Solve for x them find the measure of the angle given...can someone please help me

Solve For X Them Find The Measure Of The Angle Given...can Someone Please Help Me

Answers

Answer 1

The solution for the angle x in the figure is 130 degrees

How to determine the solution for x?

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

The transversal and the parallel line

By the theorem of vertical angles, we have the following equation

x = 5y

Also, we have the following equation

x = 2y - 78 --- by the theorem of corresponding angles

Substitute x = 2y - 78  in x = 5y

So, we have the following representation

5y = 2y - 78

Evaluate the like terms

3y = 78

Divide both sides by 3

y = 26

Substitute y = 26 in x = 5y

x = 5 * 26

Evaluate

x = 130

Hence, the value of x is 130

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Related Questions

If x< 0 and y > 0, where is the point (x,y) located ???

Answers

The points (x, y) lie in the 2nd quadrant when x<0 and y>0.

What are quadrants?

Two-dimensional Cartesian axes separate the plane into four infinite regions known as quadrants, each of which is bordered by two half-axes.

The coordinate system's two axes, the x-axis, and the y-axis constitute a region called a quadrant.

The quadrants are generated when the two axes, the x-axis, and the y-axis, cross at a 90-degree angle.

These areas include coordinates or positive and negative values of the x- and y-axes.

So, refer to the graph attached below.

Now, we know that:

Quadrant 1: x>0, y>0

Quadrant 2: x<0, y>0

Quadrant 3 x<0, y<0

Quadrant 4: x>0, y<0

We are given: x<0 and y>0

We can say that when x<0 and y>0 the point (x, y) lies on the 2nd quadrant.

Therefore, the points (x, y) lie in the 2nd quadrant when x<0 and y>0.

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one proposed solution to the funding problems faced by social security and medicare is to increase the retirement age from 67 to 70. although this would mean billions of dollars in savings for these federal programs, an unintended consequence may be

Answers

An unintended consequence may be an increase in the unemployment rate.

What is Unemployment Rate?

The percentage of workers in the labour force who do not currently have a job but are actively seeking one is measured by the unemployment rate.

The formula for calculating the unemployment rate is: unemployment rate = (Number of jobless people / sums of employed and unemployed people) x 100%.

Example: If there are 500 unemployed persons and 3000 people who are employed, the unemployment rate is calculated as follows: 500/3500 x 100% = 14.29%.

Reason:

When people retire late, new people entering the workforce would have less number of jobs. So, the unemployment rate would increase.

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Factor each completely.
5) 250a³ +54

Answers

The required factorized form of the given expression is  2(125a³ + 27).

What is the greatest common factor?

The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include of.

Here,
In the given expression,
Taking 2 common,
= 250a³ + 54
= 2(125a³ + 27)

Thus, the required factorized form of the given expression is  2(125a³ + 27).

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In the diagram below, the point O is referred to as the _____.

Answers

Answer:

d. Orthocenter

Step-by-step explanation:

⭐What is an orthocenter?

the point of concurrency of the altitudes of a triangle

⭐What is an altitude?

a perpendicular segment from the vertex to the opposite side of the vertexcreates a right angle (90°)

We can see that point O is the point of concurrency of the altitudes of this given triangle because there are 90° formed by the perpendicular lines.

Thus, O is referred to as the orthocenter.

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Which of the following equations has a solution different from the rest? (1 point)


¾ x+5=− ¼


½ x−3= ½

−1/7 x−34=¼

−0.35x−0.52=1.93

Answers

Answer: (-1/7)x - 34 = 1/4

Step-by-step explanation: The solution for all other equations is 7 and for the 3rd equation, the solution is 239.75 or 959/4

1) 3/4 X +5=-1/4

x=-7

2) 1/2X - 3 = 1/2

x=7

3) x = -137×7 /4

4) x= -7

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Graph the equation. y=-x^2-6x-3

Answers

Answer:

Step-by-step explanation:

It is easier to graph using a free online graphing utility, such as DESMOS.  See the attached graph.  If the goal is to make a graph with pencil and graph paper, then select a few values of x  and put them into the equation to find y.

A talble of a few random values is attached.  

The graph includes both the generated DEMOS line (a downwards parabola) and the calculated points from the attached table.  Add the points to a blank graph and draw a line as best you can that connects all the points.  It is clear that a few more points with negative values of x would help with the line drawing.

Cuál es la diferencia entre la ley de senos y la ley de cósenos

Answers

The law of sines uses only two sides and the angles that are opposite them, while the law of cosines uses all three sides and only one of the sides opposite an angle

What are the laws about?

An angle's cosine and sine are equal to each other, with the sine of an angle equal to the cosine of its complementary angle.

The law of cosines uses all three sides and only one of the sides that are opposite an angle, whereas the law of sines only uses two sides and the angles that are opposite them. The sine ratio is used by the law of sines, and the cosine ratio is used by the law of cosines.

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Complete question

What is the difference between the law of sines and the law of cosines

PLEASE HELP


A moth crawled 2 meters down a wall, 3 meters along the same wall, and 4 meters along an adjoining wall. Given that the walls join at a 90° angle, which most accurately expresses the distance in meters the moth will travel when flying in a straight line back to its original position?

Answers

The length of the diagonal path that leads to the original position of the moth that travels 2 meters down and, 3 meters along a wall, then 4 meters along a perpendicular wall, representing the dimensions of a rectangular prism is √(29) meters

What is the diagonal of a rectangular prism?

The diagonal of a rectangular prism is a segment that stretches from one corner of the prism to the opposite corner of the prism, passing through the center of the prism.

The distance down the wall the moth crawled = 2 meters

The distance along the same wall the moth crawled = 3 meters

The distance the moth crawled along the adjoining wall = 4 meters

Angle at which the walls join = 90°

The distance distance traveled by the moth when flying in a straight line back to its original position is a diagonal of a rectangular prism of height, h = 2 meters, width, w = 3 meters, and length, l = 4 meters

The length of the diagonal of a rectangle that has height, h, width, w, and length, l, is found using the following formula;

d = √(h² + w² + l²)

The length of the diagonal along which the moth flies is therefore;

d = √(2² + 3² + 4²) = √(29)

The distance in meters the moth will travel when flying back to its initial position is √(29) meters

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Which expression is equivalent to 10d+d-2d?
d+8
9d9d
1+8d1+8d
11d11d
pls help

Answers

Answer: 9d

Step-by-step explanation:

10d+d-2d = 9d

a frequent cause of measurement error in polls is due to a. the increased use of cell phones. b. push polling. c. poorly worded questions. d. too large sample sizes.

Answers

Polling mistakes are frequently caused by poorly written questions. People frequently misunderstand questions that are worded strangely and react to the question inaccurately, which leads to an error in the polling data. Due to misinterpretation, people frequently react differently than they would typically say , then option c is correct.

Limited respondent selections, a lack of knowledge, difficulty assessing intensity, and lack of interest in political matters are just a few of the factors that might make a poll unreliable.

Survey mistake, fewer respondent alternatives, a lack of knowledge, problems assessing intensity, and a lack of interest in political matters are some potential polling weaknesses.

The drawback of polling is that if there are too many devices to check, it may take longer to service an I/O device than it does to poll all of the devices.

Instrumental, environmental, procedural, and human errors are frequent causes. Depending on how they affect the outcomes, each of these errors can either be random or systematic.

Therefore,

Polling mistakes are frequently caused by poorly written questions. People frequently misunderstand questions that are worded strangely and react to the question inaccurately, which leads to an error in the polling data. Due to misinterpretation, people frequently react differently than they would typically say , then option c is correct.

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3, 1.6, 2.8, 2.5, 1.7, 2.8



What is the mean absolute deviation of these numbers?

Answers

The mean absolute deviation of the given numbers is 0.5.

What is a mean?

The mean is the sum of all values divided by the total number of values.

The mean of the given number is obtained by dividing the sum of the values by its total number of value.

i.e.  (1.6+1.7+2.5+2.8+2.8+3)/6 = 2.4

Then taking the difference of each number from the mean.

i.e. (1.6-2.4), (1.7-2.4),(2.5-2.4),(2.8-2.4),(2.8-2.4),(3-2.4)

i.e. -0.8,-0.7,0.1,0.4,0.4,0.6

Take the sum of the absolute value of the above numbers

i.e. |-0.8+-0.7+0.1+0.4+0.4+0.6| = 3

Divide 3 by 6 to obtain mean absolute deviation.

i.e 3/6 = 1/2 =0.5

Hence, 0.5 is the mean absolute deviation of the given numbers.

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Given the equation 18 equals y over -5, solve for y. NEED ANSWER ASAPPP!!

90
−90
23
−13

Answers

Answer: -90

Step-by-step explanation: To solve this equation for y, we need to isolate the variable y on one side of the equation. To do this, we can multiply both sides of the equation by -5 to get rid of the fraction on the right side:

18 = y / -5

18 * -5 = y / -5 * -5

-90 = y

Therefore, the value of y that satisfies the equation is -90.

20
Write "less" or "greater" in the blank.
972 is
than 792

Answers

Answer:greater

Step-by-step explanation:

Answer:

972 is greater than 792.

An airplane is preparing to land at an airport. It is 55800 feet above the ground and is descending at the rate of 3,500 feet per minute. At the same​ airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute. When will the two airplanes be at the same altitude and what will that altitude​ be? Use pencil and paper. Use two other methods to solve the problem. Explain which methods are easier to use and which are more difficult to use for the situation.

Answers

By solving a linear equation, it can be calculated that-

The two planes will be in the same altitude after 9 minutes at an altitude of 24300 feet

What is a linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, the linear equation is

Let the time taken by the airplane to meet the same altitude be t minutes

An airplane is preparing to land at an airport. It is 55800 feet above the ground and is descending at the rate of 3,500 feet per minute.

So altitude of the first airplane after t minutes = 55800 - 3500t

At the same​ airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute.

Altitude of second airplane = 2700t

By the problem,

The linear equation is

55800 - 3500t = 2700t

2700t + 3500t = 55800

6200t = 55800

t = 9 minutes

Altitude = 2700 [tex]\times[/tex] 9 = 24300 feet

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A student claims that the graph shows the player earned more points from Level 2 to Level 3 than from Level 4 to Level 5. Is the student correct?
O No, the player earned 67 points from Level 2 to Level 3 and 69 points from Level 4 to Level 5
O No, the player earned 42 points from Level 2 to Level 3 and 44 points from Level 4 to Level 5.
O Yes, the player earned 67 points from Level 2 to Level 3 and 69 points from Level 4 to Level 5.
OYes, the player earned 42 points from Level 2 to Level 3 and 44 points from Level 4 to Level 5.

Answers

No, the player earned 42 points from level 2 to level 3 and 44 points from level 4 to level 5. Explanation: 87-45=42 and 156-112=44, meaning from level 4 to 5 the player got more points.

What is transpose of matrix

Answers

Step-by-step explanation:

it is the process of changing rows to columb

Select all the possible solutions of 20y < -5 + 18y.
A) y> -2.5
B)y> -
5
2
□C) y < - //
5/2
□E) y >
□F)y <-
-
☐D)-2.5> y
5
38
5
38

Answers

The possible solutions of the inequality expression given as 20y < -5 + 18y are (c) y < -5/2, y < -2.5 and (d) -2.5 > y

How to determine the possible solutions of the inequality?

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

20y < -5 + 18y.

To start with, we need to collect the like terms of both sides

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

20y -18y < -5

Next, we need to evaluate the like terms of both sides

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

2y < -5

Lastly, we divide both sides by 2

y < -5/2

Express as decimal

y < -2.5

Switch the positions

-2.5 > y

Hence, the solutions are y < -5/2, y < -2.5 and -2.5 > y

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mathematics-help-dilate-

Answers

The dilated figure is plotted and attached and the coordinates is written as

preimage            image

A (-4, 3)               A; (-8, 6)

B (3, 2)                B' (6, 4)

C (-4, 0)               C' (-8, 0)

How to find the coordinates of the dilation

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem we have

preimage                           image

A (-4, 3)   → (-4 * 2, 3 * 2) →   A' (-8, 6)

B (3, 2)    → (3 * 2, 2 * 2)  →    B' (6, 4)  

C (-4, 0)  → (-4 * 2, 0 * 2) →    C' (-8, 0)

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yu want to determine the percentage of fortune 500 ceos who think indiana university (iu) deserves its current business week rating. you mail a questionnaire to all 500 ceos and 160 respond. exactly half of the respondents believe iu does deserve its ranking. calculate a 95% confidence interval for the fraction of fortune 500 ceos who believe iu deserves its ranking. round your answers to three decimal places, if necessary.

Answers

A 95% confidence interval for the fraction of fortune 500 ceos who believe Indiana university(IU) deserves its ranking is ( 0.279, 0.361)

According to the question,

Total number of sample taken for questionnaire = 500

Number of people responded = 160

Sample Proportion : p = 160/500

=> p = 0.32

Proportion of people who has not responded : q = 1 - p

=> q = 0.68

We have to create a 95% confidence interval for the fraction of fortune 500 ceos who believe Indiana university(IU) deserves its ranking.

Formula of C.I = p ± z√pq/n

Where p and q is sample proportion , z is value of CI at given α level of significance and n is sample size

C.I at 95% = 0.32 ± 1.96√0.32×0.68/500

=> 0.32 ± 1.96 √0.0004352

=> 0.32 ± 1.96 × 0.0208

=> 0.32 ± 0.0408

C.I = ( 0.32 - 0.0408,  0.32 + 0.0408)

=> C.I = ( 0.279, 0.361)

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Here is the graph for one equation in a system of equations:
a) Write a second equation for the system so it has infinitely many solutions.
b) Write a second equation whose graph goes through (0, 1) so the system so it has no
solutions.

Answers

The answer to each part is -

for  infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.

What is the general form of a straight line? What is a mathematical function, equation and expression?straight line equation : The general equation of a straight line equation is given by

        y = mx + c    

        where -

        [m] : slope of line
        [c] : y - intercept                    

function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given is the graph of a straight line as shown.

[A] - A second equation for the system so it has infinitely many solutions can be the one that overlaps the line given. So the second equation can be written as follows. The points are -

(0, 4) and (4, 1)

Let the line be -

y = mx + c

m = (1 - 4)/(4 - 0) = -3/4

m = -3/4

So, the equation will be -

y = (-3/4)x + 4

[B] -

For no solution, the line will be parallel to the given line. The equation of the line is → y = (-3/4)x + 4. The equation whose graph goes through (0, 1) so the system has no solutions as : y = (-3/4)x + 1.

Therefore, the answer to each part is -

for  infinitely many solutions, the equation will be y = (-3/4)x + 4.for no solution, the equation will be y = (-3/4)x + 1.

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How many leave were longer then 7 centimeters

Answers

Answer:

You could pick as many as you like. Ideally you would use all the leaves on the tree, but that would be rather a large number to measure, and your parents might not be very happy if you stripped the tree bare!So let's try 100 leaves.How to get a random sample?Here is one way you could get a random sample:Try taking all the leaves on one branch of the tree. After you've discarded any that are broken, then see how many there are. If there are less than 100, then get the leaves from another branch until you have more than 100. Then write a different number (starting with 1) on each leaf with a marking pen.Write the same numbers on small pieces of paper.Fold the pieces of paper.Put them into a hat and mix them up.Draw 100 pieces of paper (without looking) from the hat. The first 100 pieces of paper you draw would give you the numbers of the leaves to use in the experiment.The next thing you need to decide is how to measure the leaves, andhow accurate your measurements should be:How to measure?Keeping your leaves flat, use a ruler to measure the length of each leaf from the pointy part at one end of the leaf to the point where the leaf joins the stalk at the other end. Maybe your leaves bend a bit, but don't follow the main rib of the leaf as this would make measurement too difficult.Just measure in a straight line as shown in the following diagram:leafHow accurate?You should measure the length of each leaf to the nearest millimeter.Now you're ready to begin.Measure the length of each leaf to the nearest millimeter and record you results in a table, as follows:

Step-by-step explanation:

the accuracy of a sample is a measure of how closely it reports the true values of the population it represents. true false

Answers

A sample's accuracy is determined by how well it captures the genuine characteristics of the population it represents true

Accuracy is a measure of how closely a sample reflects the true values of the population it is representing. A sample that is accurate is one that accurately reflects the characteristics of the population it is representing. For example, if a sample is taken from a population of 1000 people, the sample should represent the diversity of the population, such as age, gender, race, and other characteristics. If the sample accurately reflects these characteristics, then it can be said to be accurate. The accuracy of a sample can be determined by comparing it to the population it is representing, either through surveys, interviews, or other data collection methods. If the sample closely matches the true values of the population, then it can be said to be accurate. If there are discrepancies between the sample and the population, then the sample is not accurate.

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John can ride his bicycle at a rate of 14 miles per hour. Convert this rate to
feet per second.
O 20.53 feet per second
O 25.03 feet per second
O205.33 feet per second
O250.33 feet per second

Answers

correct answer is a) 20.53 feet per second

John can ride his bicycle at a rate of 20.53 feet per second.

How do I calculate feet per second?

Multiplying your foot-per-minute speed by 60. This is how many seconds there are in a minute. Your speed in feet per second is the outcome. For instance, 88 feet per second is equal to 5,280 feet per minute divided by the 60 seconds in a minute.

How long is a second in feet?

One-degree of longitude equals 288,200 feet (54.6 miles), one minute equals 4,800 feet (0.91 mile), and one second equals 80 feet.

Is feet per second velocity?

A unit of velocity and speed (scalar) is the foot per second (plural feet per second) (vector quantity, which includes direction). It represents the traveled or displaced distance in feet (ft) divided by the time (in seconds) (s).

[tex]\frac{14 miles}{1 h}[/tex] × [tex]\frac{5280 ft}{1 mile}[/tex]= [tex]\frac{73920 ft}{1 hr}[/tex]

[tex]\frac{73920 ft}{1 hr}[/tex] × [tex]\frac{1 hr}{60 min}[/tex]= [tex]\frac{1232 ft}{1 min}[/tex] ×[tex]\frac{1 min}{60s}[/tex]= [tex]\frac{20.53ft}{1s}[/tex]

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If a fair coin is tossed 4 times, what is the probability, to the nearest thousandth, of getting exactly 4 heads?

Answers

Answer: The probability of getting exactly 4 heads in 4 tosses of a fair coin is 0.0625, or 6.25%.

Step-by-step explanation:

We can use the formula for combinations, which is:

n! / (r! * (n - r)!)

In this case, n is the total number of tosses (4) and r is the number of successes we want to count (4 heads). Plugging these values into the formula, we get:

4! / (4! * (4 - 4)!) = 4! / (4! * 0!) = 4! / (4! * 1) = 1 / 1 = 1

The probability of getting exactly 4 heads in 4 tosses of a fair coin is therefore 1, or 100%. However, this is assuming that the coin is not fair and always lands on heads. If the coin is fair, the probability of getting 4 heads in 4 tosses is actually much lower.

To find the probability of getting 4 heads in 4 tosses of a fair coin, we need to use the formula for binomial probability, which is:

(n! / (r! * (n - r)!) * p^r * (1 - p)^(n - r)

In this case, p is the probability of getting a head in a single toss of the coin (0.5), r is the number of successes we want to count (4 heads), and n is the total number of tosses (4). Plugging these values into the formula, we get:

(4! / (4! * (4 - 4)!) * 0.5^4 * (1 - 0.5)^(4 - 4) = 1 * 0.5^4 * (1 - 0.5)^0 = 0.5^4 * 1 = 0.0625

Thus, the probability of getting exactly 4 heads in 4 tosses of a fair coin is 0.0625, or 6.25%, to the nearest thousandth.

write a system of three linear equations with three variables each that has the unique solution . write your equations in standard form. use the variables , , and with non-zero coefficients.

Answers

the system of three linear equations with three variables each that has the unique solution is 2x + 3y + 4z = 30, 3x + 4y + 5z = 45 and 5x + 6y + 7z = 75.

2x + 3y + 4z = 30

3x + 4y + 5z = 45

5x + 6y + 7z = 75

The first equation is 2x + 3y + 4z = 30. The coefficients for the variables are 2, 3 and 4 which are all non-zero, meaning that this equation has a unique solution.

The second equation is 3x + 4y + 5z = 45. The coefficients for the variables are 3, 4 and 5 which are all non-zero, meaning that this equation also has a unique solution.

The third equation is 5x + 6y + 7z = 75. The coefficients for the variables are 5, 6 and 7 which are all non-zero, meaning that this equation also has a unique solution.

Therefore, the system of three linear equations with three variables each that has the unique solution is 2x + 3y + 4z = 30, 3x + 4y + 5z = 45 and 5x + 6y + 7z = 75.

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What is the axis of symmetry? What are the coordinates of the vertex?
y=-x² +8x+12

Answers

Answer:

axis of symmetry : x = 4

coordinates of the vertex : (4, 28)

Step-by-step explanation:

Before we start solving, let's define what the coefficients of this quadratic equation is.

[tex]y = ax^2 + bx + c[/tex]

[tex]y = -x^2 + 8x + 12[/tex]

a = -1

b = 8

c = 12

What is the axis of symmetry?

the vertical line that cuts through the vertex and makes the parabola into 2 symmetrical halvesequation: x=

To find the axis of symmetry, we need to find the x-coordinate of the vertex.

Equation for the x-coordinate of the vertex:

[tex]x = \frac{-b}{2a}[/tex]

Substitute the values of a, b, and c into this equation and compute.

[tex]x = \frac{-(8)}{2(-1)}[/tex]

[tex]x = \frac{-8}{-2}[/tex]

[tex]x = 4[/tex]

The axis of symmetry is x = 4

What is the vertex of a parabola?

the absolute highest or lowest point of the parabola

To find the x-coordinate of the vertex, you can use the formula: [tex]x = \frac{-b}{2a}[/tex].

To find the y-coordinate of the vertex, substitute the x-coordinate of the vertex and compute.

x-coordinate: 4

y-coordinate:

[tex]y = -x^2 + 8x + 12[/tex]

[tex]y = -(4)^2 + 8(4) + 12[/tex]

[tex]y = -(16) + 32 + 12[/tex]

[tex]y = -16 + 44[/tex]

[tex]y = 28[/tex]

y-coordinate: 28

The coordinates of the vertex is (4,28)

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The college graduate is hired at a law firm with a $10,000 signing bonus, that will be deposited into the savings account. The firm also agrees to immediately pay off
$25,000 in student loan debt. What is the college graduate's new net worth?
O$16,081
O $21,167
O$13,833
O $33,097

Answers

The college graduate's new net worth is given as follows:

$13,833.

How to calculate the net worth?

The net worth of a company or of a person is given by the sum of the values of all assets of the person subtracted by the sum of the values of all debts of the person.

The assets if the student are given as follows:

Signing bonus: $10,000.Furniture: $14,278.Savings Account Balance: $4,337.Car Value: $14,950.Computer and Software: $11,774.

The liabilities of the student are given as follows:

Car Loan: $3,250.Credit Card Balances: $5,129.Student Loans: $58,097 - $25,000 = $33,097.

Thus the student's net worth is calculated as follows:

(10000 + 14278 + 4337 + 14950 + 11774) - (3250 + 5129 + 33097) = $13,863.

Which is closest to the third option among those given.

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Answer:

the correct answer is 12057

Step-by-step explanation:

in order to calculate net worth, add up the assets, and then subtract the debt. be sure to pay attention to details

heres an UNRELATED TO THE QUESTION example:

i have...

$500 in my savings

$20 in my wallet

but im $200 deep in credit card debt..

(add 500 + 20, then subtract 200)

net worth: 320

Rewrite:4/6 : 1/3
as a unit rate.

Answers

Answer:

I think it's 2:1

Step-by-step explanation:

if I'm wrong in sorry

Answer:

Step-by-step explanation:To rewrite 4/6 : 1/3 as a unit rate, we need to first find a common denominator for the fractions. The least common multiple of 6 and 3 is 6, so we can use this as the common denominator.

We can then rewrite the fractions as follows:

4/6 : 1/3 = (4/6) * (3/3) : (1/3) * (2/2)

Simplifying, we get:

2/3 : 2/3

This is a unit rate, with a value of 2/3.

The bears in Alaska are limited to a certain area to live due to the resources available for
food and shelter. After years, the number of bears living in the area is modeled by the function below. Using the function, find the number of bears after 17 years.

Answers

The number of bears living in the area after 17 years is; 22555

How to solve exponential functions?

We are given the function;

f(t) = 103/(1 + 26e^(-0.31t))

Where f(t) is a function that models the number of bears living in the area after t period of years.

Thus, to find the number of bears living in the area after 17 years, we will just substitute 17 for t in the given function to get;

f(17) = 103/(1 + 26e^(-0.31*17))

f(17) = 103/0.00456653759

f(17) ≈ 22555 bears

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a mistake was made in the steps shown to simplify the expression. which step includes the mistake?

Answers

The step in which there is a problem is the operation in step 4. option C

Where is the mistake?

In this question, we are expected to solve the problem in a number of steps. We know that in mathematics, the solution to a given problem can only be worked out through a number of steps that can help us to be able to know what the correct solution of the problem ought to be.

In this case we have a simplification problem. It should be know that the acronym of BODMAS has to be called to mind here and that is;

BracketOfDivisionMultiplicationAdditionSubtraction

Mathematical operations would have to be carried out in this order else there would be a mistake in it. We can see that the addition in step 4 before division did not follow the principle of BODMAS thus that step is wrong.

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