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3 years ago

what is the slope of the line that passes through the points (4,4) and (10,7)? write your answer in simplest form

Mathematics

1 answer:

alexandr1967 [171]3 years ago

8 0

Answer:

$\boxed {\boxed {\sf m= \frac{1}{2}}}$

Step-by-step explanation:

We are asked to find the slope of a line that passes through 2 points. The slope tells us the steepness and direction of a line. It is calculated using the following formula:

$m= \frac {y_2-y_1}{x_2-x_1}$

In this formula, (x₁ , y₁) and (x₂, y₂) are the points the line passes through. The points are (4,4) and (10,7). If we match the value and the corresponding variable we see that:

x₁ = 4
y₁= 4
x₂ = 10
y₂= 7

Substitute the values into the formula.

$m= \frac{7-4}{10-4}$

Solve the numerator.

7-4=3

$m= \frac{3}{10-4}$

Solve the denominator.

10-4= 6

$m= \frac{3}{6}$

This fraction can be reduced. Both the numerator and denominator can be divided by 3.

$m= \frac{3/3}{6/3}$

$m= \frac{1}{2}$

The slope of the line that passes through (4,4) and (10,7) is <u>1/2.</u>

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A research study investigated differences between male and female students. Based on the study results, we can assume the popula

oksian1 [2.3K]

Answer: 0.0548

Step-by-step explanation:

Given, A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05.

Let $\overline{X}$ represents the sample mean GPA for each student.

Then, the probability that the random sample of 100 male students has a mean GPA greater than 3.42:

$P(\overline{X}>3.42)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3.42-3.5}{\dfrac{0.5}{\sqrt{100}}})\\\\=P(Z>\dfrac{-0.08}{\dfrac{0.5}{10}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>1.6)\\\\=1-P(Z$

hence, the required probability is 0.0548.

6 0

4 years ago

The rectangular prism shown has a surface area of 488 square inches. What is the length of the prism?

BigorU [14]

Answer:

length of the prism = 244 - (width x height) / width + height)

Step-by-step explanation:

Let length be a and width be b and height be c

2 (a * b) + 2 (b* c) + 2 (a * c) = 488

2ab+ 2bc + 2ac = 488

ab + bc + ac = 244

ab + ac = 244 - ac

a (b + c) = 244-ac

a = 244-bc / b + c

Therefore the length of the prism = 244 - (width x height) / width + height)

8 0

3 years ago

A triangle has side lengths of 15 10 and 7 is it a right triangle

lions [1.4K]

Answer:

No, it is not a right triangle.

Step-by-step explanation:

Given:

The sides of the triangle = 15 10 and 7

To Find:

Whether the triangle is a right triangle = ?

Solution:

According to Pythagorean theorem , In an right triangle the the sum of the squares of the two smaller sides must equal to the square of the larger side

$a^2 +b^2 =c^2\\$

where

a and b are the smaller sides

c is the larger side

Now from the given data, lets assume

a = 10 and b =7 and c =15

Substituting in the above equation we get,

$(10)^2 +(7)^2 = (15)^2$

100 + 49 = 225

149 = 225

$149 \neq 225$

So, the given triangle is not a right triangle.

7 0

3 years ago

The 1985 Mexico City earthquake measured a magnitude 8.0 on the Richter scale. The Richter scale uses the function M (I) = log (

Travka [436]

Answer:

The correct option is C: I = 10⁸I₀.

Step-by-step explanation:

The function of the Richter scale is:

$M_{(I)} = log(\frac{I}{I_{0}})$

Since the magnitude of the earthquake is 8.0, the relation between the intensity, I, with the intensity of the threshold quake, Io, is:

$8.0 = log(\frac{I}{I_{0}})$

$10^{8} = \frac{I}{I_{0}}$

$I = 10^{8}I_{0}$

Therefore, the correct option is C: I = 10⁸I₀.

I hope it helps you!

7 0

3 years ago

A customer borrowed $2000 and then a further $1000 both repayble in 12 months. What would he have saved if he had taken out one

RSB [31]

A customer borrowed $2000 and then a further $1000 both repayble in 12 months. What would he have saved if he had taken out one loan for $3000 repayable in 12 months?

He took two different loans, it charged him loan processing fee twice, two-time documentation process, and of course, extra time spent for second loan. Instead, he could take single loan of $3000 with one-time processing fee, one-time documentation process, and time-saving also.

8 0

3 years ago