Solve 4,123 ÷ 78 two different ways using partial quotients.

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Margaret [11]

Answer:

Kevin is 7, Uncle Rob is 54

Step-by-step explanation:

Let's express the information given by the question statement.

1. Tonya (T) is twice Kevin's (K) age: T = 2K

2. In three years, Tonya (T) will be 17: T + 3 = 17

3. In another three years, Uncle Rob (R) will be 3x Tonya's (T) age: R = 3(T+3+3)

From 2, we can say that Tonya is now 14.

First equation becomes: 17 = 2K ... which means K = 7, Kevin is 7.

Third equation becomes: R = 3 (14 + 3 + 3) = 3 (20) = 60

In six years, Rob will be 60. So, now, he's 54 (60-6).

3 0

3 years ago

Container a has a maximum capacity of 3 gallons. Container B has a maximum capcity of 14 quarts. How much extra capacity does co

Korolek [52]

Answer: 0.5 gallon

Step-by-step explanation:

From the question, we are informed that Container a has a maximum capacity of 3 gallons. Container B has a maximum capcity of 14 quarts.

It should be noted that 4 quarts equals 1 gallon. Therefore, 14 quarts = 14/4 = 3.5 gallons

Container A = 3 gallons

Container B = 3.5 gallons

The difference will be:

= 3.5 gallons - 3 gallons

= 0.5 gallon

7 0

3 years ago

1. Given right triangle ABC with the right angle C and sin A = 1/3, which is of the following expression is also equal to 1/3?

Fynjy0 [20]

Answer:

1) B

2) About 5°.

Step-by-step explanation:

1)

We can use the following co-function identity:

$\sin(\theta)=\cos(90-\theta)$

Substitute A for θ:

$\sin(A)=\cos(90-A)$

Since we know that sin(A) is 1/3, this means that cos(90-A) must also be 1/3.

So, our answer is B.

2)

Refer to the drawing.

Remember that 1-inch rise is a height of 1 while a 12 inch length is a length of 12.

So, to find the maximum ramp angle, we simply need to find the value of x.

We know the sides opposite and adjacent to x. So, we can use tangent:

$\tan(x)=\text{opp}/\text{adj}$

Substitute 1 for the opposite side and 12 for the adjacent side:

$\tan(x)=1/12$

Take the inverse tangent of both sides:

$x=\tan^{-1}(1/12)$

Use a calculator. Make sure you're in Degrees mode:

$x\approx4.76\textdegree\approx5\textdegree$

So, the maximum ramp angle should be about 5°

4 0

3 years ago

Plz help 50 points and brainliest <br>6x + 3(6x - 2) = -12

alexandr402 [8]

Answer:

-1/4

6x+3(6x-2)=-12

6x+18x-6=-12

24x-6=-12

24x=-6

x=-1/4

8 0

3 years ago

Read 2 more answers

A woodchuck runs 20 m to the right in 5 s, then turns and runs 10 m to the left in 3 s. (a) What is the average velocity of the

Archy [21]

Answer:

<h2>a) Average velocity = 1.25 m/s to the right</h2><h2>b) Average speed = 3.75 m/s</h2>

Step-by-step explanation:

A woodchuck runs 20 m to the right in 5 s, then turns and runs 10 m to the left in 3 s.

Total displacement = 20 - 10 = 10 m to the right

Total time = 5+3 = 8 s

Total distance = 20 + 10 = 30 m

a) We have

Total displacement = Average velocity x Time

10 = Average velocity x 8

Average velocity = 1.25 m/s to the right

b)We have

Total distance = Average speed x Time

30 = Average speed x 8

Average speed = 3.75 m/s

3 0

3 years ago