4. What is one point of intersection between the graphs of the functions
f(x) = (x+6)(x+2) and g(x) = x + 6?
A. (0,6)
B. (-1,5)
C. (-2,0)
D. (-4,-4)

Answer:

1

Step-by-step explanation:

The value of the output given by the inverse for a given input is the same as the input of the original function that results in the output equal to the given input.

So, 2x + 2 = 4, meaning the answer is 1

Answer:

The length of side AB is equal to 3.

After the translation, the length of the side AB will remain the same.

Explanation:

To determine the length of the side AB, Let us first locate the coordinates of A and B on the graph;

The length AB can be calculated using the formula for the distance between two points.

Substituting the values of the coordinates;

Therefore, the length of side AB is equal to 3.

After the translation, the length of the side AB will remain the same.

Because translation does not affect the size of an image, it only changes its position.

Check the picture below.

we can also word this as
finding the point E on UV such that UV gets split on a 3 : 4 ratio from U to V, keeping in mind that U(2 , -4) and V(4 ,3)

\(\textit{internal division of a line segment using ratios} \\\\\\ U(2,-4)\qquad V(4,3)\qquad \qquad \stackrel{\textit{ratio from U to V}}{3:4} \\\\\\ \cfrac{U\underline{E}}{\underline{E} V} = \cfrac{3}{4}\implies \cfrac{U}{V} = \cfrac{3}{4}\implies 4U=3V\implies 4(2,-4)=3(4,3)\)

\((\stackrel{x}{8}~~,~~ \stackrel{y}{-16})=(\stackrel{x}{12}~~,~~ \stackrel{y}{9})\implies E=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{8 +12}}{3+4}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-16 +9}}{3+4} \right)} \\\\\\ E=\left( \cfrac{20}{7}~~,~~\cfrac{-7}{7} \right)\implies E=\left( 2\frac{6}{7}~~,~~-1 \right)\)

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

To know more about nonzero vector refer here:

https://brainly.com/question/32673773#

#SPJ11

Answer:

Step-by-step explanation:

F(x)=x^3+6x+5

The feasibility area is empty. The solution of the LP-problem is not possible (does not exists).

With the constraint that x and y are both non-negative, the second constraint has only one point in common with each of the first and third constraints; and those two points are different.

The feasibility region is empty; so nothing can be optimized.

Plots x + 2y = 30 (red),  2x + 2y = 30 (green)  and  2x+y = 30 (blue)

The feasibility area, according to the condition, is the area of the first quadrant

   - above the red line,

   - below the green line,

   - above the blue line.

It can be seen from the plot that this set is empty.

Therefore, the feasibility area is empty. The solution of the LP-problem is not possible (does not exists).

To learn more about linear inequations refer here

https://brainly.com/question/25799000

#SPJ4

Disclaimer

The question given by you is incomplete, so the above solution is of a similar question, and the question is

Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT

Maximize p = x + y subject to

x + 2y ≥ 30

2x + 2y ≤ 30

2x + y ≥ 30

x ≥ 0, y ≥ 0.

p=

(x, y)=

The domain of r = 4cos 3θ is restricted to produce the graph shown is,

⇒ π/2 ≤ θ ≤ 5π/6

We have to given that;

The function is,

r = 4 cos 3θ

Now,

If θ = 0, then

cos 3θ = 1

Hence, r = 4 x 1 = 4

Which is not satisfy the graph.

Hence, Option A and B are incorrect.

If θ = π, then

cos 3θ = - 1

Hence, r = 4 x -1 = -4

Which is not satisfy the graph.

Hence, Option D is incorrect.

Thus, The domain of r = 4cos 3θ is restricted to produce the graph shown is,

⇒ π/2 ≤ θ ≤ 5π/6

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

The expression 5n+15 / n+3 can be simplified to 5.

To simplify the given expression, we need to simplify the numerator and denominator and then divide them.

The numerator is 5n+15, and the denominator is n+3.

We can factor out a common factor of 5 from the numerator: 5(n+3).

Now, the expression becomes (5(n+3)) / (n+3).

We can cancel out the common factor of (n+3) in the numerator and denominator.

Therefore, the simplified form of the expression is 5.

Learn more about common factor here:

https://brainly.com/question/28691421

#SPJ11

Time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

According to the question we have been given that,

Total time taken by Matilda to complete the consulting projects = \(16\frac{3}{4}\) hours

First we will convert it into simple fraction which is

         \(16\frac{3}{4} = \frac{67}{4} \\\) hours

Number of consulting projects = 3

And Matilda spends same amount of time to each of the project.

To find the time she spend on each project is by using unitary method

that is,            3 projects = \(\frac{67}{4}\) hours

                      1 project = \(\frac{67}{4} / 3\)

                                     = 67/12

                                     = \(5\frac{7}{12}\) hours

Hence time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

Learn more about unitary method here : https://brainly.com/question/24587372

#SPJ4

Answer:

We need to multiply 12 to each term to eliminate fractions.

Explanation:

Given expression:

To eliminate the fraction we need to multiply each term by least common multiple of the denominators of the fraction.

The denominators in the above expressions are:

4, 3 and 2

The multiples of each can be listed below.

2⇒ 2,4,6,8,10,12,14,16.....

3⇒ 3,6,9,12,15,18

4⇒ 4,8,12...

From the list of the multiples stated, we can see the least common multiple is 12.

So we will multiply each term by 12.

Multiplying 12 to both sides.

Using distribution,

Thus we successfully eliminated the fractions.

Answer:

12

Step-by-step explanation:

Answer:

A. It is symmetric and has no gaps.

Step-by-step explanation:

Given

See attachment for dot plot

Required

Select the true statement

From the attached plot, we can see that

Since (1) all bell shaped distribution are symmetric and (2) there is no gap between the dataset, then (a) is correct.

Answer:

See below.

Step-by-step explanation:

4*-3

A) -12

C) 2*-6

-hope it helps

The expressions that are equivalent to 4 × -3 are A) -12 and C) 2 × -6.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

Option A is a straightforward multiplication of 4 and -3, which gives -12.

Option C (2 × -6) is equal to -12.

Option B can be simplified as follows: (-4) - (-4) · (-4) = (-4) - 16 = -20.

Therefore, option B is not equivalent to 4 × -3.

Option D is equal to 1/64.

Option E is equal to 1.

Option F is equal to 2, and option G is equal to 12.

Options B, D, E, F, and G are not equivalent to 4 × -3.

Learn more about the expression here :

brainly.com/question/21751419

#SPJ2

Answer:

The graph of y = f(x) will shift up 20 units

Step-by-step explanation:

The y-value increases, therefore, the graph is shifting upwards. If the y-value was decreasing, the the graph would have shifted downwards.

Answer: 10 I think

Step-by-step explanation: Jill sold half and you dont know how much it is you know that now she has 36, but before she bought 16 so 36 - 16 = 20 but she sold half

Answer:10 magazines

Step-by-step explanation:

36-16/2=m

20/2=m

10=m. m=magazine

To write the number 900 into roman numerals you subtract 100 (C) from 1000 (M). when you subtract a quantity you write it in the left of the other quantity. Then, 900 in roman numerals is:

CM

Answer:

Okay so

Directions: find the value of x?

122 + 68 divided by 2

x = 95 degrees

Step-by-step explanation:

The perimeter of the rectangle, when the area is maximized, is approximately 24.63 units. Therefore, correct option is a.

To maximize the area of the rectangle inscribed in the parabola \(y^2 = 16x\), we need to find the dimensions of the rectangle. Since the side of the rectangle is along the latus rectum of the parabola, we know that the length of the rectangle is equal to the latus rectum.

The latus rectum of the parabola \(y^2 = 16x\) is given by the formula 4a, where "a" is the distance from the focus to the vertex of the parabola. In this case, the focus is located at (4a, 0).

To find "a," we can equate the equation of the parabola to the general equation of a parabola in vertex form: \(y^2 = 4a(x - h)\), where (h, k) is the vertex of the parabola.

Comparing the two equations, we get:

4a = 16

a = 4

Therefore, the latus rectum of the parabola is 4a = 4 * 4 = 16 units.

Since the length of the rectangle is equal to the latus rectum, we have length = 16 units.

Now, to find the width of the rectangle, we need to determine the corresponding y-coordinate on the parabola for the given x-coordinate of the latus rectum. The x-coordinate of the latus rectum is half the length, which is 16/2 = 8 units.

Substituting x = 8 into the equation of the parabola, we get:

\(y^2 = 16(8)\\y^2 = 128\\y = \sqrt{128} = 11.31\)

Therefore, the width of the rectangle is approximately 11.31 units.

The perimeter of the rectangle is given by the formula:

Perimeter = 2(length + width)

Plugging in the values, we have:

Perimeter = 2(16 + 11.31)

Perimeter ≈ 2(27.31)

Perimeter ≈ 54.62

Rounding the perimeter to two decimal places, we get approximately 54.62 units, which is equivalent to 24.63 units.

To know more about Area, visit

https://brainly.com/question/25292087

#SPJ11

Answer:

0%

Step-by-step explanation:

0% because there are no red apples in a bag of green apples.

Therefore it is impossible to pick a red apple.

Two variables are said to be positively associated when both the variables increase simultaneously. Two variables are said to be negatively associated when with the increase in one variable, the other decreases.

When we say that two variables are positively associated, it means that as one variable increases, the other variable also tends to increase. In other words, there is a direct variation between the two variables. For example, if we look at the relationship between height and weight, we would expect to see a positive association because taller people generally weigh more than shorter people.

On the other hand, when we say that two variables are negatively associated, it means that as one variable increases, the other variable tends to decrease. In other words, there is a inverse variation between the two variables. For example, if we look at the mathematical variation between studying and test scores, we would expect to see a negative association because the more someone studies, the lower their test anxiety and the better they are likely to perform on the test.

Understanding whether two variables are positively or negatively associated is important in many areas, including social sciences, healthcare, and business. By identifying these associations, we can better predict outcomes and make informed decisions based on data.

Learn more about mathematical variation here:

https://brainly.com/question/10404432

#SPJ11

Answer:

I = $ 0.74

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 4%/100 = 0.04 per year,

putting time into years for simplicity,

6 months ÷ 12 months/year = 0.5 years,

then, solving our equation

I = 37 × 0.04 × 0.5 = 0.74

I = $ 0.74

The simple interest accumulated

on a principal of $ 37.00

at a rate of 4% per year

for 0.5 years (6 months) is $ 0.74.

BRAINLIEST PLEASE

An equation in​ point-slope form of the line that passes through the points (-3,5) and (6,2) is,

⇒ x + 3y - 12 = 0

What is Equation of line?

The equation in point slope form of line is,

y - y₁ = m (x - x₁)

Where, 'm' is slope of the line.

The points are given as,

(x₁, y₁) = (-3,5) and (x₂, y₂) = (6,2)

Now, The equation in point slope form of line is,

y - y₁ = m (x - x₁)

Where, 'm' is slope of the line.

Slope (m) = y₂ - y₁ / x₂ - x₁

              = (2 - 5) / 6 - (-3)

              = - 3 / 9

              = - 1/3

Hence, An equation in point slope form of line is,

y - 5 = -1/3 (x - (-3))

3 ( y - 5) = - 1 ( x + 3 )

3y - 15 = -x - 3

x + 3y - 12 = 0

Hence, An equation in​ point-slope form of the line that passes through the points (-3,5) and (6,2) is,

⇒ x + 3y - 12 = 0

Learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ1

The indicated z-score is 0.8238.

Given the graph depicting the standard normal distribution with a mean of 0 and standard deviation of 1. The formula for calculating the z-score is z = (x - μ)/ σwherez = z-score x = raw scoreμ = meanσ = standard deviation Now, we are to find the indicated z-score which is 0.8238. Hence we can write0.8238 = (x - 0)/1. Therefore x = 0.8238 × 1= 0.8238

The Normal Distribution, often known as the Gaussian Distribution, is the most important continuous probability distribution in probability theory and statistics. It is also referred to as a bell curve on occasion. In every physical science and in economics, a huge number of random variables are either closely or precisely represented by the normal distribution. Additionally, it can be used to roughly represent various probability distributions, reinforcing the notion that the term "normal" refers to the most common distribution. The probability density function for a continuous random variable in a system defines the Normal Distribution.

Know more about z-score here:

https://brainly.com/question/30557336

#SPJ11

The statistics exam has a mean score of 75 and a standard deviation of 9.5. Accordingly, the typical student receives a score of 75, which is within 9.5 points of the mean.

The statistics exam has a mean score of 75 and a standard deviation of 9.5. Accordingly, the typical student receives a score of 75, which is within 9.5 points of the mean. As a result, the majority of students will receive scores between 65.5 and 84.5, with a small number receiving scores outside of this range. To evaluate the data and generate predictions about how students will perform on the test, the mean and standard deviation can be employed. Approximately 68 percent of pupils will achieve a score between 65.5 and 84.5, for instance, if the mean score is 75 and the standard deviation is 9.5. Therefore, if a student has a score below 65.5, they are probably performing poorer than the majority of students.

Learn more about standard deviation here

https://brainly.com/question/13905583

#SPJ4

Bayes' theorem is used to connect the probability of a person's DNA profile appearing in a sample with the possibility of that person being guilty.

Likelihood ratio (LR) is the ratio of the possibility of the evidence given the accused's guilt divided by the probability of the evidence given the accused's innocence. LR is a frequent tool used by experts to estimate the likelihood of a suspect being the source of a DNA sample. The likelihood ratio can be used to assess the probability of a given event. For example, it may be used to determine the likelihood of a crime suspect's DNA profile appearing in a sample.

It is essential to know the likelihood ratio of the first, second, third, fourth, and fifth occurrence of the same diagnosis for the same person to make an accurate assessment of this probability. This may be accomplished by calculating separate likelihood ratios for each occurrence.

In any likelihood ratio calculation, Bayes' theorem is used to link the probability of an individual's DNA profile appearing in a sample with the possibility of that person being guilty. This theorem helps to account for the possibility of coincidental matches.

The value of the likelihood ratio is determined by the strength of the DNA evidence in the case. When there is a higher probability of a match, the ratio will be higher. The value of the LR should be sufficiently large to establish the probability of the evidence given the suspect's guilt or innocence. Typically, an LR of more than 100 is considered a strong match.

The likelihood ratio for the first occurrence is calculated by dividing the likelihood of the evidence given the accused's guilt by the likelihood of the evidence given the accused's innocence. The same calculation is repeated for each additional occurrence. The sum of the likelihood ratios for all occurrences is used to compute the overall likelihood ratio for the case.

To conclude, the separate likelihood ratios for the first, second, third, fourth, and fifth occurrences of the same diagnosis for the same person can be calculated to assess the probability of a given event. Bayes' theorem is used to connect the probability of a person's DNA profile appearing in a sample with the possibility of that person being guilty. An LR of more than 100 is considered a strong match.

To know more about likelihood ratio,

https://brainly.com/question/31417586

#SPJ11

Answer:

9

Step-by-step explanation:

99 : 66 ( divide both parts by 11 )

= 9 : 6

Answer:

a. Assuming gallons of unleaded regular is denoted by r; and unleaded premium by p.

Revenue from one gallon of unleaded regular is $1.299 and from unleaded premium is $1.379.

Revenue function = 1.299r + 1.379p

b. Cost of one gallon of unleaded regular is $1.219 and for unleaded premium is $1.289.

Cost function = 1.219r + 1.289p

c. Total profit = Revenue - Cost

= 1.299r + 1.379p - 1.219r - 1.289p

= 1.299r - 1.219r + 1.379p - 1.289p

= 0.08p + 0.09p

d. If station sells 100,000 gallons of unleaded regular and 40,000 of unleaded premium;

= (0.08 * 100,000) + (0.09 * 40,000)

= 8,000 + 3,600

= $11,600

To divide the polynomial p(x) by d(x), we can use long division or synthetic division. Let's say we choose to use long division.

First, we need to write the polynomials in descending order of degree, with any missing terms filled in with zeros. Let's say the polynomials are:

p(x) = 3x^3 - 5x^2 + 2x + 4
d(x) = x - 2

Then, we set up the long division like this:

         3x^2 + x + 4
   x - 2 | 3x^3 - 5x^2 + 2x + 4

We divide the first term of p(x) by the first term of d(x), which gives us 3x^2. We write this above the division bar and multiply it by d(x), which gives us 3x^3 - 6x^2. We subtract this from p(x), bringing down the next term:

         3x^2 + x + 4
   x - 2 | 3x^3 - 5x^2 + 2x + 4
         - 3x^3 + 6x^2
             ----------
              -11x^2 + 2x

We repeat the process with the next term, dividing -11x^2 by x to get -11x, writing this above the division bar, and multiplying it by d(x) to get -11x + 22. We subtract this from -11x^2 + 2x, bringing down the next term:

         3x^2 + x + 4 - 11/(x-2)
   x - 2 | 3x^3 - 5x^2 + 2x + 4
         - 3x^3 + 6x^2
             ----------
              -11x^2 + 2x
              + 11x^2 - 22
              ----------
                     -20

Since we have no more terms to bring down, our remainder is -20. Therefore, the quotient p(x)/d(x) is:

p(x)/d(x) = 3x^2 + x + 4 - 11/(x-2) - 20/(x-2)^2

We can express this in the form p(x) d(x) by multiplying both sides by d(x):

p(x) = d(x) (3x^2 + x + 4 - 11/(x-2) - 20/(x-2)^2)
To answer your question, we'll first need the specific polynomials for p(x) and d(x) that you'd like to divide. However, I can still guide you through the general steps to perform the division and express the quotient.

1. Choose either synthetic or long division, depending on your preference and the complexity of the polynomials.
2. Divide p(x) by d(x) using the chosen method. Make sure to follow the steps of the division process carefully to obtain the correct quotient and remainder.
3. Once the division is complete, express the quotient p(x)/d(x) in the form p(x) = d(x) * q(x) + r(x), where q(x) is the quotient and r(x) is the remainder.

Visit here to learn more about polynomial brainly.com/question/11536910

#SPJ11

The singular points of the differential equation are x = -6 and x = 0, which is an irregular singular point.

To find the singular points of the differential equation, we need to determine the values of x for which the coefficients of y'', y' and y become zero or infinite.

In this case, the coefficient of y'' is (x+6), which is zero only at x = -6. The coefficient of y' is -x^2, which is zero at x = 0. However, it is also infinite at x = 0, so we need to check if this is a regular or irregular singular point.

To do this, we can substitute y = (x^r) into the differential equation, where r is a constant. We get:

(x+6)r(r-1)x^(r-2) - x^r + 8x^r = 0

Simplifying, we get:

r(r-1) + 2r - 8 = 0

r^2 + r - 8 = 0

(r+2)(r-4) = 0

Thus, the possible values of r are -2 and 4. Substituting these back into y = (x^r), we get two solutions: y = x^(-2) and y = x^4.

Therefore, the singular points of the differential equation are x = -6 and x = 0, which is an irregular singular point.

Learn more about equation here:

https://brainly.com/question/29538993

#SPJ11

Answer:6

Step-by-step explanation:

when dividing by a fraction. you can multiply by its reciprical

15/4 *8/5

(15*8)/(4*5)

120/20

If you need to simplify

6

EDIT: answer above got this right before me. for some reason I did 8*5 as 30  :/

Considering the curve x³y + y³ = sin y - x, the final i is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

Implicit differentiation is a technique used to differentiate equations that are not explicitly expressed in terms of one variable. It is particularly useful when you have an equation that defines a relationship between two or more variables, and you want to find the derivatives of those variables with respect to each other.

To find dy/dx for the curve x³y + y³ = sin y - x², the implicit differentiation will be used which involves differentiating both sides of the equation with respect to x.

It is expressed as follows;

\(\frac{d}{dx} x^3y + \frac{d}{dx} y^3 = \frac{d}{dx} sin(y) - \frac{d}{dx} x^2\)

Then we'll differentiate each term:

For the first term, x^3y, we'll use the product rule

\(\frac{d}{dx} x^3y = 3x^2y + x^3 \frac{dy}{dx}\)

For the second term, y^3, we'll also use the chain rule

\(\frac{d}{dx} y^3 = 3y^2 \frac{dy}{dx}\)

For the third term, sin(y), we'll again use the chain rule

\(\frac{d}{dx} sin(y) = cos(y) \frac{dy}{dx}\)

For the fourth term, x², we'll use the power rule

\(\frac{d}{dx} x^2 = 2x\)

Substituting these expressions back into the original equation, we get:

3x²y + x³(dy/dx) + 3y²(dy/dx) = cos(y)(dy/dx) - 2x

Simplifying the equation:3x²y + x³(dy/dx) + 3y²(dy/dx) - cos(y)(dy/dx) = -2x

Dividing both sides by 3y² - cos(y), we get:(x³ - cos(y))(dy/dx) = -2x / (3y² - cos(y))

Hence, the final answer is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

To know more about implicit differentiation, visit:

https://brainly.com/question/11887805

#SPJ11