Solve the simultaneous
equations
2x+y = 3
x+y=1

Answer:

19/9

Step-by-step explanation:

Divide 19/9 using calculator or long division to check.

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Using the length of the perimeter of the Pacman is: 29.29 mm.

Length of an arc = ∅/360 × 2πr

The length of the perimeter of the Pacman = length of the larger arc formed + 2r

∅ = 360 - 55 = 305°

r = 4.00 mm

The length of the perimeter of the Pacman = ∅/360 × 2πr + 2r

Substitute

The length of the perimeter of the Pacman = 305/360 × 2π(4.00) + 2(4.00)

The length of the perimeter of the Pacman = 21.29 + 8.00

The length of the perimeter of the Pacman = 29.29 mm

Therefore, using the length of the perimeter of the Pacman is: 29.29 mm.

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The 82nd Percentile is 89.784

The formula n = (P/100) x N, where P is the percentile, N is the number of values in a data collection (ordered from least to largest), and n is the ordinal rank of a particular value, can be used to determine percentiles. In order to comprehend exam scores and biometric measurements, percentiles are routinely utilized.

The values' percentiles as determined by the formula are displayed below.

Percentile Value 0th = 51.7 5th = 68.1 10th = 69.36 15th = 71.24 20th = 72.92 25th = 74.6 30th = 75.86 45th = 80.38 60th = 84.34 65th = 85.38 70th = 87.12 75th = 88.4 80th = 89.4 85th = 90.84 90th = 92.44 95th = 95.2 100th = 100.1

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The given algebraic equation  formula i.e., [tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex] is verified for the given values of a and b of -3 and -5 respectively.

As per the question statement, we are supposed to verify the algebraic equation formula

[tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex]

We are given that a = -3 and b = -5

Now substituting the values of a and b in the  algebraic equation formula

[tex](a^{2} -b^{2} )=(a+b)(a-b)\\LHS = (a^{2} -b^{2} )\\LHS= ([-3]^{2} -[-5]^{2} )\\LHS=(9-25)\\LHS = -16[/tex]

LHS = Left hand side of the equation

Now considering RHS i.e., Right hand side

[tex]RHS = (a+b)(a-b)\\RHS = ([-3]+[-5])([-3]-[-5])\\RHS= (-8)(2)\\RHS = -16[/tex]

As Left Hand Side LHS = Right Hand Side RHS

Hence the equation, [tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex] is verified for the given values of a and b and is true for all real values of a and b.

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Step-by-step explanation:

[tex] \sqrt{3x - 1} - 2 = 0[/tex]

[tex] \sqrt{3x - 1} = 2[/tex]

[tex] \sqrt{3x - 1} = \sqrt{4} [/tex]

[tex]3x - 1 = 4[/tex]

[tex]3x = 4 + 1[/tex]

[tex]3x = 5[/tex]

[tex]x = \frac{5}{3} [/tex]

The equation of the perpendicular line is y = x + 15.

In this problem we need to determine the equation of the line perpendicular to another line, that intersects at the point (x, y) = (- 5, 10). The explicit form of the equation of the line is defined by the following first order polynomial:

y = m · x + b      

Where:

The first line has a slope - 1 and the slope of the second line is:

m' = - 1 / m

m' = 1

Then, the intercept of the second line is:

b = y - m · x

b = 10 - (- 5)

b = 15

The equation of the perpendicular line is y = x + 15.

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Answer:

just put out + from the question.

Answer:

3.3m each day.

Step-by-step explanation:

The equation will be 18.2 = 5 + 4m18.2=5+4m

Solve for m to get 4m = 13.24m=13.2

m = 3.3m=3.3

She would have to ride 3.3 miles each day to meet her goal.

Answer: 3.3 miles per day

Step-by-step explanation: 13.2/ 4=3.3

Answer:

He needs to get 100% on his next test

Explanation:

(59 + 80 + 65 + 96 + 100) / 5

The greatest value in range of work situation is $200.

For the given question;

The one time bonus is $40.

Amount earned by Kara per hour is $8.

The range of working hours lies between 16 to 20 hours in a week.

Let 'x' be the number of hours Kara worked.

The the inequality will be;Then, the equation for the amount earned in a week is;

Total pay = one time pay + 8×number of hours

Total pay = one time pay + 8x

The greatest value will be earned by the kara when she will work for 20 hours.

Thus, put x = 20.

Total pay = one time pay + 8×20

Total pay = 40 + 8×20

Total pay = 200

Therefore, the total greatest pay earned by the Kara is $200.

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y = \frac{-x}{2 } + \frac{1}{4}  + ce^-{2x} is  the general solution to the differential equation put the problem in standard form.

What is meant by integrating factor?

x² + 2xy + x . dy/dx = 0

x dy/dx  + 2xy = [tex]- x^{v}[/tex]

[tex]\frac{dy}{dx} =+ 2y = -x[/tex]

[tex]left u(x) = e^{\int\limits^_ {} } 2dx = e^{2x}[/tex]

integration  factor p(x) = u(x) = [tex]e^{2x}[/tex]

Now ,multiply  [tex]e^{2x}[/tex] both sides

[tex]e^{2x} ( \frac{dy}{dx} + 2y ) = -x . e^{2x}[/tex]

[tex]e^{2x} \frac{dy}{dx} + 2e^{2x} . y = -x e^{2x}[/tex]

[tex]\frac{d}{dx} (e^{2x} .y) = -x e^{2x}[/tex]

integrate both sides

∫ [tex]d .( e^{2x} .y )[/tex]     = ∫[tex]-xe^{2x} .dx[/tex]

[tex]e^{2x} .y = -\frac{e^{2x}}{2} . x + \frac{e^{2x}}{4} + c[/tex]

[tex]y = \frac{-x}{2 } + \frac{1}{4} + ce^-{2x}[/tex]

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The complete question is -

Find the general solution to the differential equation 2 dy X+ + 2xy + x dx = 0 Put the problem in standard form. Find the integrating factor, p(x) = 2x - Find y(x) Use C as the unknown constant.

Answer:

sqrt of 49 is simplified as 7 so its a rational that can be put in all the rows

Step-by-step explanation:

Rational numbers: -1.3, 2.7777.., 25/2 also known as 12.5, O

Integers: sqrt of 49 also known as 7, 0

Whole numbers: sqrt of 49 also known as 7, 0

Natural numbers: sqrt of 49 also known as 7, 0

Irrational numbers: sqrt of 2, Pi,

Answer:

0.012÷2=12 thousandths ÷ 2

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -8 +2}{2}~~~ ,~~~ \cfrac{ 5 -6}{2} \right) \implies \left(\cfrac{ -6 }{2}~~~ ,~~~ \cfrac{ -1 }{2} \right)\implies \left(-3~~,~~-\cfrac{1}{2} \right)[/tex]

Answer:

x = -1

Step-by-step explanation:

5x + 3y = 26

- (6x + 7y = 21)

_________

-x - 4x = 5

-5x = 5

x = -1

The binomial expression in simplest form which represents three times this quantity is; 3n +45.

Which expression, in simplest form, represents three times this quantity?

According to the task content, it follows that the expression which represents the quantity as defined is to be expressed, in simplest form binomial.

Since the word phrase given in the task content is represented as; n +3.

Hence, three times this quantity as required in the task content is;

3(n +15).

Ultimately, when expressed as a binomial expression by expansion; we have;

(3×n) + (3×15)

=3n +45.

Therefore, the binomial expression in simplest form which represents three times this quantity as required is; 3n +45.

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Answer:

The prime factorization of 196 is 196 = 2 × 2 × 7 × 7 and can be represented as 196 = 2 2 × 7 2 using exponents.

Answer:

2² × 7² = 196

Step-by-step explanation:

He will earn 2603.16 dollar in one year.

An expression is a collection of terms that have been joined together using the operations +, -, or x, such as 4 x 3 or x 2 - x y + 17.

Two expressions are said to be equal in value by an equation, such as 4 b 2 = 6.

Given:

A copy of the entire query is provided below:

45w+ 155

He will therefore save

=45*6+155

=270+155 =425 dollars

so,  w=6.

Knowing that a year equals 52 weeks

Also,

w=52 and

w²/25+45w+155

Thus,

=52*52/25+45*52+155

=108.1602340+155

= $263.16

Hence, he will make $2603.16 in a year.

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Answer:  A

Step-by-step explanation: A because you have to find the total amount of money so you a X

i think/ hope

Answer:

123

Step-by-step explanation:

supplementary angles add up to 180

(5x - 22) + (x + 28) = 180

5x - 22 + x + 28 = 180

6x + 6 = 180

6x = 180 - 6

6x = 174

x = 174/6

x = 29

<A = 5x - 22 = 5(29) - 22 = 123

(-23/20) in a decimal form long division will be equal to (-1.15)

As per the question statement, we are provided with a fraction: (-23/20).

We are required to calculate the simplest form of the fraction in decimals using to the long division method.

The long division method works with 4 component: dividend, divisor, quotient and remainder. And the steps to perform the long division method are as follows:

Step 1: To take the first digit of the dividend from the left and check if this digit is greater than or equal to the divisor.

Step 2: Then, to divide it by the divisor and write the answer on top as the quotient.

Step 3: To subtract the result from the digit and write the difference below.

Step 4: To bring down the next digit of the dividend (if present).

Step 5: To Repeat the same process.

Hence, converting the fraction (-23/20) to decimal values using the process of long division method mentioned above, we get (-1.15).

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Answer:

the answer i got is 2 (x+1) (2x^2-2x+1) / x :)

Answer:

[tex]\frac{2x}{x-1}[/tex]

Step-by-step explanation:

[tex]\frac{4x^2+4x}{2x^2-2}[/tex] ← factor numerator and denominator

= [tex]\frac{4x(x+1)}{2(x^2-1)}[/tex] ← cancel 4 and 2 on numerator/denominator by 2

= [tex]\frac{2x(x+1)}{x^2-1}[/tex] ← x² - 1 is a difference of squares

= [tex]\frac{2x(x+1)}{(x-1)(x+1)}[/tex] ← cancel (x + 1) on numerator and denominator

= [tex]\frac{2x}{x-1}[/tex]

The number can be -3, -2, -1, 0 ,1

Here, we are given that twice a number is increased by three and the result is between negative three and seven.

Let the number be x

Twice of the number = 2x

Four more than twice the number = 2x + 4

This number is between -3, 7

⇒ -3 < 2x +4 < 7

subtracting 4 from both sides we get

-3 -4 < 2x < 7 - 4

-7 < 2x < 3

Dividing both sides by 2 we get

-7/2 < x < 3/2

- 3.5 < x < 1.5

Thus the original number lies between -3.5 and 1.5

This means that it can take 5 values-

-3, -2, -1, 0 ,1

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Answer:

Step-by-step explanation:

You want a table of values of the function sin(3x)/x as x nears zero, and an estimate of the limit of the function value as x → 0.

The function f(x) = sin(3x)/x is an even function. That is ...

  f(-x) = sin(-3x)/(-x) = -sin(3x)/-x = sin(3x)/x = f(x)

When f(-x) = f(x), the function is even. It is a reflection of itself across the y-axis. This means all of the function values for negative x-values are the same as for the corresponding positive x-values. We only need to fill in half the table to know what the other half looks like.

See the attachment for values calculated by a spreadsheet and rounded to 8 decimal places.

The table shows the difference from 3 gets smaller as x gets closer to 0. If we add more rows to the spreadsheet table (2nd attachment), we see that the value gets even closer to 3 as x nears zero. At x = 10^-7, we run up against the accuracy limits of the spreadsheet.

The limit of the expression is 3 as x approaches 0.