what's the answer for this

The product of the factors of [tex]65x^2 + 212x - 313[/tex] is equal to the original expression. Lauren may have recognized the expression as a difference of squares and factored it accordingly.

We can first simplify the expression [tex]65x^2 + 212x - 313[/tex] by factoring it:

[tex]65x^2 + 212x - 313 = (13x - 1)(5x + 313)[/tex]

(13x - 1)(5x + 313) = [tex]65x^2 + 212x - 313[/tex]

Therefore, the product of the factors is equal to the original expression.

To see this, we can rewrite the expression as:

[tex]65x^2 - 313 - 212x = (5x)^2 - (2\cdot 5x \cdot 7) + 7^2 - 7^2 - 212x[/tex]

= [tex](5x - 7)^2 - 7^2 - 212x[/tex]

= [tex](5x - 7)^2 - 212x - 49[/tex]

= [tex](5x - 7)^2 - 1^2\cdot 49 - 212x[/tex]

= (5x - 7 - 7)(5x - 7 + 7) - 49 = (5x - 14)(5x) - 49

= 5x(5x - 14) - 49

= 5x(5(x - 2) - 9)

= 5x(5x - 29)

Therefore, the factors of the expression are (5x - 7) and (5x - 29).

Lauren may have recognized the expression as a difference of squares by noticing that the coefficient of the x term (212) is twice the product of the square roots of the first and last terms (sqrt(65) and sqrt(313)), which is a common characteristic of a difference of squares.

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Answer:

a. Similar

Step-by-step explanation:

The question says the triangles are right triangles, so they can't be obtuse or equilateral.

Since they are both right triangles, they both have a 90° angle. And as stated in the question, they both have a 30° angle. By Angle-Angle (AA) they are similar. But we don't know anything about any sides in either triangle, so we don't know if they are congruent or not. Just we can only know they are similar.

Thus, the following is the rule for the given geometric sequence: [tex]a = 64 * (-2)^(n-1) (n-1)[/tex]. Thus, the solution is (C) a = 64(-2)n-1.

An structured of integers or objects that adhere to a particular pattern or rule is referred to as a sequence in mathematics. The name for each number or item in the sequence is. A series can be explicitly created or defined recursively, and it can be infinite or finite. A method or rule that directly expresses the n - th term of the series in terms of n defines an explicit sequence. For instance, the explicit sequence 2, 4, 6, 8, 10,... has the formula a = 2n, where n is the term's position inside the sequence. A starting value and recursive formula that determines the nth word of the series in terms of the preceding terms describe a recursive sequence.

given

The number sequence is as follows: 64, -128, 256, -512.

We must determine the common ratio between the following terms in order to get the rule for this sequence.

Any term can be divided by its previous term to obtain the common ratio (r). For instance, the result of subtracting the second term (-128) from the first term (64) is

r = (-128) / 64 = -2

The third term (256) divided by the second term (-128) results in:

r = 256 / (-128) = -2

And when the fourth term (-512) is divided by the third term (256), the result is

r = (-512) / 256 = -2

We can observe that for all pairings of following terms, the common ratio is -2.

Now we can apply the following formula to a geometric sequence's general term:

a = a1 * r^(n-1) (n-1)

where r is the common ratio and a1 is the first term.

In place of the values we hold:

[tex]a = 64 * (-2)^(n-1) (n-1)[/tex]

Thus, the following is the rule for the given geometric sequence: [tex]a = 64 * (-2)^(n-1) (n-1)[/tex]. Thus, the solution is (C) a = 64(-2)n-1.

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The volume of the oblique prism is 75 cm³, which is option D.

An oblique prism is a three-dimensional geometric shape that has two parallel and congruent bases that are connected by parallelogram-shaped lateral faces. Unlike a right prism, the lateral faces of an oblique prism are not perpendicular to the base faces.

The formula for the volume of an oblique prism is given by:

Volume = Base Area × Height

Since the base of the prism is a square, its area is given by:

Base Area = Side × Side = 5 × 5 = 25 square centimeters

Substituting this and the height given as 3 cm in the formula for the volume, we get:

Volume = Base Area × Height

= 25 × 3

= 75 cubic centimeters

Therefore, the volume of the oblique prism is 75 cm³, which is option D.

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To calculate the number of possible passwords, we need to find the total number of combinations of lowercase letters and digits for each character of the password.

Then raise that number to the power of 9 (since there are 9 characters in the password and replications are allowed). There are 26 lowercase letters and 10 digits (0 to 9), so the total number of options for each character is 26+10=36.

Therefore, the number of possible passwords is[tex]36^9[/tex], which is equal to 1.0333862 ×[tex]10^16[/tex] (rounded to two decimal places in scientific notation). In other words, there are over 10 quadrillion possible combinations of passwords, making it very difficult for someone to guess or hack into the system by trying different combinations.

This highlights the importance of choosing a strong and secure password that is difficult for others to guess or brute-force.

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a. A quartic function with zeroes -5/2, -1, 7/2, and 3 can be written as

f(x) = a(x + 5/2)(x + 1)(x - 7/2)(x - 3), b) Two examples of functions that belong to this family are: f1(x) = 2(x + 5/2)(x + 1)(x - 7/2)(x - 3)

f2(x) = -0.5(x + 5/2)(x + 1)(x - 7/2)(x - 3) and the equation for the member of the family that passes through the point (-2,25) is:

f(x) = (4/275)(x + 5/2)(x + 1)(x - 7/2)(x - 3)

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x.

a) A quartic function with zeroes -5/2, -1, 7/2, and 3 can be written as the product of linear factors with those zeroes:

f(x) = a(x + 5/2)(x + 1)(x - 7/2)(x - 3)

where "a" is a constant that determines the overall scaling of the function.

b) Two examples of functions that belong to this family are:

f1(x) = 2(x + 5/2)(x + 1)(x - 7/2)(x - 3)

f2(x) = -0.5(x + 5/2)(x + 1)(x - 7/2)(x - 3)

Note that these functions differ only in the value of the constant "a".

c) To find the value of "a" that makes the graph of the function pass through the point (-2,25), we can substitute x = -2 and y = 25 into the equation for f(x):

25 = a(-2 + 5/2)(-2 + 1)(-2 - 7/2)(-2 - 3)

Simplifying this expression:

25 = a(5/2)(-1)(-11/2)(-5)

25 = a(6875/4)

a = 100/6875 = 4/275

Therefore, the equation for the member of the family that passes through the point (-2,25) is:

f(x) = (4/275)(x + 5/2)(x + 1)(x - 7/2)(x - 3)

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Answer:

see the answer in the picture

Step-by-step explanation:

I don't know which equation you want. but I put both the standard and general form. but the equation should be the stander form. the radius is 13 in this case

We will see that this circle is centered at the point (-5, -49) and has a radius of 1.

For a circle of radius R centered at the point (a, b), the equation is:

(x - a)^2 + (y - b)^2 = R^2

In this case, we have:

given the equation of the circle is

x^2 + y^2 + 10x + 14y + 73 = 0

We can rewrite this as:

(x^2 + 10x) + (y^2 + 14y) + 73 = 0

(x^2 + 2*5*x + 25) + (y^2 + 2*7*y + 49) - 25 - 49 + 73 = 0

(x + 5)^2 + (y + 49)^2 -74 + 73 = 0

(x + 5)^2 + (y + 49)^2 = 1

So we have a circle centered at the point (-5, -49) with a radius equal to 1.

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complete question:

Determine the center and radius of the following circle equation

x^2 + y^2 + 10x + 14y + 73 = 0

The given points can only be represented by an exponential function.

A linear function has the following form = y = f(x) = a bx

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

a is a constant term or y-intercept. This is the value of the dependent variable when x = 0.

b is the coefficient of the independent variable. It is also called the slope and gives the rate of change of the dependent variable.

 We can determine the type of function that can represent the given points by looking at the pattern of y values ​​corresponding to the x values.

Linear Function: A linear function has a constant slope, which means that the difference between any two consecutive values ​​of y must be the same as the difference between  two consecutive values ​​of x. The difference between  two consecutive y values ​​is 9/8, which is not the same as the difference between  two consecutive x values ​​(which is 1). Therefore, the given points cannot be represented by a linear function.  Exponential function: an exponential function has a constant ratio between  two consecutive y-values, meaning that the ratio of any two consecutive y-values ​​must be the same as the ratio of any two consecutive x-values.

The ratio of  two consecutive y values ​​is 2, which is the same as the ratio of  two consecutive x values ​​(which is 1/2). Therefore, the given scores can be represented by an exponential function.  Quadratic function: A quadratic function has a quadratic term, which means that the y-values ​​should show an increasing or decreasing pattern of differences between successive x-values.  The differences between successive y values ​​are 9/8, 3/8, 1/2, and 9. There is no  pattern of increasing or decreasing differences between successive x values, so the given points cannot be represented by a square. function

Therefore, the given scores can only be represented by an exponential function.

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Answer:

(a.)  8m

(b.) 12 cm

Step-by-step explanation:

a:

given: area of square = 64m²

formula of area of a square A = s²

We will reverse the formula to find the sum of the sides:

S = √A

S =√64

S = 8

b:

Given: perimeter of a square is 48 cm

formula for a perimeter of a square: P = 4 · s

We will reverse the formula to find the sum of the sides:

S = P ÷ 4

S = 48 ÷ 4

S = 12

Answer:

Step-by-step explanation:

To find the diameter of the Andromeda galaxy in miles, we can use the given information:

Diameter of Andromeda galaxy = 2.2 X 10^5 light-years

1 light-year = 5.9 X 10^12 miles

So, we can use dimensional analysis to convert light-years to miles:

2.2 X 10^5 light-years * 5.9 X 10^12 miles/light-year = 1.298 X 10^18 miles

Therefore, the diameter of the Andromeda galaxy in miles is approximately 1.298 X 10^18 miles.

On the other hand, if the number of comic strips produced is similar to the other values in the dataset, it will have little effect on the overall skew.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

The skew of a dataset refers to the degree to which the distribution of values is asymmetrical. A dataset is said to be skewed if the majority of the values lie on one side of the mean.

In this case, the dataset has a right skew because there are more values on the right side of the distribution (higher values) than on the left side. We can see this by noting that the median (middle value) is 3, while the mean (average value) is slightly higher at 3.375.

If the writer writes 8 more comic strips on the next day, it will increase the maximum value in the dataset from 7 to 8. This will slightly shift the distribution to the right, but the skew will remain right because the majority of the values are still clustered on the right side of the distribution.

However, the effect on the overall skew will depend on the number of comic strips the writer produces on the next day relative to the other values in the dataset. If the writer produces a large number of comic strips relative to the other values, it could shift the distribution to a more symmetrical shape.

Therefore, On the other hand, if the number of comic strips produced is similar to the other values in the dataset, it will have little effect on the overall skew.

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Answer:

What I myself would do is plug in the given values, and we get: x = 41 * cos(220 degrees) ≈ -22.59 y = 41 * sin(220 degrees) ≈ -33.73

Therefore, the component form of the vector is (-22.59, -33.73).

Step-by-step explanation:

Step-by-step explanation:

A  =  S + 2

L = A + 10 =   S+2   + 10  = S + 12

S  = S

Summed , they equal 83

S+2     +  S+12   + S  = 83

3S = 69

S = 23  messages  

Answer:

Step-by-step explanation:

You have a little unclear question with "selects and apple out of the bowl?" I only chose apples (there are 3 of them)

[tex]\frac{3}{12} =\frac{1}{4}[/tex] answer

Step-by-step explanation:

Given,

n(S) = 12

n(A)=3

We have,

P(A) = n(A)/n(S)

= 3 /12

= 1 /4

Answer:

120° and 60°

Step-by-step explanation:

5x - 10 + 3x - 18 = 180

8x = 180 + 10 + 18

8x = 208 / : 8

x = 26

.

(5x - 10)° = (5 × 26 - 10)° = 120°

(3x - 18)° = (3 × 26 - 18)° = 60°

Answer:

Step-by-step explanation:

quit

The value of the number is 19

Algebraic expressions are defined as those expressions that are composed of terms, constants, variables, coefficients and factors.

These expressions are also made up of certain mathematical operation, such as;

From the information given, we have;

Let the number be x

Then,

3x + 7

4x - 12

Equate the expressions

3x + 7 = 4x - 12

collect the like terms

7 + 12 = 4x - 3x

add or subtract the values

x = 19

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After solving the linear equation Lillian is farther along in the book than Khadija after 4 days.

A linear equation is an algebraic equation of the form:

y = mx + b

where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope represents how steep the line is, and the y-intercept is the point at which the line intersects the y-axis.

As we know, Lillian was on 40 pages and Khadija was on 10 pages. So, the equation is,

And Let L represent the page of the book that Lillian is on at the end of t days into the month, and let K represent the page of the book that Khadija is on at the end of t days into the month.

[tex]L(t) = 40 + 15t[/tex]   Lillian's progress after t days

[tex]K(t) = 10 + 20t[/tex]  Khadija's progress after t days

After solving the linear equation, we will get the rate of the reading page.

Let's say t=4,

[tex]L(4) = 40 + 15(4) = 100[/tex]

[tex]K(4) = 10 + 20(4) = 90[/tex]

Therefore, after 4 days, Lillian is farther along in the book than Khadija.

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Answer:

72 degrees

Step-by-step explanation:

The length of the line that has the coordinate pairs of (-4 1/2,5) and (8 2/3, 5) is 12.16 units.

If two points of coordinates are given then we calculate the distance between them by using the following formulae

To find the length of the line is nothing but the calculation of the distance between two points that are given in the question.

[tex]d = \sqrt{(x_{2} - x_{2} )^{2} +(y_{2} - y_{1} )^{2} }[/tex]

d is the distance between two points.

(x1, x2) and (y2, y1) are the two endpoints of the line.

We can put all the values into the distance formulae and find the length of the line segment.

x1 = -4 1/2 = -3.5, y1 = 5

x2 = 26/3 = 8.6667, y2 = 5

[tex]d = \sqrt{(8.6667-(-3.5))^{2} +(5 - 5)^{2}\\[/tex]

= 12.16

Therefore, the length of the line segment is approximately 12.16 units.

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The probability of choosing water and Black & White Sundae is 1/6.

Probability is a measure of the likelihood or chance of an event occurring. It is represented as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

a. Image is attached below.

b. The probability of choosing water and Black & White Sundae is the product of the probabilities of choosing water and Black & White Sundae given that water was chosen. This can be calculated as:

P(Water and B&W Sundae) = P(Water) * P(B&W Sundae | Water)

= 1/2× 1/3

= 1/6

Therefore, the probability of choosing water and Black & White Sundae is 1/6.

c. To calculate the total number of different combinations, we need to multiply the number of drink options by the number of dessert options. Since there are 2 drink options (water and soda) and 3 dessert options (Black & White Sundae, milkshake, and banana split) with 3 different sizes for the milkshake and banana split, we can calculate the total number of different combinations as:

Total combinations = 2×(1 + 3 + 3×3)

= 2 × 13

= 26

Therefore, there are 26 total different combinations.

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The probability that at least three out of five randomly selected students will possess a GPA in excess of 3.0 is approximately 0.1772.

To solve this problem, we need to use the binomial distribution with n = 5 and the probability of success p = P(GPA > 3.0), which can be found using the normal distribution table:

P(GPA > 3.0) = P(Z > (3.0 - 2.7)/0.7) = P(Z > 0.43) = 1 - P(Z < 0.43) = 1 - 0.6664 = 0.3336

Now we can use the binomial distribution to find the probability that at least three students out of five have a GPA greater than 3.0:

P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5)

Using the binomial formula and the probabilities of success and failure:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

we get:

P(X = 3) = (5 choose 3) * 0.3336^3 * 0.6664^2 = 0.1311

P(X = 4) = (5 choose 4) * 0.3336^4 * 0.6664^1 = 0.0421

P(X = 5) = (5 choose 5) * 0.3336^5 * 0.6664^0 = 0.0040

Therefore:

P(X ≥ 3) = 0.1311 + 0.0421 + 0.0040 = 0.1772

So the probability that at least three out of five students have a GPA greater than 3.0 is approximately 0.1772.

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--The given question is incomplete, the complete question is given

"  The grade point averages (GPAs) of a large population of college students are approximately normally distributed with mean 2.7 and standard deviation 0.7. Suppose that five students are randomly selected from the student body. What is the probability that at least three will possess a GPA in excess of 3.0? "--

Answer:

B 1/4

Step-by-step explanation:

Because one coin have 1/2 to land either side, but if it was two coins then is will double it so it will be 1/4.

Answer:

22-ounce package is the best buy as it has the lowest price per ounce.

Step-by-step explanation:

To determine which package is the best buy, we need to calculate the price per ounce of each package:

Price per ounce of 6-ounce package = 1.98 / 6 = $0.33 per ounce

Price per ounce of 14-ounce package = 4.90 / 14 = $0.35 per ounce

Price per ounce of 22-ounce package = 7.04 / 22 = $0.32 per ounce

Therefore, the 22-ounce package is the best buy as it has the lowest price per ounce.

Step-by-step explanation:

he sold the house for 180000, which is 24% more than the amount he paid.

180000 = x + 0.24x

Simplifying this equation, we get:

1.24x = 180000

x = 180000 / 1.24

x ≈ 145161.29

Chengbo paid approximately 145161.29 yuan for the house.

Answer: True.

Step-by-step explanation: A person only pays interest on the balance remaining at the end of the billing cycle. If you carry a balance beyond the grace period, your credit card issuer will charge interest. Each month you carry a balance over from the previous month, you’ll have a finance charge added to your balance.

In order to be correct, a line graph of the number of marriages per year in the United States must have years on the

horizontal scale.

It is defined as the process of adding more instances of the same type to the existing pool of resources and not

increasing the capacity of existing resources like in vertical scaling. This kind of scaling also helps in decreasing the

load on the server. This is called Horizontal Scaling

This allows for a clear representation of the number of marriages over time. To create such a graph, follow these steps:

1. Label the horizontal axis with years, making sure to use equal intervals between each year.

2. Label the vertical axis with the number of marriages.

3. Plot the data points for each year, representing the number of marriages.

4. Connect the data points with a line to show the trend over time.

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Answer:

Let Length= x, Width= y

A.t.c.

3x-2=y ...(1)

Area = length × width

= xy = 40

from (1)

[tex]x(3x - 2) = 40 \\ 3 {x}^{2} - 2x = 40 \\ 3 {x}^{2} - 2x - 40 = 0 \\ 3 {x}^{2} - 12x + 10x - 40 = 0 \\ 3x(x - 4) + 10(x - 4) = 0 \\ (3x + 10)(x - 4) = 0 \\ x = - \frac{10}{3} \: or \: 4[/tex]

neglecting -10/3

length = 4

width = 3(4)-2=12-2

= 10

The following is true of primary data collection: primary data are collected specifically for the research problem at hand.Primary data collection refers to the process of collecting new data or original data that have not been collected before. Primary data are the first-hand data gathered by researchers from original sources.

The following is true of primary data: primary data are collected specifically for the research problem at hand. Primary data are collected to meet specific research objectives and to provide solutions to research problems.Primary data collection methods are affected by the biases of the respondent.

This is because the collection of primary data requires direct contact between the researcher and the respondents or participants. It is important to note that primary data collection methods are relatively more expensive than secondary data. Therefore, researchers should consider the cost implications of primary data collection methods before using them.

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