Three friends pay $1,025 to rent a vacation home. Beth contributed $80 more than Danny. Katie contributed $20 less than Beth. How much did Danny contribute?

y coordinate of midpoint of line AB is 6

Solution:

Given that endpoints of line AB is (10, 14) and (4, -2)

To find:  y-coordinate of the midpoint of line AB

The midpoint of line AB is given as:

For a containing [tex]A(x_1, y_1)[/tex] and [tex]B(x_2, y_2)[/tex] the midpoint is given as:

[tex]M(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]

Here in this question,

[tex]\left(x_{1}, y_{1}\right)=(10,14) \text { and }\left(x_{2}, y_{2}\right)=(4,-2)[/tex]

So midpoint is:

[tex]\begin{aligned}&M(x, y)=\left(\frac{10+4}{2}, \frac{14-2}{2}\right)\\\\&M(x, y)=\left(\frac{14}{2}, \frac{12}{2}\right)\\\\&M(x, y)=(7,6)\end{aligned}[/tex]

Therefore y coordinate of midpoint of line AB is 6

Answer:

Fourth degree polynomial (aka: quartic)

====================================================

Work Shown:

There isnt much work to show here because we can use the fundamental theorem of algebra. The fundamental theorem of algebra states that the number of roots is directly equal to the degree. So if we have 4 roots, then the degree is 4. This is assuming that there are no complex or imaginary roots.

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

If you want to show more work, then you would effectively expand out the polynomial

(x-m)(x-n)(x-p)(x-q)

where

m = 4, n = 2, p = sqrt(2), q = -sqrt(2)

are the four roots in question

(x-m)(x-n)(x-p)(x-q)

(x-4)(x-2)(x-sqrt(2))(x-(-sqrt(2)))

(x-4)(x-2)(x-sqrt(2))(x+sqrt(2))

(x^2-6x+8)(x^2 - 2)

(x^2-2)(x^2-6x+8)

x^2(x^2-6x+8) - 2(x^2-6x+8)

x^4-6x^3+8x^2 - 2x^2 + 12x - 16

x^4 - 6x^3 + 6x^2 + 12x - 16

We end up with a 4th degree polynomial since the largest exponent is 4.

Option A

Interest rate paid by Samantha to bank is 8.6 %

Solution:

Given that George has a credit score of 650

Samantha has a credit score of 520

The bank approved George’s loan application at 5.6% interest

To find: Interest rate paid by samantha to the bank

From given information in question,

Interest charged on Samantha’s loan is 3 percentage points higher than the interest rate on George’s loan

Thus we get,

Interest charged on Samantha’s loan = 3 percentage points higher than the interest rate on George’s loan

Interest charged on Samantha’s loan = 3 % higher than the interest rate on George’s loan

Interest charged on Samantha’s loan = 3 % + interest rate on George’s loan

Thus substituting the given George’s loan application at 5.6% interest,

Interest charged on Samantha’s loan = 3 % + 5.6 % = 8.6 %

Thus interest rate paid by samantha to bank is 8.6 %

Final answer:

Option A: 8.6%

Samantha will pay an interest rate of 8.6% on her loan from Westside Bank, which is 3 percentage points higher than George's rate of 5.6% due to her lower credit score.

Explanation:

The question involves calculating the interest rate Samantha will pay to the bank for a personal loan.

Given that George has a credit score of 650 and was approved for a loan at 5.6% interest, and Samantha has a lower credit score of 520, her interest rate will be 3 percentage points higher than George's.

To find Samantha's interest rate, we simply add 3 percentage points to George's rate of 5.6%.

Samantha's interest rate = George's interest rate + 3%
Samantha's interest rate = 5.6% + 3%
Samantha's interest rate = 8.6%

Answer:the number of miles that Henry traveled is 15

Step-by-step explanation:

Let m represent the number of miles travelled.

City Cab charges a flat fee of $3 plus 0.50 per mile. This means that the total amount that city Cab charges for m miles would be

3 + 0.5m

Henry paid $10.50 for a cab ride across town.

The equation representing Henry's cab ride would be

3 + 0.50m = 10.50

Subtracting 3 from both sides of the equation, it becomes

3 - 3 + 0.50m = 10.50 - 3

0.5m = 7.5

m = 7.5/0.5 = 15 miles

Answer: the lowest commission is $163.96

Step-by-step explanation:

Let x represent the lowest monthly commission that a salesman earned.

Let y represent the highest monthly commission that a salesman earned.

The lowest monthly commission that a salesman earned was only 1/5 more than 1/4 as high as the highest commission he earned. This means that

x = y/4 + 1/5 - - - - - - - - 1

The highest and lowest commissions when added together equal $819. This means that

x + y = 819

x = 819 - y - - - - - - -2

Substituting equation 2 into 1, it becomes

819 - y = y/4 + 1/5

Multiplying through by 20, it becomes

16380 - 20y = 5y + 4

25y = 16380 - 4 = 16376

y = 16376/25 = 655.04

x = 819 - 655.04 = 163.96

Answer:

Answer C: Becky is 27; John is 31

Step-by-step explanation:

1. John is 4 years older than Becky--27(Becky's age)+ 4=31(John's age)

2. Sum of their ages is 58--27(Becky's age)+31(John's age)=58

So, the correct answer is Answer C.

Answer:

C. Becky is 27; John is 31

I think 68 or56

It can't be 34 that would be less, 146 would be over quarter

Good evening ,

Answer:

Step-by-step explanation:

measure arc AB = 2×(m∠AXB) = 2×(34) = 68°.

:)

Answer: $116,000

Step-by-step explanation:

The net operating income will be the operation profit after deducting the expenses from the accrued revenue (reserve exclusive)

The revenue generated are $215,000 + $3,000

= $218,000

Expenses incurred;

$102,000

The net operating income = $218,000 - $102,000

= $116,000

Note that reserves is not used in business operation. Therefore it cannot be regarded either as revenue or expenses.

Answer:

he rank from least to great based on their axis of symmetry:

0, 1, -3 ⇒ g(x), h(x), f(x)

So, option C is correct.

Step-by-step explanation:

A quadratic equation is given by:

[tex]ax^2+bx+c =0[/tex]

Here, a, b and c are termed as coefficients and x being the variable.

Axis of symmetry can be obtained using the formula

[tex]x = \frac{-b}{2a}[/tex]

Identification of a, b and c in f(x), g(x) and h(x) can be obtained as follows:

[tex]f(x) = x^2 + 6x - 1[/tex]

⇒ a = 1, b = 6 and c = -1

[tex]g(x) = -x^2 + 2[/tex]

⇒ a = -1, b = 0 and c = 2

[tex]h(x) = 2^2 - 4x + 3[/tex]

⇒ a = 2, b = -4 and c = 3

So, axis of symmetry in [tex]f(x) = x^2 + 6x - 1[/tex] will be:

[tex]x = \frac{-b}{2a}[/tex]

x = -6/2(1) = -3

and axis of symmetry in [tex]g(x) = -x^2 + 2[/tex] will be:

[tex]x = \frac{-b}{2a}[/tex]

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

and axis of symmetry in [tex]h(x) = 2^2 - 4x + 3[/tex] will be:

[tex]x = \frac{-b}{2a}[/tex]

x = -(-4)/2(2) = 1

So, the rank from least to great based on their axis of symmetry:

0, 1, -3 ⇒ g(x), h(x), f(x)

So, option C is correct.

Keywords: axis of symmetry, functions

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Answer:the greatest number of pieces that can be cut is 2

Step-by-step explanation:

The total length of ribbon available is 3/4 meter. Sunday needs pieces measuring 1/3 meter for their project. This means that each length needed would be exactly 1/3 meter.

The number of pieces measuring 1/3 meter that can be cut from the ribbon would be

(3/4)/(1/3) = 3/4×3/1 = 9/4 = 2.25

Since the length needed is exactly 1/3 meter, the greatest number of pieces that can be cut will be 2

A. x²-14x+49; is a polynomial

Step-by-step explanation:

(x-7)² can be written as (x-7)(x-7)

Expanding the expression

x(x-7)-7(x-7)

x²-7x-7x+49

x²-14x+49 ⇒⇒A quadratic function, which is a polynomial of degree 2

This function demonstrates the closer property of multiplication in that the change in order of multiplication does not change the product. This is called commutative property.

(x-7)(x-7)

-7(x-7)+x(x-7)

-7x+49+x²-7x

x²-14x+49

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Answer:

A is correct

Step-by-step explanation:

I took the test and got it right

Answer: second option.

Step-by-step explanation:

In order to solve this exercise, it is necessary to remember the following properties of logarithms:

[tex]1)\ ln(p)^m=m*ln(p)\\\\2)\ ln(e)=1[/tex]

In this case you have the following inequality:

[tex]e^x>14[/tex]

So you need to solve for the variable "x".

The steps to do it are below:

1. You need to apply [tex]ln[/tex] to both sides of the inequality:

[tex]ln(e)^x>ln(14)[/tex]

2. Now you must apply the properties shown before:

[tex](x)ln(e)>ln(14)\\\\(x)(1)>2.63906\\\\x>2.63906[/tex]

3. Then, rounding to the nearest ten-thousandth, you get:

[tex]x>2.6391[/tex]

Answer:

3.8 [tex]in^{2}[/tex]

Step-by-step explanation:

We are given a square of size 6x6 in. So, area of this square is equal to 6 x 6 = 36 [tex]in^{2}[/tex]. Now, the shaded region is [tex]\frac{1}{2}[/tex] x (Area of square - area of semicircles)

The diameter of both semicircles = side of the square = 6in

So, radius (r) = [tex]\frac{1}{2}[/tex] x diameter = [tex]\frac{1}{2}[/tex] x 6 = 3in

And hence, area of semicircle is  = [tex]\frac{1}{2}[/tex] x π[tex]r^{2}[/tex]

= [tex]\frac{1}{2}[/tex] x π[tex]3^{2}[/tex]

Since, there are two semicircles we multiply above by 2, so area of both semicircles = 2 x [tex]\frac{1}{2}[/tex] π[tex]3^{2}[/tex] = 9π

Area of shaded region =  [tex]\frac{1}{2}[/tex] (36 - 9π) = 3.8628 = 3.8 [tex]in^{2}[/tex] to the nearest tenth.

Answer:

After 4 miles driven by cab the amount would be same in both cities.

Step-by-step explanation:

Let the number of miles be 'x'.

Given:

In NYC

Flat fee of cab = $4

Per mile charge = $1.25

Total cab charges is equal to sum of Flat fee of cab and per mile charge multiplied by number of miles.

Framing in equation form we get;

Total cab charges in NYC = [tex]4+1.25x[/tex]

In Chicago

Flat fee of cab = $6

Per mile charge = $0.75

Total cab charges is equal to sum of Flat fee of cab and per mile charge multiplied by number of miles.

Framing in equation form we get;

Total cab charges in Chicago = [tex]6+0.75x[/tex]

Now we need to find number of miles driven so that the amount could same in both cities.

Total cab charges in NYC = Total cab charges in Chicago

[tex]4+1.25x=6+0.75x[/tex]

Combining like terms we get;

[tex]1.25x-0.75x=6-4\\\\0.5x=2[/tex]

using Division Property we will divide both side by 0.5 we get;

[tex]\frac{0.5x}{0.5} =\frac{2}{0.5} \\\\x=4[/tex]

Hence After 4 miles driven by cab the amount would be same in both cities.

Answer:

Base of triangle is 9 inches and altitude of triangle is 14 inches.

Step-by-step explanation:

Given:

Area of Triangle = 63 sq. in.

Let base of the triangle be 'b'.

Let altitude of triangle be 'a'.

Now according to question;

altitude is 5 inches longer than the base.

hence equation can be framed as;

[tex]a=b+5[/tex]

Now we know that Area of triangle is half times base and altitude.

Hence we get;

[tex]\frac{1}{2} \times b \times a =\textrm{Area of Triangle}[/tex]

Substituting the values we get;

[tex]\frac{1}{2} \times b \times (b+5) =63\\\\b(b+5)=63\times2\\\\b^2+5b=126\\\\b^2+5b-126=0[/tex]

Now finding the roots for given equation we get;

[tex]b^2+14b-9b-126=0\\\\b(b+14)-9(b+14)=0\\\\(b+14)(b-9)=0[/tex]

Hence there are 2 values of b[tex]b-9 = 0\\b=9\\\\b+14=0\\b=-14[/tex]

Since base of triangle cannot be negative hence we can say [tex]b=9\ inches[/tex]

So Base of triangle = 9 inches.

Altitude = 5 + base  = 5 + 9 = 14 in.

Hence Base of triangle is 9 inches and altitude of triangle is 14 inches.

Answer: 5/7

Step-by-step explanation:please see attachment for explanation.

Answer:

Y=4x^5-12x^4+6x and y=5x^3-2x

Answer:

Y = 4x5 - 12x4 + 6x

Y = 5x3 - 2x

Step-by-step explanation:

Answer:

  1 cm : 800 km   or   1/80,000,000

Step-by-step explanation:

A model or map scale is often expressed as ...

  (1 unit of A on the model) : (N units of B in the real world)

We're given the relative measurements as ...

  15 cm : 12,000 km

Dividing by 15 gives the unit ratio as above:

  1 cm : 800 km

__

A scale can also be expressed as a unitless fraction. To find that, we need to convert the units of both parts of this ratio to the same unit.

  0.01 m : 800,000 m

Multiplying by 100, we get ...

  1 m : 80,000,000 m

Since the units are the same, they aren't needed, and we can write the scale factor as ...

  1 : 80,000,000   or   1/80,000,000

Answer:

  2 1/2 cups

Step-by-step explanation:

5 × (1/2 cup) = 5/2 cup = 2 1/2 cup

__

Or, you can add them up. You know from your study of fractions that two half-cups make 1 cup.

  (1/2 cup) + (1/2 cup) + (1/2 cup) + (1/2 cup) + (1/2 cup)

  = ((1/2 cup) +(1/2 cup)) +((1/2 cup) +(1/2 cup)) +(1/2 cup)

  = (1 cup) + (1 cup) + (1/2 cup)

  = (2 cup) + (1/2 cup)

  = 2 1/2 cup

Answer:

Step-by-step explanation:

k = 6

To find the value of k, rationalize the denominator of 2/√3, and compare it with 2k/3 to find k = √3.

To rationalize the denominator of the fraction 2/√3, we need to make the denominator a rational number. We can do this by multiplying both the numerator and the denominator by √3.

So, after rationalizing, the fraction becomes 2√3/3. According to the problem statement, this is equivalent to 2k/3.

Therefore, we can equate 2k to 2√3:

2k = 2√3

k = √3

So, the value of k is √3.

The complete question is

When the denominator of 2/√3 is rationalized ,it becomes 2k/3​. Find k

Answer:

  36 square feet

Step-by-step explanation:

The area of one barrier is the product of the given dimensions:

  (9 ft)(2 ft) = 18 ft²

Two such barriers will have twice the area: 36 ft².

The combined area of the two barriers is calculated by multiplying the length by the height for each barrier to get an area for each one, and then those two areas are added together. Each barrier has an area of 18 square feet, so the total combined area is 36 square feet.

The question is asking for the combined area of two barriers, each being 9 feet long and 2 feet high. In order to find this, we must multiply the length by the height for each barrier, and then add these two areas together. The calculation would look like this:

Area of each barrier = Length x Height = 9 ft x 2 ft = 18 square feet

Now, since there are two barriers:

Combined Area = 2 x Area of each barrier = 2 x 18 square feet = 36 square feet

Therefore, the combined area of the two barriers is 36 square feet.

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Answer:16 days

Step-by-step explanation:

Given

John schedule is 4 Workdays and 5 th day off i.e. John take holiday at the 5 th day

Ling Work for 7 day and then took off on 8 th and 9 th day

i.e. after every 8 th and 9 th day he take off

So to find out common day off we nee take LCM of

i)5 and 8

ii)5 and 9

LCM(5,8)=40 i.e. after every 40 th day they had same day off

and there are 8 such days in 365 days

LCM(5,9)=45 i.e. after every 45 day they had same day off

and there are total of 8 days in 365 days

therefore there are total of 16 days in total out of 365 days

By computing the LCM of their work schedules, John and Ling will have the same day off 8 times during their first year of work.

This problem can be approached using the concept of Least Common Multiple (LCM) which is widely used in mathematics to solve similar problems. Here we need to calculate the frequency of John and Ling's common days off.

John's schedule repeats every 5 days (4 workdays followed by 1 day off) and Ling's schedule repeats every 9 days (7 workdays followed by 2 days off). To know how often they both have a day off on the same day, we need to find the LCM of 5 and 9. Interestingly, since 5 and 9 are prime to each other, their LCM will be their product, which is 45. Therefore, John and Ling will have a day off together every 45 days.

To know how many such days will be there in a year, divide 365 by 45 which equals 8.111. Since the number of days cannot be fractional, we take only the whole number part which is 8. So, during the first year of their work (365 days), John and Ling will have the same day off on 8 days.

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The equation of parabola is expressed as: y² = -20x

What is the equation of the parabola?

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.

The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

Given, vertex = (0, 0)

Focus = (-5, 0)

We have to find the equation of the parabola.

The equation is of the form y = -ax²

Directrix x = 5.

As every point on parabola is equidistant from focus and directrix, the equation will be

y² + (x + 5)² = (x - 5)²

y² + x² + 10x + 25 = x² - 10x + 25

y² = - 10x - 10x

y² = -20x

Therefore, the equation of parabola is y² = -20x

Answer:

The number of child tickets sold was 36

Step-by-step explanation:

The complete question is

At the city museum, child admission is $5.80 and adult admission is $9.30. On Monday, four times as many adult tickets as child tickets were sold, for a total sales of $1548.00. How many child tickets were sold that day?

Let

x ----> the number of child tickets sold

y ----> the number of adult tickets sold

we know that

[tex]5.80x+9.30y=1,548.00[/tex] ---> equation A

[tex]y=4x[/tex] ----> equation B

Solve by substitution

Substitute equation B in equation A    

[tex]5.80x+9.30(4x)=1,548.00[/tex]

solve for x

[tex]5.80x+37.2x=1,548.00[/tex]

[tex]43x=1,548.00[/tex]

[tex]x=36[/tex]

therefore

The number of child tickets sold was 36

Answer:

The sample space for one spin of this game is: S = {00, 0, 1, 2, 3,…, 40}

Step-by-step explanation:

Consider the provided information.

In probability theory, the set of all possible outcomes or outcomes of that experiment is the sample space of an experiment or random trial. Using set notation, a sample space is usually denoted and the possible ordered outcomes are identified as elements in the set.

Here the possible number of elements in the set are 00, 0, 1, 2,...,40

The sample space is anything the ball can land on.

Thus, the sample space for one spin of this game is: S = {00, 0, 1, 2, 3,…, 40}

Answer:

No, the student is not right as his statement is against central limit theorem.

Step-by-step explanation:

Central Limit Theorem:

This theorem states that if we take large samples of a population which has a mean and standard deviation then mean samples will have a normal distribution.

Answer:

Part 12) [tex]Center\ (2,-3),r=2\ units, (x-2)^2+(y+3)^2=4[/tex]

Part 13) [tex]m\angle ABC=47^o[/tex]

Step-by-step explanation:

Part 12) we know that

The equation of a circle in center-radius form is equal to

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where

(h,k) is the center of the circle

r is the radius of the circle

In this problem

Looking at the graph

The center is the [tex]point\ (2,-3)[/tex]

The radius is [tex]r=2\ units[/tex]

substitute in the expression above

[tex](x-2)^2+(y+3)^2=2^2[/tex]

[tex](x-2)^2+(y+3)^2=4[/tex]

Part 13) we know that

The measure of the external angle is the semi-difference of the arcs it covers.

so

[tex]m\angle ABC=\frac{1}{2}[arc\ DE-arc\ AC][/tex]

we have

[tex]arc\ DE=142^o[/tex]

[tex]arc\ AC=48^o[/tex]

[tex]m\angle ABC=\frac{1}{2}[142^o-48^o][/tex]

[tex]m\angle ABC=47^o[/tex]

To evaluate the expression 2(4 - 1)^2, multiply 2 by the square of the result of subtracting 1 from 4, resulting in 18.

To evaluate the expression 2(4 - 1)^2, we need to follow the order of operations, also known as PEMDAS. First, we evaluate the expression within the parentheses: 4 - 1 = 3. This gives us 2(3)^2. Next, we calculate the exponential expression: 3^2 = 9. Finally, we multiply 2 by 9, which gives us the final result of 18.

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Answer:

13

Step-by-step explanation:

The diagonals of a rectangle are congruent.

Answer:

24 times

Step-by-step explanation:

Given:

Number of cups required = 6 cups

Measuring cup capacity = [tex]\frac{1}{4}=0.25[/tex] of a cup.

Now, each time the measuring cup fills 0.25 of a cup.

So, we use unitary method to find the number of times the measuring cup has to be used to get a total of 6 cups.

∵ 0.25 cups = 1 time the measuring cup being used.

∴ 1 cup = [tex]\frac{1}{0.25}=4[/tex] times the measuring cup being used.

So, 6 cups = [tex]4\times 6=24[/tex] times the measuring cup being used.

Hence, the number of times the measuring cup has to be used to get 6 cups of flour is 24 times.