fractorise 14p^2 + 21pq

Pwease help me ✨​

Answer:

3 tens   or 30

£12.35

Step-by-step explanation:

41,039

ten thousand thousands, hundreds tens ones

The three is in the tens place

3 tens   or 30

£12 and 35

1p = £0.01

£12.35

Answer:

2\(\sqrt{3}\)

Step-by-step explanation:

\(\frac{6}{\sqrt{3} }\)  They do not want a radical in the denominator.  So you need to multiple the numerators and the denominator by \(\sqrt{3}\)

\(\frac{6}{\sqrt{3} }\)  x  \(\frac{\sqrt{3} }{\sqrt{3} }\)  = \(\frac{6\sqrt{3} }{3}\) = 2\(\sqrt{3}\)

\( \frac{6}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{6 \sqrt{3} }{3} = 2 \sqrt{3} \)

hope it will work

The correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E. Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

She will be receiving a 2% raise per year. Her salary will increase $14,000 every year. The percent increase of her salary is 120% every year. Her salary is always 0.2 times the previous year's salary. The percent increase of her salary is 20% every year.

To calculate the salary of the vice president after n years of becoming a vice president, we use the given formula:

S(n) = 70000(1.2)

S(n) = 84000

The salary of the vice president after one year of becoming a vice president: S(1) = 70000(1.2)

S(1) = 84000

The percent increase of her salary is: S(n) = 70000(1.2)n

S(n) - S(n-1) / S(n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = (70000(1.2)n) - (70000(1.2)n-1) / (70000(1.2)n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = 20%

Therefore, the correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E.

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To approximate the integral ∫2.4 to 2 f(x) dx using Simpson's rule, we divide the interval [2, 2.4] into subintervals and approximate the integral within each subinterval using quadratic polynomials.

Given the data points (x, f(x)) = (2, 0.6931), (2.2, 0.7885), and (2.4, 0.8755), we can use Simpson's rule to approximate the integral.

Step 1: Determine the step size, h.

Since we have three data points, we can divide the interval [2, 2.4] into two subintervals, giving us a step size of h = (2.4 - 2) / 2 = 0.2.

Step 2: Calculate the approximations within each subinterval.

Using Simpson's rule, the integral within each subinterval is given by:

∫f(x)dx ≈ (h/3) * [f(x₀) + 4f(x₁) + f(x₂)]

where x₀, x₁, and x₂ are the data points within each subinterval.

For the first subinterval [2, 2.2]:

∫f(x)dx ≈ (0.2/3) * [f(2) + 4f(2.1) + f(2.2)]

≈ (0.2/3) * [0.6931 + 4(0.7885) + 0.8755]

For the second subinterval [2.2, 2.4]:

∫f(x)dx ≈ (0.2/3) * [f(2.2) + 4f(2.3) + f(2.4)]

≈ (0.2/3) * [0.7885 + 4(0.4545) + 0.8755]

Step 3: Sum up the approximations.

To obtain the approximation of the total integral, we sum up the approximations within each subinterval.

Approximation ≈ (∫f(x)dx in subinterval 1) + (∫f(x)dx in subinterval 2)

Calculating the values, we get the final approximation of the integral ∫2.4 to 2 f(x) dx using Simpson's rule.

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Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

First we have to line them up by the decimal points...

         -12.4

       +  9.2

           -3.2

That's all after you solved it you get -3.2

Answer:

Step-by-step explanation:

From the given information:

The ratio of the limiting floor area to lot area is 0.60 to 1

i.e.

= 0.60 : 1

For instance, let's take that the remodel size as p sq.ft on 1140 sq.ft

Then, the ratio = \(\dfrac{p}{11400}\)

The proportion of these equations is as follows:

\(\dfrac{p}{11400} = \dfrac{0.60}{1}\)

\(p \times 1 = 11400 \times 0.60\)

\(p = 11400 \times \dfrac{60}{100}\)

\(p =\dfrac{ 11400 \times 60}{100}\)

\(p =\dfrac{ 114 \times 100 \times 60}{100}\)

\(p = 114 \times 60\)

p = 6840 sq ft

Thus, the maximum allowable size of a remodeled house is 6840 sq.ft

b.

Recall that, the size of the home remodeled by limiting floor to lot area is

0.60:1

Then the proportion equation form is as follows:

\(\dfrac{0.60}{1}= \dfrac{5040}{x}\)

By cross multiplying

\(0.60 \times x = 5040 \times 1\)

\(x = \dfrac{5040 \times 1}{0.60 }\)

\(x = \dfrac{5040 \times 100}{60 }\)

\(x = \dfrac{84 \times 60 \times 100}{60 }\)

\(x =84 \times 100\)

x = 8400 sq.ft

Hence, the size of lot area is 8,400 sq.ft

The given probability of having six girls in a six-child family is 0.015625. To determine the method used to compute this probability, we need to analyze the information provided.

The Classical method is based on theoretical assumptions and probabilities calculated using mathematical principles. It assumes equally likely outcomes and relies on counting favorable outcomes over the total number of possible outcomes.

The Empirical method involves gathering data from observations or experiments to estimate probabilities. It relies on observed frequencies and relative frequencies to compute probabilities. However, the given probability does not suggest a sample or data collection, making it unlikely that the Empirical method was used.

The Subjective method involves assigning probabilities based on personal judgment or opinions. Individuals subjectively evaluate the likelihood of an event based on their own beliefs or knowledge.

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Answer:

m1 = 118 degrees, because it is a reflection of the other side of this line. m2 will be 180-118 = 62. This is because a straight line is always 180 degrees.

Therefore,

m1 = 118 degrees

m2 = 62 degrees

Answer:

∠ 1 = 118° , ∠ 2 = 62°

Step-by-step explanation:

∠ 1 and 118° are alternate angles and are congruent , then

∠ 1 = 118°

∠ 2 and 118° are same- side interior angles and sum to 180° , then

∠ 2 = 180° - 118° = 62°

Answer:

I hope I got it correct

Step-by-step explanation:

West Africa is known for its historical role in the transatlantic slave trade, where enslaved people were captured and transported to various parts of the world, including the Americas.

Slave Trading Centers: West Africa had numerous slave trading centers along its coastline, such as Goree Island (Senegal), Elmina Castle (Ghana), and Badagry (Nigeria). These sites served as key hubs for the capture, holding, and sale of enslaved individuals. Captured and Sold: Enslaved people were captured through various means, including warfare, kidnapping, or as victims of African slave raiders. They were then transported to coastal forts and castles, where they were held before being sold to European slave traders.

Middle Passage: The captured individuals were subsequently forced onto ships and endured the treacherous journey known as the Middle Passage. They were subjected to inhumane conditions during the voyage, with high mortality rates due to disease, maltreatment, and overcrowding. Destination: Enslaved Africans from West Africa were primarily transported to the Americas, including the Caribbean, North America, and South America, where they were enslaved and used as a labor force on plantations, mines, and in domestic service.

Profound Impact: The transatlantic slave trade from West Africa resulted in the forced displacement and suffering of millions of Africans. It had a profound impact on the demographics, culture, and history of both West Africa and the countries where enslaved individuals were taken.

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The winner received 570 votes.

Let the winner candidate be c1

Let the  second-place candidate be c2

Let the  third-place candidate be c3

\(c2=c1-155\\\).........equation 1

\(c2=c3+200\\\)

\(c3=c2-200 \\\)

\(c3=c1-155-200\\\).........by equation 1

\(c3=c1-355\)........equation 2

Now we know,

\(c1+c2+c3=1200\)

\(c1+(c1-155)+(c1-355)=1200\) .....by equations 1 and 2

\(3c1-510=1200\)

\(3c1=1200+510\\3c1=170\\c1=570\)

Hence, The winner received 570 votes.

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Answer:

1,2,5,7,8 and 9. Thus, we have 6 numbers. Then we want to form two-digit numbers without repetition. There are 6 number that is possible to occupy first digit, right? 1,2,5,7,8 or 9. Because it’s without repetition, so the number that have been filled the first digit cannot be the second digit. Thus, the numbers that is possible to occupy second are 5 digits. Thus, there are 6 x 5 = 30 numbers that can we form from those 6 numbers: 1,2,5,7,8 and 9 without repetition.

or by using permutation, there are two place would be filled by six number, so the permutation is 6P2 = 6!/ (6–2)! = 6!/4! = 6 x 5 = 30.

Step-by-step explanation:

Answer:

11,15,17,55,57,77,51,71,75,51

Step-by-step explanation:

Answer:

choice D

Step-by-step explanation:

The 99% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment is (0.41, 0.53). This means we can be 99% confident that the true difference in proportions falls within this interval.

Sample size of Democrats, n1 = 750

Number of Democrats who consider the environment as a top priority, x1 = 615

Sample size of Republicans, n2 = 850

Number of Republicans who consider the environment as a top priority, x2 = 306

Calculate the sample proportions:

Sample proportion of Democrats, p1 = x1 / n1 = 615 / 750 = 0.82

Sample proportion of Republicans, p2 = x2 / n2 = 306 / 850 = 0.36

Calculate the standard error of the difference in two sample proportions:

σd = sqrt{ [P1(1-P1) / n1] + [P2(1-P2) / n2] }

σd = sqrt{ [0.82(0.18) / 750] + [0.36(0.64) / 850] }

σd = sqrt{ 0.000180 + 0.000240 }

σd = sqrt{ 0.000420 }

σd ≈ 0.0205

Determine the level of confidence:

Given level of confidence, C = 99%

Find the critical value (z-score):

The z-score corresponding to the given level of confidence can be obtained from the standard normal table. For a 99% confidence level, the critical value is approximately z = 2.576.

Calculate the margin of error:

The margin of error is given by E = z * σd

E = 2.576 * 0.0205

E ≈ 0.0528

Construct the confidence interval:

The 99% confidence interval estimate of the overall difference in the percentages of Democrats and Republicans that prioritize protecting the environment is given by (D – d, D + d), where D is the difference in sample proportions and d is the margin of error.

(0.82 – 0.36 – 0.0528, 0.82 – 0.36 + 0.0528)

(0.41, 0.53)

Interpretation:

We can be 99% confident that the true difference in the percentages of Democrats and Republicans who prioritize protecting the environment falls within the interval (0.41, 0.53).

This means that there is a significant difference between the two groups in terms of the proportion that prioritize protecting the environment. The Democrats have a higher proportion compared to the Republicans.

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So, the system of equations representing this situation is: n + d + q = 95; 0.05n + 0.10d + 0.25q = 13.70; q = d + 11.

To represent this situation with a system of equations, we can use the following equations:

The total number of coins: n + d + q = 95

The total value of the coins in dollars: 0.05n + 0.10d + 0.25q = 13.70

The relationship between the number of quarters and dimes: q = d + 11

The first equation represents the total number of coins, which is given as 95.

The second equation represents the total value of the coins in dollars, which is given as $13.70. The values of each coin (nickel, dime, quarter) are multiplied by their respective quantities (n, d, q) and summed up to obtain the total value.

The third equation represents the relationship between the number of quarters (q) and dimes (d), which states that there are 11 more quarters than dimes.

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Answer:

5

Step-by-step explanation:

1. Add 7 to both sides of the equation:

2x = 10

2. Divide both sides by 2:

2x/2 = 10/2

x = 5

hope this helps!

Answer:

x=5

Step-by-step explanation:

2x-7+=3

add the 7 to both sides to cancel it out

2x=10

divide by 2

x=5

The longest poster that can fit in the box must have dimensions of 10 inches (height) by 20 inches (length) by 12 inches (width).

To find the longest poster that can fit in the box, we need to determine the longest dimension of the box itself. Since the box is 10 inches high, the longest poster that can fit in the box must have a height of no more than 10 inches.

Now, we need to consider the other two dimensions of the box. The box is 20 inches long and 12 inches wide, so the longest poster that can fit in the box must have a length of no more than 20 inches and a width of no more than 12 inches.

As for why we can only fit one maximum-length poster in the box but we can fit multiple 22-inch posters in the same box, it's because the length and width of the box are larger than the length and width of the 22-inch poster.

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Answer:

The 3rd option

Step-by-step explanation:

The pattern is every 2 hours is $15 so 4 hours would be equal to $30

Since 4 hours would equal 30 and we need 12 hours multiplying both numbers by 3 would get you the answer

4x3=12

30x3=90

Making it equal

Answer:

25  i used g00gle trans

Step-by-step explanation:

because, the quotient has an integer in its denominator

Explanation

A rational number is a number that is expressed as the ratio of two integers

hence

for

we can solve the root in the denominator, so we have

so, as the number can be expressed as the ratio of two integers ( 20 and 4) we can conclude

because, the quotient has an integer in its denominator

I hope this helps you

Answer:

Value of h+k = 16

Step-by-step explanation:

\(If \: a \: ,b, \: c \: are \: in \: arithmetic \: progression \\ then \: 2b \: = a + c \: \\ here \: a \: = h \: \: \: b \: = 8\: \: \: \: c \: = k \: \\ on \: substituting \: the \: values \: in \: formula \\ we \: get \: 2(8) = h + k \\ 16= h + k \\ value \: of \: h + k = 16\)

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The equation of the line is y = 2x + 8 that is parallel to the given line y = 2x + 2 and passes through the point (−3, 2)

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation of a straight line is:

y = mx + b

Where m is the rate of change and b is the y intercept.

Two lines are parallel if they have the same slope.

Let us assume that the line is parallel to y = 2x + 2 and passes through the point (−3, 2).

The slope of the line y = 2x + 2 is 2, Since it is parallel, the slope is also 2. hence:

y - y₁ = m(x - x₁)

y - 2 = 2(x - (-3))

y - 2 = 2(x + 3)

y = 2x + 8

The equation of the line is y = 2x + 8

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An equation of the line that is parallel to the given line and passes through the point (−3, 2) is: 4x + 3y = -6.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

By critically observing the graph (see attachment), we can logically deduce that the line passes through the following points:

Points (x, y) = (3, -1)

Points (x, y) = (0, 3)

Substituting the given parameters into the formula, we have;

Slope, m = (3 + 1)/(0 - 3)

Slope, m = 4/-3

Slope, m = -4/3.

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ -4/3 = -4/3

Note: m represents the slope.

At point (-3, 2), an equation of the other line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

y - 2 = -4/3(x - (-3))

y - 2 = -4/3(x + 3)

y - 2 = -4x/3 - 4

y - 2 = -4x/3 - 4 + 2

y = -4x/3 - 2

Multiplying all through by 3, we have:

3y = -4x - 6

Rearranging the equation, we have:

4x + 3y = -6

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Answer:

14, or f(-3)= 14

Step-by-step explanation:

Input the -3, so you will get f(-3)= -1/3(-3) + 13.
Do -1/3 x -3, which will get you 1.
Do 1 + 13, which will get you 14.
So, the answer will be 14, or f(-3)= 14.

Answer:

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = - 120\)

Step-by-step explanation:

By the rule of Integer multiplications,

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = [ (-1) \times (-2) ] \times [(-3) \times (-4)] \times (-5)\)

                                                      \(= [2] \times [12] \times (-5)\)

                                                      \(= -120\)

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Answer:

x = -3

Step-by-step explanation:

5x + 3 = 4x,

x + 3 = 0,

x = -3

Answer:

the answer for this would be -3

Answer:

yes they are equivalent because if you were to add those R's they would make 3r

Step-by-step explanation:

r+r+r=3r

Answer:

x = \(\frac{z+5y+3}{7}\)

Step-by-step explanation:

z = 7x - 3 - 5y ( add 5y to both sides )

z + 5y = 7x - 3 ( add 3 to both sides )

z + 5y + 3 = 7x ( isolate x by dividing both sides by 7 )

\(\frac{z+5y+3}{7}\) = x

The value for a in quadratic function a(x-1)²+3 is obtained as a = 2.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The vertex of the quadratic function is (1,3).

The line passes through the points (3,5).

The equation is in the form - a(x-1)²+3

It is known that the vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h,k) is the vertex of the parabola.

So it can be written -

f(x) = a(x-1)² + 3

Substitute the value of (1,3).

f(1) = a(1-1)² + 3 = 3

And for the point (3,5) the equation will be -

f(3) = a(3-1)² + 3 = 5

Set up a system of equations -

a(1-1)² + 3 = 3

a(3-1)² + 3 = 5

Solving for a in these equations -

a = 2

Therefore, the value of a is obtained as 2.

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The coaster starts at a height of 250, then drops down to 0 at x=500, and then rises back up to a height of 250. The bump is located at x=500 and is the highest point on the coaster.

y = -0.0005(x-500)² + 250

The coaster starts at the highest point (y=250) when x=0 and then drops down to x=500 by following the equation y=ax(x-1000). To create the bump, we need to make the coaster rise before it falls, so we use a quadratic equation that has a vertex at x=500 and y=250 (the initial height).

The equation y = -0.0005(x-500)² + 250 is a downward-facing quadratic equation with a maximum value of y=250 at x=500. This means that as the coaster approaches x=500, it starts to rise, and then falls down again. The coefficient -0.0005 controls the steepness of the coaster's drop and the height of the bump.

Here's a graph of the coaster:

         ^

       260|                               *

          |                          *    

          |                     *  

          |                *    

          |            *  

 height   |        *      

          |     *          

          |  *            

        0 +--------------->

            0      500    1000   x-axis

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