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lions [1.4K]
3 years ago
11

F(-4)=8 and f(-1)=4 write the linear equation

Mathematics
1 answer:
kobusy [5.1K]3 years ago
7 0

f(-4)=8\to(-4,\ 8)\\\\f(-1)=4\to(-1,\ 4)

The point-slope formula of a line:

y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}

Substitute:

m=\dfrac{4-8}{-1-(-4)}=\dfrac{-4}{3}=-\dfrac{4}{3}\\\\y-8=-\dfrac{4}{3}(x-(-4))\\\\y-8=-\dfrac{4}{3}x-\dfrac{16}{3}\ \ \ \ |+8\\\\y=-\dfrac{4}{3}x-\dfrac{16}{3}+\dfrac{24}{3}\\\\y=-\dfrac{4}{3}x+\dfrac{8}{3}\ \ \ |\cdot3\\\\3y=-4x+8\ \ \ |+4x\\\\4x+3y=8

The slope-intercept form: y=-\dfrac{4}{3}x+\dfrac{8}{3}

The standard form: 4x+3y=8


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Hello!

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I hope it helps!

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3 years ago
If y varies directly as x, and y=-4 when x=8, find y when x=3
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Which of the following is equivalent to 1/8?
neonofarm [45]
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Find the area of the regular trapezoid. The figure is not drawn to scale. The top side is 4, the bottom side is 7, and both side
svp [43]
A regular trapezoid is shown in the picture attached.

We know that:
DC = minor base = 4
AB = major base = 7
AD = BC = lateral sides or legs = 5

Since the two legs have the same length, the trapezoid is isosceles and we can calculate AH by the formula:

AH = (AB - DC) ÷ 2
      = (7 - 5) ÷ 2
      = 2 ÷ 2
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Now, we can apply the Pythagorean theorem in order to calculate DH:
DH = √(AD² - AH²) 
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      = √(25 - 1)
      = √24
      = 2√6

Last, we have all the information needed in order to calculate the area by the formula:

A =  \frac{(AB + CD)DH}{2}

A = (7 + 5) × 2√6 ÷ 2
   = 12√6

The area of the regular trapezoid is 12√6 square units.

7 0
3 years ago
olga worked 37.5 hours last week qt the library and earned $12.50 an hour. if she gets a $2.50 per hour raise, how many hours wi
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