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3 years ago

Given the function f(x) = -2x2 + 4x - 7, find f(-4). -55 -7 25

Mathematics

2 answers:

Neko [114]3 years ago

7 0

Answer:

f(-4)= -55

Step-by-step explanation:

We want to find f(x), or y, when x is equal to -4.

Therefore, we can substitute -4 in for x in the function.

f(x) = -2x^2 + 4x - 7

Substitute -4 in for x

f(-4) = -2(-4^2) + 4(-4) - 7

Evaluate the exponent

f(-4)=-2(16)+4(-4)-7

Multiply -2 and 16

f(-4)= -32+4(-4)-7

Multiply 4 and -4

f(-4)=-32-16-7

Subtract

f(-4)=-55

DaniilM [7]3 years ago

6 0

-2(-4)2+4(-4)-7
16-16-7
-7. -7 is correct

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Lostsunrise [7]

The answer is b . 86

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3 years ago

Suppose that y = k * (x - 1/3) ^ 2 is a parabola in the xy -plane that passes through the point (2/3, 1) :Find k and the length

Dennis_Churaev [7]

Answer:

k = 9

length of chord = 2/3

Step-by-step explanation:

Equation of parabola: $y=k (x-\frac13)^2$

Part 1

If the curve passes through point $(\frac23 ,1)$ , this means that when $x=\dfrac23$ , $y = 1$

Substitute these values into the equation and solve for $k$ :

$\implies 1=k \left(\dfrac23-\dfrac13\right)^2$

$\implies 1=k \left(\dfrac13 \right)^2$

Apply the exponent rule $\left(\dfrac{a}{b} \right)^c=\dfrac{a^c}{b^c}$ :

$\implies 1=k \left(\dfrac{1^2}{3^2} \right)$

$\implies 1=\dfrac{1}{9}k$

$\implies k=9$

Part 2

The chord of a parabola is a line segment whose endpoints are points on the parabola.

We are told that one end of the chord is at $(\frac23 ,1)$ and that the chord is horizontal. Therefore, the y-coordinate of the other end of the chord will also be 1. Substitute y = 1 into the equation for the parabola and solve for x:

$\implies 1=9 \left(x-\dfrac13 \right)^2$

$\implies \dfrac19 = \left(x-\dfrac13 \right)^2$

$\implies \sqrt{\dfrac19} = x-\dfrac13$

$\implies \pm \dfrac13 = x-\dfrac13$

$\implies x=\dfrac23, x=0$

Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)

To calculate the length of the chord, find the difference between the x-coordinates:

$\implies \dfrac23-0=\dfrac23$

**Please see attached diagram for drawn graph. Chord is in red**

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2 years ago

A torch and a battery cost £2.50 altogether. The torch costs £2.00 more than the battery.

Hitman42 [59]

Answer:

1/5

Step-by-step explanation:

To find what fraction of the total price the battery is, we need to find out how much the battery alone is first.

Since the battery and torch together are £2.50 and the torch is £2.00, we can find the price of the battery by subtracting the total price to the price of the torch.

Battery Price = £2.50 - £2.00

Battery Price = £0.50

The fraction value of the torch is:

2.00 of 2.50 = 4/5

That then leaves us with:

0.50 of 2.50 = 1/5

To check we need to add the two fractions together.

1/5 + 4/5 = 5/5 or 1

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Step-by-step explanation:

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