Which pair of statements about the lengths of two sides of the triangle is true?

The factors of [tex]2x^2 + 7x + 15[/tex]  are [tex](2x + 3)[/tex] and [tex](x + 5)[/tex].

To find the factors of  [tex]2x^2 + 7x + 15[/tex] , we can use the factoring method called "splitting the middle term." Here's how it works:

Write the expression as the product of two binomials: [tex](2x^2 + 7x + 15) = (2x^2 + ax + b)(cx + d)[/tex]

Find the factors of the constant term (15) that add up to the coefficient of the middle term (7). The factors of 15 are 1 and 15, 3 and 5, and 5 and 3. The only pair that adds up to 7 are 3 and 5.

Set the coefficients of the two binomials to 3 and 5, respectively. The expression becomes: [tex](2x^2 + 3x + 5)(5x + 3)[/tex]

Rewrite the binomials using the distributive property: [tex](2x^2 + 3x + 5)(5x + 3) = (2x^2 + 5x + 3x + 15) = 2x(x + 5) + 3(x + 5) = (2x + 3)(x + 5)[/tex]

So, the factors of  [tex]2x^2 + 7x + 15[/tex] are [tex](2x + 3)[/tex] and[tex](x + 5)[/tex].

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Answer:

B • r = s - 2

Step-by-step explanation:

Rachel will always be two year younger than Sean. if we substitute the letters with their ages...

[rachel's age] 2 = [ sean's age] 4 - 2

2 = 4 - 2

it can't be A

2 = 4 (two does not equals four)

it can't be C

2 = 4 + 2 (the correct answer is 6, Rachel is not 6 years old)

it can't be D

4 = 2 - 2 (the correct answer is 0. Rachel's not 0 years old as well.

[ also s is the subject in this case. but we are looking for r ]

Answer: B

Step-by-step explanation:

62017.2 is the answer

Answer: 3/6 or 1/2

Step-by-step explanation:

In a 6-sided die, there are 3 odd numbers 1,3 and 5. So. P(odd) is 3/6 or 1/2.

Answer:

Step-by-step explanation:

The y-intercept of g(x) is 3 * 2 = 6.

To find the x-intercepts of g(x), we need to find the values of x that make g(x) equal to 0. Since g(x) = 2f(2x + 3), this means we need to find the values of x that make f(2x + 3) equal to 0. Therefore, we can find the x-intercepts of g(x) by solving the equation f(2x + 3) = 0 for x.

Since the x-intercepts of f(x) are at 2 and -4, this means that the equation f(x) = 0 has solutions at x = 2 and x = -4. Substituting these values into the equation f(2x + 3) = 0, we get:

f(2(2) + 3) = 0

f(4 + 3) = 0

f(7) = 0

and

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

f(-8 + 3) = 0

f(-5) = 0

Therefore, the x-intercepts of g(x) are at x = 7/2 and x = -5/2. These are the only intercepts of g(x) that we can determine for certain.

The absolute value of a number is the non-negative distance between the number and zero on a number line, regardless of sign.

This means that the absolute value of a negative number is always positive. Therefore, if a and b both are negative numbers, their absolute values will be positive numbers. If a is greater than b, then the absolute value of a must be greater than the absolute value of b. This can be expressed mathematically as follows:

|a| > |b|

This equation states that the absolute value of a is greater than the absolute value of b. In other words, the distance between a and zero is greater than the distance between b and zero on a number line.

To illustrate this, let’s take an example of two negative numbers, a=-3 and b=-5. The absolute values of these two numbers are 3 and 5 respectively. Since 3 is greater than 5, the absolute value of a is greater than the absolute value of b. This holds true regardless of the sign of the numbers, as long as a is greater than b.

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A unique array value is a value that appears only once among all the other values in the given array. Hence the name unique.

An array is a set of items, images, or numbers arranged in rows and columns. Arrays are practical illustrations of multiplication ideas.

Arrays are needed in cases where you need  to store and manipulate large amounts of data efficiently.

Some of the benefits of using arrays include:

1. Arrays allow you to store a large number of items in a single data structure, which makes it easier to work with large datasets.

2. Arrays allow you to access and modify the items in the array quickly, using the index of the item.

A data structure called an array is used to hold a number of elements together. Each item in an array is recognized by its index, or place within the array. A value that only appears once in an array is considered to be unique array value. Think about the following array, for instance:

[1, 2, 3, 4, 5, 6]

Because each value only occurs once in this array, each value is distinct.

Contrarily, think about the following array:

[1, 2, 3, 3, 4, 5]

Since it appears twice in this array, the number 3 is not unique. Since they only exist once, each of the other values is distinct.

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Answer:

3. D

Step-by-step explanation:

1/10+1/8+1/15=1/x

24/240+30/240+16/240=1/x

70/240=1/x

7/24=1/x

1/3.4=1/x

x=3.4

To find the mean deviation of a set of numbers, you need to first find the average (mean) of the set, and then for each number in the set, subtract the mean and take the absolute value of the result. The mean deviation is then the average of these absolute values.

For the first 10 even natural numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20), the mean is (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20) / 10 = 60/10 = 6.

To find the mean deviation, you would subtract the mean from each number, take the absolute value of the result, and then average those values. The mean deviation of the first 10 even natural numbers is therefore (|6 - 2| + |6 - 4| + |6 - 6| + |6 - 8| + |6 - 10| + |6 - 12| + |6 - 14| + |6 - 16| + |6 - 18| + |6 - 20|) / 10 = (4 + 2 + 0 + 2 + 4 + 6 + 8 + 10 + 12 + 14) / 10 = 5.5.

So the answer is B: 5.5.

Numbers in Nature When counting or organizing objects, the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are utilized. Absolute numbers are integers and zeros. neither a fraction nor a decimal.

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Answer: 27

Step-by-step explanation:

two base ten blocks then 7

Solving the inequality  [tex]\frac{2x + 4}{2}[/tex] < 6, we get x < 4.

Linear Inequalities are mathematical expressions which consist of a left hand side and a right hand side connected with inequality signs like <, >, ≤, ≥ and ≠.

They are almost like linear equations when we see it, but the '=' sign in linear equations are substituted with inequality signs like those mentioned earlier.

The expression given here is,

[tex]\frac{2x + 4}{2}[/tex] < 6

Multiplying both sides with 2, we get,

2x + 4 < 6 × 2

2x + 4 < 12

Subtracting both sides with 4, we get,

2x + 4 - 4 < 12 - 4

2x < 8

Dividing both sides by 2,

2x / 2 < 8 / 2

x < 4

Hence the inequality [tex]\frac{2x + 4}{2}[/tex] < 6 results in x < 4.

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it will cost #150 to have a party with 9 people, and it will cost #260 to have a party with 20 people

Graph is attached:

What is Piecewise function?

A piecewise function is used to relate multiple functions at different intervals

The cost for 9 people

This means that:

n=9

When n = 9, the cost function is:

C(9)=150

Hence, it will cost #150 to have a party with 9 people

The cost for 20 people

This means that:

n=20

When n = 20, the cost function is:

C(20)=260

Hence, it will cost #260 to have a party with 20 people

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Answer:

bro what u doin this on a quiz u aint goin do this on time

Step-by-step explanation:

The basic approach to solve this problem is to first sort array and then traverse through all the the elements and check for missing value and repeating value.

Approach:

c++ implementation

#include <bits/stdc++.h>

using namespace std;

void printTwoElements(int arr[], int size)

{

   int i;

   cout << "The repeating element is ";

   for (i = 0; i < size; i++) {

       if (arr[abs(arr[i]) - 1] > 0)

           arr[abs(arr[i]) - 1] = -arr[abs(arr[i]) - 1];

       else

           cout << abs(arr[i]) << "\n";

   }

   cout << "and the missing element is ";

   for (i = 0; i < size; i++) {

       if (arr[i] > 0)

           cout << (i + 1);

   }

}

int main()

{

   int arr[] = { 8, 3, 4, 5, 5, 6, 1 };

   int n = sizeof(arr) / sizeof(arr[0]);

   printTwoElements(arr, n);

}

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Answer: an=2(-2)ⁿ⁻¹    a₉=512     a₆=-64

Step-by-step explanation:

Since we have an alternating minus sign in this sequence, therefore the first multiplier of the following sequence will be (-1)ⁿ.

And since the first term of the following sequence is positive, the first multiplier of the following sequence is (-1)ⁿ⁻¹.

The second multiplier of the following sequence is 2ⁿ because the sequence has the form: 2, 4, 8, 16, ..., 2ⁿ .

[tex]Thus,\ a_n=(-1)^{n-1}(2^n)\\\\ a_n=2(-2)^{n-1}\ \ \ (1)[/tex]

Find the 9th and 6th terms of the sequence by formula (1):

a₉=2(-2)⁹⁻¹

а₉=2(-2)⁸

a₉=2(256)

a₉=512

a₆=2(-2)⁶⁻¹

а₆=2(-2)⁵

a₆=2(-32)

a₆=-64

No, paths of planes will be not be perpendicular as their slopes comes out to be equal.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

As a result,

m = change in y/change in x  = Δy/Δx

is the formula for the change in y-coordinate with respect to the change in x-coordinate. where "m" represents a line's slope.

Slope of path of plane 1 = [tex]m_{1}[/tex]

 [tex]\frac{3-4}{4-(-2)}\\ =\frac{-1}{6} \\[/tex]

Slope of path of plane 2= [tex]m_{2}[/tex]

[tex]=\frac{0-1}{3-(-3)}\\ =\frac{-1}{6}[/tex]

As slope of paths of planes are equal so we can say they are moving parallel to each other in same direction.

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Answer:

the answer is three

Answer: Square Root Function

The inverse of a quadratic function is a square root function because

The weight of container will be 20 kg

Let x be the number of car toys packed into container. Toy cars weigh 3 kilogram apiece and are shipped in a container that weighs 5 kilograms when empty, then the total weight of container with toy cars is

x.3 + 5 = 3x + 5

The number of toy trucks is also x. Toy trucks, which weigh 2 kilograms apiece, are shipped in a container weighing 10 kilograms, then the total weight of container with toy trucks is

x.2 + 10 = 2x +10

When packed with toys and ready for shipment, both kinds of containers have the same weight. Thus,

3x + 5 = 2x + 10

x = 15

The weight of container = x + 5

= 15 + 5

= 20 kg

Hence, the weight of container will be 20 kg

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The mean absolute deviation of a set of data is the mean distance (or the average distance) between each data element and the mean of the data elements.

The steps for Finding the Mean Absolute Deviation of a Data Set are as follows:

Step 1: Find the mean of the data set.

Step 2: Find the sum of the data values, and divide the sum by the number of data values.

Step 3: Find the absolute value of the difference between each data value and the mean: |data value – mean|.

Step 4: Find the sum of the absolute values of the differences.

Step 5: Divide the sum of the absolute values of the differences by the number of data values.

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The inverse of the equation "y = 3x + 9" is "y = x/3 - 3"  .

The Inverse Function is defined as a function in which domain of the original function becomes the range of inverse function and range of given function becomes the domain of inverse function.

the equation is given to be : y = 3x + 9 ;

to find the inverse we need to express the above equation in term of y .

subtracting 9 from both sides ,

we get ;

y - 9 = 3x + 9 - 9 ;

y - 9 = 3x ;

3x = y - 9 ;

x = y/3 - 9/3 ;

x = y/3 - 3 ;

switching x and y ,

we get ;

y = x/3 - 3 ;

Therefore , the inverse is y = x/3 - 3  .

The given question is incomplete , the complete question is

What is the inverse of the equation y = 3x + 9 ?

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The sum of the interior angle of a regular nonagon will be 1,260°.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The interior angle of the polygon is given as,

Interior angle = 180° - 360° / n

And the sum of the interior angle is given as,

Sum of the interior angle = n x (Interior angle)

The number of sides of the regular nonagon is 9. Then the interior angle is given as,

Interior angle = 180° - 360° / 9

Interior angle = 180° - 40°

Interior angle = 140°

Then the sum of the interior angle of a regular nonagon will be given as,

Sum of the interior angle = 9 x 140°

Sum of the interior angle = 1,260°

The sum of the interior angle of a regular nonagon will be 1,260°.

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The required area that the label would cover is given as 3771.4 cm².

As mentioned in the question,
the wheel has a radius of 30 centimeters and a height of 20 centimeters,

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

here,
Area of the label, = 2πrh
Substitute the value in the above formula,
Area of the label = 2 × 22 / 7 × 30 × 20
Area of the label = 3771.4 cm²

Thus, the required area that the label would cover is given as 3771.4 cm².

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Answer: Then aswer the question wit your broke answer

Step-by-step explanation:

The two-column proof is given below:

Mathematics' earliest branch is geometry, along with arithmetic. The distance, size, shape, and relative position of objects in relation to one another are all aspects of space that are addressed. The term "geometer" refers to a mathematician who specializes in geometry.

Before the 19th century, Euclidean geometry which incorporates the concepts of point, line, plane, distance, angle, surface, and curve as fundamental concepts—was nearly entirely the focus of geometry.

Geometry's use was greatly expanded during the 19th century by a number of discoveries. One of the first of these discoveries is Gauss Theorema Egregium, which roughly states that the Gaussian curvature of a surface is independent of any particular embedding in a Euclidean space.

Statements                                                         Reasons

4.7(2f-0.5)=-6(1.6f-8.3f)                                      Given

4.7(2f-0.5)=-6(-6.7f)                                           Combine like terms

9.4f-2.35= -40.2f                                               Get all the terms to the one  

                                                                           side of an equation

49.6f=23.5                                                           Addition property

f=47/992                                                              Division property                  

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a) 55 people expect to be between 165 and 175 cm.

b) 76 people to be taller than 166 cm.

What is Standard normal distribution?

The standard normal distribution is a special type of normal distribution where the mean is 0, and the standard deviation is 1.

a) To answer this question, we can use the standard normal distribution table to find the proportion of heights that fall within certain ranges of the mean.

The standard normal distribution table gives us the proportion of values within a certain number of standard deviations of the mean.

Since the standard deviation of the heights is 5, we can find the proportion of heights between 165 and 175 cm by looking at the range of values that are one standard deviation below and one standard deviation above the mean.

The mean of the heights is 170, so one standard deviation below the mean is 170 - 5 = 165. One standard deviation above the mean is 170 + 5 = 175. Therefore, the range of heights that are one standard deviation below and one standard deviation above the mean is 165 to 175.

If we look at the standard normal distribution table, we find that approximately 68% of the values fall within one standard deviation of the mean. Since 80 is approximately 68% of 118, we would expect approximately 55 people to have heights between 165 and 175 cm.

Hence, 55 people expect to be between 165 and 175 cm.

b) For the second part of the question, we can find the proportion of heights that are taller than 166 cm by looking at the range of values that are more than one standard deviation above the mean.

The mean of the heights is 170, so more than one standard deviation above the mean is anything greater than 175. If we look at the standard normal distribution table, we find that approximately 95% of the values fall within two standard deviations of the mean.

Since 80 is approximately 95% of 84, we would expect approximately 76 people to be taller than 166 cm.

Hence, 76 people to be taller than 166 cm.

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The slope of a line perpendicular to 3x is [tex]-\frac{1}{3}[/tex] .

What is slope ?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

What is perpendicular ?

The word perpendicular means at right angles and this is because when two lines meet, they form right angles. Perpendicular lines can face in any direction such as up and down, crossways, and side-to-side.

Have given,

Slope of the line  y=3x ,

you can compare it to  y=mx+c  form where  m  is the slope of the line.

y = 3x

differentiate respect of x

[tex]\frac{dy}{dx} = 3[/tex]

Now, the slope of the line perpendicular to the line that has a slope of m is [tex]-\frac{1}{m}[/tex]

The slope of a line perpendicular to 3x is [tex]-\frac{1}{3}[/tex] .

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The slope-intercept form of a straight line of equation 5x + 2y = 10 is y = (-5/2)x + 5.

The slope-intercept form of a line is:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

To put the equation 5x + 2y = 10 in slope-intercept form, we need to solve for y. We can do this by rearranging the terms and isolating y:

2y = -5x + 10

y = (-5/2)x + (10/2)

Thus, the slope-intercept form of the equation 5x + 2y = 10 is:

y = (-5/2)x + 5

This means that the slope of the line is (-5/2) and the y-intercept is (0,5).

--The question is incomplete, answering to the question below--

"What is the slope-intercept form of 5x + 2y = 10?"

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Inspect the graph to see if any vertical line drawn would intersect the curve more than once.

What is graph?

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

f(x)=log(2x)

g(x)=log1/10(x-3)  the base of log is 1/10

Domain is x>3

Range is all real numbers

g(x) is decrease on the interval x>3

asymtote is x=3

x intercept is x=4

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Answer:

30% gain

Step-by-step explanation:

$30 for 10 = $3 each

$46.80 for 12 = $3.9 each

percentage change = (final price- initial price)/inital price  *100

3.9-3 = 0.9

0.9/3 = 0.3

0.3 x 100 = 30

so gain of 30%

The end behavior of the graph of f(x) = x^5 + 8x^4 + 16x^3 is asymptotic: it goes towards positive infinity as x approaches positive infinity, and negative infinity as x approaches negative infinity.

The end behavior of the graph of a polynomial function with degree 5 is determined by the leading term, which in this case is x^5. Since the degree of the leading term is odd and the coefficient is positive, the graph of f(x) = x^5 + 8x^4 + 16x^3 will approach positive infinity as x approaches positive infinity, and negative infinity as x approaches negative infinity. This is known as an asymptotic end behavior. As the x-values get larger and larger, the magnitude of the y-values will also get larger and larger, approaching infinity in either direction. This can be seen by looking at the graph of the function, which will have an "S" shape that curves up and to the right (positive infinity) for large positive x-values, and down and to the left (negative infinity) for large negative x-values.

For x > 0, the end behavior is:

f(x) = x5 + 8x4 + 16x3

lim x→∞ f(x) = lim x→∞ x5 + 8x4 + 16x3

lim x→∞ f(x) = lim x→∞ x5

lim x→∞ f(x) = +∞

For x < 0, the end behavior is:

f(x) = x5 + 8x4 + 16x3

lim x→−∞ f(x) = lim x→−∞ x5 + 8x4 + 16x3

lim x→−∞ f(x) = lim x→−∞ x5

lim x→−∞ f(x) = −∞

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