Find the volume of the prism. Please help!

Answer:

First option

Step-by-step explanation:

The result of first expression:

7(6+z) multiply 7 with inside the parenthesis

7(6+z) = 42 + 7z

the result of second expression:

since we need to do multiplying first,

7*6 = 42 and 7*z = 7z

then we add them

42 + 7z this is the same result we found for the first equation

Answer:

The answer is 405

Step-by-step explanation:

FIrst you would do 27 times 30 which is 810 then you would divided by 2 which in turn gives you 405

Hope this helped!

Answer:

See below for proof of identity.

Step-by-step explanation:

Since both terms of [tex]\sin^3\theta+\cos^3\theta[/tex] are perfect cubes, we can use the formula [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex] where [tex]a=\sin\theta[/tex] and [tex]b=\cos\theta[/tex]:

[tex]\displaystyle \frac{\sin^3\theta+\cos^3\theta}{\sin\theta+\cos\theta}\\\\\frac{(\sin\theta+\cos\theta)(\sin^2\theta-\sin\theta\cos\theta+\cos^2\theta)}{\sin\theta+\cos\theta}\\ \\\frac{(\sin\theta+\cos\theta)(1-\sin\theta\cos\theta)}{\sin\theta+\cos\theta}\\\\1-\sin\theta\cos\theta[/tex]

Thus, the identity is proven.

Answer:

11

Step-by-step explanation:

First, you replace x with 2

5×2+1

Then multiplication comes before addition so 5×2

5×2=10

Then just add the 1

10+1=11

Answer:

16

(14-6)×2=16 So initially Emma had 16 books.

Answer:

I don't know how to explain

Step-by-step explanation:

2x + 18

x = 18÷2

x=9

hence the answer is 9

Answer:

it would be a

Step-by-step explanation:

8x4=32

The base of the given triangle is calculated as: 16 ft

The formula that is used to calculate the area of a triangle is expressed as:

Area of triangle= ½ × base × height

We are given that:

Area = 32 ft²

Height = 4 ft

Thus:

32 = ½ × base × 4

32 = 2 * base

base = 32/2

base = 16 ft

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Answer:

Hypotenuse = 17

Step-by-step explanation:

if: a = 8, b = 15 c = hypotenuse:

[tex]c=\sqrt{a^{2}+b^{2} }[/tex]

[tex]c = \sqrt{(8)^{2} +(15)^{2} } =\sqrt{64+225}=\sqrt{289} =17[/tex]

Hope this helps

Answer: 21599373.37618

Step-by-step explanation:

Based on the illustration given above, the feet that she now need to ascend to get back to sea level is 40.5.

Note that the first descend was 20.6 - 12.5 =

8.1 feet

Then she drop 32.4 feet again

So to get back up she need to add:

= 32.4 feet + 8.1 feet

= 40.5

Therefore, based on the calculation given above, the feet that she now need to ascend to get back to sea level is 40.5.

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Answer:

  155 miles

Step-by-step explanation:

The sum of n terms of an arithmetic series is given by the formula ...

  Sn = (2·a1 +d(n -1))(n/2)

__

The number of miles Ryan ran in July is described by the arithmetic series ...

  0.5 +0.8 +1.1 +... (a total of 31 terms)

The first term is a1=0.5, and the common difference is d=0.3.

The total number of miles Ryan ran in July is ...

  S31 = (2(0.5) +0.3(31 -1))(31/2) = (1 +9)(31/2) = 155

Ryan ran 155 miles in July.

Answer:

(-2, -1)

Step-by-step explanation:

The easiest way to approach this problem is to think of each quadrant as being 90 degrees. As you can see, each quadrant has a 90 degree angle.

If we were to move 2 quadrants (or 180 degrees) clockwise, we would end up in the third quadrant (- , -)

Because we are moving clockwise on the graph, the shape would also turn clockwise. 180 degrees is the halfway point, so the shape will appear to be upside down.

If you're a visual learner, I'd recommend finding a website with an online graph (something like desmos or geogebra) that would allow you to actually graph the points and change their position with commands.

Hope this helps :)

Answer:

C

Step-by-step explanation:

In 3 options, the coefficient of x on both sides is the same. Hence, they will all have no solution. The only one which has exactly one solution is :

The values of the numbers m and n that makes the given expression true are 3 and 12 respectively

From the question, we are to determine the values of the numbers m and n that will make the given expression true

The given expression is

(2x + m)² = 4x² + nx + 9

Opening the bracket on the left hand side,

(2x + m)²

(2x + m)(2x + m)

4x² + 2mx + 2mx + m²

4x² + 4mx + m²

∴ 4x² + 4mx + m² = 4x² + nx + 9

By comparing,

4mx = nx;

Then, 4m = n

and

m² = 9

∴ m = ±√9

m = ±3

Since we are given that both m and n are positive numbers,

∴ m = 3

Substitute the value of m into the equation, 4m = n

4×3 = n

∴ n = 12

Hence, the values of the numbers m and n that makes the given expression true are 3 and 12 respectively

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The value of x in the given equation [ √( 1 + (25/144) ) = 1 + (x/12) ] is 5.

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given that;

First, we square both sides

√( 1 + (25/144) ) = 1 + (x/12)

(√( 1 + (25/144) ))² = (1 + (x/12))²

1 + (25/144) = 1 + ( x²/144)

Collect like terms

1 - 1 + (25/144) = ( x²/144)

25/144 = x²/144

We cross multiply

25 × 144 = x² × 144

Multiply each sides by 1/144

x² = 25

x = √25

x = 5

Therefore, the value of x in the given equation [ √( 1 + (25/144) ) = 1 + (x/12) ] is 5.

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Answer: 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

Step-by-step explanation:

First, we can ensure that 12 is the median by putting it in the middle and putting the same amount of numbers to its left and right side. To make the values have a mean of 12, the easy why to do it is to subtrate one as you move to the left and add one as you move to the right, that way they will cancel each other out and keep the mean at 12. The answer has a total of 11 values, has more than 3 values that are different, and has a mean and median of 12.

7+8+9+10+11+12+13+14+15+16+17=132

132/11=12

There are 5 values to each side of 12, making 12 the median.

Answer:

A

Step-by-step explanation:

|-20| = 20 the positive value of -20

20 is not < 20 so A is false

All the rest are true
(B) |9| = 9

(C) |-20| = 20 > 9

(D) |9| = 9, |20| = 20 and 9 < 20

Answer:

2) x=5

4) 6y-3

Step-by-step explanation:

2) 2x-3=7

Add 3 on both sides (-3+3 cancel each other out and 7+3 is 10)

Now your equation is 2x=10

Divide 2 from both sides

2x/2 cancel each other and 10/2 is. Therefore, x=5

4) 3(2y-1)

3 times 2y is 6y

3 times -1 is -3 (negative times positive is negative)

Equation: 6y-3

Answer:

b

Step-by-step explanation:

the answer is b if values are plugged in to function

Answer:

y = -(x - 2)² - 4

Step-by-step explanation:

The vertex form an equation is given as :

Substitute any point in the table to find a :

Hence, the final equation :

Answer:

35

Step-by-step explanation:

Answer: undefined

Step-by-step explanation:

slope form: [tex]\frac{y2 - y1}{x2 - x1}[/tex]

simply plug in values

[tex]\frac{4-1}{-1-(-1)}[/tex]

[tex]\frac{3}{0}[/tex]

Answer: undefined

you can also tell by realizing both x coords are the same, meaning the line is verticle and verticle lines' slopes are undefined

Answer:

The system of equation has infinite solution.

Step-by-step explanation

2x + y = 3

6x = 9 – 3y

First we re-write the second equation in standard form

So, we add 3y both sides

6x+3y=9 ---------------- (2)

2x+y = 3-----------------  (1)

3(2x)+3y = 3(3)

6x+3y=9

6x-6x + 3y-3y = 9-9

0=0

LHS=RHS

This is true statement. If statement is true then infinite number of many solution.

Answer:

infinite

Step-by-step explanation:

acellus

Answer:

0.5

Step-by-step explanation:

4 is in the tenths place and 6 is in the hundredths place

Since the digit in the hundredths place (6) is greater than or equal to 5, add 1 to the digit in the tenths place (4)

1 + 4 = 5, so the digit in the tenths place becomes 5

The digit in the hundredths place is dropped

0.46 rounded to the nearest tenth (one decimal place) = 0.5

Answer: C

Step-by-step explanation:

Because there are two pairs of opposite parallel sides, it is a parallelogram.

Since the diagonals intersect at a right angle, the parallelogram is also a rhombus.

Answer:

638 students.

Step-by-step explanation:

girl this is basic math i don’t  think i need to explain