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Dovator [93]
3 years ago
11

A student solves the equation StartFraction x + 3 Over 2 EndFraction = StartFraction 3 x + 5 Over 5 EndFraction using the steps

in the table.
Original equation
StartFraction x + 3 Over 2 EndFraction = StartFraction 3 x + 5 Over 5 EndFraction
Cross multiplication
5 (x + 3) = 2 (3x + 5)
Distributive property
5 x + 15 = 2 (3 x + 5)
Subtraction property of equality
5 = x

Which method of solving for the variable could be used instead of cross multiplication?
distributing x + 3 and then 3x + 5 to both sides of the equation
distributing x – 3 and then 3x – 5 to both sides of the equation
using the multiplication property of equality to multiply both sides of the equation by 10
using the multiplication property of equality to multiply both sides of the equation by One-tenth
Mathematics
1 answer:
bonufazy [111]3 years ago
7 0

using the multiplication property of equality to multiply both sides of the equation by 10

Step-by-step explanation:

Given equation is:

\frac{x+3}{2} = \frac{3x+5}{5}

One method to solve this equation is cross-multiplication which the student has used.

One of the alternate method can be multiplying both sides by the LCM of numerators of fractions on both sides

So multiplying both sides by 10 (multiplication property of equality)

\frac{x+3}{2} * 10 = \frac{3x+5}{5} * 10\\5(x+3) = 2(3x+5)\\5x+15 = 6x+10\\5x+15-10 = 6x\\6x = 5x+5\\6x-5x = 5\\x = 5

The alternate method of LCM produces the same answer so the correct answer is:

using the multiplication property of equality to multiply both sides of the equation by 10

Keywords: Linear equations, variables

Learn more about linear equations at:

  • brainly.com/question/11229113
  • brainly.com/question/11234838

#LearnwithBrainly

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2 years ago
A parabola intersects the x-axis at x = 3 and x = 9.
Novay_Z [31]

Answer:

6

Step-by-step explanation:

This function corresponds to 'even' function, then

in order to calculate the 'x' of the vertex: (3+9)/2=6.

3 0
3 years ago
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ccording to the U.S. National Weather Service, at any given moment of any day, approximately 1000 thunderstorms are occurring wo
viva [34]

Answer:

The critical value of <em>z</em> for 99% confidence interval is 2.5760.

The 99% confidence interval for population mean number of lightning strike is (7.83 mn, 8.37 mn).

Step-by-step explanation:

Let <em>X</em> = number of lightning strikes on each day.

A random sample of <em>n</em> = 23 days is selected to observe the number of lightning strikes on each day.

The random variable <em>X</em> has a sample mean of, \bar x=8.1\ mn and the population standard deviation, \sigma=0.51\ mn.

The (1 - <em>α</em>)% confidence interval for population mean <em>μ</em> is:

CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

Compute the critical value of <em>z</em> for 99% confidence interval is:

z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.5760

*Use a <em>z</em>-table.

The critical value of <em>z</em> for 99% confidence interval is 2.5760.

Compute the 99% confidence interval for population mean number of lightning strike as follows:

CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\=8.1\pm2.5760\times\frac{0.51}{\sqrt{23}}\\=8.1\pm0.2738\\=(7.8262, 8.3738)\\\approx(7.83, 8.37)

Thus, the 99% confidence interval for population mean number of lightning strike is (7.83 mn, 8.37 mn).

The 99% confidence interval for population mean number of lightning strike  implies that the true mean number of lightning strikes lies in the interval (7.83 mn, 8.37 mn) with 0.99 probability.

3 0
2 years ago
Given f(x) = 18x + 8, find x when f(x)= 14.
Naddika [18.5K]

The answer is 0.3 (1/3.)

Proof?

f(0.3) = 18(0.3) + 8

f(0.3) = 6 + 8

f(0.3) = 14

14 = 14

⭐ Please consider brainliest! ⭐

✉️ If any further questions, inbox me! ✉️

8 0
2 years ago
The sum of four times a number and five times another number is -28. The sum of nine times the first number and two times the se
Rina8888 [55]

Answer:

<h2>3 and -8</h2>

Step-by-step explanation:

x,\ y-the\ numbers\\\\\text{The sum of four times a number and five times another number is -28:}\\\\4x+5y=-28\\\\\text{The sum of nine times the first number and two times the second number is 11:}\\\\9x+2y=11\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}4x+5y=-28&\text{multiply both sides by2}\\9x+2y=11&\text{multiply both sides by (-5)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}8x+10y=-56\\-45x-10y=-55\end{array}\right}\qquad\text{add both sides of the equation}

.\qquad-37x=-111\qquad\text{divide both sides by (-37)}\\.\qquad\qquad\boxed{x=3}\\\\\text{Put the value of x to the first equation:}\\\\4(3)+5y=-28\\12+5y=-28\qquad\text{subtrac 12 from both sides}\\5y=-40\qquad\text{divide both sides by 5}\\\boxed{y=-8}

3 0
2 years ago
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