I need quick help plzzzzzzzzzzzzz

Given g(x) = x2 - 4x + 7 , find g (3)<br><br>a) 4<br>b) 9 <br>c) 12 <br>d) 1

galina1969 [7]

D plug 3 in for every x

5 0

2 years ago

Read 2 more answers

Which is a solution of x2 – x – StartFraction 3 Over 4 EndFraction = 0?

Anna [14]

Answer:

x = - $\frac{1}{2}$ , x = $\frac{3}{2}$

Step-by-step explanation:

Given

x² - x - $\frac{3}{4}$ = 0 ( add $\frac{3}{4}$ to both sides )

x² - x = $\frac{3}{4}$

Solve using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2( - $\frac{1}{2}$ )x + $\frac{1}{4}$ = $\frac{3}{4}$ + $\frac{1}{4}$

(x - $\frac{1}{2}$ )² = 1 ( take the square root of both sides )

x - $\frac{1}{2}$ = ± 1 ( add $\frac{1}{2}$ to both sides )

x = $\frac{1}{2}$ ± 1

Thus

x = $\frac{1}{2}$ - 1 = - $\frac{1}{2}$

x = $\frac{1}{2}$ + 1 = $\frac{3}{2}$

4 0

3 years ago

Read 2 more answers

The set of life spans of an appliance is normally distributed with a mean Mu = 48 months and a standard deviation Sigma = 8 mont

natita [175]

To solve the problem we must know about Z-Score.

<h3>What is Z-score?</h3>

A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,

$Z = \dfrac{X- \mu}{\sigma}$

Where Z is the Z-score,

X is the data point,

μ is the mean and σ is the standard variable.

The life span of an appliance that has a z-score of –3 is 24 months.

Given to us

Mean, μ = 48 months,
standard deviation, σ = 8 months,
Z-Score = -3

<h3> What is the life span of an appliance?</h3>

The life span of the appliance can be calculated using the Z-score formula,

$Z = \dfrac{X- \mu}{\sigma}$

Substitute the values,

$-3 = \dfrac{X- 48}{8}\\\\-3 \times 8 = X - 48\\\\-24+48=X\\\\X = 24\ months$

Hence, the life span of an appliance that has a z-score of –3 is 24 months.

Learn more about Z-score:

brainly.com/question/13299273

6 0

2 years ago

Find the equation of the lines, that is parallel to the line 9x-8y=1, and tangent to the elipses 9x^2+16y^2=52.

lara31 [8.8K]

Answer:

The equations of the lines that satisfy these conditions are

y = (9/8)x + (13/4)

And

y = (9/8)x - (13/4)

They can be written further as

8y = 9x + 26

and

8y = 9x - 26

Step-by-step explanation:

The line parallel to the line 9x - 8y = 1 has the same slope as 9x - 8y = 1

Writing the equation of the line in the (y = mx + c) form

8y = 9x - 1

y = (9/8)x - 1

So, the line(s) we are looking for has/have slope(s) of (9/8).

Its equation is then

y = (9/8)x + k

This line is then said to be tangent to the ellipses

9x² + 16y² = 52

So, since the line is a tangent to the ellipses, it will have the same coordinates as the ellipses at the point of contact.

9x² + 16y² = 52

y = (9/8)x + k

y² = (81/64)x² + (18k/8)x + k²

y² = (81/64)x² + (9k/4)x + k²

Substituting this into the ellipses equation,

9x² + 16y² = 52

9x² + 16[(81/64)x² + (9k/4)x + k²] = 52

9x² + (81/4)x² + 36kx + 16k² = 52

29.25x² + 36kx + 16k² - 52 = 0

Taking note that the two lines that will be tangent to the ellipses and parallel to the line given, to establish tangency, we make the discriminant of this equation 0. Hence, the roots of that equation will have equal roots.

So, the discriminant, b² - 4ac = 0

29.25x² + 36kx + 16k² - 52 = 0

a = 29.25

b = 36k

c = 16k² - 52

(36k)² - (4)×(29.25)×(16k² - 52) = 0

1296k² - 1872k² + 6084 = 0

576k² = 6084

k = ±(13/4)

So, the equation(s) of the line(s) required is

y = (9/8)x ± (13/4)

So, the equations include

y = (9/8)x + (13/4)

And

y = (9/8)x - (13/4)

Multiplying by 8, we obtain

8y = 9x + 26

8y = 9x - 26

Hope this Helps!!!

6 0

3 years ago

If triangle CDE is dilated by a scale factor of 1/5 with a center of dilation at vertex E, what is the area of triangle C'D'E'?

timurjin [86]

The correct answer would be Choice B: 4 square units.

When the scale factor is 1/5, that means the lengths of the sides are 1/5 of the original size. So instead of having a base of 20 and height of 10, the new triangle has a base of 4 and a height of 2.

The area of the triangle is: (4 x 2) / 2 = 4

8 0

3 years ago

Read 2 more answers