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3 years ago

2/3(5x-6)=6 solve for x

Mathematics

1 answer:

alisha [4.7K]3 years ago

4 0

Answer:

x=3

Step-by-step explanation:

There's many ways you can begin this, I prefer getting rid of the fraction first.

Multiply both sides by 3/2 (yes, I switched it on purpose)

You get. . .

5x-6 = 9

To isolate the 5x, add 6 to both sides

5x = 15

Divide both sides by 5 and you get . . .

x=3

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The perimeter of a rectangle is 80 feet. Find the dimensions if the length 5 feet longer than four times the width. Then find th

nydimaria [60]

Answer:

l=33 feet

w=7 feet

Area= 231 feet

Step-by-step explanation:

Solution in Picture is attached

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3 years ago

Perform the indicated operations. Write the answer in standard form, a+bi.<br> 5-3i / -2-9i

Vsevolod [243]

$\huge \boxed{\mathfrak{Answer} \downarrow}$

$\large \bf\frac { 5 - 3 i } { - 2 - 9 i } \\$

Multiply both numerator and denominator of $\sf \frac{5-3i}{-2-9i} \\$ by the complex conjugate of the denominator, -2+9i.

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2-9i\right)\left(-2+9i\right)}) \\$

Multiplication can be transformed into difference of squares using the rule: $\sf\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$ .

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2\right)^{2}-9^{2}i^{2}}) \\$

By definition, i² is -1. Calculate the denominator.

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{85}) \\$

Multiply complex numbers 5-3i and -2+9i in the same way as you multiply binomials.

$\large \bf \: Re(\frac{5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9i^{2}}{85}) \\$

Do the multiplications in $\sf5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9\left(-1\right)$ .

$\large \bf \: Re(\frac{-10+45i+6i+27}{85}) \\$

Combine the real and imaginary parts in -10+45i+6i+27.

$\large \bf \: Re(\frac{-10+27+\left(45+6\right)i}{85}) \\$

Do the additions in $\sf-10+27+\left(45+6\right)i$ .

$\large \bf Re(\frac{17+51i}{85}) \\$

Divide 17+51i by 85 to get $\sf\frac{1}{5}+\frac{3}{5}i \\$ .

$\large \bf \: Re(\frac{1}{5}+\frac{3}{5}i) \\$

The real part of $\sf \frac{1}{5}+\frac{3}{5}i \\$ is $\sf \frac{1}{5} \\$ .

$\large \boxed{\bf\frac{1}{5} = 0.2} \\$

3 0

3 years ago

Four times the lesser of two consecutive even integers is 12 less than twice the greater number. Find the integers.

valkas [14]

The numbers are: 2n and (2n+2)
we can suggest this equation:
4(2n)=2(2n+2)-12

We compute this equation:
8n=4n+4-12
8n-4n=-8
4n=-8
n=-8/4
n=-2

we compute the numbers:
2n=2(-2)=-4
2n+2=-4+2=-2

answer: the numbers are -4 and -2.

5 0

4 years ago

What can you factor out of 2x^2-4x+8

Sunny_sXe [5.5K]

Answer: 2(x^2-2x+4)

Step-by-step explanation:

You can factour out 2:

2(x^2-2x+4)

7 0

3 years ago

Read 2 more answers

Find the equation of the line that is parallel to 4x - 8y equals 9 and passes through (-3, 6)

vazorg [7]

For this case we have the following equation:

$4x-8y = 9$

We manipulate algebraically to bring the equation to the slope-intersection form y = mx + b

Where:

m: It's the slope

b: It is the cut-off point with the y axis

$8y = 4x-9\\y =\frac {4} {8} x- \frac {9} {8}\\y =\frac {1} {2} x- \frac {9} {8}$

By definition, if two lines are parallel then their slopes are equal.

Thus, the line is of the form:

$y = \frac {1} {2} x + b$

We find the cut-off point by replacing the given point:

$6 = \frac {1} {2} (- 3) + b\\6 = - \frac {3} {2} + b\\b = 6 + \frac {3} {2}\\b = \frac {12 + 3} {2}\\b = \frac {15} {2}$

Thus, the line is of the form:

$y = \frac {1} {2} x + \frac {15} {2}$

Answer:

$y = \frac {1} {2} x + \frac {15} {2}$

6 0

3 years ago