use the foil method to find the product below. (x+3) (x^2-6x)

Answer:

Your answer is -3.5 which lies between -4 and -3.

The point R is halfway between the integers on the number line below and represents the number -3.5 .

Answer:

Hours      Charge

1               y = 6.5(1) + 5 = $11.5

2              y = 6.5(2) + 5 = $18

3              y = 6.5(3) + 5 = $24.5

4              y = 6.5(4) + 5 = $31

Step-by-step explanation:

In an equation y=mx+b, we can interpret the intercept b as the value of the initial charge and the slope m as the additional charge per hour. So, we can formulate the following equation:

y = 6.5x + 5

Where x is the hours and y are the charges for the babysitting, so, we can fill the table as:

Hours      Charge

1               y = 6.5(1) + 5 = $11.5

2              y = 6.5(2) + 5 = $18

3              y = 6.5(3) + 5 = $24.5

4              y = 6.5(4) + 5 = $31

The answer should be like

Hours      Charge

1               y = 6.5(1) + 5 = $11.5

2              y = 6.5(2) + 5 = $18

3              y = 6.5(3) + 5 = $24.5

4              y = 6.5(4) + 5 = $31

Since we know that the equation should be in the form of

y = mx + b

So, here

y = 6.5x + 5

Here  x is the hours and y are the charges for the babysitting.

So, the table be like

Hours      Charge

1               y = 6.5(1) + 5 = $11.5

2              y = 6.5(2) + 5 = $18

3              y = 6.5(3) + 5 = $24.5

4              y = 6.5(4) + 5 = $31

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Answer:

1.2 miles

Step-by-step explanation:

5.3 - 4.1 = 1.2 miles

Answer:

Step-by-step explanation:

5.3 - 4.1 = 1.2

1.2 miles difference.

This is because from Washington to Lanberry it is 4.1 miles. From Washington to Newberry it is 5.3., SO, if you subtract it you will get 1.2 miles difference.

Hope this helped,

kavitha

Answer:

C.

Step-by-step explanation:

It's the most reasonable answer.

Answer: 19!!

Step-by-step explanation:

Answer:

Z (The one on the bottom right)

Step-by-step explanation:

You said that the y intercept goes down by 1 unit which makes only W and Z possible.

The slope is 1/2 and if you multiply that by -4 the new slope is -2 which means the change in y is -2 every time the change in x is 1. Which perfectly fits Z and if you have any questions please ask me with the comments!

Answer:

Step-by-step explanation:

[tex](2, 1) (5, 3)\\x_1 =2 \\y_1 =1\\x_2=5\\y_2 =3\\m =\frac{y_2-y_1}{x_2-x_1} \\\\m = \frac{3-1}{5-2} \\\\m = 2/3[/tex]

Answer:

Range = 13

Mean = 8.4

Variance= 21.24

Standard deviation= 4.61

Step-by-step explanation:

2​, 10​, 15​, 3​, 13​, 9​, 14​, 7​, 2​, 9

For the range

Let the set of data be arranged inn ascending order

Range= higehest value- lowest value

Range = 15-2

Range= 13

For the mean

Mean = (2+2+3+7+9+9+10+13+14+15)/10

Mean = 84/10

Mean = 8.4

For variance

Variance=((2-8.4)²+(2-8.4)²+(3-8.4)²+(7-8.4)²+(9-8.4)²+(9-8.4)²+(10-8.4)²+(13-8.4)²+(14-8.4)²+(15-8.4)²)/10

Variance= (40.96+40.96+29.16+1.96+0.36+0.36+2.56+21.16+31.36+43.56)/10

Variance= 212.4/10

Variance= 21.24

Standard deviation= √variance

Standard deviation= √21.24

Standard deviation= 4.609

Approximately = 4.61

Answer:

$300

Step-by-step explanation:

The couch is sold in two ways; outright payment or installment payment.

Outright payment would cost = $820

Installment payment = down payment + monthly charges

Down payment = $400

Monthly charges for a period of one year (12 months) = 12 × $60

                                         = $720

Installment payment would cost = $400 + $720

                                            = $1120

Amount saved by paying total amount at the time of purchase = $1120 - $820

                                             = $300

Thus, the outright buying the couch would save $300.

Answer:

100% = 65 Gallons; 70% = 45.5 Gallons

Step-by-step explanation:

The important piece of information here is that 13 gallons of water makes the container 1/5 of the way full, aka 20%.  If the question is simply, how many gallons will it hold, then we multiply 13 by 5 to get 100% at 65 gallons.  To get the amount held at 7/10, or 70%, we simply multiply 65 with 7/10 to get 45.5 gallons.

Cheers.

Answer:

the guarantee period should be less than 136010 miles

Step-by-step explanation:

From the given information;

Let consider Y to be the life of a car engine

with a mean μ = 170000

and a standard deviation σ = 16500

The objective is to determine what should be the guarantee period T if the company wants less than 2% of the engines to fail.

i.e

P(Y < T ) < 0.02

For the variable of z ; we have:

[tex]z = \dfrac{x - \mu }{\sigma}[/tex]

[tex]z = \dfrac{x - 170000 }{16500}[/tex]

Now;

[tex]P(Y < T ) = P( Z < \dfrac{T- 170000}{16500})[/tex]

[tex]P( Z < \dfrac{T- 170000}{16500})< 0.02[/tex]

From Z table ;

At P(Z < -2.06) ≅ 0.0197  which is close to 0.02

[tex]\dfrac{T- 170000}{16500}<- 2.06[/tex]

[tex]{T- 170000}<- 2.06({16500})[/tex]

[tex]{T- 170000}< - 33990[/tex]

[tex]{T}< - 33990+ 170000[/tex]

[tex]{T}<136010[/tex]

Thus; the guarantee period should be less than 136010 miles

Answer:

see below

Step-by-step explanation:

Using the Pythagorean Theorem:

a^2+ b^2 = c^2

5^2+ 9^2 = 13^2

25+81 = 169

106 = 169

This is not true so it is not a right triangle

Answer:

[tex]\boxed{\sf Not \ a \ right \ triangle}[/tex]

Step-by-step explanation:

Apply Pythagorean theorem to check if the triangle is a right triangle.

[tex]a^2+ b^2 = c^2[/tex]

[tex]5^2+ 9^2 = 13^2[/tex]

[tex]25+81=169[/tex]

[tex]106=109[/tex]

False statement.

The triangle is not a right triangle.

Answer:

y = 3.5 + (1/8)x

Step-by-step explanation:

Speed is the ratio of total distance traveled to the total time taken. It is given by the formula:

Speed = distance / time.

The distance Paul Revere traveled from Charlestown to Boston is 3.5 miles.

Paul Revere also traveled from Boston to Lexington by horse at a rate of 1/8 mile per minute. If he traveled for x minutes, the distance covered can be gotten by:

Speed = distance / time

1/8 = distance / x

distance = (1/8)x miles.

y = sum of the distance to Charlestown and the distance from Charlestown to Lexington

y = 3.5 + (1/8)x

Answer:

C(5, 4)

Step-by-step explanation:

The rule for a reflection over the y -axis is (x,y)→(−x,y) .

Answer:

(5, 4)

Step-by-step explanation:

when you reflect off the y-axis, you switch (x,y) to (-x,y)

So

(-5, 4) --> (5, 4)

Hope this helps,

Feel free to ask more questions if I need to explain more.

Answer:

1/2x

Step-by-step explanation:

To find the slope of a line with only 2 points we use the following formula.

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex],

So we fill it in with the following points,

(7,1)

(5,0)

0 is y2 and 1 is y1 0-1 = -1

5-7 = -2

Slope: 1/2

Thus,

the slope of the line is 1/2.

Hope this helps :)

you can use the value of sin\

sin(theta) = 12/16

Now solve for theta, and do inverse sine

so theta would be 48.59037789 , or around 50 degrees

Answer:

Step-by-step explanation:

Since, it is a right triangle.

Perpendicular (p) = 12

hypotenuse ( h) = 16

now,

[tex]sin \: (x \: degree) = \frac{perpendicular}{hypotenuse} [/tex]

[tex]sin \: x \: = \frac{12}{16} [/tex]

[tex] x = {sin}^{ - 1} ( \frac{12}{16} )[/tex]

[tex]x = 48.59 \: degree[/tex]

hope this helps...

good luck on your assignment..

Answer:

(D) -2,-3

Step-by-step explanation:

From the origin, we can find the current position of point B by counting.

B is 2 to the left of the y-axis, meaning that it's x value is -2.

B is 3 down of the x-axis, making it's y value -3.

Therefore, the coordinates of point B are -2,-3.

Hope this helped!

Answer: (D) -2,-3

Step-by-step explanation:

Answer:

x

Step-by-step explanation:

f(x)=2x+5

Input: x

Output: f(x)

For i.e:

Input: 1

Output: f(1) = 2(1) + 5 = 2 + 5 = 7

Range is [tex]y\in[-3,+\infty)[/tex].

Hope this helps.

Answer:

5x+8y+2z = 68

Step-by-step explanation:

Given the point P0 = (2, 5, 9), to Find an equation for a plane through that point and normal to the vector n = 5i+8j+2k the following steps must be followed:

The equation for the plane passing through the point is expressed as;

a(x-x0)+b(y-y0)+c(z-z0) = 0 where;

(x0, y0, z0) is the point on the plane and (a,b,c) is the normal vector n.

Given the point (2, 5, 9) and normal vector n =(5, 8, 2)

x0 = 2, y0 = 5, z0 = 9, a = 5, b = 8 and c= 2.

Substituting this values into the equation of the plane above will give;

5(x-2)+8(y-5)+2(z-9) = 0

On expansion:

5x-10+8y-40+2z-18 = 0

5x+8y+2z-10-40-18 = 0

5x+8y+2z-68 = 0

The required equation of the plane is 5x+8y+2z = 68

Answer:

A

Step-by-step explanation:

............................ ....

Step-by-step explanation:

here, the given point is (-7,-3)

now, by the formula,

p(x,y)= p-1 (-y+a+b,x-a+b) ( p-1 is p das)

p(-5,3)= p-1 (-13,-1) is answer.

hope it helps..

Answer:

.15* house price = 28,500

house price = 28,500 / .15

house price =  190,000

Step-by-step explanation:

Answer: 190,000

Step-by-step explanation:

the equation looks like this - .15x=28,500. then you divide both sides by .15 and get x=190,000

Answer:

Step-by-step explanation:

Given the formula

f(n) = n² + 5

where n is the number of terms

So from the question we were told to find the 5th term that's

n = 5

In order to find the 5th term substitute the value of n that's 5 into the rule

We have

f(5) = 5² + 5

= 25 + 5

= 30

So the 5th term of the sequence in the given rule is 30

Hope this helps you

Answer:

144 people competed in the Chess Tournament

Step-by-step explanation:

So as you can see, after the Chess Tournament took place, two boxes were empty, the rest closed. That would mean that there were 2 boxes of medals that were given out to honor the participants in the chess tournament. The spelling bee had twice as many participants, and hence used 2 [tex]*[/tex] 2 = 4 boxes. The remaining box had to have 72 medals in it, as it was the remaining amount of medals.

After the Chess Tournament, 2 boxes were given out, and we can assume they contained 72 medals in them. Therefore, the number of medals given after the chess tournament would be 2 [tex]*[/tex] 71 = 144 medals. Each medal corresponds to a participant, so the number of chess tournament participants would also be 144, 144 participants.

Answer:

(4, -3)

Step-by-step explanation:

the equation f(x-5) is a translation of the equation f(x) by 5 units to the right.

So, if all points of the equation f(x) are shifted 5 units to the right, the minimum point of the graph is also shifted 5 units to the right, so to find the minimum point of y = f(x - 5), we just need to sum 5 units to the x-coordinate:

Minimum point = (-1 + 5, -3) = (4, -3)

So the minimum point of y = f(x - 5) is (4, -3).

The minimum point on the graph of y = f(x - 5) is (-6,3)

On the graph of the equation y = f(x);

The minimum point is given as (-1,-3)

The graph of y = f(x - 5) means that, f(x) is shifted to the right by 5 units

So, the corresponding point of (x,y) of f(x) on the graph of f(x - 5) is:

[tex](x,y) \to (x - 5,y)[/tex]

This gives

[tex](-1,-3) \to (-1 - 5,3)[/tex]

Subtract 5 from -1

[tex](-1,-3) \to (-6,3)[/tex]

Hence, the minimum point on the graph of y = f(x - 5) is (-6,3)

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