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Ivan
3 years ago
11

Paula has $54. She bought some pencils, each costing $0.75, and a paper ream for $2.50. She is left with $42.50 after buying pen

cils and the ream of paper. She uses the equation Syntax error from line 1 column 49 to line 1 column 73. Unexpected 'mathsize'. to find the number of pencils she bought. How many pencils did Paula buy?
Mathematics
1 answer:
8090 [49]3 years ago
7 0

Answer:

12 pencils

Step-by-step explanation:

let no. of pencils bought be x.

54 - 0.75x - 2.50 = 42.50

9 = 0.75x

x = 12

Topic: algebraic equations

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

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Nesterboy [21]

Answer:

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EXPLANATION:

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4 0
2 years ago
Please solve 5 f <br> (Trigonometric Equations)<br> #salute u if u solved it
Zanzabum

Answer:

\beta=45\degree\:\:or\:\:\beta=135\degree

Step-by-step explanation:

We want to solve \tan \beta \sec \beta=\sqrt{2}, where 0\le \beta \le360\degree.

We rewrite in terms of sine and cosine.

\frac{\sin \beta}{\cos \beta} \cdot \frac{1}{\cos \beta} =\sqrt{2}

\frac{\sin \beta}{\cos^2\beta}=\sqrt{2}

Use the Pythagorean identity: \cos^2\beta=1-\sin^2\beta.

\frac{\sin \beta}{1-\sin^2\beta}=\sqrt{2}

\implies \sin \beta=\sqrt{2}(1-\sin^2\beta)

\implies \sin \beta=\sqrt{2}-\sqrt{2}\sin^2\beta

\implies \sqrt{2}\sin^2\beta+\sin \beta- \sqrt{2}=0

This is a quadratic equation in \sin \beta.

By the quadratic formula, we have:

\sin \beta=\frac{-1\pm \sqrt{1^2-4(\sqrt{2})(-\sqrt{2} ) } }{2\cdot \sqrt{2} }

\sin \beta=\frac{-1\pm \sqrt{1^2+4(2) } }{2\cdot \sqrt{2} }

\sin \beta=\frac{-1\pm \sqrt{9} }{2\cdot \sqrt{2} }

\sin \beta=\frac{-1\pm3}{2\cdot \sqrt{2} }

\sin \beta=\frac{2}{2\cdot \sqrt{2} } or \sin \beta=\frac{-4}{2\cdot \sqrt{2} }

\sin \beta=\frac{1}{\sqrt{2} } or \sin \beta=-\frac{2}{\sqrt{2} }

\sin \beta=\frac{\sqrt{2}}{2} or \sin \beta=-\sqrt{2}

When \sin \beta=\frac{\sqrt{2}}{2} , \beta=\sin ^{-1}(\frac{\sqrt{2} }{2} )

\implies \beta=45\degree\:\:or\:\:\beta=135\degree on the interval 0\le \beta \le360\degree.

When  \sin \beta=-\sqrt{2}, \beta is not defined because -1\le \sin \beta \le1

4 0
3 years ago
An amount of 41,000 is borrowed for 15 years at 8.5% interest, compounded annually. If the loan is paid in full at the end of th
bazaltina [42]

Answer: $139390 must be paid back.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = amount to be played back at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount borrowed.

From the information given,

P = 41000

r = 8.5% = 8.5/100 = 0.085

n = 1 because it was compounded once in a year.

t = 15 years

Therefore,

A = 41000(1 + 0.085/1)^1 × 15

A = 41000(1 + 0.085)^15

A = 41000(1.085)^15

A = $139390

3 0
3 years ago
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Does anyone know the answer for 42 ?
Trava [24]
Question 42 is B because I did the math
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3 years ago
Jimmy bought a sandwich. The price is $5 when he got the receipt he needed to pay 6% taxes, and he left a 10% tip how much did h
MA_775_DIABLO [31]
5.83............................
3 0
3 years ago
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