The distance from a focus to a vertex on a graph of a parabola is not the same as the distance from vertex to a perpendicular point on the directrix.

False

True

The value of x for which the function f(x)=g(x)-2 is x = 1 and 2

A function can be defined as an equation, expression, rule or law showing the relationship between two variables.

These variables are;

The functions are given as;

For the function (x)=g(x)-2

Substitute the values, we get;

x² -2x - 1 = x - 1 - 2

collect like terms

x² - 2x - x = -3 + 1

add or subtract like terms

x² -3x + 2 = 0

x² - 2x - x + 2 = 0

(x² -2x) - (x + 2) = 0

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

Then,

x = 1 and 2

Hence, the values are 1 and 2

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The Congruent Triangles figure are attached below.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.

The following the Congruent properties:

Given:

1. ΔFUN and ΔCAR

If the both triangles are congruent then

FU = CA

UN = AR

NF = RC

and, <FUN = <CAR, <UNF = <ARC and <NFU = <RCA.

This is because Congruent Triangles have Corresponding Side and angles equal in length.

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Answer:

The difference in elevation between the mountain and the valley is 13,158 feet.

12,790 feet (mountain elevation) - (-368 feet (valley elevation)) = 13,158 feet

Step-by-step explanation:

If the home loan compounds 12 times per year, her interest rate (APR) is 24.764%.

The annual percentage rate (APR) is the yearly cost of borrowing.

The annual percentage rate (APR) is computed as the interest rate times the principal (balance).

The APR can be computed using an online finance calculator.

N (# of periods) = 12 years

PV (Present Value) = $72,000

PMT (Periodic Payment) = $0

FV (Future Value) = $-92000

Results:

I/Y = 24.764% if interest compound 12 times per year (APR)

I/Y = 27.778% if interest compounds once per year (APY)

I/period = 2.064% interest per period

Total Interest  = $20,000.00

Thus, Alexa's interest rate (APR) for the 12-year loan of $72,000 for which she paid an extra $20,000 is 24.764%.

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Answer:

Can you answer mine? I need help too

Step-by-step explanation:

Answer:

X = -50

Y = -30

Step-by-step explanation:

To find the value of Y and X, we can solve a system of equations. One way to do this is by substitution.

From the first equation:

10 + 5Y = X

We can substitute the value of X from the second equation:

10 + 5Y = 40 + 10Y

Then, we can subtract 10Y from both sides:

10 = 40 + Y

Finally, we can subtract 10 from both sides:

Y = -30

Now that we have the value of Y, we can substitute it back into either equation to find the value of X:

X = 10 + 5Y

X = 10 + 5(-30)

X = -50

So the solution is:

X = -50

Y = -30

Answer:

(x,y)=(-20,-6)

Step-by-step explanation:

On solving the provided question we can say that to plot data - dread = $0.16; Turkey = $1.24; Cheese = $0.30

The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables. Diagrams created by hand or on a computer are also acceptable. Move 2 units to the right after starting at the origin before going 3 units up. The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points. The pink dot with the letter P thus stands for 2.3. Before creating a line chart, you need first generate a number line for each value in your data collection. Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.

to plot data -

dread = $0.16

Turkey = $1.24

Cheese = $0.30

Lettuce = $0.06

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The "net asset value" is used to compute both entry load as well as exit load as a percentage.

Entry load is the sum of money or fee that an investor must pay to join a scheme or a company as an investment.

Exit loads are fees or amounts collected from investors for quitting a plan or a corporation as a shareholder.

Thus, the "net asset value" is used to compute both entry load as well as exit load as a percentage.

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Based on the equation that models the company's profit as P = 4x - 10,000, if 5,000 units are sold, the company's profit is $10,000.

The profit equation shows the difference between the revenue and the costs during a financial period.

The revenue is a product of the units sold and the number of units.

Profit, P = 4x - 10,000

Number of units sold = x

If 5,000 units are sold:

The profit = $10,000 (4 x 5,000 - 10,000)

Check:

Total revenue = $20,000 (4 x 5,000)

Unit selling price = $4

Number of units sold = 5,000

Total costs = $10,000

Thus, using the profit equation, the company generated a profit of $10,000 from selling 5,000 floats for children.

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Answer:

true because i guessed and got it right trust me

Therefore , the solution to the given problem of composite number comes out to be Since Morgan's claim regarding Composite Numbers is true, we can infer that he is right.

Prime numbers can really be expressed as the sum of two different numbers. The sum of two or more numbers is what is referred to as a composite number. Examples of prime numbers include 2,3,5,71,11 since they only have two factors, one and itself. Examples of composite numbers include 4,6,8,10,12 since they contain more than two contributing variables.

Here,

we can see Morgan's claim that any numbers with a 2 in the place of a one are composite numbers.

We can conclude that Morgan is correct given the prior description of composite numbers by stating that all numbers with a 2 in the place of a one are composite numbers.

In actuality, any even integer—aside from 2—is a composite number.

Therefore , the solution to the given problem of composite number comes out to be Since Morgan's claim regarding Composite Numbers is true, we can infer that he is right.

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When the bargain was 40% off the standard price, the cost of the kayak trip for one adult was $53.40.

A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.

given

Shawn spent $267 on five persons,

$267 / five equals $53 (or 40%, or 40/100, or two out of five),

= $ 53.

When the bargain was 40% off the standard price, the cost of the kayak trip for one adult was $53.40.

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Answer:

B

Step-by-step explanation:

Irrational numbers are real numbers that cannot be written as a ratio of integers. They have decimal expansions that neither terminate nor become periodic.

Example: π , √2 , √3 are irrational numbers.

Negative 1 (StartFraction x over 4 EndFraction) + three-fourths 12 StartFraction negative x + 3 over 4 EndFraction = 12One-fourth (x + 3) = 12 is the equivalent equation.

An equation is a mathematical statement that two expressions are equal. It consists of two expressions separated by an equal sign (=). Equations are used to describe relationships between unknown values, such as the relationship between the circumference and diameter of a circle. Equations can also be used to solve for unknown values, such as the area of a triangle.

These three equations are equivalent to Negative one-fourth (x) + three-fourths = 12. The first equation is the original equation, while the second and third equations are equivalent forms of the original equation. In the second equation, the negative one-fourth (x) has been moved to the other side of the equation, and in the third equation, the negative one-fourth (x) has been multiplied by one-fourth.

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After 1 year Charles will earn $187 more kelvin

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

The interest rate of Kelvin's investment is 2.6% anually.

The interest rate of Charles' investment is 4.3% anually

The amount received by kelvin = 11000 + 11000× 2.6/100

= 11000+ 286 = $11286

The amount received by Charles = 11000 + 11000× 4.3/100

= 11000+ 473 = $11473

The difference in what Charles earn and kelvin earn is = 11473 - 11286 = $187

Therefore Charles will earn $187 more than kelvin

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The required equation -3x + 3y = 6 can pair with x - y= -2 to create a consistent and dependent system.

The equation is given in the question, as follows:

x - y = - 2

First, we have to convert the standard form of the equation to slope-intercept form.

As per the question, we have

x - y = -2

Subtract x from both sides of the equation,

x - y - x = -2 - x

- y = -2 - x

Divide -1 by both sides of the equation,

y = x + 2

Comparing it with the slope-intercept form y = mx + b, we get

Slope m = 1, y intercept b = 2

Considering option (B),

-3x + 3y = 6

Add 3x on both sides of the equation,

-3x + 3x + 3y = 6 + 3x

3y = 3x + 6

Divide both sides by 3 of the equation,

y = x + 2

Comparing the slope-intercept form

m = 1 and y-intercept = 2

Hence, the correct answer would be an option (C).

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The table that represents the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery used will be:

Cream cheese Cheesecake

1. 11

2. 22

3. 33

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, the bakery can make 44 cheesecakes for every 4 blocks of cream cheese. This will be Illustrated as:

= 44 / 4

= 11 cheesecake per cheese.

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The unit for the amount of time Emily paints is months

The total number of paintings after she completes the class will be 23

The number of paintings after five months will be 19

Number of paintings in her collection after six months will be 20

The variable for the amount of time Emily paints and the expression for the number of paintings is 14 + t

Since the time frame mentioned in the scenario is in months, the unit for the amount of time Emily paints is "months."

She already has fourteen (14) paintings, and she makes one (1) per month, after she completes the nine-month class, Emily will have 14 + 9 = 23 paintings in her collection.

After five months, Emily will have 14 + 5 = 19 paintings in her collection.

After six months, Emily will have 14 + 6 = 20 paintings in her collection.

Let t be the number of months that Emily paints. The number of paintings in her collection after t months is 14 + t.

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Answer:

your answer is d

Step-by-step explanation:

have a nice day.

The question is a word problem, where; the amount of money Alex has is the same as the amount Monte will have if he gives Alex $12, and the amount of money Monte will have will be twice the amount with Alex if he receives $6 from Alex, indicating that the amount of money Alex has is $30, while the amount of money with Monte is $54.

A word problem is a verbal presentation of a mathematical or science question, using words and sentences, rather than numbers and symbols, and for which the solution is found mathematically, or by using standard scientific steps.

Let x represent the amount of money Alex has, and let y represent the amount of money Monte has, we get;

x + 12 = y - 12...(1)

2·x = y + 6...(2)

Adding 12 to both sides of equation (1), we get;

x + 12 + 12 = y - 12 + 12

x + 24 = y - 0 = y

x + 24 = y

y = x + 24

Plugging in the value of y into equation (2), we get;

2·x = y + 6

2·x = x + 24 + 6 = x + 30

2·x = x + 30

Subtracting x from both sides of the above equation, we get;

2·x - x = x + 30 - x

x = x - x + 30 = 0 + 30

x = 30

The amount of money Alex has, x = $30

y = x + 24

Therefore; y = 30 + 24 = 54

The amount of money Monte has, y = $54

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Answer: $2.25

Step-by-step explanation:

We are required to find the cost per kilometer of Emmanuel.

   The cost per kilometre is $2.25 OR $2 and 25cents.

According to the question, the total cost of the journey = $32

The total distance covered during the journey =

14 2/9 km

Therefore, the cost per kilometre can be evaluated mathematically as follows;

Cost per kilometer = cost of the journey ÷ Distance of the journey

= 32 ÷ 14 2/9

By converting 14 2/9 to an improper fraction; we have;

   = 32 ÷ 128 / 9

   = 32 × 9/128

   = (32×9) / 128

   = 288 / 128

   = 2 32/128

   = 2.25 dollar per kilometer

Therefore, the cost per kilometer is $2.25

The width of the cake is 54 inches

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

The above parameters mean that

Length = 18

Width = 3 * Length

So, we have

n = 3 * length

substitute the known values in the above equation, so, we have the following representation

n = 3 * 18

Evaluate

n = 54

Hence, the width is 54 inches

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Complete question

Gilda's sponge cake is three times as long as it is wide. The sponge cake is 18 inches long. Use n to represent the cake's width.

Determine the width of the cake

The width of the cake which is represented as n would be = 54 inches

The length of the sponge cake that is owned by Gilda = 18 in.

The width of the sponge cake owned by Gilda (n) = 3( length)

That is;

n = 3( 18)

n = 54 inches.

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The store location for which  % of the data lies between $19,371.18 and $22.295.48 is location C

You should be aware that Standard deviation explains the relation of data with mean.

For normal distributions, 68% of the data lies under one SD from the mean. Two standard deviations is within  95%, and three standard deviations would take up to 99%.

This implies that on taking (mean + SD) and (mean - SD), 68% of data would cover these two numbers.

Add and subtract SD from the mean to check which location will give $19,371.18 and $22.295.48.

For location A, we have

M-SD=23,124.70-1553.43=21,571.27

M SD = 23,124.70 + 1,553.43 = 24,678.4

For location B, we have

M - SD = 24,842.18 - 1,617.20 = 23,224.98

M + SD = 24, 842.18 + 1,617.20 = 26,459.38

For location C, we have

M - SD = 20,833.33 - 1,462.15 = 19,371.18

M + SD = 20,833.33 + 1,462.15 = 22,295.48

This implies the store location is C

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Correct question:

The owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. She calculated the mean and standard deviation of the monthly profit, in dollars, for each location, as shown in the table.

For which store location does 68% of the data lie between $19,371.18 and $22,295.48?

If the owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. The location that 68% of the data lie between $19,371.18 and $22,295.48 is: A. Location C.

Location A:

Mean -Standard Deviation

=23,124.70-1553.43

=21,571.27

Mean + Standard Deviation  

= 23,124.70 + 1,553.43

= 24,678.4

Location B:

Mean -Standard Deviation = 24,842.18 - 1,617.20

Mean -Standard Deviation  = 23,224.98

Mean + Standard Deviation  

= 24, 842.18 + 1,617.20

= 26,459.38

Location C:

Mean - Standard Deviation  

= 20,833.33 - 1,462.15

= 19,371.18

Mean + Standard Deviation  

= 20,833.33 + 1,462.15

= 22,295.48

Therefore the correct option is C.

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The complete question is:

The owner of a chain of clothing stores is comparing the monthly profit earned in the past year from four different store locations. She calculated the mean and standard deviation of the monthly profit, in dollars, for each location, as shown in the table.

Location A Location B Location C Location D

Mean = 23,124.70

SD = 1,553.43 Mean = 24,842.18

SD = 1,617.20 Mean = 20,833.33

SD = 1,462.15 Mean = 21,432.82

SD = 1,512.10

For which store location does 68% of the data lie between $19,371.18 and $22,295.48?

We plotted the inequality given in question as a solid line in the graph.

In mathematics, graph of inequality means graphical representation of unequal comparison regarding an expression. Inequality having ≤ and ≥

sign is shown as a solid line. Other inequality while plotting is shown as a dotted line.

we are given an inequality x≤ - 3y

As per the rules of solving an inequality, we need to start with an isolated variable from the left side.

we notice, x is located on the left side.

the value of x must be less than or equal to -3 y. So, the graph of the inequality is located on the negative X coordinate, and it is a straight solid line. We know, the sign ≤ or ≥ indicates that inequality of the graph will be a solid line.

if we look at the graph given in question, we find that the line is drawn as a dotted line but we have less than or equal sign. So, the graph is needed to correct.

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Answer:

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

Solve each equation.

1)

2)

3)

Answer:

11x-10

Step-by-step explanation:

3x+8x-10............

The correct graph is the last one, positive at the left,  and positive at the right, when x is positive.

A relation from set A to set B is a function if every element of set Aonly one image in set B.It is a subset of A×B.The set of elements in Athat are plugged into the function  is called the domain. The set of images of the elements in A, a subset of B is called the range of the function f.

Here,

Given : Let's analyze our function, first we know that the parent cubic function:

We want to see which one of the given graphs is the graph of the function: f(x) = (1/2)*x^3

g(x) = x^3

Is positive for positive values of x and positive for positive values of x, then the graph is below the horizontal axis at the left, and above the horizontal axis at the right.

The graph below the horizontal Axis at left and above the horizontal axis at the right.

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The solution of the inequality in set-builder notation is {d I d ≤ 7}.

The correct option is A.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality,

7 - 3d ≥ 28.

To solve the inequality:

Simplifying,

-3d ≥ 28 - 7

-3d  ≥ 21

-d  ≥ 7

d ≤ 7.

Therefore, the solution is {d I d ≤ 7}.

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Using the Fundamental Counting Theorem, it is found that for each case, the total number of outcomes is:

a) 60,466,176.

b) 5,961,600.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with n1, n2, ...  ways to be done, each thing independent of the other, the number of ways they can be done is N=n1*n2*n3*....

Item a:

No restrictions, hence, for each of the five characters, there are 36 outcomes, hence n1=n5=36.

Then, the possible number of passwords is:

N=36^5=60,466,176

Item b:

The letters and the digits have to be alternated, hence:

Starting with a letter n1=n3=n5=36, n2=n4=10.

Starting with a digit n1=n3=n5=10, n2=n4=36.

Then, the possible number of passwords is:

N=36^3*10^2+10^3*36^2=5,961,600.

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Answer:

A - The exponent of 3 is 7/9.

Step-by-step explanation:

The expression 3^(7/9) can be read as "3 to the power of 7/9".
This means that the number 3 is being multiplied by itself 7/9 times.

For example
3^(2/3) can be written as cube root of 3, cube root of 3 is equal to 3^(1/3) .

When the exponent of an expression is a fraction, it can be written in radical form, with the denominator of the fraction as the index of the radical. However, it's not true in this case as the index is not 9 but 7.

So, the correct answer is A - The exponent of 3 is 7/9.