which of the following best describes the solution to the equation below?
x^2=2
A. It is a repeating decimal
B. It is greater than zero but less than one
C. It is a fraction
D. It is an irrational number​

\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

I think I need to know what the cat weighs first...

Answer:

d. x^8

Step-by-step explanation:

hope this helps :)

The increase in the minimum wage from $8.10 to $15, indicates that the percentage increase in the minimum wage is 85.\(\overline{185}\)%

A percentage represent the number, amount, proportion or ratio of an item to another (possibly larger) item per hundred (100) units of the comparison or larger item.

Percentages, quantitatively describes the idea of the amount of a substance. It is a measure of the amount or occurrence of an item.

The specified original minimum wage at Ben's Burger = $8.10

The new amount to which the minimum wage is increased = $15

The percentage increase can be obtained using the formula;

\(\% \ increase = \frac{New - Original}{Original} \times 100\)

The percentage increase is therefore; ((15 - 8.10)/8.1) × 100 = 85.\(\overline{185}\) %

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Water is the Adjacent of this right triangle. 350 yards is the length of the Hypotenuse. We have given angle B, 40 degrees.

_________________________________________________________

According to SOH CAH TOA, we use CAH (cosineΘ = adjacent/hypotenuse).

cosine40 = x/350

[multiply both sides by 350]

350 · cosine40 = x

[put calculator in degree mode]

x ≈ 268 yards

So, the distance across the water from sailboat to the island is 268 yards.

_________________________________________________________

Let's use pythagorean theorem since we already know the adjacent and hypotenuse to find the opposite (opposite is also known as height).

a^2 + b^2 = c^2

a^2 + (268)^2 = (350)^2

a^2 + 71824 = 122500

a^2 = 122500 - 71824

a^2 = 50676

[square both sides]

\(\sqrt{a^2}\) = \(\sqrt{50676}\)

a = \(\sqrt{50676}\)

a ≈ 225

So, the height, opposite, of the lighthouse is 225 yards.

_________________________________________________________

Answer:

this is true because he knows that 8 times 4 is 32 then he will automatically know that 8 divided by 32 will be 4 since 8 was a factor.

Step-by-step explanation:

I suck at explaining stuff but yeah this is true bc two factors of a number divided by it will always be the other factor yk

Answer:

i just needed points sorry

Step-by-step explanation:

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Answer:she will have $25 left .

Step-by-step explanation:

0.25(60)  = 15

$40 - $15 = $ 25

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer:

350,000

Hope this helps !!!

The equivalent equation to the (x² - 5)² - 3x² + 15 = -2 in form of 'm' is given by option c.  m² -3m + 2 = 0.

The equation is equal to,

(x² - 5)² - 3x² + 15 = -2

let the value of m be equals to x² - 5.

Simplify the equation we have,

⇒ ( x² - 5 )² - 3x² + 15 = -2

Take '3' common factor from the 3x² + 15 so that it get convert into x² - 5 we get,

⇒ ( x² - 5 )² - 3 (x² - 5 )  = -2

Now replace x² - 5 by m to get the equivalent equation,

⇒ ( m )² - 3 (m ) = -2

⇒ m² -3m + 2 = 0

Therefore, the equivalent equation to the given equation is written as option c.  m² -3m + 2 = 0.

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Answer:

Step-by-step explanation:

The first 2 pieces of this function agree at pi/4, so we will set them equal to each other and sub in pi/4 for x to solve for k:

\(ksin(\frac{\pi}{4})+(\frac{\pi}{4})^2=\frac{\pi}{4}+2\) and

\(k(\frac{\sqrt{2} }{2})+\frac{\pi^2}{16}=\frac{\pi}{4}+2\) and we'll multiply everything by 16 to get rid of the fractions. Doing that gives us:

\(8k\sqrt{2}=4\pi+32-\pi^2\) and

\(k=\frac{4\pi+32-\pi^2}{8\sqrt{2} }\) so

k = 3.067

The next one is a bit tricky if you're not up on your natural log equations.

Again, we set these equal to each other because they meet at the value of e. We sub in e for x and solve for m:

\(x +2=mlne^x\)

We'll sub in e for x. ln of e to the x power is equal to x, so

e + 2 = me and

\(m=\frac{e+2}{e}\) so

m = 1.736

Hope that helps!

Answer:

The perimeter of a rectangle is:

Step-by-step explanation:

Given

The width of a rectangle w =  8n - 8.5 feet

The length of a rectangle l = 8.5n + 10 feet

To determine

The perimeter of a rectangle = P = ?

The perimeter of a rectangle can be determined using the formula

\(P = 2(l+w)\)

substitute l = 8.5n + 10 and w = 8n - 8.5

\(P=2\left(8.5n+10+8n-8.5\right)\)

   \(=2\left(16.5n+10-8.5\right)\)

   \(=2\left(16.5n+1.5\right)\)

   \(=33n+3\)

Therefore, the perimeter of a rectangle is:

This tells us that the matrices are linearly dependent.

If a, b is a multiple of c, d, and abcd is 0, then we can write this as a matrix equation:

[a b] [c] [0]

[c d] [d] = [0]

This tells us that the matrix [a b] is a left-multiple of the matrix [c d]. In other words, there exists some scalar k such that [a b] = k[c d].

From this, we can see that a, c is a multiple of b, d. This is because a = kc and b = kd. Therefore, a is a multiple of c, and b is a multiple of d.

This tells us that the matrices are linearly dependent. In general, whether a matrix is a multiple of another matrix or not depends on the specific elements of the matrices. In order to determine if a matrix is a multiple of another, one can use matrix algebra and linear algebra techniques to simplify the matrices and look for patterns.

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A random variable assigns one and only one numeric value to each experimental outcome.

A random variable used in experimental trials assign numerical values to the members or elements of the trial. This random variable is used to study the outcome of a trial conveniently.

A random variable assigns one and only one numeric value to each experimental outcome. This assigned numeric value may not be exact. In an experimental trial the possible outcomes are denoted by a random variable. So these values are just practically assigned and not theoretically exact.

There are discrete and continuous random variables. They are usually denoted by capital letters such as X, Y,.. etc. These random variables are used to calculate the probability of each outcome in a trial.

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When we subtract 3xy from 5 we will get 3xy - 5.Both are different 3xy is a polynomial in xy and 5 is a constant we can not simplify further.

First, let's try to learn subtraction in the case of polynomials.

3xy is a polynomial.

5 is a constant.

Polynomials can be subtracted using a method that involves changing the signs to the opposite sign. The process resembles adding polynomials. Depending on the specific equation, we transform the sign while subtracting polynomials to either positive or negative. Learn more about subtracting polynomials, their techniques, procedures, and examples by reading on.

For instance, subtract 5x + 8y - 20z from 4x - 10y + 15z.

The polynomials should first be arranged in standard form. In this illustration, it has already been set up.

Place them horizontally in step two.

(4x - 10y + 15z) - (5x + 8y - 20z)

Step 3: By using parenthesis, modify the second polynomial's sign.

4x-10y-15z, and 5x+8y 20z

Step 4: Group terms that are similar together.

4x - 5x - 10y - 8y + 15z + 20z

Step 5: Resolve the problem

-x - 18y + 35z

As a result, we get -x - 18y + 35z when we subtract 4x - 10y + 15z from 5x + 8y - 20z.

In the same way, if we subtract 3xy from 5 we will get 3xy - 5.

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Answer:

How do I take 20 % off a price?

Take the original price.

Divide the original price by 5.

Alternatively, divide the original price by 100 and multiply it by 20.

Subtract this new number from the original one.

The number you calculated is the discounted value.

Enjoy your savings!

Step-by-step explanation:

The statement is true and the function f(x) = ln(x)/x is a solution of the differential equation x^2y' + xy = 1.

To determine whether the statement is true or false, we need to check whether the function f(x) = ln(x)/x satisfies the differential equation x^2y' + xy = 1.
Differentiating f(x) with respect to x, we get:
f'(x) = (1 - ln(x))/x^2
Substituting y = f(x) and y' = f'(x) into the differential equation, we get:
x^2f'(x) + xf(x) = 1
Substituting the expression for f'(x) we derived earlier, we get:
x^2[(1 - ln(x))/x^2] + x[ln(x)/x] = 1
Simplifying, we get:
1 - ln(x) + ln(x) = 1
The equation simplifies to 1 = 1, which is always true.
Therefore, the statement is true and the function f(x) = ln(x)/x is a solution of the differential equation x^2y' + xy = 1.
In conclusion, we have verified that the given function satisfies the differential equation. The importance of checking whether a given function satisfies a differential equation lies in its applications, as it enables us to model various physical and natural phenomena.

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the sum of the arithmetic series with 50 terms, a first term of 9, and a 50th term of 331 is 8500. This means that if we add up all the numbers in the series, the resulting sum will be 8500.

To explain further, an arithmetic series is a sequence of numbers in which the difference between consecutive terms remains constant. In this case, we are given that the first term, a, is 9 and the 50th term, t50, is 331.

To find the sum of the series, we use the formula Sn = (n/2)(a + tn), where Sn represents the sum of the series, n is the number of terms, a is the first term, and tn is the nth term.

Substituting the given values, we have Sn = (50/2)(9 + 331), which simplifies to Sn = 25(340) = 8500.

Hence, the sum of the arithmetic series with 50 terms, a first term of 9, and a 50th term of 331 is 8500. This means that if we add up all the numbers in the series, the resulting sum will be 8500.

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Answer:

1568 in^3

Step-by-step explanation:

Answer:

Volume = 1,568

Step-by-step explanation:

V = Bh

B = 17.5 x 14 = 245

h = 6.4

245 x 6.4 = 1,568

The easier way:

17.5 x 14 x 6.4 = 1,568

Let me know if this helps!

The perimeter of Todd’s sandbox is; 20.8 feet.

Applying the similarity of triangles.

Consider 'x' and 'y' be the two unknown sides of triangle.

14/ x = 20/8 = 18/y

14/ x = 20/8

x = 14*8 / 20

x = 5.6

20/8 = 18/y

y = 18*8 / 20

y = 7.2

Perimeter of Todd’s sandbox,

= x + y + 8

= 5.6 + 7.2 + 8

= 20.8

Thus,  the perimeter of Todd’s sandbox is 20.8 feet.

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Answer:

x=-2

Step-by-step explanation:

The mean of a binomial distribution when X = 4, where n = 8 and p = 0.20 is given as follows:

The formula for calculating the mean of a binomial distribution is:

mean = np.

We know that n = 8, and p = 0.20, so

mean = 8(0.20)

         = 1.6

The binomial distribution is a type of probability distribution in which there are only two possible outcomes: success or failure. The number of trials is usually fixed, and each trial is independent. It is often used to model the number of successes in a fixed number of trials.

The mean of a binomial distribution is a measure of the average number of successes in a given number of trials. It is calculated by multiplying the number of trials by the probability of success. In this case, we know that there are 8 trials and the probability of success is 0.20.

Therefore, the mean is 1.6

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Tables can help to see patterns in data. Tables make the most difficult problems much easier. These are the advantage to using tables.

The reader can immediately examine the results by using tables to organize data that is too complex or detailed to be fully described in the text. By omitting numerical data from the text, they can be used to highlight trends or patterns in the data and to improve the readability of manuscripts. A table is a way to organize information or data, usually in rows and columns but sometimes with more complicated structures. In research, communication, and data analysis, tables are frequently employed. Large amounts of numerical or statistical data can be efficiently and effectively represented using scientific tables and graphs. In contrast to reading a verbose description of the information, readers are frequently drawn to tables and figures because they view them as being easier to understand.

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Answer:

\(k=\frac{6+z}{3}\)

Step-by-step explanation:

We are given the following equation:

6k - 2z = 12

We want to solve it for k.

To do that, we need to isolate the variable on one side.

6k - 2z = 12

To start, add 2z to both sides.

6k - 2z = 12

     +2z    +2z

______________

6k = 12 + 2z

now, divide by 6 on both sides. When dividing on the left, we're dividing the entire expression by 6.

6k = (12 + 2z)

÷6    ÷6

______________

\(k=\frac{12+2z}{6}\)

This can be simplified to become:

\(k=\frac{6+z}{3}\)

Answer:

\(\sf{k=2+\dfrac{1}{3}z}\)

Explanation:

Our equation is

\(\sf{6k-2z=12}\)

We need to solve it for k. So I am going to start by adding 2z on each side:

\(\sf{6k=12+2z}\)

Then, I'll divide each term by 6:

\(\sf{k=\dfrac{12}{6}+\dfrac{2z}{6}}\)

\(\sf{k=2+\dfrac{1}{3}z}\)

Hence, this is the equation.

Answer:

1156528

Step-by-step explanation:

you multiply all of the numbers to get it i think hope this helps

The total lifetime of all batteries in a package exceeds that value for only 5% of all packs will be 43.29.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

\(\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}\)

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

It is given that,

mean,μ=10 hr

standard deviation,σ=1hr

n=4

The lifespan of four batteries combined is,

=4μ

=4×10

=40 hr

z = (x-μ)/σ

1.645=(x-40)/2

x-40=3.29

x=43.29

Thus, the total lifetime of all batteries in a package exceeds that value for only 5% of all packs will be 43.29.

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Answer:

CSA of cylinder = 704cm²

We know that

CSA of cylinder = 2πrh

or 2πrh = 704

or, 2*22/7 *8 *h = 704 ( since r=8cm)

or, 352h = 704*7

or, h = 4928/352 = 14cm