When 12 is subtracted from 3 times a number, the result is 24. Find the number.

In which direction must the graph of Rx) = 7% be shifted to produce the graph of g(x) = 7% + 7?

joja [24]

Answer:

B. Up

Step-by-step explanation:

If you alter a function by adding or subtracting a constant to the end of the expression, then the graph will slide up (down if subtracting) If you alter the x value by altering the expression in close to the x with addition or subtraction the graph will slide left or right.

Vertical translations (sliding up or down) go up when adding and down when subtracting as you would expect it to.

Horizontal translations are the oppoof what you might expect. A (x-h) will shift the graph right, while a (x+k) will shift the graph left.

The answer to your question is UP.

5 0

2 years ago

The length of a rectangle is (x + 1) cm and its width is 5cm less than its length.

NeX [460]

Answer:

a) the area of a square is in terms of x is

$(x+1)^2$ centimeter square

b)The length of the rectangle is l = (x+1)

l = 7+1 =8 cm

The width of the rectangle is w = [(x+1)-5]

w = (7+1)-5 =3 cm

Step-by-step explanation:

a) the area of a square is in terms of x is

area of square is $l^{2} = (x+1)(x+1)$

= $(x+1)^2$

b) Given length is l = (x+1) cm and

the width is 5 cm less than its length.

so we have take width is w = (x+1)-5 cm

Given area of triangle is 24 cm

Area of rectangle = length X width

24 = (x+1)(x+1 -5 )

now simplification $24 = (x+1)^2 - 5 (x+1)$

apply (a+b)^2 = a^2+2 a b+b^2

$x^2+2 x+1-5 x-5 =24$

$x^2 -3 x -4-24=0$

$x^{2} -3 x -28 =0$

now find factors of 28 = 7 X 4 is

$x^{2} -7 x+4 x-28=0$

$x(x-7)+4(x-7)=0$

$(x+4)(x-7)=0$

x = -4 and x=7

there fore you have to choose x = 7

The length of the rectangle is l = (x+1)

l = 7+1 =8

The width of the rectangle is w = [(x+1)-5]

w = (7+1)-5 = 3

<u>Verification:-</u>

Given area of rectangle = 24 = 8 X 3

24 =24

so we can not choose x=-4

we have to choose x =7 only

7 0

3 years ago

2. What is the domain of the following graph?

Gnoma [55]

Answer:

Step-by-step explanation:

The domain of this relation (not a function) is x = -5. The relation is not defined for any other x value.

7 0

3 years ago

Read 2 more answers

What is 9 times 3+5times 2

irina1246 [14]

The answer is 64 .............

3 0

3 years ago

Read 2 more answers

A large stand of fir trees occupies 24 hectares. The trees have an average density of 1 tree per 20m squared. A forester estimat

Leona [35]

Answer:

The yield of the stand if one-tenth of the trees are cut is 360000 board-feet.

Step-by-step explanation:

First, let is find the total amount of fir trees that occupies the area of 24 hectares. (1 hectare = 10000 square meters)

$n = \sigma \cdot A$

Where:

$\sigma$ - Surface density, measured in trees per square meter.

$A$ - Total area, measured in square meters.

Given that $\sigma = \frac{1}{20}\,\frac{tree}{m^{2}}$ and $A = 24\,h$ , the total amount of fir trees is:

$n = \left(\frac{1}{20}\,\frac{trees}{m^{2}} \right)\cdot (24\,h)\cdot \left(10000\,\frac{m^{2}}{h} \right)$

$n = 12000\,trees$

It is known that one-tenth of the tress are cut, whose amount is:

$n_{c} = 0.1 \cdot n$

$n_{c} = 0.1 \cdot (12000\,trees)$

$n_{c} = 1200\,trees$

If each tree will yield 300 board-feet, then the yield related to the trees that are cut is:

$y = S\cdot n_{c}$

Where:

$S$ - Yield of the tress, measured in board-feet per tree.

$n_{c}$ - Amount of trees that will be cut, measured in trees.

If $n_{c} = 1200\,trees$ and $S = 300\,\frac{b-ft}{tree}$ , then:

$y = \left(300\,\frac{b-ft}{tree} \right)\cdot (1200\,trees)$

$y = 360000\,b-ft$

The yield of the stand if one-tenth of the trees are cut is 360000 board-feet.

8 0

3 years ago