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2 years ago

What is the equation of the line in slope-intercept form?

Mathematics

1 answer:

timama [110]2 years ago

3 0

Answer:

i dont know

Step-by-step explanation:

123456

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The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.

Varvara68 [4.7K]

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

Step-by-step explanation:

Let the hypotenuse be y and the other legs be x.

So:

$y = 11 + x$

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

$y^2 = x^2 + x^2$

$y^2 = 2x^2$

This gives:

$(11+x)^2 = 2x^2$

Open bracket

$121 + 22x + x^2= 2x^2$

Collect like terms

$2x^2 - x^2 -22x - 121 = 0$

$x^2 -22x - 121 = 0$

Using quadratic formula:

$x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}$

$x = \frac{-(-22)\±\sqrt{968}}{2*1}$

$x = \frac{22\±31.11}{2}$

Split

$x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\$

$x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}$

x can not be negative.

So:

$x = \frac{53.11}{2}$

$x = 26.56$

Recall that:

$y = 11 + x$

$y = 11 + 26.56$

$y = 37.56$

Hence, the dimensions are:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

6 0

3 years ago

A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 77 and a standar

Shalnov [3]

Answer:

0.9007 is the probability that a student scored below 86 on this exam.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 77

Standard Deviation, σ = 7

We are given that the distribution of examination grades is a bell shaped distribution that is a normal distribution.

Formula:

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

a) P(student scored below 86)

P(x < 86)

$P( x < 86) = P( z < \displaystyle\frac{86 - 77}{7}) = P(z < 1.2857)$

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

$P(x < 1.2857) = 0.9007 = 90.07\%$

0.9007 is the probability that a student scored below 86 on this exam.

7 0

3 years ago

Algebra question please helppp

mylen [45]

Step-by-step explanation:

if u need a clearer photo please tell me

5 0

2 years ago

For what values of x is the inequality 15>_5x true?

ruslelena [56]

Answer:

-3 < x

Step-by-step explanation:

15 > -5x

Divide each side by -5, remembering to flip the inequality since we are dividing by a negative

15/-5 < -5x/-5

-3 < x

7 0

3 years ago

Help meeeeeeeeeeeeeee pls

WITCHER [35]

Answer:

Area = 15.36 ft

Step-by-step explanation:

First find the area of the dotted line triangle using the formula: base x height x 1/2, which would be 1.2ft x 12.8 x 1/2 = 7.68ft.

Next, add another triangle at the top, mirroring the shown triangle, of the parallelogram.

Then, find the area of the shape as though it were a rectangle. (base x height) - 2.4 x 12.8 = 30.72.

Next, multiply the area of the invisible triangle by 2, 7.68 x 2 = 15.36ft

and Finally, subtract the area of the rectangle shape of the the sum of the two invisible triangles, 30.72 - 15.36 = 15.36ft

The area of the parallelogram is 15.36 ft.

5 0

2 years ago