Angel scores 17 , 19 , 13 , 24 , and 14 points in the first five game of a seven game basketball season of scoring leader in Angela’s league average 18 points per game how many points must angela score in the final two games combined to end the season with the highest scoring average in the league and have a higher scoring average than any other player

The quadratic equation of x2-6x+9=0 is C) (x-2)(x+3).

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.

This equation is an example of a quadratic equation, which is an equation of the form ax2+bx+c=0, where a, b, and c are real numbers, and a is not equal to 0. In this equation, a is equal to 1, b is equal to -6, and c is equal to 9. To solve this equation, we need to use the quadratic formula, which states that the solutions to the equation are x= -b ± √b2-4ac / 2a. Therefore, the solutions to this equation are x= -(-6) ± √(-6)2-4(1)(9) / 2(1), which simplifies to x=3 ± √3 /2, or x=3 ± √9 /2. This simplifies to x=3 ± √3, or x=3 ± 1. Therefore, the solutions to this equation are x=2 and x=4. The factored form of this equation is (x-2)(x+3), which is option C.

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Answer: The binomial factor is (x+2) . This was determined by factoring the given expression x4−4x2−4x+8 x 4 − 4 x 2 − 4 x + 8 by grouping then factoring one of the binomial terms

Step-by-step explanation:

Gauss-Jordan elimination is a method used to solve a system of linear equations by reducing the augmented matrix of the system to a reduced row-echelon form through a series of elementary row operations.

The process involves manipulating the rows of the augmented matrix to obtain a triangular matrix, where all entries below the diagonal are zero. This is achieved by applying elementary row operations such as adding a multiple of one row to another row or multiplying a row by a scalar.

Once the augmented matrix is in triangular form, further elementary row operations are used to eliminate the nonzero entries above the diagonal. This results in the augmented matrix being in reduced row-echelon form, where the pivot elements are all equal to 1 and the columns corresponding to the pivot elements are linearly independent.

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You kayak 140 feet further in 5 minutes going downstream than you do in 5 minutes going upstream.

Speed is determined by dividing the distance traveled by the time taken to travel it. It gives the distance traveled and the amount of time it took to travel that distance.

Speed is directly Proportional to Distance and Inversely proportional to Time. Hence,

Distance = Speed X Time.

Given: You paddle a kayak 168 feet up a river every two minutes.

Hence, 168/2 = 84 feet per minute.

Therefore you go up  84 feet in one minute.

You reach 84*5 = 420 feet in 5 minutes.

Given: As you paddle back down the river, you cover 56 feet every 30 seconds.

Speed is determined by distance traveled divided by time, therefore when traveling downward, 56/0.5 equals 112 feet per minute.

In one minute, you descend by 112 feet.

You descend 560 feet in 5 minutes, or 5*(112) feet.

As a result, you will move on 140 feet (560 - 420)=140 feet further .

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The coefficient of variation (CV) calculator is a tool that helps you calculate the relative variability of a dataset. The coefficient of variation is the ratio of the standard deviation (SD) to the mean (μ) expressed as a percentage, and it is used to compare the variability of datasets with different units or scales.

The formula for the coefficient of variation is:

CV = (SD / μ) x 100%

To use a coefficient of variation calculator, you need to input the values of the dataset, either one by one or as a list, and select the type of data you have (sample or population). The calculator will then calculate the mean, standard deviation, and coefficient of variation of the dataset.

The coefficient of variation is commonly used in quality control, finance, and other fields to compare the variability of different datasets. A high coefficient of variation indicates that the dataset has a large amount of variability relative to the mean, while a low coefficient of variation indicates that the dataset has a small amount of variability relative to the mean.

The coefficient of variation is only meaningful when the mean is non-zero. If the mean is zero or close to zero, the coefficient of variation can be infinite or undefined.

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A coefficient of variation (CV) calculator is a tool used to calculate the coefficient of variation for a given dataset. The coefficient of variation is a statistical measure that is used to express the variation or dispersion of a dataset relative to the mean.

The CV is often expressed as a percentage and is useful for comparing the variation of different datasets that have different units of measurement and is calculated as the ratio of the standard deviation to the mean.

To use a coefficient of variation calculator, you need to input the dataset for which you want to calculate the CV. The calculator will then calculate the mean and standard deviation of the dataset and use these values to calculate the coefficient of variation. The result will be expressed as a percentage.

Alternatively, you can use a coefficient of variation calculator, which will perform these calculations for you. Many statistical software packages and online calculators offer coefficient of variation calculators, which can be a convenient tool for quickly calculating this measure for a given dataset.

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1/5(15+10x-5) is equivalent to 2(x+1).

What is equivalent equation?

Equivalent equations are algebraic equations with the same roots or solutions.

1/5(15+10x-5) can be simplified as follows:

1/5(15+10x-5) = 1/5(10x + 10)

Factor out 10 from the expression in the parentheses:

1/5(10x + 10) = 1/5 * 10 * (x + 1)

Simplify:

1/5 * 10 * (x + 1) = 2(x + 1)

Therefore, 1/5(15+10x-5) is equivalent to 2(x+1).

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Answer:

a8

Step-by-step explanation:

Here you go.

nth term is ar^n-1

The measure of a central angle in a regular hexagon where each interior angle is 60° is also 60°.

If each interior angle equals 60° in a polygon, then we know that the polygon is a regular hexagon. In a regular polygon, all angles are congruent, so the measure of each interior angle of a regular hexagon is 60°.

Now, to find the measure of a central angle of the hexagon, we can use the formula:

measure of central angle = 360° / number of sides

For a hexagon, the number of sides is 6, so:

measure of central angle = 360° / 6 = 60°

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Answer: 20

Step-by-step explanation: The volume formula for a rectangular pyramid is [tex]\frac{lwh}{3}[/tex] so the initial volume would be 540. Since you are dilating it by 1/3 the length, with, and height are all shrinking by 1/3. 1/3*1/3*1/3 is 1/27 so that means the final thing will be 1/27 of its original size.

Answer:

So, first let's understand what a scale factor is. A scale factor is a number that tells you how much you need to multiply the size of an object to make it bigger or smaller. In this case, the scale factor is 1/3, which means we're going to make the pyramid one third of its original size.

Now, let's talk about how we can find the volume of the pyramid. The formula for the volume of a pyramid is:

Volume = (1/3) x base area x height

The base area is the area of the rectangle at the bottom of the pyramid, which we can find by multiplying the length and width:

Base area = 9 cm x 12 cm = 108 square cm

The height of the pyramid is given as 15 cm, so we can substitute these values into the formula:

Volume = (1/3) x 108 square cm x 15 cm

Volume = 540 cubic cm

So the volume of the original pyramid is 540 cubic cm. But we need to find the volume of the pyramid after it is dilated by a scale factor of 1/3. To do this, we need to multiply the original volume by the scale factor cubed. The reason we cube the scale factor is because we're scaling in three dimensions (length, width, and height).

Scale factor cubed = (1/3) x (1/3) x (1/3) = 1/27

Volume of dilated pyramid = 540 cubic cm x 1/27

Volume of dilated pyramid = 20 cubic cm (rounded to the nearest whole number)

So the volume of the pyramid after it is dilated by a scale factor of 1/3 is 20 cubic cm.

Answer:

95+B=180. ( linear pair)

95+105=180

180=180

hence proved

The value of the given expression 105 times 3 is equal to 315.

Calculation of the expression 105 times 3 is equal to :

  1

1 0 5

×    3

3 1 5

Therefore, the calculated value of the expression 105 times 3 is equal to 315.

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The statement that would be true from what we have here would be that opposite angles of a parallelogram are congruent. Option C

A special kind of quadrilateral known as a parallelogram is one in which both sets of its opposite sides are parallel and equal.

PQRS is a parallelogram, therefore.

PQ ≅ RS

QR ≅ PS

Using the SSS criterion, PQR and PQS both equal RSP and RQS.

As a result, since the corresponding angles of congruent triangles are congruent, ∠QPS ≅ SRQ and ∠PQR ≅ ∠RSP.

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In case of measurement, 300 mm is equivalent to 11.811 inches.

Measurement is a critical aspect of our daily lives as it helps us quantify things and understand the world around us.

When it comes to converting units of measurement, it is essential to understand the basic conversions. One such conversion is between millimeters (mm) and inches (in).

To convert millimeters to inches, we need to know the conversion factor, which is 1 mm = 0.0393701 in. This means that if we have a measurement of 300 mm and we want to know its equivalent in inches, we simply multiply 300 by the conversion factor:

300 mm x 0.0393701 in/mm = 11.811 inches (rounded to the nearest thousandth)

It is essential to remember that understanding conversions between units of measurement is crucial in many fields such as engineering, science, and medicine. Being able to convert units accurately can prevent errors and ensure precise calculations.

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A scatter plot of the data is shown below.

The best-fitting line for the data is y = -10t + 165.8.

The predicted number of adult softball teams in 2010 is 56 thousands adult softball teams.

In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the number of years would be plotted on the x-axis of the scatter plot while the number of teams (thousands) would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the number of years and teams (thousands), a linear equation for the line of best fit is given by:

y = -10t + 165.8

Next, we would determine the predicted number of adult softball teams in 2010:

Years, t = 2010 - 1999 = 11 years.

y = -10(11) + 165.8

y = -110 + 165.8

y = 55.8 ≈ 56 thousands adult softball teams.

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Answer:

$30

Step-by-step explanation:

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

If the ratio is Jake: Kim: Lee, and the amounts are 1: 3: 6, we can use this ratio to solve for the amount of money Lee will get if Kim gets $9 more than Jake:

Well, in order to get this ratio, we need to multiply each number in the original ratio by 5.

Therefore, Kim will get $15, which is $9 more than Jake's amount, which is $5. Lee has $30.

Answer:

The total number of pizzas they will order is 2

Step-by-step explanation:

[tex]15*2=30[/tex]

30 slices total, so they need 2 pizzas for each person to get 2 slices of pizza.

The solutions of the differential equation y" - 6y' + 8y = 0 are [tex]y=3e^{2x}[/tex]

and [tex]y = Ce^{4x}[/tex]. So option D II and III only is correct.

A differential equation is an equation including dependent variables and their derivatives concerning independent variables.

Given the equation is y" - 6y' + 8y = 0. This can be written as [tex]\frac{d^2y}{dx^2}-6\frac{dy}{dx}+8y=0[/tex].

Now, let's substitute d/dx = m, and we get,

[tex]\begin{aligned}(m^2-6m+8)y&=0\\m^2-6m+8&=0\\m^2-(4+2)m+8&=0\\m^2-4m-2m+8&=0\\m(m-4)-2(m-4)&=0\\(m-4)(m-2)&=0\\m&=2,4\end{aligned}[/tex]

Then, the general solution will be written as [tex]y(x)=C_1e^{2x}+C_2e^{4x}[/tex]. Then, [tex]y_1=C_1e^{2x}[/tex] and [tex]y_2=C_2e^{4x}[/tex]. Hence, the solution of a given ODE is always this y₁ or y₂ or the combination of these. Therefore, (I) cannot be possible.

Now let's consider (II) and put [tex]y'=6e^{2x}[/tex] and [tex]y"=12e^{2x}[/tex] in the given equation. We get,

[tex]\begin{aligned}12e^{2x}-36e^{2x}+24e^{2x}&=0\\36e^{2x}-36e^{2x}&=0\\0&=0\end{aligned}[/tex]

Hence, (II) is the solution of the given equation and is possible.

Now let's consider (III) and put C₁=0 and we get, [tex]y(x)=C_2e^{4x}=Ce^{4x}[/tex]when C₂=C. Hence, (III) is possible.

Therefore, the correct option is D II and III only.

The complete question is -

Of the following, which are solutions to the differential equation y" - 6y' +8y=0?

I. y = 2 sin(4x)

II. [tex]y=3e^{2x}[/tex]

III. [tex]y = Ce^{4x}[/tex], where C is a constant.

A) I only B) Il only C) Ill only D) II and III only

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A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry and in the given parallelogram the required value of x is 3 units.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry.

A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

In a parallelogram, the diagonals are split in half while the opposite sides are equal.

In a rhombus, all four sides are equal and the diagonals intersect at 90 degrees.

So, a parallelogram's diagonals cut each other in half.

Hence, WC = CY.

This is:

2x + 5 = 3x + 2

Take away 2x from each side:

5 = 3x - 2x + 2

5 = x + 2

Take away from both sides:

5 - 2 = x + 2 - 2

3 = x

Therefore, in the given parallelogram the required value of x is 3 units.

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Correct question:

In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?

The conversion of 2.5 inches to mm is 63.5 mm.

Millimeter (mm) and inch (in) are both units of length used to measure distance, length or height.

The millimeter is a metric unit of length, commonly used in most countries around the world. One millimeter is equal to one thousandth (1/1000) of a meter. Millimeters are often used in fields such as engineering, architecture, and manufacturing.

To convert 2.5 inches to millimeters (mm), you can use the conversion factor of 25.4 mm per inch.

So, the calculation is:

2.5 inches x 25.4 mm/inch = 63.5 mm

Therefore, 2.5 inches is equal to 63.5 mm.

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Answer:

24.

Step-by-step explanation:

The pattern is clearly going up by twos.

So continuing the pattern,

1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

1 2  3   4 5   6   7   8   9   10  11    12   13

Answer:

Step 1: Given AD || BC and AB || CD.

Step 2: Angle A and Angle C are alternate interior angles, so they are congruent.

Step 3: Angle B and Angle D are alternate interior angles, so they are congruent.

Step 4: Angle B + Angle D = 180 degrees (because Angle A + Angle B + Angle C + Angle D = 360 degrees for a quadrilateral)

Step 5: Since Angle B and Angle D are congruent and their sum is 180 degrees, they must each be 90 degrees.

Step 6: Triangle ABZ and Triangle CDZ are both right triangles, since Angle B and Angle D are each 90 degrees.

Step 7: By the Angle-Angle Similarity Theorem, triangles ABZ and CDZ are similar.

Step 8: Since triangles ABZ and CDZ are similar, corresponding sides are proportional.

Step 9: Therefore, ZB/ZD = AB/CD, since ZB corresponds to AB and ZD corresponds to CD.

Step 10: Given that AB || CD, we know that AB/CD = AZ/CZ (the corresponding sides of similar triangles are proportional).

Step 11: Therefore, ZB/ZD = AB/CD = AZ/CZ.

Step 12: Since Angle A and Angle C are congruent (Step 2), we know that AZ = CZ (since they are opposite sides of an isosceles triangle).

Step 13: Therefore, ZB/ZD = AZ/CZ = 1, which means that ZB = ZD.

Thus, we have proved that ZB = ZD!

- Dante

As per the unit conversion process, 4 meters is equal to 400 centimeters.

Unit conversion is a process of changing a given value from one unit of measurement to another. For example, converting meters to centimeters, or grams to kilograms. This skill is essential in science, engineering, and everyday life. In this article, we will learn how to convert 4 meters to centimeters.

First, we need to know the conversion factor between meters and centimeters. Since there are 100 centimeters in one meter, the conversion factor is 100 cm/m.

To convert 4 meters to centimeters, we need to multiply 4 meters by the conversion factor of 100 cm/m. This will give us the equivalent value in centimeters.

4 meters x 100 cm/m = 400 centimeters

It is essential to understand the conversion factor and the units of measurement involved in unit conversion. By doing so, we can accurately and efficiently convert values from one unit to another.

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Answer:

Step-by-step explanation:

First, we split the triangles into two

Δ ADC and ΔAEB

Then we look for similar things

First, both triangles have ∠A which makes the angles equal

Then we can see that side BE is // to line CD

That makes ∠D =∠E and ∠B = ∠C

Now we can have a ratio of the sides

AE/AD = AB/AC = EB/DC

AB/AC = AE/AD

12/12 + x = 16/24

Cross multiply

12 × 3 = 2 (12 + x)

36 = 24 + 2x

36 - 24 = 2x

12 = 2x

x = 6

BC = 6cm

Answer:

y^2 - 5y = 750

Step-by-step explanation:

If length = y

then width = y - 5

Area = length x width

= y(y-5) = 750

Or, y^2 - 5y = 750

This equation can be further solved as follows:

y^2 - 5y - 750 = 0

Or, y^2 - 30y + 25y - 750 = 0

Or, y(y - 30) + 25(y - 30) = 0

Or, (y + 25)(y-30) = 0

So, there are two possibilities:

If (y + 25) = 0

then y = -25

but value of length cannot be negative,

Let us look at second possibility

If (y - 30) = 0

then y = 30

So, length = 30 feet

Check Answer:

Length = 30 feet

so, width = 30 - 5 = 25 feet

so, area  = 30 x 25 = 750 square feet

An inverse function is defined as a function, which can reverse into another function.

I'm not sure if this is right I can't exactly remember

The the required equation is, y = -7/4 *x - 7 , in slope-intercept form.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have

from the given graph we get,

the line passes through two points (-4,0) and, (0,-7)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>(y-0)/(x+4)=(-7-0)/(0+4)

=>4y= -7x -28

=>y = -7/4 *x - 7

Hence, the required equation is, y = -7/4 *x - 7 , in slope-intercept form.

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Option A. AA Similarity Postulate. The AA Similarity Postulate is a geometric principle that states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

This means that their corresponding sides are in proportion, and the triangles have the same shape, but not necessarily the same size. This postulate is one of the ways to prove the similarity of two triangles. In the case of the given question, if we know that two angles of one triangle are congruent to the two angles of another triangle, then we can use the AA Similarity Postulate to prove that the triangles are similar. This principle is widely used in geometry and helps to establish relationships between different shapes and figures.

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Ms. Howard's salary would be $360. Below, you will learn how to solve the problem.

Ms. Howard's salary can be found by first calculating the amount of money spent on groceries, entertainment, and transportation. 1/3 of her monthly salary was spent on groceries, so that would be $(1/3)x where x is her salary, 1/4 of her monthly salary was spent on entertainment, so that would be $(1/4)x. 2/5 of the remaining amount was spent on transportation, which is $(2/5)(x-(1/3)x-(1/4)x).

Ms. Howard then had $270 left, so we can set up the equation:

$(1/3)x + $(1/4)x + $(2/5)(x-(1/3)x-(1/4)x) = 270

Solving for x, Ms. Howard's salary would be $360.

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Answer: -3

Step-by-step explanation:

for an equation [tex]ax^2+bx+c[/tex] to factor you need to figure out what numbers add to b and multiply to c. In this case b is -1 and c is -6. It is easier because one of the numbers has already been figured out for you so what number combined with 2 will add to -1 and multiply to -6? the answer would be -3 because 2+(-3) is -1 and 2*(-3) is -6.