Solve the system of equations
x+y=15
Y=x^(2)-5

(-5,20) and (4,11)
(3,4) and (7,8)
(5,10) and (-4,19)
(5,20) and (4,11)

Answer:

a) In 2 hours

b) 16 km

Step-by-step explanation:

Let's first find out how far Abel has traveled in 2 hours. We can use the formula:

distance = speed x time

distance = 4 km/h x 2 h = 8 km

So when Jack starts cycling, Abel has already covered 8 km.

Now, let's say it takes Jack t hours to catch up to Abel. During this time, Abel has continued walking for t + 2 hours. So we can write:

distance covered by Abel = distance covered by Jack

4 km/h x (t + 2 h) = 8 km/h x t

Simplifying this equation, we get:

4t + 8 = 8t

4t = 8

t = 2

So Jack will overtake Abel after 2 hours of cycling. To find out how far they will have traveled, we can use the formula:

distance = speed x time

distance = 8 km/h x 2 h = 16 km

Therefore, when Jack overtakes Abel, they will have traveled 16 km in total.

Answer:

Step 1:

a.) 16 pets in total (1 + 0 + 2 + 0 + 3 + 8 + 0 + 2)

b.) the mean is 2 (16 is the total number of pets, divide that by 8 which is the total number of students asked, 16/8 = 2)

Step 2:

a.) 0, 0, 0, 1, 2, 2, 3, 8 (zero, one, two, three, four, five, six, seven, eight.)

b.) 0 and 3 are the middle numbers (center.)

c.) 3/2 = 1.5 (0+3 = 3 divided by 2 = 1.5)

Step 3:

- most of the students did not have any pets, so the mode would be 0 (it is zero because zero appears in the set of numbers 3 times. More than any other number).

Step 4:

They should use the mean of the amount of pets the students have; this is because the mean is the average amount of pets counting everyone in class—regardless on if there were zeros in the list.

Answer:

Step-by-step explanation:

From the given triangle, x has a value of 35°.

As a result, one of the triangle's sides has been stretched to create an exterior angle of 125° outside angle.

Angles that are always located near one another, sharing a similar vertex and common side but not overlapping, are said to be adjacent angles.

According to the above figure, the tringle's exterior angle is 125°, and y is an adjacent angle to that.

Now, 125°+ y =180°

y = 180°-125°

y = 55°

As a result, the supplied triangle's value for y is 55°.

The sum of the triangle law,

55°+ 90° + x  = 180°

x = 35°

Therefore the value of x = 35°

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The measure of <RTV = 1/2 * (99 - 45) = 27 degrees

Geometrically speaking, a secant is an intersecting line that marks two separate points on the circumference of a circle.

Primarily, it serves as a chord drawn across the diameter which transverses through each endpoint connecting them. The magnitude of the secant is determined by the distance between these intersectional points. This particular element of geometry has various applications in trigonometry, particularly in computing angles and lengths within circles.

According to the Exterior Angle of a Circle Theorem, the measure of an exterior angle of a circle formed by two secants is equal to half the difference of the measures of the intercepted arcs:

Using this theorem,

Thus, the measure of ∠RTV is given as 27

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Answer:

[tex]\dfrac{f}{g}(x) = \boxed{\dfrac{7}{x\left(x-3\right)}\\\\}[/tex]

Domain of  [tex]\dfrac{f}{g}: \boxed{\:\left(-\infty \:,\:0\right)\cup \left(0,\:3\right)\cup \left(3,\:\infty \:\right)}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \dfrac{7}{x} , g(x) = x - 3[/tex]

[tex]\dfrac{f}{g} = \dfrac{f(x)}{g(x)} = \dfrac{7}{x} \div x - 3\\\\= \dfrac{7}{x} \times \dfrac{1}{x-3}\\\\ = \dfrac{7}{x\left(x-3\right)}[/tex]

To find the domain of

[tex]\dfrac{f}{g} = \dfrac{7}{x\left(x-3\right)}[/tex]

note that this function is defined everywhere in the range (- ∞, ∞) except for x = 0 and x = 3

At these two points, the function is undefined since the denominator becomes 0 and division by 0 is undefined

Therefore the domain consists of three parts expressed in inequality and interval forms

-∞ < x < 0     (-∞, 0)

0 < x < 3      (0, 3)

3 < x < ∞      (3, ∞)

Therefore the domain is obtained by combining these three intervals
- ∞ < x < 0 or 0 < x < 3 or x > 3

In interval notation with union:
[tex]\:\left(-\infty \:,\:0\right)\cup \left(0,\:3\right)\cup \left(3,\:\infty \:\right)[/tex]   ANSWER

The calculated values of the sum of interior angles of the shapes are 1080 degrees and 360 degrees

The formula of the sum of interior angles of a polygon is

Sum = (n − 2) * 180

For the octagon, we have

n = 8

This means that

Sum of angles = (8 − 2) * 180

Evaluate

Sum of angles = 1080

For the square, we have

n = 4

This means that

Sum of angles = (4 − 2) * 180

Evaluate

Sum of angles = 360

Hence, the sum of interior angles of the shapes are 1080 degrees and 360 degrees

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Answer:

6 presents / minute

Step-by-step explanation:

We can represent the given information in a ratio:

amount of present wrapped : minutes it took to wrap

                                        2/3   :   1/9

Then, we can multiply both sides by 9 (the reciprocal of 1/9) so that the right side of the ratio is 1 minute.

presents : minutes

       2/3   :   1/9

       × 9       × 9

        6     :     1

So, Patricia can wrap 6 presents in 1 minute.

Answer:

A is incorrect because points are: (length [x], height [y])

B is correct because a point is not a size, it is a position, and they have no dimensions, as they are a dot.

C is incorrect, as I explained above.

D is incorrect, also as I explained above.

Select the bolded answers, as the question asks which are false

Imma get that brainliest ;)

Answer:

It's has to be D) because it says it depends on their dimensions.

Step-by-step explanation:

a) says they have no length or high which is almost the same thing as B).

Cuz B) they have no size or dimension

which that means that if you have to check if they all apply they all have to be the same thing in different words.

C) says their size variety which variety means it could be different types it could be without dimension it could be tall or etc

And D) says their size depends on their dimension all the others say don't have size or dimension. I hope this helps you

The circumference of the circle with a radius of 10 cm is 20π cm, option (C) is correct.

A circle's perimeter, or the distance encircling it, is known as its circumference. It is determined by multiplying the circle's diameter by pi. But in this case, we are given the radius of the circle, which is half of the diameter.

To get a circle's circumference, use the following formula:

C = 2πr

where;

r = radius of the circle

π = mathematical constant pi (approximately equal to 3.14).

Given the radius of the circle as 10 cm, we can use the formula to find its circumference:

C = 2πr

C = 2π(10 cm)

C = 20π cm

Hence, option C is correct.

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The correct question is:

What is the circumference of the circle with radius = 10 cm (leave your answer of π).

A) 10π cm

B) 5π cm

C) 20π cm

D) 10π cm

Answer: D

Step-by-step explanation: it equals 181

Answer: 3.14 x 12 x 2

= 75.36

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

Simply plug in the value of your 'x' and 'y':

x = 4.5

y = 5.2

[tex]2(4.5)+5(5.2)=9+26=35[/tex]

The constant of variation that exists between the weight and the volume of the objects would be = 7/5. That is option C.

A measurement is said to vary directly with another when the increase in proportion of the object leads to a direct decrease to the other one.

That is for the given object;

Weight is directly proportional to Volume

Therefore, weight = k Volume

K = constant of variation

make k the subject of formula;

k= weight/volume

but weight = 28

volume = 20

k = 28/20

= 7/5

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Answer:

Step-by-step explanation:

Answer: 1; 520/9 number 2: 9/2 number 3: d number 4:d number 5: 151.7

Step-by-step explanation:

To get a 1 in matrix row 1, column 1 all we have to do is divide the row by 7 which gives us:

[tex]\left[\begin{array}{ccc} 1\frac {-4}{7}&\frac{8}{7} \\-12&7&-13\end{array}\right][/tex]

The solution provided above uses a method of matrix called Echelon.

Echelon matrix is a matrix that has been transformed using row operations into a specific form that makes it easier to solve systems of linear equations.

By applying these row operations, a matrix can be transformed into row echelon form, which is a weaker form of echelon form where the leading non-zero entry of each row is to the right of the leading non-zero entry of the row above it, but not necessarily strictly to the right.

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The probability of needing fewer than 4 rolls to get doubles is 13/25.

Probability is a branch of mathematics that deals with the likelihood of something happening. It is used in many areas such as finance, engineering, and even gambling. Probability is the measure of how likely an event is to take place. This is usually expressed as a number between 0 and 1, where a 0 indicates an impossible event, and a 1 indicates an event that is certain to happen. Probability is an important component of decision making, as it allows us to calculate the chances of different outcomes.

This can be calculated by using the binomial probability formula. The binomial probability formula is used to calculate the probability of a certain number of successes in a certain number of trials. In this case, the number of successes is 2 (the number of doubles required to win the game) and the number of trials is 4 (the maximum number of rolls necessary to win the game).

Using the formula P(x) = nCx * pˣ* qⁿ⁻ˣ, where n is the number of trials, x is the number of successes, p is the probability of success and q is the probability of failure, we can calculate the probability of needing fewer than 4 rolls to get doubles as follows:

P(2) = 4C2 * (1/2)² * (1/2)⁴⁻² = 4 * ( 1/4 ) * (1/4) = 1/4

P(1) = 4C1 * (1/2)¹ * (1/2)⁴⁻¹= 4 * (1/2) * (1/2) = 1/4

The total probability of needing fewer than 4 rolls to get doubles is the sum of the probabilities of needing 1 or 2 rolls to get doubles, which is 1/4 + 1/4 = 1/2, or 13/25.

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Complete questions as follows-

Based on the results, what is the probability of needing fewer than 4 rolls to get doubles? 13/25.

Tyler who is buying a used vehicle and has a FICO score of 780 is likely to be offered the lowest APR. The Option A is correct.

Since, When it comes to APR for a new or used vehicle loan, a borrower's credit score is one of the main factors considered by lenders.

The higher the credit score, the very more likely that a borrower is to be offered a lower APR.

Hence, In this case,

Tyler has a FICO score of 780 which is considered excellent, and is buying a used vehicle.

This combination of a high credit score and a used vehicle purchase makes Tyler the most likely candidate to be offered the lowest APR.

Thus, Tyler who is buying a used vehicle and has a FICO score of 780 is likely to be offered the lowest APR. The Option A is correct.

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Answer:

To create a residual plot, you need to first fit a model to the data. Without any information about the problem you are trying to solve or the model you are fitting, I will assume that you are trying to fit a linear regression model to these data points.

First, you would need to find the equation of the line that best fits the data using a regression analysis software or by hand. Let's assume that the equation of the line is:

y = 0.2x + 2.5

where y is the response variable (dependent variable) and x is the predictor variable (independent variable).

Next, you would calculate the predicted values of y (i.e., the values that the model predicts) for each value of x in your dataset, using the equation of the line. For example, for the first data point (13.8, 1.42), the predicted value of y would be:

y_predicted = 0.2 * 13.8 + 2.5 = 5.06

The residual for this data point would be the difference between the actual value of y and the predicted value of y:

residual = 1.42 - 5.06 = -3.64

You would repeat this process for each data point in your dataset, to get a list of residuals.

After substituting the values as x=3 and y=7, the value of the expression "2x²-y¹+3x⁰" is 14.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified or evaluated to a numerical value.

To evaluate the expression 2x²-y¹+3x⁰ for x=3 and y=7, we substitute the given values, which are x=3 and y=7 into the expression and simplify:

On substituting the values,

We get,

= 2x² - y¹ + 3x⁰

= 2(3)² - 7¹ + 3(1)

= 2(9) - 7 + 3

= 18 - 7 + 3

= 14

Therefore, when x=3 and y=7, the value of the expression 2x²-y¹+3x⁰ is 14.

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3.5= 35/10

35/10= 7/2

which is equal to 3 1/2

Therefore: 3 1/2 and 7/2

Answer:

$140,000

Step-by-step explanation:

7*20,000 = 140,000

The equation of the regression line is Pulse = 1.301 + 7.316 * Speed. The slope parameter represents how pulse rate changes with skateboarding speed. The margin of error for a 99% confidence interval for the slope is 2.517.

Part A: The equation of the regression line can be written as: Pulse = 1.301 + 7.316 * Speed

Part B: The slope parameter of 7.316 means that for every 1 unit increase in skateboarding speed, the pulse rate increases by an average of 7.316 beats per minute. The intercept parameter of 1.301 represents the pulse rate at a speed of 0 miles per hour (which doesn't have a specific meaning in this context).

Part C: To compute the margin of error for a 99% confidence interval for the slope, we use the formula: margin of error = critical value * standard error. The critical value for a 99% confidence interval is approximately 2.896. Plugging in the values, we get margin of error = 2.896 * 0.870 = 2.517 (rounded to three decimal places).

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Selling 80 items will produce maximum profit if the profit function is [tex]P(x) = 2400x + 105x^2 - x^3 - 167,000[/tex].

To find value of x that produces maximum profit, we must get critical points of the profit function and determine which one corresponds to a maximum.

The profit function is given as:

[tex]P(x) = 2400x + 105x^2 - x^3 - 167,000[/tex]

Taking the derivative of P(x) with respect to x, we get:

[tex]P'(x) = 2400 + 210x - 3x^2[/tex]

Setting P'(x) equal to zero and solving for x, we get:

[tex]0 = 2400 + 210x - 3x^2\\3x^2 - 210x - 2400 = 0\\x^2 - 70x - 800 = 0\\(x - 80)(x + 10) = 0[/tex]

Here, the critical points are x = 80 and x = -10.

To determine one that corresponds to a maximum, we can use the second derivative test. Taking the derivative of P'(x), we get:

[tex]P''(x) = 210 - 6x[/tex]

Evaluating P''(80), we get:

[tex]P''(80) = 210 - 6(80)\\P''(80) = 210 - 420\\P''(80) = -330[/tex]

Since P''(80) is negative, the critical point x = 80 corresponds to a maximum. So, selling 80 items will produce maximum profit.

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The terminal point of 13π/6 is (-√3/2, 1/2) by using unit circle.

The quadrants of a graph are the four sections that divide the coordinate plane. The quadrants are numbered in a counterclockwise direction starting from the positive x-axis.

1. Quadrant I is located in the upper-right section and contains points with positive x and y-coordinates.

2. Quadrant II is located in the upper-left section and contains points with negative x-coordinates and positive y-coordinates.

3. Quadrant III is located in the lower-left section and contains points with negative x and y-coordinates.

4. Quadrant IV is located in the lower-right section and contains points with positive x-coordinates and negative y-coordinates.

The quadrants are useful for determining the signs of coordinates, angles, and for plotting points on a graph.

To find the terminal point of 13π/6, we can start by recognizing that this angle is greater than 2π, which is one complete revolution around the unit circle.

To bring the angle back within one revolution, we can subtract 2π, which gives us 13π/6 - 2π/1 = 13π/6 - 12π/6 = 1π/6.

The angle 1π/6 is in the standard position between the positive x-axis and the first quadrant. The reference angle is π/6, which is the angle between the terminal side and the x-axis.

Since the angle is in the 2nd quadrant, the x-coordinate will be negative and the y-coordinate will be positive. Using the unit circle, we can find the values of sine and cosine at π/6 and then negate the value of cosine since the angle is in the second quadrant.

cos(π/6) = √3/2

sin(π/6) = 1/2

Therefore, the terminal point of 13π/6 is (-√3/2, 1/2).

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A graph of the piecewise function is shown on the coordinate plane in the image attached below.

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals such as -1 < x ≤ 0.

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If Allison jogs at the same rate for 1 and a half hours, the number of miles that she would jog is 6.75 miles.

In Mathematics and Science, speed is the distance covered by a physical object per unit of time.

In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Speed = 4.5/1

Speed = 4.5 miles per hour.

Making distance the subject of formula, we have:

Distance, d(t) = speed × time

Distance, d(t) = 4.5 × 1.5

Distance, d(t) = 6.75 miles.

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