What value of k makes the statement true? xky4(2x3 + 7x2y4) = 2x4y4 + 7x3y8 k =

Final answer:

The closed form sum of the given expression is obtained by expanding and simplifying it. Comparing this with the given expression, we can find the values of a and b.

Explanation:

The closed form sum of $$12 \left[ 1² \cdot 2 + 2²\cdot 3 + \ldots + n² (n+1) \right]$$ for $n \geq 1$ is $n(n+1)(n+2)(an+b).$ To find $an + b$, we can simplify the expression by expanding it:

Expanding the sum, we have:

$$\begin{align*} 12 &\left[ 1² \cdot 2 + 2² \cdot 3 + \ldots + n² (n+1) \right] \\ &= 2[1 + (n-1) + 3 + \ldots + (2n-3) + (2n-1)-(n-1)] \\ &= 2[n + 3 + \ldots + (2n-3) + n] \\ &= 2n² \end{align*}$$

Comparing this with the given expression $n(n+1)(n+2)(an+b)$, we can see that $2n² = n(n+1)(n+2)(an+b)$. So, $an+b = \boxed{2}$.

The equation which has the steepest graph is:

             Option: A

     A.   [tex]y=11x-144[/tex]

We know that the slope-intercept form of a line is given by:

                 [tex]y=mx+c[/tex]

where m is the slope of the line and c is the y-intercept of a line.

A)

[tex]y=11x-144[/tex]

The slope is: 11

B)

[tex]y=\dfrac{1}{2}x+3[/tex]

The slope is: [tex]\dfrac{1}{2}[/tex]

C)

[tex]y=7x+16[/tex]

The slope is: 7

D)

[tex]y=3x+144[/tex]

The slope of this line is: 3

The line which has the largest absolute value of slope is:

               [tex]y=11x-144[/tex]

Hence, the graph of this equation will be steepest.

1 is the answer bruvy

Answer: 1

Step-by-step explanation:

From the given picture, it can be seen that there is a plane H on which two pints J and K are located.

One of the Axiom in Euclid's geometry says that "Through any given two points X and Y, only one and only one  line can be drawn "

Therefore by Axiom in Euclid's geometry , for the given points J and K in plane H , only one line can be drawn  through points J and K.

Final answer:

Two equivalent ratios for 9:20 are 18:40 and 27:60, found by multiplying both the numerator and denominator of the ratio by 2 and 3, respectively.

Explanation:

To find two equivalent ratios for 9:20, you can multiply or divide both terms of the ratio by the same non-zero number. Remember, an equivalent ratio has the same proportional relationship as the original one.

Here's how we can calculate two equivalent ratios:

Multiply both terms by 2: 9 × 2 = 18 and 20 × 2 = 40, so one equivalent ratio is 18:40.

Multiply both terms by 3: 9 × 3 = 27 and 20 × 3 = 60, so another equivalent ratio is 27:60.

These both represent the same ratio as 9:20 when simplified.

The property that justifies the step is the Commutative Property of Addition, which states that the order of addition does not affect the result.

The property that justifies the illustrated step in solving the equation 3x + 4 - 2x + 5 = 6x + 2 as 3x - 2x + 4 + 5 = 6x + 2 is the Commutative Property of Addition.

This property states that the order in which numbers are added does not affect the result. So, we can rearrange the terms in any order without changing their sum.

In this step, we are rearranging the terms -2x and 5 so that like terms, namely 3x and -2x, and 4 and 5, are grouped together.

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Answer:

192 feet fence would be used for 6 cows.

Step-by-step explanation:

Given,

64 feet of fence is used for 2 cows,

Ratio in fence and cows = [tex]\frac{64}{2}[/tex] = 32,

96 feet of fence is used for 3 cows,

Ratio in fence and cows = [tex]\frac{96}{3}[/tex] = 32,

128 feet of fence is used for 4 cows,

Ratio in fence and cows = [tex]\frac{128}{4}[/tex] = 32,

Thus, by the above explanation it is clear that in every case the ratio of the length of fence and number of cows is 32,

Let x be the length of cows that is used for x cows,

[tex]\implies \frac{x}{6}=32[/tex]

[tex]\implies x = 192[/tex]

Hence, 192 feet fence would be used for 6 cows.

Answer:

22sqrt(3)/3

You are correct.

Step-by-step explanation:

You have a 30-60-90 triangle.

In a 30-60-90 triangle, the hypotenuse is twice the length of the short leg. The long leg is sqrt(3) times the length of the short leg.

You are given the length of the long leg.

1) Find the length of the short leg.

HG = GI/sqrt(3) = 11/sqrt(3)

2) Find the length of the hypotenuse, HI.

HI = 2HG = 2(11/sqrt(3)) = 2(11/sqrt(3))*(sqrt(3))/(sqrt(3)) = 22sqrt(3)/3

Answer:

The second choice is correct.

Step-by-step explanation:

Reflecting ABC across the y-axis will negate the x-coordinates, which will place it directly above triangle DEF.  Counting down from A to D, B to E and C to F, we see that each is 5 units above the image; this means a translation 5 units down will finish mapping the pre-image to the image.  Since they are mapped on top of each other, they are congruent.

Answer: 28.1ft^2 so it’s C

Answer: C

Step-by-step explanation:

If there are 812 students in your school and there are 36 more girls than boys. Then there are 414 girls in the school.

In this problem, let's denote the number of boys as B and the number of girls as G. We are given two pieces of information: there are 812 students in total, and there are 36 more girls than boys.

So, we can set up two equations based on these statements:

1. Total number of students: (B + G = 812)

2. The number of girls is 36 more than boys: (G = B + 36)

Now, we can substitute the expression for G from the second equation into the first equation:

[B + (B + 36) = 812]

Combine like terms:

[2B + 36 = 812]

Subtract 36 from both sides:

[2B = 776]

Now, divide by 2 to solve for B:

[B = 388]

Now that we know the number of boys, we can find the number of girls using the second equation:

[G = 388 + 36]

[G = 424]

So, there are 388 boys and 424 girls in the school. To find the number of girls, we add the number of boys (388) to the given difference (36):

[424 = 388 + 36]

Therefore, the final answer is that there are 424 girls in the school.

Answer:

i need helppp

Step-by-step explanation:

this same problems but where is everyone getting the 6.25 from.

The volume of the solid formed by revolving the region bounded by the graphs of the given functions is (25π) / 2.

Integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions into parts.

The region bound by all three functions is in the first quadrant. If this region were rotated about the y-axis, the solid formed would have washer-shaped cross-sections.

Therefore, we can use the Washer method: V = π∫ (ROuter)² - (RInner)² dy

R(outer) = 3 and R(inner) = √y  (Note: the inner radius is formed by the function y = x2 which we solve in terms of y since we are rotating about the y-axis).

V = π∫ (3)2 - (√y)2 dy

(the limits of integration are from y = 4 to y = 9, so a = 4 and b = 9)

= π∫  9 - y dy where a = 4 and b = 9

Integrate this definite integral to find the volume,

=  (25π) / 2.

Hence, the volume of the solid formed by revolving the region bounded by the graphs of the given functions is (25π) / 2.

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Answer:

[tex]\textsf{A)} \quad \dfrac{25\pi}{2}[/tex]

Step-by-step explanation:

To find the volume of the solid of revolution created by rotating the region bounded by the curve y = x², x = 3, and y = 4 about the y-axis, we can use the method of cylindrical shells.

As the region of revolution is bounded by the graphs of two functions, y = x² and y = 4, the volume of a solid of revolution using cylindrical shells is given by the integral:

[tex]\displaystyle V=2\pi\int^b_ax\left(f(x)-g(x)\right)\;\text{d}x[/tex]

where:

The height of the shell, f(x) - g(x), is determined by the vertical distance between the curve y = x² and the line y = 4. Therefore, the height is:

[tex]f(x)-g(x)=x^2-4[/tex]

The upper bound of the integral is b = 3, since the region is bounded by x = 3.

The lower bound is the x-value of the point of intersection of the two functions y = x² and y = 4. These two functions intersect when x = 2. Therefore, the lower bound of the integral is a = 2.

Substitute these values into the integral:

[tex]\displaystyle V=2\pi\int^3_2x\left(x^2-4\right)\;\text{d}x[/tex]

Expand the brackets:

[tex]\displaystyle V=2\pi\int^3_2\left(x^3-4x\right)\;\text{d}x[/tex]

Evaluate the integral by using the power rule:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Therefore:

[tex]V=2\pi\left[\dfrac{x^4}{4}-\dfrac{4x^2}{2}\right]^3_2[/tex]

[tex]V=2\pi\left[\dfrac{x^4}{4}-2x^2\right]^3_2[/tex]

[tex]V=2\pi\left[\left(\dfrac{(3)^4}{4}-2(3)^2\right)-\left(\dfrac{(2)^4}{4}-2(2)^2\right)\right][/tex]

[tex]V=2\pi\left[\left(\dfrac{81}{4}-18\right)-\left(4-8\right)\right][/tex]

[tex]V=2\pi\left[\left(\dfrac{9}{4}\right)-\left(-4\right)\right][/tex]

[tex]V=2\pi\left(\dfrac{25}{4}\right)[/tex]

[tex]V=\dfrac{25\pi}{2}[/tex]

Therefore, the volume of the solid formed by revolving the region bounded by the graphs of y = x², x = 3, and y = 4 about the y-axis is:

[tex]\Large\boxed{\boxed{\dfrac{25\pi}{2}}}[/tex]

Answer:

y = 75

Step-by-step explanation:

23 + y - 19 = 79

We are to solve for y.

To solve for y, we are to follow the step below

23 + y - 19 = 79

subtract nineteen from twenty three

y + 4 = 79

Subtract four(4) from both-side of the equation

y + 4 - 4 = 79 - 4

On the left hand-side of the equation, 4-4=0 leaving us with just y

y = 79 - 4

y =75

Therefore y = 75

Low taxation would lead to slower economic growth because it encourages citizens and businesses to consume more and invest less is false.

We have,

Low taxation can actually lead to faster economic growth if it encourages citizens and businesses to consume and invest more.

With more money in their pockets, consumers may have more disposable income to spend on goods and services, which can stimulate demand and create more jobs.

Additionally, with lower taxes, businesses may have more money to invest in capital equipment, research and development, or expansion, which can lead to increased productivity and economic growth.

It's important to note that the relationship between taxation and economic growth is complex and multifaceted.

While lower taxes can be beneficial for growth, they may also lead to reduced government revenues, which can limit the government's ability to fund important public services and investments.

Moreover, the impact of tax policy on economic growth can vary depending on a range of factors, such as the size and structure of the economy, the nature of the tax system, and broader economic conditions.

Thus,

Low taxation would lead to slower economic growth because it encourages citizens and businesses to consume more and invest less is false.

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x = hot dogs

y = snacks

x +y = 175

x = 175-y

2.50x + 0.75y = 262.50

2.50(175-y) +0.75y = 262.50

437.50-2.50y + 0.75y = 262.50

-1.75y = -175

y = -175 / -1.75 = 100

100 snacks & 75 hot dogs

The number of hot dogs sold is 75 while the number of snacks sold is 100.

Based on the information, the equation to solve the question will be:

x + y = 175 ....... i

2.50x + 0.75y = 262.50 ....... ii

From equation i, x = 175 - y.

We'll put the value of x into 2.50x + 0.75y = 262.50 and this will be:

2.50x + 0.75y = 262.50

2.50(175 - y) + 0.75y = 262.50

437.50 - 2.50y + 0.75y = 262.50

Collect like terms

-2.50y + 0.75y = 262.50 - 437.50

-1.75y = -175

y = 175/1.75

y = 100

The number of snacks sold is 100.

Since x + y = 175

x = 175 - 100

x = 75

The number of hot dogs sold is 75

Therefore, 75 hot dogs and 100 snacks were sold.

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Answer:

the answer is (x - 1)(6 x-1) on edge, option D.

The product is (x - 1) (6x - 1).

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

The given expression is [6(x² - 1) (6x - 1)] / [6 (x + 1)]

6 is in the numerator as well as denominator. Cancel it.

[6(x² - 1) (6x - 1)] / [6 (x + 1)] =  [(x² - 1) (6x - 1)] / [(x + 1)]

We have to use one of the algebraic identity here.

a² - b² = (a + b) (a - b)

Using this,

x² - 1 = x² - 1² = (x - 1)(x + 1)

[6(x² - 1) (6x - 1)] / [6 (x + 1)] =  [(x² - 1) (6x - 1)] / [(x + 1)]

                                            = [(x - 1)(x + 1)(6x - 1)] / [(x + 1)]

Again, x + 1 is both in the numerator as well as denominator. Cancel it.

[6(x² - 1) (6x - 1)] / [6 (x + 1)] = (x – 1)(6x – 1)

Hence the product is (x – 1)(6x – 1).

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