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2 years ago

"Four times the difference of a number and seven is at least -52."

1 answer:

7 0

Remember ‘difference’ refers to subtraction, so they are looking for the ‘difference’ of a a number, which is unknown, so we can use the variable ‘x.’ X-7

The term ‘at least’ refers to our greater than, less than, equal to signs

Difference of a number and 7 = x-7
Four times = (4) or •4
At least = <
-52 = Answer negative 52
Plug them all in,

x-7(4)<-52

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Help is appreciated. Easy I just am always confused

saveliy_v [14]

Answer:

BA=BC

Step-by-step explanation:

8 0

3 years ago

Find the equation of the straight line through (–2, 3) perpendicular<br> to 2x + y =8

Thepotemich [5.8K]

Answer:

$y = \dfrac{1}{2}x + 4$

Step-by-step explanation:

The equation of a line in slope-intercept form is

y = mx + b

We need to find the slope, m, and the y-intercept, b.

The line we need is perpendicular to the line 2x + y = 8.

<em>The slopes of perpendicular lines are negative reciprocals.</em>

We solve the given equation for y to find the slope of the given line.

2x + y = 8

y = -2x + 8

The given line has slope -2.

The negative reciprocal of -2 is 1/2.

Our line has slope, m = 1/2.

Now we have

y = 1/2 x + b

Now we use the given point, (-2, 3), for x and y, using x = -2, and y = 3, and we solve for b.

y = 1/2 x + b

3 = 1/2 * (-2) + b

3 = -1 + b

4 = b

b = 4

Now we have

y = 1/2 x + 4

Answer: $y = \dfrac{1}{2}x + 4$

8 0

3 years ago

There are 3 times as many novels as comic books in a bookstore.If there are 2480 books altogether, how many comic books are ther

Allushta [10]

Answer:

620 comic books

2480 / 4 is 620.

620 x 3 is 1860.

1860 + 620 is 2480.

Done!

5 0

3 years ago

Find the point on the line 2x+4y−3=0 which is closest to the point (2,0)

Finger [1]

L1: 2x+4y-3=0 ..........(1)
P: (2,0)
The point on the line L1 closest to the given point P is at the intersection of L1 with L2, which is the perpendicular passing through P.

Slope of L1=-2/4=-1/2
Slope of L2=-1/(-1/2)=2
Since it passes throug P(2,0), we can use the point-slope formula:
(y-0)=2(x-2) =>
L2: 2x-y-4=0.............(2)

Solve for x & y using (1) and (2) to get intersection point required:
(1)-(2)
2x-2x + 4y-(-y) -3 -(-4) =0
5y=-1, y=-1/5
Substitute y=1/5 in equation (1)
2x+4(-1/5)-3=0 =>
2x-19/5=0
x=19/10

=> the point on L1 closest to (2,0) is (19/10, -1/5)

7 0

3 years ago

If f(x)=4x^2+1 and g(x)=x^2-5 find(f+g)(x)

Zepler [3.9K]

Answer:

$\large\boxed{(f+g)(x)=5x^2+6}$

Step-by-step explanation:

$(f+g)(x)=f(x)+g(x)\\\\f(x)=4x^2+1,\ g(x)=x^2-5\\\\\text{Substitute:}\\\\(f+g)(x)=(4x^2+1)+(x^2-5)\\\\=4x^2+1+x^2-5\qquad\text{combine like terms}\\\\=(4x^2+x^2)+(1+5)\\\\=5x^2+6$

6 0

3 years ago