the answer would be A because if you graph those equations they are perpindicular. They cross eachother like a t
Which of the following is NOT prime number? A 1057 B 3163 C 157 D263
True or False: Low taxation would lead to slower economic growth because it encourages citizens and businesses to consume more and invest less
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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solve 5x=5/3 using multiplication property of equality
what is the product? 6(x^2-1)*6x-1/6(x+1)
6(x – 1)2
6(x2 – 1)
(x + 1)(6x – 1)
(x – 1)(6x – 1)
Answer:
the answer is (x - 1)(6 x-1) on edge, option D.
The product is (x - 1) (6x - 1).
What is Multiplication?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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Write a word problem that can be solved using 1 3/4 divided by 1/2
Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^2, x = 3, and y = 4 about the y-axis.
25 times pi divided by 2
97 times pi divided by 3
173 times pi divided by 3
None of these
The volume of the solid formed by revolving the region bounded by the graphs of the given functions is (25π) / 2.
What is integration?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:
a and b are the lower and upper bounds along the x-axis.f(x) is the upper function.g(x) is the lower function.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]
The closed form sum of $$12 \left[ 1^2 \cdot 2 + 2^2 \cdot 3 + \ldots + n^2 (n+1) \right]$$ for $n \geq 1$ is $n(n+1)(n+2)(an+b).$ find $an +
b.$
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, $an+b = \boxed{2}$.
Which statements are true about the ordered pair (5, −6) and the system of equations?
{x+y=−1
3x−y=21
Select each correct answer.
The ordered pair (5, −6) is a solution to the first equation because it makes the first equation true.
The ordered pair (5, −6) is a solution to the second equation because it makes the second equation true.
The ordered pair (5, −6) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (5, −6) is a solution to the system because it makes both equations true.
To fence in 2 cows, josie used 64 feet of fence. for 3 cows, she used 96 feet of fence, and for 4 cows, she used 128 feet of fence. how many feet of fence will she use for 6 cows?
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.
Timothy explains to his brother that the model y=4mt has a constant of variation of 4 and is an example of _____ variation.
Given ƒ(x) = 2x2 − 3x + 7, find ƒ(2.5)
Answer:
i need helppp
Step-by-step explanation:
this same problems but where is everyone getting the 6.25 from.
Each calendar will sell for $5.00 each. Write an equation to model the total income, y, for selling x calendars
The equation to model the total income, y, for selling x calendars will be y=5x.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, each calendar will sell for $5.00. the total income is y and the calendars to be sold be x.
Since each calendar costs $5, the total revenue (y) is equal to the number of calendars sold (x).
y=5x
The above equation is in the one variable known as the linear equation in one variable. It had the form y = mx. x and y are the variables in the equation.
Thus, the equation to model the total income, y, for selling x calendars will be y=5x.
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An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of a metal ring. The distance around each dot is 24pi inches. The artist plans to fill the inside of each dot with blue colored glass.
What is the area of the blue glass will be needed to fill each butterfly dot?
Give your answer in terms of pi.
The area of the blue glass that will be needed to fill each butterfly dot would be 144π.
What is the circumference of the circle?The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
We have given the distance around each dot is 24pi inches.
So, The circumference of the circle = 2πr
24π = 2πr
r = 12
The artist plans to fill the inside of each dot with blue-colored glass.
Now, we know that
The area of the circle = [tex]\pi r^{2}[/tex]
= π x 12 x 12
= 144π
Thus, the area of the blue glass that will be needed to fill each butterfly dot would be 144π.
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Write (1-i)-(4-5i) as a complex number in standard form. I don't exactly get how to do this.. Can anyone help?
Western boundary currents are deflected by the western coastlines of the continents.True False
This IS SO HARD
NEED HELP
I THINK ITS B.. Confirmation?
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
Points J and K lie in plane H.
How many lines can be drawn through points J and K?
0
1
2
3
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.
What is 187.023 I word form
What are 2 equivalent ratios for 9:20?
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.
Write each fraction as a repeating or circulating decimal. a. 2⁄3 b. 9⁄11 c. 2⁄9 d. 11⁄3 e. 5⁄6 f. 14⁄3
Answer:
Step-by-step explanation:
repeating or circulating decimal is decimal representation of a number whose digits are periodic or infinitely repeated.
To convert a fraction into decimal form we have to divide numerator by denominator.
a. 2/3 = 0.666666
b. 9/11 = 0.8181818
c. 2/9 = 0.222222
d. 11/3 = 3.666666
e. 5/6 = 0.833333
f. 14/3 = 4.666666
Point R is between points S and T and SR = 29 and ST = 47
What is RT?
a.) 18
b.) 22
c.) 66
d.) 76
is 37% bigger than 0.37
Can someone help me with this problem too?
Evaluate the function for an input of 10
(3xy^3)^2 (xy)^6 simplify the expression
50 POINTS!
Which statement best explains whether △ABC is congruent to △DEF?
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.
Solve for y.
23+y−19=79
Enter your answer in the box.
y = ____
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
A snack stand sold hot dogs and chips at a recent game. The hot dogs cost $2.50 and the snacks cost $0.75. After the game, they tallied 175 transactions totaling $262.50.
Represent the linear system in an augmented matrix:
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.
Let the number of hot dogs be represented by xLet the number of snacks sold be represented by y.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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Which of the following has the steepest graph?
The equation which has the steepest graph is:
Option: A
A. [tex]y=11x-144[/tex]
Step-by-step explanation: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.
If the absolute value of the slope is greatest then that line is most steep.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.
find the resultant of two forces, one of 72 pounds and the other of 56 pounds if they act at and angle of 37°