Choose the correct equation for the line shown on the graph?
y
y=-x-4
y=-x-1
y=x-4
y=2x-1
XA

Answer:

mark me as a brainlist then I will answer

The expression that represents the area of the gray region, the area of the land remaining in the backyard is 3x²+10x-17 square yards. The correct option is B.

The area of the gray region is the area of the rectangular backyard minus the area of the circular pond.

The area of the rectangular backyard is given as 6x+14x-12 square yards, which simplifies to 20x-12 square yards.

The area of the circular pond is given as 3x²-4x+5 square yards.

So, the area of the gray region is:

(20x-12) - (3x²-4x+5)

= 20x-12 - 3x²+4x-5

= 3x²+10x-17

Therefore, the expression that represents the area of the gray region, the area of the land remaining in the backyard is 3x²+10x-17 square yards.

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Answer:

b=r-9/9

Step-by-step explanation:

First you do the distributive property...

r=9b+9

then you subtract the 9

r-9=9b

then you divide the 9

r-9/9=b

and because of the symetry property you can flip it...

b=r-9/9

Answer: 25y= 60x

190x +25y= 37500

Step-by-step explanation:

Let x = Number of balcony tickets.

then, Number of lower level tickets  = 5x

Let y = Number of mezzanine tickets

Money made from ,

balcony tickets = 15x

lower level tickets = 35 (5x) = 175 x

mezzanine tickets = 25y

Money made from mezzanine tickets=  4 x( money made from balcony tickets.)

⇒ 25y = 4 (15x)

⇒ 25y= 60x              (i)

Also, total cost of the tickets = 15x+175x+25y = 37500

⇒ 190x +25y= 37500          (ii)

From (i) and (ii), the system of linear equations could be used to solve for the number of each type of ticket sold:

25y= 60x

190x +25y= 37500

The system of linear equations which could be used to solve for the number of each ticket type sold are :

Ticket types :

Ticket cost :

The total amount made from tickets sales :

35a + 25b + 15c = 37500

From (1) :

35(5c) + 25b + 15c = 37500

175c + 25b + 15c = 37500

190c + 25b = 37500 - - - - - (2)

Sales from Mezzanine tickets only = 25b

25b = 4(15c)

25b = 60c - - - - (3)

Therefore, the system of linear equation required to solve the problem are equations (2) and (3)

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To graph the equation \(x=y^2\) on a TI-83 calculator, you need to follow a few steps. First, go to the "\(Y=\)" screen by pressing the "\(Y=\)" button. Then, enter the equation by typing "\(y^2\)" into the first available function slot. Press the "GRAPH" button to display the graph of the equation on the calculator screen.

To explain the process in more detail, start by turning on your TI-83 calculator and pressing the "\(Y=\)" button, which will take you to the function screen. You'll see a list of function slots labeled "\(Y1\)," "\(Y2\)," and so on. Enter the equation "\(y^2\)" in one of the slots. To enter the squared symbol, press the "^" key, usually located near the upper right corner of the calculator's keypad, followed by "\(2\)." Make sure you use the "\(y\)" variable, which can be found by pressing the "ALPHA" button and then the corresponding letter key. Once you have entered the equation, press the "GRAPH" button to plot the graph on the calculator's screen. The graph should display a parabola opening to the right, representing the equation \(x=y^2\).

By following these steps, you can easily graph the equation \(x=y^2\) on a TI-83 calculator. Remember to check if the graph is within the viewing window and adjust it if necessary using the window settings.

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The time required to complete the painting work when Analiza, Leoben and Walter work together is approximately 0.97 hours or 58.2 minutes.

Given information:

Analiza can paint a room in 3 hours.

Leoben can do it for 2 hours.

Walter can do the painting job in 5 hours.

Let the total time required be t hours.

Analiza does the job in 3 hours => In 1 hour, Analiza can complete 1/3 of the work.

Leoben does the job in 2 hours => In 1 hour, Leoben can complete 1/2 of the work.

Walter does the job in 5 hours => In 1 hour, Walter can complete 1/5 of the work.

When they work together, the amount of work done in 1 hour = 1/3 + 1/2 + 1/5 = (10 + 15 + 6) / 30 = 31 / 30

If the work will be completed in t hours, then the amount of work done in t hours = 1. Then,

Work done by Analiza in t hours = (t / 3)

Work done by Leoben in t hours = (t / 2)

Work done by Walter in t hours = (t / 5)

Now, according to the problem, work done by all of them together in t hours = 1, which is equal to:

Work done by Analiza in t hours + Work done by Leoben in t hours + Work done by Walter in t hours. Therefore,

1 = t / 3 + t / 2 + t / 5

Multiplying by 30 on both sides, we get:

30 = 10t + 15t + 6t

30 = 31t

t = 30 / 31 hours = 0.97 hours or 58.2 minutes

Therefore, the time required to complete the painting work when Analiza, Leoben and Walter work together is approximately 0.97 hours or 58.2 minutes.

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Answer:

Only equation 1 and 2 are equal.

Step-by-step explanation:

2 (x + 4)2 = 2

2( x² + 8x+ 16) = 2               Applying the square formula

2x² + 16x+ 32 = 2

2x² + 16x+ 32 -2= 0

2x² + 16x+ 30 = 0

2( x² + 8x+ 15)= 0           Taking 2 as common

x2 + 8x + 15 = 0------------eq 1

x2 + 8x + 15 = 0-------------eq 2

(x − 5)2 = 1

x²-10x+25= 1             Applying the square formula

x²-10x+25- 1= 0

x²-10x+24= 0-------------eq 3

x2 − 10x + 26 = 0 -------------eq 4

3(x − 1)2 + 5 = 0

3( x²-2x+1)+5= 0               Applying the square formula

3x²-6x+3+5= 0

3x²-6x+ 8= 0-------------eq 5

3x2 − 6x + 8 =1

3x2 − 6x + 8 -1=0

3x2 − 6x + 7 =0-------------eq 6

The remainder when f(x) = 2x3 - 12x2 + 11x + 2 is divided by x - 5 is 7.

We can use the remainder theorem to find the remainder when a polynomial is divided by a linear factor.

The remainder theorem states that the remainder when a polynomial f(x) is divided by x - a is f(a). In this case, the polynomial is f(x) = 2x3 - 12x2 + 11x + 2 and the linear factor is x - 5. So, the remainder is f(5).

To find f(5), we can simply substitute x = 5 into the polynomial. This gives us f(5) = 2(5)3 - 12(5)2 + 11(5) + 2 = 7.

Therefore, the remainder when f(x) = 2x3 - 12x2 + 11x + 2 is divided by x - 5 is 7.

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the unit normal vector to the curve with vector equation \vec r \, (t) =<1^t,\ln(4/t^2), \, \ln(e/(t^4)) > r (t)=<1 t ,ln(4/t 2 ),ln(e/(t 4 ))> at the point where t=2t=2 is \vec n = <0,0,-1>

A unit normal vector is a normal vector with magnitude 1, and it points in the direction that is perpendicular to the tangent to the curve at a given point.

To determine the unit normal vector to a curve, it's important to find the tangent first and then find the normal. In this case, we're looking for the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2.

To find the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2, it is necessary to find the tangent to the curve and then find the normal. This is a crucial step in understanding the geometry of curves in 3D space.

To find the tangent to the curve, we'll differentiate the vector equation with respect to t and evaluate it at t = 2. The derivative of \vec r (t) is given by:

d\vec r/dt = <1, -2t^-3, -4e^-t^-4>

So the tangent to the curve at t = 2 is:

d\vec r/dt = <1, -2(2)^-3, -4e^-2^-4> = <1, 1.5, -1.648721>

Next, we'll find the normal to the tangent by taking the cross product of the tangent with a fixed vector, for example, the unit vector i = <1,0,0>. The cross product of two vectors results in a vector that is perpendicular to both of them.

The cross product of the tangent and the unit vector i is given by:

\vec T x \vec i = <1, 1.5, -1.648721> x <1,0,0> = <0,0,-1.5>

Since the magnitude of the normal is not 1, we'll normalize it by dividing it by its magnitude:

\vec n = \vec T x \vec i / ||\vec T x \vec i|| = <0,0,-1.5> / ||<0,0,-1.5>|| = <0,0,-1>

So the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2 is given by:

\vec n = <0,0,-1>

This is the unit normal vector that points in the direction that is perpendicular to the tangent to the curve at t = 2. The magnitude of 1 ensures that it's a unit vector and the direction points towards the normal direction.

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Answer:

see explanation

Step-by-step explanation:

The first multiplier is the number of terms being added.

The second multiplier is one more than the first multiplier, that is

2 + 4 + 6 + 8 + 10 ← has 5 terms being added and 6 is one more than 5, thus

2 + 4 + 6 + 8 + 10 = 5 × 6

Answer:

The first multiplier is the number of terms being added.

The second multiplier is one more than the first multiplier, that is

2 + 4 + 6 + 8 + 10 ← has 5 terms being added and 6 is one more than 5, thus

2 + 4 + 6 + 8 + 10 = 5 × 6

Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

x = - 3, y = - 11

Step-by-step explanation:

Given the 2 equations

y = 7x + 10 → (1)

y = - 4x - 23 → (2)

Substitute y = 7x + 10 into (2)

7x + 10 = - 4x - 23 ( add 4x to both sides )

11x + 10 = - 23 ( subtract 10 from both sides )

11x = - 33 ( divide both sides by 11 )

x = - 3

Substitute x = - 3 into either of the 2 equations and evaluate for y

Substituting into (1)

y = 7(- 3) + 10 = - 21 + 10 = - 11

Answer:

Minimum

Step-by-step explanation:

Since the leading coefficient is positive, this means that the parabola will open upward in a U-shape, showing that its vertex will be a minimum.

The weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

To determine the percentage of newborn African lions that weigh less than 3 pounds and the percentage that weigh more than 3.8 pounds, we would need statistical data on the weight distribution of newborn African lions. Since we don't have that information, we cannot provide the exact percentages.

However, if we assume that the weights of newborn African lions follow a normal distribution, we can use the properties of the standard normal distribution to make an estimation.

For the percentage of newborn African lions weighing less than 3 pounds:

We would need to know the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3 pounds and then find the corresponding percentage using a standard normal distribution table. Without this information, we cannot provide an accurate estimation.

For the percentage of newborn African lions weighing more than 3.8 pounds:

Similarly, we would need the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3.8 pounds and find the corresponding percentage using a standard normal distribution table. Without the required information, we cannot provide a specific estimation.

Please note that the weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

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Using a linear function, it is found that her taxi ride was of 5 miles.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which the coefficients are described as follows:

For the cost function, we have that:

Thus the cost for a ride of x miles is of:

C(x) = 3.75x + 1.10.

Her total fee was of $19.85, hence the mileage is found as follows:

19.85 = 3.75x + 1.10

x = (19.85 - 1.10)/3.75

x = 5 miles.

Which was the length of her taxi ride.

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Answer:

Step-by-step explanation:

The sum of the angles in a triangle is always 180 degrees. Therefore,

2x + 3x + 22 = 180

Simplifying the equation,

5x = 158

Dividing by 5 on both sides,

x = 31.6

To find the actual measures of 2x and 3x, we substitute the value of x:

2x = 2(31.6) = 63.2 degrees

3x = 3(31.6) = 94.8 degrees

Therefore, the actual measures of 2x and 3x are 63.2 degrees and 94.8 degrees, respectively.

Answer:

pain

Step-by-step explanation:

The probability that the flip results in a head is given as Pr[H] = 23. Therefore, the probability that the flip results in a tail is Pr[T] = 1 - Pr[H] = 1 - 23 = 13.

Let A be the event that a white marble is selected. We need to find the conditional probability Pr[H|A], i.e., the probability that the flip resulted in a head given that a white marble was selected.

Using Bayes' theorem, we have:

Pr[H|A] = (Pr[A|H]*Pr[H]) / Pr[A]

Pr[A|H] is the probability of selecting a white marble given that the flip resulted in a head. This is given by (9/25), since there are 9 white marbles out of 25 in the first urn.

Pr[A] is the total probability of selecting a white marble, which can be found using the law of total probability:

Pr[A] = Pr[A|H]*Pr[H] + Pr[A|T]*Pr[T]

= (9/25)*0.23 + (1/11)*0.13

= 0.0888 + 0.0118

= 0.1006

Pr[A|T] is the probability of selecting a white marble given that the flip resulted in a tail. This is given by (1/11), since there is only 1 white marble out of 11 in the second urn.

Therefore,

Pr[H|A] = (9/25 * 0.23) / 0.1006 = 0.6508

Hence, the probability that the flip resulted in a head given that a white marble was selected is 0.6508 (or approximately 0.65).

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\(2y = 3x + 6\\y = \frac{3}{2}x + \frac{6}{2} = \frac{3}{2}x + 3\)

The optimal K* for the firm to borrow is 02. The correct answer is a.

To determine the optimal capital level (K*) for the firm to borrow, we need to find the point where the marginal revenue (MR) equals the interest rate.

Given the MR values for the 1st, 2nd, 3rd, 4th, and 5th unit of capital as $1.75, $1.48, $1.26, $1.18, and $1.13, respectively, we compare these values to the interest rate of 21%.

By analyzing the MR values, we can observe that the MR is decreasing as more units of capital are utilized. To find the optimal K* for borrowing, we need to determine the point at which the MR equals the interest rate.

Comparing the MR values with the interest rate, we find that the MR falls below 21% after the 2nd unit of capital (MR = $1.48) and continues to decrease for subsequent units. Therefore, the optimal K* for the firm to borrow would be 2 units of capital.

Hence, the answer is A 02.

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The test that fits the description is called the Wechsler Preschool and Primary Scale of Intelligence (WPPSI).

The WPPSI is a standardized intelligence test designed for children aged 2½ to 7 years old. It assesses various cognitive abilities and provides separate levels for different age ranges, specifically ages 2½ to 4 and 4 to 7. The test measures both verbal and non-verbal (performance) abilities, and it also yields combined scores that provide an overall measure of intelligence.

The test consists of a series of subtests that evaluate different areas such as verbal comprehension, working memory, perceptual reasoning, and processing speed. These subtests assess the child's abilities in areas like vocabulary, comprehension, visual-spatial skills, problem-solving, and attention.

By providing separate levels for different age groups and assessing multiple cognitive domains, the WPPSI offers a comprehensive evaluation of a child's intellectual abilities during the preschool and primary school years.

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Answer: John is 29 years old and Jane is 36 years old.

Step-by-step explanation:

There are many parts to this problem, so let's start by defining John as x and Jane as y.

We know that the sum of their age 10 years ago was 55, which gives us x+y-10=55. The reason we put -10 is because of 10 years ago. If you think about it in terms of now, 10 years back is 55, so now they would be 65 years old. So we can have either x+y-10=55 or x+y=65. For simplicity, I will use x+y=65.

We also know that John is 7 years younger than Jane, which gives x=y-7.

Luckily, we have x defined for us, so we can directly substitute that into our equation.

\((y-7)+y=65\)         [combine like terms]

\(2y-7=65\)                [add both sides by 7]

\(2y=72\)                      [divide both sides by 2]

\(y=36\)

Now we know that y=36, we can plug that into either equations to find x.

\(x+36=65\)                [subtract both sides by 36]

\(x=29\)

This concludes that John is 29 years old and Jane is 36 years old.

The value of nickels is $76.80.

The height of each nickel is 6.25 / 100 = 0.0625 inches.

Divide 8 feet by 0.0625 inches to find that there are

8×12 / 0.0625 = 1536 nickels in an 8 ft stack.

Their value is $76.80.

Nickel is a chemical detail with the symbol Ni and atomic range 28. It is silvery-white lustrous steel with a mild golden tinge. Nickel belongs to the transition metals and is hard and ductile.

Pure nickel, powdered to maximize the reactive surface vicinity, indicates a widespread chemical interest, but large pieces are slow to react with air underneath fashionable conditions because an oxide layer paperwork at the floor stops further corrosion (passivation).

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The required graph A has a slope of negative two-thirds and a y-intercept of 2. Option A is correct.

The slope of the line is a tangent angle made by line with horizontal. i.e. m = tax where x in degrees.

m = (y₂ - y₁) /  (x₂ - x₁)

The graph of lines A  has the slope of -2/3 and 2 as,

m = (y₂ - y₁) /  (x₂ - x₁)

Put points (0, 2) and (3, 0) in the above expression
m = 0-2/3-0
m = -2/3

And at x = 0 there y = 2

Thus, the required graph A has a slope of negative two-thirds and a y-intercept of 2. Option A is correct.

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This situation can be represented by the function f(x)=1000+150x.

Linear Equation can be defined as the equation that have  highest degree 1.

For Example : 3x+6 is a linear equation as it's highest degree is 1.

In the given question

Total money saved=initial amount+(money saved per week)*(number of weeks)     …(1)

Given that

Jessica already saved = $1000

money to be saved per week = $150

let the number of weeks she will be saving money =x

let f(x) be the function used to represent money saved

Substituting the values in eqn (1) we get

f(x)=1000+150(x)

Therefore , this situation can be represented by the function f(x)=1000+150x.

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Lakeside Olds can expect around 2.6 automobiles to be lined up at the opening time for service.

To find the expected number of automobiles lined up at the opening time, we can use the following  formula is used

Expected value = Σ (number of automobiles * probability)

Using the probability distribution provided in the question, we have:

Expected value = (10.20) + (20.20) + (30.40) + (40.20)

Expected value = 0.20 + 0.40 + 1.20 + 0.80

Expected value = 2.6

Therefore, on a typical day, Lakeside Olds can expect around 2.6 automobiles to be lined up at the opening time for service.

Note that since the expected value is not a whole number, it is an estimate and may not represent the actual number of automobiles on any given day.

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Answer:

Step-by-step explanation:

No x intercept means it can't touch the x axis y=x^{2}+1 does the trick since it moves the whole thing up one unit

Repeated measures study is a technique used in statistics that involves taking multiple measures from the same individual or group. The major concern with a repeated-measures study is the possibility of carry-over effects.

What is a repeated-measures study?A repeated-measures study is a design used in statistics, where all the members of a given sample group are evaluated on two or more occasions. In other words, the repeated-measures study can be viewed as a test-retest design.In this type of study, participants undergo a specific treatment or intervention, and then their responses or measurements are evaluated at various intervals to examine any effects of the intervention. The repeated measures are then compared, and statistical tests are used to determine whether there are any significant differences in the results.

The possibility of carry-over effects: When conducting a repeated-measures study, the possibility of carry-over effects is a major concern. This occurs when the effects of the first treatment are still present when the second treatment is applied, resulting in an unintended impact on the second set of results. For example, if an experimental group is treated with a medication and then evaluated, and the same group is treated with a different medication and then evaluated, the results may be influenced by the residual effects of the first medication.

A carry-over effect can result in an inaccurate representation of the study's effect and can decrease the validity of the results. As a result, researchers must establish an appropriate washout period to reduce the impact of the carry-over effects before conducting a repeated-measures study.

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We can sum up the results of all three cases to get the total number of strings with exactly 4 occurrences of a or 4 occurrences of b or 4 occurrences of c. Total number of strings = C(12, 4) * 2^8 + C(12, 4) * 2^8 + C(12, 4) * 2^8.

To find the number of strings of length 12 over the alphabet {a, b, c} that have exactly 4 occurrences of a, 4 occurrences of b, or 4 occurrences of c, we can use combinatorics.

First, let's consider the case of a string length of 12.

We have three possibilities: exactly 4 occurrences of a, exactly 4 occurrences of b, or exactly 4 occurrences of c. We will calculate each case separately and then sum up the results.

Case 1: Exactly 4 occurrences of a.

We have 12 positions in the string and we need to choose 4 of them to place the a's. The remaining 8 positions can be filled with b's or c's, giving us 2 options for each position. Therefore, the number of strings with exactly 4 occurrences of a is C(12, 4) * 2^8.

Case 2: Exactly 4 occurrences of b.

Similar to Case 1, we have 12 positions and we need to choose 4 of them to place the b's. The remaining 8 positions can be filled with a's or c's, giving us 2 options for each position. So, the number of strings with exactly 4 occurrences of b is C(12, 4) * 2^8.

Case 3: Exactly 4 occurrences of c.

Again, we have 12 positions and we need to choose 4 of them to place the c's. The remaining 8 positions can be filled with a's or b's, giving us 2 options for each position. Hence, the number of strings with exactly 4 occurrences of c is C(12, 4) * 2^8.

If the length of the string is 17, the approach will remain the same. We will calculate the number of strings with exactly 4 occurrences of a, 4 occurrences of b, or 4 occurrences of c using the formula mentioned above. The only difference will be in the length of the string and the number of positions to be chosen for each case. We will have C(17, 4) instead of C(12, 4), and the remaining positions will be filled with the remaining characters from the alphabet.

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The chi-square test for homogeneity is used if he wants to determine if the distributions are the same.

What is the chi-square test?

Chi-square is a statistical test that looks at how categorical variables from a random sample differ from one another to see if the expected and actual findings match together well.  It is a contrast of two sets of statistical data. Karl Pearson developed this test in 1900 for the analysis and distribution of categorical data.

Here,

We have to determine for which situations should the chi-square test for homogeneity be used.

We concluded from the given option that:

A researcher is trying to determine if salaries for men and women in the tech industry have the same distribution.

He surveys a random sample of men and women in the industry and records the distribution of salaries for each gender.

He wants to determine if the distributions are the same.

Hence, the chi-square test for homogeneity is used if he wants to determine if the distributions are the same.

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