2
Consider the two triangles.
B
A
H.
15
C
20
12
9
G
TIME
01
To prove that the triangles are similar by the SAS
similarity theorem, it needs to be shown that
O <= o LLC
O AC= HI
BC
O
||
BC
HI

The area of the square garden is 3481 square units, and the perimeter is 236 units.

A square garden has a width of (50 + 9). Since all sides of a square are equal, the length of each side of the garden is (50 + 9), which simplifies to 59.

To find the area of the square garden, multiply the length by the width. Since both dimensions are equal, the area can be expressed as (59)(59) or\(59^{2}\). The area of the garden is 3481 square units.

To find the perimeter of the square garden, add the lengths of all four sides. Since each side measures 59 units, the expression for the perimeter is 4(59). The perimeter of the garden is 236 units.

In summary, the area of the square garden is 3481 square units, and the perimeter is 236 units.

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Answer:

y-intercept is (0,0). Mark brainliest?

Answer:

Step-by-step explanation:

2x(\(x^{2}\) + 3)

when x = 0 then we have a y intercept

2\(x^{3}\) +6x

so b/c both terms have an x  in them

we know the only time this function hits the y intercept is when y is zero

got it?

answer y = 0

Answer:

Step-by-step explanation:

According to the remainder theorem, the remainder when f(x) is divided by (x - n) is f(n).

As per question we are given:

Substitute and solve for c:

Note: I got a different value of c. This may be a result of a typo in the given expression. I provided a guide to solve such problems. Let me know is anything is unclear.

Answer:

0%

Step-by-step explanation:

There are no brown balls, so therefore it is impossible to get one.

I recommend using desmos graphing calculator.

Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

The x-intercept of the linear equation is (7, 0).

Here we have the following linear equation:

y = x - 7

We want to find the x-intercept, this is the point where the line intercepts the x-axis, it will happen when we take the value of y = 0, then we need to solve.

0 = x - 7

Solving that, we get:

7 = x

Then we conclude that the x-intercept of the linear equation is (7, 0).

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The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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Answer:

imma say $5300

Step-by-step explanation: if right plz mark as brainliest

sorry if wrong

Step-by-step explanation:

complete the number line

The smallest value of 'n' that can be obtained by adding three consecutive numbers is 48.

By using Monte-Carlo simulations,

A large class of computational techniques known as "Monte Carlo procedures" or "Monte Carlo experiments" rely on repeated random sampling to get numerical results. The core idea is to leverage randomness to find solutions to issues that, in theory, may be deterministic.

16    22    10     7    28    13     1    19    25     4

7    10    25    13     4    28    16     1    19    22

16    10    22     7    13    28     1    19    25    4

(remember that the numbers are arranged in a circle, rather than the straight line shown here)

The underline number represent the smallest value for n that can be obtained by the summation of three consecutive numbers.

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Step-by-step explanation:

The formula for a parallelogram is A=Base x Height

So you multiply the base, which is 6, and the height, which is 4.

A=6x4

Hope it helps!

Legend

The term that refers to the labels at the right of the graph indicating how each subcategory is represented is the Legend.

The Legend is a key that indicates what the different colors, lines, or other symbols in a graph represent. It is usually located at the right or bottom of the graph and provides a clear explanation of the different subcategories.

The Legend is an essential component of a graph, as it helps the viewer understand the information presented in the graph. Without the Legend, the graph can be confusing and difficult to interpret. It is important to ensure that the Legend is clear and easy to understand so that the viewer can quickly identify the different subcategories represented in the graph.

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The slope-intercept form of the equation of the line is y = x + 6.

A linear equation with a degree of one is referred to as an equation of the line. Two variables, x, and y, are present in the equation of the line. The third parameter is the line's slope, which indicates the line's elevation.

The equation of the line's general form is:

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The formula for calculating the line's slope is

Slope = ( 6 - 4) / ( 2 - 0)

Slope = 1

The y-intercept will be calculated as:-

y = mx + c

y = x +c

6 = c

The equation of the line can be written as:-

y = x + 6

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Answer:

a = 10

b = 6

Step-by-step explanation:

(7^2 * 7^8) / 7^4 = 7^a / 7^4

7^2 * 7^8 = 7^10

7^10 / 7^4 = 7^a / 7^4

7^10 = 7^a

a = 10

7^a / 7^4 = 7^b

7^10 / 7^4 = 7^10-4

7^6 = 7^b

b = 6

The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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When using the `foreach` function, the signs of the first and second derivatives of the function appear to be negative over the given interval. What is the `foreach` function?The `foreach` function in PHP is utilized for iterating over arrays or objects. The `foreach` function works by stepping through each value of an array, and one iteration can be done for each of the array's elements, which can include key-value pairs. It is mainly utilized to execute a block of code for each element of an array.What is a derivative?A derivative is a calculus concept that refers to the slope of a function at a certain point. It is usually the rate at which a function's value changes as its input variable changes. Derivatives are widely utilized in many fields, including physics, engineering, and economics.How to determine the signs of the first and second derivative?We can determine the signs of the first and second derivative by finding the derivative of the given function f(x). Once we find the derivative of the function, we can put the values in a table like the following:X    1   1.1   1.2   1.3   1.4   1.5f(x) 7.1 6.1 5.0 3.8 2.5 1.1 We can calculate the first derivative of f(x) by the following formula:f'(x) = f(x + 1) - f(x)We can calculate the second derivative of f(x) by the following formula:f"(x) = f'(x + 1) - f'(x)Based on the table above, we can determine that the signs of the first and second derivatives of the function are negative over the given interval.

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The signs of the first derivative of the function F(x) over the given interval are not consistent, so it is difficult to determine whether it appears to be positive or negative.

The first derivative of a function represents the rate of change of the function at a given point, while the second derivative represents the curvature or concavity of the function at that point.

To determine the signs of the first derivative of F(x) over the given interval, we need to find the slope of the tangent line at each point. We can do this by calculating the difference between consecutive y-values and dividing by the corresponding difference in x-values.

For example, the slope between (1, 7.1) and (1.1, 6.1) is (6.1 - 7.1)/(1.1 - 1) = -1, which indicates a negative slope. However, the slope between (1.2, 5.0) and (1.3, 3.8) is (3.8 - 5.0)/(1.3 - 1.2) = -12, which indicates a much steeper negative slope.

We can repeat this process for each pair of consecutive points to find the sign of the first derivative at each point. However, since the signs of the slopes are not consistent over the given interval, we cannot determine whether the first derivative appears to be positive or negative.

In other words, the function may be increasing or decreasing at different rates over different portions of the interval, which makes it difficult to make a general statement about the sign of the first derivative.

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It  takes 18.31s for the two window washers to reach the same height.

The equation of motion can be used which is

y= o.5gt^2 -vt =yo

g serves as the acceleration of gravity

vo serves as the  initial speed

yo serves as the  initial height

If we input the values , we have t= 18.31 secs.

Therefore  it takes 18.31s for the two window washers to reach the same height.

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Answer:

5 students

Step-by-step explanation:

85 has the stem of 8.

The only leaf in stem 8 that has a number higher than the leaf 5 is 8.

The stem 9 is higher than the stem 8 so all of it's leaves are higher than 85.

There are 4 leaves under the stem 9 and there is one leaf in stem 8 that's higher than 5.

So there are 5 students that have a score higher than 85.

Answer:

Commutative Property  

Associative property

Additive inverse  

Identity property

Step-by-step explanation:

In a  commutative property multiplication and addition which posses commutative property takes place without considering the order of arrangement of data

12.2 + 18.6 + –4.3 + (–18.6)

12.2 + –4.3 + 18.6 + (–18.6)

The second step results into the presence of a commutative property.

The next step 12.2 + –4.3 + [18.6 + (–18.6)] is an associative property because here, re-grouping of numbers which gives the same result takes place

[18.6 + (–18.6)] is an additive inverse since the result is zero. Additive inverse occurs when the addition of a number to another number results into zero

12.2 + –4.3 + (0)   is an Identity property

Identity property occurs when the addition of any number with zero eventually resulted into that number.

Answer:

Commutative Property  

Associative property

Additive inverse  

Identity property

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

Given

\(f(x) = \frac{x^2 - x -6}{x^2 - 9}\)

Required

Why is the function not continuous at x = 3

First substitute 3 for x at the denominator

\(f(x) = \frac{x^2 - x -6}{x^2 - 9}\)

Factorize the numerator and the denominator

\(f(x) = \frac{x^2 - 3x+2x -6}{x^2 - 3^2}\)

\(f(x) = \frac{x(x - 3)+2(x -3)}{(x - 3)(x+3)}\)

\(f(x) = \frac{(x+2)(x - 3)}{(x - 3)(x+3)}\)

Divide the numerator and denominator by (x - 3)

\(f(x) = \frac{x+2}{x+3}\)

Substitute 3 for x

\(f(3) = \frac{3+2}{3+3}\)

\(f(3) = \frac{5}{6}\)

Because \(f(x) = \frac{x^2 - x -6}{x^2 - 9}\) is defined when x = 3;

Then the function is continuous

Answer:

A: f is not defined at x = -3

Step-by-step explanation: EDGE 2020

The method that can not be used to prove that lines i and k are parallel is the statement "shows that both lines are perpendicular to a third line".

and the measures of the other three angles are 60°, 60°, and 120°

Interior angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles

The method that can not be used to prove that lines i and k are parallel is the statement "shows that both lines are perpendicular to a third line".

Lines l and k intersect forming two pairs of vertical angles. If one of these angles measures 120°,

As per the given question,

Let angle ∠1 is 120°

here angles ∠1 and ∠2 are supplementary

So  ∠2 = 180° - 120° = 60°

However, if a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.

∠2 = ∠4 = 60°

∠1 = ∠3 = 120°

Therefore, the measures of the other three angles are 60°, 60°, and 120°.

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the box with the largest volume has dimensions approximately 3.48 in. x 3.48 in. x 5.76 in.

Let x be the side length of the square cut from each corner of the tin sheet. Then the dimensions of the base of the box will be (10-2x) by (10-2x), and the height of the box will be x. Thus, the volume of the box is given by:

V = (10-2x)^2 * x = 4x^3 - 40x^2 + 100x

To maximize V, we take the derivative of this expression and set it equal to zero:

dV/dx = 12x^2 - 80x + 100 = 0

Solving for x using the quadratic formula, we get:

xx = (80 ± sqrt(80^2 - 4*12*100))/24 ≈ 1.74, 5.76

The solution x = 1.74 is extraneous, since it would result in negative dimensions for the box. Thus, the optimal size of the square to be cut from each corner is x = 5.76 inches.

The dimensions of the box with the largest volume are:

Length = Width = 10 - 2x = 10 - 2(5.76) ≈ 3.48 inches

Height = x = 5.76 inches

Therefore, the box with the largest volume has dimensions approximately 3.48 in. x 3.48 in. x 5.76 in.

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The correlation values that represent the perfect linear relationship between x and y are = b) 1 and d) -1

Now first we need to understand what is meant by correlation,

The mutual relation or degree to which two or more quantities are mutually linear or related to each other, hence their degree or relation of correlation is qualified by correlation coefficient.

According to the question we need to find the correlation value that represents a perfect linear relationship between x and y

Since we know according to the definition of correlation, the perfect linear relationship between x and y could be represented if their magnitude is 1.

Both positive and negative values of magnitude 1 (i.e 1 and -1)  are defined as the linear relationship between x and y.

Therefore, The correlation values that represent the perfect linear relationship between x and y are both 1 and -1

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Answer:

#13. line QR is 26.

#14. a) x = 2 b) m = 6

Step-by-step explanation:

13. We can use the Pythagorean therom: a^2 + b^2 = c^2

We will substitue PQ for a and PR for b

10^2 + 24^2  = c^2

100 + 576 = c^2

100 + 576 = 676

Then, we find the square root of 676, which is 26.

14. a) 3(2x -1) = 9

we first use distributive property:

6x - 3 = 9

then we add 3 to both sides to counteract the -3:

6x = 12

we divide both sides by 6 to get x alone:

x = 2

b) 3m - 12 = 6

we add 12 to both sides to counteract the -12:

3m = 18

we divide both sides by 3:

m = 6

The given triangles are obtuse = 36 m, right angled = 225 m and right angled = 2500 m.

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

7.) This triangle is obtuse.

To see this, we can use the Pythagorean theorem:

4*4 + 5*5 = 16 + 25 = 41

6*6 = 36 m

Since 41 > 36, we know that the triangle is obtuse.

8.) This triangle is right.

To see this, we can again use the Pythagorean theorem:

11*11 + 12*12 = 121 + 144 = 265

15*15 = 225 m

Since 265 = 225 + 40, we know that the triangle is right.

9.) This triangle is also right.

We can use the same method as before:

30*30 + 40*40 = 900 + 1600 = 2500

50*50 = 2500 m

Since 2500 = 2500, we know that the triangle is right.

Therefore, The given triangles are obtuse , right angled and right angled.

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Answer:

Why do you need a step by step

Step-by-step explanation:

Answer:

Your answer is <, Hope it helps.

The standard deviation of the given quiz scores is approximately 16.537.

To compute the standard deviation of the quiz scores, we can follow these steps:

Calculate the mean (average) of the scores.

Calculate the squared difference between each score and the mean.

Calculate the average of the squared differences.

Take the square root of the average of the squared differences to get the standard deviation.

Let's calculate it:

Calculate the mean:

Sum of scores = 50 + 12 + 38 + 25 + 16 + 48 + 58 = 247

Mean = Sum of scores / Number of scores = 247 / 7

= 35.286 (rounded to three decimal places)

Calculate the squared difference between each score and the mean:

For each score, subtract the mean and square the result:

(50 - 35.286)^2 = 213.672996

(12 - 35.286)^2 = 540.421796

(38 - 35.286)^2 = 7.426796

(25 - 35.286)^2 = 106.796996

(16 - 35.286)^2 = 372.739996

(48 - 35.286)^2 = 161.828996

(58 - 35.286)^2 = 512.968996

Calculate the average of the squared differences:

Sum of squared differences = 213.672996 + 540.421796 + 7.426796 + 106.796996 + 372.739996 + 161.828996 + 512.968996 = 1915.855572

Average = Sum of squared differences / Number of scores

= 1915.855572 / 7

= 273.693653 (rounded to six decimal places)

Take the square root of the average of the squared differences:

Standard deviation = √(Average)

= √(273.693653)

≈ 16.537 (rounded to three decimal places)

Therefore, the standard deviation of the given quiz scores is approximately 16.537.

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