Coach Sanchez is setting up a court for
a game of four-square. He has a
square space, with an area of 64
square feet. What is the longest side
length Coach Sanchez can make for
one side of the court?

The name of the segment inside the large triangle is called the: 3. angle bisector.

The word "bisect" means to divide into two equal halves. Therefore, an angle bisector can be defined as a line segment that divides the an angle in a triangle into two parts that are of the same angle measure.

The image shows a triangle which has a segment that divides a vertex angle into equal parts. Thus, the segment can be named as an angle bisector.

A perpendicular bisector divides a segment into two equal halves at right angle, while a midsegment joins the middle points of two sides of a triangle. The median also, is a segment that joins a vertex of a triangle to the midpoint of the side that is opposite the angle.

Therefore, we can state that the name of the segment is: 3. angle bisector.

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Answer:

angle B, angle A, angle C

Step-by-step explanation:

Given triangle ABC,

Where, length side of AB = 22

side BC = 16

side AC = 12

We can determine the order of the angles of the triangle without any calculation bearing in mind that each angle would correspond with the sides opposite each of them.

What this means is that, the larger the length of the side, the larger the angle opposite it, while the smaller the length of the side, the smaller the angle opposite it would be.

Now let's order our angles judging by the length of the sides opposite each of them.

Angle A is opposite side BC (16)

Angle B is opposite side AC (12)

Angle C is opposite side AB (22)

There, the largest angle would be the angle with the largest side opposite it = angle C, followed by angle A, and angle B, which is the smallest angle with the smallest side length opposite it.

Angle B < angle A < angle C

The answer is: angle B, angle A, angle C

Answer:

•angle B, angle A, angle C

Given:

\(\Delta ABC\sim \Delta QRS\)

To find:

The missing value of m.

Solution:

We have,

\(\Delta ABC\sim \Delta QRS\)

Corresponding parts of similar triangles are proportional.

\(\dfrac{AB}{QR}=\dfrac{AC}{QS}\)

Putting the given values, we get

\(\dfrac{m}{10}=\dfrac{2}{4}\)

\(\dfrac{m}{10}=\dfrac{1}{2}\)

Multiply both sides by 10.

\(\dfrac{m}{10}\times 10=\dfrac{1}{2}\times 10\)

\(m=5\)

Therefore, the value of m is 5.

Answer:

-22

Step-by-step explanation:

Plug in 5 for x.

y = -3(5) - 7

y = -15 - 7

y = -22

The number 42 could be qualitative if it is a designation instead of a measurement, count, or calculation.

Qualitative data describes qualities or characteristics. It is collected using questionnaires, interviews, or observation, and frequently appears in narrative form. For example, it could be notes taken during a focus group on the quality of the food at Cafe Mac, or responses from an open-ended questionnaire. Qualitative data may be difficult to precisely measure and analyze. The data may be in the form of descriptive words that can be examined for patterns or meaning, sometimes through the use of coding. Coding allows the researcher to categorize qualitative data to identify themes that correspond with the research questions and to perform quantitative analysis.

Quantitative data is numbers-based, countable, or measurable. Quantitative data is numeric, the result of a measurement, count, or some other mathematical calculation. Qualitative data is descriptive. The number 42 could be qualitative if it is a designation instead of a measurement, count, or calculation.

The seven characteristics that define relational database are:

Accuracy and Precision

Legitimacy and Validity

Reliability and Consistency

Timeliness and Relevance

Completeness and Comprehensiveness

Availability and Accessibility

Granularity and Uniqueness

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Answer:

take a time lapse video of yourself doing your homework on your phone! this way you won't be able to use your phone bc it will be doing the timelapse, and then after you finish you'll be able to go back and watch it :)

Step-by-step explanation:

Answer:

Make up a random doodle and name it bob.....YOU CAN DO THIS

Step-by-step explanation:

Answer:

1=8

2=16

5=40

6=48

10=80

12=96

Step-by-step explanation:

you have to multiply by 8 with the left numbers and you divide by 8 with the right numbers

Answer:

1/216

Step-by-step explanation:

6^-3=1/216

Answer:

god help you

Step-by-step explanation:

i think we should add all the ratio together.......

Answer:

h(2) = 0

Step-by-step explanation:

1) 2 * 2 = 4

2) 4 * 3 = 12

3) 5 * 2 = 10
4) 12 - 10 - 2 = 0

Answer:

Therefore, Alex buys 20 cans of corn.

Step-by-step explanation:

Let's assume Alex buys x cans of tomatoes and y cans of corn.

Given that he buys 36 cans in total, we can write the equation:

x + y = 36 ----(1)

The cost of tomatoes per can is 80 cents, and the cost of corn per can is 40 cents. The total cost is $20.8, which can be expressed as 2080 cents.

The cost of the tomatoes (80 cents per can) multiplied by the number of tomato cans (x) gives the cost of tomatoes, and the cost of corn (40 cents per can) multiplied by the number of corn cans (y) gives the cost of corn. The sum of these costs should equal 2080 cents.

80x + 40y = 2080 ----(2)

Now we have a system of equations (equations (1) and (2)) that we can solve to find the values of x and y.

To solve the system, we can use substitution or elimination. Let's use the substitution method here.

From equation (1), we have:

x = 36 - y

Substituting this value of x into equation (2), we get:

80(36 - y) + 40y = 2080

Expanding and simplifying:

2880 - 80y + 40y = 2080

2880 - 40y = 2080

-40y = 2080 - 2880

-40y = -800

y = (-800) / (-40)

y = 20

Therefore, Alex buys 20 cans of corn.

Answer:

20

Step-by-step explanation:

Let x be the number of cans of corn Alex buys.

Then, the number of cans of tomatoes he buys is 36-x.

The cost of the cans of tomatoes is:

\((36 - x) \times 0.80\)

The cost of the cans of corn is:

\(x \times 0.40\) dollars

The total cost is:

\((36-x) \times 0.80 + x \times 0.40 = 20.8 dollars\)

Simplifying the expression, we get:

28.8 - 0.40x = 20.8

0.40x = 8

x = 20

Therefore, Alex buys 20 cans of corn.

hope it helps...

Yes, ΔLMN is a right triangle.

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

Sides of a triangle are, 15, 9, and 12.

Now, We can apply the Pythagoras theorem as;

⇒ 15² = 9² + 12²

⇒ 225 = 81 + 144

⇒ 225 = 225

Thus, We can say that;

⇒ ΔLMN is a right triangle.

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Answer:

0.74

Step-by-step explanation:

Based on the provided information, there is evidence to suggest that the marble floor is unsafe on rainy days since the sample mean coefficient of static friction exceeds the accepted standard of 0.5.

The coefficient of static friction is a measure of how easily an object can move across the surface of another object without slipping. In the context of a marble floor, a higher coefficient of static friction indicates a greater resistance to slipping, thus indicating a safer floor. The accepted standard for a safe marble floor is a coefficient of static friction no greater than 0.5.

In this scenario, a random sample of 50 rainy days was selected, and the coefficient of static friction was measured on each day. The resulting sample mean coefficient of static friction was found to be 0.6. Since the sample mean exceeds the accepted standard of 0.5, it suggests that, on average, the marble floor is unsafe on rainy days.

To draw a more definitive conclusion, statistical analysis can be performed to assess the significance of the difference between the sample mean and the accepted standard. This analysis typically involves hypothesis testing, where the null hypothesis assumes that the population mean is equal to or less than the accepted standard (0.5 in this case). If the statistical analysis yields a p-value below a predetermined significance level (e.g., 0.05), it provides evidence to reject the null hypothesis and conclude that the marble floor is indeed unsafe on rainy days.

Therefore, based on the provided information, there is evidence to suggest that the marble floor is unsafe on rainy days due to the sample mean coefficient of static friction exceeding the accepted standard of 0.5. Further statistical analysis can provide a more precise evaluation of the evidence.

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The values of t for which g(x) ≤ 2 - t are:

-7 ≤ t ≤ 3

To solve for the values of t, we need to set up the inequality:

g(x) ≤ 2 - t

Substituting the given function g(x) in the inequality, we get:

3x^2 - 5 ≤ 2 - t

Adding 5 to both sides, we get:

3x^2 ≤ t + 7

Dividing both sides by 3, we get:

x^2 ≤ (t + 7)/3

Taking the square root of both sides, we get:

x ≤ ±√((t + 7)/3)

Therefore, the values of t for which g(x) ≤ 2 - t are:

-7 ≤ t ≤ 3

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Answer:

11/40

Step-by-step explanation:

The SUM (addition) of -1/10 and ⅜?

−1 /10  +  3 /8

=  −1 /10  +  3 /8

=  −4 /40  +  15 /40

=  −4 + 15 /40

=  11 /40

Answer:

C. 43.6% Increase

Step-by-step explanation:

Each bullet would cost 100/80 = $1.25 if 100 bullets cost $80.

Let's denote the amount invested at 8% as x and the amount invested at 10% as y.

According to the given information, Karim wants to invest a total of $100,000, and the combined annual income from both investments should be $9,000.

Set up the equations based on the information:

The first equation represents the total amount invested:

x + y = 100,000

The second equation represents the total annual income from the investments:

0.08x + 0.1y = 9,000

Solve the equations:

We can use the substitution or elimination method to solve the system of equations. Let's use the elimination method:

Multiply the first equation by 0.08 to match the coefficients of x:

0.08x + 0.08y = 8,000

Now subtract this equation from the second equation to eliminate x:

(0.08x + 0.1y) - (0.08x + 0.08y) = 9,000 - 8,000

0.02y = 1,000

Divide both sides of the equation by 0.02:

y = 1,000 / 0.02

y = 50,000

Substitute the value of y back into the first equation to solve for x:

x + 50,000 = 100,000

x = 100,000 - 50,000

x = 50,000

Calculate the amounts to invest:

Karim should invest $50,000 at 8% and $50,000 at 10% in order to obtain an annual income of $9,000 from both investments.

Karim should invest $50,000 at 8% and $50,000 at 10% in order to obtain an annual income of $9,000 from his investments.

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The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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Answer:

7 1/2 pounds

Step-by-step explanation:

A geometric sequence goes from one term to the next by always multiplying or dividing by the constant value except 0. The constant number multiplied (or divided) at each stage of a geometric sequence is called the common ratio (r).

A geometric series is the sum of an infinite number of terms of a geometric sequence.

A geometric series is convergers if |r| < 1.

A geometric series is diveres if |r| > 1.

Calculate the common ratio:

\(r=\dfrac{18}{27}=\dfrac{18:9}{27:9}=\dfrac{2}{3}\\\\r=\dfrac{12}{18}=\dfrac{12:6}{18:6}=\dfrac{2}{3}\\\\r=\dfrac{8}{12}=\dfrac{8:24}{12:4}=\dfrac{2}{3}\)

\(\left|\dfrac{2}{3}\right| < 1\)

Therefore exist the sum.

Formula of a sum of a geometric series:

\(S=\dfrac{a_1}{1-r},\qquad|r| < 1\)

Substitute:

\(a_1=27,\ r=\dfrac{2}{3}\)

\(S=\dfrac{27}{1-\frac{2}{3}}=\dfrac{27}{\frac{1}{3}}=27\cdot\dfrac{3}{1}=81\)

\(\huge\boxed{S=81}\)

Answer: The initial value for Z= 8 * 3w is 8 and the growth factor for it is 3. The initial value for A= 6(2.5)t is 6 and the growth factor for it is 2.5.

Step-by-step explanation: Exponential growth equations.

Answer:

3,675 people

Step-by-step explanation:

First row, a = 20

Common difference, d = 5

number of terms, n = 35

Sn = n/2 {2a + (n - 1)d}

= 35/2 {2*20 + (35 - 1)5}

= 35/2 {40 + ( 34)5}

= 17.5(40 + 170)

= 17.5(210)

= 3,675 people

The answer is actually 3675.

My reasoning: Plug it in and you shall see!

Answer:

-5/6,-1/2,2/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x + 5y = 1     ⇒    2x = 1 - 5y

y = 2xy + 5

y = (1 - 5y)y + 5

y = y - 5y² + 5

5y² = 5

y² = 1

 y₁ = 1               ∨           y₂ = -1

2x₁ = 1 -5(1)                   2x₂ = 1 - 5(-1)

2x₁ = 1 - 5                      2x₂ = 1 + 5

2x₁ = -4                         2x₂ = 6

 x₁ = -2                           x₂ = 3

Midpoint:

\(M=\left(\frac{x_1+x_2}2\ ,\ \frac{y_1+y_2}2\right)=\left(\frac{-2+3}2\ ,\ \frac{1+(-1)}2\right)=\left(\frac12\ ,\ 0\right)\)

The coordinates of the midpoint of the line AB is (0, 1/2).

The equation of the curve is given by y = 2xy + 5.

The equation of the line is given by 2x + 5y = 1.

We have to first find the point of intersection between the curve and the line and then find the coordinates of the midpoint of line AB where A and B is the point of intersection between the curve and the line.

If C(x, y) divides a line AB in m:n then we have,

\(x = \frac{mx_2 +nx_1}{m+n},~~~y =\frac{my_2+ny_1}{m+n}\)

And if C(x,y) is the midpoint then m = n.

we have,

\(x = \frac{x_2 +x_1}{2},~~~y =\frac{y_2+y_1}{2}\)

Where x and y are the coordinates of the midpoint o the line AB.

Find the point of intersection between the line and the curve.

y = 2xy + 5............(1)

2x + 5y = 1..............(2)

From (2) we have,

2x = 1 - 5yx = (1-5y) / 2..........(3)

Substituting (3) in (1).

\(y =2\frac{(1-5y)}{2}y + 5\\\\y =\frac{2y-10y^2}{2} + 5\\\\2y = 2y - 10y^2 + 10\\\\10y^2 = 10\\\\y^2 = 1\)

So we have,

y = 1 and y = -1

Puttin y = 1 in (3) we get,

x = (1 - 5) / 2 = - 4 / 2 = -2

Puttin y = -1 in (3) we get,

x = {1-5(-1)} / 2 = (1+5) / 2 = 6 / 2 = 3

Now we have two points of intersection A( 1, -2 ) and B( -1, 3 ).

Finding the coordinates of the midpoint of the line AB.

we have,

\(A(1, -2) = A (x_1, y_1)~~and~~B(-1, 3) = B(x_2, y_2)\)

Substituting in the given equation.

\(x = \frac{x_2 +x_1}{2},~~~y =\frac{y_2+y_1}{2}\\\\x = \frac{-1 +1}{2},~~~y =\frac{3+(-2)}{2}\\\\x = 0,~~~y=\frac{1}{2}\)

So the coordinates of the midpoint is (x,y) = ( 0, 1/2 ).

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Answer:

19/3

Step-by-step explanation:

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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The rate of change of the height of the candle remains constant at -3.2 inches per hour throughout the burning process.

a. i. g(4.2) = 20 - 3.2(4.2) = 6.96 inches

ii. g(4.6) - g(2.1) = (20 - 3.2(4.6)) - (20 - 3.2(2.1)) = 2.94 inches

iii. g(t) = 14 has no real solution since the candle will be completely burned out before reaching 14 inches.

iv. g(t) = 20 - 3.2t

v. The candle is 2/4 or 1/2 times as long (height) after 2 hours compared to 4 hours.

vi. To measure the height of the candle in feet instead of inches, we divide g(t) by 12: h(t) = g(t)/12.

b. i. The range of g(t) is (0, 20].

ii. The domain of g(t) is [0, ∞).

c. The rate of change of the candle's height with respect to time is given by the derivative of g(t):

g'(t) = -3.2 inches per hour

The rate of change from 18 to 5.6 hours is:

g'(5.6) - g'(18) = (-3.2) - (-3.2) = 0 inches per hour

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