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3 years ago

What is the y-intercept of the line passing through the point (9,-7) with a slope of -1/8 ?

Mathematics

1 answer:

Black_prince [1.1K]3 years ago

5 0

Answer:

-47/8.

Step-by-step explanation:

If the line has a slope of -1/8, that means the equation y = mx + b will be y = -1/8x + b.

In this case, we are given a point: (9, -7). That means that x = 9 and y = -7.

-7 = (-1/8)(9) + b

b - 9/8 = -7

b = -56/8 + 9/8

b = -47/8 = -5.875 = -5 and 7/8, which is your y-intercept!

Hope this helps!

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If f(x) =4x2 - 8x - 20 and g(x) = 2x + a, find the value of a so that the y-intercept of the graph of the composite function (fo

amm1812

Answer:

The possible values are a = -2.5 or a = 4.5.

Step-by-step explanation:

Composite function:

The composite function of f(x) and g(x) is given by:

$(f \circ g)(x) = f(g(x))$

In this case:

$f(x) = 4x^2 - 8x - 20$

$g(x) = 2x + a$

$(f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20$

Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).

This means that when $x = 0, f(g(x)) = 25$ . So

$4a^2 - 8a - 20 = 25$

$4a^2 - 8a - 45 = 0$

Solving a quadratic equation, by Bhaskara:

$\Delta = (-8)^2 - 4(4)(-45) = 784$

$x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5$

$x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5$

The possible values are a = -2.5 or a = 4.5.

5 0

3 years ago

"three food trucks are set up at points a, b, and c. each of the three trucks is the same distance from the food distributor. at

jolli1 [7]

Answer:

circumcenter

Step-by-step explanation:

Suppose the three food trucks points a,b,c are joined together in such a way that the form a triangle. The perpendicular bisectors of the triangle are concurrent . The point of concurrency is called <u>circumcenter.</u>

According to the circumcenter theorem the points ( vertices of the triangle a,b,c) are equidistant from the center D ( point of concurrency) called the circumcenter.

As the food distributor is equidistant from each of the trucks it lies at the circumcenter point of concurrency.

The drawing is just a generalizations to give an idea. It does not show actual bisectors perpendicular.

3 0

3 years ago

If correct I’ll give brainlest pls help

VladimirAG [237]

Answer:

Step-by-step explanation:

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7 0

3 years ago

Use a number line to compare the numbers. Which shows the correct symbol to compare the numbers? 1.2 1 1/5

Leno4ka [110]

For this case we must compare the following expressions:

$1.2\\1 \frac {1} {5}$

We convert the mixed number to a fraction:

$1 \frac {1} {5} = \frac {5 * 1 + 1} {5} = \frac {5 + 1} {5} = \frac {6} {5} = 1.2$

So, we have to compare:

1.2 and 1.2

It is observed that the expressions are equal, so we have the sign of equality "=":

$1.2 = 1.2$

Answer:

$1.2 = 1.2$

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3 years ago

Which points are a distance of 5 units from (2, 3) if d = square root (x2 - x1)2 + (y2 - y1)?

qwelly [4]

Answer:

Step-by-step explanation:

hello :

note :

note : distance between A(X1,Y1) an B (X2,Y2) is :

AB= √((X2 - X1)² + (Y2 - Y1)²) (given point B(2 , 3)

in this exercice : X1 = 2 X2 = ? Y1 = 3 Y2 = ? d=AB=5

d² = (X2 - 2)² + (Y2 - 3)² =25

the points are a distance of 5 units from B (2, 3) if d = 5 :

the points are located on a circle with center B and radius 5

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3 years ago