Find 4ab when (a+b)=15 and (a-b)=12

Answer:

x = 16

Step-by-step explanation:

3x + 1 = 49 ( vertical angles )

Subtract 1 from both sides )

3x = 48 ( divide both sides by 3 )

x = 16

Answer:

21 ounces of juice.

63 ounces of water

Step-by-step explanation:

let :

x = ounces of strawberry juice to make the strawberry infused water.

3x = ounces of water needed to make the strawberry infused water.

3x + x = 84

4x = 84

divide both sides of the equation by 4

x = 21 ounces

3x = 3 x 21 = 63 ounces

\(10x-8y =4~~~....(i)\\\\-5x+3y=-9~~~...(ii)\\\\\text{Multiply equation (ii) by} -2\\\\10x-6y = 18~~~...(iii)\\\\(iii)-(i):\\\\10x-6y - 10x +8y = 18 -4\\\\\implies 2y = 14\\\\\implies y= \dfrac{14}2 = 7\\\\\text{Substitute y = 7 in equation (i):}\\\\10x-8(7) =4\\\\\implies 10x - 56 =4\\\\\implies 10x = 4+56\\\\\implies 10x = 60\\\\\implies x = \dfrac{60}{10} = 6\\\\\\\text{Hence (x,y) = (6, 7)}\)

Answer:

\(\dfrac{3x-1}{2x^2-3x}\)

Step-by-step explanation:

Given rational expression:

\(\dfrac{x^{-1}+3x-4}{2x^2-5x+3}\)

First, we need to eliminate the negative exponent in the numerator.

To do this, multiply the numerator by x / x:

\(\begin{aligned}(x^{-1}+3x-4) \cdot \dfrac{x}{x}&=\dfrac{ x^{-1}\cdot x+3x\cdot x-4 \cdot x}{x}\\\\&=\dfrac{1+3x^2-4x}{x}\end{aligned}\)

Therefore:

\(\dfrac{x^{-1}+3x-4}{2x^2-5x+3}=\dfrac{\frac{1+3x^2-4x}{x}}{2x^2-5x+3}\)

\(\textsf{Apply\:the\:fraction\:rule:}\:\dfrac{\frac{a}{b}}{c}=\dfrac{a}{b\cdot \:c}\)

                       \(=\dfrac{1+3x^2-4x}{x\cdot (2x^2-5x+3)}\)

                       \(=\dfrac{3x^2-4x+1}{x(2x^2-5x+3)}\)

Factor the quadratics in the numerator and the denominator:

\(\begin{aligned}\textsf{Numerator:}\quad 3x^2-4x+1&=3x^2-3x-x+1\\&=3x(x-1)-1(x-1)\\&=(3x-1)(x-1)\end{aligned}\)

\(\begin{aligned}\textsf{Denominator:}\quad 2x^2-5x+3&=2x^2-2x-3x+3\\&=2x(x-1)-3(x-1)\\&=(2x-3)(x-1)\end{aligned}\)

Therefore:

\(\dfrac{x^{-1}+3x-4}{2x^2-5x+3}=\dfrac{(3x-1)(x-1)}{x(2x-3)(x-1)}\)

Factor out the common term (x - 1):

                      \(=\dfrac{3x-1}{x(2x-3)}\)

Simplify the denominator:

                      \(=\dfrac{3x-1}{2x^2-3x}\)

Therefore:

\(\dfrac{x^{-1}+3x-4}{2x^2-5x+3}=\boxed{\dfrac{3x-1}{2x^2-3x}}\)

Yes, Victor needs to have similar portion of the population in the sample.

What is population size?

The number of objects inside a geographical area that has been arbitrary assigned as the population size.

In a fair, unbiased poll

Population proportion plus random error equals sample proportion.

According to the Normal Approximation, the standard deviation of the distribution of these random mistakes across all feasible samples is

\(\sqrt{\frac{\text{Population proportion}(1-\text{Population proportion})}{n}}\)

The sample estimate's variance from the actual population value is known as the random error. Numerous alternative summaries, such as sample averages or discrepancies between two sample proportions or averages, are likewise consistent with the observation that random mistakes follow the normal curve.

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Answer:

soo u go 0.12*100

0.15*100

Answer:

A.

Step-by-step explanation:

when you distribute it you keep the subtraction sign and have to multiply 6 by 50 and then 6 by 1

It would take approximately 1.20 hours (or 1 hour and 12 minutes) for the runner to finish the 11 km race at a pace of 5.7 mi/hr.

To determine how long it would take a runner to finish an 11 km race at a pace of 5.7 mi/hr, we need to convert the pace from miles per hour to kilometers per hour. Once we have the pace in kilometers per hour, we can calculate the time it takes to cover 11 km.

1 mile is approximately equal to 1.60934 kilometers.

So, the pace of 5.7 mi/hr is equal to 5.7 * 1.60934 km/hr ≈ 9.17 km/hr.

Now, we can calculate the time it takes to cover 11 km at a pace of 9.17 km/hr:

Time = Distance / Speed

Time = 11 km / 9.17 km/hr

Time ≈ 1.20 hours

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The probability that a high school student did not cheat is 0.51, the probability in the survey that a student did not cheat last year is 0.549, the sampling error is -0.0039 and the margin of error is 0.549 ± 0.0067.

a. The national percentage of high school students that reported they didn't cheat on a test last year is 51%. Therefore, the probability that a high school student did not cheat last year is:

p = 0.51

b. In the survey, 11,731 out of 21,413 students said that they have not cheated on one or more tests in the last year. Therefore, the sample proportion or the probability in the survey that a student did not cheat last year is:

p1 = 11,731/21,413 ≈ 0.549

c. The sampling error is the difference between the population proportion (p) and the sample proportion p1). Therefore, the sampling error is:

sampling error = p - p1 = 0.51 - 0.549 = -0.039

d. The margin of error (MOE) is the maximum expected difference between the sample proportion (p1) and the population proportion (p) due to chance. A common formula for the margin of error is:

MOE = z√[(p1(1-p1))/n]

Where z is the z-score corresponding to the desired level of confidence, and n is the sample size.

Assuming a 95% level of confidence, the z-score is 1.96. Therefore, the margin of error is:

MOE = 1.96√[(0.549(1-0.549))/21413] ≈ 0.0067

So we can say with 95% confidence that the true proportion of high school students who did not cheat on a test last year is between:

0.549 - 0.0067 = 0.5423

and

0.547 + 0.0067 = 0.5557

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The system of equations {y = x^2 + 5x - 2, y = 3x - 2} intersects at the points (0, -2) and (-2, -8).

To find the points of intersection of the given system of equations, we need to solve them simultaneously.

Let's denote the first equation as Equation 1 and the second equation as Equation 2.

Equation 1: \(y = x^2 + 5x - 2\)

Equation 2: \(y = 3x - 2\)

To find the points of intersection, we'll set Equation 1 equal to Equation 2:

\(x^2 + 5x - 2 = 3x - 2\)

Now, let's solve this quadratic equation:

\(x^2 + 5x - 2 - 3x + 2 = 0\)

\(x^2 + 2x = 0\)

Factoring out x, we have:

\(x(x + 2) = 0\)

Setting each factor equal to zero, we find two possible values for x:

x = 0 or x + 2 = 0

For x = 0:

Substituting x = 0 into Equation 2:

\(y = 3(0) - 2\)

\(y = -2\)

So, we have one point of intersection: (0, -2).

For \(x + 2 = 0\):

Solving for x:

x = -2

Substituting x = -2 into Equation 2:

\(y = 3(-2) - 2\)

\(y = -8\)

So, we have another point of intersection: (-2, -8).

Therefore, the system of equations \([y = x^2 + 5x - 2, y = 3x - 2]\) intersects at the points (0, -2) and (-2, -8).

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Answer:

C, 10^3

Step-by-step explanation:

To get from 22 to 22000, you need to times by 1000. The power in this case represents the amount of zeros added to a number. Hope this helped!

10³ multiply 22 by to get an answer of 22,000.

The correct option is (D)

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

We have to multiply 22 such that it gives 22, 000.

let the number that being multiplied be x.

So, 22x = 22000

x= 22000/22

x= 1000

x= 10³

Hence, 10³ multiply 22 by to get an answer of 22,000.

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Answer:

15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

:) Have a good day!

Answer:

x = 0 x = 1/3

The fourth-order accurate finite difference approximation is:

u00(x) = c−2u(x − 2h) + c−1u(x − h) + c0u(x) + c1u(x + h) + c2u(x + 2h) + O(h4).

Compute the coefficients using the matlab code fdstencil.m and check that they satisfy the system you determined in part (a).

Test this finite difference formula to approximate u

00(1) for u(x) = sin(2x) with values of h from the array hvals = log space(-1, -4, 13). Make a table of the error vs. h for several values of h and compare against the predicted error from the leading term of the expression printed by  fdstencils.

You should observe the predicted accuracy for larger values of h. For smaller values, numerical cancellation in computing the linear combination of u values impacts the accuracy observed.

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Answer:

ratio of manga to anime: 7 : 56

Explanation:

Here we see light novels common in both, but has different ratio, in order to make them same and join them together, equal the ratio to "6", for light novels.

→ manga to light novels:  ( 7 : 6 ) * 1        → novels to anime: ( 3: 28 ) * 2

                                         →  7 : 6                                           →  6 : 56

Now

\(\\ \tt\rightarrowtail 7:6=6:56\)

\(\\ \tt\rightarrowtail 7;56\)

The ratio is 7:56

RHS criterion of congruence stands for Right Angle-Hypotenuse-Side.

According to the RHS congruence theorem, two right-angled triangles are congruent if their respective hypotenuses and sides are the same as those of another right-angled triangle.

Only right-angled triangles may use this rule.

An important point to note here is that when we keep hypotenuse and any one of the other 2 sides of two right triangles equal, we are automatically getting three similar sides, as all three sides in a right triangle are related to each other and that relation is popularly known as Pythagoras theorem.

hypotenuse²=base²+perpendicular²

So, in two right triangles, if the length of the base and hypotenuse are 3 units and 5 units respectively, then the perpendicular of both the triangles is of length 4 units.

Applying, hypotenuse²=base²+perpendicular²

5²=3²+perpendicular²

25=9+perpendicular²

perpendicular²=16

perpendicular=√16 = 4 units

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Answer:

Step-by-step explanation:

Answer:First, write the expression

✔ p – 5

.

Second,

✔ substitute

7 in for the variable, p.

Third,

✔ simplify

by

✔ subtracting

7 and 5.

The answer is

✔ 2

Step-by-step explanation:

The present value today of four years of college costs starting 18 years from today, assuming a discount rate of 8% compounded annually, is approximately $290,360.

To calculate the present value, we need to discount the future college costs back to the present using the discount rate of 8%. The formula for calculating the present value of a future cash flow is:

Present Value = Future Value / \((1 + Discount Rate)^{n}\)

Here, the future value is $100,000 per year for four years, and n is the number of years from today to when the college costs start, which is 18 years. Plugging in these values into the formula, we get:

Present Value = ($100,000 / \((1 + 0.08)^{18}\)) + ($100,000 /\((1 + 0.08)^{19}\)) + ($100,000 / \((1 + 0.08)^{20}\)) + ($100,000 / \((1 + 0.08)^{21}\))

Evaluating this expression, we find that the present value today of the four years of college costs is approximately $290,360.

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The given relations are as follows:

(a) UCP KC
(b) a = (KRT)^(1/2), for an ideal gas

To demonstrate the validity of these relations, let's break them down step by step:

(a) UCP KC:
This relation states that UCP is equal to KC.

First, let's understand the variables involved:
- U is the internal energy of the fluid.
- C is the heat capacity of the fluid.
- P is the pressure of the fluid.
- K is a constant.

To show the validity of this relation, we need to know that UCP is constant. In other words, the internal energy multiplied by the heat capacity is always constant. This is true for many substances, including fluids. Therefore, we can say that UCP = KC.

(b) a = (KRT)^(1/2), for an ideal gas:
This relation states that the speed of sound, a, for an ideal gas is equal to the square root of KRT.

Again, let's understand the variables:
- a is the speed of sound.
- K is a constant.
- R is the ideal gas constant.
- T is the temperature of the gas.

To demonstrate the validity of this relation, we need to look at the equation that relates the speed of sound to the density and the compressibility of the fluid. For an ideal gas, the compressibility factor is equal to 1. Therefore, we can use the equation a = (KRT)^(1/2), where the compressibility factor is implicitly assumed to be 1.

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By recognizing the relationship between Exponentiation and logarithms, we can transform the given expression into a more concise and equivalent form.

To rewrite the expression 3 log(5) in the form log(c), we can use the logarithmic property that states log(a^b) = b log(a). Applying this property, we have:

3 log(5) = log(5^3)

Simplifying further, we find that 5^3 is equal to 125:

3 log(5) = log(125)

Therefore, we can rewrite 3 log(5) as log(125).

In summary, the expression 3 log(5) can be rewritten as log(125) using the logarithmic property. It is important to understand logarithmic properties and their application to manipulate and simplify expressions involving logarithms. By recognizing the relationship between exponentiation and logarithms, we can transform the given expression into a more concise and equivalent form.

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Answer:

Step-by-step explanation:

2(x+y)=32  means :

x+y =16

Answer:

Using inverse operations to isolate teh variable 'X'.

Step-by-step explanation:

THE FIRST STEP IS TO MULTIPLY EACH AND EVERY TERM IN THE BRACKETS BY 5

\(5(2x) + 5(7) - 15 = 15 \\ 10x + 35 - 15 = 15\)

THEN GROUP THE LIKE TERMS TOGETHER. WHEN TERMS MOVE ACROSS THE EQUAL SIGN THEY CHANGE SIGNS.

\(10x = 15 - 35 + 15 \\ 10x = - 5\)

\( \frac{10x}{10} = \frac{ - 5}{10} \\ x = \frac{ - 5}{10} \\ x = - \frac{1}{2} \)

ATTACHED IS THE SOLUTION

P = 90 is the solution for the given equation.

Given: Qd=95−4

PQs=5+P

To find Qd if P=5:

Put P = 5 in the equation

Qd=95−4P

Qd = 95 - 4 x 5

Qd = 75

So, Qd = 75.

To find P if Qs = 20:

Put Qs = 20 in the equation

Qs = 5 + PP

= Qs - 5P

= 20 - 5P

= 15

So, P = 15.

To solve Qd=Qs, substitute Qd and Qs with their respective values.

Qd = Qs

95 - 4P = 5 + P

Subtract P from both sides.

95 - 4P - P = 5

Add 4P to both sides.

95 - P = 5

Subtract 95 from both sides.

- P = - 90

Divide both sides by - 1.

P = 90

Thus, P = 90 is the solution for the given equation.

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Using the Pigeonhole Principle, it can be shown that in a set of n positive integers, none exceeding 2n, there is at least one integer that divides another integer.

We can prove this statement by contradiction using the Pigeonhole Principle.

Suppose we have a set of n positive integers, none of which exceed 2n, and assume that no integer in the set divides another integer.

Consider the prime factorization of each integer in the set. Since each integer is at most 2n, the largest prime factor in the prime factorization of any integer is at most 2n.

Now, let's consider the possible prime factors of the integers in the set. There are only n possible prime factors, namely 2, 3, 5, ..., and 2n (the largest prime factor).

By the Pigeonhole Principle, if we have n+1 distinct integers, and we distribute them into n pigeonholes (corresponding to the n possible prime factors), at least two integers must share the same pigeonhole (prime factor).

This means that there exist two integers in the set with the same prime factor. Let's call these integers a and b, where a ≠ b. Since they have the same prime factor, one integer must divide the other.

This contradicts our initial assumption that no integer in the set divides another integer.

Therefore, our assumption must be false, and there must be at least one integer in the set that divides another integer.

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Answer:

Eww your ugly

Step-by-step explanation:

it is too messy

Answer:

-2/15

Step-by-step explanation:

8/15-2/3

8/15-10/15

-2/15

Common Denominator

The equation of the line passing through the point (-2, 5) and perpendicular to the line 6x + 2y = 8 is \(y = \frac{1}{3}x + \frac{17}{3}\).

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line:

6x + 2y = 8

Solve for y:

2y = -6x + 8

y = -3x + 4

From the equation above, we can see that the slope of the given line is -3.

The negative reciprocal of -3 is 1/3.

So, the slope of the line perpendicular to the given line is 1/3.

Plug the slope m = 1/3 and point (-2,5) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

\(y - 5 = \frac{1}{3}( x + 2) \\\\y - 5 = \frac{1}{3}x + \frac{2}{3} \\\\y = \frac{1}{3}x + \frac{17}{3}\)

Therefore, the equation of the line is \(y = \frac{1}{3}x + \frac{17}{3}\).

The complete question is:

Find the equation of the line passing through the point (−2,5) that is perpendicular to the line 6x + 2y = 8.

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Answer:

36

Step-by-step explanation:

2(10)+4^2

20+4^2

20+16

36

Answer: The result of the math formula =2*10+4^2 is 28.

To calculate this formula, you first need to perform the exponentiation operation of 4^2, which is 16. Then, you multiply 2 by 10, which gives you 20. Finally, you add 20 to 16, which gives you the final answer of 28.

Here's the solution,

The given triangle is a right angled triangle,

So, by Using Trigonometry :

=》

\( \sin(30) = \dfrac{x}{13} \)

=》

\( \dfrac{1}{2} = \dfrac{x}{13} \)

=》

\(x = \dfrac{13}{2} \)

=》

\(x = 6.5\)

hence, value of x = 6.5 units