Write an equation of a parabola with the given information.
vertex (3,2) , focus (4,2)

y = x - 4 is an equation of the line in slope-intercept form passing through points (4 , 0) and (-3 , -7)

An equation of a line in slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept.

Given two points passed through by the line, you can use them to write the equation of the line in slope-intercept form.

1. Find the slope of the line using the two given points.

let Point 1(4 , 0) and Point 2(-3 , -7)

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

m = (-7 - 0) / (-3 - 4)

m = -7/-7

m = 1

2. Use the value of the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.

y = mx+ b

y = 1x + b

Using Point 1,

0 = 1(4) + b

b = -4

3. Write the equation of the line in slope-intercept form.

y = mx+ b

where m = 1 and b = -4

y = x - 4

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Ben joins a reading group. Each order costs him $12 for the book and $5 for postage and handling. A. Identify the variables that change and the variables that don't change in this issue. Identify the dependent and independent components of each quantity.

I can say that the price of the books is independent and the shipping and handling charges is dependent.

Given that Ben joins a book club.

Ben pays $12 for each book and $5 for shipping and handling charges for each order.

Shipping and handling quantities remain the same.

The amount he pays for each book quantities change every time so it is not constant.

Therefore, We can say that the price of the books is independent and the shipping and handling charges is dependent.

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Answer: c=5

Step-by-step explanation:

5(c-3)=10

5c-15=10

5c=10+15

5c=25

c=5

Answer:

5(c-3)=10

(c-3) =10-5

(c-3)=5

c=5+3

c=8

The coordinates of Z are (2,7).

What is coordinates in math?

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).

The formula to calculate the midpoint between two points is equal to

[tex]Y = ( \frac{(x_{1} + x_{2}) }{2} , (\frac{y_{1} + y{2} }{2} )[/tex]

we have

X(-10,9),Y(-4,8)

Let

(x2,y2) ----> the coordinates of Z

substitute the values

( -4.8) = ( -10 + x₂ /2 , 9 + y₂/2)

Solve for x2

-4 = ( -10 + x₂/2

-8 = -10 + x₂

x₂ = -8 + 10

x₂ = 2

Solve for y2

8 = (9 + y₂)/2

16 = 9 + y₂

y₂ = 16 - 9

y₂ = 7

therefore, The coordinates of Z are (2,7)

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The Cookie Shop's profit at the end of January due to the decrease was $12000

An equation is an expression that shows the relationship between two or more numbers and variables.

The Cookie Shop had a profit of $15,000. At the end of January, their profit had decreased by 20%. Hence:

Decrease in profit = 20% of $15000 = 0.2 * 15000 = $3000

Profit at end of January = $15000 - $3000 = $12000

The Cookie Shop's profit at the end of January due to the decrease was $12000

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Answer:

6 1/3

Step-by-step explanation:

Well 5 goes into 15 3 times because 5 * 3 = 15.

So the answer would be 1/3 for the fraction and 6 1/3 for the answer.

Answer:

6 1/3

Step-by-step explanation:

6 is already in its simplest form.

5/15 = 1/3

^ 5/15 is equivalent to 1/3

The require answers are,

Part a: The equation for the total cost of the calendars is C = 125 + 3.25*100 = 350

Part b: The model that gives the average cost A per calendar as a function of the number of calendars printed is A = 125 + 3.25x

Part c: The estimate number of calendars that must be sold before the average cost drops to $5 per calendar is 70.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now it is given that,

Cost of the digital images and the permission = $125

“one time” charges = $3.25

Part a: The equation for the total cost of the calendars

THere are 100 calendars printed.

So, “one time” charge = 3.25*100

So, the total cost of the calendars C is given as,

C = 125 + 3.25*100

C = 125 + 325 = 450

Thus, the equation for the total cost of the calendars is given as,

C = 125 + 3.25*100 = 450

Part b: The model that gives the average cost A per calendar as a function of the number of calendars printed

Let there are x calendars printed

Total “one time” charges = 3.25x

So, Average cost is given as,

A = 125 + 3.25x

this is the model that gives the average cost A per calendar

Part c: The estimate number of calendars that must be sold before the average cost drops to $5 per calendar

Now from the graph it must be seen that the average cost drops to $ 5 per calender at 70.

Thus, number of calendars that must be sold before the average cost drops to $5 per calendar = 70

Thus, the require answers are,

Part a: The equation for the total cost of the calendars is C = 125 + 3.25*100 = 350

Part b: The model that gives the average cost A per calendar as a function of the number of calendars printed is A = 125 + 3.25x

Part c: The estimate number of calendars that must be sold before the average cost drops to $5 per calendar is 70.

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$59 increase in her bank account during that week.

Any of the basic arithmetic operations—addition, subtraction, multiplication, division, raising to the power of a whole number, and taking roots (fractional power)—is considered an algebraic operation. These procedures could be applied to numerical data, in which case they are frequently referred to as arithmetic operations. Similar operations can be carried out on variables, algebraic expressions, and, more generally, on components of algebraic structures like groups and fields. Another way to describe an algebraic operation is as a function from the Cartesian power of a set to the same set.

Given that : Sheila made four withdrawals of each from an ATM. . She also made a $156 purchase with her check card. She then deposited her $375 salary.

It's difficult to determine the solution because we don't know how much money she had in her bank account before making 4 withdrawals, thus a like and rating would be really appreciated. We know she took out $40 four times, which is $160. She also used her card to make a $156 purchase, so when we sum the two amounts, we get $316. She then placed a check for $375 into the bank account, therefore we must deduct $316 from that sum to get at $59; but, since we deducted, Given that we end up with $59 rather than the money we wasted at the beginning, the fact that the price is higher than $316 indicates that there has been an increase.

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The coordinates of D' are D' = (-2, -4)

The given paramaters are

D = (2, 4)

The rule is given as

180 degrees about the origin.

This is represented as

(x, y) = (-x, -y)

So, we have

D' = (-2, -4)

Hence, the coordinates of D' are D' = (-2, -4)

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Answer:

21

Step-by-step explanation:

Answer:

The answer is -20

Step-by-step explanation:

This prblem calls for substitution. In this case, if a = 3 and b = -4, then

(3)²(-4) - (-4)²

Now we can solve using order of operations.

(9)(-4) + 16 << (two negatives make a positive)

-36 + 16

= -20

Hope this helps!

Answer: 0.75

Step-by-step explanation:

Negative one sixth times the quantity 3 minus 15 times the quantity one third squared end quantity end quantity will be C. negative two ninths

Based on the information given, the expression will be:

= 1/6 ×( 3 - 15 ) × (1/3)²

= -1/6 × -12 × 1/9

= -2 × 1/9

= -2/9

In conclusion, the correct option is D.

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The solution of given expression 12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y after evaluation is 14.5 .

The given expression is 12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y.

We have x = 2 and y = -2 as per the question.

To evaluate the expression, first we need to simplify the given expression and then we can substitute the given value of  x and y in simplified expression.

The given expression can be simplified as,

   12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y

⇒ 9x - (1/2)y - 3x - (3/4)y

⇒ 6x - ((1/2)+(3/4))y

On taking LCM of coefficient of y, we will get

6x - (5/4)y

Now on substituting x = 2 and y = -2, we get

6(2) - (5/4)(-2)

= 12 + (5/2)

= 29/2 = 14.5

The solution of given expression 12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y after evaluation is 14.5 .

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Answer:

Between -3 and -2, but closer to -2

Step-by-step explanation:

The square root of 45 is approximately 6.708.

Subtract 9 from that and you get -2.292.

-2.292 is between -3 and -2, but is closer to -2.

Answer:

See attached image.

Step-by-step explanation:

Substitute 1,2,3, or 4 for [tex]x[/tex]. Then calculate using the order described by PEMDAS.

Answer: 4

Step-by-step explanation: We can identify the number of significant digits by counting all the values starting from the 1st non-zero digit located on the left. For example, 12.45 has four significant digits.

Answer - 9,369 divided 53 = 176.773584906

a. The probability that a first number is 4 is 1/10

b. The probability that the second number is less than 8/10.

c. The probability that there will not be any zero's is 81/100

Given, a number generator produces two digits in a box, each of it is generated randomly from 0 to 9.

a. The probability that the first number is 4 = ?

probability of an event = favourable number of outcomes/ Total number of outcomes.

Total number of outcomes = 10

P(n) = 1/10

b. The probability that the second number is less than 8 = ?

probability of an event = favourable number of outcomes/ Total number of outcomes.

Total number of outcomes = 10

P(n) = 8/10

c. The probability that there are no zero's = ?

since there are two boxes, there is possibility of getting two zero's.

probability of an event = favourable number of outcomes/ Total number of outcomes.

9/10 × 9/10

= 81/100

Hence we get the required results.

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the plants height would be 69cm

The truth value of the statement "If you have a f e v e r, then you are s i c k." can be classified as T because it is true.

The truth value of the statement "You have a f e v e r, and you are not s i c k." can be classified as Fa l s e.

The definition of a truth value is the a t t r i b u t e of a p r o p o s i t i o n as to whether the p r o position is true or false.

For example, the truth value for "3 is odd" is true, which can be denoted as T. The truth value of "2 + 2 = 5" is false.

Now, it is well known that fever is a symptom of a s i c k n e s s. Thus, if you have f e v e r, then you are classified as being s i c k. Thus;

The truth value of the statement "If you have a fever, then you are s i c k." can be classified as T because it is true.

The truth value of the statement "You have a f e v e r, and you are not s i c k." can be classified as False

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Answer:

[tex]f^{-1}(x)=\dfrac{x}{\boxed{5}}+\boxed{3}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=5x-15[/tex]

An inverse function is a reflection of the function in the line y = x.

To find the inverse of the given function, replace f(x) with y to get an equation for y in terms of x:

[tex]\implies y=5x-15[/tex]

Rearrange the equation to make x the subject:

[tex]\implies y+15=5x-15+15[/tex]

[tex]\implies y+15=5x[/tex]

[tex]\implies 5x=y+15[/tex]

[tex]\implies \dfrac{5x}{5}=\dfrac{y}{5}+\dfrac{15}{5}[/tex]

[tex]\implies x=\dfrac{y}{5}+3[/tex]

Replace x with f⁻¹(x) and y with x. This is the inverse function:

[tex]\implies f^{-1}(x)=\dfrac{x}{5}+3[/tex]

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The Roebling Suspension Bridge extends over the Ohio River connecting Cincinnati, Ohio, to Covington, Kentucky,  the lines formed buy the bridge and the river is skew lines

Given,

The situation, the Roebling Suspension Bridge extends over the Ohio River connecting Cincinnati, Ohio, to Covington, Kentucky.

The line formed by the bride and the river that do not intersect and are not coplanar

So, those are skew lines

Hence, the Roebling Suspension Bridge extends over the Ohio River connecting Cincinnati, Ohio, to Covington, Kentucky,  the lines formed buy the bridge and the river is skew lines

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Answer:

A. $93.28

Step-by-step explanation:

The reason why is because 110 - 20% would leave you only paying 88 dollars. but when you add the 6% sales tax you get $93.28

The given sentence about polygon is true.

A statement is given in the question.

We have to tell whether the statement is true or false.

What is a polygon ?

A polygon is a two-dimensional geometric figure that has a finite number of sides i.e., triangle has three sides.

As per the question ;

The statement given is , "An included side is the side located between two consecutive angles of a polygon."

Let's check whether it is true or false ;

We know that ,

Included side is one which links two angles together.

For example in a right angle triangle ABC ;

Side (base) AC links two angles one a right angle at A and other angle at C.

So ,

We can conclude that the given statement is true i.e., an included side is located between two consecutive angles of a polygon.

Thus , the given statement about polygon is true.

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The value for  x = -2,0,1 , and 4 will be -9, -8, -15/2 and -6 respectively.

For x = -2

The value will be -

(1/2)x-8

(1/2)(-2) - 8

= -9

For x = 0

The value will be -

(1/2)x - 8

(1/2)(0) - 8

= -8

For x = 1

The value will be -

1/2(1) - 8

= -15/2

For x = 4

The value will be -

1/2(4) - 8

= -6

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At present, the age of the woman is 29 years, while the age of her daughter is 6 years.

In the question, we are given two characters, a woman and her daughter, and told to find their present age. We are also given some clues as to how we will arrive at the answer. Let's consider the first one.

In the first sentence, we are told that 5 years ago, the woman was 4 times as old as her daughter. We don't know the woman's age or her daughter's, so let's call the woman's present age x and her daughter's present age y for now. To know the age of the woman 5 years ago, we will subtract 5 from her current age, which will give us x - 5. Also, the woman was 4 times as old as her daughter 5 years ago, hence:

                                    x - 5 = 4y

If we rearrange that;      x = 4y + 5 (let's call this equation 1)

Now, on to the second clue.

In the second sentence, we are told that in four years time, the woman will be two and a half times as old as her daughter. The woman's age in 4 years time is x + 4, hence:

                                 x + 4 = 2[tex]\frac{1}{2}[/tex]y

                                 x + 4 = 5y/2

                                 2x + 8 = 5y (let's call this equation 2)

Next, we will find the value of y (the daughter's present age) by substituting equation 1 into equation 2, that is, putting '4y + 5' in place of x in equation 2, thus:

                            2(4y + 5) + 8 = 5y

                            8y + 10 + 8 = 5y

                            8y - 5y = 18

                             3y = 18

                              y = 6

Therefore, at present, the daughter is 6 years old. To find the mother's age, we will substitute the daughter's age in place of y in equation 1:

                        x = 4y + 5

                        x = 4(6) + 5 = 29

Hence, the woman is 29 years old, and her daughter is 6 years old.

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Answer:

1353.4 x 10^3

Step-by-step explanation:

(7.2 x 107) + (5.5 x 106) = 770.4 + 583 = 1353.4

Scientific Notation: 1353.4 = 1353.4 x 10^3

Answer: 1.3534x10^3

Step-by-step explanation:

(7.2 x 107) + (5.5 x 106) =6767/5 = 1353.4 =  1.3534x10^3

Answer:

400,000,000 or [tex]4*10^{8}m[/tex]

Step-by-step explanation:

Put them both into standard form.

[tex]0.0001=1*10^{-4} and 4 trillion is 4*10^{2}[/tex]

Multiply them together.

[tex](1*10^{-4})*(4*10^{12}=4*10^{8}[/tex]