How are the properties of exponents used when dividing a polynomial by a monomial?

The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.

A quadratic equation's roots are equal to the second term's coefficient negated, divided by the leading coefficient. The constant term (the third term), divided by the leading coefficient, is equivalent to the product of the roots of a quadratic equation.

According to the Product Rule, the derivative of a product of two functions is equal to the product of the first function times the second function's derivative plus the second function times the first function's derivative.

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The function g(x) = 8x is increasing over the interval from x=3 to x=5.

The graph of the function g(x) = 8x is shown below.

We can observe that the graph of g(x) is a staright line passing through origin (0, 0)

This means that the function g(x) is a linear function.

For x = 3, the value of function would be,

g(3) = 8 × (3)

g(3) = 24

And for input value x = 5, the value of function would be,

g(5) = 8 × (5)

g(5) = 40

This means that the value of function g(x) increases from x = 3 to x = 5

Also, from the graph the function g(x) is increasing over the interval [3, 5]

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To use the linear combination method to solve the system of equations:

2x – 3y = 13

3x + y = -8

We can multiply the second equation by 3 to get:

9x + 3y = -24

Now we can add this equation to the first equation to eliminate the y term:

2x – 3y + 9x + 3y = 13 - 24

Simplifying the left-hand side and the right-hand side of the equation:

11x = -11

Finally, we can solve for x:

x = -1

Substitute x = -1 in either of the original equations:

2x – 3y = 13

2(-1) - 3y = 13

-2 - 3y = 13

-3y = 15

y = -5

Therefore, the solution to the system of equations is x = -1 and y = -5.

Explanation: We used the linear combination method to eliminate one of the variables by adding the two equations together. Then, we solved for the remaining variable and substituted the value back into one of the original equations to solve for the other variable.

The transformation of the vertices of the triangle is a. L' = (-7 + 5, 4 - 6) = (-2, -2), M' = (-3 + 5, 0 - 6) = (2, -6), N' = (-8 + 5, 1 - 6) = (-3, -5). b. L' = (-7, 4) = (-4, 7), M' = (-3, 0) = (0, 3), and N' = (-8, 1) = (-1, 8).

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.

The vertices of the triangle are L (-7, 4), M(-3, 0) and N(-8, 1).

a. Translation: (x,y) → (x + 5, y-6) is as follows:

L' = (-7 + 5, 4 - 6) = (-2, -2)

M' = (-3 + 5, 0 - 6) = (2, -6)

N' = (-8 + 5, 1 - 6) = (-3, -5)

b. Reflection in line y = -x is as follows:

Here, the value of y coordinate is negative x coordinate and x coordinate is negative y coordinate.

L' = (-7, 4) = (-4, 7)

M' = (-3, 0) = (0, 3)

N' = (-8, 1) = (-1, 8)

Hence, the transformation of the vertices of the triangle is a. L' = (-7 + 5, 4 - 6) = (-2, -2), M' = (-3 + 5, 0 - 6) = (2, -6), N' = (-8 + 5, 1 - 6) = (-3, -5). b. L' = (-7, 4) = (-4, 7), M' = (-3, 0) = (0, 3), and N' = (-8, 1) = (-1, 8).

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Using the equation given, the four ordered pair solutions are:

x     |   y  

0       5

-2      -5

6       35

-8     -35

To find the ordered pair solutions to the given equation as shown in the table, plug in the known value into y = 5x + 5 to find the other coordinate pair.

Therefore:

When x = 0:

y = 5(0) + 5

y = 5

When y = -5:

-5 = 5x + 5

-5 - 5 = 5x

-10 = 5x

-10/5 = x

-2 = x

x = -2

When x = 6:

y = 5(6) + 5

y = 35

When y = -35:

-35 = 5x + 5

-35 - 5 = 5x

-40 = 5x

-40/5 = x

-8 = x

x = -8

The four ordered pair solutions are:

x     |   y  

0       5

-2      -5

6       35

-8     -35

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The volume of the cylinder is 162πx, the volume of the cone (1/3)πx^3 and the volume of the hemisphere is (162πx + (1/3)πx^3)/2

Volume of the cylinder:

The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height of the cylinder.

In this case, the height of the cylinder is equal to the diameter of the paperweight hemisphere, which is twice the radius of the cone.

Let's call the radius of the cone "x". The diameter of the paperweight hemisphere is equal to 2x, so the height of the cylinder is equal to 2x. The radius of the cylinder is 9 cm, so we can calculate the volume of the cylinder as follows:

V = πr^2h = π * 9^2 * 2x = 162πx

Volume of the cone:

The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius and h is the height of the cone. In this case, the height of the cone is equal to the radius of the cone, so we can calculate the volume of the cone as follows:

V = (1/3)πr^2h = (1/3)π * x^2 * x = (1/3)πx^3

Volume of the hemisphere:

The volume of a hemisphere can be calculated using the formula V = (2/3)πr^3, where r is the radius of the hemisphere. To estimate the volume of the hemisphere, we can calculate the average of the volumes of the cylinder and cone.

V_hemisphere = (V_cylinder + V_cone)/2 = (162πx + (1/3)πx^3)/2

This expression represents the estimated volume of the hemisphere in terms of x, the radius of the cone.

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Answer:

The vertex form of 8-2x=3(y+1)^2 is: y= -1/6x^2 + 4x - 8.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Constant: Mug price = $8.95, Refill price = $1.50, Rate: Refill rate = $1.50, Equation: 8.95 + 1.50x = 26.95, Solve: x = 15 refills​. Jalissa purchased 15 refills last month, paying $26.95 for the mug and refills combined.

To calculate the number of refills Jalissa purchased last month, we must first define the constants of the equation. The cost of the mug is $8.95 and the cost of the refill is $1.50. After establishing these constants, we can create an equation using the rate of refills ($1.50) and the total amount that Jalissa spent ($26.95). The equation is 8.95 + 1.50x = 26.95. This equation can then be solved to find the value of x, which is the number of refills Jalissa purchased. To solve the equation, subtract 8.95 from both sides to get 1.50x = 18. This equation can then be divided by 1.50 to find the value of x, which is 15. This means that Jalissa purchased 15 refills last month, paying $26.95 for the mug and refills combined.

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Answer: 3/10

Step-by-step explanation: Convert given fractions into like terms. In this case 1/5 becomes 2/10 and 1/2 becomes 5/10. Add them up and you get 7/10. Subtract from the total of 10/10 and the result is 3/10. Since the final fraction can't be simplified, this is the final answer.

We could calculate the weight of individual balloons from given density and empty mass. From that calculate the total weight of balloons and added to the weight of fixings. So the weight of archway becomes 111.33g.

Volume of helium each balloon is holding = 1.2L

Density of helium = 0.1785

Density = mass/volume

Mass = density/volume

So mass of helium in each balloon = 1.2×0.1785 = 0.2142 g =  214.2 mg

Mass of empty balloon = 27 mg

So the total mass of a balloon after filled with helium = 214.2 + 27 = 241.2 mg

Mass of 275 such balloons = Mass of 1 balloon × 275

                                             = 241.2 ×275 = 66330 mg = 66.33 g

Mass of all strings and fixings = 45 g

Total mass of archway = mass of 275 balloons + mass of fixings and strings = 66.33 + 45 = 111.33 g

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Step-by-step explanation:

It may be your last point

[tex]y = 2x + 6[/tex]

[tex]y = 2(2) + 6 = 10 \: not \: 8[/tex]

You have the point (2,8) when it should be (1,8)

Keep me updated

Answer:

y = 2

Step-by-step explanation:

2x + y = 8 → (1)

x - 3y = - 3 → (2)

multiplying (1) by 3 and adding will eliminate y

6x + 3y = 24 → (3)

add (2) and (3) term by term to eliminate y

7x + 0 = 21

7x = 21 ( divide both sides by 7 )

x = 3

substitute x = 3 into either of the 2 equations and solve for y

substituting into (1)

2(3) + y = 8

6 + y = 8 ( subtract 6 from both sides )

y = 2

Answer:

y = 2

Step-by-step explanation:

The question has given us two equations with two unknown variables and told us to solve the system of equations.

To do this, there are multiple methods. The method used in this solution will involve taking any one of the variables and making it the subject of both equations and then equating the resulting equations.

Let's take the first equation:

[tex]2x + y = 8[/tex] ,

and rearrange it to make x the subject:

[tex]2x + y = 8[/tex]

⇒ [tex]2x = 8 - y[/tex]         [Subtracting y from both sides]

⇒ [tex]x = \frac{8 - y}{2}[/tex]  ------(i)         [Dividing both sides by 2]

Now let's take the second equation and rearrange it to also make x its subject:

[tex]x - 3y = -3[/tex]

⇒ [tex]x = -3+3y[/tex]  ------(ii)        [Adding 3y to both sides]

As both equations (i) and (ii) are equal to [tex]x[/tex], we can say:

(i) = (ii)

⇒ [tex]\frac{8-y}{2} = -3+3y[/tex]

⇒ [tex]8 - y = 2(-3+3y)[/tex]        [Multipying both sides by 2]

⇒ [tex]8-y = -6 +6y[/tex]

⇒ [tex]8 - y - 6y=-6[/tex]            [Subtracting 6y from both sides]    

⇒ [tex]8-7y=-6[/tex]

⇒ [tex]-7y = -6-8[/tex]                [Subtracting 8 from both sides]

⇒ [tex]-7y = -14[/tex]

⇒ [tex]y = \frac{-14}{-7}[/tex]                          [Dividing both dies by -7]

⇒ [tex]y = \bf 2[/tex]

Therefore, the answer to the question is 2.

We can now easily calculate the value of x by substituting y = 2 into either equation (i) or (ii).

Substituting into (i):

[tex]2x + 2= 8[/tex]

⇒ [tex]2x = 6[/tex]

⇒ [tex]x = \bf 3[/tex]

Answer:

11

Step-by-step explanation:

lets suppose the number is x

twice the number would be 2x and 15 more than that will be

2x + 15

and this is equal to 37

2x + 15 = 37

2x = 37 - 15

2x = 22

x = 22/2

x = 11

Answer: 398 + 399 + 400 equals 1197 

Step-by-step explanation: The sum of three consecutive natural numbers is 1197, find the numbers X) + (X + 1) + (X + 2) = 1197 To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:X + X + 1 + X + 2 = 11973X + 3 = 11973X + 3 - 3 = 1197 - 33X = 11943X/3 = 1194/3X = 398Which means that the first number is 398, the second number is 398 + 1 and the third number is 398 + 2. Therefore, three consecutive integers that add up to 1197 are 398, 399, and 400. 

The commission he earned last month was amount of $360.

The commission is determined by the product of the commission rate and the total sales.

A salesman receives a 6% commission on all merchandise sold.

He sold $6000 in merchandise last month.

Salesman earns 6% = 6/100 = 0.06

Now, we have to evaluate 6% of $6000

= 0.06 x 6000

Apply the multiplication operation, and we get

= 360$

Thus, the commission he earned last month was the amount of $360.

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The question seems incomplete, the complete question would be as:

A salesman earns 6% commission on all the merchandise that he sells. Last month he sold $6000 worth of merchandise. How much commission (in dollars) did he earn last month?

Correlation is to "measurement of variables", as experimentation is to "manipulation of variables".

Correlation refers to the statistical relationship between two or more variables, where changes in one variable are related to changes in the other variable(s). It measures the strength and direction of the relationship, but it does not establish cause and effect.

Experimentation, on the other hand, involves the manipulation of variables to determine the cause-and-effect relationship between variables. The experimenter changes the independent variable and measures the effect it has on the dependent variable.

This method allows the experimenter to establish cause and effect and to control extraneous variables that might interfere with the relationship between the independent and dependent variables.

Therefore, the correct answer is D.

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--The given question is incomplete; the complete question is

"Correlation is to___as experimentation is to___.

A. manipulation of variables; measurement of variables

B. unobtrusiveness: correlation

C. single variables; multiple variables

D. measurement of variables; manipulation of variables"--

Answer:9

Step-by-step explanation:

add

Answer:

Step-by-step explanation:

Sorry did you already finish?

1. B. 2/3 = 8/12 b/c 2x4 = 8 and 3x4 = 12

2. D. 5/6 = 10/12 b/c 5x2 = 10 and 6x2 = 12

3. 2

4. A. simplified is 2/3 C. self-explanatory D. simplified is 3/4

Answer:

its A. x² + 3x + 2/5x because it's the right answer

The area of the triangle in the diagram is one square foot.

We know that the area of a triangle of base B and height H is given by the formula:

Area = B*H/2

On the diagram we can se that the measure of the base is 3 ft, and the height is 2/3 ft, then the area of that triangle will be:

Area = (3 ft)*(2/3 ft)/2 = 1 ft²

The area of the triangle is one square foot.

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Kweku would save $180 in a year buying electricity for the Desla electric compared to buying gas for the Deswagon.

To make up for the higher sale price,

it will take him more than 66 years.

And hybrid cars save money in the long term.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

Deselectric costs $11900 more than the Deswagon.

Unit cost:

Deselectric: $0.11 per mile.

Deswagon: $0.12 per mile.

Kweku drives about 18,000 miles a year.

That means

the cost for each car;

Deselectric: 18000 x 0.11 = $1980

Deswagon: 18000 x 0.12 = $2160

The more cost is,

= $2160 - $1980

= $180 of savings in a year.

Now, the make-up for the higher sale price,

= 11900/180

= 66.11 in years.

And hybrid cars save money in the long term.

Therefore, it will take him more than 66 years.

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The system of equations has no solution

From the question, we have the following parameters that can be used in our computation:

y = x - 7

y = x + 7

By substituting the first equation in the second equation

So, we have the following representation

x + 7 = x - 7

Evaluate the like terms

7 = -7

The above equation is false

Hence, the system has no solution

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Part A: By comparing B and L, L has greater rate of change.

Part B: By comparing B and L, B has greater y-intercept.

This can be solved using the concept of equation of function.

Function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). A function is described as a relationship between a group of inputs and one output each. In simple terms, a function is a connection between inputs, with each input corresponding to exactly one output. Every function has its own domain and codomain, as well as a range. f(x), where x is the input, is a common way to refer to a function.

Part B:

Let, the equation of function B is,

Y = mx+c

Where m is slope and C is intercept

At (-3,-7)

-7 = -3m+c

C = 3m-7

At (-1,-1)

-1 = -m+3m-7

-1 = 2m -7

2m = 6

m = 3

C = 3m-7

C = 3×3 - 7

C =2

So, equation of line B is

Y = mx+c

Y = 3x+2

Where intercept is 2, note y intercept can also be found by putting x = 0, slope = 3

Part A:

Rate of change is slope for B can also be found by -1-(-7)/-1-(-3)=6/2=3

For equation L.

Y=6x+4

Slope=6, intercept =4

For L: when x=0, y=4,x=1,y=10

Rate of change=slope=(10 - 4)/ (1 - 0)=6

Line            Equation              Rate of change(slope(m)      Y intercept (c)

B                    y = 3x+2                      3                                         2

L                     y = 6x- 4                     6                                         - 4

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Answer:

6 days

Step-by-step explanation:

This is an easy problem if you think about it. Let’s start by identifying unnecessary information. I’ll go ahead and point this out: we don’t need to know how long it takes Johnny to watch the episodes. The question already says he’s only watching 12 episodes per day, so the time information is useless. If you rewrite the problem with only message information, you get something like this:

“The show Johnny wants to binge watch is 61 episodes long. If Johnny were to watch 12 episodes a day, how many days would it take him to finish the show?”

That makes it seem so much easier! Let’s start by dividing the show into sets of 12 episodes. 61 divided by 12 is 5 R1. Since he needs another day to finish the show, even if he only watches one episode, the answer is 6 days.

The equivalent expressions to t(-7.4s+3.8-4.5)-t are:

This expression can be simplified as follows:

t(-7.4s + 3.8 - 4.5) - t

= t(-7.4s - 0.7) - t

= -7.4st - 1.7t.

t(-7.4s+3.8-4.5)-t

= t(-3.6s-4.5)-t

-7.4s + 3.8 - 4.5t - t

= t(7.4s+3.8)-5.5t

Therefore the correct options are A, B, E.

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Answer: The slope of a line can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line. Plugging in the given points, we get:

slope = (-1 - 3) / (2 - (-4)) = -4 / 6 = -2/3

So the ratio expressing the slope of line k is -2/3.

Step-by-step explanation:

Answer:

0.43 cup of water

Step-by-step explanation:

We know

For every 1 1/8 cups of water, she uses 2 5/8 of flour.

1 1/8 = 9/8 = 1.125

2 5/8 = 21/8 = 2.625

How much water does Cindy need for each cup of flour?

1.125 divided by 2.625 = 0.43 cup of water

So, Cindy needs 0.43 cup of eater for each cup of flour

The distance between D(-5, -6) and E(5,2) is 12.8, and the slope is 0.8. The distance between E(5,2) and F(4, -4) is 6.08, and the slope is 6. The distance between F(4, -4) and G(-6, -12) is 12.8, and the slope is 0.8.

Distance Formula:

The distance between two points A(x1, y1) and B(x2, y2) is calculated using the following formula:

d = √((x2-x1)² + (y2-y1)²)

Slope Formula:

The slope of the line between two points A(x1, y1) and B(x2, y2) is calculated using the following formula:

m = (y2-y1)/(x2-x1)

Distance between D(-5, -6) and E(5,2):

d = √((5-(-5))² + (2-(-6))²)

d = √((10)² + (8)²)

d = √(100 + 64)

d = √164

d = 12.8

Slope between D(-5, -6) and E(5,2):

m = (2-(-6))/(5-(-5))

m = (8)/(10)

m = 0.8

Distance between E(5,2) and F(4, -4):

d = √((4-5)² + (-4-2)²)

d = √((-1)² + (-6)²)

d = √(1 + 36)

d = √37

d = 6.08

Slope between E(5,2) and F(4, -4):

m = (-4-2)/(4-5)

m = (-6)/(-1)

m = 6

Distance between F(4, -4) and G(-6, -12):

d = √((-6-4)² + (-12-(-4))²)

d = √((-10)² + (-8)²)

d = √(100 + 64) …

d = √164

d = 12.8

Slope between F(4, -4) and G(-6, -12):

m = (-12-(-4))/(-6-4)

m = (-8)/(-10)

m = 0.8

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The slope is 0.8 and the distance between D(-5, -6) and E(5,2) is 12.8.

The slope is 6 and the distance between E(5,2) and F(4, -4) is 6.08.

The slope is 0.8 and the distance between F(4, -4) and G(6, -12) is 12.8.

The formula for Distance:

The following formula is used to determine the distance that separates points A (x1, y1) and B (x2, y2) from one another:

d = √((x2-x1)² + (y2-y1)²)

Slope Method:

The following formula can be used to determine the slope of the line that connects the two points A (x1, y1) and B (x2, y2):

m = (y2-y1)/(x2-x1)

The distance that separates D(-5, -6) from E(5,2):

d = √((5-(-5))² + (2-(-6))²)

d = √((10)² + (8)²)

d = √(100 + 64)

d = √164

d = 12.8

Slope from D(-5, -6) to E(5,2):

m = (2-(-6))/(5-(-5))

m = (8)/(10)

m = 0.8

Between E(5, 2) and F(4, -4):

d = √((4-5)² + (-4-2)²)

d = √((-1)² + (-6)²)

d = √(1 + 36)

d = √37

d = 6.08

Slope between E(5,2) and F(4, -4):

m = (-4-2)/(4-5)

m = (-6)/(-1)

m = 6

Distance between F(4, -4) and G(-6, -12):

d = √((-6-4)² + (-12-(-4))²)

d = √((-10)² + (-8)²)

d = √(100 + 64) …

d = √164

d = 12.8

Slope between F(4, -4) and G(-6, -12):

m = (-12-(-4))/(-6-4)

m = (-8)/(-10)

m = 0.8

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Answer:

t ≈ 2.61

Step-by-step explanation:

13.7t - 4.7 = 9.9 + 8.1t ( subtract 8.1t from both sides )

5.6t - 4.7 = 9.9 ( add 4.7 to both sides )

5.6t = 14.6 ( divide both sides by 5.6 )

t ≈ 2.61 ( to the nearest hundredth )