What is the volume of the following rectangular prism?

Answer:

x = 75

Step-by-step explanation:

FGE is a straight line so it equals 180 degrees

FGA + AGC + CGE = FGE

x + 90 + 15 = 180

Combine like terms

x+ 105 = 180

Subtract 105 from each side

x = 180-105

x = 75

Answer:

x = 75º

Step-by-step explanation:

The Vertical Angle Theorem shows that:

∠CGE ≅ ∠DGF

So:

∠DGF = 15º

∠AGD = 90º

90º - 15º = 75º

x = 75º

Answer:

4*10^6

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{8\times 10^2^4}{2\times 10^1^8}=\\\\\mathrm{Divide\:the\:numbers:}\:\frac{8}{2}=4\\\\=\frac{10^{24}\times \:4}{10^{18}}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{10^{24}}{10^{18}}=10^{24-18}\\\\=4\times \:10^{24-18}\\\\\mathrm{Subtract\:the\:numbers:}\:24-18=6\\\\=10^6\times \:4\\\\10^6=1000000\\\\=1000000\times \:4\\\\=4000000\\\\= 4\times10^6[/tex]

Answer:

(C) Annie did not make a mistake

Step-by-step explanation:

To isolate the variable k in the equation [tex]7.5 + k = 10[/tex], we'd have to subtract 7.5 from both sides so we just had k on one side.

This is exactly what Annie did, and therefore, her answer is correct.

Hope this helped!

Answer:

C. Annie did not make a mistake

Step-by-step explanation:

Substitute 2.5 for k in the equation and see if it is correct

Each time you substitute you should see that Annie answered the equation correctly

Answer:

[tex]\boxed{x=8y^2-16y-68}[/tex]

Step-by-step explanation:

Hello, please consider the following.

[tex]x=8(y- 1)^2-76\\\\x=8(y^2-2y+1)-76\\\\x=8y^2-16y+8-76\\\\\boxed{x=8y^2-16y-68}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

7

Step-by-step explanation:

Answer:

[tex] 0.7287[/tex]

Step-by-step explanation:

Let $534.9=a$

Thus, given:

$\log a=2.7287$

Hence:

$\log \Big( \frac{a}{100}\Big)=\log a- \log 100$

$\implies \log \Big( \frac{a}{100}\Big)=2.7287-2=0.7287$

Answer:

[tex]\sqrt{10}[/tex]

Step-by-step explanation:

[tex]\sqrt{(x_{2} - x_{1}) ^ {2} + (y_{2} - y_{1}) ^ {2}}[/tex]

[tex]\sqrt{(5-4) ^ {2} + (12 - 9) ^ {2}} = \sqrt{1^{2}+3^{2}} = \sqrt{10}[/tex]

Answer:

233.5 in²

Step-by-step explanation:

First we have to find the slant height.

5²+14²=c²

25+196=c²

221=c²

c=14.866

Now we can find the lateral area.

[tex]\pi[/tex]rl

[tex]\pi[/tex](5)(14.866)

=233.51566

To the nearest tenth=

233.5 in²

Answer:

Enlargement

Step-by-step explanation

It is enlargement, because it went up by three. Instead of reducing.

We cannot tell the result because the actual size of blocks used for modelling the Empire State Building is not known.

For a particular scaled construct, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

[tex]\rm 1\: ft : \dfrac{s}{k}\: in.[/tex]

All feet measurements will then be multiplied by s/k to get the corresponding lengths in the constructed scaled structure.

For case a) or b), we used the scale factors as:

1 block : x feet, where x was either 2 or 5 feet.

But we are not specified what size is of the block which is used to model the building.

It may be that block is greater than x feet, or may be smaller. This will decide whether there is enlargement or reduction of the actual building, respectively.

Thus, we cannot tell the result because the actual size of blocks used for modelling the Empire State Building is not known.

Learn more about scale factors here :

https://brainly.com/question/8765466

Answer:

Step-by-step explanation: I hope it helps :)

[tex]-1.5(4-r)=-12\\\\\mathrm{Multiply\:both\:sides\:by\:}10\\\\-1.5\left(4-r\right)\cdot \:10=-12\cdot \:10\\\\= -15\left(4-r\right)=-120\\\\\mathrm{Divide\:both\:sides\:by\:}-15\\\\\frac{-15\left(4-r\right)}{-15}=\frac{-120}{-15}\\\\4-r=8\\\\\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}\\\\4-r-4=8-4\\\\-r=4\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\\\frac{-r}{-1}=\frac{4}{-1}\\\\r=-4[/tex]

Answer:

r = -4

Step-by-step explanation:

-1.5(4-r)=-12

Divide each side by -1.5

-1.5/-1.5(4-r)=-12/-1.5

(4-r)=8

Subtract 4 from each side

4-r-4 = 8-4

-r = 4

Divide each side by -1

r = -4

Answer:

B. $38.50

Step-by-step explanation:

The original price of item (before tax) is 100% of the price of the item since 100% means the whole amount.

The tax is 10% of the original price, so add 10% to 100% making it 110%.

The total price including tax is 110% of the original price.

We need to find 110% of $35.00.

To find a percent of a number, multiply the percent by the number.

110% of $35.00 = 110% * $35.00

Change the percent to a decimal by moving the decimal point two places to the left.

110% becomes 1.10 as a decimal

110% of $35.00 = 110% * $35.00 = 1.10 * $35.00 = $38.50

Answer: B. $38.50

Divide total km by the km in the scale:

112 / 16 = 7

The answer is A. 7 cm

Answer:

7 cm

Step-by-step explanation:

1 cm : 16 km   :: x cm : 112 km

Product of mean = Product of extreme

16 * x = 1 * 112

x =[tex]\frac{112}{16}[/tex]

x = 7cm

Answer:

I believe it might be 2over 6

Step-by-step explanation:

my guess but it might be wrong or right i dont know

C)

Because if you choose some points for example x = 0 and x = 3.14 (≈ pi)

you will see that there's only one match.

Answer:

Option C. y = cos x -2

Step-by-step explanation:

Answer:

The probability of 3 students having blood type A is 1.23 , having blood type B is 0.3 and having blood type AB is 0.12

Step-by-step explanation:

Answer:

measure A is half 110

measure B is (180-A)

so A is 55 , and B is 125

Answer:

measure A is half 110

measure B is (180-A)

so A is 55 , and B is 125

Step-by-step explanation:

Answer:

Multiply the amount of money that Newton saves by 3 to find the amount of money that Descartes saves.

Descartes's savings after 9 weeks is $108

Answer:

can you send a picture please? i have no clue how to answer this. it seems confusing with the numbers

the above photos is the solution

Answer: Khan Academy 2020! The answer is 40!

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Answer:

y=15x+25, the cost is 205 dollars

Step-by-step explanation:

The simplest way to write a rule for this is to write it in slope intercept form, y=mx+b. Let y represent the cost of the membership. Every month the cost is 15 dollars. If we let x represent the months we can rewrite this as 15x. The one time cost is 25 dollars so we can just add that to the end of the equation. y=15x+25. There are 12 months in a year so we just have to substitute. y=15(20)+25=205 so the answer is 205 dollars.

Answer:

the one selected, the one on top

Step-by-step explanation:

Answer:

She can cut 3 pieces of ribbon.

None will be left over.

Answer:

80°

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the measure of angle x we use cosine

[tex] \cos( \alpha ) = \frac{adjacent}{hypotenuse} [/tex]

From the question

PO is the hypotenuse = 13

The adjacent is 12

Substitute the values into the above formula

That's

[tex] \cos(x) = \frac{12}{13} [/tex]

[tex]x = \cos^{ - 1} ( \frac{12}{13} ) [/tex]

x = 22.6198

We have the final answer as

Hope this helps you

Answer:

Since the value of all angles within a triangle must equal 180 degrees, if you know at least two angles, you can subtract them from 180 to find the missing third angle. If you are working with equilateral triangles, divide 180 by three to find the value of X. All of the angles of an equilateral triangle are equal.

Step-by-step explanation:

Answer:

Area=576 cm²

Perimeter=123.4 cm

Step-by-step explanation:

We have to assume that ABCD would form a square and not a rectangle.  If so, the area is simple:  24x24=576 (Just picture the half circle sliding into the empty space - it’s the same area.)

For the perimeter, we find it for the half circle first. 1/2(2)[tex]\pi[/tex](12)=37.7

Then add the top and bottom (24 and 24) to the left and right (37.7 And 37.7)

24+24+37.7+37.7=123.4

Answer:

The average temperature per hour:

-2.5 °F

Step-by-step explanation:

(-12-48) / 24 =  -60/24

-60/24 = -2.5

In average decrease:

2.5°F

per hour

Answer:

Tan D = 7 / 4

Sin D = 7 / 8.1

Cos D = 4 / 8.1

IG = 4.95 Cm

Step-by-step explanation:

In question number 3

Tan D = Perpendicular / Base

Tan D = 7 / 4

Sin D = Perpendicular / hypotenuse

Sin D = 7 / 8.1

Cos D = Base / hypotenuse

Cos D = 4 / 8.1

In question number 4

Tan 68° = IG / GH

2.475 = IG / 2

IG = 4.95 Cm

Answer:

1. b.  2. a.  3. a.

Step-by-step explanation:

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

= x^2 + 2x + 4

(f + g)(-1) =  (f + g)(x)  where x = 1 so it is

(-1)^2 + 2(-1) + 4

=  1 - 2 + 4

= 3.

2.  We find (f o g)(x) by replacing the x in f(x) by g(x):

= √(x + 1) and

(f o g)(3) =  √(3 + 1)

= √4

= 2.

3. (f/g) c  = f(x) / g(x)

= (x - 3)/(x + 1)

The domain is the values of x which give real values of (f/g).

x cannot be - 1 because the denominator x + 1 = -1+1 = 0 and dividing by zero is undefined. So x can be all real values of x except x = -1.

The domain is (-∞, -1) U (-1, ∞)