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DerKrebs [107]
3 years ago
15

You are buying a Lego set. Target has it listed for $34.99 which is 70% of the original price. What is the original cost of the

Lego set? You are buying a Lego set. Target has it listed for $34.99 which is 70% of the original price. What is the original cost of the Lego set?
Mathematics
1 answer:
dedylja [7]3 years ago
6 0

Answer:

Original price = $49.98

Step-by-step explanation:

Target has it listed for $34.99 which is 70% of the original price.

Let the original price be x.

ATQ,

70\%\ of\ x=34.99\\\\x=\dfrac{34.99\times 100}{70}\\\\x=\$49.98

So, the original price of the Lego set is $49.98.

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The hypotenuse of a right triangle is 37 units long. Find the other two sides if the perimeter of the triangle is 84 units. Sepa
taurus [48]

Answer:

The lengths of the legs are 12 and 35 units

Step-by-step explanation:

Let c represent the hypotenuse and a and b represent the legs.  Then the Pythagorean Theorem requires that a^2 + b^2 = c^2 = 37^2 = Hypotenuse^2

Also:  a + b + c = Perimeter = 84 units.  

Since c = 37 units, a + b + 37 units = 84 units, or a + b = 47 units, or a = 47 - b.

Then a^2 + b^2 = 37^2 becomes (47 - b)^2 + b^2 = 37^2, or 1369.  Therefore:

2209 - 94b + b^2 + b^2 = 1369.

Simplifying by combining like terms, we get:  

840 - 94b + 2b^2 = 0, which is a quadratic equation in standard form.

Reducing all terms by division by 2, we get:

420 - 47b + b^2 = 0.  Here the coefficients are a = 1, b = -47 and c = 420.

The discriminant is therefore b^2 - 4ac, or 529, whose square root is ± 23.

Then the b values of this quadratic in b are

      47 ± 23

b = -------------- , so that b is either 35 or 12

             2

and then side a has length a = 47 - b = 12  or  35.

Thus, a = 12 and b = 35, and c is given:  37.

Check:  Is 12^2 + 35^2 = 37^2 true?  Is 144 + 1225 = 1369?  YES

The lengths of the legs are 12 and 35 units.

7 0
3 years ago
What is the <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B24%7D%20" id="TexFormula1" title=" \sqrt{24} " alt=" \sqrt{24} "
asambeis [7]

4.89897948557 is the answer

4 0
4 years ago
The high school is hosting an event for seniors but will also allow some juniors to attend. The principal approved the event for
Flura [38]

Answer:

50

Step-by-step explanation:

The total is 200 and 25% are juniors so u multiply 200 by 25%

Hope this helps

Correct me if this is wrong

8 0
3 years ago
Read 2 more answers
A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company g
Evgen [1.6K]

Answer:

16 responses

Step-by-step explanation:

we know that

A geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

a_n=r^{n-1}

where

a_n----> n^{th} term of the sequence

r ---> is the common ratio

a ---> the first term of the sequence

a=50\\r=100\%-10\%=90\%=90/100=0.90

substitute

a_n=50(0.90)^{n-1}

For n=12

substitute

a_n=50(0.90)^{12-1}=16

3 0
4 years ago
M is directly proportional to r cubed when r = 4, m = 160. Find the value of r when m = 540
Anarel [89]

Answer:

r = 6

Step-by-step explanation:

Given that M is directly proportional to r³ then the equation relating them is

M = kr³ ← k is the constant of proportionality

To find k use the condition r = 4 when M = 160

k = \frac{M}{r^3} = \frac{160}{64} = 2.5, so

M = 2.5r³ ← equation of proportionality

When M = 540, then

540 = 2.5 r³ ( divide both sides by 2.5 )

216 = r³ ( take the cube root of both sides )

r = \sqrt[3]{216} = 6

5 0
3 years ago
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