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4 years ago

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In a certain triangle the longest side is twice as long as the shortest side and the shortest side is 4 inches shorter than midd

le side. If the perimeter of the triangle is 52 inches how long is the longest side?

1 answer:

rodikova [14]4 years ago

5 0

Answer:

24 inches

Step-by-step explanation:

Let the longest side be x, the middle side be y and the shortest side be z

Rest is in the attached file

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Triangles PQR and FGH are similar. Also, What is the ratio of the area of triangle PQR to the area of triangle FGH?

svlad2 [7]

Theorem : If two similar triangles have a scale factor of a : b, then the ratio of their areas is a^2 : b^2<span>.
We have a</span>: b = 1: 1; then a^2 : b^2 = 1^2 : 1^2 = 1;

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3 years ago

Find the sum and express it in simplest form.<br> (-7n2 - 8n - 8) + (-n2 + 9n + 9

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Only the coefficients change, not the exponents when adding
-8n^2 + n + 1

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3 years ago

What’s the answer for m

Archy [21]

Answer:

$m\angle D=35.5^o$

Step-by-step explanation:

we know that

An isosceles triangle has two equal sides and two equal interior angles

In this problem

Triangle CDE is an isosceles triangle

because

EC ≅ DE

therefore

$m\angle C=m\angle D$ ----> equation A

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

$m\angle C+m\angle D+m\angle E=180^o$ ----> equation B

$m\angle E=109^o$ ---> equation C

substitute equation A and equation C in equation B

$m\angle D+m\angle D+109^o=180^o\\$

$2m\angle D=180^o-109^o$

$m\angle D=35.5^o$

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4 years ago

Pam and Meg each have a picture frame. Pam’s picture frame is a square with an area of 3 square feet. Meg’s picture frame is a c

kondaur [170]

Answer:

The circumference of Meg’s picture frame is the perimeter of Pam’s picture frame by approximately 0.65 ft

Step-by-step explanation:

Pam's picture frame : Square with area of 3 sq. foot

Meg’s picture frame is a circle with a radius, r of 1 foot.

The circumference of Meg’s picture frame is the perimeter of Pam’s picture frame by approximately feet.

Let's calculate circumference of Meg's picture frame:

Circumference c, = 2πr

r = 1 ft

c = 2 * 3.14 *1 = 6.28 ft

Now calculate Perimeter of Pam's picture frame:

A is area of square and s is the side

A = s²

s² = 3

s = √3

Permeter of square = 4s

= 4√3 = 6.93ft

Now in order to find circumference of Meg’s picture frame is the perimeter of Pam’s picture frame, we have to find their difference.

Permimeter of square frame - Circumference of circle frame = 6.93 - 6.28 = 0.65

8 0

3 years ago

A quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain bra

tensa zangetsu [6.8K]

Answer:

We conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

Step-by-step explanation:

We are given that a quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain brand of soft drink contains 120 calories as the labeling indicates.

Using a random sample of 10 cans, the manager determined that the average calories per can is 124 with a standard deviation of 6 calories.

<u><em>Let </em></u> $\mu$ <u><em> = average calorie content of a 12-ounce can.</em></u>

So, Null Hypothesis, $H_0$ : $\mu \leq$ 120 calories {means that the average calorie content of a 12-ounce can is less than or equal to 120 calories}

Alternate Hypothesis, $H_A$ : $\mu$ > 120 calories {means that the average calorie content of a 12-ounce can is greater than 120 calories}

The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average calories per can = 124 calories

s = sample standard deviation = 6 calories

n = sample of cans = 10

So, <em><u>test statistics</u></em> = $\frac{124-120}{\frac{6}{\sqrt{10} } }$ ~ $t_9$

= 2.108

The value of t test statistics is 2.108.

<em>Now, at 0.05 significance level </em><em>the t table gives critical value of 1.833 at 9 degree of freedom for right-tailed test</em><em>. Since our test statistics is more than the critical values of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which </em><u><em>we reject our null hypothesis</em></u><em>.</em>

Therefore, we conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

7 0

3 years ago