A right rectangular prism is shown.
7 inches
5 inches
12 inches
To the nearest tenth of an inch, what is the length of the diagnal, d?

Answer:

XZ = 26.7

ZY = 11.7

Area =  140.4 sq inches

Step-by-step explanation:

m∠Z = 180-(26+90) = 64°

to get XZ you can use the law of sines:

sin 90°/XZ = sin 64°/24

1/XZ = sin(64°)

cross-multiply to get:

XZ·sin(64°) = 24

XZ = 24/sin(64°)

XZ = 26.7

to get ZY you can use the law of sines again:

sin 64°/24 = sin 26°/ZY

cross-multiply to get:

ZY·sin(64°) = 24·sin(26°)

ZY = 24·sin(26°) ÷ sin(64°)

ZY = 11.7

Area = 1/2(11.7)(24)

= 12(11.7)

= 140.4 sq inches

Answer:

To make a "clean getaway"

Step-by-step explanation:

haha, nice one :D

Answer:

110degrees

Step-by-step explanation:

Complete question

Q4: If x and y are two supplementary angles whereas m<x=70 then find the m<y.

The sum of two supplementary angles is 180degrees, hence;

m<x + m<y = 180

70 + m<y = 180

m<y = 180 - 70

m<y = 110degrees

Hence the measure of ,=m<y is 110degrees

Answer:

Surface Area = 1633.63 square yd

Step-by-step explanation:

[tex]r = 10, \ h = 16\\\\Surface \ Area = 2 \pi r^2 + 2 \pi r h\\\\[/tex]

[tex]= 2 \pi \times 10^2 + 2 \pi \times 10 \times 16\\\\=200 \pi + 320 \pi\\\\= 520 \pi\\\\ =1633.63 \ yd ^2[/tex]

Answer:

The amount with which she should increase the length and the with of the sandbox is 2 feet each

Step-by-step explanation:

The dimensions of Melissa's rectangular box are;

Width of the box = 4 feet

Length of the box = 8 feet

The total area of the new sandbox, A = 60 square feet

Let 'x' represent the amount by which she increases the width and lengths of sides that not against the fence, we have;

The area of the new sandbox, A = The new length × The new width

A = 60 ft.²

The new length = 8 + x

The new width = 4 + x

∴ A = 60 = (8 + x) × (4 + x) = x² + 12·x + 32

60 = x² + 12·x + 32

60 - 60 = 0 = x² + 12·x + 32 - 60

∴ x² + 12·x - 28 = 0

(x + 14)·(x - 2) = 0

x = -14 or x = 2

Therefore, the amount she can increase the width and lengths of sides that not against the fence to have make a new sandbox with an area of 60 ft.² is, x = 2 feet

The amount of increase of the length and the width of the sandbox, x = 2 feet each.

Answer:

math.way

Step-by-step explanation:

Answer:

Step-by-step explanation:

y^2=49

y=[tex]\sqrt{49}[/tex]

y=7

Answer:

4 x 3 = 12

2 x 3 = 6

12 + 6 = 18 cubic cm

Answer:b

Step-by-step explanation:

Answer:

it is option C

Step-by-step explanation:

using Pythagoras theorem

hyp^2=adj^2+opp^2

a^2+b^2=c^2

Answer: tasha's investment will be worth $1,440

Step-by-step explanation:

4%= 4/100= 0.04

PRT=6,000*0.04*6= $1,440

Answer:

B) 28 in

Step-by-step explanation:

Pythagorean thm formula:

a² + b² = c²

Given:

b = 45

c = 53

Work:

a² + b² = c²

a² + 45² = 53²

a² + 2025 = 2809

a² = 2809 - 2025

a² = 784

[tex]\sqrt{a^2} =\sqrt{784}[/tex]

a = 28

Answer:

-8/9, 2

Step-by-step explanation:

see the steps below:)

It 's c my friend

okayyyyyyyyyyyyyyy

Answer:

9.97 i think

Step-by-step explanation:

Answer:

r = 24.41cm

Step-by-step explanation:

If you're only trying to find the radius, use the equation:

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

When rearranged to make r the subject:

[tex]r = \sqrt\frac{Area}{\pi }[/tex]

When the variables are added:

[tex]r = \sqrt\frac{1872}{\pi }[/tex]

[tex]r = 24.41[/tex]

Answer:

0.006

Step-by-step explanation:

We are actually looking for the area under the standard normal curve to the left of 50.  The proper distribution function on my old TI calculator is normalcdf(:

normalcdf(-1000,50,75, 10),

which returns 0.006   (Answer B)

Answer:  sorry i dont know this

Step-by-step explanation:

Answer:

Step-by-step explanation:

Below is the pic of how this would be set up in order to determine what it is you are looking for. The angle is set in QI, and since csc A is the reciprocal of sin, the ratio is hypotenuse over side opposite. Solve for the missing side using Pythagorean's Theorem:

[tex]37^2=12^2+b^2[/tex] and

1369 = 144 + b² and

1225 = b² so

b = 35

The sec ratio is the reciprocal of cos, so if cos is adjacent over hypotenuse, the sec is hypotenuse over adjacent, which is 37/35

Answer:

857.766cm^3

Step-by-step explanation:

Given data

Lenght = 3m

Internal radius r = 3m

External radius R= 10m

Volume of pipe= πr^2h

Volume of metal= External - Internal

Volume= πR^2h-πr^2h

Volume= πh(R^2-r^2)

Volume= 3.142*3(10^2-3^2)

Volume= 3.142*3(100-9)

Volume= 9.426*(91)

Volume= 857.766cm^3

Hence the volume of the metal is 857.766cm^3

Given:

The graph of a function.

To find:

The average rate of change of h over the interval [tex]5\leq t\leq 9[/tex].

Solution:

The average rate of change of a function f(x) over the interval [a,b] is:

[tex]m=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

So, the average rate of change of h over the interval [tex]5\leq t\leq 9[/tex] is:

[tex]m=\dfrac{h(9)-h(5)}{9-5}[/tex]

From the given graph it is clear that [tex]h(9)=7,h(5)=3[/tex]. Substituting these values, we get

[tex]m=\dfrac{7-3}{9-5}[/tex]

[tex]m=\dfrac{4}{4}[/tex]

[tex]m=1[/tex]

Therefore, the average rate of change of h over the interval [tex]5\leq t\leq 9[/tex] is 1.

Answer:

1. 1

2. -3

3. yes

4. no, it is not, because the function stop at point (-6, -2)

5. -2

Answer:

A. Yes, [tex]12\cdot 32> 360[/tex]

B. An underestimate could lead to you being stranded on a road trip in the middle of nowhere without guess. When it comes to these things, it's better to have more than necessary. After all, you'd rather have gas and not need it than need it and not have it.

Step-by-step explanation:

A. We can quickly calculate that 12 x 30 = 360. We need to travel 10 more miles to get to 370, but we have 2 miles per gallon and 12 gallons of gas, or 12 x 2 = 24 more miles! Upon further inspection it is evident that 12 x 32 = 360 + 24 = 384 which is indeed larger than 370.

B. Answer contains explanation.

Answer:

The probability of drawing exactly one blue marble is 15 over 32

Step-by-step explanation:

did test

Answer:

Of is a keyword for multiplication.

So, your equation is really 2 X 1,800,000÷3=?

Final answer: 1,200,000

Step-by-step explanation:

Hope that this helps! :)

Have a great rest of your day/night!

Answer: 1 1/2

Step-by-step explanation:

Here is the correct answer

Answer:

Option B

Step-by-step explanation:

By plotting the points given in the table,

All points lie below the dark red line.

Let the equation of the line is,

y - y' = m(x - x')

Here, m = Slope of the line

(x', y') is a point lying on the given line.

Slope of the line passing through two points (-1, 3) and (0, 1) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{3-1}{-1-0}[/tex]

m = -2

Therefore, equation of the line passing through (0, 1),

y - 1 = -2(x - 0)

y = -2x + 1

Since all the points given in the table lie below the dark red line so the solution are will be,

y ≤ -2x + 1

Option B will be the correct option.

Answer:

The answer is

B

D

F

Step-by-step explanation:

Squaring a fraction is like squaring a whole number really so you just square the fraction by multiplying it by itself.