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2 years ago

Is anyone good with triangle inequalities? I provided a picture for the problem.

Mathematics

1 answer:

alisha [4.7K]2 years ago

3 0

Answer:

1 < x < 19

Step-by-step explanation:

Triangle Inequality Theorem

Let y and z be two of the side lengths of a triangle. The length of the third side x cannot be any number. It must satisfy all the following restrictions:

x + y > z

x + z > y

y + z > x

Combining the above inequalities, and provided y>z, the third size must satisfy:

y - z < x < y + z

We are given the measures y=10, z=9. The third side must satisfy:

10 - 9 < x < 10 + 9

1 < x < 19

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What is the area of a sector with a central angle of 255 and a radius of 18.4 m?

Igoryamba

Answer:

The answer is 753.01 m².

Step-by-step explanation:

Given that the formula of sector is θ/360×π×r² where r represents radius of circle. Then, you have to substitute the values into the formula :

$area = \frac{θ}{360} \times \pi \times {r}^{2}$

Let θ = 255°

Let π = 3.14,

Let r = 18.4m,

$area = \frac{255}{360} \times 3.14 \times {18.4}^{2}$

$area = 753.01 {m}^{2} \: (near.hundredth)$

5 0

2 years ago

MakcuM [25]

Answer: C) 4.20

Explanation:

Multiply each value with its corresponding frequency:

1*450 = 450
10*35 = 350
50*10 = 500
100*4 = 400
400*1 = 400

Add up the products

450+350+500+400+400 = 2100

Then divide this over the total frequency (450+35+10+4+1 = 500)

So we get 2100/500 = 4.20 as the expected value.

4 0

2 years ago

Tricia made a circular mat from a square piece of cloth as shown in the diagram below.

kap26 [50]

The option C) 49 inches is the circumference of the circular mat.

<u>Step-by-step explanation:</u>

Tricia made a circular mat from a square piece of cloth.
The measure of the side length of the square = 14 inches.
The length of the side is same as the diameter of the circle.
Therefore, the diameter of the circular mat = 14 inches.

<u>To find radius :</u>

Radius = diameter / 2

⇒ 14/2

⇒ 7 inches.

<u>To find the circumference of the circular mat :</u>

Circumference = 2πr

where,

π has the default value of 3.14

r is the radius of the circular mat.

⇒ 2 × 3.14 × 7

⇒ 44 inches.

∴ The circumference of the circular mat is 44 inches.

Since, it is not given in the option. The option C) 49 inches which is close to 44 inches is the right option.

8 0

3 years ago

PLEASE GUYS THIS IS THE HARDEST MATH PORBLEMS PLEASE ASAP PLEASE I NEED HELP PLEASE T_T

Alexandra [31]

The simplified form of R(x) is $R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}$

<h3>Simplifying an expression </h3>

From the question, we are to simplify the expression

From the given information,

$f(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30}$

and

$g(x) =\frac{x^{2}-9x+20 }{x^{2}-12x+36}$

Also,

$R(x) = f(x) \div g(x)$

∴ $R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \div \frac{x^{2}-9x+20 }{x^{2}-12x+36}$

$R(x) =\frac{x^{2}-11x+28 }{x^{2}-11x+30} \times \frac{x^{2}-12x+36 }{x^{2}-9x+20}$

Factoring each of the quadratics

$R(x) =\frac{x^{2}-7x-4x+28 }{x^{2}-6x-5x+30} \times \frac{x^{2}-6x-6x+36 }{x^{2}-4x-5x+20}$

$R(x) =\frac{x(x-7)-4(x-7) }{x(x-6)-5(x-6)} \times \frac{x(x-6)-6(x-6) }{x(x-4)-5(x-4)}$

$R(x) =\frac{(x-4)(x-7)}{(x-5)(x-6)} \times \frac{(x-6)(x-6)}{(x-5)(x-4)}$

Simplifying

$R(x) =\frac{(x-7)}{(x-5)} \times \frac{(x-6)}{(x-5)}$

$R(x) =\frac{(x-7)(x-6)}{(x-5)(x-5)}$

$R(x) =\frac{x^{2} -6x-7x+42}{x^{2} -5x-5x+25}$

$R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}$

Hence, the simplified form of R(x) is $R(x) =\frac{x^{2} -13x+42}{x^{2} -10x+25}$

Learn more on Simplifying an expression here: brainly.com/question/1280754

#SPJ1

7 0

1 year ago

In a random sample of fivefive microwave ovens, the mean repair cost was $75.0075.00 and the standard deviation was $13.0013.

Radda [10]

<h2>Answer with explanation:</h2>

As per given , we have

Sample size : n= 5

Degree pf freedom = : df= 5-1=4

$\mu=\$75.00$

$\sigma=\$13.00$

Significance level for 90% confidence = $\alpha=1-0.90=0.1$

Using t-value table , t-critical value for 90% confidence:

$t_{\alpha/2, df}=t_{0.05, 4}=2.132.$

Margin of error of $\mu$ : $E=t_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\(2.132)\dfrac{13}{\sqrt{5}}=12.3949720129\approx12.39$

Interpretation : The repair cost will be within $12.39 of the real population mean value $\mu$ 90% of the time.

7 0

3 years ago