I add 12 to a certain number and then double the result. The answer is 42. Find the original number​

Volume of a figure is measure of the space it occupies. The volume of the larger rectangular prism is given as: Option C: 1620 cm³

If a rectangular prism has dimensions a unit, b unit, and c units, then its volume is given as

[tex]V = a \times b \times c \: \rm unit^3[/tex]

They are scaled. It means, if two figures are similar, then we can get one figure from another by multiplying some constant value(same for one pair of similar figure) to its dimensions.

For example,

if for given case, one rectangular prism has got dimensions a, b, and c centimetres, then

the second rectangular prism, which is similar, let the scale factor is 'd',t then second prism's dimensions will be a x d units, b x d units, and  c x d units.

For first prism(smaller), its one side is given to be 5 cm, let its other two sides be 'b' cm, and 'c' cm, then,

[tex]60 \: \rm cm^3 = 5\times b\times c \\\\b\times c = \dfrac{60}{5} = 12[/tex]

Now, the larger prism has 15 cm corresponding side, thus, scale factor was 3 (since 15 is 3 times 5).

Thus, its dimensions would be 15, 3 x b, 3 x c

Thus, its volume would be

[tex]15 \times 3 \times b \times 3 \times c = 135 \times b\times c = 135 \times 12 = 1620 \: \rm cm^3[/tex]

Thus,

The volume of the larger rectangular prism is given as: Option C: 1620 cm³

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Answer:

I can confirm that the answer is 1620 because I just finished my test

Step-by-step explanation:

The worth of the bond is $307.50.

The worth of the bond is the sum of the bond when it was bought and the interest earned on the bond.

Worth of the bond = interest rate + value when the bond was bought

Interest = 105% x $150

1.05 x $150 = $157.70

Worth of the bond = $157.70 + $150 = $307.50

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Answer:

[tex]\frac{43}{2}[/tex] or 21.5

Step-by-step explanation:

8(x - 16) = 44

8x - 128 = 44

    + 128 + 128

8x = 172

/8  /8

x = [tex]\frac{43}{2}[/tex] = 21.5

To check:

8(x - 16) = 44

8(21.5 - 16) = 44

172 - 128 = 44

    44   =  44

This is a true statement, which makes our answer true.

Hope that helps!

Product of two polynomials can be done by distribution of multiplication over addition. The product of  [tex]-2x(x^2 - 3)[/tex] is [tex]-2x^3 + 6x[/tex]

Suppose a, b and c are three numbers. Then we have:

[tex]a(b + c) = a\times b + a\times c[/tex]

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

The product result of the given expression is

[tex]-2x(x^2 - 3) = -2x^{1 + 2} + 6x = -2x^3 + 6x[/tex]

It is because when bases are same and there is multiplication, then powers add up, so we have: [tex]a^b \times a^c = a^{b+c}[/tex]

Thus,

The product of  [tex]-2x(x^2 - 3)[/tex] is [tex]-2x^3 + 6x[/tex]

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Answer:

The tamaraw or Mindoro dwarf buffalo (Bubalus mindorensis) is a small hoofed mammal belonging to the family Bovidae. It is endemic to the island of Mindoro in the Philippines, and is the only endemic Philippine bovine.

Answer:

(3, 10)

Step-by-step explanation:

f(3) means substitute the value of x = 3 into f(x)

[tex]\implies f(3) = (3 \times 3) + 1 = 10[/tex]

Therefore, when x = 3, y = 10

So the ordered pair is (3, 10)

[tex]\\ \tt\longmapsto f(x)=3x+1[/tex]

[tex]\\ \tt\longmapsto f(3)=3(3)+1=9+1=10[/tex]

Pair is (3,10)

Answer:

waait Im ma wriiting

Step-by-step explanation:

hope it helps

Answer:

2×r=2r

2r×9=18r

Hope this helps:)

Answer:

9(2r)

Step-by-step explanation:

2×r =2r

9×2r can be written as 9(2r)

We could write this as 18r but it is best to leave it at 9(2r)

Answer: $10762 when rounded

Step-by-step explanation:

25,000 times 0.9 (since it is decreasing by 10%)^8 (number of years)

here I found it online

.......ya

hope this helpa

Answer:

The dimensions of the park on the scale drawing are 12 inches by 20 inches

The actual dimensions are given as:

Park = 600 feet by 1000 feet

Swing set = 25 feet by 100 feet

The dimension of the swing set on the scale drawing is given as: 0.5 inch by 2 inches

The above means that, the scale factor (k) is:

--- i.e. divide the scale measurement by the actual measurement

Evaluate both equations

So, we have:

Multiply the scale factor by the dimensions of the park, to get the scale measurement

Hence, the dimensions of the park on the scale drawing are 12 inches by 20 inches

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Step-by-step explanation:

Answer:

Y must be greater than X

X must be less than Y

Step-by-step explanation:

the point-slope form in general is

y - y1 = m(x - x1)

where (x1, y1) are the coordinates of a point, and m is the slope.

so, we have

y - -1 = 4/3 × (x - 3)

or simplified

y + 1 = 4/3 × (x - 3)

Answer:

[tex]y + 1 =\frac{4}{3} (x-3)[/tex]

Step-by-step explanation:

We are given that a line contains the point (3, -1), and has a slope of [tex]\frac{4}{3}[/tex].

We want to write the equation of this line in point-slope form.

Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1 ,y_1)[/tex] is a point.

Since we are already given the slope and the point of the line, we can plug these values into the formula to get the equation.

Let's start with the slope; replace m with [tex]\frac{4}{3}[/tex] in the formula.

[tex]y-y_1=\frac{4}{3}(x-x_1)[/tex]

Now, replace 3 as [tex]x_1[/tex] and -1 as [tex]y_1[/tex]. Remember that the formula has subtraction in it.

[tex]y--1=\frac{4}{3} (x-3)[/tex]

This can be simplified to become:

[tex]y + 1 =\frac{4}{3} (x-3)[/tex]

Topic: writing the equation of the line

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Answer:

   Angle at x is 75°

Step-by-step explanation:

Data :

  Angle at A = 65°

  Angle at B = 40°

According to  the porperty of triangle we know that total interior angle a triangle has is 180° irrespect of type or size

              A + B + C = 180

      65 + 40 + C = 180

        C = 180 - 65 - 40 = 75°

Mark brainliest if you understand

Answer:

Below.

Step-by-step explanation:

Complete the multiplication and the equation becomes

4/6−3/6=?

The two fractions now have like denominators so you can subtract the numerators.

Then:

4−3/6=1/6

This fraction cannot be reduced.

Therefore:

2/3−1/2=16

Solution by Formulas

Apply the fractions formula for subtraction, to

2/3−1/2

and solve

(2×2)−(1×3)3×2

=4−3/6

=1/6

Therefore:

2/3−1/2=1/6

Answer:

Answer:

x = 0 and y = 3, x = 3 and y = 0

Step-by-step explanation:

Just make one of the numbers 0 and the other one 3.

Answer:

29 if I’m Wrong I’m sorry

Step-by-step explanation:

Answer:

eight pieces

Step-by-step explanation

Answer:

x equals 14

Step-by-step explanation:

If u plug in 14 as X. The equation would equal 180.

It's 360 feet (The person above)

Answer:

360 ft squared

Step-by-step explanation:

you have 3 (2 shapes but one is done twice)

2 rectangles and a larger rectangle

the 2 rectangles

3 is the width, and 15 is the length

15*3 = 45 * 2 (for the other one)

and you get 90ft squared

then you have the larger rectangle. it is 15 feet wide and 18 in length (15+3)

15*18 = 270

270 ft squared + 90 ft squared = 360 ft squared

Answer:

D, 24

Step-by-step explanation:

5 10/11 is about 6 and 3 6/17 is about 4.

6 x 4 = 24.

Answer:

  D.  24

Step-by-step explanation:

5 10/11 ≈ 6

3 16/17 ≈ 4

A reasonable estimate of the product is 6×4 = 24.

Answer:

22.5

Step-by-step explanation:

[tex]\frac{15}{6} = \frac{x}{9}[/tex]

cross multiply

15x = 6*9

15x = 54

devide 15 from both sides

x =  22.5

Answer:

Step-by-step explanation:

This is a basic right angle problem relating to Pythagoras theorem as one approach.

we know.

[tex]a^2+b^2=y^2[/tex]

(letting the hypotenuse of the left triangle as y)

then,

[tex]7^2+8^2=y^2\\y=\sqrt{113}[/tex](neglecting negative root)

now since you know the value of y use the same formula to find the value of x. Keep in mind the identification of opposite , adjacent and hypotenuse sides.

Answer:

5,184

Step-by-step explanation:

multiply each unit by 6 and then you end up with 12, 24, and 18. Then you multiply all these answer by each other and get 5,184.

Answer:

AB = 7

Step-by-step explanation:

The y-coordinate of point A and B is the same.

Therefore, both points lie on the same horizontal line (y = 2).

So determine the distance between them, subtract the x-coordinate of B from the x-coordinate of A:

AB = 4 - -3 = 4 + 3 = 7

However, to calculate the distance between 2 points, regardless if the points are on a horizontal (or vertical) line, you can always use the distance between 2 points formula that is derived from Pythagoras' Theorem, as follows:

let [tex](x_1,y_1)[/tex] = point A (4, 2)

let [tex](x_2,y_2)[/tex] = point B (-3, 2)

using the distance between two points equation:

[tex]AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\implies AB=\sqrt{(-3-4)^2+(2-2)^2}[/tex]

[tex]\implies AB=\sqrt{(-7)^2+(0)^2}[/tex]

[tex]\implies AB=\sqrt{49}[/tex]

[tex]\implies AB=7[/tex]

*Edited to add a plot diagram*

Answer:

x≈3.75

Step-by-step explanation:

lets use the equaition sinα=a/c

sin32°= x/6.8

lets solve sin

0.55=x/6.8

multiply it by 6.8 to get the x

0.55*6.8= x

x≈3.75

Answer:

10.35

Step-by-step explanation:

The total billing amount is $31.05. The share of each person on the total billing amount is $10.35. Option C is the correct answer.

Given that the billing amount is $27.00. The additional tip is 15% of the billing amount. The final bill will be split into 3 persons.

The amount of tip is calculated as given below.

[tex]Tip = \dfrac { 15}{100} \times \$27.00[/tex]

[tex]Tip = \$4.05[/tex]

Now the total billing amount is the sum of the final bill and the amount of tip.

Total Bill = $27.00 + $4.05

Total Bill = $31.05

The share of each person on the total amount is given as,

Share = [tex]\dfrac {\$31.05}{3}[/tex]

Share = $10.35

Hence we can conclude that the share of each person on the total billing amount is $10.35. Option C is the correct answer.

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