what is first even number that is a multiple of 5 and 7?

Answer:

x

Step-by-step explanation:

We are required to simplify the rational expression:

[tex]\dfrac{4}{x^2+4x-5} -\dfrac{5}{x^2-25}[/tex]

First, we factorize the denominators where possible

[tex]x^2+4x-5=x^2+5x-x-5=x(x+5)-1(x+5)=(x-1)(x+5)\\x^2-25=x^2-5^2 \\$Applying difference of two squares\\x^2-5^2=(x-5)(x+5)[/tex]

Therefore, our rational expression becomes:

[tex]\dfrac{4}{(x-1)(x+5)} -\dfrac{5}{(x-5)(x+5)}\\$Taking LCM\\=\dfrac{4(x-5)-5(x-1)}{(x-1)(x-5)(x+5)}\\=\dfrac{4x-20-5x+5}{(x-1)(x-5)(x+5)}\\=\dfrac{-x-15}{(x-1)(x-5)(x+5)}\\$Factoring out minus in the numerator and -(x-5)=(5-x)\ in the denominator\\=\dfrac{x+15}{(x-1)(5-x)(x+5)}[/tex]

Therefore, the leading coefficient of the numerator is x.

Answer:

5 and –8 are solutions.

Step-by-step explanation:

8 is a solution to the original equation. The value –5 is an extraneous solution.

5 and 8 are both extraneous solutions.

5 is a solution to the original equation. The value –8 is an extraneous solution.

Answer: 5 and –8 are solutions

Step-by-step explanation:

We have been given 4 choices. We are asked to choose the volume that could belong to a cube with a side length that is an integer.

We know that volume of a cube is cube of each side length.

To solve our given problem, we will take cube root of each given value. The cube root of which value will be an integer that will be our correct choice.

A. [tex]s^3=18[/tex]

[tex]\sqrt[3]{s^3}=\sqrt[3]{18}[/tex]

[tex]s=2.62074[/tex]

Since cube root of 18 is not an integer, therefore, 18 is not a correct choice.

B. [tex]s^3=36[/tex]

[tex]\sqrt[3]{s^3}=\sqrt[3]{36}[/tex]

[tex]s=3.301927[/tex]

Since cube root of 36 is not an integer, therefore, 36 is not a correct choice.

C. [tex]s^3=64[/tex]

[tex]\sqrt[3]{s^3}=\sqrt[3]{64}[/tex]

[tex]s=4[/tex]

Since cube root of 64 is 4 and 4 is an integer, therefore, 64 is the correct choice.

D. [tex]s^3=100[/tex]

[tex]\sqrt[3]{s^3}=\sqrt[3]{100}[/tex]

[tex]s=4.641588[/tex]

Since cube root of 100 is not an integer, therefore, 100 is not a correct choice.

Answer:

c

Step-by-step explanation:

have a nice day :)

The cube and rectangular prism.

Step-by-step explanation:

The triangular prism has 5 and the other two both have 8.

None of the shapes mentioned in the question, a cube, a rectangular prism, or a triangular prism, have more than six faces. For more complex shapes like Icosahedron, they do carry more than six faces.

The student's question is about understanding which among the shapes - a cube, a rectangular prism, and a triangular prism - has more than six faces. To answer this, we should first understand that a cube and a rectangular prism (or cuboid) both have 6 faces and a triangular prism also has 5 faces only. Hence, none of these shapes deliver more than 6 faces as specified in the question. For a three-dimensional shape to have more than 6 faces, one has to move towards more complex shapes. For example, the provided reference suggests Icosahedron, a shape with 20 faces is an example of a shape with more than six faces.

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Answer:

[tex]2\frac{1}{12}[/tex] cups of sugar required for 5 cups of flour

Step-by-step explanation:

Number of cups of sugar required for 3 cups of flour =[tex]1 \frac{1}{4}[/tex]

Number of cups of sugar required for 3 cups of flour = [tex]\frac{5}{4}[/tex]

Number of cups of sugar required for 1 cup of flour [tex]=\frac{\frac{5}{4}}{3}[/tex]

Number of cups of sugar required for 5 cups of flour =[tex]\frac{\frac{5}{4}}{3} \times 5[/tex]

Number of cups of sugar required for 5 cups of flour =[tex]\frac{25}{12}[/tex]

Number of cups of sugar required for 5 cups of flour =[tex]2\frac{1}{12}[/tex]

Hence [tex]2\frac{1}{12}[/tex] cups of sugar required for 5 cups of flour

Answer:

Step-by-step explanation:

diameter = 8 units

r = 8/2 = 4 units

h = 6 units

[tex]Volume=\frac{1}{3}\pi r^{2}h\\\\=\frac{1}{3}*\pi*4*4*6\\\\[/tex]

= π*4*4*2

=32π cubic units

The mean of the discounted prices is $736.25, the median is $810, the mode is $810, and the range is $645.

To find the mean of the discounted prices, we add up all the prices and divide by the total number of prices. In this case, the mean is $736.25 because (640 + 810 + 755 + 810 + 1175 + 900 + 1080 + 530) / 8 = 736.25.

To find the median of the discounted prices, we arrange the prices in ascending order and find the middle value. Since there are 8 prices, the median is the average of the 4th and 5th values, which are $810 and $810, respectively. So, the median is $810.

To find the mode of the discounted prices, we look for the value that appears most frequently. In this case, $810 appears twice, which is more often than any other price. Therefore, the mode is $810.

To find the range of the discounted prices, we subtract the smallest price from the largest price. In this case, the range is $645 because $1175 - $530 = $645.

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Answer:

x>7

Step-by-step explanation:

We do 2 steps

2x > x + 7

that means

2x - x > x - x + 7

then

x > 7

That is the answer. Hope it useful for you!

Answer:

10 miles

Step-by-step explanation:

Use pythagorean theorem:

[tex]6^{2} +8^{2} = 10^{2}[/tex]

Answer:

10.95

Step-by-step explanation:

anything under 4 rounds down and anything over 4 rounds up. so your answer would be 10.95

10.9544 rounded to the nearest tenth would be 11.0. When rounding to the nearest anything, remember to look at the number to the right of it. If it is greater or equal to five, round up. If the number is less than five, round down. In this situation, the number to the right of "9" (the position of the tenth) is five, which means we should round up, which would equal 11.

I hope this helped -- if it did, please thank, rate, and mark as brainliest! If you have any more questions or concerns, feel free to ask! Thank you, stay safe, and have a great rest of your day/quarantine! (i know it's hard, but we're almost through. we've got it!)

Answer:

73

Step-by-step explanation:

When you have a line intersecting another line, the angles produced by the intersection will be equal to 180.

This means that  (-39 + x) + 146 = 180.  Solve for x.

(-39 + x) + 146 = 180

-39 + x = 34

x = 73

Answer:

B

Step-by-step explanation:

First, find the y-intercept form of the equation:

x - y = 4

x - x - y = 4 - x

-y = 4 - x

-y = -x + 4

-y/-1 = -x/-1 + 4/-1 (to get the y positive)

y = x - 4

The y-intercept is -4. This means that a y-intercept two units above 4 would be -2. Whichever line crosses the y axis at the value of -2 is the answer (line B)

hope this helps :)

Question:

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If​ convenient, use technology to construct the confidence intervals. A random sample of 45 home theater systems has a mean price of ​$114.00. Assume the population standard deviation is ​$15.30. Construct a​ 90% confidence interval for the population mean.

Answer:

At the 90% confidence level, confidence interval = 110.2484 < μ < 117.7516

At the 95% confidence level, confidence interval = 109.53 < μ < 118.48

The 95% confidence interval is wider

Step-by-step explanation:

Here, we have

Sample size, n = 45

Sample mean, [tex]\bar x[/tex] = $114.00

Population standard deviation, σ = $15.30

The formula for Confidence Interval, CI is given by the following relation;

[tex]CI=\bar{x}\pm z\frac{\sigma}{\sqrt{n}}[/tex]

Where, z is found for the 90% confidence level as ±1.645

Plugging in the values, we have;

[tex]CI=114\pm 1.645 \times \frac{15.3}{\sqrt{45}}[/tex]

or CI: 110.2484 < μ < 117.7516

At 95% confidence level, we have our z value given as z = ±1.96

From which we have [tex]CI=114\pm 1.96 \times \frac{15.3}{\sqrt{45}}[/tex]

Hence CI: 109.53 < μ < 118.48

To find the wider interval, we subtract their minimum from the maximum as follows;

90% Confidence level: 117.7516 - 110.2484 = 7.5

95% Confidence level: 118.47503 - 109.5297 = 8.94

Therefore, the 95% confidence interval is wider.

Answer:

B. is the correct option.

With 90% the population mean price is

in lies in (127.01,134.99). With 95% confidence, it can be said that the population mean price lies in ( 126.24,135.76)

Therefore, the 95% confidence interval is wider than 90%.

The calculation is attached

Look at the attached picture

Hope it will help you...

Good luck on your assignment

~pragya

Answer:

(0,0)

Step-by-step explanation:

Answer:

(0,0)

Step-by-step explanation:

The graph is not shifted to the right, left, up, or down, so the vertex is still the origin. Even though the equation is negative, all this means is it is reflected across the x-axis. So, the vertex is still at the origin.

Answer:

c.140

Step-by-step explanation:

Answer:

C. 140 degrees

Step-by-step explanation:

Answer: CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

Step-by-step explanation: HOPE IT HELPS YOU

Answer:

B. 6.3%

Step-by-step explanation:

For each time that the coin is tosse, there are only two possible outcomes. Either it comes up tails, or it does not. The probability of coming up tails on a toss is independent of any other toss. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Fair coin:

Equally as likely to come up heads or tails, so [tex]p = 0.5[/tex]

Probability that the first tails comes up on the 4th flip of the coin?

0 tails during the first three, which is P(X = 0) when n = 3.

Tails in the fourth, with probability 0.5. So

[tex]p = 0.5P(X = 0)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]p = 0.5P(X = 0) = 0.5*(C_{3,0}.(0.5)^{0}.(0.5)^{3}) = 0.0625[/tex]

0.0625 * 100 = 6.25%

Rounding to the nearest tenth of a percent, the correct answer is:

B. 6.3%

Answer: C 1.6 APE.X approved

Answer:

The calculated value is "0.214"

Step-by-step explanation:

Given expression :

[tex]\bold {\frac{-2}{3}+ 1 -\frac{3}{\frac{2.8}{9}} }\\[/tex]

solution:

[tex]\Rightarrow \frac{-2}{3}+ 1 -\frac{3}{\frac{2.8}{9}}\\\\\Rightarrow \frac{-2}{3}+ 1 -\frac{3}{\frac{2.8}{\frac{9}{1}}}\\\\\Rightarrow \frac{-2}{3}+ 1 -\frac{3}{2.8} \times \frac{1}{9}}}\\\\\Rightarrow \frac{-2}{3}+ 1 -\frac{1}{8.4}\\\\\Rightarrow \frac{-16.8 + 25.2- 3}{25.2}\\\\\Rightarrow \frac{5.4}{25.2}\\\\\Rightarrow 0.214[/tex]

The amount of flour alice had used at the end of the week is;

Amount = ¹/₂ pounds

Amount of flour she had at the start of the week = 3¹/₄ pounds

Amount she had at the end of the week = 2³/₄ pounds

Thus;

3¹/₄ pounds = 13/4 pounds

2³/₄ pounds = 11/4 pounds

Thus,

amount of flour she used = amount at the start of week - amount left at end of week

The denominator is the same and so our solution is to just subtract the numerator and retain the common denominator. This gives;

Amount of flour she used = ¹/₂ pounds

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Answer:

(0,1)

Step-by-step explanation:

Any real number to the power of 0, including 6, is equal to 1. Therefore, f(0) is 1, and the y intercept is (0,1). Hope this helps!

Answer: 54 miles per hour

Step-by-step explanation:

Max travles to see his brother 's family by car and he drives 216 miles in 4 hours. To calculate his rate in miles per hour, we divide the amount of distance he travelled by the number of hours used. This will be:

Distance= 216 miles

Time taken= 4 hours

Speed = Distance travelled/Time taken

= 216/4

= 54 miles per hour

Answer:

20 +200

Step-by-step explanation:

Answer:

200 + 20h = x

could be wrong so sorry

Answer:

hard

Step-by-step explanation:

Answer:

d) none of the above

Step-by-step explanation:

correct me if wrong .

Final answer:

The equation tan^2(x) + 3 = 0 has no real solutions within the given range.

Explanation:

To solve the equation tan^2(x) + 3 = 0, we need to isolate the term with the tangent squared. Subtracting 3 from both sides gives us tan^2(x) = -3. Since the tangent function is positive for angles between 0° and 360°, it is not possible for the square of the tangent to be negative. Therefore, there are no real solutions to this equation, given the specified range of 0 ≦ x < 360°. So, the correct answer is (D) None of the above.

Answer:

The answer is c I think

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I took test and got 100%

Answer:

C. 16

Step-by-step explanation:

12÷2×3−(7−5) = 16.

I hope this helps!

Following the order of operations (PEMDAS/BODMAS), the expression simplifies as:- 12 ÷ 2 * 3 - (7 - 5) = 6 * 3 - 2 = 18 - 2 = 16. So, the value is 16.

To find the value of the expression 12 ÷ 2 * 3 - (7 - 5), we need to follow the order of operations, often remembered using the acronym PEMDAS (or BODMAS):

1. Parentheses (or Brackets): First, we evaluate what's inside the parentheses. In this case, (7 - 5) equals 2.

2. Exponents (or Orders): There are no exponents or orders in this expression.

3. Multiplication and Division: After dealing with parentheses, we move from left to right. So, 12 ÷ 2 * 3 is calculated as follows:

  12 ÷ 2 * 3 = 6 * 3 = 18

4. Addition and Subtraction: Again, we move from left to right. Now we subtract 2 (the result from step 1) from 18 (the result from step 3):

  18 - 2 = 16

So, the final answer is 16.

In summary, using the order of operations, the expression simplifies to 16. It's crucial to follow these rules to ensure that mathematical expressions are evaluated correctly, as different orders can lead to different results.

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