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Softa [21]
2 years ago
6

Anyone can help me solve this equation using cross multiplying

Mathematics
1 answer:
Natali5045456 [20]2 years ago
8 0

9514 1404 393

Answer:

  x = 1 or 5

Step-by-step explanation:

The notion of "cross-multiplying" is the idea that the numerator on the left is multiplied by the denominator on the right, and the numerator on the right is multiplied by the denominator on the left. This looks like ...

  \displaystyle \frac{x-1}{7}=\frac{2x-2}{3x-1}\ \longrightarrow\ (x-1)(3x-1)=(7)(2x-2)

Then the solution proceeds by eliminating parentheses, and solving the resulting quadratic equation.

  3x^2-4x+1=14x-14\\\\3x^2-18x+15=0\qquad\text{subtract $14x-14$}\\\\x^2-6x+5=0 \qquad\text{divide by 3}\\\\(x-1)(x-5)=0\qquad\text{factor}\\\\x\in\{1,5\}

_____

<em>Comment on "cross multiply"</em>

Like a lot of instructions in Algebra courses, the idea of "cross multiply" describes <em>what the result looks like</em>. It doesn't adequately describe how you get there. The <em>one and only rule</em> in solving Algebra problems is "<em>whatever is done to one side of the equation must also be done to the other side of the equation</em>." If you multiply one side by one thing and the other side by a different thing, you are violating this rule.

What looks like "cross multiply" is really "<em>multiply by the product of the denominators</em> and cancel like terms from numerator and denominator." Here's what that looks like with the intermediate steps added.

  \displaystyle \frac{x-1}{7}=\frac{2x-2}{3x-1}\\\\\frac{x-1}{7}\times7(3x-1)=\frac{2x-2}{3x-1}\times7(3x-1)\\\\(x-1)(3x-1)=(2x-2)(7)\qquad\textit{looks like}\text{ cross multiply}

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Kobotan [32]
The correct answer is C. 2,836

when 2836 is divided by 2 it equals 1418. when it is divided by 4 it equals 709. 709 is a whole number, therefore it is correct, and can be divided by both 2 and 4.
3 0
3 years ago
Read 2 more answers
Find the value of 1415×211 Although these numbers aren't quite as nice as the ones from the example, the procedure is the same,
BabaBlast [244]

Answer:

298565

Step-by-step explanation:

Given problem,

1415 × 211

∵ Direct multiplication is quite tough so we can split the number into smaller one for making the multiplication easier,

= (1400 + 15) × (210 + 1)

By using distributive property,

= 1400 × (210 + 1) + 15(210 + 1)

Again by distributive property,

= 1400 × 210 + 1400 + 15 × 210 + 15

Simplifying,

=  294000 + 1400 + 3150 + 15

= 298565

Hence, 1415 × 211 = 298565

9 0
3 years ago
A leprechaun places a magic penny under a​ girl's pillow. The next night there are 2 magic pennies under her pillow. The followi
vfiekz [6]

Answer:

34

Step-by-step explanation:

Since the pennies need to be kept under the pillow in order to be doubled, we're really looking for the day the girl will wake up with 5 billion pennies under her pillow.

The general formula of that geometric sequence will be: t = 1 + 2^(n-1)

We need to find the value of n when t will be over 5,000,000,000.

So, the equation becomes:

5,000,000,001 = 1 + 2^(n-1)

2^{n-1}= 5,000,000,001

log(2^{n-1}) = log(5,000,000,000)

(n-1) * log(2) = log(5,000,000,000)

n-1 = log(5,000,000,000) / log(2)

n-1 = 22.25

n = 33.25

Since it has to be complete days, and we have to reach over 5 billion, then we round it up to 34.

7 0
3 years ago
The first number is 4. A rule is multiply by 2 and then subtract 3. What are the fist 6 numbers in the pattern?
Komok [63]
I believe the answer would be: 4.7.9.11.13.15.17
3 0
3 years ago
I don’t understand, help me out
Vikki [24]

Answer:

a. 76 b. 52

Step-by-step explanation:

The perimeter of a rectangle is the sum of its four sides.

Now all rectangles have a width and a length.

To find the perimeter it is 2 width + 2 length or 2W +2L.

So if the Perimeter P = 344 and Width W = 76 and P = 2W + 2L

Then...

2(76) + 2L = 344 multiply 2 and 76

2L + 152 = 344 subtract 152 from both sides

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L = 96

The length is 96.

The equation of an area of a rectangle is A or  area = width x length or W x L

So the equation is A = W x L

If the area is 4732 and the length is 91 then

91W = 4732 divide both sides by 91

W = 52

The width is 52.

Hope that helps, good luck with your homework!

7 0
2 years ago
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