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3 years ago

Function f(x)=2x+1 and g(x)=x^2+1 and f(x)=g(x) then find the value of x

Mathematics

1 answer:

Sever21 [200]3 years ago

4 0

Answer:

x = 0 or x = 2

Step-by-step explanation:

Since f(x) = g(x) then equate the right sides, that is

x² + 1 = 2x + 1 ( subtract 2x + 1 from both sides )

x² - 2x = 0 ← in standard form

x(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x = 0

x - 2 = 0 ⇒ x = 2

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Which table contains ordered pairs that lie on the graph of the equation -2x + 4y = 16?

tia_tia [17]

Answer:

Step-by-step explanation:

To figure out which pairs lie on -2x+4y = 16, we can plug the x and y values into the equation to see if they work. We need all pairs of x and y values in a table to work for the answer to be correct

x=-4, y=2

-2x+4y = -2 * (-4) + 4 * (2) = 8 + 8 = 16. This works. Note that two negatives multiplied together make a positive, and 4*2 = 8

x=0, y=8

-2x + 4y = -2 * (0) + 4 * (8) = 0 + 32 = 32. This does not work, as 32 is not 16. Note that anything multiplied by 0 is 0

x=8, y=0

-2x+4y = -2 * (8) + 4 * (0) = -16. This is not equal to 16. Note that a negative multiplied by a positive is still a negative

x=2, y=3

-2x + 4y = -2 * (2) + 4 * (3) = -4 + 12 = 8. This is not equal to 16.

x=0, y=4

-2x + 4y = -2 * (0) + 4 * (4) = 0 + 16 = 16. This works

x=4, y=6

-2x + 4y = (-2)* (4) + 4 * (6) = -8 + 24 = 16. This works. As both pairs of values in the table works, this is the correct answer. Nevertheless, we can check D to make sure.

x=-2, y=5

-2x+4y = -2 * (-2) + 4 * (5) = 4 + 20 = 24. This is not 16

x=-8, y=0

-2x+4y = -2 * (-8) + 4 * (0) = 16. This works, but the other pair does not work, so D is incorrect

3 0

3 years ago

Quick algebra 1 question for 10 points!

trasher [3.6K]

$m = m \\ \frac{97 - 68}{2 - 1} = \frac{134 - 97}{3 - 2} \\ 29 = 37 \\ this \: function \: is \: non \: linear$

<h3>Since the only two other options are quadratic and given that it must satisfy one of them i will assume the following general form of the function.</h3>

$f(1) = 68 \: \: \: f(2) = 97 \: \: \: \: f(3) = 134 \\ f(x) = ax {}^{2} + bx + c$

<h3>Substitute in the first function any point.</h3>

$f(1) = 68 \\ 7.8(1) {}^{2} - 2.9(1) + 67.1 = 68 \\ 7.8 - 2.9 + 67.1 = 68 \\ 72 = 68 \\ this \: is \: false$

<h3>I'm pretty sure something is wrong with the given</h3>

7 0

2 years ago

Solve for the following equation step by step and justify your steps when using an exponential property.

Flura [38]

(7^x)^4 is equal to 7^(4x).

7^2 * 7^3 is equal to 7^(2+3) which is equal to 7^5.

7^5 / 7^(3x) is equal to 7^(5 - 3x).

you wind up with 7^(4x) is equal to 7^(5 - 3x)

this is true if and only if 4x = 5 - 3x.

8 0

3 years ago

A friend has a 83% average before the final exam for a course. That score includes everything but the final, which counts for 25

Klio2033 [76]

Answer:

$\mathrm{Best\:course\:grade\:possible:\:}87.25\%,\\\mathrm{Minimum\:score\:on\:final\:to\:earn\:at\:least\:a\:75\%\:for\:the\:course:\:}51\%$

Step-by-step explanation:

Assuming the maximum score for the final is $100\%$ , we can multiply each score by its respective course weight and add them together to give a final score. If your friend did receive this maximum score of $100\%$ , their overall grade for the course would be: