Given f (x) = x2 + 7, evaluate f (4).

Mathematics

2 answers:

Blizzard [7]3 years ago

8 0

Answer:

f(4) = 23

Step-by-step explanation:

$f(x) = x^2 + 7$

Plug x = 4

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

$f(4) = 16 + 7$

$f(4) = 23$

trapecia [35]3 years ago

3 0

Answer: f(4) = 23

Step-by-step explanation: Notice that f is a function of x.

So we want to find f(4).

We find f(4) by plugging 4 in for x, everywhere that x appears in the function.

So we have f(4) = (4)² + 7.

(4)² is 16 so we have 16 + 7 which is 23.

So f(4) is 23.

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svetlana [45]

Factor the following:
4 p (4 p - 1) - 3 (4 p - 1)^2

Factor 4 p - 1 from 4 p (4 p - 1) - 3 (4 p - 1)^2:
(4 p - 1) (4 p - 3 (4 p - 1))

-3 (4 p - 1) = 3 - 12 p:
(4 p - 1) (4 p + 3 - 12 p)

Grouping like terms, 4 p - 12 p + 3 = 3 + (4 p - 12 p):
(4 p - 1) (3 + (4 p - 12 p))
4 p - 12 p = -8 p:

Answer: (4 p - 1) (-8 p + 3)

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Factor the following:
m (m + n) - 3 m (m + n)^2

Factor m + n out of m (m + n) - 3 m (m + n)^2, resulting in (m + n) (m - 3 m (m + n)^(2 - 1)):
(m + n) (m - 3 m (m + n)^(2 - 1))

2 - 1 = 1:
(m + n) (m - 3 m (m + n))

Factor m out of m - 3 m (m + n), resulting in m (1 - 3 (m + n)):
m (1 - 3 (m + n)) (m + n)

-3 (m + n) = -3 m - 3 n:
Answer: m (m + n) (-3 m - 3 n + 1)

___________________________________________________________Answer : -(-6 + p^2) (-1 - 6 q + p^2 q)

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Factor the following:
6 u^2 (2 u - 5)^2 - 12 u^2 (2 u - 5) (u + 5)

Factor u^2 out of 6 u^2 (2 u - 5)^2 - 12 u^2 (2 u - 5) (u + 5), resulting in u^2 (6 (2 u - 5)^2 - 12 (2 u - 5) (u + 5)):
u^2 (6 (2 u - 5)^2 - 12 (2 u - 5) (u + 5))

(2 u - 5) (2 u - 5) = (2 u) (2 u) + (2 u) (-5) + (-5) (2 u) + (-5) (-5) = 4 u^2 - 10 u - 10 u + 25 = 4 u^2 - 20 u + 25:
u^2 (6 4 u^2 - 20 u + 25 - 12 (2 u - 5) (u + 5))

6 (4 u^2 - 20 u + 25) = 24 u^2 - 120 u + 150:
u^2 (24 u^2 - 120 u + 150 - 12 (2 u - 5) (u + 5))

(u + 5) (2 u - 5) = (u) (2 u) + (u) (-5) + (5) (2 u) + (5) (-5) = 2 u^2 - 5 u + 10 u - 25 = 2 u^2 + 5 u - 25:u^2 (150 - 120 u + 24 u^2 - 122 u^2 + 5 u - 25)

-12 (2 u^2 + 5 u - 25) = -24 u^2 - 60 u + 300:
u^2 (-24 u^2 - 60 u + 300 + 24 u^2 - 120 u + 150)

Grouping like terms, 24 u^2 - 24 u^2 - 60 u - 120 u + 150 + 300 = (-120 u - 60 u) + (24 u^2 - 24 u^2) + (150 + 300):
u^2 ((-120 u - 60 u) + (24 u^2 - 24 u^2) + (150 + 300))

-120 u - 60 u = -180 u:
u^2 (-180 u + (24 u^2 - 24 u^2) + (150 + 300))
150 + 300 = 450:
u^2 (-180 u + (24 u^2 - 24 u^2) + 450)

24 u^2 - 24 u^2 = 0:
u^2 (450 - 180 u)

Factor 90 out of 450 - 180 u:
Answer: u^2×90 (5 - 2 u)

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5 0

3 years ago

Find the slope of the line that goes through the given points (8,5) (6,7)

vazorg [7]

To find the slope of a line that goes through given points with known coordinates, you divide the subtraction of the y of the second point minus the y of the first point, by the subtraction of the x of the second point minus the x of the first point:
m = (yB-yA) / (xB-xA)

Let A(8,5) and B(6,7).
With yB = 7; yA = 5; xB = 6; xA = 8
m = (7-5) / (6-8)
m = 2/-2
m = -1

So the slope of the line that goes through the given points (8,5) and (6,7) is m = -1.

I've added a pic of the line with both points under the answer.

Hope this Helps! :)