Caitlin went to the store to buy school clothes .She had a store credit from from a previous return in the amount of $39.58 if she bought 4 of the same style shirt in different colors and spent atotal of $52.22 after the store credit was taken off her total, what was the price of each shirt she bought?

Answer: 118.40, 300, $18,000

Step-by-step explanation:

a) p(x) = [tex]-\frac{1}{5} (8) + 120[/tex]

   p(8) =  [tex]-\frac{8}{5} + 120[/tex]

          = -1.60 + 120

          = 118.40

b) R(x) = x * p(x)

         = [tex]x(-\frac{1}{5}x + 120)[/tex]

         = [tex]-\frac{1}{5}x^{2} + 120x[/tex]

           a=[tex]-\frac{1}{5}[/tex], b=120

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

  = [tex]\frac{-120}{-\frac{2}{5}}[/tex]

  = [tex]\frac{-120(5)}{-2}[/tex]

  = 300

c)  R(x) = [tex]-\frac{1}{5}x^{2} + 120x[/tex]

R(300) = [tex]-\frac{1}{5}(300)^{2} + 120(300)[/tex]

           = -18,000 + 36,000

           = 18,000

***********************************************************************

sec θ = [tex]\sqrt{6}[/tex]

[tex]\frac{hypotenuse}{adjacent} = \frac{\sqrt{6}}{1}[/tex]

adjacent² + opposite² = hypotenuse²

      1²       + opposite² =      (√6)²

      1         + opposite² =        6

                   opposite² =        5

                   opposite =        √5

csc θ = [tex]\frac{hypotenuse}{opposite} = \frac{\sqrt{6}}{\sqrt{5}} = \frac{\sqrt{30}}{5}[/tex]

cot θ = [tex]\frac{adjacent}{opposite} = \frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5}[/tex]

sin θ = [tex]\frac{opposite}{hypotenuse} = \frac{\sqrt{5}}{\sqrt{6}} = \frac{\sqrt{30}}{6}[/tex]

cos θ = [tex]\frac{adjacent}{hypotenuse} = \frac{1}{\sqrt{6}} = \frac{\sqrt{6}}{6}[/tex]

tan θ = [tex]\frac{opposite}{adjacent} = \frac{\sqrt{5}}{1} = \sqrt{5}[/tex]

**********************************************************************

Answer: 144°

Step-by-step explanation:

[tex]\frac{\pi}{180}=\frac{4\pi}{5(x)}[/tex]

π(5x) = 180(4π)

    x   = [tex]\frac{180(4\pi)}{5\pi}[/tex]

         = 36(4)

         = 144

[tex]\text{The domain}\\\\x\neq0\ \wedge\ x\neq-2\ \wedge\ x\neq2[/tex]

[tex]\dfrac{5}{x^2-4}+\dfrac{2}{x}=\dfrac{2}{x-2}\qquad\text{subtract}\ \dfrac{2}{x-2}\ \text{from obth sides}\\\\\dfrac{5}{x^2-2^2}+\dfrac{2}{x}-\dfrac{2}{x-2}=0\\\\\dfrac{5}{(x-2)(x+2)}+\dfrac{2}{x}-\dfrac{2}{x-2}=0\\\\\dfrac{5x}{x(x-2)(x+2)}+\dfrac{2(x-2)(x+2)}{x(x-2)(x+2)}-\dfrac{2x(x+2)}{x(x-2)(x+2)}=0\\\\\dfrac{5x+2(x^2-4)-2x(x+2)}{x(x-2)(x+2)}=0\\\\\dfrac{5x+2x^2-8-2x^2-4x}{x(x-2)(x+2)}=0\\\\\dfrac{x-8}{x(x-2)(x+2)}=0\iff x-8=0\to\boxed{x=8}\in D[/tex]

Answer:

The simplified form of the given expression is 6-a.

Step-by-step explanation:

The given expression is

[tex](3-a)\cdot 2+a[/tex]

According to distributive property.

[tex]a\cdot (b+c)=ab+ac[/tex]

Use distributive property.

[tex]3(2)-a(2)+a[/tex]

[tex]6-2a+a[/tex]

Combine like terms.

[tex]6+(-2a+a)[/tex]

[tex]6-a[/tex]

Therefore the simplified form of the given expression is 6-a.

Answer:

15?

Step-by-step explanation:

If Binu is 15, in 5 years they will be 20. And if Banu is 20 years older, in 5 years they will be 40 (becuase 15 + 20 = 35 and then + the 5 years) Thats twice Binu's age. So Binu is 15 I would assume?

Final answer:

The total cost can be expressed as 5t + 10p or (5t) + (5 × 2p), representing the combined cost of five movie tickets and twice the amount of popcorn boxes for each of the five family members.

Explanation:

The total amount Xander's family spent on movie tickets and popcorn can be expressed with two different algebraic expressions. The cost for one family member is the cost of one ticket plus the cost of two boxes of popcorn. Since there are five members in the family, we multiply the cost of one person by five.

The first expression is 5t + 10p, which represents the cost of five tickets (5t) and ten boxes of popcorn (2 boxes per person), therefore, 5 times 2 boxes of popcorn (10p).

An alternative expression is (5t) + (5 × 2p), which explicitly shows the cost of five tickets (5t) plus the cost of two boxes of popcorn for each of the five members (5 × 2p).

Answer:

[tex]x>-3[/tex]

Step-by-step explanation:

To solve equations, we use inverse operations. Normally, we use PEMDAS to simplify an equation. To solve it, we use the inverse of each in this order SADMEP. Solving an inequality is the same except for step. When dividing by a negative, the sign of the inequality changes.

We have [tex]5x+7>2(x-1)\\5x+7>2x-2[/tex] in simplified form. We begin by subtracting or adding constants across the equal sign. Then doing the same with the variable terms. We finish by dividing by the coefficient of the variable term.

[tex]5x+7>2x-2\\5x+7-7>2x-2-7\\5x>2x-9\\5x-2x>2x-2x-9\\3x>-9\\x>-3[/tex]

To graph, we draw a number line, draw an open circle at -3.

Since it is not equal to, we do not fill it in. We leave it open. We also draw an arrow to the right of -3

Answer:

y=0.5x-2

Step-by-step explanation:

if it is perpendicular to the line y=-2x-6, then you know that its slope is the negative reciprocal of that line, and it has a different y intercept which you need to solve for using the point given. You solve by plugging in the x and y values from the point and plugging in the slope into the standard equation, and solving for b, the y intercept

y=0.5x+b

1=0.5(6)+b

1=3+b

-2=b

The equation of the line that passes through the point (6, 1) and is perpendicular to the line whose equation is y=−2x−6  is y = 0.5x - 2.

From the classic definition of straight lines, we know that if we have to find an equation of a straight line being perpendicular to another straight line then the slope of the new equation of straight lines becomes negative reciprocal of the slope of given perpendicular line.

Mathematically, let m1 be the slope of the new straight line and m be the slope of the given perpendicular line, then we have

m1 = -(1/m)

Now, we have given equation y = -2x - 6

Thus slope of the required equation is say (m1) = -(-1/2) = 0.5

Thus the equation formed is y = (m1)x + c [where c is the y-intercept]

∴ y = 0.5x + c

The point given is (6,1) , thus y = 1 and x = 6

Thus the given equation can be formed as

⇒ 1 =  0.5*6 + c

∴  c = 1 - 0.5*6 = -2

The value of y-intercept of the required straight line is -2

The equation of straight line formed is y = 0.5x - 2.

Thus the equation of the line that passes through the point (6, 1) and is perpendicular to the line whose equation is y = − 2x − 6  is y = 0.5x - 2.

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Assuming what is meant by "infinite solutions" are infinite number of solutions of a logarithmic equation.  

[tex]\frac{1}{2}\log x^2 - \log \sqrt{x} - \log \sqrt{x} = 0[/tex]

and

[tex]\frac{1}{2}x-2\ln e^x=-\frac{3}{2}x[/tex]

Logarithmic equations with infinite solutions have graphs that look like dying-out exponentials. They can have infinite solutions because there are infinitely many values of y that satisfy the equation.

Examples of Logarithmic Equations with Infinite Solutions:
1. Logarithms to the base 10 (common logarithms):

In the equations below, y is the exponent to which 10 must be raised to equal x, so y is the common logarithm (log) of x.
x = 10^y
x = 10^y+1

2. Logarithms to the base e (natural logarithms):

In the equations below, y is the power to which e must be raised to equal x, so y is the natural logarithm (ln) of x.
x = e^y
x = e^y+1

Both of these equations have graphs that look like dying-out exponentials. They have infinite solutions because there are infinitely many values of y that satisfy the equation. Whenever the base is positive and not equal to 1, logarithmic equations can have infinite solutions.

Answer:

[tex]y=3x[/tex]

y=57, when x is 19.

Step-by-step explanation:

We are asked to write an equation of variation where y varies directly as x.

Since we know that a directly proportional equation is in form: [tex]y=kx[/tex], where k is the constant of proportionality.

Upon substituting x=5 and y= 15 in our equation of variation we will get,

[tex]15=k*5[/tex]

[tex]k=\frac{15}{5}[/tex]

[tex]k=3[/tex]

Upon substituting k=3 in the standard equation of variation we will get our desired equation of variation as: [tex]y=3x[/tex].

Now let us find y, when x is 19.

[tex]y=3*19[/tex]

[tex]y=57[/tex]

Therefore, y equals 57, when x is 19.

Answer:

The answer is BD is the bisector angle

Answer: (d-21) represent in this context

The number of days the book is late

Step-by-step explanation:

The expression represents the amount of total money. Then the total late fee Camilla owes will be $2.1.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

Camilla borrows a book from the library for d days.

The library charges a late fee 0.10 dollars per day that the book is late.

If Camilla returns the book more than 21 days after she borrowed it.

Then the expression will be 0.10d.

The total amount is given as

Total amount = 0.10 d

Total amount = 0.10 x 21

Total amount = $2.1

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The width of the rectangular strip of land is 2/3 miles whose the width of the rectangular strip of land is 2/3 miles.

To find the width of the rectangular strip of land, we can use the formula for the area of a rectangle, which is:

Area = Length × Width

Given that the length of the rectangular strip of land is 3/4 miles and the area is 1/2 square mile, we can plug these values into the formula and solve for the width (W):

Area = 1/2 square mile

Length = 3/4 miles

1/2 = (3/4) × Width

To solve for the width (W), divide both sides by 3/4:

Width = (1/2) ÷ (3/4)

When dividing by a fraction, you can multiply by its reciprocal:

Width = (1/2) × (4/3)

Now, multiply the numerators and denominators:

Width = 4/6

The fraction 4/6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:

Width = 2/3

So, the width of the rectangular strip of land is 2/3 miles.

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Answer:

Domain: [tex]( -\infty,\infty )[/tex] and Range: [tex][ -1,\infty )[/tex]

Step-by-step explanation:

We have the parametric equations [tex]x= 2t[/tex] and [tex]y=t^{2}+t+3[/tex].

Now, we will find the values of 'x' and 'y' for different values of 't'.

t                       :   -3       -2.5     -2     -1.5     -1     0       1      1.5      2

[tex]x= 2t[/tex]             :   -6       -5       -4       -3      -2    0      2      3        4

[tex]y=t^{2}+t+3[/tex]  :    9       6.75     5     3.75     3    3      5     6.75     9

Now, we can see that these parametric equations represents a parabola.

The general form of the parabola is [tex]y=ax^{2}+bx+c[/tex].

Now, we have the point ( x,y ) = ( 0,3 ). This gives that c = 3.

Also, we have the points ( x,y ) = ( -2,3 ) and ( 2,5 ). Substituting these in the general form gives us,

4a - 2b + 3 = 3 → 4a - 2b = 0 → b = 2a.

4a + 2b + 3 = 5 → 4a + 2b = 2 → 2a + b = 1 →  2a + 2a = 1 ( As, b = 2a ) → 4a = 1 → [tex]a=\frac{1}{4}[/tex].

So, [tex]b=\frac{1}{2}[/tex].

Therefore, the equation of the parabola obtained is [tex]y=\frac{x^{2}}{4}+\frac{x}{2}+3[/tex].

The graph of this function is given below and we can see from the graph that domain contains all real numbers and the range is [tex]y\geq -1[/tex].

Hence, in the interval form we get,

Domain is [tex]( -\infty,\infty )[/tex] and Range is [tex][ -1,\infty )[/tex]

Answer:

Domain:

[tex](-\infty,\infty)[/tex]

Range:

[tex][2.75,\infty)[/tex]

Step-by-step explanation:

we are given parametric equation as

[tex]x=2t[/tex]

[tex]y=t^2+t+3[/tex]

We can change into rectangular equation

we can eliminate t from first equation and plug into second equation

[tex]x=2t[/tex]

[tex]t=\frac{x}{2}[/tex]

now, we can plug that into second equation

[tex]y=(\frac{x}{2})^2+\frac{x}{2}+3[/tex]

now, we can draw graph

Domain:

we know that

domain is all possible values of x for which any function is defined

we can see that our equation is parabolic

and it is defined for all values of x

so, domain will be

[tex](-\infty,\infty)[/tex]

Range:

we know that

range is all possible values of y

we can see that

smallest y-value is 2.75

so, range will be

[tex][2.75,\infty)[/tex]

Answer:

52

Step-by-step explanation:

One way is to simply count the number of yellow squares.

I count 52, so the area is 52 square units.

Another way is to find the area of the larger rectangle and subtract from it the area of the smaller rectangle.

The larger rectangle is 11 by 6. Area = 11 * 6 = 66.

The smaller rectangle is 7 by 2. Area 7 * 2 = 14.

Area shaded in yellow = 66 = 14 = 52

Answer: area = 52 square units

Answer:

"i cant do math cuz im pretty" such pick me vibes LOL

Step-by-step explanation:

Answer:

r=0.6

Step-by-step explanation:

Consider geometric sequence

[tex]b_1=6,\\ \\b_2=3.6,\\ \\b_3=2.16,\\ \\b_4=1.296,...[/tex]

In geometric sequence

[tex]b_i=b_{i-1}\cdot r,[/tex]

then

[tex]b_2=b_1\cdot r[/tex]

and

[tex]3.6=6r,\ r=\dfrac{3.6}{6}=0.6.[/tex]

Note that

[tex]2.16=3.6\cdot 0.6,\\ \\1.296=2.16\cdot 0.6.[/tex]

This means that ratio r=0.6.

Answer:

x = 1.3472 to the nearest ten thousandth.

Step-by-step explanation:

14^x + 1 = 36

14^x = 35

Taking logarithms:-

x ln 14 = ln 35

x = ln 35 / ln 14

= 1.3472.

The solution, rounded to the nearest ten-thousandth, is x = 1.5404.

To solve the equation [tex]14^x + 1 = 36[/tex], we first isolate the exponential term by subtracting 1 from both sides of the equation, which gives us [tex]14^x = 35.[/tex]

The next step is to take the logarithm of both sides of the equation.

We could use any base for the logarithm, but it's common to use base 10 or the natural logarithm base (e). In this case, let's use the natural logarithm:

[tex]ln(14^x) = ln(35)[/tex]

We can then use the property of logarithms which allows us to bring the exponent down as a multiplier:

[tex]x * times ln(14) = ln(35)[/tex]

Now, you can solve for x by dividing both sides by ln(14):

[tex]x = ln(35) / ln(14)[/tex]

Using a calculator, we find the quotient and then round to the nearest ten-thousandth:

x = 1.5404

This value is the solution to the original equation.

Answer:

852 miles

Step-by-step explanation:

We presume the speed is constant, so the satellite will travel 3/8 the distance in 3/8 the time.

... d = (3/8)·(2272 miles) = 852 miles

_____

1 minute is 1/8 of 8 minutes, so 3 minutes is 3/8 of 8 minutes.

Answer:

200 adults

Step-by-step explanation:

We can set-up a system of equations to find the number of adults. We know children and adults attended. We will let c be the number of children and a be the number of adults. Since 200 people attended, then c+a=200.

We also know they made $800 and adult tickets cost $4 and child tickets cost $2. We can write 2c+4a=800.

We will solve by substituting one equation into the other. We start by solving the first equation for c. c+a=200 becomes c=200-a.

Now we substitute c=200-a into 2c+4a=800. Simplify and isolate the variable a.

This means that 200 adults attended and 0 children attended.

Answer:

Function formula P(t) = -52t +480

Step-by-step explanation:

here, P(t) denotes the number of pages to read and t represents the time in hour.

Given the statement: Shryia read a 480-page-long book cover to cover in a single session, at a constant rate. After reading for 1.5 hours, she had 402 pages left to read.

⇒Total number of page in a long book = 480

After reading for 1.5 hours, she had 402 pages left to read.

Then,

Total number of page Shryia read in 1.5 hours is:

[tex]480-402 = 78[/tex]

Constant rate at which she is reading her book = [tex]\frac{78}{1.5} = 52[/tex] page per hour

Then, the function formula is given by:

P(t) = -52t + 480 ;  where t is in hours.

Check:

P(t) = -52t + 480

P(1.5) = -52(1.5) + 480 = -78 + 480 = 402     True.

Answer:8

Step-by-step explanation:6%3=2

4x2=8

I swear its 8 check if i'm wrong I dare you

Answer:

84°

Step-by-step explanation:

2 complementary angles sum to 90°

let x be the angle then complement = x - 78, hence

x + x - 78 = 90 ( add 78 to both sides )

2x = 168 ( divide both sides by 2 )

x = 84

hence the angle is 84°

Answer:

25 miles

Step-by-step explanation:

[tex]\frac{6}{40} :\frac{3.75}{y} \\y=25[/tex]

Answer: In the question, 3.75 miles is equal to 6 kilometers (that's rounding in a real life situation. It would actually be about 3.72... but who cares?! :)). So, if you divide 3.75/6... you get 0.625. Now, you multiply 40 by 0.625. After so, you get 25. 40 kilometers is equal to 25 miles!

Answer:

3746148

Step-by-step explanation:

i know you probably just want the answer but hear me out it is just simple math and can be resolved with a quick search. Find or search 1.8% of 3,381,000 and multiply it times the years progressed.

60858 x 6 = 3746148

Final answer:

Using the exponential growth formula, the approximate population of Henderson City in the year 2000 is calculated to be around 3,769,706 if the annual growth rate remains constant at 1.8%.

Explanation:

To calculate the approximate population of Henderson City in the year 2000, we can use the formula for exponential growth. The formula is
[tex]A = P(1 + r)^t[/tex]

where A is the amount of the final population, P is the initial population, r is the growth rate expressed as a decimal, and t is the time in years. In this case:

So the equation becomes:

A =[tex]3,381,000(1 + 0.018)^6[/tex]

Calculating this gives us the approximate population, A:

A ≈[tex]3,381,000(1.018)^6[/tex]

A ≈ 3,381,000(1.1155)

A ≈ 3,769,706

Therefore, the approximate population of Henderson City in the year 2000 would be 3,769,706 residents if the growth rate remains constant at 1.8%.

Ava must work 43.5 more hours in order to save the rest of the money

Money is any item that generally accepted as payment for goods and services and repayment of debts, such as taxes, in a particular country or socio-economic context. In math, it can be defined as the medium of exchange such as notes, coins, and demand deposits, to pay for commodities and services.

If you're self-employed, it's unwise  to work more than 40 hours a week on a regular basis because, you'll get a burst of productivity, the extra hours have diminished returns over time and within any time period.

Ava is saving for A new computer that cost 1218 she has already saved half of the money

[tex]\frac{1218 }{2} = 609[/tex]  $, hence  she has already saved half of the money ($609), so  she needs $609

Ava earns $14 per hour

Hence [tex]\frac{609}{14} = 43.5[/tex] hours

Ava must work 43.5 more hours in order to save the rest of the money

Hope it helps!

Grade:  5

Subject:  math

Chapter:  hours

Keywords:  hours, money, saved, order, Ava

Answer: Census.

Step-by-step explanation:

Given statement:- A research study is done to find the average age of all U.S. factory workers. The researchers asked every factory worker in Ohio what their birth year is.

This research is an example of a census because research in which information is obtained through the responses that all available members of an entire population give to questions.

In other words "Census is an official survey of population in a certain area and records various details about the individuals".

The study querying every factory worker in Ohio for their birth year to determine the average age of all U.S. factory workers is a census, as it attempts to gather data from every member of the entire population of interest. (First option)

The research study done to find the average age of all U.S. factory workers where the researchers asked every factory worker in Ohio their birth year is an example of a census. A census involves gathering information about every individual in the entire population of interest.

In this case, the population of interest would be all factory workers, and by querying every one of them (assuming it was indeed every single factory worker in Ohio), it constitutes a census, not a survey, which typically involves a representative sample.

It is not a convenience sample since that would imply a non-random selection based on ease of access, and it's not a simple random sample because not all members of the larger population (nationwide factory workers) have an equal chance of being included.

Answer:

28 degrees

Step-by-step explanation:

180 = 10x + 5 + 65 because they are supplementary. x = 11.

Angle 2 = 180 - (Angle 1 + (4x - 7))

Angle 2 = 180 - ((180 - 65) + 4x - 7)

Angle 2 = 180 - (115 + 4x - 7)

Angle 2 = 180 - 152

Angle 2 = 28 degrees

Answer:

See attachment.

Step-by-step explanation:

The main part of the function is an absolute value function and so it forms a V with the center of the V at (0,0). The sides of the V go up and over 1 unit at a time. However, since 2 is added to the it outside of the absolute value, the center of the V moves from (0,0) to (0,2). The sides stay the same. The division by 2 changes the sides. The sides move from up and over 1 unit to up 1 unit and over two units. It spreads or widens the graph. Lastly, the interval selects a specific part of the graph only from 0 to 6 on the x-axis. This takes just one side of the V and looks like a line segment. See attachment.

Answer:

We are given a function,

[tex]y=\frac{|x|+2}{2}[/tex]    if 0 ≤ x < 6

We need to draw the graph of the function.

We know that Parent function of the given function is Modulus function | x |.

Consider given function,

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

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

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

So, the given function is translated 1 unit upward and compressed by factor of 1/2.

So the obtained graph is attached.

Answer:

the answer is a

Step-by-step explanation: