What is the volume of the trapezoidal right prism?A. 70m^3

B. 196m^3

C. 98m^3

D. 392m^3

Answers

Answer 1

Answer: B. 196m^3 because it's a complex figure so you are supposed to break it down into objects you know to find the volume of.

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the ratio of cats to dogs seen by a veterinarian in one day is 2 to 5. If a vet saw 40 dogs in one day,how many cats did he see?

Answers

If the number of dogs seen by the veterinarian is 40 then the number of cats seen by him will be equal to 16.

What is the ratio?

The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is. A ratio divides two quantities in order to compare them.

As per the data given in the question,

The ratio of cats to dogs seen by veterinarian = 2:5

Number of dogs seen by veterinarian = 40

Let the number of cats seen by him be x.

Then, the ratios will be,

C : D

2 : 5

x : 40

Use cross-multiplication to find the number of cats,

5x = 2 × 40

x = (2 × 40)/5

x = 2 × 8

x = 16

To know more about Ratios:

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2 cats to every 5 dogs
x cats to every 40 dogs

x/40 = 2/5
(here you can cross multiply OR multiply the second fraction by 8/8)

x = 16 the vet saw 16 cats

4 over 9 - 1 over 5

Answers

4/9 - 1/5
=20/45 - 9/45
=11/45

Simplify

(2x^{2} - 5x + 3) - (-x^{2} + 4x - 5)

Answers

Answer:

3x^2 - 9x + 8

Step-by-step explanation:

To simplify:

Distribute the -1 into the second term.
Collect and combine like-terms (terms with the same variables or powers)

The expression can be rewritten has (2x^2 - 5x + 3) -1(-x^2 + 4x - 5)

After distributing the -1, the equation becomes:

(2x^2 - 5x + 3) + (x^2 - 4x + 5)

The like-terms are:

2x^2 and x^2
-5x and -4x
3 and 5

Combine the like-terms:

2x^2 + x^2 = 3x^2
-5x - 4x = -9x
3 + 5 = 8

Substitute the simplified like-terms into the expression, in descending order:

3x^2 - 9x + 8

Seventy-five percent of what number is 33.75?A.144
B.25.3125
C.45
D.27

Answers

Make an equation:

75% * x = 33.75

0.75x = 33.75

Divide 0.75 to both sides:

x = 45

Anna, Elisa and Tiara are selling candy bars to raise money for the track team. The ratio of candy bars sold by Anna, Elisa and Tiara are 2 to 4 to 7.Elisa has sold 28 candy bars. How many candy bars do the girls sold altogether?

Answers

Number of candy bars sold by girls altogether is 91

Solution:

Given that The ratio of candy bars sold by Anna, Elisa and Tiara are 2 to 4 to 7

So ratio of candy bars sold by Anna, Elisa and Tiara = 2 : 4 : 7

Let the candy bars sold by Anna be 2a

Let the candy bars sold by Elisa be 4a

Let the candy bars sold by Tiara be 7a

Given that Elisa has sold 28 candy bars

Number of candy bars sold by Elisa = 28

4a = 28

a = 7

So we have found "a" as 7

Thus we get,

candy bars sold by Anna = 2a = 2(7) = 14

candy bars sold by Elisa = 4a = 4(7) = 28

candy bars sold by Tiara = 7a = 7(7) = 49

We have to find the number of candy bars sold by girls altogether

number of candy bars sold by girls altogether = candy bars sold by Anna + candy bars sold by Elisa + candy bars sold by Tiara

number of candy bars sold by girls altogether = 14 + 28 + 49 = 91

So altogether girls sold 91 candies

7. To which set or sets does the number37 belongA integers onlyB rational numbers onlyC integers and rational numbers onlyD whole numbers, integers, and rationalnumbers