PLEASE HELP QUICK

Use function notation to write the equation of the line.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The percentage at which the dress was sold from its original price is 28%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The selling price of the dress = $56

The original price of the dress = $200

The percentage at which the dress was sold from its original price.

= 56/200 x 100

= 56/2

= 28 %

Thus,

The percentage at which the dress was sold from its original price is 28%.

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The result of division of (x² - x - 12) by (x - 4) is (x + 3).

The given equation is;

(x² - x - 12) / (x - 4)

where, (x² - x - 12) is the numerator and (x - 4) is the denominator.

Find the factors of the numerator.

= (x - 4)(x + 3)/(x - 4)

Cancel the values (x - 4) from the numerator an denominator part.

= (x + 3)

Thus, the solution of the factorization is found as (x + 3).

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Answer:

4

Step-by-step explanation:

15-2x=7

8=2x

4=x

---

HOPE THIS HELPS <3

Answer:

x=11

Step-by-step explanation:

let us name the unknown number: x

15 - 2x = 7

collect like terms,

-2x= 7 - 15

-2x= - 8

divide both sides by -2( coefficient of x)

-2x = -8

__ __

-2 -2

x= 4

The inequality used to determine Jaya's maximum number of Gigabytes available for use, within her budget is 60.50 + 5x ≤ 75.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

Jaya pays a flat cost of $60.50 per month and $5 per gigabyte and  keep her bill under $75 per month.

According to given question we have

Let the cost of  gigabyte be x

flat cost =$60.50 per month

Budget=  $75 per month

i.e

60.50 + 5x ≤ 75

Therefore, the inequality used to determine Jaya's maximum number of Gigabytes available for use, within her budget is 60.50 + 5x ≤ 75.

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Answer:

Solution:  x < -2 or x > 3

Interval notation:  (-∞, -2) ∪ (3, ∞)

Step-by-step explanation:

Given inequality:

[tex]||2x-1|-2| > 3[/tex]

Apply the absolute rule:

[tex]\textsf{If $|u| > a$, $a > 0$ \;then \;$u > a$ \;or \;$u < -a$}.[/tex]

Therefore:

[tex]\textsf{Case 1}: \quad |2x-1|-2 > 3[/tex]

[tex]\textsf{Case 2}: \quad |2x-1|-2 < -3[/tex]

Solve each case independently.

Isolate the absolute value on one side of the equation:

[tex]\begin{aligned}\implies |2x-1|-2& > 3\\\implies |2x-1| & > 5 \end{aligned}[/tex]

Apply the absolute rule:

[tex]\textsf{If $|u| > a$, $a > 0$ \;then \;$u > a$ \;or \;$u < -a$}.[/tex]

[tex]\begin{aligned}\underline{\textsf{Equation 1}} & & \quad \quad\underline{\textsf{Equation 2}}\\2x-1 & > 5 & 2x-1 & < -5\\2x& > 6 & 2x& < -4\\x& > 3 & x& < -2\end{aligned}[/tex]

Therefore, x < -2 or x > 3.

Isolate the absolute value on one side of the equation:

[tex]\begin{aligned}\implies |2x-1|-2& < -3\\\implies |2x-1| & < -1 \end{aligned}[/tex]

As an absolute value cannot be less than zero, there is no solution for x∈R.

Solution:  x < -2 or x > 3

Interval notation:  (-∞, -2) ∪ (3, ∞)

Possible coordinates for points B  (-3, 13)

Given that

point A (5 , -7)

and there are 8 points between A and B.

The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.

The equation of a circle centerd in the point (x0, y0) is:

(x - x0)² + (y - y0)² = r²

where r = radius of the circle

So we can draw a circle of 8 units around A, and get:

(X - 5)² + (Y - (-7))² = 8²

So from this equation we can find all the possible values of B.

Y = √(8² - (X- 5)²) - 7

So for a given value of X, you can find the value of Y. where (8² - (X-5)²) can not be a negative number, so

8² ≥ (X - 5)²

So X = -3 (because (-3 - 5)² = 8²)

to X = 13 (because (13 - 5)² = 8²)

So X is in the range (-3, 13)

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The equation of the line that is perpendicular to the given line and that passes through the given points is x + 3y = 6

From the question, we are to determine the equation of the described line.

First,

We will determine the slope of the line that the equation was given.

The equation of the line is

y = 3x - 9

Comparing the equation to the general form of the equation of a straight line

y = mx + b

Where m is the slope

and b is the y-intercept

Thus,

By comparison,

m = 3

That is, the slope of the given line is 3

NOTE: Two lines are perpendicular if the product of their slope is -1.

That is,

m₁ × m₂ = -1

3 × m₂ = -1

m₂ = -1/3

The slope of the line that is perpendicular to the given line is -1/3.

We have that the line passes through the point (3, 1).

Then,

Using the point-slope form of the equation of a line

y - y₁ = m(x - x₁)

m = -1/3

x₁ = 3

y₁ = 1

Then,

y - 1 = -1/3(x - 3)

Multiply through by 3

3(y -1) = -1(x - 3)

3y - 3 = -x + 3

3y + x = 3 + 3

x + 3y = 6

Hence, the equation of the line that is perpendicular to the given line and that passes through the given point is x + 3y = 6

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Answer:The answer would be negative.

Step-by-step explanation:There is already a negative balance of -$25 and you would add $23.-25+23=-2.So therefore the answer would be negative.

Please give brainliest if answer is correct.

The period of the function is 48 minutes if the periodic function goes through 5 complete cycles in 4 min.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

A periodic function goes through 5 complete cycles in 4 min

From the question:

f = 5/4 cycles per minutes

f = 5/240 cycles per seconds  [1 minutes = 60 seconds]

f = 1/48

Period = 1/f

Period = 48 minutes

Thus, the period of the function is 48 minutes if the periodic function goes through 5 complete cycles in 4 min.

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The period of the given periodic function is 48 sec.

A periodic function is a function which returns same values at regular intervals. Let f be a periodic function then  

f( x +P ) = f(x) , for every x in the domain of f and P is some non zero constant

P is the regular interval or period after which a periodic function returns same values.

P=[tex]\frac{1}{f}[/tex]

where [tex]f[/tex] is the frequency of the periodic function

or [tex]f[/tex] = no of cycles per unit time

Given that a periodic function goes through 5 cycles in 4 min

therefore frequency for this periodic function , f  is given by

[tex]f=\frac{5}{4}[/tex] cycles per min

or

[tex]f=\frac{5}{4*60} \\f=\frac{5}{240} \\[/tex]

[tex]f=\frac{1}{48}[/tex]   cycles per sec

Thus,

Period of the given periodic function , P =[tex]\frac{1}{f}=1/\frac{1}{48}=48[/tex] sec

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APR, or effective annual rate, can also be called an effective annual rate or EAR when "r" is the annual interest rate and "n" is the number of compounding periods to be completed each year. :D

The length of the side of the equilateral triangle is 20.76 inches.

Here it is given that the length of the altitude of the equilateral triangle is 18 inches.

The formula of the altitude(h) of the equilateral triangle is

h = [tex]\frac{\sqrt{3} }{2}[/tex]a

Here a is the side of an equilateral triangle.

So we have

18 = [tex]\frac{\sqrt{3} }{2}[/tex]a

a = 18 × 2/[tex]\sqrt{3}[/tex]

For the rationalization of the fraction multiply numerator and denominator by [tex]\sqrt{3}[/tex].

a = [tex]\frac{18 * 2 * \sqrt{3} }{\sqrt{3}\sqrt{3} }[/tex]

  = [tex]\frac{18 * 2 * \sqrt{3} }{3}[/tex]

  = 6 × 2 × √3

  = 12×√3

  = 12 × 1.73

  = 20.76 inches

Therefore the length of the side of the triangle is 20.76 inches.

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Answer:

1/4, alternate forms are .25 and 2^-2

Step-by-step explanation:

Square Root of 25 is 5

6-5 =1

1/4

Answer:

y = 5x + 7

Step-by-step explanation:

I am guessing, but you are leaving something out.

y = the total cost.

x = the number of shirts.

Answer:

The total cost for the 7 shirts including tax is 7n + 6

Step-by-step explanation:

We want to find the Cost of 7 t-shirts and $6 tax.

Now, the let the cost of the 7 shirts be n. Thus, we can now say that cost of 7 shirts is 7n.

Now, since there is an additional cost of $6 for tax, we can now say that the total cost for the 7 shirts including tax is expressed as;

7n + 6

Thus, we conclude that the total cost for the 7 shirts including tax is 7n + 6

For given survey of 62 customers was taken at a bookstore regarding the types of books purchased,

a) The number of customers surveyed who purchased only science fiction = 9

b) The number of customers surveyed who purchased mysteries and science fiction, but not romance novels = 13

c) The number of customers surveyed who purchased mysteries or science fiction = 51

d) The number of customers surveyed who purchased mysteries or science fiction, but not romance novels = 46

e) The number of customers surveyed who purchased exactly two types of books = 2

In this question,

we have been given a survey of 62 customers was taken at a bookstore regarding the types of books purchased.

38 customers purchased mysteries,

31 purchased science fiction,

21 purchased romance novels,

18 purchased mysteries and science fiction,

12 purchased mysteries and romance novels,

9 purchased science fiction and romance novels,

and 5 purchased all three types of books.

Let S represents the set of customers who purchased science fiction books,

R represents the set of customers who purchased romance novels books and

M represents the set of customers who purchased mysteries books.

From given information,

n(S) = 31

n(R) = 21

n(M) = 38

n(M ∩ S) = 18

n(M ∩ R) = 12

n(S ∩ R) = 9

n(M ∩ R ∩ S) = 5

a) we need to find the number of customers surveyed who purchased only science fiction.

= n(S) - n(M ∩ S) - n(S ∩ R) - n(M ∩ R ∩ S)

= 31 - (18 - 5) - (9 - 5) - 5

= 31 - 13 - 4 - 5

= 9

b)  we need to find the number of customers surveyed who purchased mysteries and science fiction, but not romance novels

= n(M ∩ S) - n(M ∩ R ∩ S)

= 18 - 5

= 13

c) we need to find the number of customers surveyed who purchased mysteries or science fiction

n(M ∪ S) = n(M) + n(S) - n(M ∩ S)

              = 38 + 31 - 18

              = 51

d) we need to find the number of customers surveyed who purchased mysteries or science fiction, but not romance novels

= n(M ∪ S) - n(M ∩ R ∩ S)

= 51 - 5

= 46

e)  we need to find the number of customers surveyed who purchased exactly two types of books

=  n(M ∩ S) - n(S ∩ R) - n(M ∩ R)

= (18 - 5) - (9 - 5) - (12 - 5)

= 13 - 4 - 7

= 2

Therefore, for given survey of 62 customers was taken at a bookstore regarding the types of books purchased,

a) The number of customers surveyed who purchased only science fiction = 9

b) The number of customers surveyed who purchased mysteries and science fiction, but not romance novels = 13

c) The number of customers surveyed who purchased mysteries or science fiction = 51

d) The number of customers surveyed who purchased mysteries or science fiction, but not romance novels = 46

e) The number of customers surveyed who purchased exactly two types of books = 2

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Option number (4) i.e., (3+7)+2=3+(7+2)  illustrates the associative property of addition.

As per the question statement, we are supposed to identify the equation which illustrates the associative property of addition.

Before solving this, we should be aware about the concept of associative property of addition which states that rearranging the parentheses in an expression will not change the result i.e., a+(b+c) = (a+b)+c

Therefore using the above property, we conclude that option number (4) i.e., (3+7)+2=3+(7+2)  illustrates the associative property of addition.

As (3+7)+2=3+(7+2) can be written in the standard form a+(b+c)=(a+b)+c which is  a characteristic equation of associative property of addition.

      e.g.,  a+(b+c)=(a+b)+c OR a*(b*c)=(a*b)*c

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Thunder from a bolt of lightning can travel 1/5 miles in one second.

Given, distance = 1/10 mile and

time = 1/2 second .

we need to find distance travelled in one second.

The distance travelled by thunder bolt from lightning in one second can be calculated using unitary method. So, to calculate we will relate the known distance with given time. Further, we will compare it at with desired time.

So, distance travelled in 1/2 second = 1/10 mile

Hence, distance travelled in 1 second = 1/10 ₊ 1/10

Shifting 2 to the numerator and 10 to the denominator. The new fraction will be -

Distance travelled in 1 second = 2/10 = 1/5

Distance travelled in 1 second = 1/5 mile

Hence, thunder from a bolt of lightning can travel 1/5 miles in one second.

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Answer:

h = 0.01g

Step-by-step explanation:

[tex]{ \tt{g = kh + c}}[/tex]

When g is 0, h is 0 hence c is 0

[tex]{ \tt{g = kh}}[/tex]

when g is 1, h is 0.01

[tex]{ \tt{1 = 0.01k}} \\ { \tt{k = 100}} \\ { \boxed{ \tt{ equation \to \: {g = 100h}}}} \\ { \rm{or}} \\ { \boxed{ \tt{equation \to \: h = 0.01g}}}[/tex]

By applying direct proportion, the information should be filled in the table are as follows:

Number of containers                     Weight (in pounds)

4                                                               16,000

8                                                               32,000

10                                                              40,000

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a direct proportion can be represented the following equation:

y = kx

Where:

Since the boat carried containers that weigh 4000 pounds each, we would multiply each of containers by 4000 as follows:

Number of containers                     Weight (in pounds)

4                                                               16,000

8                                                               32,000

10                                                              40,000

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The temperature outside at night is 2 degrees.

One degree Celsius, for instance, is one-hundredth of the temperature difference between the point at which water changes state from solid to liquid to its gaseous stage. A degree can be defined as a fixed change in temperature measured against a specific scale.

Let's say the temperature outside is x.

Now, the initial temperature was - 17 degrees, then it rises to 9 degrees during the day before it drops 10 degrees at night.

So,

x = - 17 degrees

The temperature rises by 9 degrees.

Then,

x = - 17 degrees + 9 degrees

x = - 8 degrees

The temperature drops 10 degrees at night.

Then,

x = -8 degrees + 10 degrees

x = 2 degrees

Hence, the temperature at night is 2 degrees.

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The total amount that's is borrowed by Benjamin is $3.75.

It should be noted that from the information, Benjamin borrowed $0.75 from his friend cltyde five days last week to buy ice cream.

Therefore, the product will be:

= Amount borrowed × Number of times

= $0.75 × 5

= $3.75

The amount borrowed is $3.75.

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Answer:

2456x =

Step-by-step explanation:

Simple i know but you didnt really specify.

Answer: 4,912/2=2,456

Step-by-step explanation:hope it helps, brainliest? i could really use it

Let’s solve this step-by-step

First factor the equation,

(9x - 5) (4x - 5) = 0

Then set each factor equal to zero,

9x - 5 = 0 and 4x - 5 = 0

Both x = 5 / 9 or x = 5 / 4 are correct

The given function is exponential growth and the y-intercept is y=11.

Given that the given function is y=11(0.75)ˣ.

Exponential growth or decay describes the process of reducing or growing an amount by a consistent percentage rate over a period of time and it is represented by the function y=a(1-b)ˣ where, y is the final amount, a is the original amount and b is the growth or decay factor and x is the amount of time passed.

If a is positive and b is greater than 1 then it is exponential growth.

If a is positive and b is less than 1 but greater than 0 then it exponential decay.

The graph of the given function y=11(0.75)ˣ is shown in attached image.

From the graph, it is visible that the given function is an exponential growth because a is 11 and it is positive and it is greater than 1.

Now, we will find the y-intercept by substituting x=0, we get

y=11(0.75)⁰

y=11(1)

y=1

Hence, the given function or situation y=11(0.75)ˣ as an example of exponential growth and the y-intercept is 11.

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Answer: 11 and 26

Step-by-step explanation:

log (x + 4) = 8 => x =  [tex]10^8[/tex], by properties of logarithm.

Given:

log ( x + 4) = 8

Raising both sides by 10, in order to remove the logarithm.

=> [tex]10^{log_{10}(x+4)} = 10^{8}[/tex]

=> x + 4 = [tex]10^8[/tex] (as [tex]a^{log_a(x)} = x[/tex] )

=> x =  [tex]10^8[/tex] (as the value of  [tex]10^8[/tex] is so large, subtracting 4 from it won't make much difference).

Hence, log (x + 4) = 8 => x =  [tex]10^8[/tex], by properties of logarithm.

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If a student population of 1200 was estimated to increase by 15% in the next five years but the population actually increased by 20%, then the most estimated and actual student populations are equal to 1380 and 1440 students respectively, and the percent error is equal to 4.2%.

The estimated and actual student populations can be calculated as follows,

Estimated increase = 15% = 15 / 100 = 0.15

Initial population = 1200

0.15 × 1200 = 180

Estimated population in the next five years = 1200 + 180 = 1380

Actual increase = 20% = 20 / 100 = 0.2

Initial population = 1200

0.2 × 1200 = 240

Actual population in the next five years = 1200 + 240 = 1440

We can find the percentage error as follows,

percentage error = [(actual value - estimated value) / actual value] × 100

percentage error = [(1440 - 1380) / 1440] × 100

percentage error = [60 / 1440] × 100

percentage error = 0.042 × 100 = 4.2%

Hence the estimated and actual student populations is calculated to be 1380 and 1440 respectively and the percentage error is equal to 4.2%.

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Cost of 25 pound flour is $30.75.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Price of 3 pound flour = $3.69

She needs 25 pounds of flour to make enough cookies for a bake sale.

Now, Price of 3 pound flour = $3.69

Hence, Cost of 1 pound flour = $3.69 ÷ 3 = $1.23

So, Cost of 25 pound flour = 25 x $1.23

                                          = $30.75

Therefore, Cost of 25 pound flour is $30.75.

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Answer:

A. 69 strides per minute

Step-by-step explanation:

In order to find the strides per minute divide 759 by 11

➟ 759/11

➟ 69

∴ Her rate was 69 strides per minute