The Outdoor Furniture Center buys wooden benches for $50 each. The owner of the Outdoor Furniture Center sells the benches for a 120% markup. At the end of the season, the owner wants to sells all the benches that are in stock. He sells the benches for 20% off.

What is the total price of a bench with the 20% discount plus a 5% sales tax?

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Answer:

x = 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define equation

4x - 1 = 7x - 16

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 19 does indeed equal 19.

∴ x = 5 is a solution to the equation.

Answer:

4x−1=7x−16

Step 1: Subtract 7x from both sides.

4x−1−7x=7x−16−7x

−3x−1=−16

Step 2: Add 1 to both sides.

−3x−1+1=−16+1

−3x=−15

Step 3: Divide both sides by -3.

−3x

−3

=

−15

−3

x=5

Step-by-step explanation:

Given:

[tex]y=\dfrac{3}{4}x[/tex]

[tex]y=\dfrac{1}{2}x-6[/tex]

To find:

Whether the above functions are proportional or non-proportional?

Solution:

If y is proportional to x, then

[tex]y\propto x[/tex]

[tex]y=kx[/tex]

where, k is constant of proportionality.

The proportional relationships are in the form of  [tex]y=kx[/tex] and they passes through (0,0).

Putting x=0 and y=0 in the given equations.

[tex]y=\dfrac{3}{4}x[/tex]

[tex]0=\dfrac{3}{4}(0)[/tex]

[tex]0=0[/tex]

It is a true statement.

[tex]y=\dfrac{1}{2}x-6[/tex]

[tex]0=\dfrac{1}{2}(0)-6[/tex]

[tex]0=0-6[/tex]

[tex]0=-6[/tex]

It is a false statement.

Therefore, [tex]y=\dfrac{3}{4}x[/tex] is proportional and [tex]y=\dfrac{1}{2}x-6[/tex] is non-proportional.

The interval notation for the solution to the given inequality is:

(6,∞).

The inequality is solved similarly to an equality, applying the operations to isolate the variable.

For this problem, the inequality is given by:

3(3a - 6) > 12.

Dividing both sides by 3:

3a - 6 > 12.

Then:

3a > 18

a > 18/3

a > 6.

In interval notation, the solution is:

(6,∞).

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Answer:

B. 0.75

Step-by-step explanation:

this is what I think cuz the graph at 1 is 0.75

I think the answer would be A because 5% ×100=0.05 , and in the question they have been telling us that it decreased by 5 from the last week so the equation would be g of the last week - 0.05

Answer:

Width of walkway = 3.71625 feet

Step-by-step explanation:

Let the width of the walkway be w. Then the length of entire area of the pool including the walkway is 32 + 2w and the breadth of the entire walkway is 16 + 2w since there is a width of w on both sides of length and breadth

Total Area of pool with pathway
(16+ 2w)(32+2w) = 924

Using the FOIL method we can expand the term on the left as follows:
= [tex]\sf 16\cdot \:32+16\cdot \:2w+2w\cdot \:32+2w\cdot \:2w[/tex]

= [tex]\sf 512+96w+4w^2[/tex]

Rearrange terms to get
[tex]\sf 4w^2 + 96w + 512[/tex]

So we get
[tex]\sf 4w^2 + 96w + 512 = 924[/tex]

Subtract 924 from both sides
[tex]\sf 4w^2 + 96w + 512 - 924 = 0[/tex]

==> [tex]\sf 4w^2 + 96w -412 = 0[/tex]

This is a quadratic equation of the form [tex]\sf ax^2 + bx + c[/tex] whose roots(solutions) are
[tex]\displaystyle \sf x_{1,\:2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here a = 4, b = 96 and c = -412

Plugging in these values we get
[tex]\sf w_{1,\:2}=\dfrac{-96\pm \sqrt{96^2-4\cdot \:4\left(-412\right)}}{2\cdot \:4}[/tex]

[tex]\sf \sqrt{96^2-4\cdot \:4\left(-412\right)}\\\\ = \sqrt{96^2+4\cdot \:4\cdot \:412} \\\\= \sqrt{96^2+6592} \\\\= \sqrt{9216+6592} \\\\= \sqrt{15808} = 125.73\\\\[/tex]

So
[tex]w_{1,\:2}=\dfrac{-96\pm \:125.73}{2\cdot \:4}[/tex]

[tex]w_1=\dfrac{-96+125.73}{2\cdot \:4},\:w_2=\dfrac{-96-125.73}{2\cdot \:4}[/tex]

We can ignore w₂ since it is a negative value

So
[tex]\sf w = \dfrac{-96 + 125.73}{8} = 3.71625\; feet[/tex]

[tex]\boxed{ \mathsf{Width\; of\; walkway = 3.71625\;feet}}[/tex]

Answer:

49 degrees

Step-by-step explanation

Answer:

I think 49 °F

Step-by-step explanation:

42 - (-7) = 49 °F

So the temperature raised 49 degrees since 7pm last night.

I think thats right. :)

Answer:

C, Perimeter is 40

Step-by-step explanation:

To find perimeter add up all the sides, to find area, multiply the sides.

Answer:

she can go on 30 rides I think

Answer:

30 rides

Step-by-step explanation:

Ok first you have to subtract 5 because you payed 5$ to get in and then you divide 15$ by 0.50 and that will give you 30. So she can ride 30 rides total!

Answer:

[tex]3.75\ \text{m}[/tex]

Step-by-step explanation:

A escala da réplica é  [tex]1:80[/tex]. Isso significa que 1 metro da réplica da escala representa 80 metros do edifício real.

Portanto, 1 metro do edifício real representa [tex]\dfrac{1}{80}[/tex] metros da réplica.

Precisamos encontrar a altura da réplica

[tex]420\ \text{m}=420\times\dfrac{1}{80}=5.25\ \text{m}[/tex]

Assim, a réplica da escala terá uma altura 5.25 m.

Está colocado numa sala com 9 m de altura.

A distância entre o topo da réplica e o teto do corredor é [tex]9-5.25=3.75\ \text{m}[/tex].

Answer:

Rotate Each dot in the proper way each right angle is 90 Degrees

Step-by-step explanation:

Rotate the Coordinates

pretty simple

Answer:

its D/ 56.25

Step-by-step explanation:

because the other numbers are too small

Answer:

E. 10 feet

F. RS

Step-by-step explanation:

E. Height of actual tree = [tex]\frac{2.5}{1.5}[/tex] × 6 inches

                                       = 10 feet

F. CD is like ST but bigger.

DA is like TQ but bigger.

AB is like QR but bigger.

BC is like RS but bigger.

Their proportion stays the same.

Answer:

BC=SR

Step-by-step explanation:

BC and SR both have the same length in their sides. Therefore SR is the "?".

I didn't fully understand the question, but its alright.

Answer:

B. 96%

Step-by-step explanation:

Sara only missed 7 days of 184 days this year meaning 184 - 7 = 177 and

177 is how many days she attended school, so to figure out percentage take the number of days she attended school and divide by the total amount of days in this year which is 184: 177/184 = 0.96195652173

then multiply by 100 to get percentage so approximately 96%.

Answer:

i got 0 for the value of x

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

hi

d=first diver depth

s=second diver depth

d= 30

S= 30-12=18

the equation given and the gauge must be wrong because the equation for the second duvet souls be s=d-12 since the first diver is DEEPER than the second.

Answer:

irrational

Step-by-step explanation:

Answer:

I think irrational but I can be wrong

Answer:

523.33 cm³

Step-by-step explanation:

The volume of a sphere is [tex]\frac{4}{3}[/tex]πr³

[tex]\frac{4}{3}[/tex]π * (5)³

[tex]\frac{4}{3}[/tex]π * 125

523.333 mm³

Answer: 97

Step-by-step explanation:

Answer:

97 natural numbers

Step-by-step explanation:

[tex]49^2-48^2\\2401-2304=97[/tex]

the distance between the points A and B that is AB is equal to 5.39 units.

We are given the points as:

A = ( 2, 3 )

B = ( 0, - 2 )

We need to find the distance AB between the points.

The distance between the points is given by the formula:

Distance = √ ( y₂ - y₁ )² + ( x₂ - x₁ )²

Substituting the values in the formula, we get that:

Distance AB = √ ( - 2 - 3 )² + ( 0 - 2 )²

Distance AB = √ ( - 5 )² + ( - 2 )²

Distance AB = √ 25 + 4

Distance AB = √ 29 units

Distance AB = 5.39 units.

Therefore, we get that, the distance between the points A and B that is AB is equal to 5.39 units.

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Step-by-step explanation:

Parallel lines have the same slope so they can therefore never touch. Just change the y-int. (Any number as long as it's not the same as the previous)

I.E.:

y = -3x - 12

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

let n be the number , then

[tex]\frac{1}{6}[/tex] n + [tex]\frac{1}{3}[/tex] = [tex]\frac{2}{3}[/tex] n

multiply through by 6 ( the LCM of 6 and 3 ) to clear the fractions

n + 2 = 4n ( subtract n from both sides )

2 = 3n ( divide both sides by 3 )

[tex]\frac{2}{3}[/tex] = n

Answer:

[tex]{\mathsf {n=\frac{2}{3}}}[/tex]

Step-by-step explanation:

In word problems like this, you have to break down the problem description into math form

This is an equation description so we need a variable to work with. Let's call this variable n

1/6th of this number can be translated to:
[tex]\displaystyle \mathsf {\frac{1}{6}n}[/tex]  

1/6th of this number plus one-third translates to:
[tex]\displaystyle \mathsf {\frac{1}{6}n} + \frac{1}{3}[/tex]

1/6th of this number, plus one-third returns two-thirds of that number
returns is just a fancy way of saying equal to.

So returns two-thirds of that number translates to
= two-thirds of that number

Two-thirds of the number is
[tex]\displaystyle \mathsf {\frac{2}{3}n}[/tex]

So putting all this together we get the equation
[tex]\displaystyle \mathsf {\frac{1}{6}n} + \frac{1}{3} = \frac{2}{3}\mathsf n[/tex]

We have to now solve for the equation.

Bring all the n terms to the left side and the constant(1/3) to the right to solve for n

[tex]\displaystyle \mathsf{ Subtract\:}\frac{1}{3}\mathsf {\:from\:both\:sides}[/tex]
[tex]\mathsf {\frac{1}{6}n+\frac{1}{3}-\frac{1}{3}=\frac{2}{3}n-\frac{1}{3}}[/tex]

Simplify to get
[tex]\mathsf {\frac{1}{6}n=\frac{2}{3}n-\frac{1}{3}}[/tex]

Subtract [tex]\mathsf {\frac{2}{3}}[/tex] from both sides
[tex]\mathsf {\frac{1}{6}n-\frac{2}{3}n=\frac{2}{3}n-\frac{1}{3}-\frac{2}{3}n}[/tex]

Simplify  to get
[tex]\mathsf{\frac{1}{6}n-\frac{2}{3}n= -\frac{1}{3}}[/tex]

The left side term is [tex]\mathsf {\frac{1}{6}n-\frac{2}{3}n}[/tex]
Factor out the common term [tex]n[/tex]:
[tex]\mathsf {n\left(\frac{1}{6}-\frac{2}{3}\right)}[/tex]
[tex]\mathsf {\frac{1}{6}-\frac{2}{3}=-\frac{1}{2} }[/tex]

So we get our equation as
[tex]\mathsf {-\frac{1}{2}n=-\frac{1}{3}}[/tex]

Multiply both sides by -2 to get

[tex]\boxed {\mathsf {n=\frac{2}{3}}}[/tex]

Answer:

-4.08333

Step-by-step explanation:

2 1/3 + 1 3/4 = 4912 = 4 112 ≅ 4.0833333. Spelled result in words is forty-nine twelfths (or four and one twelfth)

Answer:

B m pretty sure...

Step-by-step explanation:

Answer:

a) The equation of line perpendicular to above line and passes through point (-7,-4) is [tex]\mathbf{y=\frac{7}{2}x+\frac{41}{2}}[/tex]

b) The equation of line parallel to above line and passes through point (-7,-4) is [tex]\mathbf{y=-\frac{2}{7}x-6}[/tex]

Step-by-step explanation:

We are given the line: [tex]y=-\frac{2}{7}x-7[/tex]

The slope of the above equation is: [tex]m=-\frac{2}{7}[/tex] (By comparing with general form [tex]y=mx+b[/tex] where m is slope)

a) Find equation of line perpendicular to above line and passes through point (-7,-4)

If two lines are perpendicular there slopes are opposite reciprocal i.e [tex]m_1=-\frac{1}{m_2}[/tex]

The slope of new line will be: [tex]m = \frac{7}{2}[/tex]

Now finding y-intercept using slope and point (-7,-4)

[tex]y=mx+b\\-4=\frac{7}{2}(-7)+b \\-4=\frac{-49}{2}+b \\b=-4+\frac{49}{2}\\b=\frac{-8+49}{2}\\b=\frac{41}{2}[/tex]

So, the equation of line perpendicular to above line and passes through point (-7,-4) will be:

[tex]y=mx+b\\y=\frac{7}{2}x+\frac{41}{2}[/tex]

So, the equation of line perpendicular to above line and passes through point (-7,-4) is [tex]\mathbf{y=\frac{7}{2}x+\frac{41}{2}}[/tex]

b) Find equation of line parallel to above line and passes through point (-7,-4)

If two lines are parallel there slopes are same i.e [tex]m_1=m_2[/tex]

The slope of new line will be: [tex]m = -\frac{2}{7}[/tex]

Now finding y-intercept using slope and point (-7,-4)

[tex]y=mx+b\\-4=-\frac{2}{7}(-7)+b \\-4=-2(-1)+b\\-4=+2+b \\b=-4-2\\b=-6[/tex]

So, the equation of line parallel to above line and passes through point (-7,-4) will be:

[tex]y=mx+b\\y=-\frac{2}{7}x-6[/tex]

So, the equation of line parallel to above line and passes through point (-7,-4) is [tex]\mathbf{y=-\frac{2}{7}x-6}[/tex]

Answer:

6*(10^26)

Step-by-step explanation:

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The correct option is C. 3.52/(22 - n) = 24/100.

The equation which can be used to find n, the number of gallons of water he should remove is 3.52/(22 - n) = 24/100.

Mathematical symbols can represent numbers (constants), variables, functions, operations, brackets, punctuation, and grouping, as well as the order of operations and other features of logical syntax.

Now, as per the given question.

22 gallons of water is evaporated from the grant plans which is 16% ammonia solution to make a 24% ammonia solution.

First, we determine how much ammonia is in 22 gallons of 16% ammonia solution.

16%  x 22 gal  =  3.52 gal

That after water evaporates, the quantity of ammonia remains constant, however the total quantity of solution is diminished by the quantity of water that evaporates.

Amount of ammonia: 3.52 gal

Amount of water that sustained: 22 - n

Requires concentration of ammonia is  24% = 24/100

The measurement will be formatted as follows:

(3.52)/(22 - n) = 24/100

Therefore, the equation which is used for the formation of the  number of gallons of water he should remove ammonia is (3.52)/(22 - n) = 24/100.

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The complete question is -

Grant plans to evaporate enough water from 22 gallons of a 16% ammonia solution to make a 24% ammonia solution. which equation can he use to find n, the number of gallons of water he should remove?

The options are-

A. 3.52(22 - n) = 0.24

B. (22 - n)/3.52 = 24/100

C. 3.52/(22 - n) = 24/100

D. 3.52 + (22 - n)  = 0.24

Answer:

y=1/2x-5.................

Step-by-step explanation:

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