the perimeter of the rectangle is 22 feet. The perimeter of the triangle is 12 feet. Find the dimensions of the rectangle.

According to the Synthetic Division, the Quotient is equal to  7x² -4x + 5 and the Remainder is equal to 8.

Synthetic division can divide two polynomials more quickly than the standard long division algorithm.

With this method, the dividend and divisor polynomials are reduced to a set of numerical numbers.

Given:

(7x³-25x² +17x -7) ÷ (x-3).

So, Synthetic Division for this is as follows:                                    

                      (x-3) | (7x³-25x² +17x -7) | 7x² -4x + 5

                                                    7x³-21x²

                                                 _________

                                                           -4x² + 17x

                                                           -4x² + 12x        

                                                    _______________

                                                                        5x - 7              

                                                                        5x - 15

                                                                      ________

                                                                               8

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Answer:

Step-by-step explanation:

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Answer:

Median is a middle number.

Step-by-step explanation:

You can use any set of number with 12 in the middle

14, 18, 12, 12, 17, 18

Middle numbers are third and forth number added together and divided by 2

The correct symbol in the expression is 95/56 < 2 5/7

From the question, we have the following parameters that can be used in our computation:

95/56 and 2 5/7

Convert the improper number to a mixed number

So, we have the following representation

1 39/56 and 2 5/7

By comparison;

1 39/56 is less than 2 5/7

So, the inequality symbol is a less than inequality

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Yes, H is a subgroup. We can prove this by using the subgroup criterion, which states that a subset H of a group G is a subgroup if and only if it satisfies the following three conditions:

1. The identity element of G is in H.

2. If h1 and h2 are in H, then h1*h2 is in H.

3. If h is in H, then h^(-1) is in H.

Let's check if these conditions are satisfied for H:

1. The identity element of ???? is the zero function, f(x) = 0, which is differentiable. Therefore, the identity element is in H.

2. If h1 and h2 are in H, then they are both differentiable functions. The sum of two differentiable functions is also differentiable, so h1 + h2 is in H.

3. If h is in H, then it is a differentiable function. The inverse of a differentiable function under addition is its negative, which is also differentiable. Therefore,[tex]h^{-1} = -h[/tex] is in H.Since all three conditions are satisfied, H is a subgroup.

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15 - 60%

x - 100%

1500 = 60x

x = 25

∴ There are 25 students in the class in all.

Answer:

We would need to know the percentage of discount offered during the sale to determine the sale price of the polo shirt. Here's an example calculation for a 25% discount:

If the discount offered is 25%, Bert will only need to pay 75% of the original price. We can calculate this as:

Sale price = (100% - 25%) x $20

Sale price = 75% x $20

Sale price = 0.75 x $20

Sale price = $15

Therefore, if the discount offered during the sale is 25%, Bert will pay $15 for the polo shirt. However, if the discount is different, the sale price will be different.

The value of the digit 4 in 5,040 is 100 times more than that of the digit 4 in 4,670.

At the unit place of both numerals, there is a digit 4. The place value of a digit determines how valuable it is in a number. The position of the digit from the number's rightmost side determines its place value.

The value of the digit 4 in the tens place of the number 4,670 is 4 x 10 = 40.

The value of the digit 4 in the thousands position of the number 5,040 is 4 x 1000, or 4000.

Therefore, As 4000/40 = 100, the value of the digit 4 in 5,040 is 100 times more than that of the digit 4 in 4,670.

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The period of the function is 10 and the amplitude is 4.

The period and amplitude of the function \[ y=-4 \sin \left(\frac{\pi x}{5}\right) \] can be found by examining the coefficients in the equation.

The amplitude is the absolute value of the coefficient in front of the sine function, which in this case is |-4| = 4. Therefore, the amplitude of the function is 4.

The period is found by dividing 2π by the coefficient in front of the x variable inside the sine function. In this case, the coefficient is \[\frac{\pi}{5}\]. So, the period is \[\frac{2\pi}{\frac{\pi}{5}} = 10\].

Therefore, the period of the function is 10 and the amplitude is 4.

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Answer:

if I'm correct it's 3(4x5)

BUT RECHECK JUST INCASE

Step-by-step explanation:

Answer:

reads 64 pages in one hour

Step-by-step explanation:

For simplicities' sake, we'll convert 1/4 of an hour into 15 minutes (60 minutes x 1/4 = 15 mins)

Since we have a ratio, of 16 pages to 15 mins, we can create the ratio by making a fraction of 16/15. Since we want to get to 1 hour, to find how many pages she read in an hour, we can multiply the top and bottom (to equalize) by 4 (because 4 x 15 = 60).

16•4/15•4

64/60

Because of this, we can see that the ratio is now 64 pages to 60 mins or one hour. Therefore, she reads 64 pages in one hour.

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Answer:

64

Step-by-step explanation:

To do this problem you have to figure out Michelle's hourly rate for reading pages. We are given that she will read 16 pages in 1/4 of an hour. This means that in 15 minutes (60 minutes in an hour / 4 for the 1/4 an hour) she will read 16 pages. We only have 15 minutes though and need 60 minutes so 60/15 gives us 4. This means that we will need 4, 15 minute periods to get to a hour. So 4*15minutes = 60 minutes or one hour and 16pages*4 = 64 pages. So in one hour she will read 64 pages.

A faster way to do this is to just multiply both sides by the recripical.

16 pages = 1/4 hour

*4/1              *4/1

64 pages = 4/4 hour

64 pages = 1 hour

The measure of the height of the tin in mm can be found using the steps below.

What are Measurements?

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is essential to determine the quantity of any object.

Here, the activity is to measure the height of a tin.

Height of the tin is the vertical distance from the base of the tin to the top of the tin.

The height of the tin is the exact straight line measurement when the tin is placed upright on a flat surface.

The measurement has to be in millimeters.

So the best tool is the ruler.

Place the ruler vertically with point 0 at the baseline of the tin.

Mark the point in millimeters that the ruler coincides with the top of the tin.

Read the height to the nearest millimeter.

Hence, the height of the tin can be measured as above.

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The complete Question:

Measure the height of the tin in the mm and write down the real height in mm

Answer:

35 miles.

Step-by-step explanation:

A=3x+65

B=2x+100

3x+65=2x+100

x+65=100

x=35

The equation that gives the cost of each juice bottle is 24j + 2.19 = 40.83

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

Let j represent the cost of each juice.

Sophie bought a popcorn for $2.19 and 24 juice bottles for a total of $40.83.

The equation that represents this problem is:

24j + 2.19 = 40.83

The equation is 24j + 2.19 = 40.83

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The solution of the given expression is y = -12 and there are no extraneous solutions.

A solution to an equation that appears during the solving process but does not fulfil the original problem is known as an extraneous solution. In other words, it is a solution that, when inserted back into the original equation, yields an untrue assertion. Extraneous solutions typically result from certain algebraic operations, such squaring an equation's two sides, which might introduce new solutions that don't truly satisfy the original problem.

The given expression is:

7y+3−6y+9=0

y = -12

Substitute y = -12 back into the original equation:

7y + 3 - 6y + 9 = 0

7(-12) + 3 - 6(-12) + 9 = 0

-84 + 3 + 72 + 9 = 0

The left-hand side simplifies to:

0 = 0

Hence, the solution of the given expression is y = -12 and there are no extraneous solutions.

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Answer:

1 / 625

Step-by-step explanation:

To write 5^-24 without exponents, simplify.

5^-4

1 / 5^4

1 / 625 or .0016

The correct answer is C. the probability of incorrectly rejecting the null hypothesis.

A P-value is used in hypothesis testing to determine the likelihood of observing a test statistic as extreme as the one observed under the null hypothesis. It is a measure of the strength of evidence against the null hypothesis.

A small P-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. A large P-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

It is important to note that a P-value is not the same as the significance level (option E), which is the threshold used to determine whether to reject or fail to reject the null hypothesis.

The P-value is also not the same as the correlation between two variables (option A), which measures the strength of a linear relationship between two variables.

The P-value is also not the ratio between the test statistic and the standard error (option B), which is used to calculate the P-value but is not the same thing.

Therefore, the correct answer is option C, the probability of incorrectly rejecting the null hypothesis.

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Answer:

C

Step-by-step explanation:

I think its c because it said x = 3 less than 6, what is three less than 6? 3 so if you were to plug in 3 for x so bc = 3 and ab = 6 you multiply those two together but when you are doing area for a triangle its 1/2 bh so how i do this is i multiply 6 and 3 and get 18 and divide that by 2 and my final answer is 9. Hope this works, let me know if it doesnt!

Answer:

Step-by-step explanation:

lets take the top part as 1 and the seconds part as 2

so for the first part

1 Area= L*B

so 8*5 =40

2 Area=L*B

so 11*4=44

44+40=84cm2

Answer:

G

Step-by-step explanation:

Since these triangles are similar, side lengths in one must be proportional to the other.  Segment AB is similar to DE, AC similar to DF, and BC similar to EF. With that in mind, G is the only possible answer because DE/AG correspond to one another, just as DF/AC correspond to one another.

Answer: C

Step-by-step explanation:

replace n=1 with f(n)= 5n-2 we have

f(1)=3 => remove answers B and D

f(n)= 5n-2 so f(n-1)= 5(n-1) -2=5n-7

Try with answers C and D to see if it satisfies this

f(n)= f(n-1)+5= 5n - 7+5=5n-2 => C is correct

When f(x) = 4, then, the value of x = 2 (domain = 2, range = 4).

According to the mapping above, the given relationship is bijective (one-to-one and onto or one-to-one correspondence) because each element of the range is mapped to by exactly one element of the domain.

When we say a relationship is bijective, it means the satisfies both the injective (one-to-one function) and surjective function (onto function) properties. Therefore, as a result, f(x)=4 implies f(2)=4 or simply x=2.

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The Cartesian equation y = 3x^2 as a polar equation can be write as r(θ) = 3 sec(θ) / (1 + tan²(θ)).

To rewrite the Cartesian equation y = 3x² as a polar equation, we need to use the conversion formulas between Cartesian coordinates (x, y) and polar coordinates (r, θ):

x = r cos(θ)
y = r sin(θ)

Substituting these formulas into the Cartesian equation gives us:

r sin(θ) = 3(r cos(θ))²

Dividing both sides by r and rearranging terms gives us:

r = 3 cos²(θ) / sin(θ)

Using the identity 1 + tan²(θ) = sec²(θ), we can rewrite the equation in terms of tan(θ) and sec(θ):

r = 3 (1 / (1 + tan²(θ))) / (1 / sec(θ))

Simplifying gives us the final polar equation:

r(θ) = 3 sec(θ) / (1 + tan²(θ))

Therefore, the Cartesian equation y = 3x²can be rewritten as the polar equation r(θ) = 3 sec(θ) / (1 + tan²(θ)).

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The answer of two possible values for p are 26 and 22

If (mx+3)(nx+5)=8x^(2)+px+15 for all values of x, and m+n=6, we can use the distributive property to expand the left side of the equation:

mnx^(2)+(5m+3n)x+15=8x^(2)+px+15

Next, we can compare the coefficients of each term to find the values of m, n, and p:

mn=8

5m+3n=p

m+n=6

Since m+n=6, we can solve for one variable in terms of the other:

n=6-m

Substituting this into the equation for p gives us:

5m+3(6-m)=p

5m+18-3m=p

2m+18=p

Now we can substitute this back into the equation for mn:

m(6-m)=8

6m-m^(2)=8

m^(2)-6m+8=0

Using the quadratic formula, we can find the two possible values for m:

m=(6±√(6^(2)-4(1)(8)))/(2(1))

m=(6±√(36-32))/2

m=(6±√4)/2

m=(6±2)/2

m=4 or m=2

If m=4, then n=6-4=2, and p=2(4)+18=26

If m=2, then n=6-2=4, and p=2(2)+18=22

Therefore, the two possible values for p are 26 and 22.

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a.  The total number of possible outcomes is 16 x 96 = 1,536.

b. She should expect to see a difference of 1 approximately 12/16 x 96 = 72 times.

c. She should expect to see a difference of 0 approximately 8/16 x 96 = 48 times.

a) There are a total of 16 possible pairs of numbers that can be rolled on the two pyramids:

(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), and (4,4).

We can use a probability distribution to calculate the probability of each pair of numbers being rolled. Since each pyramid has four sides, there are 4 x 4 = 16 possible outcomes when both pyramids are rolled. Therefore, the probability of each outcome is 1/16.

Since Natalie is going to toss each pair of pyramids 96 times, the total number of possible outcomes is 16 x 96 = 1,536.

To calculate the difference between each pair of numbers, we can simply subtract the smaller number from the larger number.

Here is a table that shows the probability of each difference:

Difference                  Possible Pairs                           Probability

0                               (1,1), (2,2), (3,3), (4,4)                            4/16 = 1/4

1                               (1,2), (1,3), (1,4), (2,3), (2,4), (3,4),          12/16 = 3/4

                                     (2,1), (3,1), (4,1), (3,2), (4,2), (4,3)  

2                                None                                             0

3                                None                                             0

Therefore, the probability of the difference being 0 is 1/4, the probability of the difference being 1 is 3/4, and the probability of the difference being 2 or 3 is 0.

Since Natalie is going to conduct the experiment a total of 96 times, we can use these probabilities to calculate the expected number of times each difference will occur:

Difference             Probability          Expected Number of Occurrences

0                                1/4                     96 x 1/4 = 24

1                                 3/4                     96 x 3/4 = 72

2                                      0                     96 x 0 = 0

3                                 0                     96 x 0 = 0

b) we can expect the difference between each pair of numbers to be 0 about 24 times and

c) to be 1 about 72 times over the course of the experiment.

Differences 2 and 3 are not expected to occur.

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The correct question should be:

Natalie has two number pyramids each labeled 1 to 4. Natalie is going to conduct an experiment by tossing both pyramids a total of 96 times. She will find the difference of each pair of numbers rolled by subtracting the lesser number from the greater number.

a. How many possible outcomes are there? _________________

b. How many times should Natalie toss a difference of 1? ______________

c. How many times should Natalie toss a difference of 0?

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=8\\ y=30 \end{cases} \\\\\\ 30=\cfrac{k}{8}\implies 240=k\hspace{9em}\boxed{y=\cfrac{240}{x}} \\\\\\ \textit{when y = 20, what's "x"?}\qquad 20=\cfrac{240}{x}\implies x=\cfrac{240}{20}\implies x=12[/tex]

Given- A sequence as -6,-9,-12,-15

To find- The equation for the nth term of the arithmetic sequence and to find the value of [tex]a_{10}[/tex].

Explanation- The common difference is [tex]-9-(-6)=-3[/tex]

We know the arithmetic sequence formula is

[tex]a_n=a_1+(n-1)d\\a_n=-6+(n-1)(-3)[/tex]

When n=10

[tex]a_{10}=-6+(10-1)(-3)\\a_{10}=-6+9(-3)\\a_{10}=-6-27\\a_{10}=-33[/tex]

Final answer- The value of 10th term is -33.

Answer:

A

[tex]2y {}^{4} \div x {}^{4} [/tex]

Step-by-step explanation:

Divide 14 by 7 it will be 2.

Now divide the variables.

X variable will give you X{}^{-4} and y{}^{4}.

So bring X variable in the denominator to make it positive.

So your answer will be option A.

Answer:

A

Step-by-step explanation:

It was right for me

The first five terms of the sequence whose general term is given as a_(n)=2n-8 are a_1=-6, a_2=-4, a_3=-2, a_4=0, and a_5=2.

To explain this in more detail, the general term for a sequence is given by an equation in the form a_(n)= some expression. In this case, the expression is 2n-8, so it can be read as “2 times the term number minus 8”.

To calculate the first term, we substitute n=1 into the equation and solve, so a_1=2*1-8=-6. To calculate the second term, we substitute n=2 into the equation and solve, so a_2=2*2-8=-4. Continuing in this manner, we calculate the third term as a_3=2*3-8=-2, the fourth term as a_4=2*4-8=0, and the fifth term as a_5=2*5-8=2.

Therefore, the first five terms of the sequence are a_1=-6, a_2=-4, a_3=-2, a_4=0, and a_5=2.

In conclusion, to find the first five terms of a sequence given by a general term a_(n)= some expression, substitute the values n=1, n=2, n=3, n=4, and n=5 into the expression and solve to get the desired terms.

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