MATHEMATICS HIGH SCHOOL

Is (x +1) a factor of f(x) = x^3 + x^2 −4x − 4? Select the appropriate response:
Yes
or
No

Answers

Answer 1

Answer:

Answer:

Yes

Step-by-step explanation:

f(x) = x^3 + x^2 −4x − 4

Factor by grouping taking x^2 out of the first group and -4 out of the second

0 = x^3 + x^2 −4x − 4

x^2(x+1) -4(x+1)

Factor out (x+1)

0=(x+1)(x^2-4)

Now we have the difference of squares

0=(x+1) (x-2)(x+2)

x+1 is a factor

Answer 2

Answer:

Answer:

Yes

Step-by-step explanation:

( x^3 + x^2) (-4x - 4)

x^2 ( x+1) -4 (x+1)

(x^2 - 4) (x+1)

(x-2) (x+2) (x+1)

X= 2 x=-2 x=-1

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5 over 8 divided by 3 over 10 in simplest form
Simplify the expression.-50 + 3r + 50 - 3r
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A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. the total area of the flower garden is 150 square yards. what will the length of each base be
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The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the function? A. Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.

B. Locate the ordered pair (0, –6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.

C.Locate the ordered pair (–6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.

D.Locate the ordered pair (–6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.

Answers

A because (0,-6) is the y-intercept so you start at the point you know. Then because slope is a rise over run fraction the slope can also be written as 2/1 which is rise 2 over 1.

Answer:

A is the correct option.

Step-by-step explanation:

The slope of the line is 2 and the y-intercept is -6.

y-intercept is the point where x is zero. Hence, the point is (0,-6)

When we graph a linear function by slope-intercept method, first of all we plot the y-intercept.

Hence, first of all we plot the point (0,-6)

Now, slope is given by

$\text{slope}=(rise)/(run)$

if rise is positive then we move up from the y -intercept and if negative then move down. We keep run always positive and hence we move right from the rise point.

$\text{slope}=2=(rise)/(run)$

rise = 2

run = 1

Rise is positive hence, we move 2 units up from the point (0,-6) and then move 1 unit right to get the next point. Then we draw a line passing through these points.

A is the correct option.

The ratio of the number of boys to the number of girls in a school is 5:7.If there are 600 students in the school,how many girls are there?

Answers

So,

The secret to solving problems with ratios is to find the value of one unit.

5:7 = 12 units total

To find one unit, divide the total number of students by the total number of units.
600/12 = a

Simplify
50/1 = a
50 = a

The value of each unit is 50.

Now, multiply the units by the numbers in the ratio.
50(5) = b
250 = boys

50(7) = x
350 = x

There are 350 girls.

$5x- number\ of\ boys\n7x-\ number\ of\ girls\n\n5x+7x=600\n12x=600\ \ \ \ | divide\ by\ 12\nx=50\n\n5x=250\n7x=350\n\nThere\ are\ 250\ boys\ and\ 350\ girls.$

What is the mean of the following data values?22, 37, 49, 15, 72

A. 49
B. 39
C. 37
D. 47

Answers

If you add them all together and divide by 5, then the answer is B (39) :)

use the counting principle to find the probability of choosing the 8 winning lottery numbers when the numbers are chosen at random from 0 to 9

Answers

Answer: $1/10^8$

Step-by-step explanation:

Here the total numbers are 10 ( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

Since, the probability of choosing one number = $(1)/(10)$

Therefore, the probability of choosing 8 numbers =

$(1)/(10)*(1)/(10)* (1)/(10)* (1)/(10)* (1)/(10)* (1)/(10)* (1)/(10)* (1)/(10)*$ ( because there is no replacement)

= $(1)/(10^8)$

The total feasible numbers are: 10*10*10*10*10*10*10*10 = 10^8

The probability is 1/10^8

The yard behind the Cindy’s house is rectangular in shape and has a perimeter of 72 feet. If the length l of the yard is 18 feet longer than the width w of the yard, what is the area of the yard, in square feet?

Answers

let
L----------> the length of the yard
W--------> the width l of the yard

we know that
the perimeter is equal to
$P=2*[W+L]$
$72=2*[W+L] \n 36=W+L$ --------> equation 1
$L=W+18$ ------> equation 2
substitute equation 2 in equation 1
$36=W+18+W \n 36=2W+18 \n W=(36-18)/2$
$W=9 ft$
$L=W+18 \n L=9+18 \n L=27 ft$

we know that
Area of the rectangular yard is equal to
$A=L*W \n A=27*9 \n A=243 ft^(2)$

Answer:

$2187\text{ ft}^2$

Step-by-step explanation:

Let l be the length and w be the width of yard behind Cindy's house.

We have been given that the length of the yard is 18 feet longer than the width of the yard. We can represent this information in an equation as:

$l=w+18...(1)$

We have been also given that the perimeter of the yard is 72 feet. Since perimeter of a rectangle is 2 times the sum of its length and width, so we can represent this information in an equation as:

$2(l+w)=72...(2)$