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Irina-Kira [14]
3 years ago
11

Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)?

Mathematics
2 answers:
Tomtit [17]3 years ago
7 0

D is the only x-intercept out of the options listed below.



In order to find an x-intercept, you need a value that will cause the y-value to equal 0, since this is where x-intercepts exist.



Automatically, A and B do not work since the y-values in the ordered pairs do not equal 0. By definition they are not x-intercepts. Next we can try the x-values in the equation to see which gives us a 0 y-value.



C


f(x) = (x + 6)(x - 3)


f(6) = (6 + 6)(6 - 3)


f(6) = (12)(3)


f(6) = 36



Since this does not equal 0, it is not an x-intercept.



D


f(x) = (x + 6)(x - 3)


f(-6) = (-6 + 6)(-6 - 3)


f(-6) = (0)(-9)


f(-6) = 0



This shows us that D yields a 0 value for y and is thus a x-intercept.

Veronika [31]3 years ago
6 0

Answer:

d. (–6,0)

Step-by-step explanation:

edge 2020

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MrRissso [65]

Answer:

35

Step-by-step explanation:

Since we know that 7 b is the equation and 5 is the value of b we can substitute b in 7 b.

b = 5

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4 0
3 years ago
The line passing through (-2,5) and (2,p) has a gradient of -1/2. <br><br> Fnd the value of p
makkiz [27]

Given:

The line passing through (-2,5) and (2,p) has a gradient of -\dfrac{1}{2}.

To find:

The value of p.

Solution:

If a line passes through two points, then the slope of the line is:

m=\dfrac{y_2-y_1}{x_2-x_1}

The line passing through (-2,5) and (2,p). So, the slope of the line is:

m=\dfrac{p-5}{2-(-2)}

m=\dfrac{p-5}{2+2}

m=\dfrac{p-5}{4}

It is given that the gradient or slope of the line is -\dfrac{1}{2}.

\dfrac{p-5}{4}=-\dfrac{1}{2}

On cross multiplication, we get

2(p-5)=-4(1)

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2p=-4+10

2p=6

Divide both sides by 2.

p=3

Therefore, the value of p is 3.

4 0
3 years ago
Simplify the expression 4x3 2x3
Fittoniya [83]

Answer:

onc

Step-by-step explanation:

3 0
2 years ago
From a thin piece of cardboard 30 in. by 30 in., square corners are cut out so that the sides can be folded up to make a box. Wh
Brilliant_brown [7]

Answer:

Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

Step-by-step explanation:

Volume =  height x length x width

considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.

square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x

therefore,

V = x  (30-2x) (30-2x) ---> eq(1)

V=( 30x - 2x²) (30-2x)

V= 900x- 60x² - 60x² + 4x³

V=  4x³ - 120 x²+ 900x

Taking derivative w.r.t 'x'

dV/dx = 12x² - 240 x +900

dV/dx = 4 (3x² - 60x +225)

For maximum dV/dx, make it equal zero

dV/dx = 0

so,  4 (3x² - 60x +225)=0

3x² - 60x+225=0   (taking 3 common)

x² - 20x + 75 =0

Solving this quadratic equation

x² - 15x -5x + 75 =0

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Either (x-15)=0

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if we substitute x=15 in eq(1), volume becomes zero.

therefore, x cannot be 15

When x= 5

eq(1)=>V = 5  (30-2(5)) (30-2(5))

V= 5 (10) (10)

V= 500 cubic inches,

Therefore, Dimensions 5in x 10in x 10in will yeild a box with a max. volume of  500 cubic inches

7 0
3 years ago
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myrzilka [38]
The first number will be 500
the second number will be 600
and the last number will be 990

8 0
3 years ago
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