All categories

3 years ago

The perimeter of a rectangle is 24mm. The length is 4mm less than triple the width. What are the dimensions of the rectangle

Mathematics

1 answer:

Bess [88]3 years ago

4 0

<h3><u>The length is equal to 8.</u></h3><h3><u>The width is equal to 4.</u></h3>

2l + 2w = 24

l = 3w - 4

Because we have a value for l, we can plug it into the first equation to solve for the exact value of w.

2(3w - 4) + 2w = 24

Distributive property.

6w - 8 + 2w = 24

Combine like terms.

8w - 8 = 24

Add 8 to both sides.

8w = 32

Divide both sides by 8.

w = 4

Now that we have a value for w, we can plug it into the second equation to solve for the exact value of l.

l = 3(4) - 4

l = 12 - 4

l = 8

You might be interested in

80% of Vanessa's final grade is based on the average score of her quizzes, which is 73.

Misha Larkins [42]

80% of quizzes + 20% of final = final grade

80% * 73 + 20% * x = 70

0.8 * 73 + 0.2x = 70

58.4 + 0.2x = 70

0.2x = 11.6

x = 58

8 0

3 years ago

Two groups of staff at a store are making flowers to decorate the entrance. If Group A were to do it alone, it would take them 1

Tcecarenko [31]

Answer:

$\dfrac{6750}{7}$

Step-by-step explanation:

Let x be the number of flowers. If Group A were to make x flowers alone, it would take them 10 hours to complete the task, then they make $\dfrac{x}{10}$ flowers in an hour. If Group B were to make x flowers alone, it would take them 15 hours to complete the task, then they make $\dfrac{x}{15}$ flowers in an hour.

The groups decided to work together. They can make $\dfrac{x}{10}+\dfrac{x}{15}=\dfrac{x}{6}$ together in an hour and it takes them $\dfrac{x}{\frac{x}{6}}=6$ hours. Group B took a break for 1 hour and 40 minutes ( $1\dfrac{2}{3}$ hour), then Group B works

$6-1\dfrac{2}{3}=4\dfrac{1}{3}$ hours.

Thus,

$\dfrac{x}{10}\cdot 6-\dfrac{x}{15}\cdot 4\dfrac{1}{3}=300,\\ \\\dfrac{3x}{5}-\dfrac{13x}{45}=300,\\ \\14x=300\cdot 45=13500,\\ \\x=\dfrac{13500}{14}=\dfrac{6750}{7}.$

6 0

3 years ago

In a sample of eight whitefish caught in Yellowknife Bay, the mean arsenic concentration in the liver was 0.32 mg/kg, with a sta

Advocard [28]

Answer:

The 95% confidence interval for the concentration in whitefish found in Yellowknife Bay is (0.2698 mg/kg, 0.3702 mg/kg).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 8 - 1 = 7

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 7 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 2.3246