both have same value itz 1/root 2 hope it may help u

Answer:

45ml

Step-by-step explanation:

10 kg needs 18mL

So, 1kg = 1.8ml

25kg needs = 1.8kg/ml x 25 kg

25 kg dog would need 45ml.

Answer:

45 ml

Step-by-step explanation:

Weight of the dog and quantity of medicine is in Direct proportion.

Let the quantity required for 25 Kg dog =x

10 : 18 :: 25 : x

Product of extremes = product of means

10 * x = 18 * 25

[tex]x = \frac{18 * 25}{10}\\\\x = 9 * 5 \\\\x = 45[/tex]

69,120

Step-by-step explanation:

You multiply 15 times 4608

The volume of solid B cylinder is 9000π cubic units.

A cylinder is a 3-D solid figure that has two identical circular bases joined by a curved surface at a fixed distance from the center, that is the height of the cylinder.

For the given situation,

Cylinder A:

Let the radius of cylinder A be r1 = 12 inches

Let the height of cylinder A be h1

The volume of the cylinder A, V1 = 4608 π cubic inches

Cylinder B:

Let the radius of cylinder A be r2 = 15 inches

Let the height of cylinder A be h2

The volume of the cylinder A, V2

The formula of volume of cylinder is

[tex]V=\pi r^{2}h[/tex]

For cylinder A,

⇒ [tex]4608\pi =\pi (12)^{2}h1[/tex]

⇒ [tex]h1=\frac{4608}{144}[/tex]

⇒ [tex]h1=32[/tex]

Cylinder A and cylinder B are similar, so

[tex]\frac{h1}{h2} =\frac{r1}{r2}[/tex]

⇒ [tex]\frac{32}{h2} =\frac{12}{15}[/tex]

⇒ [tex]h2=\frac{(32)(15)}{12}[/tex]

⇒ [tex]h2=40[/tex]

Volume of cylinder B is

⇒ [tex]V=\pi (15)^{2}(40)[/tex]

⇒ [tex]V=9000\pi[/tex]

Hence we can conclude that the volume of solid B cylinder is 9000π cubic units.

Learn more about cylinders here

https://brainly.com/question/15891031

#SPJ2

Answer:

b = 2.5

Step-by-step explanation:

→ Utilise Pythagoras theorem

b² = c² - a²

→ Substitute in the numbers

b² = 6.5² - 6²

→ Simplify

b² = 6.25

→ Square root both sides

b = 2.5

Answer:

+0.1

Step-by-step explanation:

when we subtract 2.9 and 2.8 we get -0.1 and to make it zero we have to keep +0.1

Answer:

Option d

Step-by-step explanation:

→ Perimeter of rectangle = 2(l + w)

→ 14 = 2(4 + w)

→ 14 ÷ 2 = 4 + w

→ 7 = 4 + w

→ 7 - 4 = w

→ 3 ft = w

Therefore, width is 3 ft. (Option D)

Answer:

Will cost 123 dollars.

Step-by-step explanation:

Find perimeter (50 m)

50 meters = 164 ft

164/10 ft = 16.4 ft

16.4 ft x 7.50 = 123 Dollars

Hope this helps. Consider giving brainliest :)

Step-by-step explanation:

hey :) I can't help you BUT there is a very good app I recommend it's called "algebrator". I really hope it helps you :)

Answer:

[tex]x=\frac{33}{7}[/tex]

Step-by-step explanation:

Since ED is parallel to CA, the two triangles in the figure share all 3 angles and therefore must be similar. By definition, the corresponding sides of similar polygons are in a constant proportion.

Therefore, we have:

[tex]\frac{11}{11+x}=\frac{14}{20},\\14(11+x)=20\cdot 11,\\11+x=\frac{20\cdot 11}{14},\\x=\frac{110}{7}-11=\boxed{\frac{33}{7}}[/tex]

Answer:

Step-by-step explanation:

what do you know about the angles of a triangle? They make 180° right?

since you know that, now you can find  angle  Y  , by using the triangle on the left,   and you can find X by using the triangle on the right,  then,  when you know  X & Y , use both of those to find  Z  :)   got it?

Answer:

we know that a triangle's angles MUST add up to 180 degrees.

We can look at the triangle with the angles of 55, 80, and y. As the angles must add to 180, 55+80+y must be 180. Therefore, we find that y is equal to 45.

We can look at the triangle with the angles of 100, 60, and x. As the angles must add to 180, 100+60+x must be 180. Therefore, we find that x is equal to 20.

We then look at the triangle formed from x, y, and z. As the angles must add to 180, x+y+z must be 180. x is 20, y is 45, so 20+45+z = 180. Thus, z is 115.

So:

y = 45

x = 20

z = 115.

Answer:

0.60 & 60%

Step-by-step explanation:

Answer:

Find the degree, leading term, and leading coefficient.

Polynomial Degree:  

3

Leading Term:  

8x^3

Leading Coefficient:  

8

Step-by-step explanation:

Answer:

Option (3)

Step-by-step explanation:

Properties for the vertical stretch or shrink of a function,

If a function is f(x) = k|x|

1). Function will be vertically stretched if k > 1

2). Function will have a vertical shrink if 0 < k < 1

To fit the given data graph of f(x) = |x| will vertically shrink without any translation along x or y-axis.

And the value of k will be, 0 < k < 1.

Therefore, g(x) = [tex]\frac{1}{3}f(x)[/tex] will be the transformed graph.

Therefore, Option (3) will be the correct option.

[tex]\orange{\underline{{\bold{\mathbb{\blue{ \huge{QUESTION}}}}}}} [/tex]

What scale is used on the graph

[tex] \huge \bf {\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]

b). 2 cm to 2 units on both axes

As we can se there is gap of 2 boxes (side length= 1cm of one box so 2 boxes side length= 2cm) between 2 units so we can conclude that scale is equal to 2 cm to 2 units on both axes

[tex] \bold \red{DEFINATION \: \: OF \: \: SCALE }[/tex]

IT IS THE RELATIONSHIP BETWEEN THE UNIT USED AND ACTUAL VALUE ON THE GRAPH

Answer:

d.

Step-by-step explanation:

Answer:

there is a 4% decrease in the number of pages read by Melissa

Step-by-step explanation:

Percentage change = (books read this week - books read last week) / books read last week x 100

(240 - 250) / 250 x 100

= -10/250 x 100 = -4%

Answer:Hope This Helps ☺️

Step-by-step explanation:

She is not correct because she did not substitute the same number in both expressions in Step 1

Step-by-step explanation:

CASE 1: substitute 1 for x to both sides of the equations

L.H.S

-(4x-5)+2(x-3)

-(4 (1) - 5)+ 2(1-3) = - (-1) + 2(-2) = 1 - 4 = -3

R.H.S

-2x - 5

-2(1) - 5 = -2-5 = -7

Hence for x= 1

-(4x-5)+2(x-3) ≠ -2x -5

Because -3 ≠ -7

CASE 2: substitute -1 for x to both sides of the equations

L.H.S

-(4x-5)+2(x-3)

-(4 (-1) - 5)+ 2(-1-3) = - (-9) + 2(-4) = 9 - 8 = 1

R.H.S

-2x - 5

-2(-1) - 5 = 2-5 = -3

Hence for x= -1

-(4x-5)+2(x-3) ≠ -2x -5

Because 1 ≠ -3

Answer:

She is not correct because she did not substitute the same number in both expressions in Step 1

Answer:

[tex]{ \tt{7.1 \times {10}^{ - 3} }} \\ { \bf{negative \: means \: { \green{increase \: in \: decimal \: places}}}} \\ = { \tt{0.71 \times {10}^{ - 2} }} \\ = { \tt{0.071 \times {10}^{ - 1} }} \\ = { \tt{0.0071 \times {10}^{0} }} \\ { \boxed{ but \: {10}^{0} = 1}} \\ \therefore{ \tt{ = 0.0071 \times 1 = 0.0071}}[/tex]

Answer:

a. £25142.86

b. £16833.33

Step-by-step explanation:

According to the Question,

Given, The Salary Of 7 People in An Office are,

Andy ⇒ £9500

Bevan ⇒ £25000

Cheryl ⇒ £13250

Deva ⇒ £75000

Elliott ⇒ £12750  

Frankie ⇒ £29500

Grace ⇒ £11000

a. The mean income = Total Sum of Salaries ÷ Number of Workers

Mean = (9500+25000+13250+75000+12750+29500+11000) ÷ 7

Mean = 176000 / 7 ⇒ £25142.86

b. Now, The Mean income After Excluding Deva's Salary is,

Mean = (9500+25000+13250+12750+29500+11000) ÷ 6

Mean = 101000 / 6 ⇒ £16833.33

Answer: 3x^2-2x+1

Step-by-step explanation:

Answer:

3x² - 2x + 1

Step-by-step explanation:

To get 3x²

6x³ ÷ 2x

To get -2x

-4x² ÷ 2x

To get +1

2x ÷ 2x

Answer:

cos 62=adjacent/hypotenuse

cos62=x/6

x=cos 62*6

x=2.8units

Answer:

x ≈ 2.8 units

Step-by-step explanation:

find measure of ∠B:  180-(90+62) = 28°

law of sines:

sin90°/6 = sin28°/x

1/6 = sin28°/ x

cross-multiply to get:

x = 6·sin28°

x ≈ 2.8 units

Answer:

1/2, 4/8, 5/10, 6/12 (examples of equivalent fractions)

Step-by-step explanation:

all you have to do is keep the ratio the same, so whatever change you make to one side of the fraction, you do the same to the other

here's an example: 2/4 divided by 2/2 = 1/2

- you would divide 2 by 2 AND 4 by 2

m<H + m< D = 180°

Since m<H and m<D are supplementary angles.

128°+m<D =180°

m<D = 180-128

m<D = 52°

Answer: m<D = 52°

Answer:

angle D=52 degree

Step-by-step explanation:

In supplementrary angles sum of two angles is always 180 degree

angle H +angle D=180 degree (since they are supplementary angles)

sbstitute the value of H

128 + angle D=180

angle D=180-128

angle D=52 degree

therefore angle D is 52 degree.