Is 4,5, or 6 the solution of the equation c + 8 = 13?

What is the equation of the line that is perpendicular to y = -2/3x + 4 and that passes through (–2,–2)?

Rama09 [41]

Answer: y = 3/2x + 1

Step-by-step explanation: For a perpendicular line, take the reciprocal of "m" and reverse the sign.

- 2/3 becomes +3/2

Then substitute the y and x values of the given coordinate into the equation and solve for "b"

y = mx + b

-2 = 3/2(-2) + b

-2 = -3 + b

-2 +3 = b

+1 = b Substitute for b in y = (3/2)x + 1

6 0

3 years ago

F(x) = x^2. What is g(x)

Alexeev081 [22]

Answer:

g(x) = - x² - 4 ⇒ A

Step-by-step explanation:

Let us revise the reflection and translation of a function

If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)

If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)

If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)

If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k

If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k

f(x) = x² is the blue curve

g(x) is its image is the red curve

∵ g(x) is the image of f(x)

∵ f(x) is opened upward

∵ g(x) is opened downward

→ That means the sign of y-coordinates of all points on the blue

graph are opposite

∴ f(x) is reflected about the x-axis

∴ Its image is - f(x)

∵ The vertex of f(x) is (0, 0)

∵ The vertex of g(x) = (0, -4)

→ That means the function translated 4 units down

∴ - f(x) is translated 4 units down

∴ Its image is - f(x) - 4

∴ g(x) = - f(x) - 4

∵ f(x) = x²

∴ g(x) = - x² - 4

4 0

3 years ago

Find the value of x in the equation x⁄ 4 + x⁄14 + x⁄17 = 71

Morgarella [4.7K]

Hello from MrBillDoesMath!

Answer:

33769/181

Discussion:

Each term contains "x" so factoring it out gives

x( 1/4 + 1/14 + 1/17) = 71 (*)

Use common factor (17*14*4 = 952) as the denominator to combine terms:

1/4 = (17*14)/ 952 = 238/952

1/14 = (17*4)/952 = 68/952

1/17 = (14*4)/952 = 56/952

so 1/4 + 1/14 + 1/17 = (238 + 68 + 56)/ 952 = 362/952 = 181/476

Substituting in (*) gives

x ( 181/476) = 71 => multiply both sides by 476/181

x = (71 * 476)/181 => 71* 476 =33769

x = 33769/181

Thank you,

MrB

4 0

3 years ago

The function f(x)=/-x is shown on the graph

Katyanochek1 [597]

we know that

For the function shown on the graph

The domain is the interval--------> (-∞,0]

$x\leq0$

All real numbers less than or equal to zero

The range is the interval--------> [0,∞)

$y\geq 0$

All real numbers greater than or equal to zero

so

Statements

case A) The range of the graph is all real numbers less than or equal to $0$

The statement is False

Because the range is all numbers greater than or equal to zero

case B) The domain of the graph is all real numbers less than or equal to $0$

The statement is True

See the procedure

case C) The domain and range of the graph are the same

The statement is False

Because the domain is all real numbers less than or equal to zero and the range is is all numbers greater than or equal to zero

case D) The range of the graph is all real numbers

The statement is False

Because the range is all numbers greater than or equal to zero

therefore

the answer is

The domain of the graph is all real numbers less than or equal to $0$

8 0

3 years ago

Read 2 more answers

In ΔXYZ, ∠Y=90° and ∠X=73°. ∠ZWY=80° and XW=80. Find the length of ZY to the nearest 100th.

lawyer [7]

Answer:

Solution given:

Y=90°

∠X=73°.

∠ZWY=80°

and XW=80.

ZY=?

We know that

In right angled triangle ∆ XYZ

Tan 73= $\frac{p}{h}$

3.27= $\frac{yz}{xy}$

3.27×[xy]=yz

xw+wy= $\frac{yz}{3.27}$

wy= $\frac{yz}{3.27}$ -80...........(1)

again

In right angled triangle WYZ

Tan 80= $\frac{yz}{wy}$

5.67×wy=yz

wy= $\frac{yz}{5.67}$

yz=5.67×wy............................................(2)

Equating equation 1&2

$\frac{yz}{5.67}$ = $\frac{yz}{3.27}$ -80

$\frac{yz}{3.27}$ - $\frac{yz}{5.67}$ =80

5.67yz-3.27yz=80*5.67*3.27

2.4yz =1483.272

yz= $\frac{1483.272}{2.4}$

yz=618.03

:.y=618.03unit.the length of ZY to the nearest 100th is 618.

8 0

3 years ago