Set equal to zero and solve for x. f(x)=4(x+4)(x-7)^2

Answer:

It sounds like the store is offering a sale on televisions where you can get a 30% discount on the original price of the television, as well as an additional $100 off with a coupon. This means that you can use both the discount and the coupon to save money on your purchase of a television. If you have a coupon for $100 off, you can use it to save an additional $100 on top of the discount you receive from the sale. This can help you save even more money on your purchase. It's always a good idea to check for sales and coupons when shopping for big-ticket items like TVs, as it can help you save a significant amount of money.

If $13.31 in three fourth of the cost then the cost of the present is $17.747   .

In the question ,

it is given that ,

the amount of money that mother gave to buy the present is = $13.31 ,

the part of cost that the amount covered is = three fourth ,

that means the fraction is 3/4 = 13.31

So , the cost of the present will be = (13.31*4)/3

Simplifying further ,

we get ,

= 53.24/3

Simplifying further ,

we get ,

= 17.746666

rounding off ,

we get,

≈ 17.747

Therefore , the cost of the present is $17.747  .

The given question is incomplete , the complete question is

Your mother gave you $13.31 with which to buy a present. This covered 3 fourth of the cost. How much did the present cost ?

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Answer:

7. No

8. Yes

Step-by-step explanation:

7. No

For example, sides RS and TQ are not given as congruent, but this statement of congruence makes them congruent.

8. Yes

AB is congruent to CD

BD is congruent to DC

AD is congruent to CD

Triangle ABD is congruent to triangle CDB has all the corresponding parts in the correct order.

The combination selecting five players from a 10-member tennis team to make a trip to a match at another school = 252

What do you mean by permutations and combinations?

A permutation is an act of arranging objects or numbers in order.

Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.

given that

selecting five players from a 10-member tennis team to make a trip to a match at another school

we solve this by using combinations

=10[tex]C_{5}[/tex]

= [tex]\frac{10!}{5!(10-5)!}[/tex]

=[tex]\frac{3628800}{120*5!}[/tex]

=252

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A table of values is a collection of ordered pairs that is often produced by replacing numbers in an equation (relation).

Given,

Table of value;

When numbers are substituted into an equation, they typically produce a set of ordered pairs called a table of values (relation). Each ordered pair of numbers in the values table's table of values is related to one another according to the equation.

The relationship between the various data points is displayed using tables of values. In scientific lesson, a table of values could be used. Tables of values are used by scientists and researchers to record their data, which is subsequently examined for patterns. Then, they can utilize this pattern to forecast outcomes.

Therefore,

The process of substituting numbers in an equation results in the creation of a table of values, which is a collection of ordered pairs (relation).

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Answer:

[tex]\textsf{$f(1) = \boxed{1}$ , meaning when a $\boxed{1}$ is rolled on the die, the player is awarded}\\\\ \textsf{ $\boxed{1}$ point. This interpretation $\boxed{\sf makes \; sense}$ in the context of the problem.}[/tex]

[tex]\textsf{$f(4.5) = \boxed{8}$ , meaning when a $\boxed{4.5}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{8}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}[/tex]

[tex]\textsf{$f(10) = \boxed{19}$ , meaning when a $\boxed{10}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{19}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}[/tex]

[tex]\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is $\boxed{ \{1, 2, 3, 4, 5, 6\}}$ .}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=2x-1[/tex]

where:

----------------------------------------------------------------------------------------------------

f(1) means the value of the function when x = 1.  

Therefore, substitute x = 1 into the given function to find f(1):

[tex]\begin{aligned}x=1 \implies f(1)&=2(1)-1\\&=2-1\\&=1\end{aligned}[/tex]

[tex]\textsf{$f(1) = \boxed{1}$ , meaning when a $\boxed{1}$ is rolled on the die, the player is awarded}\\\\ \textsf{ $\boxed{1}$ point. This interpretation $\boxed{\sf makes \; sense}$ in the context of the problem.}[/tex]

----------------------------------------------------------------------------------------------------

f(4.5) means the value of the function when x = 4.5.

Therefore, substitute x = 4.5 into the given function to find f(4.5):

[tex]\begin{aligned}x=4.5 \implies f(4.5)&=2(4.5)-1\\&=9-1\\&=8\end{aligned}[/tex]

As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6.  Therefore, rolling a "4.5" does not make sense.

[tex]\textsf{$f(4.5) = \boxed{8}$ , meaning when a $\boxed{4.5}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{8}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}[/tex]

----------------------------------------------------------------------------------------------------

f(10) means the value of the function when x = 10.

Therefore, substitute x = 10 into the given function to find f(10):

[tex]\begin{aligned}x=10 \implies f(1)&=2(10)-1\\&=20-1\\&=19\end{aligned}[/tex]

As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6.  Therefore, rolling a "10" does not make sense.

[tex]\textsf{$f(10) = \boxed{19}$ , meaning when a $\boxed{10}$ is rolled on the die, the player is awarded} \\\\ \textsf{ $\boxed{19}$ points. This interpretation $\boxed{\sf does \; not \; make \; sense}$ in the context of the problem.}[/tex]

----------------------------------------------------------------------------------------------------

The domain of a function is the set of all possible x-values.

As the faces of the six-sided die are labelled 1 to 6, the only possible values of x are 1, 2, 3, 4, 5 and 6.  

[tex]\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is $\boxed{ \{1, 2, 3, 4, 5, 6\}}$ .}[/tex]

The domain can also be written as:

[tex]\{x \in \mathbb{N} \; | \; 1 \leq x \leq 6 \}[/tex]  

or [tex]\{x \in \mathbb{Z} \; | \; 1 \leq x \leq 6 \}[/tex]

The probability that all four will be heads or all four will be tails is 1/8.

What is probability?

Total number of outcomes = 2⁴

Probability of all four will be tails:

P(TTTT) = 1/2⁴

Probability of all four will be heads:

P(HHHH) = 1/2⁴

P(TTTT or HHHH)

= P(TTTT) + P(HHHH)

=  1/2⁴ +  1/2⁴

= 1/16 + 1/16

= 2/16

P(TTTT or HHHH) = 1/8

Hence, the probability that all four will be heads or all four will be tails is 1/8.

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Answer:

19,200

Step-by-step explanation:

multiply them all together

By using division, it can be calculated that

Jeremy can row 1 mile in 4 hours

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

This is a word problem on division

Jeremy can row 3 miles in 12 hours

Jeremy can row 1 mile in [tex]12 \div 3[/tex] = 4 hours

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The slope of the points (3, -5) and (-2, 4) is -9/5.

Slope in general term means that the elevation or the steepness of any curve. We use slope in order to find the equation of the line between two points. The formula for finding the slope between two points (x₁, y₁) and (x₂, y₂) is expressed as

m = (y₂ - y₁)/(x₂ - x₁)

where m is the slope between the points, y₂ - y₁ is difference between the y coordinates and x₂ - x₁ is the difference between the x coordinates for the same y coordinates.

We have  (x₁, y₁) = (3, -5) and (x₂, y₂) = (-2, 4)

So, the slope will be

m = (4 + 5)/(-2 -3)

m = 9/(-5)

m = -9/5 which is the required slope.

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Complete Question:

What is the slope given the points (3, -5) and (-2, 4)?

Answer:

0

Step-by-step explanation:

The [tex]y[/tex] coordinates are the same, meaning the line is horizontal. Thus, the slope is 0.

Answer:

6.23yx-8y

Step-by-step explanation:

simplified answer!

The choice that is true are:

f(0) > g(0)

f(6) = g(12)

f(-4) = g(-4)

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 4x + 2

g(x) = (5/2)x - 4

Now,

f(0) = 2

g(0) = -4

f(0) > g(0)

f(6) = 24 + 2 = 26

g(12) = (5/2) x 12 - 4 = 30 - 4 = 26

f(6) = g(12)

f(-4) = -16 + 2 = -14

g(-4) = -10 - 4 = -14

f(-4) = g(-4)

f(2) = 8 + 2= 10

g(2) = 1

f(2) > g(2)

Thus,

f(0) > g(0) is true

f(6) = g(12) is true

f(-4) = g(-4) is true

g(2) > f(2) is not true

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The length of the radius of a circle with the equation x² + y² = 8 is 2√2 units  .

In the question ,

it is given that ,

the equation of the circle is ⇒ x² + y² = 8 ,

we know that the general equation of the circle is given as x² + y² = b² ;

and "b" is the radius of circle ,

On comparing both the equations ,

we get ,

b² = 8

Simplifying the above equation further ,

we get ,

b = √8 = √2 × 2 × 2

the radius "b" is

b = 2√2 units .

Therefore , the length of the radius of the circle is 2√2 units .

The given question is incomplete , the complete question is

What is the length of the radius of a circle given the equation x² + y² = 8 ?

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We have -2 from the values in the provided solution set, which is the necessary value.

what is solution set?

A solution set is a group of values in mathematics that satisfy a specified set of equations or inequalities. A constrained optimization problem's viable zone is its solution set of constraints.

Given: - 5x - 15 > 10 + 20x

Let's eliminate the variable x in order to solve the inequality.

5 times both sides,

- 5x - 15 + 5x > 10 + 20x + 5x

- 15 > 10 + 25x

Subtracting 10 from both sides

- 15 - 10 > 10 - 10 + 25x

- 25 > 25x

Dividing both sides by - 25

-1 > x

x < - 1

We have -2 from the values in the provided solution set, which is the necessary value.

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Answer:

B

Step-by-step explanation:

Answer:

2 cups

Step-by-step explanation:

there should be two cups of milk in it. If I’m not correct I will redo this.

Answer:

To find the account balance after 17 years, we need to first calculate the annual interest rate. Since the interest is compounded 4 times per year, the effective annual interest rate is equal to (1 + 0.04/4)^4 - 1, which is about 4.169%.

To find the account balance after 17 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. Plugging in the values we know, we get:

A = 5360(1 + 0.04169/4)^(4*17)

A = $9,907.35

So the account balance after 17 years will be about $9,907.35.

Kinetic Energy is referred to as "energy possessed by an object as a result of its MOTION".

What is Kinetic Energy?

The energy that an item or particle has as a result of its motion is known as kinetic energy. An object accelerates and gains kinetic energy when work—the transfer of energy—is done on it by exerting a net force.

An object in motion always has a velocity, or "v," at any given moment. This energy is referred to as "kinetic energy," and it comes from:

Kinetic Energy = 12×m×v2

Here, m = Mass of the object in motion

Kinetic energy is a type of power that a moving object or particle possesses. An item accumulates kinetic energy when work, which involves the transfer of energy, is done on it by exerting a net force. A moving object or particle has kinetic energy, which depends on both its mass and its rate of motion. The type of motion can be vibration, rotation on an axis, translation (or travel along a path from one place to another), or any combination of these.

A body's translational kinetic energy is equal to 1/2mv2, which is the product of its mass, m, and square of its velocity, v.

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The value of sin(e) in the given right angle triangle DEF is 3/5

Given the Right angle DEF,

It is not specified whether angle D= angle F =90°.

Based on the alternatives presented, either base and altitude =3 or 4 and

5 is the hypotenuse.

Case 1. When ∠D=90° In Δ E D F

Sin (E) =altitude/hypotenuse

= 3/5  OR 4/5 [ if base=3, then altitude =4 and if Base =4, Altitude=3]

Case 2. When ∠F=90°, In ΔEFD

Sin (E) =altitude/hypotenuse

= 3/5 or 4/5 [Depending on whether Base =3 then altitude  =4, OR Altitude =3 , then Base =4]

Looking at all of the possibilities, 3/5 and 4/5 are accurate.

However, the solution is 3/5, so whether you pick angle D or angle F as 90°, take Altitude=3, Hypotenuse =5, and Base=4.

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Answer:

A. 3/5

Step-by-step explanation:

For right triangle, c^2 = a^2 + b^2

given c = EF = 10, a = DE = 8, b = DF

10^2 = 8^2 + DF^2

DF^2 = 100 - 64 = 36

DF = 6

sin(E) = opposite/hypotenuse = 6/10 = 3/5

Control variables are the type of variable that does not change during an experiment, and serves as a comparison point for all data points.

Control variables are also called constant variables or control variables.

A control variable in an experiment is a variable that is held constant or controlled by the researcher.

A control variable is a variable or item that the researcher wants to keep constant throughout the study so as not to affect the results.

A typical study design measures the influence of an independent variable on the dependent variable. In order for this to be done properly, it is important to control another external or standardized variable. Experimentation is not as simple as changing factors and recording results. In practice, any study has many different factors that can affect its results. A control variable is a way to keep some of these factors constant so that comparisons are unbiased and transparent.

In many experiments, even slight variations in some factors can lead to inaccurate or skewed results. Voxco's Experimental Research Toolkit aims to give researchers greater control over variables to help them achieve the results they want.

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Answer:

128,340 words

Step-by-step explanation:

People who are looking for a job are unemployed that is the term used  by the bureau of labor statistics which classified people who would like to work but have given up .

Step to Step explanation:

Therefore, the people who would like to work but given up who are looking for a job are unemployed classified by bureau of labor statistics.

The complete question is:

The bureau of labor statistics classifies people who would like to work but have given up looking for a job as:______.

a. Unemployed

b. A discouraged worker

c. Not in the labor force

d. Employed

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Answer: the answer is -193

Answer:

Jamie swims 1/2 the length of the swimming pool every 1/4 of a minute. This means that Jamie swims 1/8 of the length of the pool in one second. If the pool is 25 meters long, it would take Jamie 200 seconds, or about 3 minutes and 20 seconds, to swim the length of the pool. This is just an estimation, as the actual time it would take Jamie to swim the length of the pool would depend on factors such as Jamie's swimming ability and the speed at which they swim.

Answer:

x=12degrees

Step-by-step explanation:

1st Angle=23degrees

2nd Angle=(4x+19)

3rd Angle=(In order to find this angle we need to take this angle as angle3)

angle3+90=180

angle3=180-90

angle3=90degrees

Now lets start with the sum

Sum of angles of a triangle=180degrees

23+(4x+19)+90=180

113+(4x+19)=180

(4x+19)=180-113

(4x+19)=67

4x=67-19

4x=48

x=48/4

x=12degrees

Hope this helps you

Answer:

The expression √x+5+√1-x is defined for all values of x such that the value under the square root sign is non-negative. We can find the values of x that satisfy this condition by considering each of the square roots separately.

For the first square root, the value under the square root must be non-negative, so we have the following inequality:

x + 5 ≥ 0

x ≥ -5

For the second square root, the value under the square root must be non-negative, so we have the following inequality:

1 - x ≥ 0

x ≤ 1

Therefore, the expression is defined for all values of x that satisfy both of these inequalities. This means that the expression is defined for values of x in the range -5 ≤ x ≤ 1. The correct answer is therefore option D.

If the car goes to the top of spike's peak and back, the mileage of the car is 16 miles per gallon

The mileage of car in uphill = 12 miles per gallon

The mileage of car in downhill = 24  miles per gallon

The total distance traveled in up hill = 48 miles

The number of gallon of gas used = 48/12

= 4 gallon

The total distance traveled in down hill = 48 miles

The number of gallon of gas used = 48 / 24

= 2 gallon

Total distance traveled = 48 + 48

= 96 miles

Total number of gallons of gas = 4 + 2

= 6 gallon

The mileage = Total distance / The number of gallon

= 96 / 6

= 16 miles per gallon

Therefore, the mileage of the car is 16 miles per gallon

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D. x=12 and y=-8

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Given:

[tex]x+y=4\\2x+3y=0[/tex]

from first equation,

[tex]x=4-y[/tex]

substituting this value x in another equation,

[tex]2(4-y)+3y=0\\8-2y+3y=0\\y=-8[/tex]

putting this value of y in  [tex]x=4-y[/tex]

[tex]x=4-(-8)\\x=12[/tex]

hence D is the correct option.

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The cos(m) In the right triangle lmn is  19/20.

Complementary angles are formed when the total of two angles equals 90 degrees. 30 degrees and 60 degrees, for example, are complementary angles.

We have L + M = 90 because the angles L and M are complimentary.

Assuming that,

sin L = sin (90 - L) = sin M

sin (L) = 19/20.

As we know from our rule, the sine of angle L is equal to the cosine of L's complement, which is M.

This implies that the cosine of M is 19/20.

As a result, cos(M) equals 19/20.

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