Which is the graph of the function f(x) = x3 – x2 – 17x - 15?

Answer:

Domain : [-4,4} or  [tex]-4\leq x\leq 4[/tex]

Zeros of the function: (-2, 0, 2)

Intervals when function is positive: (0,2)

Intervals where function is negative: (-4,0), (2,4)

Step-by-step explanation:

Domain can be defined as the input of all possible values of x in the given interval. We can se from the graph that minimum value of x is -4 while maximum value of x is 4. So

[tex]-4\leq x\leq 4[/tex]

The value of function becomes 0 at three places, when x becomes -2,0 or 2

We can see that the function is negative throughout the interval (-4,0), then it become positive from (0,2), then it becomes negative again from (2,4)

Answer:

1. 10218

2. 9720

Step-by-step explanation:

1 ---------------

need to find the least 5 -digit number leaving same remainder when divided by 12, 18, 21, 28

Least 5-digit number is 10000, when it is divided by 262, we get

10000/262= 38.17

39*262= 10218, this number leaves 0 remainder when divided by all 4 given numbers, any number leaving more remainder will be greater than this

Answer: 10218

2 -----------------

Greatest 4-digit number exactly divisible by 12, 18, 40, 45

Greatest 4 digit number is 9999

9999/360= 27.78

360*27= 9720 is the greatest number we are looking for

Answer: 9720

Answer:

hope this helps!

Step-by-step explanation:

3x-2.5x+0.5=4.5

We move all terms to the left:

3x-2.5x+0.5-(4.5)=0

We add all the numbers together, and all the variables

0.5x-4=0

We move all terms containing x to the left, all other terms to the right

0.5x=4

x=4/0.5

x=8

Answer:

Green ball. $11

Step-by-step explanation:

Let's see.

15 balls. 7 are red. 6 are green. rest are yellow. That means there are 2 yellow balls.

Since there are more greens than yellows, you have a better chance of getting a green. That means you have a higher chance of getting $11

The total expected value of the game is $2 if you pay $8 to play the following game of chance.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

You pay $8 to play the following game of chance. There is a bag containing 15 balls, 7 are red, 6 are green and the rest are yellow.

Yellow balls = 15 - 7 - 6= 2

Probability of yellow = 2/15

Probability of green = 6/15

Expected value of the game = 6(2/15) + 3(6/15) = $2

Thus, the total expected value of the game is $2 if you pay $8 to play the following game of chance.

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Answer:

[tex]4\sqrt{5}[/tex] miles.

Step-by-step explanation:

From the given figure it is clear that the coordinates of Elm station are (-3,-6) and coordinates of Symphony station are (1,2).

Distance formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula, the distance between Elm and Symphony stations is

[tex]D=\sqrt{(1-(-3))^2+(2-(-6))^2}[/tex]

[tex]D=\sqrt{(1+3)^2+(2+6)^2}[/tex]

[tex]D=\sqrt{(4)^2+(8)^2}[/tex]

[tex]D=\sqrt{16+64}[/tex]

[tex]D=\sqrt{80}[/tex]

[tex]D=4\sqrt{5}[/tex]

Therefore, the distance between Elm and Symphony stations is [tex]4\sqrt{5}[/tex] miles.

Answer:

108

Step-by-step explanation:

6x8 = 48

10x4= 40

5x4= 20

add them up and you get 108

Answer:

the area is 108

Step-by-step explanation:

cut the shape into parts.

6x8=48

10x4=40

5x4=20

48+40+20=108

Answer:

4800 joules

4.8 kilojoules

Step-by-step explanation:

[tex]Work done = Force * distance\\Workdone = (mass*acceleration)*distance\\Note : force = (mass*acceleration) , Acceleration- due- to -gravity =10m/s^2\\W.D = 24 * 10*20\\W.D = 4800 joules\\W.D =4.8Kilo joules[/tex]

Answer:

1. The slope of the line is 7/3

2. y intercept is -3

3. y= 7/3x -3

Step-by-step explanation:

To find the slope of the line you use the equation y2-y1/x2-x1

y2 and y1 are y coordinates of the 2 coordinates on the same line that you want to find the slope of and the same with x2 and x1

The y-intercept is the point where the line crosses the y axis and x= 0

the equation of a line is y= mx+b

m= slope

b= y intercept

Answer:

10 inches

Step-by-step explanation:

The length of the playground in its actual size is 120 feet.

The scale drawing uses a scale of 1 inch to 12 feet.

This means that 1 inch in the drawing equals 12 feet in actual size.

Therefore, the length of the playground on the scale drawing is:

1 inch = 12 feet

x = 120 feet

Cross-multiply:

120 * 1 = 12 * x

=> x = 120 / 12 = 10 inches

The length of a side of the playground on  the scale drawing is 10 inches.

Answer:

Step-by-step explanation

The person drove 128 miles in one hour

I divided 640/5 and got 128 as my answer

Answer:

For every one hour you drive 128 miles.

Step-by-step explanation:

First you would need to find the unit rate.

Divide 640 by 5

[tex]640/5=128[/tex]

Unit rate=

[tex]y=128x[/tex]

Hope this helps

Answer:

19 1/2 inches.

Step-by-step explanation:

edge 2020 OwO

Answer:

19.5 inches a.k.a. 1 foot and 7.5 inches

Step-by-step explanation:

1) To make it easier, convert Sean's dad's height into solely inches.

6 feet and 6 inches = 6(12) + 6 = 72 + 6 = 78 inches

2) Find out what is one-fourth of Sean's dad's height.

In order to do that, you must simply multiply 78 by [tex]\frac{1}{4}[/tex].

[tex]78(\frac{1}{4} ) = 19.5[/tex]

3) Convert back to feet and inches (if necessary)...

19.5 inches = 12 + 7.5 = 1 foot and 7.5 inches

I hope this helps!

Answer:

Not widely used. If you continue to increase an angle it will eventually 'double back' on itself and form a full 360° angle. This is the Full Angle. One could argue that this is the same as a zero-sized angle. But we generally mean the reflex angle and so it is a full circle or 360°. Adjust the angle above and try to create the full angle going around in both directions.

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a binomial probability problem. There are only two outcomes. It is either a chosen person has immunity to a particular disease or he does not. The probability of success in this case, p is the probability that a chosen person has immunity to a particular disease. Thus

p = 0.6

The probability of failure, q is q = 1 - p

Thus, q = 1 - 0.6 = 0.4

Mean = np

Where n represents sample size. Thus,

Mean = 12 × 0.6 = 7.2

Answer:

Length: 84 ft

Width: 56 ft

Step-by-step explanation:

Let's define some variables first.

Call the length l and width w.

We know that w = 2/3l. Therefore, we can express w in terms of l with this expression.

Now, let's set up an equation. The flower garden is rectangular, and 280 feet of fencing are used to enclose the garden. This represents perimeter.

Remember the formula for perimeter of a rectangle: 2l + 2w

Let's substitute 2/3l for w:

2l + 2*2/3l = P

2l + 4/3l = 280

2 4/3l = 280

10/3l = 280

l = 84

Now, we know that the length is equal to 84 feet. We can multiply 84 feet by 2/3 to find the width.

84*2/3 = 56

Length: 84 ft

Width: 56 ft

Let's plug these values into the formula and see if they give us the correct perimeter:

2l + 2w = P

2*84 + 2*56 = P

168 + 112

= 280 feet

These are the correct dimensions!  

Hope this helps! You can reach out to me if you have further questions or concerns! :)

Answer:

length = width + 10

4*width + 20 ≤ 90

width ≤ 17.5 feet

Step-by-step explanation:

The perimeter of a rectangle is given by:

Perimeter = 2*length + 2*width

The length needs to be 10 feet longer than the width, so we have:

length = width + 10

Using this length in the perimeter equation, we have:

Perimeter = 2*(width + 10) + 2*width = 4*width + 20

The perimeter needs to be up to 90 feet, so we have:

P ≤ 90

4*width + 20 ≤ 90

4*width ≤ 70

width ≤ 17.5 feet

the maximum width of the garden is 17.5 feet

Answer:

4.12

Step-by-step explanation:

[tex]\sqrt{17} = 4.1231[/tex] ≈ 4.12

Answer:

x+y=15 ; 2x+4y=50

Step-by-step explanation:

Let x be the number of people

Let y be the number of dogs.

Total number of heads = 15

As

1 person has 1 head

1 dog has 1 head

Total no. of heads of people = 1 * x = x

Total number of heads of dogs = 1*y = y

Equation becomes:

x+y=15

Total number of legs = 50

As

1 person has 2 legs

1 dog has 4 legs

Total no. of legs of people = 2 * x = 2x

Total number of legs of dogs = 4*y = 4y

Equation becomes:

2x+4y=50

Answer:

25104

Step-by-step explanation:

PRODUCT=MULTIPLICATION, SO

423 X 48= 25104

The quadrilaterals that are rhombus is

Figures B and C.

Options B and C are the correct answer.

A rhombus is a quadrilateral whose all four sides are equal and the parallel sides are equal and the opposite angles are equal

We have,

A rhombus has all four sides equal.

A rhombus has equal parallel sides.

A rhombus's opposite angles are equal.

Now,

The figure in option B has the following properties:

All sides are equal.

Parallel sides are equal.

The figure in option C has the following properties:

All sides are equal.

Parallel sides are equal.

Opposite angles are equal.

Thus,

Figures B and C are rhombus.

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Answer:

The same number was not added to both sides.

Step-by-step explanation:

Given:

t - 8 = 65

in the next step it states something wrong, because it should have been this:

t - 8 = 65

add +8 left and right of the = sign.

t - 8 + 8 = 65 + 8

t + 0 = 73

t = 73

So the error made what's that

The same number was not added to both sides.

Answer:

The same number was not added to both sides

Step-by-step explanation:

t - 8 = 65

Add 8 to each side

t - 8+8 = 65+8

The  student added 8 on one side and 65 on the other

t = 73

Answer:

Once

Step-by-step explanation:

I put it into slope intercept first

(5/6)x - (2/3) = y

(2/3)x - (7/3) = y

Both lines are linear so they are straight. Since the two are not parallel or have the same slope then they will cross once.

Answer:

x=6

Step-by-step explanation:

As MK and ML are tangent to the circle, they are also congruent (MK = ML). Thus we can set the equation:

6x-15 = 2x+9

Now solve for x:

6x-2x = 9+15

4x=24

x=6

Answer:

B.

Step-by-step explanation:

MK and ML are tangents to a circle and " originating from the same point" so

MK=ML

Since MK = 6x-15 and ML = 2x+9

So,

6x-15 = 2x+9

6x-2x = 9+15

4x = 24

Dividing both sides by 4

So, we'll get

x = 6

Answer:

Any integer x can be represent in form of 3k, 3k+1, or 3k + 2 (k is integer).

Case 1: x = 3k => x^2 - 2 = 9k^2 - 2, which will not be divisible by 3

(notice that 2 is not divisibble by 3, but 9k^2)

Case 2: x = 3k + 1 => x^2 - 2 = 9k^2 + 6k + 1 - 2 = 9k^2 + 6k - 1, which will not be divisible by 3

(notice that 1 is not divisibble by 3, but 9k^2 + 6k)

Case 3: x = 3k + 2 => x^2 - 2 = 9k^2 + 12k + 4 - 2 = 9k^2 + 12k - 2, which will not be divisible by 3

(notice that 2 is not divisibble by 3, but 9k^2 + 12k)

=> x^2 - 2 will never be divisible by 3

Hope this helps!

:)

Answer:

radius is 8; center is at (13, 0).

Step-by-step explanation:

Compare the given  (x - 13) ^ 2 + y ^ 2 = 64 to:

                                  (x - h)^2 + (y - k)^2 = r^2.  (h, k) represents the center

                                                                             and r the radius.

Since 64 = r^2, r = the radius = 8 units  = r

We also see that h = 13 and k = 0.  

Thus, the center of the given circle is (13, 0).

Answer:

6/12

Step-by-step explanation:

[tex]\sqrt{\frac{6}{8}} × \sqrt{\frac{6}{18}}[/tex]

= 6/2√2 × 3√2

= 6/12

Answer:

true

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

closed circles can mean greater than or equal to/less than or equal to

Answer:

Some equations have two solutions because a quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solution.

The answer to the quation is x = -2 or x =10

Step-by-step explanation:

Quadratic equation are equations with a leading degree of two. The solutions to the given quadratic equation is 10 or -2

Quadratic equation are equations with a leading degree of two. Given the equation

(x-4)^2-28=8

The equation has two solution because it has a leading degree of 2.

Given

(x-4)^2-28=8

Add 28 to both sides

(x-4)^2-28 + 8=8 + 8

(x-4)^2= 36

Take square root of both sides

√(x-4)^2= ±√36

x - 4 = ±6
x = 6 + 4 or -6 + 4
x = 10 or -2

Hence the solutions to the given quadratic equation is 10 or -2

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Answer:

P(RR) = 3/7 * 3/7 = 9/49

P(BB) = 4/7 * 4/7 = 16/49

We want to know P(RR) + P(BB)

P(RR) + P(BB) = 9/49 + 16/49 = 25/49

Step-by-step explanation: