Complete the equation of the line whose y-intercept is (0,5) and the slope is 9.

What is the y-intercept of the quadratic function f(x) = (x – 8)(x + 3)? (8,0) (0,3) (0,–24) (–5,0)

DiKsa [7]

The correct answer is: [C]: " (0, 24) " .
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Explanation:
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Given the quadratic function:
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→ " y = (x − 8) (x + 3) " ; ← Note: Replace the "f(x)" with: "y" ;

→ Find the "y-intercept".
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→ Note: The "y-intercept" is the coordinate of the point(s) of the graph of the equation at which the graph crosses the "x-axis" when "x = 0" .

→ So; we set plug in "0" for "x" into our equation; and solve for "y" ;

 → " y = (x − 8) (x + 3) " ;

 → y = (0 − 8) (0 + 3) ;

 → y = (-8) * (3) ;

 → y = - 24 ;
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So, the "y -intercept" of the given quadratic function is:

the point at which: "x = 0 ; y = -24 " ;

→ that is; the point the coordinates: " (0, - 24) " ;
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→ which is: Answer choice: [C]: " (0, - 24) " .
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9 0

3 years ago

Read 2 more answers

Chau's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Chau $5.50 per pound, and type B

Anettt [7]

84 pounds of Type B coffee is used

Solution:

Let "x" be the pounds of type A coffee

Let "y" be the pounds of type B coffee

Cost per pound of type A = $ 5.50

Cost per pound of Type B = $ 4.20

This month, Chau made 143 pounds of the blend

x + y = 143

x = 143 - y -------- eqn 1

For a total cost of $677.30. Thus we frame a equation as:

pounds of type A coffee x Cost per pound of type A + pounds of type B coffee x Cost per pound of Type B = 677.30

$x \times 5.50 + y \times 4.20 = 677.30\\\\5.5x + 4.2y = 677.30 -------- eqn 2$

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

$5.5(143-y) +4.2y = 677.30\\\\786.5 -5.5y + 4.2y = 677.30\\\\5.5y - 4.2y = 786.5 - 677.30\\\\1.3y = 109.2\\\\Divide\ both\ sides\ by\ 1.3\\\\y = 84$

Thus 84 pounds of Type B coffee is used

8 0

3 years ago

Consider the function f(x)=9-x^2/x^2-4 For which intervals is f(x) positive? Check ALL that apply.

solong [7]

Answer:

a. f (x) < 0 for x ∈ (-∞ ,-3)

b. f (x) > 0 for x ∈ (-3,-2)

c. f (x) < 0 for x ∈ (-2,2)

d. f (x) > 0 for x ∈ (2,3)

e.f (x) < 0 for x ∈ (3,∞)

Step-by-step explanation:

Here, the given function is: $f(x)= \frac{9-x^2}{x^2-4}$

Now, to check for the sign of f(x) at x = k, put the value of x from the given interval.

We get:

a. (-infinity, -3)

put k = -4 from the given interval

We get $f(-4)= \frac{9-(-4)^2}{(-4)^2-4} = \frac{9-16}{16-4} = \frac{-7}{12}$

⇒ f (x) < 0 for x ∈ (-∞ ,-3)

b. (-3, -2)

put k = -2.5 from the given interval

We get $f(-2.5)= \frac{9-(-2.5)^2}{(-2.5)^2-4} = \frac{9-6.25}{6.25-4} = \frac{2.75}{2.25} > 0$

⇒ f (x) > 0 for x ∈ (-3,-2)

c. (-2, 2)

put k = 0 from the given interval

We get $f(0)= \frac{9-(0)^2}{(0)^2-4} = \frac{9}{-4} = -\frac{9}{4} < 0$

⇒ f (x) < 0 for x ∈ (-2,2)

d. (2, 3)

put k =2.5 from the given interval

We get $f(2.5)= \frac{9-(2.5)^2}{(2.5)^2-4} = \frac{9-6.25}{6.25-4} = \frac{2.75}{2.25} > 0$

⇒ f (x) > 0 for x ∈ (2,3)

e. (infinity, 3)

put k = 4 from the given interval

We get $f(4)= \frac{9-(4)^2}{(4)^2-4} = \frac{9-16}{16-4} = \frac{-7}{12}$

⇒ f (x) < 0 for x ∈ (3,∞)

7 0

4 years ago

20 + 30 x 0 + 1 = what ?

natta225 [31]

21 is the real answer
because of BODMAS

6 0

3 years ago

Read 2 more answers

A cube with 3-inch edges is to be constructed from 27 smaller cubes with 1-inch edges. Twenty-one of the cubes are colored red a

Diano4ka-milaya [45]

The volume of the larger cube is 3*3*3, which is 27.
The volume of the smaller cubes is 1*1*1, which is 1.
27/1=27
That means all cubes will be used, so only the placement of the cubes matter.
The center of the cube will show no sides,
The center of the face will show 1 side, which has a surface area of 1sq.in.
Since there are 6 white cubes and 6 faces with 6 face centers, and only one cube center, there will be 5 cubes on the center of the faces and 1 in the cube center.

This means there will be 0 faces of 1 cube and 1 faces shown for the rest of the cubes. Since each face is 1sq.un., the rest is math

(0*1)+((1*1)5)
(0)+(1*5)
0+5
5sq.un. of the cube is white.

a=The fraction of surface area showing
b=Surface area of large cube

b=3*3*number of sides on cube(6)

5*a=b
5*a=54
a=54/5

Your answer is 54/5.

5 0

3 years ago