In a secondary school there are 40 classes altogether.
8 of the classes are Year 7 classes.
What fraction of the classes in the school are Year 7?
Give your answer in its simplest form.

Answer:

Step-by-step explanation: 1. distribute

distribute the x into (3x-5) -> 3x*x=3x^2 and x*-5=-5x. you will get

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

now distribute the 3 into the other (3x-5) -> 3*3x=9x and 3*-5=-15. you will get

3x^2-5x+9x-15

2. Combine like terms

3x^2-5x+9x-15 can be simplified to 3x^2+4x-15 by combining -5x and 9x.

3. Factor (there are many strategies use the one easiest for you)

In this case no number can be taken out to simplify the equation so set up your answerer as (3x   ) (x  ). you can do this because your first term will have to be 3x^2 and the only multiples are 3 and 1.

By using your 3rd term (-15) you can get the possible numbers after the x's by its multiples 5*3 and 15*1

Using the middle term (4x) find what multiplies to -15 (only one number can be negative) and is able to add up to 4 while one number is multiplied by 3 because of the 3x ( -5*3=15 and 3*3-5 -> 9-5=4)

plug your numbers in (3x-5) (x+3)

feel free to ask any questions!

Answer:

4

Step-by-step explanation:

In 36y/9y, the y's cancel out and it becomes 36/9

36/9=4

The values of the missing angles and sides after dilation are:

m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

m∠C'B'D = 180° - m∠B'C'D' - m∠B'D'C'

m∠B'C'D = m∠BCD, m∠B'D'C' = m∠BDC  (dilation)

m∠C'B'D = 180° - 34° - 51° = 95°

Thus, by way of scale factor we can say that:

BC/B'C' = BD/B'D' = 36/18 = 2

B'D' = ¹/₂BD = ¹/₂ * 22 = 11

ΔC'P'Q ∼ ΔCPQ

Thus:

C'Q'/CQ = C'D'/CD = D'Q'/DQ

CQ = 2C'Q' = 2 * 3 = 6

Therefore, m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

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Answer:

18x

Step-by-step explanation:

4x+3=7x

2x+9=11x

7+11x=18x

the answer is. 1.449, 0. You might have to put it into a decimal. sorry if wrong

The formula for the surface area of the box, in terms of the length of one side of the square base (s), is A = s^2 + 4s^2 = 5s^2.

The derivative of the surface area function with respect to s, denoted as dA/ds, gives us the rate of change of the surface area with respect to the length of one side of the base.

1. The surface area of the box consists of the area of the square base and the four equal sides. The area of the square base is s^2, and each side has a length of s. Therefore, the total surface area is given by A = s^2 + 4s^2 = 5s^2.

2. To find the derivative of the surface area function, we differentiate 5s^2 with respect to s using the power rule of differentiation. The power rule states that if we have a function f(x) = cx^n, then the derivative is f'(x) = cnx^(n-1).

  Applying the power rule, we have dA/ds = d(5s^2)/ds = 10s.

3. The derivative, dA/ds = 10s, represents the rate of change of the surface area with respect to the length of one side of the square base. This means that for every unit increase in s, the surface area increases by 10s units.

  The derivative does not provide information about minimizing the amount of material used. To find the dimensions of the box that minimize the amount of material used, we need to set up an optimization problem and solve for the critical points. This involves setting the derivative equal to zero and finding the values of s that satisfy this equation. However, since the problem statement does not provide a specific volume constraint or objective function, we cannot proceed with the optimization process.

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To see the steps of  sum a column in Excel on a Mac.

Now, According to the question:

1. Click the first empty cell below a column of numbers.

2. Do one of the following: Excel 2016 for Mac: : On the Home tab, click  AutoSum. Excel for Mac 2011: On the Standard toolbar, click AutoSum. ...

3. Press RETURN .

How do you sum cells on a Mac?

Once the cells are selected, press the Command key and the = (equal sign) key at the same time. This will automatically sum the selected cells. If you want to sum a specific range of cells, you can do so by selecting the first cell in the range, pressing the Shift key, and then selecting the last cell in the range.

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Answer:

X= 5

Step-by-step explanation:

The value of x in the equation 19x - 36 and 6x + 31 are 36 / 19 and -31 / 6 respectively.

A formula known as an equation uses the equals sign to denote the equality of two expressions. Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

19x - 36 = 0

6x + 31 = 0

Solve the above equation by using the transformed  as shown below,

19x - 36 = 0

19x = 36

x = 36 / 19

x = 1.895

For the second one, do the same as shown below,

6x + 31 = 0

6x = -31

x = -31 / 6

x = -5.167

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Savings = $4000

The ratio of income to expenditure = 6 : 5

Expenditure = $20000

Income = $24000

Savings = Income - Expenditure

Savings = $24000 - $20000

Savings = $4000

The Slope intercept form of the line passing through a (3, 8) and perpendicular to BC is \(y = -\frac{5}{2}x + \frac{31}{2}\)

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If \(\theta\)  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  \(tan\theta\)

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line

Here,

A(3,8), B(7,5), and C(2,3)

Slope of BC = \(\frac{3 - 5}{2 - 7}\) = \(\frac{2}{5}\)

Slope of line perpendicular to this line = \(-\frac{5}{2}\)

The line passes through (3, 8)

Equation of required line

\(y - 8 =- \frac{5}{2}(x - 3)\\2y - 16 = -5x + 15\\2y = -5x + 15 +16\\2y = -5x + 31\\y = -\frac{5}{2}x + \frac{31}{2}\)

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Answer:

Step-by-step explanation: A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.

Answer:

77/32...2 13/32

Step-by-step explanation:

11/12*21/8

Keep Change Change

HOPE THIS HELPS

Answer:

Length of leg of triangle = \(9\sqrt2\ cm\)

Step-by-step explanation:

We are given a 45°-45°-90° triangle with hypotenuse measuring 18 cm.

Let us assume the following labeling of the diagram, as attached in the answer area.

\(\angle XYZ =90^\circ\\\angle YXZ =45^\circ\\\angle ZXY =45^\circ\\\\Hypotenuse, XZ = 18 cm\)

The two angles here are equal to 45° so two sides of the triangle opposite to the equal angles will also be equal to each other i.e. it is an isosceles triangle.

i.e. The sides XY and YZ will be equal.

Let XY = YZ = x cm

It is known that in a right angled triangle, pythagorean theorem holds well.

As per pythagoream theorem:

\(\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Height}^{2}\)

Putting the values:

\(\text{XZ}^{2} = \text{YZ}^{2} + \text{XY}^{2}\\\Rightarrow 18^2 = x^{2} +x^{2} \\\Rightarrow 2x^{2} = 18^2\\\Rightarrow 2x^{2} = 324\\\Rightarrow x^{2} = 162\\\Rightarrow x = \sqrt{2 \times 81}\\\Rightarrow x = 9\sqrt2\ cm\)

So, the length of leg of triangle = \(9\sqrt2\ cm\)

Answer:

answer is B    9 root 2 cm

Step-by-step explanation:

got it right on edg 2020-2021

Step-by-step explanation:

(x - 1)² = 50

Either x - 1 = +√50 or x - 1 = -√50.

Hence, x = +/-√50 + 1 = +/-(5√2) + 1.

Answer:

they take 5 dollars and 40 cents off of it so it would be $48.60

The binomial theorem states that theorem states that the second term of (a+b) ^100 is 100a^99b.

The second term of (a+b)^100, we first need to understand the binomial theorem. The binomial theorem states that for any positive integer n,
(a+b)^n = C(n,0)a^n b^0 + C(n,1)a^(n-1) b^1 + C(n,2)a^(n-2) b^2 + ... + C(n,n-1)a^1 b^(n-1) + C(n,n)a^0 b^n
where C(n,k) is the binomial coefficient, given by
C(n,k) = n! / (k!(n-k)!)
Using this formula, we can find the second term of (a+b)^100 by plugging in n=100 and k=1:
C(100,1)a^(100-1) b^1 = 100a^99 b


The second term of (a+b)^100 can be found using the binomial theorem, which states that the expansion of (a+b)^n is the sum of the terms: C(n, k) * a^(n-k) * b^k, where C(n, k) represents the binomial coefficient, also known as "n choose k".
For the second term (k=1), we have:
C(100, 1) * a^(100-1) * b^1 = 100! / (1! * 99!) * a^99 * b

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Answer:

No, because a triangle will have to add up to 180 degrees. And if the two angles are already set for both triangles, there is only one answer that will make these triangles equal 180 degrees. So no there is no way possible.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

121+11 divided 37

hope this helped:)

Answer:

-121

Step-by-step explanation:

You can plug it in to a calculator, or use pemdas: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Answer:

2. y= -5/3 + 13/3

Step-by-step explanation:

I used Desmos Graphing Calculator

(BTW you have very nice handwriting ;-)

The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.

The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/4.A spinner is a gambling tool used for games and competitions. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result.

When it stops, a pointer will land on one of many different numbered segments of the spinner, each of which corresponds to a particular reward or consequence. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result. Probability is the study of the likelihood of events taking place.

Probability is expressed as a fraction, decimal, or percentage and is always between 0 and 1. The probability of an event can be calculated using the following formula: Probability = number of favorable outcomes / total number of possible outcomes. Given the spinner has a polka-dot section, 2 white sections, and 1 shaded section, it has a total of 4 sections.

Therefore, the probability of the spinner stopping at a polka-dot section is 1/4.Also, after the first spin, the spinner still has 2 white sections. Therefore, the probability of stopping at a solid white section is 2/4 or 1/2 (since there are only 2 possible outcomes after the first spin).

To determine the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section, we must multiply the probability of each event.1/4 × 1/2 = 1/8

Hence, the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.

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Answer:

The answer is 1

Step-by-step explanation:

Answer:

the process is correct

Step-by-step explanation:

hope u like it

Answer:

\(f(a) = 4(a + 4) - 3 = 4a + 16 - 3 \\ f(x) = 4a + 13 \\ f(5) = 4(5) + 13 = 20 + 13 \\ \boxed{f(5) = 33}\)

Answer:

The correct answers to this question would be 2. Tengo un hermano y dos hermanas and 4. Yo tengo tres hermanos.

120 meters = 120 x 1.09361 yards = 131.2332 yards. Multiplying by 10 to get the answer in tenths, we get: 120 meters = 1312.332 tenths of a yard.

To convert 120 meters to yards, we can use the conversion factor of 1 meter = 1.09361 yards. Multiplying 120 meters by this conversion factor gives us the length in yards, which is approximately equal to 131.2332 yards. To express the answer in tenths, we can multiply by 10 to get 1312.332 tenths of a yard. This means that 120 meters is equal to 1312.332 tenths of a yard. The conversion factor is a ratio of equivalent measurements and is used to convert between different units of measurement.

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Answer:

Yes, you can find the cube root of a negative number. The answer will be negative!

Step-by-step explanation:

Example: Find the cube root of -27

We know that a cube root is a number multiplied by itself 3 times (NOT MEANING THE NUMBER TIMES 3)

For example, The cube root of 27 positive is 3 because 3 x 3 x 3 = 27

But if we are using a negative number: It is really different because we got to know the rules.

The setup: -3 x -3 x -3 = -27

If we started with -3 x -3 first we know that a negative times a negative equals positive so the answer will be 9 positive, then we have this equation left:

9 x -3 = -27

The rule with this is a number times a negative is negative, so the answer of the question "Find the cube root of -27 is -3"

The given 95% confidence interval is (51.3, 54.7) and the null hypothesis is H0:

µ = 50

while the alternative hypothesis is Ha: µ ≠ 50. We have to determine the P-value for the test.

Therefore, the correct answer is (b)

The answer is (b) the P-value for the test is less than 0.05. Since the null hypothesis is that the population mean is 50, and the given confidence interval doesn't contain the value 50, the null hypothesis is rejected.

We can reject the null hypothesis at the 5% level since 50 is not in the 95% confidence interval.Hence, the null hypothesis is rejected with 5% significance level i.e. This implies that the P-value for the test is less than 0.05. the P-value for the test is less than 0.05.

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