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2 years ago

Add or subtract. Simplify your answer. x+2/x^2−100 + 8/x^2−100

1 answer:

8 0

$\dfrac{x+2}{x^2-100}+\dfrac{8}{x^2-100}=\dfrac{x+2+8}{x^2-100}=\dfrac{x+10}{x^2-10^2}\\\\=\dfrac{x+10}{(x+10)(x-10)}=\dfrac{1}{x-10}\to\fbox{B.}\\\\\\The\ domain:\\D:m\neq0\ and\ m\neq-7\\\\\dfrac{1}{m}=\dfrac{2}{m+7}\ \ \ \ |cross\ multiply\\\\2\cdot m=1\cdot(m+7)\\2m=m+7\ \ \ \ |subtract\ "m"\ from\ both\ sides\\\boxed{m=7}$

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A line, y = mx + b, passes through the point (10, 3) and is parallel to the line 2x+5y=12.

slava [35]

We have been given that a line $y=mx+b$ passes through the point (10, 3) and is parallel to the line $2x+5y=12$ . We are asked to find the y-intercept of the line.

First of all we will rewrite our given equation in slope-intercept form as:

$2x-2x+5y=12-2x$

$5y=-2x+12$

$\frac{5y}{5}=-\frac{2}{5}x+\frac{12}{5}$

$y=-\frac{2}{5}x+\frac{12}{5}$

We know that slope of parallel lines is equal, so slope of parallel line to our given line would be $-\frac{2}{5}$ .

Now we will use slope-intercept form of equation to find y-intercept.

$y=mx+b$ , where,

m = Slope,

b = The y-intercept.

Let us substitute $m=-\frac{2}{5}$ and coordinates of point $(10,3)$ in above equation as:

$3=-\frac{2}{5}(10)+b$

$3=-2(2)+b$

$3=-4+b$

$3+4=-4+4+b$

$7=b$

Therefore, the y-intercept is 7 and our required equation would be $y=-\frac{2}{5}x+7$ .

5 0

3 years ago

The histograms below show the heights (in meters) of the tallest buildings in China and the United States.

USPshnik [31]

Answer:

A and B

Step-by-step explanation:

I tried it and it was correct. The United states has the tallest... and China has more buildings... are the correct ones.

6 0

2 years ago

A car travels 2 1/3 miles in 3 1/2 minutes at a constant speed. Write an equation to represent the car travels in miles and minu

Korvikt [17]

Answer:

d = 0.666t , where d is in miles and t is in minutes.

d = 39.94h, where d is in miles and h is in hours.

Step-by-step explanation:

A car travels $2\frac{1}{3} = 2.33$ miles in $3\frac{1}{2} = 3.5$ minutes at a constant speed.

Let the relation between the distance (d) traveled by car in miles after traveling t minutes is d = kt ......... (1)

Now, putting d = 2.33 miles and t = 3.5 minutes in the above equation we get,

2.33 = 3.5k

⇒ k = 0.666 (Approx.)

So, the equation (1) becomes d = 0.666t. (Answer)

Let us assume that the relation between the distance (D) traveled by car in miles after traveling h hours is d = Kh ............ (2)

Now, putting D = 2.33 miles and T = 3.5/60 = 0.058 hours in the above equation, we get

2.33 = 0.058K

⇒ K = 39.94

So, the equation (2) we get, d = 39.94h (Answer)

3 0

3 years ago

Find the value of x<br>

riadik2000 [5.3K]

Answer:

need more information

Step-by-step explanation:

more information is needed to answer this question

3 0

2 years ago

Solve the system by substitution.<br> -8x - y = 30<br> -2y = x

masya89 [10]

Answer:

Solution: (-4, 2), x= -4 and y =2

Step-by-step explanation:

-8x - y = 30

-2y = x

Substitute for x

-8*(-2y) - y = 30

16y - y = 30

15y = 30

y = 30/15 = 2

Then x = -2y = -2*(2) = -4

Solution: (-4, 2), x= -4 and y =2

4 0

3 years ago