The points on the graph of the function y=3+f(x-1) can be obtained from the points on y=f(x) by a shift of:

I need to know the improper fractions answers for:

zmey [24]

Answer:

Part 1) $x=\frac{15}{2}\ units$

Part 2) $z=\frac{15\sqrt{3}}{2}\ units$

Part 3) $y= \frac{15\sqrt{3}}{4}\ units$

Part 4) $b= \frac{45}{4}\ units$

Step-by-step explanation:

step 1

Find the value of x

In the large right triangle

$cos(60^o)=\frac{x}{15}$ ----> by CAH (adjacent side divided by the hypotenuse)

Remember that

$cos(60^o)=\frac{1}{2}$

substitute

$\frac{1}{2}=\frac{x}{15}$

solve for x

$x=\frac{15}{2}\ units$ ---> improper fraction

step 2

Find the value of z

In the large right triangle

Applying the Pythagorean Theorem

$15^2=x^2+z^2$

substitute the value of x

$15^2=(\frac{15}{2})^2+z^2$

solve for z

$z^2=15^2-(\frac{15}{2})^2$

$z^2=225-\frac{225}{4}$

$z^2=\frac{675}{4}$

$z=\frac{\sqrt{675}}{2}\ units$

simplify

$z=\frac{15\sqrt{3}}{2}\ units$

step 3

Find the value of y

In the right triangle of the right

$sin(30^o)=\frac{y}{z}$ ---> by SOH (opposite side divided by the hypotenuse)

substitute the given values of y and z

Remember that

$sin(30^o)=\frac{1}{2}$

so

$\frac{1}{2}=y:\frac{15\sqrt{3}}{2}$

solve for y

$\frac{1}{2}= \frac{2y}{15\sqrt{3}}$

$y= \frac{15\sqrt{3}}{4}\ units$

step 4

Find the value of b

In the right triangle of the right

$cos(30^o)=\frac{b}{z}$ ---> by CAH (adjacent side divided by the hypotenuse)

substitute the given values of y and z

Remember that

$cos(30^o)=\frac{\sqrt{3}}{2}$

so

$\frac{\sqrt{3}}{2}=b:\frac{15\sqrt{3}}{2}$

solve for y

$\frac{\sqrt{3}}{2}= \frac{2b}{15\sqrt{3}}$

$b= \frac{45}{4}\ units$

7 0

3 years ago

A cube has an edge measuring 4 inches. What is the surface area of the cube, in inches²?

BlackZzzverrR [31]

Answer: 96 in2

Step-by-step explanation: This is because u have to mutiple the two bases and the lateral sides to get your area

4 0

3 years ago

Find the volume of a sphere that has a diameter of 11 feet.

Softa [21]

Solution:

Diameter=11ft

Therefore radius=5.5 ft(Since radius=Diameter/2)

Volume of sphere=4/3py r^3

= 4/3.22/7.5.5^3

=697.19 Cubic feet.

Therefore the volume of sphere is 697.19 cubic feet.This is your required solution.

5 0

3 years ago

Can someone please help me I’ll upvote PLEASE

masha68 [24]

So two lines that are parallel will have the same slope, and to calculate the slope you have to use the formula $\frac{y_2-y_1}{x_2-x_1}$

CD: $\frac{10-2}{4-6} =\frac{8}{-2} =-4$ .

JK: $\frac{3-2}{12-8} =\frac{1}{4}$

EF: $\frac{5-9}{2-1} =\frac{-4}{1} =-4$

GH: $\frac{4-0}{1-1} =\frac{4}{0}$ (undefined)

In short, Lines CD and EF are parallel.

5 0

3 years ago

Read 2 more answers

Factor completely. x^2+4x-12

STatiana [176]

Answer:

(x + 6)(x - 2)

Step-by-step explanation:

To factor the quadratic

Consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term ( + 4)

The factors are + 6 and - 2 since

+ 6 × - 2 = - 12 and + 6 - 2 = + 4, hence

x² + 4x - 12 = (x + 6)(x - 2)

8 0

3 years ago