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4 years ago

10

Find the inverse of f(x)=2x^2+5

1 answer:

irina1246 [14]4 years ago

5 0

F^-1(x) = sqrt 2(-5+x)/2, - sqrt 2(-5+x)/2

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Find the equation of the line through point (5,1) and perpendicular to 5x−y=−3. Use a forward slash (i.e. "/") for fractions (e.

IRINA_888 [86]

Y = -1/5x + 2

A line perpendicular to another line has an opposite reciprocal slope. What opposite means is that you flip the sign (from - to + or from + to -) and reciprocal means that you flip the numerator and denominator (so if line A is perpendicular to line B and line As slope is -3, line Bs slope would be 1/3).

First find the slope of 5x - y = -3
Add y to both sides
5x = y - 3
Add 3 to both sides
y = 5x + 3

So the slope of the line is 5. That means the slope of of the perpendicular line is -1/5.

Plug the slope of the perpendicular line and the point (5, 1) into point slope form to solve the equation

y - y1 = m(x - x1)
y - 1 = -1/5(x - 5)
y - 1 = -1/5x + 1
y = -1/5x + 2

3 0

3 years ago

Select the correct answer.

EleoNora [17]

Answer:

Option (B)

Step-by-step explanation:

There are two lines on the graph representing the system of equations.

First line passes through two points (-3, 1) and (-2, 3).

Slope of the line = $\frac{y_2-y_1}{x_2-x_1}$

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

m = 2

Equation of the line passing through (x', y') and slope = m is,

y - y' = m(x - x')

Equation of the line passing through (-3, 1) and slope = 2 will be,

y - 1 = 2(x + 3)

y = 2x + 7 ----------(1)

Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.

Let the equation of this line is,

y = mx + b

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

= $\frac{4-1}{-1-0}$

= -3

Here 'b' = 1

Therefore, equation of the line will be,

y = -3x + 1 ---------(2)

From equation (1) and (2),

2x + 7 = -3x + 1

5x = -6

x = $-\frac{6}{5}$

x = $-1\frac{1}{5}$

From equation (1),

y = 2x + 7

y = $-\frac{12}{5}+7$

= $\frac{-12+35}{5}$

= $\frac{23}{5}$

= $4\frac{3}{5}$

Therefore, exact solution of the system of equations is $(-1\frac{1}{5},4\frac{3}{5})$ .

Option (B) will be the answer.

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4 years ago

there are 4 performers who will present their comedy acts this weekend at a comedy club. how many different ways are there to sc

DiKsa [7]

There should be 6 per number
ex.
1234
1243
1342
1324
1432
1423

8 0

3 years ago

Find the mass of the cone using triple beam balance

FromTheMoon [43]

Answer: it’s 542.0 ur welcome

Step-by-step explanation:

4 0

3 years ago

Katy and Jane construct a four-sided wall to surround their castle. The wall has a perimeter of

PilotLPTM [1.2K]

Answer:

The correct length is <em>34 feet</em>.

Step-by-step explanation:

Let us assume that the wall created is a rectangle <em>ABCD</em> as shown in the attached image.

We know that opposite sides of a rectangle are equal.

<em>Perimeter</em> of a <em>closed figure is calculated by adding all the sides of the figure</em>.

Here, from the figure, the perimeter is : AB + BC + CD + DA

AB and CD are equal to length.

BC and DA are equal to width.

So,

$Perimeter = 2 \times (length + width) ....... (1)$

Here, we are given that <em>perimeter </em>is 100 feet and <em>width</em> = 16 feet

Putting values in equation (1):

$100 = 2 \times (16 + length)\\\Rightarrow 50 = 16 + length \\\Rightarrow length = 34 feet$

Hence, length is 34 feet.

5 0

3 years ago