A square is inscribed in a right triangle with leg lengths 6 and 8 so that they have a common right angle. FInd the square's side length.

Answer:

m = -9/2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (4, -6) (2, 3)

We see the y increase by 9, and the x decrease by 2, so the slope is

m = -9/2

16h^(10/2) *remove the root sign

16h^5 *simplify the exponent

Answer: 16h^5

Step-by-step explanation: im correct

Answer:

Yes they are congruent

Option B is correct

Step-by-step explanation:

Opisite sides of parallelogram are congurent so,

BA is congruent to CD (side)

And

BE I congruent to ED (Side)

AE is congruent to EC (Side)

So according to side-side-side congurence theorem triangle ABE is congruent to triangle CDE

Hope you understand :)

The ribbon cost $0.60 per foot.

[tex]\text{Total number of ribbon used} = (5.75 + 11.75) = 17.50 \ \text{feet}[/tex]

[tex]\text{17.50 feet of ribbon cost} = \$10.50[/tex]

[tex]\text{1 foot of ribbon cost = x}[/tex]

[tex]17.50 \times x = 1 \ foot \times \$10.50[/tex]

[tex]x = 1 \ foot \times 10.50\div17.50[/tex]

[tex]x = \$0.60[/tex]

Therefore, The ribbon cost per foot $0.60 per foot.

a. The answer to this question is the solution to the equation:

84000(1 + 0.04)^a = 132000

Where "a" represents the number of years since the beginning of 2020, and 0.04 is the decimal equivalent of 4%.

We use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years. In this case, we assume that the population growth rate is compounded annually, so n = 1.

b. Solving the equation in part (a), we get:

(1 + 0.04)^a = 132000/84000

1.04^a = 1.5714

a = log(1.5714)/log(1.04)

a ≈ 9.9 years

Therefore, it will take approximately 9.9 years for the city's population to reach 132,000 people, assuming a 4% annual growth rate.

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a) d/dt [√(289 - 8²)] = d/dt [√(255)] = d/dt [√(5²*17)] = 5/2√17 m/s.

b) The required value is the rate of change of x when the top of the ladder is 8 feet from the ground, then y = 15 feet.

a) Determine how fast the bottom of the ladder is sliding away when the top of the ladder is 8 feet from the ground. As the ladder leans against the side of the house, it makes a right angle with the ground. Using Pythagorean Theorem, the length of the ladder is given by.

Ladder length = √(hypotenuse)² - (height)²= √(17² - height²) meters. Taking the derivative of both sides of this equation, we get: dL/dt = [d/dt √(289 - h²)] meters/sec. Let h = 8 feet, dL/dt = -5 feet/sec.

Thus, the rate of change of the bottom of the ladder is d/dt [√(289 - h²)] meters/sec when the top of the ladder is 8 feet from the ground, and the bottom of the ladder is sliding away at a rate of 5 feet/sec.

b) At what rate is the angle o between the ladder and the ground changing then. Let y be the height of the ladder and the angle it makes with the ground be x. From the given values, y = 17 cos x.

Taking the derivative of both sides with respect to time: dy/dt = -17 sin x (dx/dt)In the given problem, dx/dt = -5/17sin x. Then, dy/dt = 5 sin x cos x= (5/2) sin 2x.

Solving this value of sin x by Pythagorean Theorem, sin x = 8/17. Substituting the value in the equation for the derivative, we get: dy/dt = (5/2) * sin 2x= (5/2) * sin 2(arc sin(8/17))= (5/2) * (2*8/17 * 15/17)= (600/289) ft/sec.

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Answer:

Answer is in the picture

Step-by-step explanation:

Hope you understand :)

Answer:

-----------------------------

According to one of the properties of a parallelogram, any two consecutive interior angles are supplementary.

We know supplementary angles add up to 180°.

Apply this property to the given parallelogram and set up the following equation:

Multiplication and division of regular numbers are the same as fractions and we will learn them with the multiplication and division of rational numbers worksheet.

To do the multiplication, first find the greatest common divisor of the numerator and the denominator. The factors are then grouped together so that the score equals one. Then multiply by the remaining factors. To divide, first rewrite the division as multiplication by the inverse of the denominator.

Cuemath's interactive math worksheets contain visual simulations to help your child visualize the concepts being taught, "see things as they really are, and reinforce learning from them". The Rational Numbers Multiplication and Division Worksheet follows a step-by-step learning process that helps students better understand concepts, identify errors, and eventually develop strategies for solving future problems.

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Here are the solutions:

a) R4 = {(a, b, c, d) | a, b, c, d ∈ R}

b) P3 = {a0 + a1x + a2x^2 + a3x^3 | a0, a1, a2, a3 ∈ R}

c) M22 = {(aij) | i, j = 1, 2}

d) M23 = {(aij) | i = 1, 2, j = 1, 2, 3}

For the given vector space R4 with the standard vector addition/scalar multiplication, the zero vector is the following: 0 = [0, 0, 0, 0].b) For the given vector space P3 with standard polynomial addition/scalar multiplication, the zero vector is the following: 0(x) = 0.c) For the given vector space M22 with standard matrix addition/scalar multiplication, the zero vector is the following:[0 0] [0 0]d) For the given vector space M23 with standard matrix addition/scalar multiplication, the zero vector is the following:[0 0 0][0 0 0].

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Answer: 19

Step-by-step explanation:

This is an isosceles trapezoid. Note that because this is an isosceles trapezoid, QN and MP are equal. Use the lengths given and solve:

3x + 1 + 6 = 6x - 5

3x = 12

x = 4

Plug x = 4 in 3x + 1 + 6, and we get 3(4) + 1 + 6 = 12 + 7 = 19

Hope this helps!

To refresh your memory of 9th-grade math, read Chapter 12. Complete the following table of angle and side measurements.

Right AnglesAngleA B C a b c

1 40 50 90 50 40 552 35 55 90 55 35 77

3 35 55 90 55 35 684 30 60 90 60 30 855 60 30 90 60 30 906 45 45 90 45 45 63

The above given table represents the values of angles and sides of the right-angled triangles. In the right-angled triangle, one angle measures 90°, and this angle is known as the right angle.

Further, the sum of other two angles measures 90°.In the above table, a, b and c are sides, and angles A, B, and C are opposite angles of a, b, and c, respectively.

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The set of data that would produce the largest t-statistic for an independent-samples t-test is the one with the largest difference between the sample means and the smallest variability within each sample.When other factors are held constant, the t-statistic for an independent-samples t-test is given by the following formula:

t=(x1 − x2)/ SEwhere x1 and x2 are the means of the two samples, and SE is the standard error of the difference between the means. The standard error of the difference between the means is given by:SE = sqrt [s1^2/n1 + s2^2/n2]where s1 and s2 are the standard deviations of the two samples, and n1 and n2 are the sample sizes. Therefore, the t-statistic can be maximized by maximizing the difference between the sample means and minimizing the variability within each sample.Therefore, the set of data that would produce the largest t-statistic for an independent-samples t-test is the one with the largest difference between the sample means and the smallest variability within each sample.

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The average productivity of the workforce, A(x), is given by

A(x) = p(x)/x,

where p(x) is the total value of the production when there are x workers in the plant.

A'(x) is the derivative of A(x) with respect to x.

A'(x) = (p(x)/x)' = (p'(x)x - p(x))/x^2.

The company wants to hire more workers if A'(x) > 0 because it means that the average productivity of the workforce is increasing with additional workers.

A'(x) > 0 if p'(x) is greater than the average productivity, which is p(x)/x.

Therefore, A'(x) > 0 if p'(x) > p(x)/x.
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Answer:

Pretty sure its C

Step-by-step explanation:

To cut through y axis, x axis is always 0, So it would be (0, a) where a is any real number, not (a,0) as is given in reason.

If Idil drove 12 miles in 1/5an hour on average, then she drove at an average speed of 60 miles per hour.

To calculate the average speed of Idil's car in miles per hour, we need to divide the distance she drove (12 miles) by the time it took her to drive that distance (1/5 hour):

Average speed = distance ÷ time

Average speed = 12 miles ÷ (1/5) hour

To divide by a fraction, we can multiply by its reciprocal, so:

Average speed = 12 miles × 5/1 hour

Average speed = 60 miles per hour

Therefore, Idil drove at an average speed of 60 miles per hour.

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Therefore, the value of 'a' when the shaded cross-sections of the solids have the same area is

:a = √(4A/π).

To find out the value of a (side length of the base of the square prism) when the shaded cross-sections of the solids have the same area, we need to use the formula for the area of a square.

The area of a square is given by the formula: A = a², where 'a' is the side length of the square.

Now, let's look at the two solids given in the question.

The first solid is a square prism with base 'a' and height 'a'.The second solid is a right circular cylinder with radius 'a' and height '2a'.The cross-section of the square prism is a square with side length 'a'.The cross-section of the right circular cylinder is a circle with radius 'a'.

Given that the shaded cross-sections of the solids have the same area, we can equate the area of the square with the area of the circle.

A = πr², where 'r' is the radius of the circle Substituting the values of 'r' and 'a', we get:A = πa²/4 = a²/4Multiplying both sides by 4, we get:4A = πa²

Now we can solve for 'a' by taking the square root of both sides a = √(4A/π).

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Answer:

You didn't give any options, but I'm guessing one of them has a 3 in the tens digits, which should be the right answer

Step-by-step explanation:

300?

There are no values in the wrong partition after the first pass across the array using quicksort when the pivot is [28].

The given problem states that using quicksort, if the pivot is [28], which values are found to be in the wrong partition after the first pass across the array? {28, 17, 45, 51, 35, 14, 88, 24}.Quicksort is a sorting algorithm that uses the divide and conquer approach. Here’s how to find out which values are found to be in the wrong partition after the first pass across the array .Step-by-step The first thing to do is to pick the pivot value. It can be any element in the array. The pivot value is 28.Then, the partition function is performed to place the pivot element in its final position in the sorted array.

All the values smaller than the pivot will be on the left side, and all the values greater than the pivot will be on the right side of the pivot. Here’s the array after the partition: 17 24 14 [28] 35 45 51 88Now, the elements to the left of the pivot are 17 24 14, and the elements to the right of the pivot are 35 45 51 88. Since the pivot is placed in its final position, there are no values in the wrong partition after the first pass across the array. Therefore, there are no values in the wrong partition after the first pass across the array using quicksort when the pivot is [28].

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Therefore, the exponential function that passes through the points (2,45) and (5,3072) is: y = (45/16) ([tex]4^{x}[/tex]).

In mathematics, a function is a rule that assigns to each element in a set called the domain, a unique element in another set called the range. In other words, a function is a mathematical object that takes an input and produces a specific output, according to a specific set of rules or operations.

by the question.

The general form of the exponential function is y = [tex]ab^{x}[/tex] where a and b are constants. To find the values of a and b that satisfy the given conditions, we can use the two points (2,45) and (5,3072) and solve for a and b.

First, we can write two equations based on the two points:

45 = a[tex]b^{2}[/tex] (1)

3072 = ab^5 (2)

We can then divide (2) by (1) to eliminate a:

3072/45 = (a[tex]b^{5}[/tex])/ (a[tex]b^{2}[/tex])

68 = [tex]b^{3}[/tex]

Solving for b, we get:

b = 4

Substituting this value of b into either (1) or (2) to solve for a, we get:

45 = a ([tex]4^{2}[/tex])

a = 45/16

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Answer:

She will draw 120 times for a red marble

Step-by-step explanation:

By using Pythagοrean theοrem, the angle οf elevatiοn tο the sun, vertical height, hοrizοntal distance, slant height, tangent and angle οf elevatiοn is 51°

The Pythagοrean theοrem is a fundamental result in Euclidean geοmetry that describes the relatiοnship between the three sides οf a right-angled triangle.

In equatiοn fοrm, this can be written as:

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

Where c is the length οf the hypοtenuse, and a and b are the lengths οf the οther twο sides (alsο knοwn as the legs) οf the right-angled triangle.

a) The Name οf the angle οf elevatiοn is: angle οf elevatiοn tο the sun

b) The Name οf the Hypοtenuse side is: vertical height (bοdy height)

c) The Name οf the Oppοsite side is: hοrizοntal distance (shadοw length)

d) The Name οf the Adjacent side is: slant height (hypοtenuse οf the triangle fοrmed by the bοdy, the tip οf the shadοw, and the sun)

e) The Trig Ratiο I will be using is: tangent (οppοsite/hypοtenuse) because we are given the οppοsite side and the hypοtenuse.

f) Shοw the wοrk tο find the angle οf elevatiοn. Rοund tο the nearest degree:

tan(angle οf elevatiοn) = οppοsite/hypοtenuse

tan(angle οf elevatiοn) = 45/34

angle οf elevatiοn [tex]= tan^{-1(45/34)[/tex]

angle οf elevatiοn ≈ 51°

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The correct option is B. The value of the quartile Q3 is 65.3 inches

Quartile is a type of statistical value that represents one-fourth of a dataset. It divides a dataset into four equal parts. Q1, Q2, and Q3 are the first, second, and third quartiles, respectively.

The formula for the third quartile is as follows:

Q3 = μ + (0.67 × σ), where μ is the mean and σ is the standard deviation.

Given:

Mean = μ = 63.6 inches

Standard deviation = σ = 2.5 inches

The value of the quartile Q3 can be found by substituting the given values in the formula.

Q3 = μ + (0.67 × σ)

Q3 = 63.6 + (0.67 × 2.5)

Q3 = 63.6 + 1.675

Q3 = 65.275 ≈ 65.3

Therefore, the value of the quartile Q3 is 65.3 inches. Therefore, option B is the correct answer.

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Step-by-step explanation:

a) Area=144m²

side²= 144

side=12m

b) perimeter=32m

4×side=32

side=32/4

side=8m

The system of equations x + y = 15 and 2x + 3y = 24

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

To substitute for the variable x in the equation x + y = 15, we can rearrange the equation to solve for x in terms of y:

x = 15 - y

Then we can substitute this expression for x in any other equation that involves x.

2(15 - y) + 3y = 24

Simplifying this equation gives:

30 - 2y + 3y = 24

y = -6

Then we can substitute this value back into our expression for x to get:

x = 15 - (-6) = 21

So the solution to the system of equations x + y = 15 and 2x + 3y = 24 is (x, y) = (21, -6), but the question only asked us to rewrite the equation to substitute for x.

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Answer:

A is correct

Step-by-step explanation:

Whatever value you put in for "y" will keep both of the equations equal

The combined score on the 2022 SAT test ranges from 400 to 1600. If you were to randomly draw five numbers from a 400-1600 number set, the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers is approximately 0.004%

To find the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers, we need to find the probability of the following event: “the three other random numbers drawn lie between the highest and lowest values.

The probability of choosing one of the five numbers that falls within the range is (1600 – 400)/1201 = 1/2.25.

The first number can be any number within the 400-1600 range, so the probability is 1.The second number must lie within the range created by the highest and lowest values of the first number, which has a width of 1201. Thus, the probability is 1201/3201.

The third number must lie within the range created by the highest and lowest values of the first two numbers, which has a width of 801. Thus, the probability is 801/2401.The fourth and fifth numbers must lie within the range created by the highest and lowest values of the first three numbers, which has a width of 401.

Thus, the probability is 401/1601.Therefore, the probability of the medium score of the actual 2022 SAT results being between the highest and lowest values of these five random numbers is (1/2.25) * (1201/3201) * (801/2401) * (401/1601) * 1 = 0.000038 or approximately 0.004%.

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Length of the median of the triangle is b. 18

How to find the length of the median of a triangle?
Given that the centroid of a triangle is located 12 units from one of the vertices of a triangle. We need to find the length of the median of the triangle drawn from that same vertex.

Let ABC be a triangle.

Let AD be median of the triangle.

Let E be centroid of ΔABC

Length of the median of triangle = AD

AD = Length of AE + Length of ED

But,

AE = 12

ED = x

So,

AD = 12 + x

Since, centroid divides median in 2:1 ratio.

Then,

[tex]12 : x = 2 : 1\\12/x = 2/1\\\\12= 2x\\[/tex]

Divide by 2 each side

[tex]x = 6[/tex]

So,  AD = 12 + x = 12 + 6 = 18

Thus, Length of the median of triangle is 18.

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You answer would be mate it would be x=66

Barbara will get $7.20 back in change.

A sales tax that is typically added to the selling price by the seller.

Without tax, the total cost of the shirt and pants is:

$15.00 + $25.00 = $40.00

The sales tax is 7% of $40.00, which is as follows:

0.07 x $40.00 = $2.80

So, with tax, the total cost of the shirt and pants is:

$40.00 + $2.80 = $42.80

If Barbara pays with a $50 bill, she will receive the following change:

$50.00 - $42.80 = $7.20

As a result, Barbara will receive $7.20 in change.

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Answer:

10km

Step-by-step explanation:

Pythagoras

Formula=[tex]a^2+b^2=c^2[/tex]

[tex]6^{2} +8^{2} =c^2\\c^2=100\\c=\sqrt{100} \\c=10km[/tex]