How is substitution used to determine if an ordered pair is the solution to a system of equations?.

The coordinates of the vertices of the image are:

A' = (-1, 5)

B' = (-4, 0)

C' = (-2, -2)

Option A is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Counterclockwise means the coordinates will interchange and the sign will be depending on the quadrants.

The coordinates of the triangle ABC.

A = (5, -1)

This is in the 4th quadrant.

If rotated 90 degrees counterclockwise A will be in the 1st quadrant.

A' = (-1, 5)

B = (0, 4)

This is in the first quadrant.

If rotated 90 degrees counterclockwise B will be in the 2nd quadrant.

B = (-4, 0)

C = (-2, 2)

This is in the 2nd quadrant.

If rotated 90 degrees counterclockwise C will be in the 3rd quadrant.

C = (-2, -2)

Thus,

The coordinates of the image are:

A' = (-1, 5)

B' = (-4, 0)

C' = (-2, -2)

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The answer is option (D) : Find the midpoint of segment NP.

What is Midpoint?

The midpoint of a line segment is a point that lies exactly halfway between two points. It is the same distance from each endpoint of the straight line segment. Midpoint formula is a mathematical equation that is used to locate the halfway point between two data points. The midpoint formula is applied when one is required to find the exact center point between two defined points.

As Shown in below diagram given below,

suppose need to park at point M (i.e. midpoint of NP)

distance = NM + MP

so, when M is the midpoint of NP and has the minimum distance.

Therefore, the answer is option (D) : Find the midpoint of segment NP.

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The inverse of a logarithmic function is an

The inverse of the inverse logarithmic function is simply the exponential function.

The inverse logarithmic function (also known as the logarithm or log) takes as input a number x and returns the power to which a fixed number (usually 10 or e) must be raised to produce x. The inverse of the logarithmic function is the exponential function, which takes as input a power and returns the number that would result from raising a fixed number to that power. In other words, if log_b(x) = y, then b^y = x, where b is the fixed number.

In other words, the exponential function is the inverse of the inverse logarithmic function.

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The greater than sign is '>'. If one value is greater than the other, use greater than. Therefore, we can write more than 50 as x > 50.

Greater Than:

In mathematics, the greater than sign is placed between two values ​​where the first number is greater than the second number.

Example: 60 > 50, where 60 is greater than 50.

In inequalities, the greater-than sign always refers to the greater value, and the sign consists of two equal length dashes joined at an acute angle on the right increase (>).

The greater than sign is used in linear inequalities when the value of a variable is not known to be greater than to a certain value. This symbol is a greater-than symbol (>) with a sleep line below it.

Here are some more examples.

x > 100 means the value of x is greater than to 100.

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By applying the future values, the amount of money the parents should deposit to have $8,250 for a child’s education in 10 years is $2,529.09

A current asset's future value, abbreviated as FV, is the value that asset is expected to have at some point in the future, based on a projected rate of growth. The future value is essential for investors and financial planners because they use it to estimate how much money an investment made now will be worth in the future.

To find the future values, we can use this following formula:

FV = I x (1 + R)^T

Where:

I = investment amount

R = interest rate

T = number of years

In this case, we are given that:

Future values (FV) = $8,250

The periodic rate = 12% : 4 = 0.03 (compounded quarterly)

Number of period = 10 years x 4 = 40

Hence, the amount of money the parents should deposit to have $8,250 for a child’s education in 10 years is:

8,250 = I x (1 + 0.03)⁴⁰

I = 8,250: ((1 + 0.03)⁴⁰)

I = $2,529.09

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Answer:

linear equation represents the graph below

The height of the cylinder is given by the equation h = 12 cm

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

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the cylinder be represented as A

Now , the radius of the cylinder be r = 6 cm

Let the height of the cylinder be h

Let the volume of the cylinder be V = 432π cm³

Volume of Cylinder = πr²h

Substituting the values in the equation , we get

432π = π ( 6 )² x h

On simplifying the equation , we get

432 = 36h

Divide by 36 on both sides of the equation , we get

h = 12 cm

Hence , the height of the cylinder is 12 cm

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A front-end loader to load trucks with granular material that has a swell factor of 15%. If the loader has a heaped capacity of 10 cu. Yd.  the total cycle time for the loader, if it can move 55 cu, is 16.2 hours(  55 cu. Yd. / 10 cu. Yd. (heaped capacity) * 15% (swell factor) * 48 min. /hr)

The total cycle time for a front-end loader to load trucks with granular material with a swell factor of 15% can be calculated by taking the total amount of in-bank material to be loaded and dividing it by the heaped capacity of the loader. This will give us the total number of cycles the loader must complete. Once we have this number, we must multiply it by the swell factor. This gives us the total number of heaped cycles the loader will have to complete.

Finally, we must multiply the total number of heaped cycles by the efficiency of the loader. Efficiency is the amount of time it takes for the loader to complete one heaped cycle. In this case, the total cycle time for the loader to load is 55 cu. Yd. Of in-bank material with a swell factor of 15% and a heaped capacity of 10 cu. Yd. Is 16.2 hours, assuming the loader has an efficiency of 48 min. /hr.

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Picking a green marble from bag A is D. impossible.

The probability of an impossible occurrence is the likelihood that an event won't occur at all and won't have any chance of happening in the future. As a result, the likelihood of such an event is always zero. An impossible event is one that doesn't take place. There is no chance that it may occur. Therefore, there is no chance of that happening.

There are no green marbles in Bag A which means that it is not possible to pick a green marble from Bag A. The probability of picking a green marble is 0 and the likelihood is impossible.

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The full question is:

Bag a has 2 yellow marbles,2 red marbles, and 3 blue marbles picking a green marble from bag a is certain,likely,unlikely,impossible

Answer:

  (a) negative three halves (-3/2)

Step-by-step explanation:

You want the slope of the line through points (1, 0) and (3, -3).

The slope can be found using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (-3 -0)/(3 -1) = -3/2

(a) The slope of the line is -3/2.

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The base angle for the isosceles triangle is 53°.

Any triangle with two sides that have the same length is said to be an isosceles triangle. If the two sides of a triangle are congruent, then the angle across from them must likewise be, according to the theorem that explains the isosceles triangle. As a result, the two angles of an isosceles triangle that are on opposite sides with equal numbers are equal in size.

Given base length = 6 and leg length = 5

draw a perpendicular to the base that divides the base into equal parts,

as shown in the image attached

let the base angle be Ф,

and using a cosine formula for the base angle

cosФ = base/hypotenuse

from construction  base = 3 and hypotenuse = 5

cosФ = 3/5

Ф = cos⁻¹(3/5)

Ф = 53.13°

Ф = 53° (approx)

Hence the base angle is 53°

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Yes, it is possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(4.5cm + 5.8cm) =10.2cm

10.3cm = 10.2cm

LHS>RHS

A triangle is possible.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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12 white socks, 8 black socks, 20 total socks:

a.

[tex]\dfrac{12}{20}\cdot\dfrac{8}{19}\approx 0.252631578​947\approx 25.3\%[/tex]

b.

[tex]\dfrac{12}{20}\cdot\dfrac{11}{19}\approx 0.347368421053\approx 34.7\%[/tex]

c.

[tex]\dfrac{8}{20}\cdot\dfrac{7}{19}\approx 0.147368421053 \approx 14.7\%[/tex]

Answer:The value of the coins is $0.70. Write and solve a system of linear equations to find the numbers of nickels and dimes in your pocket. There are 6 nickels and 4 dimes.

Step-by-step explanation:

a) Graham's employer contributes $561.60 per year towards his coverage.

b) Claudia contributes 28.2% towards the total coverage cost.

What is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is typically represented by the symbol "%", and is often used to express a change or a part of a whole.

a) Graham makes $62,800 per year, which is less than $65,000, so he pays $52 per month for individual coverage. His yearly contribution is 10% of the total cost, so his employer contributes 90% of the total cost. To find the total cost, we can multiply the monthly cost by 12: $52/month * 12 months/year = $624/year. So Graham's employer contributes $624 * 90% = $561.60 per year towards his coverage.

b) Claudia's annual salary is $75,400, which is at least $65,000, so she pays $122 per month for family coverage. Her employer contributes $1,052 per month towards her total coverage cost. To find the total cost, we can multiply the monthly cost by 12: $122/month * 12 months/year = $1,464/year. To find the percentage Claudia contributes, we divide her contribution by the total cost and multiply by 100: $1,464-$1,052 / $1,464 * 100 = 28.2%. So Claudia contributes 28.2% towards the total coverage cost.

Hence,

a) Graham's employer contributes $561.60 per year towards his coverage.

b) Claudia contributes 28.2% towards the total coverage cost.

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First, you need to find the slope between the two points:

      [tex]\begin{aligned}\dfrac{8-2}{-1-1} & = \dfrac{6}{-2}\\[0.5em]&=-3\endaligned}[/tex]

Now, you use one of the points to find the equation.

You can use point-slope form:

     y - 1 = -3 (x-2)

Or you can use slope-intercept form:

    y = -3x + 5

Note:

You can find the slope-intercept form by taking y = mx + b and substituting in the slope and a point and solving for b:

    2 = -3 (1) + b

The sum of the polynomials (-x² + 9) + (-3x² - 11x + 4) is -4x² - 11x - 5.

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Complete Question:

What is the sum of the polynomials (-x² + 9) + (-3x² - 11x + 4)?

If overtime was compensated at time and a half, Mr. Riley would receive 15 hours of base pay.

By first figuring out the value of a single unit and then multiplying that value to get the requisite value, a problem can be solved using the unitary technique. For multiplication and dividing by fractions, the unitary strategy is frequently beneficial because it makes sense immediately and can be executed mentally if the numbers add up. Since written methods for fractions are frequently employed, notably division by a fraction, it is useful to explain or defend these algorithms. The unitary method's formula is to get the value of one unit, multiply it by the number of units, and then divide the result by the desired value.

given

The standard workweek is 40 hours.

Gross wages totaled $490.15.

Pay for overtime: $156.75

Total compensation based on a basic week = Total Gross salaries minus overtime pay

Total wages calculated based on a standard week are $490.15 - $156.75 = $334.

Let the basic hourly salary be $8.36 ($x = x).

Let y hours equal the number of overtime hours.

Due to the fact that overtime pay is time-and-a-quarter.

According to the calculation: Equals 15 hours

If overtime was compensated at time and a half, Mr. Riley would receive 15 hours of base pay.

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A polynomial or a rational function in simplest form is (f. g)(x) is 4x² + 25x + 6.

The exponents of all the variables of an algebraic statement known as a polynomial must all be whole numbers. In any polynomial, the exponents of the variables must be non-negative integers.By identifying which phrases only contain the processes of adding, subtract, multiplying, and non-negative integer exponents, the polynomials can be located. Expressions with additional processing are considered as non expressions.

Given,  f(x) = 4x + 1

          g(x) = x + 6

Now, (f. g)(x) = f(x).g(x)

                   = (4x + 1)(x + 6)

                   = 4x² + 24x + x + 6

                   = 4x² + 25x + 6

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A square root function is the inverse of a quadratic function. If a function f is the inverse of another function f1, then f is the inverse of f1.

The order of positive integers is preserved by the square function: greater numbers have larger squares. The square, then, is a monotonic function on the range [0, +]. Since negative integers have squares that are proportional to their absolute values, the square on [(,0] is a monotonically declining function.

The horizontal line test determines whether or not f has an inverse if any horizontal line crosses its graph more than once.

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Answer: R160.10

Step-by-step explanation:

R700-R189.75=R510.25

R510.25-R203.20=R307.05

R307.05-R146.95=R160.10

For the nine-day rental, the expression for the same sum will be charged as $1,610

The formula combines numerical elements and operations symbolised by the signs for addition, subtraction, multiplication, and division.

Expression are the Mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping in addition to numbers (constants). The operation order and other characteristics of the logical syntax can also be indicated by them.

Given that Mr. White will be leasing an enormous vehicle for a week plus a few more days, He is not required to pay a per-mile charge. The formula is 440 + 130d.

The sum will be computed as follows by the expression:

A = 440 + 130d

A = 440 + ( 130 x 9 ) ( 130 x 9 )

A = 440+ 1170

A = 1,610

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To change the log base 2 to log base 10, we can use the change of base formula for logarithms.

We know that the change of base formula for logarithms.

The formula to change the base of a logarithm from base 'a' to base 'b' is:

[tex]log_a(m)=\frac{log_b(m)}{log_b(a)}[/tex]

Here, we need to change log base 2 to base 10

By using this change of base formula, we can change the log base 2 to log base 10.

We know that log base 10 is called the common logarithm.

We denote [tex]log_{10} (x)[/tex] as log(x).

Let us assume that we want to change a number log of x to the base 2 to log of x to the base 10

From above formula of change of base we get,

[tex]log_2(x)\\\\=\frac{log_{10}(x)}{log_{10}(2)}\\\\=\frac{log(x)}{log(2)}[/tex]

Thus, we can use the change of base formula for logarithms  to change the log base 2 to log base 10,

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The present value of the bond is $3,345.90. This is calculated by taking the future value of the bond ($4,500) and dividing it by the present value factor for 4.25% for 10 years (1.427).

PV = FV / (1 + r)n

PV = $4,500 / (1 + 0.0425)10

PV = $4,500 / 1.427

PV = $3,345.90

The present value of an asset is the value of the asset today, taking into account the time value of money and the interest rate of the investment. In this example, the Exxon Corporation bond will pay $4,500 ten years from now, and the going interest rate on safe 10-year bonds is 4.25%. To calculate the present value of the bond today, we use the present value formula, which is the future value of the bond divided by the present value factor for the given interest rate and number of years. In this case, the present value factor is 1.427, and the present value of the bond is $3,345.90. This means that the bond is worth $3,345.90 today, taking into account the time value of money and the given interest rate.

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Answer:

17/20

Step-by-step explanation:

_(_2/3)*6/10*17/8

2/3×6/10×17/8

=17/20

f(-2) = 3 (value on y axis)

if f(x) = -1, x = 0 (when y = -1)

Answer:

-13, -22, -31, -40

Step-by-step explanation:

substitute n for each term

g(x) must be equal to f(x).

An equivalent function is a mathematical expression that produces the same result as another expression. It is a function that is mathematically equivalent to a given function, meaning that its graph is the same as that of the given function. Equivalent functions are useful in problem solving as they can be used to simplify a problem or to show a relationship between two functions.

g(x) = 3x² - 2x + 1. This means that f(x) and g(x) are equivalent functions, and thus have the same output for any given input. This means that when x is plugged in to both equations, the resulting output will be the same. Therefore, g(x) must be equal to f(x).

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Answer: Look at the image below.

Step-by-step explanation: I traced it out and did the math for you.

Hope this helps! :)