Are these triangles similar? If so why?​

We can use the power rule to find the derivative of f(x) = x^n + x^(n-1). The power rule states that the derivative of x^n is nx^(n-1).

So, the derivative of x^n is nx^(n-1)

And the derivative of x^(n-1) is (n-1)x^(n-2)

So the derivative of f(x) = x^n + x^(n-1) is:

f'(x) = nx^(n-1) + (n-1)x^(n-2)

Now, if we combine the exponents we have :

f'(x) = nx^n-1 + nx^n-2

And we can factor out x^n-2 from the second term, we have:

f'(x) = nx^n-1 + (n-1)x^n-2*x^2

Now, we can simplify the expression by canceling the x^n-2 factor.

f'(x) = nx^n-1 + (n-1)x

And finally, by simplifying the exponent and factoring the constants, we have:

f'(x) = (nx + n - 1) / x^(2-n)

So the derivative of f(x) = x^n + x^(n-1) is f'(x) = (nx + n - 1) / x^(2-n)

Answer: Given a line represented by the equation 3x + y = 9, the slope of the line is -3/1. Since we know that the slope of the line perpendicular to this line is the negative reciprocal of the original line's slope, we can find the slope of the perpendicular line by taking -1/-3 = 1/3.

To find the equation of the perpendicular line that passes through the point (1,-2), we can use the point-slope form of the line equation, which is: y - y1 = m(x - x1) where m is the slope of the line and (x1,y1) is a point on the line.

Therefore, the equation of the perpendicular line that passes through the point (1,-2) is:

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

y + 2 = (1/3)x + (1/3)

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

So the final equation of the perpendicular line is y = (1/3)x - (2/3)

Step-by-step explanation:

The width of a rectangular field is  20 meters

Let l represents the length of a rectangular field, w represents the width of a rectangular field and d represents the diagonal of a rectangular field

We know that all the four angles of rectangle are right angle.

A diagonal of rectangle divides a rectangle into two equal right triangles.

Consider a right triangle with hypotenuse = diagonal (d) and the sides of the right triangle are nothing but the length and width of recangle.

Using Pythagoras theorem,

d² = l² + w²

52² = 48² + w²

w² = 52² - 48²

w² = 400

w =  ±20

But the width can not be -20

So, w = 20

Thus , the width is 20 meters

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Answer:

the interest rate required in order for Josiah to end up with $5,400, assuming the interest is compounded daily, is 10.3%

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^nt

Where:

A = the amount of money in the account after the interest has been added

P = the initial investment (principal) of $4,800

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years the money is left in the account

We know that A = $5,400 and t = 6 years, so we can substitute these values into the formula:

5400 = 4800(1 + r/n)^(6n)

To find the interest rate, we need to solve for r.

we know that the interest is compounded daily, so we will use n = 365

5400 = 4800(1 + r/365)^(6*365)

To find the interest rate, we need to solve for r, we can use a calculator to find the value of r.

r ≈ 0.103 or 10.3% to the nearest tenth of a percent

So, the interest rate required in order for Josiah to end up with $5,400, assuming the interest is compounded daily, is 10.3%

Answer:

Step-by-step explanation:So, the interest rate required in order for Josiah to end up with $5,400, assuming the interest is compounded daily, is 10.3%

3,686 seats were empty. This  number indicates that the stadium was not full to capacity.

1. Subtract the number of people in  from the number of people the stadium can hold:

62,005 - 58,319 = 3,686

2. The answer is 3,686 seats were empty.

The football stadium was able to accommodate up to 62,005 people, but only 58,319 were in attendance at the game. This means that 3,686 seats were left empty. To calculate this, subtract the number of people in attendance from the number of people the stadium can hold. 62,005 - 58,319 = 3,686. Therefore, 3,686 seats were empty. This number indicates that the stadium was not full to capacity.

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Answer:

-792 is this right lmk

Step-by-step explanation:

free fire is one of mugi game

The summation notation of the sum is:

[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]

The total amount is $84.

Summation notation, also known as sigma notation, is a mathematical notation used to represent the sum of a sequence of numbers. The notation typically uses the Greek letter sigma (∑) to represent the operation of summation.

Since each week Tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job.

Let n represent the number of weeks

Thus, this can be written using summation notation as:

[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]

Thus, the total amount = 4¹ + 4² + 4³ = $84

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Answer:  [tex]volume =[/tex] [tex](\frac{x2+11x+30}{x2+7x+6})[/tex] X [tex](\frac{x^{2}-1}{6x^{3} +30x^{2} })[/tex] X [tex]\frac{3x}{8}[/tex]

Step-by-step explanation:

Volume= b x h x l

            = [tex](\frac{x2+11x+30}{x2+7x+6})[/tex] X [tex](\frac{x^{2}-1}{6x^{3} +30x^{2} })[/tex] X [tex]\frac{3x}{8}[/tex]

Hey there!

Answer:

18 is 90% of 20.

Solution:

We already have our first value 18 and the second value 90. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 1

[tex]18=90*y[/tex]

STEP 2

[tex]18=\frac{90}{100} *y[/tex]

Multiplying both sides by 100 and dividing both sides of the equation by 90 we will arrive at:

STEP 3

[tex]y=18*\frac{100}{90}[/tex]

STEP 4

[tex]y=18*100[/tex] ÷ [tex]90[/tex]

STEP 5

[tex]y=20[/tex]

Finally, we have found the value of Y which is 20 and that is our answer.

You can easily calculate 18 is 90 percent of what number by using any regular calculator, simply enter 18 × 100 ÷ 90 and you will get your answer which is 20.

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What is a percentage?

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

We can convert 90% into a fraction, making it 90/100 or 9/10.

Now that we have that fraction, we can multiply that by 20.

9/10 × 20 = 18

Therefore, 18 is 90% of 20.

The roots of the equation are x = -1 + [tex]4i[/tex] and x = -1 - [tex]4i[/tex].

Quadratic equations are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

Given equation is x² + 2x + 17 = 0.

x² + 2x + 17 = 0

Discriminant = [tex]\sqrt{2^2-(4*1*17)}[/tex] = [tex]\sqrt{4 -68}[/tex] = [tex]\sqrt{-64}[/tex] = ± [tex]8i[/tex]

x = (-2 + [tex]8i[/tex]) / 2 or x = (-2 - [tex]8i[/tex]) / 2

x = -1 + [tex]4i[/tex] or x = -1 - [tex]4i[/tex]

Roots of the equation are imaginary.

Hence the roots of the quadratic equation are x = -1 + [tex]4i[/tex] and x = -1 - [tex]4i[/tex].

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(a) The missing value of y is 8

(b) The missing value of x is 144

Now, According to the question:

The ration table is:

X      Y

2      ?

4     16

5     20

?      36

We have to find the value of y

Now, According to the table :

The value of x is 2

So, value of y will be 8

x/y = 2/8 = 1/4

Next, x/y = 4/16 = 1/4

=> 5/20 = 1/4

Similarly, we are multiplying the first column by 1/4 to get the second column, we can set up the following equation for x.

1/4x = 36

x = 144

Hence,  the missing value of y is 8

(b) The missing value of x is 144.

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The numeric value of the expression 36x + 42y - 18x + 6 when x = 0.25 and y = -1 is given as follows:

-31.5.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The expression in this problem is given as follows:

36x + 42y - 18x + 6.

We want to find the numeric value at:

x = 0.25 and y = -1.

Hence:

Then the numeric value is given as follows:

36(0.25) + 42(-1) - 18(0.25) + 6 = -31.5.

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The surface area of the triangular prism is 224 square units.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area. The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given;

Surface area = ( S₁ + S₂ + S₃) × Length

Side1 S₁ = 6

Side2 S₂= 8

Side3 S₃ = 2

Length = 14

Surface area = ( 6+8+2)14

Surface area = 16(14)

Surface area = 224

Therefore, the surface area of the triangular prism will be 224 square units;

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Answer:

Step-by-step explanation:

GE = 89 feet when using the definition of a rectangle's diagonals.

The rectangle room's diagonals are as follows:

DF and GE

So,

DF = GE

DH = 1/2(DF)

Put

44.5 = 1/2(DF)

DF = 2(44.5)

DF = 89

Thus,

DF = GE = 89

GE = 89 ft.

Therefore, GE = 89 feet when using the definition of a rectangle's diagonals.

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To find the base of a trapezoid, you need to know the length of at least one of the bases and the height (or the length of the median). Since you know that PO is 13 (top base) and QR is 18 (median), you can use the following formula to find the length of the bottom base (MN):

Height x ((base1 + base2) / 2) = Area

Where the height is the length of the median (QR) and base1 and base2 are the lengths of the two bases (PO and MN).

So, in this case, you would have:

QR x ((PO + MN) / 2) = Area

18 x ((13 + MN) / 2) = Area

Solving for MN:

MN = (2 * Area) / QR - PO

So you can fill the area of trapezoid and substitute the values in the above formula.

===============================================

Explanation:

x = length of MN

A trapezoid has exactly one pair of parallel sides. The median is parallel to those mentioned sides. Think of it like the median to a highway.

A useful property is the median is the average of the parallel sides. We add up the outer sides, then divide by 2, and it gets us the median.

So,

QR = (MN + PO)/2

18 = (x + 13)/2

18*2 = x+13

36 = x+13

x = 36-13

x = 23

Side MN is 23 units long.

The diagram is below.

The graph of the piece-wise function for this problem is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

The two definitions for the function in this problem are given as follows:

Both of the lines will meet at the y-intercept of y = 1, as shown in the image presented at the end of the answer.

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Answer: The first one

Step-by-step explanation:

On a coordinate plane, a piecewise function has 2 connecting lines. The first line goes from (4, 5) down to (0, 1). The second line goes from (0, 1) up through (4, 5).  

Basically it should look like a wide V staring at point 1 on the y axis facing upwards.

Answer:

15640

let me know If I got it!

Both triangles are similar using angle-angle-angle similarity theorem and the similarity ratio is 2

Two figures are similar if they have the same shape and ratio of their corresponding sides are proportional.

Two triangles are similar if they have the same shape, all the three angles are congruent and the ratio of their corresponding sides are proportional.

Triangle TUV and triangle FGH are given.

∠U = ∠G = 54° (given)

∠T = ∠F = 50° (given)

∠V = ∠H = 76° (given)

Since all three angles of both triangles are equal, therefore both triangles are similar using angle-angle-angle similarity theorem

Similarity ratio = GF / UT = 26/13 = 2

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The x-intercept of the quadratic function y = x2 is equal to true at the origin.The x-intercept of the quadratic function y = x2 + 3 is false at the origin.

View the photo that is attached.The x-intercept of the quadratic function y = x2 is equal to true at the origin.

The x-intercept of the quadratic function y = x2 + 3 is false at the origin.

The average rate of change for both functions from x = -2 to x = 0 is positive, which is false.

When examining a graph, you move your cursor from left to right. The graph is dropping from left to right from -2 to 0.

The average rate of change for both functions between x = -2 and x = 0 is negative, which is true.

If you read the graph from left to right, both are declining.

y = x^2

Our point (2,3) has y = 3 but y = 4 if we add 2 to y = x2.

The coordinate (2, 7) is a solution to the quadratic function's equation, which is y = x2 + 3.

= TRUE

We can see that y = x2 + 3 = y = 2 by substituting 2 for x.

Our y value at the position (2, 7) is 7 because 2 + 3 Equals y = 7.

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Answer:

83 degrees

Step-by-step explanation:

Angles inside a triangle is what we called interior angles, which its sum should be equal to 180. Thus, the equation would be like this:

44 + 53 + x = 180

We simply re-arrange the equation to get the value of x.

x = 180 - (44 + 53)

x = 180 - 97

x = 83

Answer:

2/3

Step-by-step explanation:

the answer is explain up in the link or photo show up

There are 400 different ways possible to form 20 pairs consisting of 1 boy and 1 girl

In mathematics, a combination or combinations are all the possible groupings that can be made of a given number of elements, without repeating them and regardless of the order in which they are found.

To solve this problem the formula and the combination procedure we must use is:

C(n/r) = n! / [(n-r)! *r!]

Where:

C(n/r) = combination

n = total number of objects

r = number of selected objects

! = factorial of the number

Information about the problem:

Applying the combination formula we have:

C(n/r) = n! / [(n-r)! *r!]

C(20/1) = 20! / [(20-1)! *1!]

C(20/1) = 20! / [(19)! *1!]

C(20/1) = 20*19! / [(19)! *1!]

C(20/1) = 20/1!

C(20/1) = 20

Cgirl(20/1) * Cboy(20/1) = 20*20

Cgirl(20/1) * Cboy(20/1) = 400

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The researcher could also use a random number generator to select the members of the sample, instead of selecting them at regular intervals.

The formula for calculating a systematic sample is p = (n/N) x 100, where p is the percentage of the population to be sampled, n is the sample size, and N is the total population size. For example, if a researcher wanted to sample 100 people from a population of 500, the formula would be p = (100/500) x 100 = 20%. This means that the researcher would select every fifth person in the population to be included in the sample. The researcher could also use a random number generator to select the members of the sample, instead of selecting them at regular intervals.

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“Although part of your  question is missing, you might be referring to this full  question: In the given triangle with base length =[tex]8\sqrt{3}[/tex] and angles at  vertices are 60°,90°, and 30° respectively find the length of side x ”

The length of side x in the given triangle is 4√3 units.

In the given triangle with a base length of 8√3 and angles at the vertices of 60°, 90°, and 30°, we can use trigonometry to find the length of side x.

Since we know that one angle is 90°, we can use the 30-60-90 triangle ratios to determine the other sides. The ratios for a 30-60-90 triangle are as follows:

Opposite side (x) / hypotenuse (8√3) = sin 30° = 1/2

Adjacent side (y) / hypotenuse (8√3) = cos 30° = √3/2

So, using these ratios, we can calculate the length of the opposite side (x):

x = (8√3) (1/2) = 4√3

Therefore, the length of side x in the given triangle is 4√3 units.

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Answer:

1. 20... 2. 31... 3. -50

Step-by-step explanation:

1. 8+12=20

2. 13+18=31

3.-20+-30=-50

4. -15+3=-12

5. -80+20=-60

1. 8-12=-4

2. 13-18=-5

3. -20--30=-50

4. -15-3=-18

5. 80--20=60

A placebo is a medication or procedure that is given to a patient for psychological rather than physiological reasons.

The most typical sources of caffeine in nature are the cocoa, tea, and coffee plants. It functions by activating the central nervous system and brain, keeping you alert and delaying the development of fatigue.

Coffee has a maximum of 86 mg of caffeine per serving.

The highest daily dose of caffeine recommended by health authorities, excluding those who are pregnant or breastfeeding, is 400 mg for healthy individuals. Additionally, it is advised to consume no more than 200 mg of caffeine daily from all sources while pregnant or nursing.

Unwanted adverse effects might arise from placebos. Negative placebo effects, often referred to as nocebo effects, have been documented as nausea, drowsiness, and allergic reactions, including skin rashes.

Considering everything, it's clear that placebos aren't used in studies all that frequently. Therefore, the 86mg of placebo is employed in a regulated manner in the study.

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The amount of money raised during the first 3 months will be $1,680. Then the correct option is D.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The Helping Hands Student Club set a goal to raise $4,000 by the end of the school year for a project. After 3 months, it reaches 42% of its goal.

Then the amount of money raised is given as,

⇒ 42% of $4,000

⇒ 0.42 x $4,000

⇒ $1,680

The amount of money raised will be $1,680. Then the correct option is D.

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Regarding the likelihood of a student chosen at random joining a club and the interpretation of the likelihood, the correct answer is C. Because P(Robotics) = P, the student will be equally likely to join the robotics club or the zoology club (Zoology).

The random events are represented by probability. When there are numerous potential outcomes, it is the likelihood that the expected outcome will occur.

Probability is obtained by dividing the total number of outcomes by the expected number of outcomes.

Probability gives a quotient lying between zero and one as decimals, fractions, or percentages.

Club              Percent of Students

Garden Club            0.1

Robotics Club         0.2

Technology Club    0.5

Zoology Club          0.2

P(Robotics) = 0.2

P(Zoology) = 0.2

P(Robotics) = P(Zoology)

Thus, Option C is true about the probabilities.

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