12. Determine if the relation represents y as a function of x. If it is a function, identify the domain and the range. More than one answer may be correct, select all that apply.

Answer:

\(x=\dfrac{2}{3},-\dfrac{3}{2}\)

Step-by-step explanation:

Given equation:

\(6x^2+5x-6=0\)

First, factor the left side of the given equation.

To factor a quadratic in the form \(ax^2+bx+c\) find two numbers that multiply to \(ac\) and sum to \(b\):

\(\implies ac=6\cdot-6=-36\)

\(\implies b=5\)

So the two numbers are: 9 and -4

Rewrite \(b\) as the sum of these two numbers:

\(\implies 6x^2+9x-4x-6=0\)

Factorize the first two terms and the last two terms separately:

\(\implies 3x(2x+3)-2(2x+3)=0\)

Factor out the common term \((2x+3)\):

\(\implies (3x-2)(2x+3)=0\)

To solve for x:

\(\begin{aligned}\implies (3x-2) & =0 & \implies (2x+3) & = 0\\3x & = 2 & 2x & = -3\\x & = \dfrac{2}{3} & x & = -\dfrac{3}{2}\end{aligned}\)

Therefore:

\(x=\dfrac{2}{3},-\dfrac{3}{2}\)

The expected value of cream-filled donuts the store City Donuts is selling should be 2.

We are aware of In the realm of probability theory, the expected value, commonly referred to as the expected average, is a generalization of the weighted average.

Given, City Donuts recently sold 14 donuts, of which 4 were cream-filled donuts.

So, The probability of cream-filled donuts is = 4/14 = 2/7.

Therefore, The expected number of cream-filled donuts is,

= (2/7)×7.

= 2.

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To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?

The conclusion the residuals have an increasing variance as the dependent variable increases is correct.

What is scatter chart?

Charts that depict the relationship between two variables are known as scatter charts, also known as scatter plots. They are a very effective type of chart because they enable viewers to see relationships or trends right away that are difficult to see in almost any other form.

In order to observe and visually display the relationship between variables, a scatter plot is a common type of chart. Other names for it include scatter gram, scatter graph, and scatter chart.

The conclusion can be drawn from the scatter chart is,

The residuals have an increasing variance as the dependent variable increases.

There is a violation of the homoskedasticity (homogeneity of variance for residuals) assumption.

The given plot is used to check the assumption for homoskedasticity (homogeneity of variances) of data points.

Hence if the homoskedasticity assumption hold, the spread of data points should be along the line and the line should be approximately horizontal.

From the given plot we can see that spread is centered at the middle not equally distributed along the line which is a violation of the homoskedasticity assumption

Hence, the conclusion the residuals have an increasing variance as the dependent variable increases is correct.

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The scatter chart is attached below.

Jerry's Paint Service uses 3 gallons of

paint in 2 hours. At this rate how

many hours will it take them to use 14 gallons of paint?

Apply proportion

2/3=x/14

solve for x

x=14*2/3

x=9.33 hours or 9 1/3 hours

How to make the proportion

2 ways

First

2 hours/3 gallons=x hours/14 gallons

solve for x

multiply in cross

14*2=3x

x=28/3

second way

3 gallons/2 hours=14 gallons/x hours

solve for x

multiply in cross

3x=14*2

x=28/3

the result is the same both ways

Given parameters:

Number of pencils = \(4\frac{1}{2}\) pencils

Time taken = \(3\frac{1}{3}\) minutes

Unknown:

Number of pencils produced in 1 minute;

Solution:

To solve this problem, let us first find the rate of the machine;

       Rate of machine = \(\frac{number of pencils }{time taken}\)

       Rate of machine = \(\frac{\frac{9}{2} }{\frac{10}{3} }\)   = \(\frac{9}{2} x \frac{3}{10}\)   = \(\frac{27}{20}\) pencils/minute

Now, number of pencils produces in 1 minute;

            Number of pencils  = rate of machine x time taken

             Number of pencils = \(\frac{27}{20}\)  pencils/ min x 1 min

             Number of pencils = \(\frac{27}{20}\)pencils

The number of pencils produced in 1 minute is \(\frac{27}{20}\)

The missing values are

<UTQ = 41 degree

x= 1

<UQT = 47 degree

We have a parallelogram QRST.

We know that the opposite sides of the parallelogram is equal and parallel then

QR || ST

QT || SR

Then, <SRT = <RTQ (<UTQ) (alternate Interior Angle)

<UTQ = 41

Similarly, <UQT = <SRQ = 47

Now, RU = UT

2x + 1= 3

2x = 2

x= 1

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12%= 30

-> 100%= 30÷12×100

-> 100%= 250

4% of 250

-> 4%=250÷100×4

-> 4%= 10

To find f(g(x)), we substitute g(x) in place of x in the function f(x).

f(g(x)) = f(5x/(1-x)) = (5x/(1-x)) / (5 + (5x/(1-x))) = 5x / (1-x+5-5x) = 5x / 6 - 4x/6 = x/6

To find g(f(x)), we substitute f(x) in place of x in the function g(x).

g(f(x)) = g(x/(5+x)) = (5(x/(5+x))) / (1 - (x/(5+x))) = 5x / (5+x-x) = 5x/5 = x

Therefore, f(g(x)) = x/6 and g(f(x)) = x.

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Answer:

5x-7+8=-27

Step-by-step explanation:

5x-7+8=-27

Answer: x = 41

For x in the equation

5/25=9/(x+4)

5(x+4) =9(25)

5x + 20 = 225

5x = 205

x = 41

Therefore, the value of x for the equation 5/25=9/(x+4) is x = 41

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Question:

Solution:

By definition we have that:

On the other hand, it is not always true that

In fact, the only case in which the above occurs is when f (x) = g (x) = 1

Thus, we can conclude that the correct answer is:

The statement is not true for all pairs of functions. A statement that is true for every f(x) and g(x) is

Answer:

∠ABC = 32

∠DBC = 42

Step-by-step explanation:

∠ABD = ∠ABC + ∠DBC

74 = 5x - 3 + 5x + 7

= 5x + 5x + 7 - 3

74 = 10x + 4

74 - 4 = 10x

70 = 10x

x = 70 / 10

x = 7

∠ABC = 5x - 3

= 5 ( 7 ) - 3

= 35 - 3

∠ABC = 32

∠ABD = ∠ABC + ∠DBC

∠DBC = ∠ABD - ∠ABC

= 74 - 32

∠DBC = 42

Answer:

12,280

Step-by-step explanation:

just do 1456×5 :))

An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

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the answer would be 0.56

Answer:

a: 0.0016

Step-by-step explanation:

Got it right on the test.

Hope this helps :)

x=16/3

10=3x-6

10+6=3x-6+6

10+6=3x-6+6

16=3x-6+6

16=3x-6+6

16=3x

16/3 3x/3

16/3 3x/3

16/3

Answer:

x = 25.4

Step-by-step explanation:

Recall: SOHCAHTOA

Reference angle = 48°

Hypotenuse = x

Adjacent = 17

Apply the trigonometric function, CAH, since the Adj and Hyp are involved

Thus:

Cos 48° = Adj/Hyp

Cos 48° = 17/x

x*Cos 48° = 17

x = 17/Cos 48°

x = 25.4061013 ≈ 25.4 (nearest tenth)

The future value of the loan is $5807.65.

It is expressed as a percentage of the amount borrowed and is paid over a specific period of time. The interest rate represents the cost of borrowing money and is one of the key factors in determining the overall cost of a loan. Interest is usually calculated on a yearly basis and can be compounded, meaning that the interest earned on a loan is added to the original principal and the interest rate is then applied to the new, higher amount. This process continues over time, leading to the growth of the original loan amount. The purpose of charging interest is to compensate the lender for the risk they are taking in lending the money and for the opportunity cost of not being able to invest the money elsewhere.

The future value of a loan is equal to the present value plus the interest earned over a specified time period. The formula to calculate the future value of a loan with simple interest is:

FV = PV (1 + rt)

where:

PV is the present value of the loan, which is $5250

r is the interest rate as a decimal, which is 5.3% ÷ 100 = 0.053

t is the time period in years, which is 24 months ÷ 12 months/year = 2 years

Substituting the values into the formula, we get:

FV = $5250 (1 + 0.053 * 2)

FV = $5250 (1.106)

FV = $5807.65

So, the future value of the loan is $5807.65. This is the amount Lynne will have to repay to her grandmother after 24 months, including the interest earned.

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Answer:

c. Y has a binomial distribution with n=40 observations and probability of success p=0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected.

Step-by-step explanation:

if wrong pls tell

Answer:

-3

Step-by-step explanation:

-3k / ( k-2)   + 6 / ( k-2)

since the denominators are the same we can add the numerators

(-3k+6) / ( k-2)

Factor out -3

-3 ( k-2)/ ( k-2)

Cancel like terms

-3

Answer:

\(\boxed{\sf -3}\)

Step-by-step explanation:

The denominators are same. Add fractions.

\(\displaystyle \sf \frac{-3k+6}{k-2}\)

Factor out the expression in the numerator.

\(\displaystyle \sf \frac{-3(k-2)}{k-2}\)

Cancel common terms.

\(\displaystyle \sf \frac{-3}{1}=-3\)

So the three integers are 4, 6, and 8 such that 6 times the first integer is 10 more than the sum of the second and the third integers.

An integer is a whole number that does not have any fractional or decimal parts. Integers include positive numbers (1, 2, 3, etc.), negative numbers (-1, -2, -3, etc.), and zero (0).

Here,

Let's call the first even integer x. Since the three integers are consecutive even integers, the second and third integers are x + 2 and x + 4, respectively.

From the problem statement, we know that:

6x = (x + 2) + (x + 4) + 10

Simplifying the right side of the equation:

6x = 2x + 16

Subtracting 2x from both sides:

4x = 16

Dividing both sides by 4:

x = 4

Therefore, the three consecutive even integers are:

x = 4

x + 2 = 6

x + 4 = 8

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Complete question:

"There are three consecutive even integers such that 6 times the first integer is 10 more than the sum of the second and the third integers."  find the integers.

x₁ = - 1

x₂ = 2

2²ˣ⁺¹ - 9ₓ2ˣ + 4 = 0

2²ˣₓ2 - 9ₓ2ˣ + 4 = 0

2ˣ = n

2n² - 9n + 4 = 0

2n² - n - 8n + 4 = 0

n(2n - 1) - 4(2n - 1) = 0

(2n - 1)(n -4) = 0

2n - 1 = 0 => n₁ = 1/2

n - 4 = 0 => n₂ = 4

2ˣ = 1/2 => 2ˣ = 2⁻¹ => x₁ = - 1

2ˣ = 4 => 2ˣ = 2² => x₂ = 2

Answer:

24%

Step-by-step explanation:

If Mario bought shares for 12.5 and sold them for 15.5, he made 3 dollars per share. Since he bought 37 shares, we multiply 37 by 3 to get 111

Since he spent 37*12.5, or 462.5 originally,

111/462.5=0.24

Therefore is ROI is 24%

Please give branliest

Where the above relations are given, note that Options A,  D, and E are the relations that represents a function. The others are just relations.

To distinguish a function from a relation, look to see if any of the x values are repeated; if not, the relationship is a function. If some x values are repeated but the accompanying y values differ, we have a relation rather than a function.

Note that where you are given domain and range, only the range is represented on the x-axis.

Some of the x values may be seen repeated in B, and C.

How is this so?

B) In a coordinate system, values are represented as (x, y). so

In relations, B 2 is repeated twice to in connection with -5, and -6. That is:

(2, -5) , (2, -6)

Since two is x, then its repetition nullified the relation as a function.

C) On table indicated on C, it is much easier to identify the x and y values. As is seen, -3 is repeated twice in connection with 4 and 2. Thus, its repetition nullified the relation as a function.

As a result, Options A,  D, and E are the relations that represent a function.

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Answer:

245-125=15w

120=15w

120÷15=w

w=8

Answer:

a triangle that may not have the same dimensions as the bases

Step-by-step explanation:

The cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases would be a triangle that may not have the same dimensions as the bases.

Answer:

D.  -3/5.

Step-by-step explanation:

6x + 10y = 8

We convert this to slope-intercept form:

Subtract 6x from both sides of the equation:

10y = -6x + 8

Divide through by 10:

y = -6/10 x +  8/10   (Slope-intercept form)

The slope is -6/10

= -3/5.

By the substitution property of equality, ∠AOB ≅ ∠COD. Then the correct option is B.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Given: Line segment AC and line segment BD intersect at O.

Prove: ∠AOB ≅ ∠COD

By the supplementary angles property, the equations are given as,

∠AOB + ∠BOC = 180°            .....1

∠BOC + ∠COD = 180°            ....2

By the substitution property of equality, ∠AOB ≅ ∠COD. Then the correct option is B.

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Answer: By the congruent complements theorem

Step-by-step explanation: I took the test

Answer:

prob wrong but

first one is-3/4

second is 3/5 since you convert the decimal