Prove that the difference between quare of conecutive even number i alway a multiple of 4
let n tand for any integer in your working

Answer:

 ( -5•2x8y)

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "^-1" was replaced by "^(-1)".

Equation at the end of step 1

 ((5•(x3))•(y2))•(0-(2x5•y(-1)))

Equation at the end of step

 (5x3 • y2) •  -2x5y(-1)

Multiplying exponential expressions :

3.1    x3 multiplied by x5 = x(3 + 5) = x8

Multiplying exponential expressions :

3.2    y2 multiplied by y(-1) = y(2 + (-1)) = y1 = y

Answer:

 60xy

Step-by-step explanation:

Evaluate :  (5x+3y)2   =    25x2+30xy+9y2

Evaluate :  (5x-3y)2   =    25x2-30xy+9y2

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Answer:

There are 192 employees in the company.

Step-by-step explanation:

Let x be the total number of employees

Use ratio and proportion

\(\frac{120}{x} =\frac{5}{8} \\5x = 120(8)\\5x = 960\\\frac{5x}{5} = \frac{960}{5} \\x = 192\)

x = 192

Answer: The answer is 27

Step-by-step explanation:

if a=5 and b=10 and c=12 then just put the numbers in place of the letters so that's going to be :

P=5+10+12
P=15+12
P=27

Answer:

it is 8

Step-by-step explanation:

because EG is E+G which is 8+3 which equals 11 so it is 8

Answer:

I dont know the answer but maybe this page can help, it even gives you the explanation or the steps.

Explanation:

symbolab.com

Answer:

Option A

Step-by-step explanation:

To find out if a function is nonlinear, you can graph the points in the table. If it forms a straight line, then it is linear. If it does not, then it is nonlinear.

1) Let's graph three points from Option A's table. Graph (1,3), (2,9), and (3,27) and see if you can draw a completely straight line passing through them. When you do, you will have something similar to the picture below. The line they form is not straight, therefore Option A is a nonlinear function.

Answer:

It will be 381. You round up if it is five and over, and round down if 5 and below.

Step-by-step explanation:

A decimal cannot be a whole number so rounding to the nearest whole number means getting rid of the decimal. You do this by rounding up if it 5 and up, and rounding down if it is 5 and below. 380.5 means you would round up to 381. If it it were 380.4, you would round down to 380.

Answer:

381

Step-by-step explanation:

any number 5 and over will round up

Answer:

two and a half to three and one third

Step-by-step explanation:

Answer:

R = 19.17 ohms

Step-by-step explanation:

Given that,

The voltage of a subwoofer, V = 115 V

The current through its coil, I = 6 A

We need to find the resistance of the subwoofer. Let it s R. Using Ohm's law to find it such that,

V = IR

So,

\(R=\dfrac{V}{I}\\\\R=\dfrac{115}{6}\\\\R=19.17\ \Omega\)

So, the resistance of the subwoofer is 19.17 ohms.

Answer:

a) 5/7 b) 12/8, 1 4/8

Step-by-step explanation:

Answer:

a) 5/7

b) 2/3

c) 1/6

Step-by-step explanation:

a) 2/7 + 3/7

since the denominators are both 7 we use 7 as the LCM ( lowest common multiple)

2+3/7 = 5/7

b) 5+7/8 = 12/8. 4 can go into both numbers so it gives 3/2

c) 2/3 - 1/2 multiply the denominator since they are different (3×2) =6

4-3/6 = 1/6

Answer:

Step-by-step explanation:

No, the presence of an effect does not necessarily imply that error variance will go away.

The presence of an effect does not necessarily imply that error variance will go away. In fact, error variance is an inherent part of any statistical model and represents the amount of variation in the response variable that is not explained by the predictor variables.

Even if a predictor variable has a significant effect on the response variable, there may still be some unexplained variation in the response that is attributable to error variance.

It is important to take into account and control for error variance in any statistical analysis, as it can affect the precision and accuracy of the estimates of the model parameters and can also influence the interpretation of the results.

One way to control for error variance is to use appropriate statistical methods, such as analysis of variance (ANOVA), regression analysis, or other modeling techniques that take into account the variability in the data.

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To find the value of C, we can use the formula for the gradient (slope) of a line, which is the change in y divided by the change in x between two points on the line. In this case, the points are A(5, -C²) and B(C, -3).

The gradient (m) is given by:

m = (change in y) / (change in x)

Let's calculate the change in y and the change in x:

Change in y = y₂ - y₁

= (-3) - (-C²)

= -3 + C²

Change in x = x₂ - x₁

= C - 5

Now, using the gradient formula:

C = (change in y) / (change in x)

= (-3 + C²) / (C - 5)

We can solve this equation for C. Multiplying both sides by (C - 5) gives:

C(C - 5) = -3 + C²

C² - 5C = -3 + C²

-5C = -3

C = -3 / -5

C = 3/5

Therefore, the value of C is 3/5.

Answer:

Y/X=

172.50/23=

7.50/1

Step-by-step explanation:

The value of the angle \(y\) within the quadrilateral \(OABC\) inscribed the circle is 142°.

Let suppose that quadrilateral \(OABC\) is a parallelogram. Then, the following conditions must be fulfilled:

In addition, if we have a rhombus we have the additional condition as A, B and C lie on the circle:

\(\overline{OA} \cong \overline {AB} \cong \overline {BC} \cong \overline{OC}\) (4)

If we know that \(\angle AOC = 142^{\circ}\), then the value of \(\angle ABC = y = 142^{\circ}\).

Based on all these finding, we conclude that the value of the angle \(y\) within the quadrilateral \(OABC\) inscribed the circle is 142°.

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The level surfaces of f(x, y, z) = x² + y² + z² are spheres. To find the level surfaces, we set f(x, y, z) equal to a constant c.

This gives us the equation x² + y² + z² = c. This is the equation of a sphere with center at the origin and radius √c.

For example, if c = 1, then the level surface is the sphere x² + y² + z² = 1. This is a sphere with radius 1.

The level surfaces are all spheres because the function f(x, y, z) is a sum of squares. This means that the level surfaces are all concentric spheres.

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Answer:

Step-by-step explanation:

Point of intersections of the graph with x-axis are not clear.

Let these points are x = -a, -b and c

Therefore, function representing the graph will be,

f(x) = p(x + a)(x + b)(x - c)

Since, this graph crosses y-axis at (0, -6),

f(0) = p(0 + a)(0 + b)(0 - c) = -6

-pabc = -6

p = \(\frac{6}{abc}\)

Therefore, equation of the given function will be,

f(x) = \(\frac{6}{abc}(x+a)(x+b)(x-c)\)

Answer:

375

Step-by-step explanation:

3x5=15

15X5=75

75x5=375

Answer: 375

Step-by-step explanation: Hello!

First, we need to identify what the sequence is.

It seems to multiplied by 5 every time.

3x5=15x5=75x5=?

So if we follow that sequence we can determine the next one will be

75 x 5

which equals

375

75x5=375

Hope this helps!

The solution of the given linear equation can be obtained as x = 0.4.

The distributive property states that the product of a number and the sum of other numbers is equal to the sum of their individual products.

It can be expressed as a(b + c + d) = ab + ac + ad.

The given linear equation can be solved as follows,

-2.5(4x - 4) = -6

Use distribute property in the RHS to obtain,

-2.5 × 4x - 2.5 × -4 = 6

=> -10x + 10 = 6

=> -10x = -4

=> x = 0.4

Hence, the given equation can be solved as x = 0.4.

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Error is distributing 7 to both the numerator and denominator of the second term. Correction: multiply the second term by (x/x) to obtain a common denominator. The correct solution is \((5x^2+7x)/(x(x+7))\) in rational expression.

The error that the student made in their solution is that they incorrectly distributed the 7 to both the numerator and denominator of the second term. This mistake led to an incorrect addition of two rational expressions.

To correct error, the student should've multiplied the second term by (x/x), which is equivalent to multiplying by 1 and won't change value of the rational expression. This would have given:

\(5x/(x+7) + 7/x * (x/x) = 5x/(x+7) + 7x/(x(x+7))\)

Now, to add these two rational expressions, we need to find a common denominator. In this case, the common denominator is (x+7)x. Therefore, Multiply first term by x/x and simplify:

\(5x/(x+7) * (x/x) = 5x^2/(x(x+7))\)

Now, add two rational expressions:

\(5x^2/(x(x+7)) + 7x/(x(x+7)) = (5x^2+7x)/(x(x+7))\)

Thus, the correct solution is:

\((5x^2+7x)/(x(x+7))\)

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Answer:

4,20,11,2,1y

Step-by-step explanation:

The first graph has a constant additive rate of change of -1/4.

First of all, when we talk about a rate of change, that means a linear relation between variables, which is proper of a linear function represented by the first function showed in the image.

Also, if you observe the linear graph, you would see that the line represents a negative rate of change, because the line is going down (the function is decreasing). In other words, as x-variable increases, y-variable decreases.

Therefore, the first graph shows a ratio of change of -1/4.

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The contrapositive of the theorem: "for any two real numbers, x and y, if x and y are both rational then x + y is also rational" is given by this:

If x + y is irrational then x is irrational or y is irrational.

If we have two statements p and q, such that p ⇒ q, then the contrapositive of this relation is q' ⇒ p', that is negative of q implies a negative of p.

Let our statements be,

p: x and y are both irrational

∴ p': x is irrational or y is irrational

q: x + y is irrational.

∴ q': x + y is irrational.

The given theorem is the relation, p ⇒ q.

We are asked to find the contrapositive of this theorem. The contrapositive of the relation is, q' ⇒ p'.

This relational statement is:

If x + y is irrational then x is irrational or y is irrational.

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To find the expected number of times Joan rolls a 3, we use the formula for mean of a binomial distribution.

The correct option is, option (C) 6.

The probability of rolling a number 3 on any given roll is 1/4

If Joan rolls the die 20 times, the number of times she rolls a 3 will follow a binomial distribution with n = 20 (number of trials) and p = 1/4 (probability of success).

The formula for the probability mass function of a binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the random variable representing the number of successes (the number of times Joan rolls a 3), k is the number of successes, n is the number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

Using this formula, we can calculate the probability of rolling a 3 exactly k times out of 20 rolls:

P(X=k) = (20 choose k) * (1/4)^k * (3/4)^(20-k)

To find the expected number of times Joan rolls a 3, we can use the formula for the mean of a binomial distribution:

E(X) = n * p

In this case, E(X) = 20 * 1/4 = 5

Therefore, the expected number of times Joan rolls a 3 is 5.

Since the possible answers are integers, the closest answer to 5 is 6. Therefore, the answer is (C) 6.

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The statements that are true from the list of options are x = 7, y = 10 and QM = 38

Given that

This means that

NM = LM

So, we have

7x - 18 = 31

This gives

7x = 49

So, we have

x = 7

Next, we have

QM = PM

So, we have

6x - 4 = 5y - 12

So, we have

6(7) - 4 = 5y - 12

This gives

5y = 50

So, we have

y = 10

Calculating the lengths, we have

QM = 6(7) - 4

QM = 38

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Answer:

2.50 or 2.5

Step-by-step explanation:

1/4=.25 so 25% of a number=5/8=0.625

So we multiply .625*4 to get the number. Since it's 25% and we want 100% to get it back to the original number

.625*4=2.50 or 2.5

Step-by-step explanation:

\(the \: length \: of \: the \: ladder \: becomes \: the \: hypotenuse \: \)

\(the \: base \: becomes \\ = \sin( \alpha ) \times hypotenuse \\ = \sin(12) \times 15 \\ = 3.119ft\)