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1 year ago

F(x) = - 3x + 4; g(x) = f(x) + 1 Graph it and then describe the graph

Mathematics

1 answer:

inna [77]1 year ago

3 0

The graph of function f(x) and g(x) is parallel lines separated by 1 unit.

In this question we have been given two functions f(x) = - 3x + 4 and g(x) = f(x) + 1

We need to graph these functions and then describe the graph.

The graph of given functions is as shown below.

The graph of function f(x) is a straight line with slope -3 and y-intercept 4.

The function g(x) is nothing but but function f(x) translated upward by 1 unit.

The graph of function g(x) is also a straight line with slope -3 and y-intercept 5.

Therefore, the graph of function f(x) and g(x) is parallel lines separated by 1 unit.

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WORTH 20 POINTS HELP

vfiekz [6]

Below represents the proof that the quadrilateral QRST is a parallelogram

<h3>How to prove that QRST is a parallelogram?</h3>

The coordinates are given as:

Q = (-1,-1)

R = (2,9)

S = (-4,5)

T = (-7,-5)

Calculate the length of each side using:

$d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

So, we have:

$QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}$

$RS = \sqrt{(-4 - 2)^2 + (5 - 9)^2} = \sqrt{52}$

$ST = \sqrt{(-7 + 4)^2 + (-5 - 5)^2} = \sqrt{109}$

$TQ = \sqrt{(-7 + 1)^2 + (-5 + 1)^2} = \sqrt{52}$

The above computations show that opposite sides are equal.

Next, we determine the slope of each side using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$QR = \frac{9 + 1}{2 + 3} = \frac{10}3$

$RS = \frac{5-9}{-4 - 2} = \frac{2}3$

$ST = \frac{5+5}{-4 + 7} = \frac{10}3$

$TQ = \frac{-5+1}{-7 + 1} = \frac{2}3$

The above computations show that opposite sides are parallel, because they have equal slope

Hence, the quadrilateral QRST is a parallelogram

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6 0

2 years ago

PLEASE HELP ME WITH THIS QUESTION!!!!!!

mr Goodwill [35]

From the table, y varies directly as x. Therefore, the constant of variation is k = 2 and y = 2x.

<h3>How to find a direct variation?</h3>

For direct variation,

y ∝ x

Therefore,

y = kx

where

k = constant of proportionality

Hence,

(-2, -4)

-4 = -2k

k = -4 / -2

k = 2

(-4, -8)

y = -4(2) = -8

Therefore,

k = 2 and y = 2x

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5 0

1 year ago

(a) Use the fundamental theorem of algebra to determine the number of roots for 2x^2 + 4x + 7

zysi [14]

Answer:

Step-by-step explanation:

A 2nd order polynomial such as this one will have 2 roots; a 3rd order polynomial 3 roots, and so on.

The quadratic formula is one of the faster ways (in this situation, at least) in which to find the roots. From 2x^2 + 4x + 7 we get a = 2, b = 4 and c = 7.

Then the discriminant is b^2 - 4ac, or, here, 4^2 - 4(2)(7), or -40. Because the discriminant is negative, we know that the roots will be complex and unequal.

Using the quadratic formula:

-4 ±√[-40] -4 ± 2i√10

x = ------------------ = ------------------

4 4

-2 ± i√10

Thus, the roots are x = ------------------

4 0

2 years ago

In the diagram below of regular pentagon ABCDE,<br> EB is drawn.<br><br> What is the measure of AEB?

Drupady [299]

Answer:

36°

Step-by-step explanation:

< EAB = 180 - (360/5) = 180-72=108°

so, < AEB = (180-108)/2 = 72/2 = 36°

6 0

2 years ago

Express the recurring decimal 0.042 as a fraction in its simplest form.

rodikova [14]

Answer:

7/165

Step-by-step explanation:

This is a mixed recurring decimal (the zero is not repeating)

We take number after the decimal point 042

then we subtract the non repeating.In this case is 0 so we not subtract anything

This will be the numerator 42

Now ,the denominator:

For each repeating decimal we write a 9 (in this case 2 nines)

For each non repeating decimal we write a zero

Denominator is 990

42/990 = 7/165

7:165 = 0.0424242......

5 0

3 years ago