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GenaCL600 [577]

3 years ago

8

Does this table represent a linear function?

1 answer:

IRINA_888 [86]3 years ago

5 0

I think yes because the number are not all the same

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Let f(x)= x^2-4x-c. Find a nonzero value of c such that f(c)=c.

Dimas [21]

Answer:

The nonzero value of c will be:

$c = 6$

Step-by-step explanation:

Given the function

$f\left(x\right)=\:x^2-4x-c$

$f\left(c\right)=\:c^2-4c-c$

as

$f(c) = c$

so

$c=\:c^2-4c-c$

switching the sides

$c^2-4c-c=c$

subtract c from both sides

$c^2-4c-c-c=c-c$

$c^2-6c=0$

$c\left(c-6\right)=0$

Using the zero factor principle

$\:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)$

$c=0\quad \mathrm{or}\quad \:c-6=0$

so, the solutions to the quadratic equations are:

$c=0,\:c=6$

Therefore, a nonzero value of c will be:

$c = 6$

5 0

3 years ago

What is the equivalent to 28/42

grigory [225]

2/3, since those numbers can be divided by 14.

5 0

3 years ago

Find f(-2) when f(t) = -2t + 3<br><br> A) -7 <br> B) -1 <br> C) 1 <br> D) 7

Lady bird [3.3K]

Answer: -1

Step-by-step explanation:

f(t) = -2t + 3

f(-2) = -2 x -2 + 3 [ substituting the value]

f(-2) = -4 + 3

f(-2) = -1

5 0

3 years ago

What two rational expressions sum to 3x+4/x^2-6x+5?

Lubov Fominskaja [6]

Answer:

$\frac{3x+4}{x^2-6x+5}=\frac{-7}{4(x-1)} +\frac{19}{4(x-5)}$

Step-by-step explanation:

The given rational expression is:

$\frac{3x+4}{x^{2}-6x+5} = \frac{3x+4}{(x-1)(x-5)}$

We can use concept of Partial Fractions to solve this problem. Let,

$\frac{3x+4}{(x-1)(x-5)}=\frac{A}{x-1} +\frac{B}{x-5}$

Multiplying both sides by (x - 1)(x - 5), we get:

$3x+4=A(x-5)+B(x-1)$

Substituting x = 5, we get:

$3(5)+4=A(5-5)+B(5-1)\\\\ 15+4=0+4B\\\\ 19=4B\\\\ B=\frac{19}{4}$

Substituting x = 1, we get:

$3(1)+4=A(1-5)+B(1-1)\\\\ 7=-4A\\\\ A=-\frac{7}{4}$

Substituting the value of A and B, back in the original equation, we get:

$\frac{3x+4}{x^2-6x+5}=\frac{-7}{4(x-1)} +\frac{19}{4(x-5)}$

4 0

3 years ago

Given the graph, find the distance of GH. Round to the nearest tenth.

lord [1]

Answer:

GH = 6.3 units

Step-by-step explanation:

Assuming that 1 box represents 1 unit, the coordinate pair of G = (-2, -3), while H = (0, 3).

Distance between G and H = $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let,

$G(-2, -3) = (x_1, y_1)$

$H(0, 3) = (x_2, y_2)$

$GH = \sqrt{(0 - (-2))^2 + (3 - (-3))^2}$

$GH = \sqrt{(2)^2 + (6)^2}$

$GH = \sqrt{4 + 36} = \sqrt{40}$

$GH = 6.3 units$ (nearest tenth)

5 0

3 years ago