c) Which triangles are congruent in the given triangles? ​

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)

Learn more on inverse of a function here;

https://brainly.com/question/3831584

#SPJ1

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

Learn more about proportion:https://brainly.com/question/30657439

#SPJ1

The inequality is graphed on the number line is

Inequality can be graphed on a number line by shading the appropriate region of the number line.

To graph an inequality x > -7, follow these steps:

Plot the critical points on the number line. The critical points are the values of x that make the inequality true with an equal sign. For example, to graph the inequality x > -7, we plot the critical point x = -7 on the number line.

Determine the direction of the shading or line. If the inequality is "greater than" or "greater than or equal to," shade to the right of the critical point..

If the inequality includes "or equal to," use a closed circle at the critical point. If the inequality does not include "or equal to," use an open circle at the critical point.

Learn more about inequality at

https://brainly.com/question/24372553

#SPJ1

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.

To know morw about angles and radian visit:

https://brainly.com/question/30989204

#SPJ1

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.

Learn more about equation here,

https://brainly.com/question/1214333

#SPJ1

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:

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.

North Division’s direct fixed expenses for February is $34000.

Segment margin = Contribution margin - Direct fixed expenses

We are given that the North Division's segment margin for February is $18,000, and its contribution margin is $52,000. Let X represent the North Division's direct fixed expenses:

$18,000 = $52,000 - X

Solving for X, we get:

X = $52,000 - $18,000

X = $34,000

Therefore, the North Division's direct fixed expenses for February is $34,000.

The answer is: Multiple Choice $34,000.

Hence, North Division’s direct fixed expenses for February is $34000.

To know more about margin check the below link:

https://brainly.com/question/30459935

#SPJ1

Complete question:

American Manufacturing Incorporated operates two divisions with the following selected information for the month of February: North Division South Division Sales $ 120,000 $ 90,000 Contribution margin $ 52,000 $ 40,000 Segment margin $ 18,000 $ 12,000 North Division’s direct fixed expenses for February is: Multiple Choice $34,000. $96,000. $60,000. $78,000.

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

Learn about parallel lines at: https://brainly.com/question/24607467

#SPJ1

The correct option is D, the x-intercept is 2pi

To find this, we need to solve the equation:

y = cos(x/2) = 0

Remember that the cosine function is zero for the arguments pi and (3/2)pi.

Then the x-intercepts are:

x/2 = pi

x/2 = (3/2)pi

Solving these:

x = 2pi

x = 3pi

From these the one that appears in the options is 2pi, at option D.

Learn more about cosine functions at:

https://brainly.com/question/26993851

#SPJ1

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

Answer:

8

Step-by-step explanation:

x^2-4x=32

Subtract from both sides:

x^2-4x-32=32-32

Simplify the expression

x^2-4x-32=0

To find the coefficients, use the standard form of a quadratic equation:

ax^2+bx+c=0

x^2-4x-32=0

a coefficient =1

b coefficient =-4

c coefficient =-32

Find the factors which product equals to coefficient a multiplied by coefficient c:

a coefficient ∙ c coefficient = 1 ∙ -32 = -32

List the factors of -32:

1, 2, 4, 8, 16, 32

Because the product of coefficient a and coefficient c equals a negative number (-32) one factor needs to be positive and the other one negative.

From the list of factors, find a pair which sum equals to the b coefficient.

b coefficient = -4

This pair doesn't work.

1*-32=-32

2*-16=-32

2-16=-14

Found it - this pair does the trick:

4*-8=-32

4-8=-4

The product of 4 and -8 equals to coefficient a(1) multiplied by coefficient c (-32) and their sum equals to coefficient b (-4).

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.

More can be learned about the median of a data-set at https://brainly.com/question/3514929

#SPJ1

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:

To factor the polynomial 40x^3 + 70x^2 + 30x, we can first factor out the greatest common factor of the terms, which is 10x:

10x(4x^2 + 7x + 3)

Next, we can factor the quadratic expression inside the parentheses. We need to find two numbers that multiply to give 4 × 3 = 12 and add to give 7. These numbers are 4 and 3:

10x(4x + 3)(x + 1)

Therefore, the factored form of the polynomial is:

10x(4x + 3)(x + 1)

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 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.

Read more on ratios here: brainly.com/question/27817533

#SPJ1

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.

On solving the provided question ,we can say that In order to find holes in a mathematical proof or the boundaries of a theory or hypothesis, counterexamples might be helpful.

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

Evidence is utilised to back up a claim or argument in a direct proof. A direct proof's objective is to connect known facts or presumptions logically to the desired conclusion in order to show that a certain assertion is true. Direct proofs sometimes take the form of a series of logical stages that are combined to get the desired result.

A counterexample, on the other hand, is a solitary instance that refutes a claim or argument. A counterexample presents a particular situation in which a claim is wrong in order to demonstrate that the claim is not always true. In order to find holes in a mathematical proof or the boundaries of a theory or hypothesis, counterexamples might be helpful.

To know more about sequence visit:

https://brainly.com/question/21961097

#SPJ1

The distance from point C to A that is AC = 7.5 cm and CB = 10.5 cm.

While distance and displacement appear to have the same meaning, they actually have very different definitions and implications. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion."

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Let us suppose the distance between C to A = x.

Now, for C to B we have = 3 + x

Given, AB = 18

Thus,

AC + CB = AB

x + (x + 3) = 18

2x + 3 = 18

2x = 15

x = 7.5

Now, CB = 3 + x = 3 + 7.5 = 10.5

Hence, the distance from C to A that is AC = 7.5 cm and CB = 10.5 cm.

Learn more about distance here:

https://brainly.com/question/15172156

#SPJ1

Answer:

If 45% of the fruit on a table are apples, then 55% of the fruit are oranges (since the total percentage must add up to 100%).

The probability of selecting a piece of fruit that is not an apple is equal to the percentage of oranges on the table, which is 55%.

Therefore, the probability of selecting a piece of fruit that is not an apple is 55%.

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.

Learn more about degree of polynomial here:

https://brainly.com/question/29182596

#SPJ1

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

Read more about combination at

https://brainly.com/question/11732255

#SPJ1

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.

Read more about maximum value here:

https://brainly.com/question/14582614

#SPJ1

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.

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.

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.

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.

Learn more about inequalities at:

https://brainly.com/question/24372553

#SPJ1