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Kazeer [188]
3 years ago
14

One leg of a right triangle is 28 inches longer than the other leg, and the hypotenuse is 52 inches. Find the lengths of the leg

s of the triangle.
The lengths of the legs are
Mathematics
1 answer:
katovenus [111]3 years ago
7 0

Step-by-step explanation:

Let x represent the missing sides measurement.

x+x+28=52

combine like terms

2x + 28 = 52

subtract 28 from both sides

2x + 28 = 52

     - 28  - 28

2x = 24

divide both sides by 2

x = 12

plug it back in

one leg is 12 inches

the other leg is 40 inches

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3) Solve each equation using the quadratic formula. Show<br> a. x2 – 3x – 10 = 0
Naya [18.7K]

Answer:

<h2>x = -2 or x = 5</h2>

Step-by-step explanation:

The quadratic formula of a quadratic equation

ax^2+bx+c=0\\\\\text{If}\ b^2-4ac>0\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

\text{If}\ b^2-4ac=0\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}

\text{If}\ b^2-4ac

We have:

x^2-3x-10=0\to a=1,\ b=-3,\ c=-10\\\\b^2-4ac=(-3)^2-4(1)(-10)=9+40=49>0\\\\x=\dfrac{-(-3)\pm\sqrt{49}}{2(1)}=\dfrac{3\pm7}{2}\\\\x=\dfrac{3-7}{2}=\dfrac{-4}{2}=-2\\or\\x=\dfrac{3+7}{2}=\dfrac{10}{2}=5

5 0
3 years ago
A certain standardized test's math scores have a bell-shaped distribution with a mean of 530 and a standard deviation of 119. Co
kumpel [21]

Answer:

a) 68.2%

b) 31.8%

c) 2.3%

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 530

Standard Deviation, σ = 119

We are given that the distribution of math scores is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(test scores is between 411 and 649)

P(411 \leq x \leq 649)\\\\= P(\displaystyle\frac{411 - 530}{119} \leq z \leq \displaystyle\frac{649-530}{119})\\\\= P(-1 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -1)\\= 0.841 - 0.159 = 0.682 = 68.2\%

b) P(scores is less than 411 or greater than 649)

P(x < 411 < x, x > 649)\\=1 = P(411 \leq x \leq 649)\\=1 - 0.682\\=0.318 = 31.8\%

c) P(score greater than 768)

P(x > 768)

P( x > 768) = P( z > \displaystyle\frac{768 - 530}{119}) = P(z > 2)

= 1 - P(z \leq 2)

Calculation the value from standard normal z table, we have,  

P(x > 768) = 1 -0.977 = 0.023 = 2.3\%

5 0
3 years ago
Matter is in a liquid state when its temperature is between its melting point and its boiling point. Suppose that some substance
slavikrds [6]

Answer:

x<39.76 OR x>388.23 (In degrees Celsius.

Step-by-step explanation:

Melting point is when a a substance turns from a solid to liquid, and boiling point is the point where it turns from a liquid to a gas. That means in between these points is when the matter is in the liquid state, so it could be anything not included from the range 39.76-388.23.

7 0
2 years ago
Select the correct answer.
Ratling [72]
I think it’s D but not completely sure!
5 0
2 years ago
What is the area of an equilateral triangle with a side length of 14 inches?
lidiya [134]
The equation for a equilateral triangle is the side squared times root 3 divided by 4

6 0
3 years ago
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