Complete each ordered pair so that it is a solution of the given linear equation. x +2y=4

The value of y in the equation in term of x is y= (1-8x)/(3)

An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. For example, 8x = 1-3y is an algebraic equation with two variables x and y with coefficient 8 and 3 respectively and 1 is the constant.

The value of y can there be solved by firstly making 3y the subject of formula

3y= 1-8x

dividing both sides by 3

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

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

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The equation that can be used to determine the total number of words Abigail knows from the vocabulary list, y, over x days is A. y = 50x + 150

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, Abigail already knows 150 words from the vocabulary list and each day, she learns 50 additional words from the vocabulary list.

Let x be the number of days.

y = vocabulary list

The equation will be:

y = 150 + 50x

Therefore, the correct option is A.

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The person must walk 2.61 miles to use 220 calories with speed of 4mph.

What is speed?

 The pace at which an object's position changes in any direction is known as its speed. The distance traveled relative to the time it took to travel that distance is how fast something is moving. Due to its lack of magnitude and only having a direction, speed is a scalar quantity.

Here, At 4 mph 5.6 calories are used in = 1 minute

So, at 4 mph, 220 calories are used in,

=> 220/5.6

=> 39.28 minutes

Hence, a person must walk for 39.28 minutes to burn 220 calories.

To find the distance a person should walk, when the speed is 4 miles per hour.

In 60 minutes a person is walking = 4 miles

So, in 39.28 minutes a person will walk = 4/60*39.28

= 2.61 miles

Therefore The person must walk 2.61 miles to use atleast 220 calories.

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Answer:

[tex]( \frac{1}{2} )^5 = \frac{1}{32}[/tex]

Step-by-step explanation:

The probability of "not a tail" is 1/2.  The five tosses are independent, so the probability of "not a tail" 5 times in succession is

[tex]\left(\frac{1}{2}\right) \cdot \left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right)[/tex]

The no. of truffles than can be included in the box is 135.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

Given, The dimensions of the box you decided to purchase are 15 inches by 12 inches by 1.5 inches.

∴ The volume of the box is,

= (15×12×1.5) inches³.

= 270 inches³.

Given each truffle has a volume of 2 iches³.

∴ No. of truffles than can be included in the box is,

= (270/2).

= 135.

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Cash 2300

Accumulated Depreciation  4940

Gain one of fixtures 240

Store fixtures  7000

From the question, we have

Bonham’s Bakery sold shelving units (store fixtures) that were 13 years old for $2,300 cash.

Accumulated Depreciation = (7000-1300)/15*13

=4940

Gain one of fixtures = 240

Store fixtures = 7000

Multiplication:

Mathematicians multiply the numbers in order to calculate the sum of two or more. A fundamental mathematical operation, it is applied frequently in daily life. In order to combine groups of similar sizes, we use multiplication. An illustration of the fundamental concept of repeated addition of the same number is multiplication. The product of two or more numbers refers to the result of the multiplication, and the factors are the amounts that are being multiplied. It is easier to add the same number repeatedly after it has been multiplied.

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Answer:

Step-by-step explanation:

Intrest = PRT\100

$1089. =. ($1100x12xR)\100

$1089. = 132R

 Divide through by 132.

R. =. 8.25%

Answer:

$26.33

Step-by-step explanation:

The equation of the parabola that has one real solution with the line y = x - 5 is y = x² + 7·x + 4

The standard form of the equation of a parabola is y = a·x² + b·x + c

The equation of the line is; y = x - 5

The parabola that has one real solution with the line is given by the parabola that is equal to both (x - 5) and the equation for the parabola;

Analyzing the quadratic equations of the parabolas with the equation y = x - 5, gives;

x² + x - 4 - x + 5 = 0

x² + 1 = 0

x² = -1

x = ±√(-1) (Complex solution)

x² + x + 4 = 0

The discriminant, b² - 4·a·c is 1² - 4 × 1 × 4 = -15 < 0 (Complex solution)

x² + 5·x + 14 = 0

The discriminant, b² - 4·a·c is 5² - 4 × 1 × 14 = -31 < 0 (Complex solution)

x² + 6·x + 9 = 0

The quadratic equation that gives one real solution with the equation y = x - 5 is therefore;

y = x² + 7·x + 4

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The example that would be continuous data is A. The volume of liquid in a pop can.

Continuous data is data that has no fixed value. Continuous data includes height, weight, temperature, and length. Some continuous data, such as a baby's weight in its first year or the temperature in a room throughout the day, will change over time.

Discrete data is a type of numerical data that consists of whole, concrete numbers that have specific and fixed data values determined by counting. Continuous data consists of complex numbers and varying data values measured over a specific time period.

In this case, the volume of the liquid is s continuous data.

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Answer:

It's B. A good way to look at it is the last number. The last number is the y-intercept. Here the y-intercept is -3. That's how I would always figure it out.

The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B  t = ln(3) / 0.05

Given,

The population of a city can be modeled using the formula P=100,000e^(0.05t)

t is the number of years after 2012

P is the population of the city

We have to find the equation that can be used to find the number of years after 2012 that the population will triple to 300,000.

Here,

Substitute 300000 in for P and solve for t

300000=100000e^0.05t

Divide both sides by 100000:

We get,

3 = e^0.05t

Multiply both sides by the natural log (ln)

Then,

ln(3) = 0.05t

Now, divide 0.05 on both sides to get t by its self

t = ln(3) / 0.05

Therefore,

The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B  t = ln(3) / 0.05

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The contribution margin rate is 40%.

What is contribution margin rate?

A company's contribution margin rate is the total revenue minus variable costs divided by the revenue.

First we need to determine the contribution margin in order to calculate the contribution margin rate. There are two approaches to determine the contribution margin.

Contribution Margin = $15 - $9 = $6

The contribution margin is $6.

Now we will calculate the contribution margin rate using this formula,

Contribution Margin Rate = Contribution Margin [tex]/[/tex] Sales Revenue

Contribution Margin Rate = $6 / $15

                                             = 0.4 * 100

                                             = 40%.

Hence the contribution margin rate is 40%.

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Answer: im pretty sure the answer is c

Step-by-step explanation:

if the answer is  not c im sorry but i hope this helps! Have a good day!

The equation of the line that passes through the point (8, 2) and has a slope of -3/4 is y = -3/4(x-8)+2.

In the given question we have to find the equation of line that passes through the point (8, 2) and has a slope of -3/4.

The given points are (8, 2).

The slope(m) = -3/4

The standard equation of slope intercept form is

y-y(1) = m(x-x(1))

From the question; x(1) = 8 and y(1) = 2.

Putting the value

y-2 = -3/4(x-8)

Add 2 on the both side, we get

y = -3/4(x-8)+2

Hence, the equation of the line that passes through the point (8, 2) and has a slope of -3/4 is y = -3/4(x-8)+2.

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Answer:

Add the picturess!!!!!

Step-by-step explanation:

[tex](2a^7b^5\cdot 3ab^8)^2\implies \left( 2^2 a^{(7)(2)} b^{(5)(2)} \cdot 3^2 a^2 b^{(8)(2)}\right)\implies 4a^{14}b^{10}\cdot 9a^2b^{16} \\\\\\ (4)(9)a^{14}a^2b^{10} b^{16}\implies 36a^{14+2}b^{10+16}\implies 36a^{16}b^{26}[/tex]

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=1\\ k=-9 \end{cases}\implies y=a(x-1)^2 - 9\qquad \textit{we also know that} \begin{cases} x=2\\ y=-7 \end{cases} \\\\\\ -7=a(2-1)^2-9\implies 2=a(1)^2\implies 2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-1)^2 -9 \end{array}} ~\hfill[/tex]

By using division, it is obtained that

The Quotient of 8 and cube of 2 is 1

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division.

Divisor x Quotient + Remainder = Dividend.

Let the number be 2

cube of 2 = [tex]2^3 = 8[/tex]

Quotient of 8 and 8 = [tex]\frac{8}{8}[/tex] = 1

The Quotient of 8 and cube of 2 is 1

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Answer:

False

Step-by-step explanation:

using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

given

[tex]\frac{9x^7}{3x^2}[/tex]

= [tex]\frac{9}{3}[/tex] × [tex]\frac{x^7}{x^2}[/tex]

= 3 × [tex]x^{(7-2)}[/tex]

= 3[tex]x^{5}[/tex]

The slope of the line tangent to f(x) at x = 1 is -8

The instantaneous rate of change of f(x) at x = 1 is -8

The equation of line tangent to f(x) at x = 1 is y  = -8x + 9

The tangent line to a curve at a given point is the line which intersects the curve at the point and has the same instantaneous slope as the curve at the point.

so the slope of a line at that point is the slope of the curve at that point.

f(x) = -4[tex]x^{2}[/tex] + 5

To find the slope, we differentiate f(x) with respect to x

dy/dx  = d/dx( -4[tex]x^{2}[/tex]) + d/dx(5)

           = -8x + 0

dy/dx = -8x

The slope = -8x

at x = 1,

the slope becomes, -8(1) = -8

The instantaneous rate of change of f(x) at x = 1 is the same as the slope of the line tangent to f(x) = -8

The slope of the line is -8

to find the equation of the tangent line, we need to find the coordinates of the point the line touches the curve.

one of the coordinates x = 1, to find y, we substitute x into f(x)

f(x) = -4[tex](1)^{2}[/tex] + 5

f(x) = 1

so the point is (1, 1)

so equation of straight line

[tex]\frac{y - y_{1} }{x - x_{1} }[/tex] = m

y - 1/x - 1 = -8

by cross multiplying

y - 1 = -8(x - 1)

y - 1 = -8x +8

y = -8x + 9

In conclusion,

The slope o the line tangent to f(x) at x = 1 is -8

The instantaneous rate off change of f(x) at x = 1 is -8

The equation of line tangent to f(x) at x = 1 is y  = -8x + 9

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The measure of ∠QTS = 58°

Given; A triangle QPR

PQ = PR

this means that ∠ Q = ∠ R

and QR = QT this means ∠ R = ∠ T

And ST ║ QR

and QT is the transversal

From the above mentioned information we can conclude that

∠QTS = ∠TQR -------------- 1

Thus since ∠ Q = ∠ R  

by using angle sum property of triangle we can conclude that

∠ Q + ∠ R = 116  [ exterior angle sum property ]

2 ∠ Q = 116

∠ Q = 58°

this means ∠ TQR = 58°

And from 1 we know that this angle is equal to angle QTS

Thus ∠QTS = ∠TQR = 58°

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The angle of elevation of the ramp to doorway of a building to the ground is found as 11°.

The ramp is the hypotenuse of a right angle triangle formed by the doorway, the ground, and the ramp.

The ramp's elevation angle is the angle Ф it makes with the ground.

Apply the tan function;

Tan Ф = length of doorway/ distance along ramp of building

Tan Ф = 1/5

Ф = 11°

Thus, the angle of elevation of the ramp to doorway of a building to the ground is found as 11°.

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If the number of different account numbers are possible if repetitions of letters and digits are allowed is:45,697,600,000.

Let assume you have 26 choices for each of the first 4 slots and 10 choices for each of the last 5 slots.

Hence,

Total possibilities = (26× 26× 26×26) × (10×10×10×10×10)

Total possibilities = 26^4 × 10^5

Total possibilities = 456976×100000

Total possibilities = 45,697,600,000

Therefore we can assume that the total possibilities is : 45,697,600,000.

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Answer:

The distance between two points on a 2D coordinate plane can be found using the following distance formula. d = √ (x2 - x1)2 + (y2 - y1)2. where (x 1, y 1) and (x 2, y 2) are the coordinates

Step-by-step explanation:

The angle measures are <1 = 86 degrees, <2 = 94 degrees and <3 = 86 degrees

The possible diagram that completes the question is added as an attachment

From the attached diagram, we have the following representation

<1 + <2 = 180 degrees --- by the theorem of supplementary angles

Also, we have the following angle measure

Given that

<1 = 86 degrees

Substitute the known values in the above equation

So, we have the following equation

86 + <2 = 180

Evaluate the like terms

<2 = 94

Also, we have

<3 = <1  --- by the theorem of vertical angles

Substitute the known values in the above equation

<3 = 86

This is so because <1 = 86 degrees

Hence, the measures of the angles are <1 = 86 degrees, <2 = 94 degrees and <3 = 86 degrees

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