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3 years ago

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

Step-by-step explanation:

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

∴ Length of Hypotenuse = 2x - 9 feet

To Find:

Length of Shorter leg = ?

Solution:

Now In Right Angle Triangle, By Pythagoras theorem we have

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

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

3 years ago

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
Thus:
P(X≤52)=0.9633

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3 years ago

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A researcher computes a 2 x 3 factorial anova. in this example, how many interactions can be observed?

Ivan

The one-way ANOVA or one – way analysis of variance is used to know whether there are statistically substantial dissimilarities among the averages of three or more independent sets. It compares the means between the sets that is being examined whether any of those means are statistically pointedly dissimilar from each other. If it does have a significant result, then the alternative hypothesis can be accepted and that would mean that two sets are pointedly different from each other. The symbol, ∑ is a summation sign that drills us to sum the elements of a sequence. The variable of summation is represented by an index that is placed under the summation sign and is often embodied by i. The index is always equal to 1 and adopt values beginning with the value on the right hand side of the equation and finishing it with the value over head the summation sign.

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3 years ago

32 3/4 take away 12 1/2

Otrada [13]

Answer:

The answer is 20 and 1/4

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3 years ago

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PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!! What is [100(−4)^n-1} equal to?

nikklg [1K]

Answer: -5100

Step-by-step explanation:

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

3 0

3 years ago