30. A rectangular prism has a volume of
285.6 cubic feet. The prism is
12 feet long and 3.4 feet wide. What is
the height of the prism?

A 7 ft
C 19 ft
B 15 ft
D 22 ft​

Answer:

19

Step-by-step explanation:

Answer:

36 ft.

Step-by-step explanation:

11+11+7+7=

22+14= 36

Answer:

36 ft

Step-by-step explanation:

The rectangle's sides lengths are 7 ft and 11 ft, wich are the width and the length.

The formula of the perimeter is:

P= 2w+2L with w the width and L the length

P= 2*7+2*11

P= 14+22

P= 36 ft

The perileter is 36 ft

Answer:

2

Step-by-step explanation:

Answer:

volume=3x³+15x²+12x

Step-by-step explanation:

v= l*w*h =(3x )(x+1) (x+4)

v=3x(x²+5x+4)

volume=3x³+15x²+12x

Answer/Step-by-step explanation:

Common ratio of a sequence can be gotten by dividing any of the consecutive term in a sequence, by the term before it.

Thus,

For the sequence, [tex] 3, 9, 27. . . [/tex] : [tex] a_1 = 3 [/tex]

[tex] r = \frac{9}{3} = 3 [/tex]

For the sequence, [tex] 8, 4, 2, 1. . . [/tex] : [tex] a_1 = 8 [/tex]

[tex] r = \frac{4}{8} = \frac{1}{2} [/tex]

For the sequence, [tex] -16, 64, -256 . . [/tex] : [tex] a_1 = -16 [/tex]

[tex] r = \frac{64}{-16} = -4 [/tex]

Answer:

Step-by-step explanation:

Let us find the acceleration of box .  

v² = u² + 2as

Putting the values

7² = 3² + 2 a x 14

a = 1.43 m /s²

If coefficient of friction be μ

force of friction = μ mg

= μ x 10 x 9.8

= 98μ

Net force pushing the box

= 85 - 98μ

Applying newton's second law

85 - 98μ = 10 x 1.43

98μ = 85 - 14.3

μ = .72

Answer:jac ganko

Step-by-step explanation:

Answer:

[tex]\boxed{\frac{25\pi }{36}}[/tex]

Step-by-step explanation:

Use the formula to convert from degrees to radians: [tex]x * \frac{\pi }{180}[/tex], where x is the value in degrees.

[tex]125 * \frac{\pi }{180}[/tex] = [tex]\frac{125\pi }{180}[/tex]

Then, simplify your fraction ⇒ [tex]\frac{125\pi }{180} = \boxed{\frac{25\pi}{36} }[/tex]

Answer:

Step-by-step explanation:

Let x be the height of the box . x will be cut at four corners .

each side of the box = 6 - 2x

volume of box V = ( 6 - 2 x )² x

V = ( 36 + 4 x² - 24 x ) x

V = 4x³ - 24 x ² + 36 x

For maximum volume

dV / dx = 12 x² - 48 x + 36 = 0

x² - 4 x + 3 = 0

( x - 3 ) ( x - 1 ) = 0

x = 1 , x = 3 ( not possible )

Possible solution x = 1

Volume  , for x = 1

V = V = ( 6 - 2 x )² x

V = 4² x 1

= 16 m³.

Answer:

A. 25°

Hope it helped

Answer:

4>Y>-2 :) ..............

Answer:

[tex]\boxed{-2 < y \leq 4}[/tex]

Step-by-step explanation:

For y is no greater than 4, it would be either less than or equal to 4. So, the inequality for it would be:

y ≤ 4

Now, the inequality for y more than -2:

-2 < y

Combining the inequality:

-2 < y ≤ 4

Answer:

9 cm.

Step-by-step explanation:

Let the height of the pyramid be h cm, then the height of the cuboid is (15 - h) cm.

Volume of the pyramid:

= 1/3 * h * s^2      where s is the length of a side of the square base.

= hs^2/3 cm^3

Volume of the cuboid:

= s^2(15 - h).

So we have:

hs^2/ 3 = 300.......................(1)

s^2(15 - h) = 600..................(2)

From  equation (1) :

h s^2 = 900

s^2 = 900/h

Now substitute for s^2 in  equation (2) :

(900/h)(15 - h) = 600

Multiply through by h:

900(15 - h) = 600h

13500 - 900h = 600h

1500h = 13500

h = 9 cm (answer).

If the total height of the solid is 15 cm. If the volume of the pyramid and cuboid are 300 cm and 600 cm respectively, then height of pyramid is 9cm.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Let the height of the pyramid be h cm, then the height of the cuboid is (15 - h) cm.

Volume of the pyramid:

300= 1/3 ×h×s²  

300= hs²/3

hs²=900

Volume of the cuboid:

600= s² (15 - h).

600=15s²-hs²

600=15s²-900

600+900=15s²

1500=15s²

100=s²

s=10

Now substitute s value in hs²=900

h(100)=900

Divide both sides by 100

h=9cm

Hence height of the pyramid is 9cm.

To learn more on Three dimensional figure click:

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Answer:

A. The domain is (1,∞), and the range is (-7,∞)

Step-by-step explanation:

Well lets graph it first,

Look at the image below ↓

By looking at the image we move it 3 units right and 3 units down.

Then it will be located at the point (1,-7).

Meaning for the domain it starts at 1 and goes on for infinity.

And For the range it starts down at -7 and goes down for infinity.

Thus,

the correct answer is choice A.

Hope this helps :)

Answer:

A

Step-by-step explanation:

Solution:-

- First we will go through the guidelines that are followed when a given function [ f ( x ) ] is translated in a cartesian coordinate system domain.

Horizontal shifts:

Where, the constant ( a ) denotes the magnitude of shift  

Vertical shifts:

Where, the constant ( b ) denotes the magnitude of shift  

- The generalized form of a translated function is defined by the combination of both horizontal and vertical shifts as follows:

                    General: f ( x ) -> f ( x ± a ) ± b

Where, (a) and (b) are constants of respective translation shifts.

- We are given a function H ( x ) is to be translated 3 units to right and 3 units down. Use the above guidelines to determine the translated function H* ( x ) as follows:

                    [tex]H ( x ) = \sqrt{x+2} - 4\\\\H^* ( x ) = H ( x - 3 ) - 3[/tex]

- Substitute ( x - 3 ) in place of all ( x ) in the given function H ( x ) and subtract ( 3 ) from H ( x ) as follows:

                   [tex]H^* ( x ) = \sqrt{x-3 + 2} -4 - 3\\\\H^* ( x ) = \sqrt{x-1} -7\\[/tex]

- Now we will look for any transcendental functions in the translated function H*(x). These are " Radicals, fractions, Logs, trigonometric ratios "

- We have a radical - > " square root " in H* ( x ). To find the domain of H*(x) we need to determine for what real values of x is the function H*(x) is defined.

- The square root exist for all only positive numbers. So the terms under the square root must be positive; hence,

                     [tex]x - 1 \geq 0\\\\x \geq 1[/tex]

- Since the square root is the only transcendental in the given function H*(x) we have a one sided closed interval for the domain of the translated function.

                    Domain: [ 1 , ∞ )       ... Answer  

- The range of the function is the corresponding output of function H*(x) for the domain established above. We can determine this by plugging in the end-points of the defined domain in the translated function H*(x) as follows:

                    [tex]H^* ( 1 ) = \sqrt{1 - 1} - 7 = -7\\\\H^* ( inf ) = \sqrt{inf - 1} - 7 = inf - 7 = inf\\\\[/tex]

Therefore the range of the function is also a one sided closed interval bounded by x = 1.

                    Range: [-7 , ∞ )       ... Answer

Answer: y=9x+33

33 gallons of water to begin with.

Step-by-step explanation:

So we essentially are given two coordinates: (6,87) and (21,222). To find an equation, we simply need to find the slope and y-intercept. We know it's a linear equation because it's a steady stream, meaning a constant slope.

The slope is:

So, the rate at which the stream flows is 9 gallons per minute.

Now, let's find the initial amount of water. To do this, we can use point-slope form. Pick either of the two points. I'm going to use (6,87).

So, there were 33 gallons of water in the tank to begin with.

Answer:

There were 33 gallons.

Step-by-step explanation:

Answer: Center D I think

Step-by-step explanation:

Answer:

158.73 yd

Step-by-step explanation:

A picture of the situation is needed, investigating I could find a related one, in the same way the important thing is the solution, the data can be exchanged. I attach the drawing.

Let use the formula of the law of cosine:

c ^ 2 = a ^ 2 + b ^ 2 - 2 * a * b * cos C, to solve the problem

Let the third side be c, we replace:

c ^ 2 = 375 ^ 2 + 240 ^ 2 - 2 * 375 * 240 * cos 16 °

c ^ 2 = 198225 - 173027.10

c ^ 2 = 25197.9

c = 158.73

So the distance is 158.73 yd

Answer: the right answer is 195.4

Step-by-step explanation: this guy does not what's happening

The answers are did not make, and both the slope and the y-intercept match if the line of the best fit is represented by the equation y = 0.77x + 1.34

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

We have a line of best fit:

y = 0.77x + 1.34

Here the slope of the line is 0.77 and y-intercept is 1.34

From the graph and line of best fit, we can say heather did not make an error when writing the equation of the line in her notebook because both the slope and the y-intercept match the slope and the y-intercept of the equation she recorded

Thus, the answers are did not make, and both the slope and the y-intercept match if the line of the best fit is represented by the equation y = 0.77x + 1.34

Learn more about the line of best fit here:

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Answer:

Heather likely did not make an error when writing the equation of the line in her notebook because both the slope and the y-intercept match the slope and the y-intercept of the equation she recorded.

Answer:

d. 20

Step-by-step explanation:

To answer the question given, we will follow the steps below:

we need to first find p(3)

p(x) = x+ 7/ x-1

we will replace all x by 3 in the equation above

p(3) = 3+7 / 3-1

p(3) = 10/2

p(3) = 5

Similarly to find q(2)

q (x) = x^2 + x - 2,

we will replace x by 2 in the equation above

q (2) = 2^2 + 2 - 2

q (2) = 4 + 0

q (2) = 4

The product of p(3) and q(2)   =   5 × 4   = 20

Answer:

2065.5

Step-by-step explanation:

You have to approximate the following calculation 3.5^6

The binomial theorem is given by:

[tex](a+b)^n=\Sigma_{k=0}^{k=n}\left[\begin{array}{c}n&k\end{array}\right] a^{n-k}b^k[/tex]      (1)

You can express the number 3as follow:

[tex]3.5^6=(3+0.5)^6=(3+\frac{1}{2})^6[/tex]          (2)

by comparing the equation (1) with the equation (2) you have

a = 3

b = 1/2

To calculate the first three terms of the binomial theorem you use k=3. You replace the values of a, b, n and k in the equation (1):

[tex](3+\frac{1}{2})^6=\Sigma_{k=0}^{k=6}\left[\begin{array}{c}6&k\end{array}\right] (3)^{6-k}b^k[/tex]

You only take the first three terms:

[tex](3+\frac{1}{2}^6)\approx(1)(3)^6(\frac{1}{2})^0+(6)(3)^5(\frac{1}{2})^1+\frac{6\cdot 5}{1\cdot 2}(3)^4(\frac{1}{2})^2\\\\(3+\frac{1}{2}^6)\approx729+729+\frac{1215}{2}=2065.5[/tex]

By using the first three terms of bynomial theorem you obtain 2065.5

Answer:

[tex]30 u^{2}[/tex]

Step-by-step explanation:

The computation of the area of kite ABCD is shown below:

Given data

AC = 10 ;

BD = 6

As we can see from the attached figure that the Kite is a quadrilateral as it involves two adjacent sides i.e to be equal

Now the area of quadrilateral when the diagonals are given

So, it is

[tex]\text { area of kite }=\frac{1}{2} \times d_{1} d_{2}[/tex]

where,

[tex]d_{1}=10\ and\ d_{2}=6[/tex]

So, the area of the quadrilateral is

[tex]=\frac{1}{2}(10)(6)\\\\=30 u^{2}[/tex]

Answer:

C

Step-by-step explanation:

I just took the test

Answer:

its simplest form for the question is 2:1

Answer:

If it is warm outside, then it is summer

Step-by-step explanation:

To find the converse, interchange the hypothesis and the conclusion

"If it is summer, then it is warm outside"

If it is warm outside, then it is summer

Answer:

A. If it is warm outside, then it is summer

Step-by-step explanation:

statement "If it is summer, then it is warm outside" : warm=summer

A. If it is warm outside, then it is summer. : warm = summer ✓

B. If it is not warm outside, then it is summer. : not warm = summer x

C. If it is warm outside, then it is not summer. : warm =not  summer x

D. If it is not warm outside, then it is not summer. : not warm = not summer x

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

- 3y + 4x = 9

3y = 4x - 9

Divide both sides by 3

y = 4/3x - 3

Comparing with the above formula

Slope / m = 4/3

Since the lines are parallel their slope are also the same

So slope of the parallel line l is also 4/3

Equation of the line using point (-12 , 6) is

y - 6 = 4/3(x + 12)

Multiply through by 3

That's

3y - 18 = 4(x + 12)

3y - 18 = 4x + 48

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Step one:

Applying the SOH CAH TOA principle

assuming all dimensions are in cm

Step two:

Given data

opposite= 1 cm

hypotenuse= 2 cm

Sin(θ)= opp/hyp

Sin(θ)= 1/2

Sin(θ)= 0.5

θ= sin-1 0.5

θ= 30°

hence  from tables cos 30°= 0.866

Answer:

420

Step-by-step explanation:

To find 63% of 6000, we can do 0.63 * 6000 = 3780 because 63% = 0.63.

1/9th of that is 1/9 * 3780 = 420.

Answer:

420

Step-by-step explanation:

Let's first start by finding 63% of 6000 so we can later find 1/9 of that number.

We can set up a percentage proportion.

[tex]\frac{x}{6000} = \frac{63}{100}[/tex]

[tex]6000\cdot63=378000\\378000\div100 = 3780[/tex]

Now to find 1/9 of 3780.

[tex]\frac{1}{9} \cdot \frac{3780}{1}\\\\\frac{3780}{9} = 420[/tex]

So, the answer is 420.

Hope this helped!

Answer:

The correct option is;

Heads lands 3 times and tales lands 5 times in 8 coin flips

Step-by-step explanation:

A compound event is one in which the probability of more than one outcome or event to have occurred at the same time is sought. The probability of a compound event is the sum of the probabilities of the individual events less the probabilities already captured in both event probabilities

Answering compound event questions can be done by the use of a tabular or diagram format.

Therefore, the compound event in the list is heads lands 3 times and tales lands 5 times in 8 coin flips.

Answer:

work is shown and pictured

Answer:

Alternate interior angles.

17x + 6 = 18x - 1.

x = 7.

Step-by-step explanation:

According to the diagram below, the angles are alternate interior angles.

Since they are alternate interior angles, they are congruent. So, 17x + 6 = 18x - 1.

17x + 6 = 18x - 1

18x - 1 = 17x + 6

x = 7

Hope this helps!