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1 year ago

If a ∝ b and a = 18 when b = 3, then find a when b = 5.

Mathematics

1 answer:

Elden [556K]1 year ago

4 0

"a ∝ b" means "a is proportional to b", which in turn means there is some constant k such that

a = kb

We're given that a = 18 and b = 3, so that

18 = 3k ⇒ k = 6

Then when b = 5, we would have

a = 6 × 5 = 30

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11. What is the length of the missing side, x?

Dimas [21]

Answer:

x = 40 in

Step-by-step explanation:

the missing angle in the triangle on the left is

180° - (74 + 51)° = 180° - 125° = 55°

the missing angle in the triangle on the right is

180° - (74 + 55)° = 180° - 129° = 51°

the 2 triangles have 3 pairs of congruent angles and are therefore congruent.

Corresponding sides and angles are then congruent

consider the corresponding sides opposite 74° , that is x and 40 in , so

x = 40 in

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9 months ago

Two counters are selected at random from a bag containing 5 red counters and 3 blue counters.

azamat

Answer:

1.4

Step-by-step explanation:

Probability of selecting a red counter :

Number of red counter / total number of counters

5 / (5 + 3) = 5 /8 = 0.625

Probability of selecting a blue counter = 0.375

Let number of red counters :

0, 1 or 2

0 red counters :

Expected value = x * p(x)

0 + (0.625*1) + (0.390625 * 2)

0 + 0.625 + 0.78125 = 1.40625

Expected number of red counters = 1.4

6 0

2 years ago

48 = 3/2y simplify your answer as much as possible

Sloan [31]

$48 = 1\frac{1}{2}y \\48(\frac{2}{3}) = 1\frac{1}{2}y(\frac{2}{3}) \\32 = y$

4 0

3 years ago

3(2x - 4) + x = 9 help with homework

natita [175]

6x - 12 + x = 9

6x + x - 12 = 9

Collect like terms

7x - 12 = 9

Add both sides 12

7x - 12 + 12 = 9 + 12

7x = 21

Divide both sides by 7

7x ÷ 7 = 21 ÷ 7

x = 3

7 0

2 years ago

Read 2 more answers

Emma is playing miniature golf. Her ball is 2 feet to the left of the right-hand wall. The hole is 4 feet to the left of the wal

NISA [10]

Answer:

She should aim 6 feet down the wall

Explanation:

The diagram attached sketches the situtation.

Since the angle with which the ball hits the wall is the same with which it bounces, angle β is the same for the two shown triangles.

Then, since both are right triangles, then all the angles are congruent and the triangles are similar. Hence, you can equal the ratios of the sides, to make an equation:

x/4 = y/2 ⇒ x = 2y

You have other equation:

x+ y = 18

Substitute

2y + y = 18
3y = 18
y = 18/3
y = 6 ← this is the distance down the wall where the ball should hit

x = 2(6) = 12

Then, she should aim 6 feet down the wall.

8 0

3 years ago