two different ratios equivalent to 6:9

Dividing 4x³ + x² - 27x + 18 by 4x - 3 will result to a quotient of x² + x - 6 and a remainder of 0

The long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder.

We shall divide the 4x³ + x² - 27x + 18 by 4x - 3 as follows;

4x³ divided by 4x equals x²

4x - 3 multiplied by x² equals 4x³ - 3x²

subtract 4x³ - 3x² from 4x³ + x² - 27x + 18 will result to 4x² - 27x + 18

4x² divided by 4x equals x

4x - 3 multiplied by x equals 4x² - 3x

subtract 4x² - 3x from 4x² - 27x + 18 will result to - 24x + 18

-24x divided by 4x equals -6

4x - 3 multiplied by -6 equals - 24x + 18

subtract - 24x + 18 from - 24x + 18 will result to a remainder of 0

Therefore by the long division method, 4x³ + x² - 27x + 18 by 4x - 3 gives a quotient x² + x - 6 and a remainder of 0.

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The expression √7. √7² is equivalent to [tex]7\sqrt{7}[/tex].

According to the quadratic formula, x = (-b (b2 - 4ac)) /2a gives the roots of the quadratic equation ax2 + bx + c = 0. Convert the quadratic equation into standard form, ax2 + bx + c = 0, then find the values of a, b, and c, substitute them in the quadratic formula, and simplify to find the solution to any quadratic equation.

Let's say that multiplying 5 by 5 yields the number 25. Therefore, we can state that 5 is equal to 25 squared. Similar to this, the root values of 16, 36, 49, etc. are 4, 6, and 7, respectively.

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Triangle a is a shape that is formed by connecting three points.

Triangle is a geometric figure with three sides and three angles. It is one of the basic shapes in geometry. Triangles are either right, acute, or obtuse, depending on the size of each angle. The sum of the angles in a triangle is 180 degrees. Triangles can be classified into equilateral, isosceles, and scalene triangles, depending on the length of the sides. All three types of triangles have various applications in mathematics, physics and engineering.

In order to reflect triangle a in the x axis, triangle b must be a mirror image of triangle a. To achieve this, each point in triangle a must be reflected across the x axis. This is done by multiplying the y coordinate of each point in triangle a by -1. As a result, triangle b will have the same three points as triangle a, except that the y coordinates of each point in triangle b will be the opposite of what they are in triangle a.

After reflecting triangle a in the x axis to form triangle b, the next step is to rotate triangle b around the origin 90°. This can be achieved by finding the coordinates of each point in triangle b, then rotating each point around the origin. To do this, the x coordinates of each point in triangle b remain the same, while the y coordinates are multiplied by -1. As a result, triangle c will be formed as a 90° rotation of triangle b around the origin.

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Answer:

X=10%

Y=30%

Step-by-step explanation:

The required percentages X and Y of copper and zinc in alloy A are given as 10% and 13.34%.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Percentage of copper in A = 1/2 [percentage of copper in ingot]
                                         = 1/2 × 20% = 10%

Percentage of zinc in A = 1/3 [percentage of zincin ingot]
                                    = 1/3 × 40% = 13.34%

Thus, the required percentages X and Y of copper and zinc in alloy A are given as 10% and 13.34%.

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The question seems to be incomplete,
Complete question.
Three specimens of Alloys A, B, and C containing copper and zinc are melted together to create an ingot containing 20% copper and 40% zinc. What are the percentages X and Y of copper and zinc in alloy A when copper is half of the copper in the ingot and zinc is 1/3 of the zinc in the ingot?

Answer:

[tex]\sf \frac{2A-hb}{h}=c[/tex]

Step-by-step explanation:

[tex]\sf A=\frac{1}{2}h(b+c)[/tex]

First, multiply both sides by 2.

[tex]\sf 2A=h(b+c)[/tex]

Solve the brackets.

[tex]\sf 2A=hb+hc[/tex]

Subtract h b from both sides.

[tex]\sf 2A-hb=hc[/tex]

Divide both sides by h.

[tex]\sf \frac{2A-hb}{h}=c[/tex]

To find the 95% confidence interval for the mean Sales on days that have 12 employees working, we would need to know the population standard deviation and the sample size. The formula for a 95% confidence interval for the mean is:

(sample mean) ± (critical value) x (standard deviation / sqrt(sample size))

Without the information about sample size, standard deviation and sample mean, it's not possible to find the exact 95% confidence interval for the mean Sales on days that have 12 employees working.

Similarly, to find the 95% prediction interval for Sales on a day with 12 employees working, we would need to know the population standard deviation, sample size, and the sample mean. The formula for a 95% prediction interval for a single observation is:

(sample mean) ± (critical value) x (standard deviation of the mean) x sqrt(1 + (1/sample size))

Again, without the information about sample size, standard deviation and sample mean, it's not possible to find the exact 95% prediction interval for Sales on a day with 12 employees working.

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There are 231+d pies baked in two years.

expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An equation is made up of two expressions connected by an equal sign.

Since we have given that

Number of pies baked for bake sale last year = 231

Number of pies baked for bake sale this year = d

So, total number of pies baked in two years is given by

231 +d

Hence, there are 231+d pies baked in two years.

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Substituting into the formula for the perimeter of a rectangle, the perimeter is [tex]2\left(n+3 \frac{1}{2} n +4 \frac{1}{2} \right)=2n+7n+9=\boxed{9n+9}=\boxed{9(n+1)}[/tex]

The formula that represents the arithmetic sequence is f(n) = 32-7(n-1) (optionC)

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term. For example in the arithmetic sequence 3, 9, 15, 21, 27, the common difference is 6. An arithmetic sequence can be known as an arithmetic progression.

The formula for the nth of an arithmetic sequence is a(n) = a+(n-1)d. Where d is the common difference and n is the number of terms.

In the sequence 39, 32, 25, 19, 12,. The first term is 32 and the common difference is 32-39= -7.

Therefore the formula for the sequence is formed by inserting the values of a and 7.

f(n) = 32+(n-1)-7

f(n) = 32-7(n-1)

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Answer:

f(n) = 39-7(n-1)

Step-by-step explanation:

Trust I took test

Answer:

109

I wish you luck in your assignments.

Answer:

$1.83

Step-by-step explanation:

5.50÷3 = 1.8333333 = 1.83

The statements that describe that actions that are helpful to our credit score includes:

The Option C is correct.

Our credit score are based on credit history including the number of open accounts, total amount of debt, history of repayment, and other elements.

To improve your credit score, some actions you can take include:

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The correct answer is the second option.

What is typing speed?

Typing speed is the measure of how many correct words are typed in a 60-second time frame.

The average typing speed is 40 words per minute or wpm.

Therefore the correct answer is the second option.

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Correct option is C, The typing speed is measured in words per minute.

The typical typing rate is 40 words per minute (wpm). Aim for a typing speed of 65 to 70 words per minute if you want to be really productive. With the appropriate approach, it's simple!

There are various typing tests available. This typing test measures your speed of typing in words per minute. Your WPM score will increase the more you practice typing and the more you measure your typing speed. Only WPM typing is the topic of certain online typing tests and typing test games. The WPM typing test has the drawback of simply teaching you how to type quickly. The WPM typing test does not demonstrate your accuracy.

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Answer: The Midpoint of P and Q are (-0.5, -3.5)

Step-by-step explanation: To find the coordinates of the intersection points of the line and the curve, we can substitute the equation of the line into the equation of the curve and solve for x and y.

From the equation of the line: x - y = 3, we can see that y = x - 3

Substituting this into the equation of the curve:

3x^2 - (x-3)^2 + x(x-3) = 9

Now we can simplify and group

3x^2 - x^2 + 6x - 9 + x^2 - 3x = 9

3x^2 + 3x - 9 = 9

3x^2 + 3x = 18

3x(x+1) = 18

x(x+1) = 6

We can see that x = 2 and x = -3 are the solutions.

Substituting the x value back into the original equation of the line to find the y coordinate:

x = 2 => y = 2 - 3 => y = -1

x = -3 => y = -3 - 3 => y = -6

So the intersection points are (2,-1) and (-3,-6)

To find the midpoint of these two points, we take the average of their x and y coordinates:

x = (2 + -3) / 2 = -0.5

y = (-1 + -6) / 2 = -3.5

so the midpoint of the two intersection points is (-0.5, -3.5)

Answer:

Point, [tex](p,q)[/tex], is [tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex].

Step-by-step explanation:

Given the equations  [tex]x-y=3[/tex]  and  [tex]3x^{2} -y^{2} +xy=9[/tex] . Find where they intersect and find the midpoint, [tex](p,q)[/tex], of the two intersection points. To find find points of intersection, you can either set up these equations as a system and solve algebraically or you can use a graphing calculator to graph the functions and see where they cross.

I will set up these equations as a system of equations,

[tex]\left \{ {{x-y=3} \atop {3x^{2} -y^{2} +xy=9}} \right.[/tex]

I will solve the top equation for [tex]x[/tex], and substitute it into the bottom.

[tex]x-y=3 = > x=3+y[/tex]

Now substitute [tex]x=3+y[/tex] for x into the bottom equation. Solve for y,

=> [tex]3x^{2} -y^{2} +xy=9[/tex]

=>[tex]3(3+y)^{2} -y^{2} +(3+y)y=9[/tex]

=> [tex]3(y^{2}+6y+9) -y^{2} +y^{2}+3y =9[/tex]

=>[tex]3y^{2}+18y+27 -y^{2} +y^{2}+3y =9[/tex]

=> [tex]3y^{2}+18y+27+3y =9[/tex]

=> [tex]3y^{2}+21y+27 =9[/tex]

=>[tex]\frac{3y^{2}+21y+27 =9}{3}[/tex]

=>[tex]y^{2}+7y+9 =3[/tex]

=>[tex]y^{2}+7y+6 =0[/tex]

=> [tex](y+1)(y+6)=0[/tex]

=>[tex]y=-1[/tex] or [tex]y=-6[/tex]

Now plug these values for [tex]y[/tex] into [tex]x=3+y[/tex].

When y=-1:

[tex]x=3+(-1)[/tex]

=> [tex]x=2[/tex]

When y=-6:

[tex]x=3+(-6)[/tex]

=> [tex]x=-3[/tex]

The solution to the system (points of intersection) is [tex](-3,-6)[/tex] and [tex](2,-1)[/tex]. I also attached a graph of the intersection points.

Now to find the midpoint of the two intersection points, [tex]midpoint=(\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )[/tex]

[tex](x_{1},y_{1}) = > (-3,-6)[/tex]

[tex](x_{2},y_{2}) = > (2,-1)[/tex]

=>[tex]midpoint=(\frac{-3+2}{2} ,\frac{-6+(-1)}{2} )[/tex]

=>[tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex]

Thus, the point, [tex](p,q)[/tex], is [tex](\frac{-1}{2} ,\frac{-7}{2} )[/tex].

The degree of correlation required for significance reduces as the sample size increases. As a result, the correlation size needed to determine significance will be smaller.

The size of our sample and the sample size has an impact on the significance of a sample link. For results to be relevant for high sample sizes, a minimal correlation is required. Fewer correlations and linkages are required for significance as the sample size increases.

Each sampling distribution's variability declines with the sample number and gradually moves toward leptokurtic behavior. The sample distribution's range is smaller than the range of the initial population.

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Therefore , the solution of the given problem of inequality comes out to be graph 2 shows the solution for this system.

In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are.

Here,

Given :

=> x + y ≥ 5

and

=> - 3x + 2y ≤-2

So,

=> x ≥ 5- y

=> - 3(5- y) + 2y ≤-2

=> -15 + 3y + 2y ≤-2

=> 5y ≤ 13

=> y  ≤  13/5

and

=> x ≥ 5-  13/5

=>  x ≥  12/5

Therefore , the solution of the given problem of inequality comes out to be graph 2 shows the solution for this system.

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The slice when cube is sliced through all faces is hexagon.

A cross-section is a shape that is yielded from a solid (e.g. cone, cylinder, sphere) when cut by a plane.

For example, a cylinder-shaped object is cut by a plane parallel to its base; then the resultant cross-section will be a circle.

Given,

A cube is sliced with a plane,

The plane meets all faces of cube,

When a plane intersects a cube there is a variety of shapes of the resulting cross section.

A hexagon, If the plane meets all faces of the cube.

Hence, slice is hexagon when cube is sliced through all faces.

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The linear equation for given citation will be 35/10+5/8x where x is the number.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

As given citation is thirty five to ten added to five eights of a number

It can be changed into the linear equation

35/10+5/8x.

where x is the number.

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The value of the logarithm equation is given by x = [ ln ( 4 ) - 5 ] / 4

The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm

The properties of Logarithm are :

log A + log B = log AB

log A − log B = log A/B

log Aⁿ = n log A

Given data ,

Let the logarithm equation be represented as A

Now , the value of A is

e⁽ ²ˣ ⁺ ⁵ ⁾ = 4   be equation (1)

On simplifying the equation , we get

Taking logarithm on both sides of the equation , we get

2x + 5 = ln ( 4 )

On simplifying the equation , we get

ln ( 4 ) = 2x + 5

Subtracting 5 on both sides of the equation , we get

2x = ln ( 4 ) - 5

Divide by 2 on both sides of the equation , we get

x = [ ln ( 4 ) - 5 ] / 4

Hence , the equation is  x = [ ln ( 4 ) - 5 ] / 4

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The equation of the straight line passing through the point (-4, -4) with slope 3 can be written as y = 3x + 8.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the line with slope 3 passing through the point (-4, -4)

The equation of the straight line passing through the point (-4, -4) with slope 3 can be written as follows. We can write -

y = 3x + c

For the point ( -4, -4), we can write -

- 4 = 3 x - 4 + c

c = - 4 + 12

c =  8

Therefore, the equation of the straight line passing through the point (-4, -4) with slope 3 can be written as y = 3x + 8.

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Answer: There were 304 children and 89 adults at the public pool on that hot summer day.

Step-by-step explanation:    

Let's say the total number of people at the pool that day is x + y = 393

   The total cost of admission for all the people is $678.50

   The cost for each child's admission is $1.50 and the cost for each adult's admission is $2.50

We can use this information to set up two equations:

   x + y = 393 (Total number of people)

   1.5x + 2.5y = 678.5 (Total cost of admission)

Now we can use the first equation to solve for one of the variables. For example, we can solve for y:

y = 393 - x

We can substitute this value of y into the second equation:

1.5x + 2.5(393 - x) = 678.5

We can then solve this equation for x:

1.5x + 982.5 - 2.5x = 678.5

-x = -304

x = 304

This means that there were 304 children at the pool that day. We can use the first equation to find the number of adults:

x + y = 393

304 + y = 393

y = 393 - 304

y = 89

Therefore, there were 304 children and 89 adults at the public pool on that hot summer day.

The percentage of voters that plan to vote for the Democrat candidate is given as follows:

Number of voters for the Democrat / 540 x 100%.

A percentage is obtained applying a proportion, which is the division of the number of desired outcomes by the number of total outcomes, which is then multiplied by 100%.

A poll was conducted of 540 voters asking for which candidates they planned to vote, hence the total number of outcomes is given as follows:

540.

Then the division of the desired number by the total number is given as follows:

Number of voters for the Democrat / 540

The multiplication to write the proportion as a percentage is given as follows:

Number of voters for the Democrat / 540 x 100%.

This problem is incomplete, as the table is not given, hence the general procedure is presented to obtain the percentage of voters that plan to vote for the Democrat candidate.

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Answer:

k = 58

Step-by-step explanation:

k = 15 litres + remaining petrol

Remaining petrol:

The car travels 8 km/litre.

344 km / (8 km/litre) = 43 litre

The car uses 43 litres to travel 344 km.

k = 15 + 43

k = 58

Answer:

3 1/2 cups of oats = 28 grams of fiber

Step-by-step explanation:

1 whole cup equals 8 grams (add halves for this)

8 x 3 = 24

24 + additional 4 from the remaining half makes 28 grams of fiber total.

Answer:

7.5 hours

Step-by-step explanation:

let t represent time, l represent length and n represent number of painters.

given t varies directly with l and inversely with n then the equation is

t = [tex]\frac{kl}{n}[/tex] ← k is the constant of variation

to find k use the condition t = 5 when l = 200 and n = 3 , then

5 = [tex]\frac{200k}{3}[/tex] ( multiply both sides by 3 )

15 = 200k ( divide both sides by 200 )

0.075 = k

t = [tex]\frac{0.075l}{n}[/tex] ← equation of variation

when l = 500 and n = 5 , then

t = [tex]\frac{0.075(500)}{5}[/tex] = [tex]\frac{37.5}{5}[/tex] = 7.5 hours

The inverse of f(x) = 2/3 x³ + 1 is f^-1(x) = (3/2)(x-1)^(1/3).

In other words, we can set y equal to the original equation and solve for x.

Let y = 2/3 x³ + 1

We can then subtract 1 from both sides to get y – 1 = 2/3 x³

We can then divide both sides by 2/3 to get (y – 1) • (3/2) = x³

Finally, we can take the cube root of both sides to get the inverse function:

x = (y – 1)¹/₃ • (3/2)¹/₃

Therefore, the inverse of f(x) = 2/3 x³ + 1 is x = (y – 1)¹/₃ • (3/2)¹/₃.

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Answer:

6358 mm

Step-by-step explanation: multiply the value of decimeters by 100,

we get 6300 mm and then we add the 58 mm in 6300 mm.