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KiRa [710]
3 years ago
10

What is the Value of x?

Mathematics
2 answers:
satela [25.4K]3 years ago
8 0

\text{It's an isosceles triangle. Therefore}\ m\angle C=m\angle A:\\\\9y-3=69\qquad\text{add 3 to both sides}\\\\9y=72\qquad\text{divide both sides by 9}\\\\\boxed{y=8}\\\\\text{We know: The sum of the measures of the angles of a triangle is 180}^o.\\\\\text{Therefore we have the equation:}\\\\m\angle A+m\angle B+m\angle C=180^o\\\\\text{Substitute}\ m\angle A=m\angle C=69^o:\\\\69+(5x+2)+69=180\\\\138+5x+2=180\\\\140+5x=180\qquad\text{subtract 140 from both sides}\\\\5x=40\qquad\text{divide both sides by 5}\\\\\boxed{x=8}

Answer:\ \boxed{\boxed{x=8}}

Ronch [10]3 years ago
7 0

Answer:

x=8

Step-by-step explanation:

Since this is an isosceles triangle <A is equal to <C

<A = <C = 69

<A+ <B +<C = 180  because the 3 angles of a triangle add to 180 degrees.

69 + 5x+2 + 69 = 180

Combine like terms

140+ 5x = 180

Subtract 140 from each side

140-140 +5x =180-140

5x = 40

Divide by 5

5x/5 =40/5

x=8


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Answer : Option D is correct i.e [2.5,4]

Explanation :

Suppose our function is f(x)

then the value of f(x) is minimum where

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As we know that for finding the local minimum ,

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So, here

f'(-0.44)=0 and

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both are the local minimum point for the function f(x)

but -0.44 is the global minimum point .

In our case for [2.5,4] is the required interval where f(x) reaches its  local minimum.

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An adult soccer league requires a ratio of at least 2 women per 7 men on the roster. If 14 men are on the roster, how many women
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Answer:

Atleast 4 women

Step-by-step explanation:

Ratio of

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Number of women needed to maintain the ratio if there are 14 men on the roster :

The minimum number of women required :

(2 : 7) * number of men in roster

(2 / 7) * 14

2 * 2 = 4 women

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A university researcher wants to estimate the mean number of novels that seniors read during their time in college. An exit surv
lys-0071 [83]

Answer:

Population mean = 7 ± 2.306 × \frac{2.29}{\sqrt{9} }

Step-by-step explanation:

Given - A university researcher wants to estimate the mean number

            of  novels that seniors read during their time in college. An exit

            survey was conducted with a random sample of 9 seniors. The

            sample mean was 7 novels with standard deviation 2.29 novels.

To find - Assuming that all conditions for conducting inference have

              been met, which of the following is a 94.645% confidence

              interval for the population mean number of novels read by

              all seniors?

Proof -

Given that,

Mean ,x⁻ = 7

Standard deviation, s = 2.29

Size, n = 9

Now,

Degrees of freedom = df

                                = n - 1

                                = 9 - 1

                                = 8

⇒Degrees of freedom = 8

Now,

At 94.645% confidence level

α = 1 - 94.645%

   =1 - 0.94645

  =0.05355 ≈ 0.05

⇒α = 0.5

Now,

\frac{\alpha}{2} = \frac{0.05}{2}

  = 0.025

Then,

t_{\frac{\alpha}{2}, df }  = 2.306

∴ we get

Population mean = x⁻ ± t_{\frac{\alpha}{2}, df } ×\frac{s}{\sqrt{n} }

                           = 7 ± 2.306 × \frac{2.29}{\sqrt{9} }

⇒Population mean = 7 ± 2.306 × \frac{2.29}{\sqrt{9} }

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