Write the following as an algebraic expression. Simplify if possible.
Subtract 5y−6 from y−3.

Answer:

Option A

Concept Applied:

(g-f)(x) = g(x)-f(x)

Step-by-step explanation:

Substitute and solve

Answer:

Let the cost of one apple pie be A and the cost of one blackberry pie be B.

From the first statement, we can write the equation:

SA + 4B = 8140 ----(1)

From the second statement, we can write the equation:

4*B = 152

Solving for B:

B = 38

Substituting B in equation (1) and solving for A:

SA + 438 = 8140

S*A = 8008

A = 8008/S

We do not have enough information to find the value of S or A individually, but we can find the relationship between them:

A/B = (8008/S)/38 = 211/S

Therefore, the cost of one apple pie is 211 times the cost of one blackberry pie.

Answer:

Write

f

(

x

)

=

2

x

2

+

12

x

+

10

as an equation.

y

=

2

x

2

+

12

x

+

10

Step-by-step explanation:

Write

f

(

x

)

=

2

x

2

+

12

x

+

10

as an equation.

y

=

2

x

2

+

12

x

+

10

The polynomial function with fifth degree and given zeroes is 4x⁵ - 20x⁴ + 64x³ + 324x² - 432x.

The maximum power of the variable in a polynomial function is its degree. For instance, since 2 is the largest power of x, the polynomial function f(x) = 3x2 + 2x + 1 has a degree of 2. We only take into account the degree of the term with the highest power of x when a polynomial function comprises many terms. A polynomial with no x terms is a constant function, and thus has degree zero.

To determine the polynomial, we determine the zeroes.

Given that, 3 is a zero of multiplicity 3,-4 is the only other zero thus:

(x - 3)³(x + 4)

Now, for leading coefficient 4 we have:

4x(x - 3)³(x + 4)

Thus, solving the parentheses we have:

4x(x³ - 9x² + 27x - 27)(x + 4)

(4x⁴ - 36x³ + 108x² - 108x)(x + 4)

4x⁵ - 36x⁴ + 108x³ - 108x² + 16x⁴ - 144x³ + 432x² - 432x

4x⁵ - 20x⁴ + 64x³ + 324x² - 432x

Hence, the polynomial function with fifth degree and given zeroes is 4x⁵ - 20x⁴ + 64x³ + 324x² - 432x.

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There are 10 ways that you can answer the 3 questions

Given that

Questions = 3

Options = 5

The number of many ways you can  answer the questions is calculated as

Ways = OptionsCQuestions

So, we have

Ways = 5C3

Evaluate

Ways = 10

Hence, the number of ways is 10

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that L looking shape is a right angle, which is 90 degrees. and the question is saying that the part they cut off is 56 degrees. to find x you will need to subtract 90 from 56 to get 34.

The answer is 34 :)

Answer:0

Step-by-step explanation: -

-7 x -7 = 49

11 x 77 = 77

-7 + 7 = 0

49 + 77 + 28 = 154

154 ÷ 0 = 0

Answer:

The perimeter of the entire frame is equal to the sum of the perimeters of the mat and the picture. The expression for the perimeter of the mat is (2m + 10) + (2m + 8) = 4m + 18, and the expression for the perimeter of the picture is 2(8) + 2(10) = 36. Therefore, the expression for the perimeter of the entire frame is (4m + 18) + 36 = 4m + 54.

From the calculations, only question 2 shows that f(x) is the inverse of function g(x) as the rest shows the parent functions are not inverse of g(x)

In the given question, we are to determine if the parent function f(x) is an inverse to g(x).

1. f(x) = 2x - 9

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

Let's switch the variables: y = 2x - 9 to x= 2y - 9.

We can proceed to solve the equation as;

x =2y - 9 for y.

y= x + 9 / 2

Therefore, f(x) is not an inverse of g(x)

2. f(x) = x - 3 / 4

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

Let's switch the variables:

y = x / 4 - 3/4 to x = y / 4 - 3/4

we can solve the equation for y to give us;

y = 4x + 3

This shows that f(x) is inverse of g(x)

4. f(x) = 7x^3/2 - 4

To find the inverse function, swap x and y and solve the resulting equation for x

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables:

y = 7x^3/2 - 4 will become x = 7y^3/2 - 4

Solving for y;

y = [(∛7(x + 4))^2/3] / 7

This shows f(x) is not the inverse of g(x)

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The median number of points scored for each team is given as follows:

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

Considering the stem-and-leaf plot, the data-sets for each team are given as follows:

Team 1 has an even number of games, hence the median is given by the mean of the two middle elements, as follows:

Median = (13 + 14)/2 = 13.5.

For team 2, the median is given as follows:

Median = (10 + 12)/2 = 11.

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The ratio of spots to eyes can be described as follows;

There are 6 spots for every 2 eyes.

There are 3 spots for every 1 eye.

In Mathematics and Geometry, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

Based on the information provided above, we have the following ratio parameters:

The total number of spots = 6 spots.

The total number of eyes = 2 eyes.

Ratio = 6/2 = 3 spots.

In this context, we can reasonably infer and logically deduce that there are 6 spots for every two (2) eyes and three (3) spots for every one (1) eye.

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Complete Question:

Use the following image to complete the sentences describing the ratio of spots to eyes.

There are 6 spots for every ____ eyes.

There are _____ spots for every 1 eye.

The solution set of the inequality is:

m > 12

Here we want to solve the inequality:

5m > 60

To find the solution set of the inequality, we need to isolate the variable, m, in one of the sides of it.

To do so, divide both sides by 5, we will get:

5m/5 > 60/5

m > 12

So any value of m that is larger than 12 is a solution.

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The surface area of the cylinder is 1851.97 square meters

From the question, we have the following parameters that can be used in our computation:

Radius, r = 13.1 meters

Height, h = 9.4 meters

Using the above as a guide, we have the following:

Surface area = 2πr(r + h)

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2π * 13.1 * (13.1 + 9.4)

Evaluate

Surface area = 1851.97

Hence, the surface area is 1851.97 square meters

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Determining the highest point of value for a particular solution relies heavily on the type of problem which needs to be resolved.

Evaluate equations or functions: If you possess an equation or function that symbolizes the desired answer, it is prudent to study it intensely in order to pinpoint its maximum value. For instance, taking the derivative of the equation and establishing zero as an equalizer will allow you to determine any critical points. Shortly afterward, evaluating those points alongside endpoints within its domain verifies what its maximum value is.

Optimization strategies: In cases where a particular quantity must be maximized amidst constraints, such as linear programming or quadratic programming techniques, it is useful to implement optimization strategies to resolve these kinds of problems conveniently and effectively.

Experimentation via simulation: In instances where mathematical analyses prove too difficult given the complexity involved, it becomes necessary to use simulation or experimentation techniques to investigate potential solutions thoroughly. It involves improvising input parameters while watching output meticulously with an eye to spotting the corresponding maximum value.

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Answer: -13/17

Step-by-step explanation: To find the slope of the line that passes through the points (-9, 7) and (8, -6), you can use the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-9, 7) and (x2, y2) = (8, -6)

Substituting the values in the formula, we get:

slope = (-6 - 7) / (8 - (-9))

slope = -13 / 17

Therefore, the slope of the line that passes through the points (-9, 7) and (8, -6) is -13/17.

Answer:

[tex]\frac{-14}{17}[/tex]

Step-by-step explanation:

Slope is the change in y's (-9,7) (8,-6) over the changes in x's (-9,7)(8,-6).  You find the changes by subtraction

[tex]\frac{-6-7}{8-(-9)}[/tex] = [tex]\frac{-14}{8+9}[/tex] = [tex]\frac{-14}{17}[/tex]

Helping in the name of Jesus.

The annual depreciation expense for this car is $1,833.33.

Simply deduct the vehicle's current fair market value from the purchase price, less any applicable sales tax or fees, to determine how much value has been lost.

We must determine the total depreciation throughout the vehicle's useful life and divide it by the number of years to determine the annual depreciation expense:

Total depreciation = purchase price - resale value

= $28,500 - $17,500

= $11,000

Annual depreciation expense = total depreciation / useful life = $11,000 / 6 = $1,833.33 (rounded to the nearest hundredth)

Therefore, the annual depreciation expense for this car is $1,833.33.

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Answer:

The answer in the simplest form is (32y-3)/8

Step-by-step explanation:

1/4(13y-3)+1/8(6y+3)

13y/4-3/4+6y/8+9/8

(13y-3)/4+(6y+9)/8

[2(13y-3)+(6y+9)]/8

[26y-6+6y+9]/8

C.L.T

[26y+6y-6+9]/8

(32y-3)/8

Angle measure in radians 9π/5 3π/4

Angle measure in degrees 324° 135°

Note:

9π/5 can also be written as 1.8π radians or 324 degrees

3π/4 can also be written as 0.75π radians or 135 degrees

The table provides values for angle measures in radians and degrees. To convert between radians and degrees, The exact measures in radians for 9rt/5 is 3π/5 and for 3π/4 is 135°. The exact measure in radians for 20 degrees is π/9 and for 275 degrees is 55π/36.

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. It is used to measure the amount of rotation between the two rays or line segments.

A radian is a unit of measure for angles, where the measure of the central angle is equal to the length of the corresponding arc on the unit circle. It is equal to approximately 57.3 degrees.

According to thw given information:

The table displays measures of angles in radians and degrees. Radians are a unit of measurement for angles, and they relate the length of the arc of a circle to the radius of that circle. One radian is equivalent to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. Pi radians, or 180 degrees, represent a straight angle.

In the table, the first angle measure in radians is given as 9√5, which is an exact measure. The second angle measure in radians is given as 3π/4, which represents a quarter of the circumference of the circle, and is equal to 45 degrees. The first angle measure in degrees is given as 20°, which is the equivalent of π/9 radians, and the second angle measure in degrees is given as 275°, which is equivalent to 55π/36 radians.

Knowing how to convert between radians and degrees is important in many mathematical calculations, especially those involving trigonometry. Understanding the relationship between these units of measure can help to solve problems in many areas of mathematics and science.

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An expression for the height of the cuboid is 3p - 245q/49 meters.

In Mathematics and Geometry, the volume of a cuboid with a square base can be calculated by using this following formula:

Volume of a cuboid = L² × H

Where:

By substituting the given parameters into the formula for the volume of a cuboid cuboid with a square base, we have the following;

(147p - 245q) = 7² × H

(147p - 245q) = 49 × H

Height, H = (147p - 245q)/49

Height, H = 3p - 245q/49 meters.

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The amount in the account at the end of the year is $4998.

Percentage decrease is the measure of the reduction in the value of a quantity over time, expressed as a percentage of its original value. It is calculated by taking the difference between the original value and the new value, dividing it by the original value, and then multiplying the result by 100.

We know that;

Percentage decrease = 26.5%

Then the decrease in dollars = 26.5/100 * 6800

= $1802

The amount at the end of the year = $6800 - $1802

= $4998

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The mass of the sugar that is contained in the juice is 19.6 g.

In mathematics, a proportion is a statement that two ratios are equal. A ratio is the relationship between two quantities, usually expressed in the form of a fraction.

To solve a proportion, you can use cross-multiplication. Cross-multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio, and vice versa.

We know that;

24.5 g of sugar is contained in 250 ml of the juice

x g of sugar is contained in 200 mL of the juice

x = 24.5 * 200/250

x = 19.6 g

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Answer:

The roots of the quadratic equation x² + 4x + 7 = 0 can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 1, b = 4, and c = 7. Substituting these values into the formula, we get:

x = (-4 ± √(4² - 4(1)(7))) / 2(1)

x = (-4 ± √(16 - 28)) / 2

x = (-4 ± √(-12)) / 2

x = (-4 ± 2i√3) / 2

x = -2 ± i√3

Therefore, the roots of the equation x² + 4x + 7 = 0 are: A) 2 + i√3 or 2 - i√3.

So, the correct answer is A

Answer:

To find out how much change Luke should receive if he pays the cashier $20 for a Helmond that costs $19.67, we can subtract the cost of the Helmond from the amount of money Luke pays:

$20.00 - $19.67 = $0.33

Therefore, Luke should receive $0.33 in change.

Required solution of the given equation 3.1 = -0.5 + 0.3x is x = 12.

What is equation?

A mathematical statement that asserts that two expressions are equal is called equation

. It is consist of variables, constants, and mathematical operations such as , subtraction, addition, division, multiplication . We can use equations in mathematics to model real-world situations or to solve problems. It can also be used to express relationships between quantities, to find unknown values, and to test hypotheses. Equations can be written in various forms, such as linear, exponential, trigonometric ,quadratic. Equation depends on the type of relationship being modeled.

Here given equation is 3.1 = -0.5 + 0.3x.

We are Simplifying it,

[tex]3.1 + 0.5 = 0.3x \\ 0.3x = 3.6 \\ x = \frac{3.6}{0.3} \\ x = 12[/tex]

So, required solution of the given equation is 12.

Therefore, option C is the correct answer.

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Correct question is "What is the solution to this equation? 3.1 = -0.5 + 0.3x A:x=6 B:x=3 C:x=12 D:x=0.8".

Answer:

C. z < -19 or z > 11

Step-by-step explanation:

|z+4| > 15

z+4<-15 or z+4<15

z < -19 or z > 11

Answer:

[tex]-i\sqrt{7}[/tex]

Step-by-step explanation:

We can write this expression as:

[tex]-\sqrt{-1 \cdot 7}[/tex]

From here, we can take the square root of negative 1 ([tex]i[/tex]):

[tex]\boxed{-i\sqrt{7}}[/tex]

No further simplification can be done.

The value of the angle x is 108 degrees

To determine the value, we need to note that the sum of the angles on a straight line is 180 degrees.

Also, parallel lines are lines that do not meet or intersect each other on any side of a plane

From the information given, we have that;

x + 72 = 180

now, collect the like terms in the equation, we have;

x = 180 - 72

subtract the values

x  = 108 degrees

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