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2 years ago

FIND THE SUM: (6x^2-2x-3)+(x^2-3x+1) 1.6x^2+6x+3 2.7x^2+5x+2 3.7x^2-5x-2

Mathematics

1 answer:

Butoxors [25]2 years ago

5 0

8x^2-5x-2

method

open bracket

6x^2-2x-3+x^2-3x+1

collect like terms

6x^2+2x^2-3-3x+1

8x^2-3-3x+1

again collect like terms

8x^2-2x-3x-3+1

8x^2-5x-3+1. (-×-=+ addition but keeping sign minus

8x-5x-2. (-×+=-)

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In 2013, the moose population in a park was measured to be 5,100. By 2018, the population was measured again to be 5,200. If the

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Answer:

$P(t) = 5100e^{0.0039t}$

Step-by-step explanation:

The exponential model for the population in t years after 2013 is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the population in 2013 and r is the growth rate.

In 2013, the moose population in a park was measured to be 5,100

This means that $P(0) = 5100$

$P(t) = 5100e^{rt}$

By 2018, the population was measured again to be 5,200.

2018 is 2018-2013 = 5 years after 2013.

So this means that $P(5) = 5200$ .

We use this to find r.

$P(t) = 5100e^{rt}$

$5200 = 5100e^{5r}$

$e^{5r} = \frac{52}{51}$

$\ln{e^{5r}} = \ln{\frac{52}{51}}$

$5r = \ln{\frac{52}{51}}$

$r = \frac{\ln{\frac{52}{51}}}{5}$

$r = 0.0039$

So the equation for the moose population is:

$P(t) = 5100e^{0.0039t}$

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3 years ago

Solve for r in the scientific formula d = rt.<br><br> r = _______

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R = d/t is the answer. Hope this helped

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2 years ago

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Carlos Martin received a statement from his bank showing a balance of $56.75 as of March 15th his check book shows a balance of

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Answer:

$48.87

Step-by-step explanation:

Let the deposited amount between the March 15th and the March 20th be x

Balance on 15th march = $56.75

The bank returned all the cancelled checks but too. One check was for $5 and the other was for $13.25

And he also deposited x amount

After deposits and deductions

So, balance = 56.75 +x - (13.25+5)

The new balance on 20th march = $87.37

⇒ $56.75 +x - (13.25+5)=87.37$

⇒ $56.75 +x - 18.25=87.37$

⇒ $38.5 +x =87.37$

⇒ $x =87.37-38.5$

⇒ $x =48.87$

Hence Carlos deposited $48.87 in his account between the March 15th and the March 20th.

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2 years ago

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2/7m-1/7=3/14 solve step by step

yulyashka [42]

Solution for $\frac{2}{7}m - \frac{1}{7} = \frac{3}{14} \ is \ m = \frac{5}{4} \ or \ m = 1\frac{1}{4} \ or \ m = 1.25$

<h3>Further explanation</h3>

It is a case about one variable linear quations and we have to solve the equation to get the variable m. There are two ways to solve it!

Our main plan is to isolate the variable m alone at the end of the process on one side of the equation until the variable will be equal to the value on the opposite side.

<u>First way</u>

$\frac{2}{7}m - \frac{1}{7} = \frac{3}{14}$

Let us add $\frac{1}{7}$ to both sides

$\frac{2}{7}m - \frac{1}{7} + \frac{1}{7} = \frac{3}{14} + \frac{1}{7}$

$\frac{2}{7}m = \frac{3}{14} + \frac{1}{7}$

On the right side for the addition operation, we equate the common denominator by multiplying $\ \frac{1}{7} \ by \ \frac{2}{2}$

$\frac{2}{7}m = \frac{3}{14} + \frac{2}{14}$

Then we combine terms to get

$\frac{2}{7}m = \frac{5}{14}$

Divide by the coefficient of m, or in other words, multiply both sides by $\frac{7}{2}$

$\frac{2}{7}m \times \frac{7}{2} = \frac{5}{14} \times \frac{7}{2}$

Finally, the solution is obtained as follows

$m = \frac{35}{28}$

Simplify fractions, both the numerator and denominator are divided equally by 7.

$\boxed{ \ m = \frac{5}{4} \ }$

Convert into mixed fractions, we get:

$\boxed{ \ m = 1 \frac{1}{4} \ }$

In decimal form, we get

$m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }$

<u>Second way (a quick way)</u>

$\frac{2}{7}m - \frac{1}{7} = \frac{3}{14}$

Because the denominators 7 and 14 have LCM = 14, both sides are multiplied by 14 (LCM is the Least Common Multiple)

$14 \times \big( \frac{2}{7}m - \frac{1}{7} \big) = 14\times \big( \frac{3}{14} \big)$

We use the distributive property of multiplication on the left side

$\frac{28}{7}m - \frac{14}{7} = \frac{42}{14}$

or it can also directly lead to

$4m - 2 = 3$

Add 2 to both sides, we get

$4m = 5$

Divide by the coefficient of m, or in other words, both sides are divided by 4

$\boxed{ \ m = \frac{5}{4} \ }$

Or, $\boxed{ \ m = 1 \frac{1}{4} \ }$

Or, $m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }$

Wanna check the solution into the equation?

$\big( \frac{2}{7} \times \frac{5}{4} \big) - \frac{1}{7} = \frac{3}{14}$

$\frac{10}{28} - \frac{1}{7} = \frac{3}{14}$

$\frac{5}{14} - \frac{2}{14} = \frac{3}{14}$

$\frac{3}{14} = \frac{3}{14}$

Both sides show the same value, so the solution is correct.

Note:

Remember, how to manipulate both sides of the equation with the algebraic properties of equality such as:

adding,
subtracting,
multiplying, and/or
dividing both sides of the equation with the same number.

In the form of fractions, the steps that must be considered are

equate the denominator,
simplify fractions, and
for the final answer, convert fractions to mixed fractions or decimal forms

All these processes can occur repeatedly until the isolated variables are obtained on one side of the equation.

<h3>Learn more</h3>

A word problem that forms a single variable linear equation brainly.com/question/1566971
Learn more about the single variable linear equation that has no solution, has one solution, and has infinitely many solutions brainly.com/question/2595790
Questioning the stages of solving a word problem about one variable linear equations brainly.com/question/2038876

<h3>Answer details </h3>

Grade : Middle School

Subject : Mathematics

Chapter : Linear Equation in One Variable

Keywords : solve, solution, variable, coefficient, 2/7m - 1/7 = 3/14, 5/4, 1 1/4, 1.125, algebraic properties of equality, one, linear equation, isolated, manipulate, operations, add, subtract, multiply, divide, fraction, equate, denominator, numerator, both sides, decimal

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3 years ago

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Each month, 8 magazines arrive at Sydney's home. Write an equation that would show the number of motnths (n) it took for Sydney

Dovator [93]

C.
Since 8 magazines are areiving each month (n) and the total is 56, all you have to do is multiply 8 by n and you get 56, the actual answer would be 7 though.

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3 years ago