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12345 [234]
3 years ago
13

What is the slope of the line with equation 3x - 2y = 12

Mathematics
1 answer:
n200080 [17]3 years ago
5 0

The slope of the line is 2/3

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The product of two consecutive odd integers is 782. What are the integers?
Alex Ar [27]

Call the smaller of the two odds = n

Call the next number in the sequence = n + 2

n*(n +2) = 782           Remove the brackets.

n^2 + 2n = 782          Subract 782 from both sides.

n^2 + 2n - 782 = 0    We are going to have to factor this.

Discussion

This problem can't be done the way it is written. The product of an odd integer with another odd integer is and odd integer. There are no exceptions to this. So you need to give a number that has two factors very near it's square root for this question to work.

For example, you could use 783, (which factors) instead of 782 .

Solve

n^2 + 2n - 783 = 0

(n + 29)(x - 27) = 0

<u>Solution One</u>

n - 27 = 0

n = 27

The two odd consecutive integers are 27 and 29.

<u>Solution Two</u>

n + 29 = 0

n = - 29

The two solution integers are -29 and - 27 Notice that - 29 is smaller than - 27.

7 0
4 years ago
one-third of the people from country A claim that they are from country B, and the rest admit they are from country A. One-fourt
In-s [12.5K]

Answer: 3 : 2

Step-by-step explanation:

Let A represents the total population of country A and B represents the total population of country B.

According to the question,

 \text{The population of country A that admit they are from B} = \frac{1}{3}\text{ of }A

⇒ \text{ The population of A that admit they are from country A }= A - \frac{1}{3} \text{ of } A

= \frac{3-1}{3} A

= \frac{2}{3} A

\text{The population of country B that admit they are from A} = \frac{1}{4}\text{ of }B

⇒ \text{ The total population that claims that they are from A }= \frac{2}{3} A +\frac{1}{4} B

But, Again according to the question,

The total population that claims that they are from A =  one half of the total population of A and B.

⇒ \frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}(A+B)

⇒ \frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}A+\frac{1}{2}B

⇒ \frac{2}{3} A + \frac{1}{4} B= \frac{1}{2}A+\frac{1}{2}B

⇒ \frac{2}{3} A - \frac{1}{2}A= \frac{1}{2}B-\frac{1}{4} B

⇒ \frac{4}{6} A - \frac{3}{6}A= \frac{2}{4}B-\frac{1}{4} B

⇒ \frac{1}{6} A = \frac{1}{4} B

⇒ A =\frac{6}{4}B

⇒ \frac{A}{B} =\frac{3}{2}

8 0
4 years ago
The value of the surface area of the cylinder is equal to the value of the volume of the cylinder. Find the value of x.
zlopas [31]

Answer:

x = 2.5

Step-by-step explanation:

Surface area of cylinder = 2πr(h + r)

Volume of cylinder = πr²h

Given that S.A = Volume of the cylinder, therefore, we have:

2πr(h + r) = πr²h

Radius (r) is given as 2.5 cm

height (h) = x cm

Input the values and solve for x

2πr(h + r) = πr²h

2πr(h + r) = πr(rh)

2(h + r) = rh (πr cancels πr)

2(x + 2.5) = 2.5*x

2x + 5 = 2.5x

Subtract 2x from both sides

2x + 5 - 2x = 2.5x - 2x

5 = 0.5x

Divide both sides by 0.5

\frac{5}{0.5} = \frac{0.5x}{0.5}

2.5 = x

x = 2.5

8 0
3 years ago
Quadrilateral EFGH was dilated by a scale factor of 2 from the center (1, 0) to create E'F'G'H'. Which characteristic of dilatio
alisha [4.7K]

Answer:

It's the last choice.

Step-by-step explanation:

A segment in the image is proportionally longer or shorter than the corresponding one in the pre-image.

8 0
3 years ago
Read 2 more answers
What is the volume of the pyramid (base: 7in. , height: 9in. , length 8in.)
Anna71 [15]

Answer:

504

Step-by-step explanation:

7*8*9=504

6 0
3 years ago
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