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maks197457 [2]
3 years ago
13

A store is having a sale in which all items are reduced by 20%. Including tax, Jennifer paid $21 for a pair of shorts. If the sa

les tax is 5%, what was the original price of the shorts?
Mathematics
1 answer:
Tju [1.3M]3 years ago
5 0

Answer: the original price of the shorts was $25

Step-by-step explanation:

Let x represent the original price of the shorts.

The store is having a sale in which all items are reduced by 20%. This means that the amount of discount on the shorts is

20/100 × x = 0.2x

The price of the shorts would be

x - 0.2x = 0.8x

If the sales tax is 5%, then the amount of sales tax charged is

5/100 × 0.8x = 0.04x

The final cost of the shorts would be

0.8x + 0.04x = 0.84x

Including tax, Jennifer paid $21 for a pair of shorts. This means that

0.84x = 21

x = 21/0.84

x = 25

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In triangle ABC, AD is a median. FE is a straight line parallel to BC cutting the remaining sides AB at F and AC at E and cuttin
daser333 [38]

Answer:

Step-by-step explanation:

since AD is a median it implies that triangle ABC is bisected to two equal right angled triangle which are ADB and ADC.

FE is parrallel to BC and cuts AB at F and AC at E shows that there are two similar triangles formed which are AFE and ABC.

Recall that ADC is a right angled triangle, ED bisects a right angled triangle the the ADE = 45^{o}.

Now, Let FD bisect angle ADB,

  then ADF = 45^{o} too.

Since AFX is similar to Triangle ABD and that Triangle AEX is similar to Triangle ACD, then EDX is similar to FDX

FDE = ADF + ADE = 90^{o}

4 0
3 years ago
Q ÷ 2 -qp ÷ 6; let p = -6 and q = 10
ozzi

Answer:

15

Step-by-step explanation:

1. Plug in the values.

q=10

p=-6

10÷2-(10)(-6)÷6

2. Use PEMDAS.

10÷2+60÷6

5+10

15

5 0
3 years ago
Help Fast
swat32

The answer on E2020 is A: Rolling a six-sided number cube 24 times and recording if a 4 comes up.

4 0
3 years ago
Read 2 more answers
Solve the equation. Check your solution. - 6y + 5 = 29y - 2​
mr_godi [17]

Answer:

y = 0.2

Step-by-step explanation:

Simplifying

-6y + 5 = 29y + -2

Reorder the terms:

5 + -6y = 29y + -2

Reorder the terms:

5 + -6y = -2 + 29y

Solving

5 + -6y = -2 + 29y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-29y' to each side of the equation.

5 + -6y + -29y = -2 + 29y + -29y

Combine like terms: -6y + -29y = -35y

5 + -35y = -2 + 29y + -29y

Combine like terms: 29y + -29y = 0

5 + -35y = -2 + 0

5 + -35y = -2

Add '-5' to each side of the equation.

5 + -5 + -35y = -2 + -5

Combine like terms: 5 + -5 = 0

0 + -35y = -2 + -5

-35y = -2 + -5

Combine like terms: -2 + -5 = -7

-35y = -7

Divide each side by '-35'.

y = 0.2

Simplifying

y = 0.2

3 0
3 years ago
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The function f(x) = 200 × (1.098)x represents a village's population while it is growing at the rate of 9.8% per year.
AlexFokin [52]

The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.

<h3>How to graph a function?</h3>

For a function f(x) = y, the steps to draw a graph for the given function are as follows:

  • Consider certain values of x
  • Substitute x values in the given function to obtain y values
  • Plot the x and y values in the graph
  • Join the points to know the variation.

<h3>Calculation:</h3>

It is given that,

f(x) = 200 × (1.098)^x

Village's population growing rate = 9.8%

Creating a table for x and f(x) values:

x: 0   2   4   6   8   10

f(x = 0) = f(0) = 200 × (1.098)^0 = 200

f(x = 2) = f(2) = 200 × (1.098)^2 = 241

f(x = 4) = f(4) = 200 × (1.098)^4 = 291

f(x = 6) = f(6) = 200 × (1.098)^6 = 350

f(x = 8) = f(8) = 200 × (1.098)^8 = 423

f(x = 10) = f(10) = 200 × (1.098)^1^0 = 509

So,

(x, f(x)): (0, 200)  (2, 241)  (4, 291)  (6, 350)  (8, 423)  (10, 509)

Plotting these points in the graph and joining the points, the graph is shown below.

Finding the time for the village to dig a new well:

It is given that the population doubled from its current size, the village will need to dig new water well.

The current size of the village = 200

If it doubles for a certain time 't' = 400

So,

400 = 200 × (1.098)^t

⇒ (1.098)^t = 2

⇒ log(1.098)^t = log 2

⇒ t log(1.098) = 0.301

⇒ t × 0.04 = 0.301

∴ t = 7.525 years

Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.

Learn more about the function and its graph here:

brainly.com/question/4025726

#SPJ1

3 0
1 year ago
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