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3 years ago

What value of x makes the equation true? 15(2x−10)+4x=−3(15x+4)

Mathematics

1 answer:

muminat3 years ago

5 0

Answer:

x = 1.74

Step-by-step explanation:

It is required to find the value of x in the following equation :

$15(2x-10)+4x=-3(15x+4)$

Firstly, it is required to solve brackets such that,

$30x-150+4x=-45x-12$

Collecting variable on one side and constants on another side.

$30x+4x+45x=150-12$

$79x=138$

Dividing both sides by 79 such that,

$x=\dfrac{138}{79}\\\\x=1.74$

So, the value of x = 1.74.

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Please help me on this question I really need help. :,)

Kazeer [188]

Answer:

a. (7, 27) Polly was incorrect.

b. (3, 1) Polly was correct.

Step-by-step explanation:

y = 4x - 1

2x - y = -13

We can solve this by substitution. Our first equation gives us y. Plug that into our second equation for each instance of y.

2x - y = -13

2x - (4x - 1) = -13

First distribute the negative sign across the parentheses.

2x - 4x + 1 = -13

Combine like terms.

-2x + 1 = -13

-2x = -14

Divide both sides by -2.

x = 7

Now that we know x, plug its value into one of our original equations.

y = 4x - 1

y = 4(7) - 1

Solve.

y = 28 - 1

y = 27

Our solution is (7, 27).

Let's check our answer by plugging both values into one of our original equations.

2x - y = -13

2(7) - 27 = -13

Solve.

14 - 27 = -13

-13 = -13

Your solution is correct.

Polly's solution was (-2, -9), which is incorrect.

3x + 6y = 15

-2x + 3y = -3

Let's solve this by elimination. To solve by elimination means to eliminate a variable from the equation.

We have 3x & -2x and 6y & 3y. Notice that 6 and 3 can be simplified easily. To eliminate y, we want to multiply each factor of the second equation by -2.

-2x + 3y = -3

-2(-2x + 3y = -3)

4x - 6y = 6

Write the equations together.

3x + 6y = 15

4x - 6y = 6

Now we can see that the y variable will cancel out.

Apply the elimination method.

3x + 6y = 15

4x - 6y = 6

________

7x = 21

Divide both sides by 7.

x = 3

Now that we know x, plug its value into one of our original equations.

3x + 6y = 15

3(3) + 6y = 15

Solve.

9 + 6y = 15

6y = 15 - 9

6y = 6

y = 1

Our solution is (3, 1).

Let's check our answer by plugging both values into one of our original equations.

-2x + 3y = -3

-2(3) + 3(1) = -3

Solve.

-6 + 3 = -3

-3 = -3

Your solution is correct.

Polly's solution was (3, 1), so she was correct.

Hope this helps!

6 0

2 years ago

A sample of bacteria is decaying according to a half-life model. If the sample begins with 200 bacteria and after 5 minutes ther

77julia77 [94]

<h2>Hello!</h2>

The answer is:

There will remain a total of 134 bacteria after 7 minutes.

Exponential decay calculations are commonly used to find the decrease of amounts of populations, bacterias, and other situations when using proportional relationships. In order to find the problem, we must remember the equation used to calculate the exponential decay.

$Decay=S(1-r)^{t}$

Where,

S, is the starting value/amount

r, is the rate (% to real number)

t, is the time elapsed.

We are given that the numbers of bacteria decrease by 50 after 5 minutes, starting with 200, and after 5 minutes the number of bacteria is 150

Calculating the rate of decrease, we have:

$Rate=\frac{Decrease}{Starting}=\frac{200-150}{200}=\frac{50}{200}=0.25$

Therefore, the rate of decrease is 0.25 or 25% (after multiplying the number by 100)

Then, substituting the given information and the rate of decrease into the decay equation, we have:

$Decay=200(1-0.25)^{\frac{t}{5}}$

Now, to calculate how many bacteria will remain after 7 minutes, we need to substitute it into the decay equation:

$Bacteria(After7Minutes)=200(1-0.25)^{\frac{7}{5}}=133.69$

So, rounding to the nearest whole number, there will remain a total of 134 bacteria after 7 minutes.

Have a nice day!

3 0

2 years ago

Help with this please will give brainliest!

Viktor [21]

Answer:

y = 3/2 x - 11

Step-by-step explanation:

y = -2/3 x + 5; slope = -2/3

Perpendicular line, slope is reciprocal and opposite so slope of the line that is perpendicular to the y = -2/3 x + 5 is 3/2

Passes through (8,1)

Equation

y -1 = 3/2 (x - 8)

y - 1 = 3/2 x - 12

y = 3/2 x - 11

7 0

3 years ago

What is 28% of 63%? Round your answer to the nearest tenth

Zina [86]

Answer: 17%

Step-by-step explanation:

1. First divide the percentages by 100 to turn the percentages into a decimal (28/100) x (63/100) = 0.1764

2. Then turn that decimal into a percentage again.

0.1764 x 100 = 17.64 but if you’re rounding to the nearest tenth without any decimals it’ll just be 17%

3 0

2 years ago

NEED HELP ASAP!!!!!!

melamori03 [73]

Okay so you can add up all the marbles to find a rate and divide.
Total: 20 marbles
Blue: 25% chance
Red: 40% chance
Green: 45% chance

8 0

2 years ago

Read 2 more answers