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Artist 52 [7]
3 years ago
9

Determine the value of x. Write the answer in an inequity. Use x only once in the inequality

Mathematics
1 answer:
Romashka-Z-Leto [24]3 years ago
4 0

Answer:  1 < x < 25

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

The sum of two sides must be GREATER than the third side.

      a +  b > c              a + c > b              b + c > a

     12 + 13 > x             12 + x > 13            13 + x > 12

          25  > x                     x > 1                      x > -1

           x < 25                     1 < x

Length cannot be negative so disregard x > -1

We are left with   1 < x  and   x < 25  

                                 1 < x < 25

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Find the length of the shorter leg of a right triangle with the longer leg is 9 feet more than the shorter leg the hypotenuse is
Jobisdone [24]

Answer:

Length of Shorter leg = 27 feet

Length of Longer leg = 36 feet

Length of Hypotenuse = 45 feet

Step-by-step explanation:

Given:

Let,

    Length of Shorter leg = x,

According to the given condition we have

∴  Length of Longer leg = x + 9 feet

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To Find:

Length of Shorter leg = ?

Solution:

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(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}

substituting the given values we get

(2x-9)^{2} = (x)^{2}+(x+9)^{2}\\

By using Identity (A ± B)² = A² ± 2AB +B²  we get

4x^{2} -36x+81=x^{2} +(x^{2} +18x+81)\\\\4x^{2} -2x^{2} -36x-18x=81-81\\\\2x^{2} -54x=0\\2x(x-27)=0\\2x=0 or x-27=0\\\therefore x\ cannot\ be \ zero\\\therefore x = 27 \feet

Substituting x=27 we get

∴  Length of Longer leg = x + 9 =27 +9 = 36 feet

∴  Length of Hypotenuse = 2x - 9 = 2×27 -9 = 45 feet

7 0
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Suppose babies born in a large hospital have a mean weight of 3215 grams, and a variance of 84,681. if 67 babies are sampled at
ziro4ka [17]
The z-score is given by:
z=(x-μ)/σ
but
x-μ=52
thus
z=52/√84681
z=0.1787
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P(X≤52)=0.9633
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32 3/4 take away 12 1/2​
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Answer:

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PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!<br><br> What is [100(−4)^n-1} equal to?
nikklg [1K]

Answer:   -5100

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

\sum^4_1[100(-4)^{n-1}]\qquad \rightarrow \qquad a_1=100\ \text{and r = -4}\\\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\\\\\S_4=\dfrac{100(1-(-4)^4)}{1-(-4)}\\\\\\.\quad=\dfrac{100(1-256)}{1+4}\\\\\\.\quad=\dfrac{100(-255)}{5}\\\\.\quad=20(-255)\\\\.\quad=-5100\\

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3 years ago
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