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stealth61 [152]
2 years ago
11

Riley makes a mistake in step 2 while doing her homework. what was her mistake? startfraction x over x squared minus 5 x 6 endfr

action startfraction x over x 3 endfraction
Mathematics
1 answer:
Nastasia [14]2 years ago
6 0

She used wrong common denominator.

<h3> Correct solution:</h3>

\frac{x}{{x}^2-5x+6} + \frac{3}{x+3}\\\\=\frac{x}{{x}^2 - 3x - 2x + 6} + \frac{3}{x+3}\\\\=\frac{x}{(x-3)(x-2)} + \frac{3}{x+3}\\\\=\frac{x(x+3) + 3(x-2)(x-3)}{(x-3)(x-2)(x+3)}\\\\=\frac{{x}^2 + 3x + 3{x}^2-15x + 18}{(x-3)(x-2)(x+3)}\\\\= \frac{4{x}^2 -12x + 18}{(x-3)(x-2)(x+3)}\\\\= \frac{2(2{x}^2 - 6x + 9)}{(x-3)(x-2)(x+3)}

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Jean sold cupcakes and cookies yesterday. Each cupcake sold for $2.25 and each cookie sold for $0.50. At the end of the day, Jea
slega [8]

Answer:number of cupcakes sold is 13

Number of cookies sold is 27

Step-by-step explanation:

Let x represent the number of cupcakes that Jane sold.

Let y represent the number of cookies that Jane sold.

Each cupcake sold for $2.25 and each cookie sold for $0.50. At the end of the day, Jean had sold $42.75 worth of cookies and cupcakes.

This means that

2.25x + 0.5y = 42.75 - - - - - - - - - -1

she sold 40 cupcakes and cookies combined, it means that

x + y = 40

Substituting x = 40 - y into equation 1, it becomes

2.25(40 - y) + 0.5y = 42.75

90 - 2.25y + 0.5y = 42.75

- 2.25y + 0.5y = 42.75 - 90

- 1.75y = - 47.25

y = - 47.35/-1.75

y = 27

x = 40 - y

x = 40-27 = 13

.

4 0
3 years ago
I had $3.00. My Mom gave me $10.00. My Dad Gave me $30.00. My Aunt &amp; Uncle gave me $100.00. I had another $7.00. How much di
zysi [14]

Answer:

150

Step-by-step explanation:

i did addition so yeah

7 0
3 years ago
Find the smallest positive $n$ such that \begin{align*} n &amp;\equiv 3 \pmod{4}, \\ n &amp;\equiv 2 \pmod{5}, \\ n &amp;\equiv
Alex777 [14]

4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.

We construct a number x such that taking it mod 4, 5, and 7 leaves the desired remainders:

x=3\cdot5\cdot7+4\cdot2\cdot7+4\cdot5\cdot6

  • Taken mod 4, the last two terms vanish and we have

x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod4

so we multiply the first term by 3.

  • Taken mod 5, the first and last terms vanish and we have

x\equiv4\cdot2\cdot7\equiv51\equiv1\pmod5

so we multiply the second term by 2.

  • Taken mod 7, the first two terms vanish and we have

x\equiv4\cdot5\cdot6\equiv120\equiv1\pmod7

so we multiply the last term by 7.

Now,

x=3^2\cdot5\cdot7+4\cdot2^2\cdot7+4\cdot5\cdot6^2=1147

By the CRT, the system of congruences has a general solution

n\equiv1147\pmod{4\cdot5\cdot7}\implies\boxed{n\equiv27\pmod{140}}

or all integers 27+140k, k\in\mathbb Z, the least (and positive) of which is 27.

3 0
3 years ago
How I divide by negative?? I forgot completely
allochka39001 [22]

Answer:

I hope this helps. If I misunderstood the question let me know

Step-by-step explanation:

1. When dividing a negative by a negative, your answer would be positive.

2. When dividing a negative by a positive, your answer will be negative.

3. When dividing a positive by a negative,your answer will be negative.

3 0
2 years ago
Read 2 more answers
15. Sofie bought a desk for $45 that was
Alchen [17]

Answer:

10%

Step-by-step explanation:

50+50=100

45+45=90

100-90=10

8 0
2 years ago
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