Graph each equation using a table of values
y = 2x² + 4x

The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given,  line containing the point (5, −3) and is parallel to: y = − 2/5x − 3/4

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept

In our case Line is parallel to the Line y = − 2/5x − 3/4,

So the slope would be the same.

m = -2/5

Thus, the equation of the line:

y = -2/5x + b

Since the line passes through the point (5, -3)

-3 = -2/5 * 5 + b

b = -1

Thus the final equation of a line:

y = -2/5x - 1

Therefore, The slope-intercept form of the line containing the point (5, −3) and is parallel to y = − 2/5x − 3/4 is y = -2/5x - 1.

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The expression which can be used to represent the given using the fewest possible terms is 2x + 2

The correct answer choice is option B.

(−5x − 12) + (14 + 7x)

open parenthesis

-5x - 12 + 14 + 7x

collect like terms

-5x + 7x - 12 + 14

2x + 2

In conclusion, 2x + 2 is the expression which represents the fewest possible terms of (−5x − 12) + (14 + 7x)

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Answer:

its C

Step-by-step explanation:

other guy wasn't reasonable and chose the actual shortest one possible instead of the one that made sense

The parametric equations of a line can be determined using a point on the line and a direction vector. To find the parametric equation of a line that passes through a point A and is parallel to a direction vector b, we can use the following formula:

x = x0 + tbx

y = y0 + tby

z = z0 + tbz

where (x0, y0, z0) is the position vector of point A, (bx, by, bz) is the direction vector, and t is the parameter that varies along the line.

An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.

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Based on each given quadrilateral, we know that:

Rectangle ABCD has:

Rhombus FGHJ:

Square LMNO:

Let's discuss each quadrilateral we have:

ABCD is a rectangle; then:

DC = AB = 12

BD² = BC² + CD²

13² = BC² + 12²

169 = BC² + 144

BC² = 25

BC = 5

DE = 1/2 BD

DE = 1/2 (13)

DE = 6.5

∠DBA and ∠BDC are alternate interior angles and congruent, then:

∠DBA = ∠BDC = 35°

∠DBA = ∠BAC because triangle BAE is isosceles triangle.

∠BAC is the alternate interior angle of ∠DCA; then:

∠BAC = ∠DCA = 35°

∠DAB = ∠DAC + ∠BAC

90° = ∠DAC + 35°

∠DAC = 55°

Focus on triangle DEC:

∠DEC + ∠EDC + ∠ECD = 180°

∠DEC + 35° + 35° = 180°

∠DEC = 110°

Focus on triangle CEB:

∠CEB + ∠EBC + ∠CBE = 180°

∠CEB + 55° + 55° = 180°

∠CEB = 70°

FGHJ is a rhombus; then:

∠JGH = ∠FJH = 2∠FJG

∠JGH = ∠FJH = 2(60)

∠JGH = ∠FJH = 120°

Since FGHJ is a rhombus, then:

∠JGH + ∠JHG + ∠FGH + ∠JFG = 360°

120° + ∠JHG + 120° + ∠JGH = 360°

240° + 2∠JHG = 360°

2∠JHG = 120°

∠JHG = 60°

∠KFG = 1/2∠JHG

∠KFG = 1/2 (60)

∠KFG = 30°

GH = FG = 10

To find KG, we need to focus on triangle F.KG. Under the Sines Law:

KG / sin 30 = FG / sin 90 = F.K / sin 60

KG / √3/2 = 10 / 1 = F.K / 1/2

KG = 5

F.K = 5√3

FH = 2F.K

FH = 2(5√3)

FH = 10√3

LMNO is a square, then:

∠OMN = 45°

Please focus on triangle MNP. Under the Sines Law:

PM / sin 45 = MN / sin 90

PM / √2/2 = 8√2 / 1

PM = 8

LN = 2PM

LN = 2(8)

LN = 16

∠OPL = 90°

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The independent quantity is the number of days into the monitoring and the dependent quantity is the number of mole rats counted.

The independent quantity refers to a variable that is not influenced by any other factor and can be changed freely in an experiment or study.

In this case, the number of days into the monitoring is the independent quantity because it can be varied at the discretion of the zoo keeper.

The dependent quantity, on the other hand, is a variable that depends on the independent quantity and is affected by changes in it.

In this case, the number of mole rats counted is the dependent quantity because it is determined by the number of days into the monitoring. The zoo keeper counts a different number of mole rats based on how many days have passed, which is determined by the independent quantity.

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A zoo keeper thinks there is a problem with the Mole-Rat population at the zoo. He starts keeping track of the animals in the tunnels. 7 days into his monitoring he counts 120 mole rats, 13 days in he counts 108.

what information is provided?

Answer:

Below

Step-by-step explanation:

Value will be original value * ( 1 + i)^n      i = decimal annual interest

                                                                      n = years

  Value = 300 ( 1 + .07)^10 = 590.15  (dollars ?)

Work is defined as the product of force and distance, and can be calculated using the equation W = F * d, where W is work, F is force, and d is distance.

When lifting the whole log, the force required is equal to the weight of the log, and the distance over which the force is applied is the distance from the ground to the height of the shoulder.

When lifting one end of the log, the force required is still equal to the weight of the log, but the distance over which the force is applied is reduced. This is because the lever arm (the distance from the axis of rotation, which is the shoulder joint, to the point where the force is applied, which is the end of the log) is reduced.

So the equation for work done in lifting the whole log would be  W = m * g * h, where m is the mass of the log, g is the acceleration due to gravity, and h is the height from the ground to the shoulder. The equation for work done in lifting one end of the log would be W = (m/2) * g * h', where h' is the reduced height.

It can be seen that the work done in lifting one end of the log is equal to half the work done in lifting the whole log, because the force applied is the same, but the distance over which it is applied is reduced.

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The length of the side x in the triangle is 82.1 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sun of angle in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using trigonometric ratios as follows

Hence,

tan 75 degrees = opposite / adjacent

opposite side = x

adjacent side = 22 units

Therefore,

tan 75° = x / 22

cross multiply

x = 22 tan 75

x = 22 × 3.73205080757

x = 82.1

Therefore,

x = 82.1

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The difference 120.45-116.9 is 3.55.

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given:

The two decimal numbers,

120.45 and 116.9.

Applying subtraction operation,

the difference 120.45-116.9.

By adding on strategy,

116.9 is 3.55 left to the number 120.45 on the number line.

That means,

116.9 + 3.55 = 120.45.

Therefore, the difference is 3.55.

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If  ∆AFD, m ∠F = 90° AD = 14, m ∠D = 30° .The  Area of ∆AFD is 49 square units.

To find the area of triangle AFD, we can use the formula for the area of a triangle given its base and height. In this case, the base is AD, and the height can be found by constructing an altitude from F to AD.

First, we will find the length of FD. Since m ∠D = 30°, we can use the trigonometric  function sine to find the length of FD. Using the sine formula:

FD = AD * sin(∠D) = 14 * sin(30°) = 14 * 1/2 = 7

Next, we will find the length of A.F. Since m ∠F = 90°, FD is the height of the triangle. So, the area of triangle AFD is given by:

Area = (AD * FD) / 2 = (14 * 7) / 2 = 49 square units

Therefore the area of ∆AFD is 49 square units.

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The length and width of a rectangle are 36cm and 4.5cm

Finding the Width:

The formula to find the perimeter of the rectangle is:

P=2(l+w),

where P is the perimeter, l be the length, and w be the width.

Now substitute the given values to solve for w, since we need to find the width.

The given information is:

the length of a rectangle is six inches more than eight times the width so the equation becomes:

L=8w+6

P=120

w=8w

now plug the values in the above formula:

P=2(l+w),

120=2(8w+6)+8w

120=16w+12+8w

120=24w+12

24w=108

w=4.5

To find the length just substitute in the L.

L=8(4.5)+6

L=30+6

L=36

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The new volume of the cylinder is 39.94cm³

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.

The volume of a cylinder is expressed as V = πr²h

The volume of the original cylinder = 10cm³

The radius and height of the new cylinder = 4r and 4h

10 = 3.14 × r²h

V 2= 3.14 × 4r²4h

V2 = 3.14× 4( r²h)

10=3.14 × r²h

r²h = 10/3.14

r²h = 3.18

from

V2 = 3.14 × 4(r²h)

represent 3.18 by r²h in the equation

V2 = 3.14 × 4 ( 3.18)

V2 = 39.94cm³

therefore the volume of the new cylinder is 39.94 cm³

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The correct options of the solution of the equation 2x+7y=-5 is (a) -6,1 and (c) 8,-3.

In mathematics, two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.

In  order to determine whether an ordered pair is a solution, all we have to do is plug in the values of x and y and see if we end up with a true statement.

(a) for (-6, 1)

put the value of 1 for y and -6 for x:

2(-6)+7(1)=-5

-12+7=-5

-5=-5

Yes! Here we have a true statement. Therefore, this ordered pair is a solution.

(b) for (9, 2)

put the value of 2 for y and 9 for x:

2(9)+7(2)=-5

18+14=-5

32≠-5

Well, we can see that we have a false statement, because ≠ means "not equal to". Therefore, this ordered pair is not a solution.

(c) for (8, -3)

put the value of -3 for y and 8 for x:

2(8)+7(-3)=-5

16-21=-5

-5=-5

Yes! Here we have a true statement. Therefore, this ordered pair is a solution.

Let's try the last option.

(d) for (-5, -4)

put the value of -4 for y and -5 for x:

2(-5)+7(-4)=-5

-10-28=-5

-38≠-5

Well, we can see that we have a false statement, because ≠ means "not equal to". Therefore, this ordered pair is not a solution.

Hence, the correct options of the solution of the equation 2x+7y=-5 is (a) -6,1 and (c) 8,-3.

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The amounts of bacteria are given as follows:

The exponential function y = 8^x is graphed by the image presented at the end of the answer.

An exponential function is defined as follows:

y = ab^x.

In which:

The parameters for this problem are given as follows:

Hence the function is defined as follows:

y = 8^x.

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Option (a) is correct. There'll be No Solution to the given system of linear equations.

According to the solutions of linear equations, we know the following things,
1. If two intersecting lines are at one common point, the system has only one solution.
2. If two coincidental lines mean both equations give the same line, that means the system has infinitely many solutions.
3. If the lines are parallel to each other, the system will have no solution.

We can see lines are parallel but we can also find whether the given lines are parallel or not by simply finding their slope m.

For Line 1, we have the following data
[tex]$\left(\mathrm{x}_1, \mathrm{y}_1\right)=(0,2)$[/tex]

[tex]$\left(\mathrm{x}_2, \mathrm{y}_2\right)=(3,1)$[/tex]

For slope m of the line 1,
slope m₁ = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{1-2}{3-0}=-\frac{1}{3}[/tex]

For Line 2, we have the following data

[tex]$\left(\mathrm{x}_1, \mathrm{y}_1\right)=(0,-1)$[/tex]

[tex]- $\left(x_2, y_2\right)=(3,-2)$[/tex]

For slope m of line 2,
slope m₂[tex]$=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-(-1)}{3-0-x_1}=-\frac{1}{3}$[/tex]

As the slope of both lines is equal, so lines are parallel to each other, and hence, if lines are parallel so there'll be no solution to the system.
Hence, option (a) is correct.

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Your question was incomplete, the most probably question you asked was:

How many solutions does the system of linear equations represented in the graph have? Coordinate plane with one line that passes through the points (0, 2) and (3, 1) and another line that passes through the points (0, -1) and (3, -2).
(a) No solution
(b) One solution at (−1, 0)
(c) One solution at (0, −1)
(d) Infinitely many solutions

The amount of the bottle that is filled with sand is; The whole bottle is full of sand

When talking about fraction word problems we are simply referring to fraction parameters being represented in the form of word problems.

The parameters given are;

Fraction with pink sand = 1/6

Fraction with red sand = 3/6

Fraction with white sand = 2/6

Thus;

Total sand = 1/6 + 2/6 + 3/6

= 6/6 = 1

Thus, the bottle will be full

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Every year, 1800 units crossover point. The process focus is less expensive for volumes over 1800.

When all tax credits have been used up by a limited partnership and the limited partners are left with a tax burden, that moment is known as the crossover point.

When both projects have positive values, the crossover point is formed by the intersection of two IRR curves.

The weighted average cost of capital, also known as the crossover rate, is the rate of return at which the net present values (NPV) of two projects are equal.

The rate of return at which the net present value profiles of two projects cross each other is what this term denotes.

So, annual crossover sales are 1800 units.

Process emphasis is less expensive and less important for volumes under 1800 units; repeated manufacturing concentration is less expensive and less important for volumes exceeding 1800 units.

Fixed cost ÷ variable cost

$90000÷50 =$1800

$9,000÷5=$1800

Therefore, every year, 1800 units cross over. The process focus is less expensive for volumes over 1800.

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Correct question:

A product is currently made in a process-focused shop, where fixed costs are $9,000 per year and variable costs are $50 per unit. The firm is considering a fundamental shift in process, to repetitive manufacturing. The new process would have fixed costs of $90,000, and variable costs of $5. The cross over is at 1800 units annually. for volumes over 1800, the process focus is cheaper.

The population of the green sea turtle on the island in 2012 is 68 turtle

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristics.

To find the exponential decrease in a population which obtain it by using the formula;

P(t) = P(o) e^-kt

P(o) = 750

k = 0.2

t = 12

P (t) = 750 e ^ -0.2 ×12

p(t) = 750 e^ -2.4

p(t) = 750 × 0.09

p(t) = 68( approximately) turtle

Therefore in 2021 the population of turtle on the island is 68

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Answer:

B

Step-by-step explanation:

10*10*10 =1000

5*5 =25

2*2 =4

1000+25+4 =1029

Answer: $6000

Step-by-step explanation:

The initial value will be what the person deposits before the interest. Because Liam deposited $6000 the initial value would be $6000.

Hope this helps!

Answer:

y= x/2 - 3 : linear

y= 6/x -2 : nonlinear

3x + y = 12: linear

y = x: linear

The measure of the supplementary angles is:

∠X = 117°

∠Y = 63°

Here we know that angles ∠X and ∠Y are supplementary angles. Remember that two angles are supplementary if their measures add up to 180°.

Here we know that the measures are:

∠X = 3n − 18

∠Y = 2n − 27

We can write:

∠X + ∠Y = 180°

(3n - 18) + (2n - 27) = 180

Then we can solve that for n.

3n + 2n - 18 - 27 = 180

5n = 180 + 45

n = 225/5 = 45

Then the measures of tha angles are:

∠X = 3n − 18 = 3*45 - 18 = 117°

∠Y = 2n − 27 = 2*45 - 27 = 63°

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The order of the numbers from least to greatest is as follows:

7, 31/4,7¹⁹/₂₅,7.765,8.44

A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32, etc.

Given here: The numbers containing fractions and decimal numbers.

To get a clarity on the magnitude of the numbers, let's convert every fraction to decimal numbers

Thus 7¹⁹/₂₅=7.76

31/4=7.75

Hence, The order of the numbers from least to greatest is as follows:

7, 31/4,7¹⁹/₂₅,7.765,8.44

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Based on the data of increase in ice cream sales as the weather gets warmer the data is

A statistical measure known as correlation expresses how linearly connected two variables are (meaning they change together at a constant rate). It is frequently used to describe straightforward relationships without explicitly stating cause and effect.

In this case, the data shows a relationship between the weather (one variable) getting warmer and an increase in ice cream sales (another variable). However, just because two variables are correlated does not necessarily mean that one causes the other.

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If p represents the total profit in dollars and cents when the store buys any number of sweaters, s, then the  proportional equation for p in terms of s is, p = $21 x s

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Let's call the selling price of each sweater "sp".

The store buys 15 sweaters for $90, so each sweater must cost

=$90 / 15

= $6

The store sells each sweater for

= $405 / 15

= $27,

so sp = $27

The total profit is equal to the selling price minus the buying price, so the equation for the total profit, p, in terms of the number of sweaters sold, s, is:

p = sp x s - $6 x s

We can simplify this equation to:

p = ($27 - $6) x s

p = $21 x s

So, the proportional equation for the total profit in dollars and cents when the store buys any number of sweaters, s, is:

p = $21 x s

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A woman you know has five children among which all five  are boys. probability for a woman that she will have all five boy as a five children is  0.5.

The probability or the outcome  in which a women with five children have all the girls and none of them as boys is :-

0.5x0.5=0.25.

So for the  first child there is a a 50% chance that is will be of a male. And same for the  second child being male there will be equal probability that it can be boy so it  also will have a probability .

So the probability of having five females is  0.55=0.03125

Except the above define value all the other outcome or choices means that the women have a least one son in the five children  and the total probability of an event is 1.

.The theoretical probability is mainly reasoning bases which is behind probability. For example, if a coin is tossed then the theoretical probability or the outcome of getting a head will be ½.

Probability provides information about the happening of   something which might happen and might not depending upon the outcome demand happen. Meteorologists, also take the help of probability to predict whether the rain may happen or not for instance In epidemiology, also probability theory is used to understand  about various risk related to life an to demonstrate various relation .

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There are 3600 ways to seat 6 people at two round tables, with at least one person at each table.

In this scenario, we have 6 people to seat at 2 round tables, meaning each table must have at least 3 people.

We can start by finding the number of ways to seat 6 people at one table, then divide that by 2 to account for the two tables.

For one round table, there are 6! (6 factorial) ways to seat 6 people. This is because, for the first seat, there are 6 options. For the second seat, there are 5 options remaining; for the third seat, there are 4 options, and so on.

However, this number counts the same arrangement of people multiple times, as the arrangement can start with any person. So, to correct this, we divide 6! by 6, which gives us 720/6 = 120 ways to seat 6 people at one round table.

Now, since we have two tables, each table must have 120/2 = 60 arrangements. This means there are 60 x 60 = 3600 ways to seat 6 people at two round tables.

In conclusion, there are 3600 ways to seat 6 people at two round tables, with at least one person at each table.

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72 cm²  

3 * ( 6+2+2) + 2 * (2 * 6) + 6 * 3

The total amount spent by Mrs. Rivera is given by the equation A = $ 2.25

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount spent by Mrs. Rivera be represented as A

Now , the equation will be

The cost of one pound of banana = $ 0.45

The total amount of bananas = 5 pounds

So , the total amount of money for 5 pounds = 5 x cost of one pound of banana

Substituting the values in the equation , we get

The total amount of money for 5 pounds of banana A = 5 x 0.45

The total amount of money for 5 pounds of banana A = $ 2.25

Hence , the total amount is $ 2.25

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