Factor each polynomial completely.
a. 5a²c - 3a²d + 5b²c-3b²d
b. x^2n+ 6x^n +9

Step-by-step explanation:

the answer is 151200

In order to find the hypotenuse of the triangle

We need to find the other sides of a right triangle

Length of the 1st side of a right triangle is connected with a square with area 144[tex]cm^{2}[/tex]

Hence in order to find the side we

[tex]\sqrt{144} = side[/tex]

[tex]12 = side[/tex]

Length of the second side is connected to a small square with area 25[tex]cm^{2}[/tex]

[tex]\sqrt{25} = side[/tex]

[tex]5 = side[/tex]

Now we can find the hypotenuse of a right triangle with the phytogorean theorem

[tex]a^{2}+ b^{2} = c^{2}[/tex]

[tex]12^{2}+ 5^{2} = c^{2} \\169 = c^{2}[/tex]

[tex]\sqrt{169}= c[/tex]

[tex]13 = c[/tex]

Hence , the hypotenuse of a right triangle is 13cm

When estimating a population mean (μ) with a known population standard deviation (σ), the proper distribution to use is the standard normal distribution. So, correct option is A.

This is because the sampling distribution of the sample mean follows a normal distribution when the population standard deviation is known. The central limit theorem guarantees that the sample mean will be normally distributed with mean μ and standard deviation σ/√n, where n is the sample size.

The formula for constructing a confidence interval for μ when σ is known is:

CI = x' ± zα/2 * (σ/√n)

where x' is the sample mean, zα/2 is the z-score corresponding to the desired confidence level (α), σ is the population standard deviation, and n is the sample size.

Since the standard normal distribution has a mean of 0 and a standard deviation of 1, we can use z-scores to find the appropriate values for zα/2. This is why the standard normal distribution is used for interval estimation when σ is known.

In summary, the standard normal distribution is used for interval estimation of μ when σ is known because the sampling distribution of the sample mean is normally distributed when the population standard deviation is known.

So, correct option is A.

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Answer:

Step-by-step explanation:

The perimeter of a regular pentagon is equal to the sum of the lengths of its sides. The length of each side of a regular pentagon inscribed in a circle with radius 1 meter can be found using the formula: side length = 2 * radius * sin(180/number of sides).

For a regular pentagon, the number of sides is 5. Plugging this into the formula gives us:

side length = 2 * 1 * sin(180/5) = 2 * 1 * sin(36) = 2 * 0.587785 = 1.175570

So the perimeter of the regular pentagon is equal to 5 * 1.175570 = 5.877849 meters.

B. The function shown on the graph has a smaller rate of change, but a higher starting point.

Rate of change = slope of a linear graph.

Given the linear function, [tex]y=4x+2[/tex] , the rate of change here is represented by the slope of the line, which is 4.

Let's find the rate change of the function represented on the graph using slope formula:

Rate of change = [tex]\frac{y2-y1}{x2-x1}[/tex]

Use coordinates of any two points on the line. Let's take,

[tex](0,4)= (x1,y1)\\(1,7)=(x2,y2)[/tex]

Rate of change = [tex]\frac{7-4}{1-0} = 3[/tex]

Rate of change of the linear function of the graph = 3.

Thus the function on the graph has a smaller rate of change, than the function, y = 4x + 2.

The starting value of a function is the y-intercept, that is, the value of y, when x = 0. It is the point at which the line intercepts the y-axis.

The starting value of the linear function, y = 4x + 2 is 2.

The starting value of the function on the graph is 4. At this point, x = 0.

Thus, the function on the graph has a higher starting point.

The statement that correctly compares the function shown on this graph with the function y= 4x+2 is:

B. The function shown on the graph has a smaller rate of change, but a higher starting point.

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Answer:

3p^3 (-p^4 + 1)

Step-by-step explanation:

The common factor of both -3p^7 and 3p^3 is 3p^3

Divide -3p^7 by 3p^3 and get -p^4

Divide 3p^3 by 3p^3 and get 1

So the factorisation is 3p^3 (-p^4 + 1)

Answer:

15 lessons

Step-by-step explanation:

Answer:

Didn't move the 12 on the other side of the equal sign to make

2x^2 + 5x - 12 = 0

the other steps error city.

Step-by-step explanation:

2x^2 + 5x - 12 = 0

(2x - 3)(x + 4)= 0

2x - 3 = 0

2x = 3

x = 3/2

x + 4 = 0

x = -4

Let H be the number of hamburgers sold and C be the number of cheeseburgers sold.

The total number of hamburgers and cheeseburgers sold is given by the equation: H + C = 429

The number of cheeseburgers sold is given by the equation: C = 2H

Substituting the second equation into the first equation, we get: H + 2H = 429

Combining like terms, we get: 3H = 429

Dividing both sides by 3, we get: H = 143

On Thursday, 143 hamburgers were sold.

No, horizontal asymptote is not represented by y- axis it is represented by the x -axis.

Therefore, the horizontal asymptote is not represented by the y-axis, it is represented by the x-axis.

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The linear regression equation that represents the given set of data is y=0.2x+865.

Linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables. The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression.

The line of best fit is in the form y=bx+a

The slope is b= [tex]\frac{\sum (x-\bar x)\sum (y-\bar y)}{\sum (x-\bar x)^2}[/tex]

Here, [tex]\bar x[/tex] =(0+1+2+3+4)/5

= 1.8

[tex]\bar y[/tex] = (856+871+924+961+961)/5

= 914.6

∑(x-[tex]\bar x[/tex])=(0-2.5)+(1-2.5)+(2-2.5)+(3-2.5)+(4-2.5)

= -2.5-1.5-0.5+0.5+1.5

= -2.5

∑(y- [tex]\bar y[/tex]) =(865-914.6)+(871-914.6)+(924-914.6)+(961-914.6)+(961-914.6)

= -49.6-43.6+9.4+46.4+46.4

= 9

So, slope b= 1.8×9/9²

b=0.2

Substitute b=0.2 and (0, 865) in y=bx+a, we get

865=0.2×0+a

a=865

Substitute b=0.2 and a=865 in y=bx+a, we get

y=0.2x+865

Therefore, the linear regression equation that represents the given set of data is y=0.2x+865.

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"Your question is incomplete, probably the complete question/missing part is:"

The number of newly reported crime cases in a county in New York State is shown in the accompanying table; where X represents the number of years since 1995, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected number of new cases for 2003, rounded to the nearest whole number: Years since 1995 (x) New Cases (y) 856 871 924 961 961

P (X)= [tex]x^3+4 x^2-3x+2[/tex]  moreover, [tex]\frac{P(x)}{x - 1} = x^{2} + 5x +2[/tex] as a result, the actual claim is  [tex]$p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$[/tex]

The likelihood of an event occurring is determined by probability:       P(A) = f / N. Probability and odds are related, but probability is necessary for odds to exist. Prior to calculating the likelihood that an event will occur, probability is required.

The steps listed below can be used to determine an event's likelihood: Step 1: Identify an event that has only one outcome. Step 2: Compile a list of all potential outcomes, including any positive ones. Step 3: Subtract the number of favourable outcomes from the total number of outcomes that are feasible. The probability of A or B is equal to p(A or B) = p(A) + p(B) if occurrences A and B are mutually exclusive (B). A probability is a number that expresses the possibility or likelihood that a specific event will take place.

Therefore the correct answer is option A ) [tex]$p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$[/tex]

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Considering  the given triangle, the information given helped to apply similar triangle principle to determine v to be 3.9

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

TS and TR , SU and QR

The solution is worked out using sides WX and XV, WY and YU

TS / TR = SU / QR

TS / TR = 1/2 since it is a mid segment

1 / 2 = (19v - 38) / (-5v + 96)

-5v + 96 = 2 * (19v - 38)

-5v + 96 = 38v - 72

96 + 72  = 38v + 5v

168 = 43v

v = 3.9

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A student needs to receive 20 out of a possible 50 points on the test in order to receive a passing grade of 40%.

The term "proportionate" refers to relationships that always have the same ratio. For instance, the average number of apples per tree influences how many trees there are in an orchard and how many fruits there are in a harvest of apples. A linear relationship between two numbers or variables is referred to in mathematics as being proportionate. In the same way as the first quantity doubles, so does the other. The other decreases as well when one of the variables is reduced to 1/100th of its previous value. When two quantities are proportional, it means that when one rises, the other rises as well and that the ratio between the two quantities is constant at all values. As an example, consider a circle's diameter and circumference.

given

test score to 50 points

test score of 40 %

= 50/100 * 40

= 20

A student needs to receive 20 out of a possible 50 points on the test in order to receive a passing grade of 40%.

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The admission fee for the zoo and for the state park is given as follows:

For the zoo, the costs are divided as follows:

20 students are going to the zoo, hence the total cost spent at the zoo is given as follows:

20(2x + 3.25) = 40x + 65.

For the state park, the costs are divided as follows:

25 students are going to the state park, hence the total cost spent at the state park is given as follows:

25(x + 6.50) = 25x + 162.50.

The costs spent at both parks are the same, hence the value of x can be obtained as follows:

40x + 65 = 25x + 162.5

15x = 97.5

x = 97.5/15

x = 6.5.

Hence the admission fees are given as follows:

The table is given by the image presented at the end of the answer.

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The value of x in the triangle WXY is 27°

An equation shows how two or more numbers and variables are related to each other.

∠VWY + ∠XWY = 180° (sum of angle in straight line)

6x + ∠XWY = 180°

∠XWY = 180 - 6x

∠XYW + ∠ZYW = 180° (sum of angle in straight line)

∠XYW + 4x = 180°

∠XYW = 180 - 4x

∠XWY + ∠XYW + ∠YXW = 180° (angle in a triangle)

(180 - 6x) + (180 - 4x) + 90 = 180

450 - 10x = 180

10x = 270

x = 27°

The value of x is 27°

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The measure of the missing length of the trapezoid is equal to 3√39 units.

Trapezoids are quadrilaterals with only one pair of congruent sides and two pairs of congruent angles. The relationship between the longest and shortest legs (D, d) in a trapezoid is defined below:

D = d + 2 · c

Where c is the length of the horizontal leg of the right triangle in a trapezoid.

And the missing leg can be found by means of Pythagorean theorem:

x = √(r² - c²)

Where:

First, determine the length of shortest leg: (D = 40, d = 26)

40 = 26 + 2 · c

14 = 2 · c

c = 7

Second, find the longest leg by Pythagorean theorem:

x = √(20² - 7²)

x = 3√39

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For Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.

What are Trigonometric functions?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here,

We have to find out why trigonometric ratios are used only for right triangles.

We concluded that when we are dealing with triangles other than right triangles, the solution is to draw a perpendicular line to create right triangles. For Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.

Hence, for Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.

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The solutions of the given quadratic equation are 4 and -3/2. Solved using the factoring method to solve a quadratic equation.

what is a quadratic equation?

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation's general form is ax^2 + b*x + c = 0.

where a, b, and c are constant terms and x is the unknown variable.

Here I am using the factoring method to solve a quadratic equation.

Given quadratic equation is

[tex]2x^2 - 5x -12 = 0.[/tex]

By comparing the General form of the quadratic equation we will get

a = 2, b = -5 and c = -12.

2x^2 - (8-3)x - 12 = 0.

2x^2 - 8x + 3x -12 = 0.

2x(x-4) + 3(x-4) = 0

(x - 4) (2x + 3) = 0.

x - 4 = 0 or 2x + 3  = 0

x = 4 or x = -3/2

Given Question is incomplete complete question here:

What are the solutions of the quadratic equation 2x^2-5x-12 =  0?

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Answer: I believe is the first one

Step-by-step explanation:  It says animal in hundreds right. so looking at it 200 animals is right. But also x = 2 and y = 12

Hope this helps I'm sorry if it does not help

By the Number line, the true statements are,

⇒ 1 < 3

⇒ - 3 < 1

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

We have to given that;

In Number line, Plot the numbers - 3, 1 and 3.

Now, After plotting the numbers in Number line, we get;

⇒ - 3 < 1 < 3

Thus, The correct statements are,

⇒ 1 < 3 and - 3 < 1

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The inverse of 12  as calculated by the given data is found to be 1/12.

The inverse can be found by finding its reciprocal the number ,

inverse of 1 = 1 / 12

There are two types of inverse , additive inverse and multiplicative inverse .

The additive inverse can be found by finding the negative of  the number.  The multiplicative inverse, often known as the reciprocal, is another inverse of a number.

The multiplicative inverse, often known as the reciprocal, is another inverse of a number. The product of a reciprocal multiplied by the original number is always 1.

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The branch of statistics used to make the given statement is Option(D) Descriptive Statistics.

Which are the different branches of statistics?

The area of mathematics that deals with data is statistics. Data collection, descriptive statistics, and inferential statistics are the three main subfields of statistics.

For the given question, we are presented with data quantitatively. The data shows out of 500 students, 31% missed class due to alcohol consumption.

Therefore the branch of statistics that was used to make the above statement is descriptive statistics.

Hence Option(d) is correct.

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Answer:

Isosceles triangle

Step-by-step explanation:

Thorough explanation: Through the angles in the triangle ABC.

First, observe that angle ACD = 50 degrees (given)

Since lines AB and DE are parallel to each other,

angle BAC = angle ACD = 50 degrees (by the property of alternate angles)

It is also given that angle ABC = 80 degrees.

Since ABC is a triangle, the sum of the three angles must add up to 180 degrees.

Angle BAC + Angle ABC + Angle ACB = 180 degrees

50 + 80 + Angle ACB = 180

Angle ACB = 180 - 50 - 80

                   = 50 degrees

Since two of the angles, angles ACB and BAC are the same at 50 degrees, triangle ABC is an isosceles triangle. (With sides AB and BC equal)

Vertices are at (-7, 5) and (-1, 5) and foci are at (-9, 5) and (1, 5) of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16.

As per the given data the given equation is:

[tex]\\$$\frac{ (x+4)^2}{9} - \frac{(y-5)^2 }{16}=1$$[/tex]

The standard form for the equation of a hyperbola with center (h, k) is [tex]\frac{(x-h)^{2} }{a^{2} } - \frac{(y-k)^2}{b^{2} } =1[/tex]

Your hyperbola opens left/right, because it is of form x - y.

Comparing terms, we find that

h = -4, k = 5, a = 3, y = 4

In the general equation, the coordinates of the vertices are at [tex]$(h \pm a, k)$[/tex].

Thus, the vertices of your hyperbola are at (-7,5) and (-1,5).

The foci are at a distance c from the center, with coordinates [tex]$(\mathrm{h} \pm \mathrm{c}, \mathrm{k})$[/tex], where [tex]$c^2=a^2+b^2$[/tex]

[tex]c^2=9+16=25$[/tex], so c = 5.

The coordinates of the foci are (-9, 5) and (-1, 5).

The Figure below shows the graph of the hyperbola with its vertices and foci.(attached at the end of solution)

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On solving the provided question we can say that  so the value of the data from histogram graphs will be x [tex]\alpha[/tex] 0.123 * 125 / 100  = 0.15375

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

the best way to describe the data that was used to create this histogram (keep in mind that there is no scale on the horizontal axis, so you must choose based simply on the appearance of the histogram graphs

so the value of the data from histogram graphs will be

z = 0.123

u = 100

x = 125

x [tex]\alpha[/tex] 0.123 * 125 / 100  = 0.15375

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Answer: 54 inches squared

Step-by-step explanation:

Since it is a scale drawing, when we scale one variable up or down, we have to scale the other value the same amount because they are proportional. For example, if we divide one value by 3, we have to divide the other value by 3 also.

In this case, the real length is 30 feet, and the scale drawing length is 15 in. We divided by 2, so we have to divide the width by the same amount. 24/2 = 12 inches, so the width would be 12 inches or 1 foot.

8/10 liters of water she spilled. This can be solved using the concept of fraction.

A fraction is a piece of the entire. The number is stated in arithmetic as a quotient, which signifies the numerator divided by the denominator. Both are integers in a straightforward fraction. The numerator or denominator of a complex fraction is a fraction. A suitable fraction has a numerator that is smaller than its denominator.

Three main fractional kinds exist. They come in three varieties: appropriate fractions, incorrect fractions, and mixed fractions. The numerator and denominator words are known as fractions. We define its kinds in light of these two words.

Given that,

There were 57/10 liters of water in a bucket than she spilled some so she added another 15/10, now she get:

(57/10) + (15/10) = 72/10

After that, there was 64/10 liters of water in the bucket, now she spilled:

(72/10) - (64/10) = 8/10

So, 8/10 liters of water she spilled.

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