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2 years ago

The variable z is directly proportional to x. When x is 11, z has the value 44. What is the value of z when x = 21?

Mathematics

1 answer:

dimulka [17.4K]2 years ago

4 0

Directly proportional, both increase/decrease, Multiple k(constant you needed to solve for)..

Inversely --one increases as the other decreases, increase the denominator & fraction gets smaller.... So

Problem:

Dirextly to X (× by X)

Inversely to Y, (÷ by Y)

Z= k X/Y

Solve, working backwards: Z =5 becomes

5 = k (X) ÷ (Y). And

X=15 and Y =9 becomes

5= k(15)/(9). Undo ÷9, ×9 both sides

45= k(15). Now undo ×15 by ÷15 both sides

45/15 = 3. So k=3, (also called your constant of variation)....and your Equation/Proportion becomes...

Z = 3X/Y

Use the new #s.... X=23, Y=14

Z= 3×23÷14 = 69/14. If they want spirochete answer divide and round to corresponding # if decimals

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butalik [34]

The answers to each of the given problems are;

1) Sum of two smallest integers = 23

2) 3x + 6

3) 7.5 m/s²

<h3>How to find the sum of consecutive Integers?</h3>

1) We are told that sum of 4 consecutive integers is increased by 20 and equals 70. Thus, we have;

x + (x + 1) + (x + 2) + (x + 3) + 20 = 70

4x + 26 = 70

4x = 70 - 26

4x = 44

x = 44/4

x = 11

Thus, sum of two smallest integers = 11 + 11 + 1 = 23

2) Let the consecutive odd numbers be;

x, (x + 2) and (x + 4)

Sum of these consecutive odd numbers is;

x + x + 2 + x + 4 = 3x + 6

3) We are given the equation to find the acceleration as;

(v_final)² - (v_initial)² = 2ad

We are given;

v_final = 40 m/s

v_initial = 10 m/s

d = 100 m

Thus;

40² - 10² = 2a(100)

1500 = 200a

a = 1500/200

a = 7.5 m/s²

Read more about sum of integers at; brainly.com/question/17695139

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9 months ago

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Step-by-step explanation:

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2 years ago

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2 years ago

Suppose that

Diano4ka-milaya [45]

Answer:

sin(B) = 12/13

cos(B) = 5/13

tan(B) = 12/5

csc(B) = 13/12

sec(B) = 13/5

cot(B) = 5/12

Step-by-step explanation:

If ABC is a right triangle, assuming that ∠C = 90°, then the segment AB =13 is the hypotenuse and the other two sides are:

$BC = 5\\AC = \sqrt{13^2 - 5^2}\\AC = 12$

The six trigonometric functions of angle B are:

$sin(B) =\frac{AC}{AB}= \frac{12}{13}\\cos(B) = \frac{BC}{AB} =\frac{5}{13}\\tan(B) = \frac{AC}{BC} =\frac{12}{5}\\\csc(B) =\frac{1}{sin(B)}= \frac{13}{12}\\sec(B) = \frac{1}{cos(B)} =\frac{13}{5}\\cot(B) = \frac{1}{tan(B)} =\frac{5}{12}\\$

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3 years ago

Solve the problem. When going more than 38 miles per hour, the gas mileage of a certain car fits the model where x is the speed

Lubov Fominskaja [6]

Answer:

73 mph

Step-by-step explanation:

The question seems to be incomplete because the model is missing, I found a similar question with the addition of the model, so if we can solve it (see attached image).

We have that the model would be:

y = 43.81 - 0.395 * x

We need to solve for x, if y = 15

Replacing:

15 = 43.81 - 0.395 * x

Solving for x we have:

0.395 * x = 43.81 - 15

0.395 * x = 28.81

x = 28.81 / 0.395

x = 72.9

We are asked to round to the nearest number therefore x = 73.

The car will average 15 miles per gallon at the speed of 73 miles per hour.

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2 years ago