If 3y+5=7x, then 21y-49x=?

Mathematics

1 answer:

FromTheMoon [43]3 years ago

3 0

3y+5=7x

3y=7x-5

y=(7x-5)/3

...

21y-49x becomes

7(7x-5)-49x

49x-35-49x

-35

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The table represents a quadratic function. Write an equation of the function in standard form.

kakasveta [241]

The equation of the quadratic function in standard form as required in the task content is; f(x) = -x² + 12x - 43.

<h3>Standard form equation of a quadratic function.</h3>

It follows from the task content that the standard form equation of the quadratic function is to.be determined.

Since the standard form equation can be derived from the vertex form equation as follows;

f(x) = a (x - h)² + k

f(x) = a (x - 6)² - 7

Hence, to find the value of a, Substitute x = 8 and f(x) = -11 so that we have;

-11 = a (8 - 6)² - 7

-11 = 4a - 7

4a = -4

a = -1.

Hence, the equation in vertex form is; f(x) = -1 (x -6)² - 7 and when expressed in standard form we have;

f(x) = -1(x² - 12x + 36) - 7

f(x) = -x² + 12x - 43

Therefore, the required equation in standard form is; f(x) = -x² + 12x - 43.

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5 0

1 year ago

7b ÷ 12 = 4.2 what does b =

Luda [366]

7b/12=4.2
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3 0

3 years ago

Read 2 more answers

Marty is taking piano lessons. She is going to practice every afternoon. The 1st week she practiced for 11 minutes each day. The

defon

Answer:

$m=7w+4$

Step-by-step explanation:

<u>Linear Modeling</u>

It consist is setting up a linear relationship between two variables, given some experimental data. Only 2 points are needed to set up the equation of a line, but if more than 2 points are used, then the result should use statistical approaches like linear regression to find the best-fit line.

For the question at hand, Marty practices his piano lessons 11 minutes the week #1. It provides the first point (1,11). He practices 25 minutes per day on the third week. It gives us another point (3,25). This is enough to find the equation of a line. The general formula for a line, having two points (m1,w1) (m2,w2) is

$\displaystyle m-m_1=\frac{m_2-m_1}{w_2-w_1}(w-w_1)$