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3 years ago

Tashia ate 1/3 of a pizza, and Jay ate 3/8 of the same pizza. What fraction of the pizza was eaten?

1 answer:

7 0

This is basically saying how much of the pizza did Tashia and Jay both ate, thus combining their portions together.

1/3 + 3/8 = fraction of pizza eaten

To add fractions, you must have a common denominator. Which is 24 in this case because 3*8 = 24.

So you multiply 1/3 with 8 and multiply 3/8 with 3.

1/3*8= 8/24
3/8*3= 9/24

Now you add the fractions.
8/24+9/24= 17/24. You add the numerator, the denominator stays the same.

17/24 of the pizza was eaten.

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If a cyclist increases his speed by 3 miles per hour, he can reduce the time required for a 6 mile trip by 10 minutes. What is t

raketka [301]

Answer:

Slower speed = 9 mph

Step-by-step explanation:

Let the initial speed (slower speed) = s mph

Speed 's' = $\frac{\text{Distance}}{\text{Time}}$

s = $\frac{6}{t}$ -------(1)

If the cyclist increases the speed by 3 mph then the final speed = (s + 3) mph

He can reduce the time 't' by 10 minutes ( $\frac{1}{6}$ hours)

Now, (s + 3) = $\frac{6}{t-\frac{1}{6}}$

s + 3 = $\frac{36}{6t-1}$ --------(2)

Substitute the value of 's' from equation (1) to the equation (2).

$\frac{6}{t}+3=\frac{36}{6t-1}$

$\frac{2}{t}+1=\frac{12}{6t-1}$

$\frac{2}{t}-\frac{12}{6t-1}=-1$

$\frac{2(6t-1)-12t}{t(6t-1)}=-1$

$\frac{12t-2-12t}{t(6t-1)}=-1$

$-\frac{2}{t(6t-1)}=-1$

6t² - t = 2

6t² - t - 2 = 0

6t² - 4t + 3t - 2 = 0

2t(3t - 2) + 1(3t - 2) = 0

(2t + 1)(3t - 2) = 0

t = $-\frac{1}{2},\frac{2}{3}$ hours

But the time can't be negative.

Therefore, t = $\frac{2}{3}$ hours is the answer.

From equation (1),

s = $\frac{6}{\frac{2}{3}}$

s = 9 miles per hour.

Slower speed = 9 mph is the answer.

6 0

3 years ago

Jay and Blair went fishing. Together, they caught 27 fish. Jay caught 2 times as many fish as Blair. How many fish did Jay and B

enyata [817]

<span>Leah, Let x=Blair's fish and 2x= Jay's fish; yet together they caught 27 fish. So, x + 2x=27; Combine the like terms. So, 3x=27; Now divide both sides of the equation by 3, therefore, x=9 which is the amt of fish Blair caught. So, 2(9)=18 is the amt of fish Jay caught. Check: 9 +2(9)=27; 27=27.</span>

5 0

3 years ago

8 stones and 2 pounds − 4 stones and 2 pounds

son4ous [18]

Answer:

4 stones is the answer use basic mathematics

7 0

3 years ago

Given various values of the linear functions f(x) and g(x) in the table, determine the y-intercept of (f- g)(x).

lisabon 2012 [21]

The y-intercept of linear function (f- g)(x) is (0,9)

<h3>How to determine the y-intercept?</h3>

The table of values is given as:

x -6 -4 -1 3 4

f(x) 15 11 5 -3 -5

g(x) -36 -26 -11 9 14

The equations of the functions is calculated using:

$y = \frac{y_2 -y_1}{x_2-x_1} * (x -x_1) + y_1$

So, we have:

$f(x) = \frac{11 -15}{-4 + 6} * (x + 6) + 15$

Evaluate

f(x) = -2x + 3

Also, we have:

$g(x) = \frac{-26 + 36}{-4 + 6} * (x + 6) - 36$

Evaluate

g(x) = 5x - 6

Next, we calculate (f - g)(x) using:

(f - g)(x) = f(x) - g(x)

This gives

(f - g)(x) = -2x + 3 - 5x + 6

Substitute 0 for x

(f - g)(0) = -2(0) + 3 - 5(0) + 6

Evaluate

(f - g)(0) = 9

Hence, the y-intercept of (f- g)(x) is (0,9)

Read more about linear functions at:

brainly.com/question/24896196

#SPJ1

7 0

2 years ago

Alain throws a stone off a bridge into a river below.

podryga [215]

I did get the one in the tux ‍♂️ and the other one ☝️

5 0

3 years ago