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2 years ago

9. What is the slope of the line through the points (-2, -1) and (4, 3)?

Mathematics

1 answer:

Fofino [41]2 years ago

4 0

Step-by-step explanation:

given points,

(-2, -1) and (4,3)

we know,

slope of line = y_2 - y_1/ x_2 - x_1

x_1 and y_1 = -2 , -1

x_2 and y_2 = 4 , 3

according to the formula

3 - (-1)/4 - (-2)

→ 3 + 1/4 + 2

→ 4/6

→ 2/3

or (2,3)

therefore, slope of the given line is (2,3).

Hope this answer helps you dear!

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5(x-3) /8 +2=7 solve?

SVETLANKA909090 [29]

Answer:

Okay I'm not thoroughly understanding your question. But here is my answer for BOTH ways.

Step-by-step explanation:

If it's 5 TIMES 3x/8 +2=7

x= 8/3 or x=2.6

If it's 5(3x) OVER 8 in fraction form +2=7

x= 11

Hope this answers your question.

3 0

2 years ago

Forty percent of students at pine crest middle school have a school sweatshirt. There are 560 students at the school.

Oksi-84 [34.3K]

Answer: 224 students own a school sweatshirt.

Step-by-step explanation:

40% of 560 means 60% do not have one

0.60 is 60% as a decimal

560 x 0.60 = 336 students without a sweatshirt

560 - 336 = 224

4 0

2 years ago

Find the volume of the solid that lies between planes perpendicular to the x-axis at x = pi/4 and x = 5pi/4. The cross-sections

svp [43]

Answer:

The volume of the solid = π²

Step-by-step explanation:

As per the given data of the questions,

The diameter of each disk is

D = 2 sin(x) - 2 cos(x)

So its radius is

R = sin(x) - cos(x).

The area of each disk is

$= \pi \times(sinx-cosx)^{2}$

$= \pi \times [sin^{2}(x) - 2 sin(x) cos(x) + cos^{2}(x)]$

$= \pi[1-2sin(x)cos(x)]$

$= \pi[1-sin(2x)]$

Now,

Integrate from $x=\frac{\pi}{4}\ \ \ to\ \ \ x=\frac{5\pi}{4}$ , we get volume:

$V=\int_{\frac{\pi}{4}}^{\frac{5\pi}{4}} \pi[1-sin(2x)]dx$

After integrate without limit we get

$V=\pi[x+\frac{cos2x}{2}]$

Now after putting the limit, we get

V = π²

Hence, the required volume of the solid = π²

3 0

3 years ago

Pluto is 5,560,000,000 years old. Estimate the age of Pluto by writing it in the form of x×10y years, where x and y are single-d

SashulF [63]

Answer:

The age of pluto is:

5,560,000,000 years old = 5.56 × 10⁹ years old

x = 5.56

y = power of 9

Step-by-step explanation:

Pluto is 5,560,000,000 years old. Estimate the age of Pluto by writing it in the form of x×10y years, where x and y are single-digit numbers.

We write this in standard form or scientific notation.

5,560,000,000 years old = 5.56 × 10⁹ years old

x = 5.56

y = power of 9

4 0

2 years ago

Explain why any of the four operations placed between two terms 5 and -3 sqrt (8) will result in an irrational number

Gnoma [55]

Sum/difference:

Let

$x = 5 + (-3\sqrt{8}) = 5-3\sqrt{8}$

This means that

$3\sqrt{8} = 5-x \iff \sqrt{8} = \dfrac{5-x}{3}$

Now, assume that $x$ is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that $x$ was rational, which proves that the sum/difference of the two given terms was irrational

Multiplication/division:

The logic is actually the same: if we multiply the two terms we get

$x = -15\sqrt{8}$

if again we assume x to be rational, we have

$\sqrt{8} = -\dfrac{x}{15}$

But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.

7 0

2 years ago