What solid will be produced if rectangle ABCD is rotated around line m? Assume that the line bisects both sides it intersects. What will the dimensions of the three-dimensional solid be?

rectangular prism; length = 12 in.; width = 6 in.; height = 5 in.

triangular prism; length = 12 in.; width = 6 in.; 
height = 5 in.

cylinder; radius = 12 in.; height = 5 in.

cylinder; radius = 6 in.; height = 5 in.

Answers

Answer 1

Answer:

D) cylinder; radius = 6in.; height = 5 in.

Answer 2

The solid  produced if rectangle ABCD is rotated around line m is a cylinder with radius of 6 in and height of 5 in.

What is a solid figure?

A solid figure is a three dimensional shape having length, width and height. Examples of three dimensional figures are prism, pyramid, cone, cylinder and so on.

The solid  produced if rectangle ABCD is rotated around line m is a cylinder with radius of 6 in and height of 5 in.

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Related Questions

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

Answers

Answer:

4x-10y thingi 3

Step-by-step explanation:

The actual value of the population that the statistic tries to estimate is called the parameter. A.true B. False

Answers

true

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

the parameter tells you something about the whole population

Which of the following describes the graph of y=sq -4x-36 compared to the parent square root function

Answers

Answer:

Step-by-step explanation:

First, let's simplify the equation:

y = √(-4x - 36)

y = √(4(-x - 9))

y = 2√(-x - 9)

The 2 coefficient in front means the function is stretched by a factor of 2.

The - sign in front of the x means the function is reflected over the y axis.

The -9 constant means the function is shifted 9 units to the right.

The third one is the correct answer.

Answer:

D:  Stretched by a factor of 2, reflected over the y-axis, and translated 9 units left

Step-by-step explanation:

I actually just did this and used the answer above and got it wrong, so the answer I put down is the correct answer according to edg... Good Luck!!!

A and B are complementary angles of right triangle ABC, COS A = 0.83, and cos B = 0.55. What is sin A + sin B?

Answers

Answer:

Complementary angles are two angles which add up to 90° or forms a right angle. First, we find the value of A and B.

A = arccosine (0.83) = 34°

B = 90 - 34 = 56°

Thus, sin A = 0.56 and sin B = 0.83.

Step-by-step explanation:

hampton has an 8 foot tall oak tree in his backyard.if the tree will grow n feet in height each year,which of the following represents the height of the tree,in feet,4 years from now?​

Answers

Answer:

8+4n=height of tree in 4 years

Step-by-step explanation:

start of with 8

then every year add N feet

4 years times n feet + what we started with(8)

and you get 8+4n

Final answer:

The height of the tree, in feet, 4 years from now can be calculated as 8 + 4n, where n is the number of feet the tree grows each year.

Explanation:

The subject of this question is a mathematical problem involving height growth over time, specifically about a tree that grows at a constant rate each year. In this case, the height of a tree in the future can be represented by a simple equation which considers the current height of the tree (8 feet), the rate of growth each year (n feet per year), and the number of years in the future we want to calculate for (4 years). The formula to calculate the height of the tree 4 years from now is:

Future Height = Current Height + Growth Rate * Time

Plug in the values we know:

Future Height = 8 feet + n feet/year * 4 years

So, the height of the tree, in feet, 4 years from now is 8 + 4n.

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Find the values of a and b so that the polynomial x^3 -10x^2 +ax +b is exactly divisible by x-1 as well as x-2

Answers

Answer:

a = 23, b = - 14

Step-by-step explanation:

If the polynomial is divisible by (x - 1) then f(1) = 0

f(x) = x³ - 10x² + ax + b

f(1) = 1³ - 10(1)² + a + b = 0, that is

1 - 10 + a + b = 0, hence

a + b = 9 → (1)

Similarly if (x - 2) is a factor then f(2) = 0

f(2) = 2³ - 10(2)² + 2a + b = 0, that is

8 - 40 + 2a + b = 0, hence

2a + b = 32 → (2)

Subtract (1) from (2)

a = 23

Substitute a = 23 into (1)

23 + b = 9 ⇒ b = 9 - 23 = - 14

2. A bag contains six red marbles, eight yellow
marbles, and nine blue marbles.
a. What is the probability that you pick a yellow
marble or a red marble?​

Answers

Answer:

14/23

Step-by-step explanation:

The total number of marbles is 6 + 8 + 9 = 23.

The probability of yellow or red is:

P(yellow or red) = P(yellow) + P(red)

P(yellow or red) = 8/23 + 6/23

P(yellow or red) = 14/23

Answer:

8 in 23 chance of picking a yellow marble

6 in 23 chance of picking a red marble

Explanation:

Firstly, we must determine the total number of marbles. To do this, we add all the marbles together:

6+8+9 = 23

Since the question says we have 8 yellow marbles, that means 8/23 marbles are yellow. Therefor, you would have a 8 in 23 chance (8/23) of picking a yellow marble. Similarly, the question states that we have 6 red marbles. Meaning 6/23 marbles are red. So, one would have a 6 in 23 or 6/23 chance of picking a red marble.

Right triangle ABC is shown . Which equation can be used to solve for c

Answers

Answer:

A^2+B^2=C^2

-/(A^2+B^2)=C

Step-by-step explanation:

-/ means squareroot whats in the parenthese

Answer:

sin(50°) = 3/c

Step-by-step explanation:

Thank you in advance

Answers

4. The value f issue is the quantity  of shares multiplied by the price of each share.

25,000 shares x $9.20 = $230,000.

The answer is b.$230,000

5. Total selling expense would be the commission plus all the fees.

Multiply the value of issue by the commission percentage and then add the other costs.

230,000 x 0.065 = 14,950

14,950 + 1,985 = $16,935

The answer is a. $16,935

6. Divide the total selling expense by the number of shares:

750,000 / 900,000 = 0.83

The answer is d. $0.83

The inequality x + 2y ≥ 3 is satisfied by which of the following points? (Select all that apply.)

(1, 1)
(-3, 4)
(-2, 2)
(5, -2)

Answers

Answer:

(1,1), (-3,4)

Step-by-step explanation:

Given  x + 2y ≥ 3

Rewrite the inequality as;

x + 2y = 3

Form a table for values of x and y

x        y

3        0

1         1

-3        3

Plot the points on a Cartesian plane

From the graph, the points are; (1,1), (-3,4)

For this case we have the following inequality:

[tex]x + 2y \geq3[/tex]

We substitute each of the points and see which one is fulfilled:

Point A: (1,1)

[tex]1 + 2 (1) \geq3\\1 + 2 \geq3\\3 \geq3[/tex]

Is fulfilled!

Point B: (-3,4)

[tex]-3 + 2 (4) \geq3\\-3 + 8 \geq3\\5 \geq3[/tex]

Is fulfilled!

Point C: (-2,2)

[tex]-2 + 2 (2) \geq3\\-2 + 4 \geq3\\2 \geq3[/tex]

It is not fulfilled!

Point D: (5, -2)

[tex]5 + 2 (-2) \geq3\\5-4 \geq3\\1 \geq3[/tex]

It is not fulfilled!

Answer:

Option A and B

6x + 4(3x-7) = 116 x=​

Answers

Answer:

x = 8

Step-by-step explanation:

Given

6x + 4(3x - 7) = 116 ← distribute the parenthesis on the left side

6x + 12x - 28 = 116 ← collect like terms on left side

18x - 28 = 116 ( add 28 to both sides )

18x = 144 ( divide both sides by 18 )

x = 8

Find the value of the expression.
y3 + x
for x = 6 and y = 1

Answers

Final answer:

Given the expression y^3 + x, upon substituting y = 1 and x = 6 into the equation, the resultant value of the expression is 7.

Explanation:

The question requires finding the value of the expression y3 + x when x = 6 and y=1. Since y is equal to 1, y3 (1 cubed) is also 1. So the expression becomes 1 + 6, which equals 7. Therefore, the value of the expression y3 + x for y = 1 and x = 6 is 7.

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Final answer:

The value of the expression  [tex]y^3 + x[/tex] for x = 6 and y = 1 is 7, which is found by substituting the values into the expression and performing the arithmetic operations.

Explanation:

To find the value of the expression [tex]y^3 + x[/tex]for x = 6 and y = 1, you simply substitute the given values into the expression and perform the arithmetic operations.

Here's the step-by-step calculation:

Replace y with 1: (1)3 + 6.

Calculate 1 cubed, which is 13 = 1.

Add the result to x, where x is 6: 1 + 6.

The final answer is 7.

This means that the value of the expression [tex]y^3 + x[/tex]when x = 6 and y = 1 is 7.

How can you express 1/1000 as a decimal

Answers

Answer:

0.001

Step-by-step explanation:

1/1000 is one-thousandths. As a decimal, the first place is the tenth, the second is the hundredths, and the third place is the thousandths. That is three steps away from the decimal point. That's where we put our 1, which gives us 0.001.

1/1000 can be expressed as one-thousandths and in decimal form as 0.001

How to convert from decimal to fraction?

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point, then we write 10 raised to that many power as the denominator and the considered number without any decimal point as the numerator.

As a decimal, the first place is the tenth, the second is the hundredths, and the third place is the thousandths.

1/1000

Which is three steps away from the decimal point 1, gives us 0.001.

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What will be the simple interest earned when you invest $1,000 for 3 years at 10 percent and the compound interest earned when you invest the same sum for 2 years at 5 percent ? The simple interest earned when you invest $1,000 for 3 years at 10 % is $ . The interest compounded when you invest the same sum for 2 years at 5 % is $ .

Answers

Answer:

Simple interest = $1,000(.10)(3) = $300

Compound interest =

$1,000(1.05)² - $1,000 = $102.50

the total cost of a jacket and a sweater was $77.54. if the price of the jacket was $3.98 less than the sweater, what was the price of the jacket ?​

Answers

Answer: The jacket cost $34.79

What are the solutions to the system of equations? Y=x^2-7x+12 and y=-x+7

Answers

[tex]\bf \begin{cases} y=x^2-7x+12\\ y=-x+7 \end{cases}\implies \stackrel{y}{x^2-7x+12}=\stackrel{y}{-x+7} \\\\\\ x^2-6x+12=7\implies x^2-6x+5=0 \\\\\\ (x-5)(x-1)=0 \implies \blacktriangleright x= \begin{cases} 5\\ 1 \end{cases} \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf y=-x+7\implies \stackrel{x=5}{y=-(5)+7}\implies \blacktriangleright y=2\blacktriangleleft \\\\\\ y=-x+7\implies \stackrel{x=1}{y=-(1)+7}\implies \blacktriangleright y=6 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (5,2)\qquad (1,6)~\hfill[/tex]

Answer:

[tex](5, 2)[/tex], [tex](1, 6)[/tex]

Step-by-step explanation:

We have a system composed of two equations

The first is a quadratic equation and the second is a linear equation.

[tex]y=x^2-7x+12[/tex]

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

To solve the system, equate both equations and solve for x

[tex]x^2-7x+12 = -x+7\\\\x^2 -6x +5=0[/tex]

To solve the quadratic equation we must factor it.

You should look for two numbers a and c that when multiplying them obtain as result 5 and when adding both numbers obtain as result -6.

This is:

[tex]a * c = 5\\a + c = -6[/tex]

The numbers searched are -5 and -1

So

[tex]x^2 -6x +5 = (x-5)(x-1) = 0[/tex]

Finally the solutions to the system of equations are:

[tex]x= 5[/tex], [tex]x=1[/tex]

What is the greatest common factor of the terms in the polynomial 8xt – 4х – 18x??
o 2х
o2x?
ООО

Answers

2x

so...

2x (4t - 2 - 9)

2x (4t -  11)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

It's 2x.

Step-by-step explanation:

The GCF of 8, 4 and 18 is 2.

The GCF of xt x and x  is x.

Which of the following is the equation of a hyperbola with center at (0, 0), with a = 4, b = 1, opening horizontally?

Answers

Answer:

The equation of the hyperbola is x²/16 - y²/1 = 1

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (0 , 0) and transverse axis parallel to the x-axis is

  x²/a² - y²/b² = 1

# The length of the transverse axis is 2a

# The coordinates of the vertices are (±a , 0)

# The length of the conjugate axis is 2b

# The coordinates of the co-vertices are (0 , ±b)

# The coordinates of the foci are (± c , 0),  

# The distance between the foci is 2c where c² = a² + b²

* Now lets solve the problem

∵ The center of the hyperbola is (0 , 0)

∵ It is opening horizontally

∴ x²/a² - y²/b² = 1

∵ a = 4 , b = 1

∴ a² = (4)² = 16

∴ b² = (1)² = 1

∴ x²/16 - y²/1 = 1

∴ The equation of the hyperbola is x²/16 - y²/1 = 1

x²/16 - y²/1 = 1

Step-by-step explanation:

HURRY ILL GIVE BRAINLIEST!!!
Suppose a line has slope m and passes through the point (a, b). Which other point MUST also be on the graph?
A) (a + m, b + 1)
B) (a + m, b - 1)
C) (a + 1, b - m)
D) (a + 1, b + m)

Answers

ANSWER

D) (a + 1, b + m)

EXPLANATION

The given line passes through (a,b) and has slope m.

The equation is:

[tex]y - b = m(x - a)[/tex]

When x=a+1, we obtain

[tex]y - b = m(a + 1 - a)[/tex]

This

[tex]y = m( 1 ) + b[/tex]

[tex]y = m + b[/tex]

Therefore,(a + 1, b + m) must also lie on this line.

The correct answer is D.

Answer:

d

Step-by-step explanation:

I got it correct

Write the point-slope form of an equation for a line that passes through the point with the given slope (–6, –6), slope = -4/7
a.
y – 6 = -4/7(x + 6)
c.
y + 6 =-4/7(x + 6)
b.
y + 6 = -4/7(x – 6)
d.
y + 6 = -4/7(x + 6)

Answers

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - [tex]\frac{4}{7}[/tex] and (a, b) = (- 6, - 6), hence

y - (- 6) = - [tex]\frac{4}{7}[/tex] (x - (- 6) ), that is

y + 6 = - [tex]\frac{4}{7}[/tex](x + 6) ← c or d

Answer:

y + 6 = -4/7(x + 6)

Step-by-step explanation:

The point-slope form of an equation for a line that passes through a point

( a, b )with a slope m is given as;

[tex]y-a=m(x-b)[/tex]

we substitute the given values into the given equation above and simplify. Our point is given as (–6, –6) while the slope is -4/7;

[tex]y-(-6)=-\frac{4}{7}(x-(-6))\\\\y+6=-\frac{4}{7}(x+6)[/tex]

An alloy is composed of nickel, zinc, and copper in a ratio of 3:4:13. How many kilograms of each metal is needed to make 4 kg of this alloy?

Answers

Answer:

3/5 kg of nickel, 4/5 kg of zinc and 13/5 kg of copper

Step-by-step explanation:

we know that

An alloy is composed of nickel, zinc, and copper in a ratio of 3:4:13

so

(3+4+13)=20 kg

That means

For 20 kg of alloy is needed 3 kg of nickel, 4 kg of zinc and 13 kg of copper

so

using proportion

Find the kilograms of nickel needed for 4 kg of alloy

20/3=4/x

x=3*4/20

x=12/20

x=3/5 kg of nickel

Find the kilograms of zinc needed for 4 kg of alloy

20/4=4/x

x=4*4/20

x=16/20

x=4/5 kg of zinc

Find the kilograms of copper needed for 4 kg of alloy

20/13=4/x

x=13*4/20

x=52/20

x=13/5 kg of copper

Final answer:

To create 4 kg of an alloy with nickel, zinc, and copper in a 3:4:13 ratio, you will need 0.6 kg of nickel, 0.8 kg of zinc, and 2.6 kg of copper.

Explanation:

In this problem, we are being asked to make 4 kilograms of an alloy for which the mixture ratio of nickel, zinc, and copper is given as 3:4:13 respectively.

To find the quantity of each metal needed, we first need to understand that the ratio represents parts of the whole. In this case, the whole is the total weight of the alloy, which is 4 kilograms. Therefore, the sum of the ratio numbers (3+4+13=20) represents this total weight. Each part of the ratio represents a fraction of this total weight, so for any individual metal, the weight in kilograms will be  (its ratio number / the total ratio number) * the total alloy weight.

For nickel, it would be (3/20)*4 = 0.6 kg. For zinc, the calculation is (4/20)*4 = 0.8 kg. And for copper, it will be (13/20)*4 = 2.6 kg.

So, to make 4 kg of this alloy, 0.6 kg of nickel, 0.8 kg of zinc, and 2.6 kg of copper are required.

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math help plss !! uwu im stuck.

Answers

Step-by-step explanation:

1) The four points are:

(x₁, y₁) = (-2, -1)

(x₂, y₂) = (3, 13)

(x₃, y₃) = (15, 5)

(x₄, y₄) = (13, -11)

Using the distanced formula the four side lengths are:

d₁₂ = √((13−-1)² + (3−-2)²) = √221

d₂₃ = √((5−13)² + (15−3)²) = √208

d₃₄ = √((-11−5)² + (13−15)²) = √260

d₄₁ = √((-1−-11)² + (-2−13)²) = √325

None of the lengths are equal, so we know this isn't a rhombus, parallelogram, or kite.  Is it a trapezoid?  To find out, let's find the slopes between the two lines that look like they might be parallel.

m₂₃ = (5 - 13) / (15 - 3) = -2/3

m₄₁ = (-1−-11) / (-2−13) = -2/3

They are indeed parallel.  So this is a trapezoid.

2) Given:

PS ≅ QR

m∠P + m∠Q = 180

m∠R + m∠S = 180

∠P ≅ ∠S

By converse of Alternate Interior Angles Theorem, since ∠P and ∠Q are supplementary, line PS and QR must be parallel.

If a quadrilateral has one pair of opposite sides that are both parallel and congruent, then it is a parallelogram.

Adjacent angles of a parallelogram are supplementary, so m∠P + m∠S = 180.

Since ∠P ≅ ∠S, then by definition of congruent angles, m∠P = m∠S.

Substitution:

m∠P + m∠P = 180

m∠P = 90

Substitution:

m∠S = 90

Opposite angles of a parallelogram are congruent, so m∠Q = m∠S = 90 and m∠R = m∠P = 90.

A parallelogram with four right angles is a rectangle.

Find the circumference of the circle. Use π ≈ 3.14.


8 cm

50.24 cm

200.96 cm

16 cm

Answers

Answer:

50,24cm

Step-by-step explanation:

For circumference, you can use C = πd OR 2πr = C:

3,14[16] = 50,24

2[3,14][8] = 50,24

The diameter is double the radius.

I am joyous to assist you anytime.

A recent study on the relationship between children's weight and their achievement test scores determined the correlation coefficient to be .9734. Which is the most reasonable conclusion based on the correlation coefficient?
A) Children who weigh more score lower on achievement tests.
B) As age increases, so do body weight and achievement test scores.
C) Children who weigh more spend more time on studying for achievement tests.
D) Children should increase their food intake to increase their achievement test scores.​

Answers

Answer:

C. Children who weigh more spend more time on studying for achievement test .

Step-by-step explanation:

Correlation is a measure of relationship , mutual co-interdependence (fluctuation) between two quantitative variables .

Direct / Positive (+) correlation means the variables are directly related - one increase , other increase & one increase , other decrease .                                         Inverse / Negative (-) correlation means the variables are inversely related - one increase , other decrease & one decrease, other increase .                       It lies between -1 to +1 . Correlation more than + 0.5 implies Strong correlation, less than that implies Weak correlation.

The correlation between above variables - weight and achievement test score is 0.9734 i.e there is Strong Positive relationship . So , increase in one strongly leads to increasing trend in other

Answer:

B) As age increases, so do body weight and achievement test scores.

Step-by-step explanation:

if f(x)= x squared-2x-8 and g(x)= 1/4x-1 for which values of x is f(x)=g(x)? explain and show work please A. -1.75 and -1.438 B. -1.75 and 4 C. -1.438 D. 4 and 0 ​

Answers

Answer:

B. -1.75 and 4

Step-by-step explanation:

f(x)=g(x)

Input the equations

x²-2x-8 = 1/4x-1

add 1 to both sides

and subtract 1/4x from both sides

x²-2 1/4x - 7 = 0  

factor

a + b = -2 1/4

a * b = -7

1.75 + -4 = -2 1/4

1.75 * -4 = -7

reverse their symbols

1.75 becomes -1.75 and -4 becomes 4.

Answer:

[tex]\boxed{\text{B. x = 4 and x = -1.75}}[/tex]

Step-by-step explanation:

ƒ(x) = x² - 2x – 8; g(x) = ¼x -1

If ƒ(x) = g(x), then

x² - 2x – 8 = ¼x -1

One way to solve this problem is by completing the square.

Step 1. Subtract ¼ x from each side

[tex]x^{2} - \dfrac{9}{4}x - 8 = -1[/tex]

Step 2. Move the constant term to the other side of the equation

[tex]x^{2} - \dfrac{9}{4}x = 7[/tex]

Step 3. Complete the square on the left-hand side

Take half the coefficient of x, square it, and add it to each side of the equation.

[tex]\dfrac{1}{2} \times \dfrac{9}{4} = \dfrac{9}{8};\qquad \left(\dfrac{9}{8}\right)^{2} = \dfrac{81}{64}\\\\x^{2} - \dfrac{9}{4}x + \dfrac{81}{64} = 7\dfrac{81}{64} = \dfrac{529}{64}[/tex]

Step 4. Write the left-hand side as a perfect square

[tex]\dfrac{1}{2} \times \dfrac{9}{4} = \dfrac{9}{8};\qquad \left(\dfrac{9}{8}\right)^{2} = \dfrac{81}{64}\\\\x^{2} - \dfrac{9}{4}x + \dfrac{81}{64} = 7\dfrac{81}{64} = \dfrac{529}{64}[/tex]

Step 5. Take the square root of each side

[tex]x - \dfrac{9}{8} = \pm\sqrt{\dfrac{529}{64}} = \pm\dfrac{23}{8}[/tex]

Step 6. Solve for x

[tex]\begin{array}{rlcrl}x - \dfrac{9}{8} & =\dfrac{23}{8}& \qquad & x - \dfrac{9}{8} & = -\dfrac{23}{8} \\\\x & =\dfrac{23}{8} + \dfrac{9}{8}&\qquad & x & = -\dfrac{23}{8} + \dfrac{9}{8} \\\\x& =\dfrac{32}{8} &\qquad & x & \ -\dfrac{14}{8} \\\\x& =4 & \qquad & x & -1.75 \\\end{array}\\\\\text{f(x) = g(x) when \boxed{\textbf{x = 4 or x = -1.75}}}[/tex]

Check:

[tex]\begin{array}{rlcrl}4^{2} - 2(4) - 8 & = \dfrac{1}{4}(4) -1&\qquad & (-1.75)^{2} - 2(-1.75) - 8 & = \dfrac{1}{4}(-1.75) - 1\\\\16 - 8 -8& = 1 - 1&\qquad & 3.0625 +3.5 - 8 & = -0.4375 - 1 \\\\0& =0&\qquad & -1.4375 & = -1.4375 \\\\\end{array}[/tex]

The diagram below shows that the graph of g(x) intersects that of the parabola ƒ(x) at x = -1.7 and x = 4.

Simplify the expression. Write the answer using scientific notation. 0.3(8.2 x 10^-3)

Answers

Answer:

0.3(8.2 x 10^-3) = 2.46 X 10 ^ -3

Step-by-step explanation:

We need to solve the equation 0.3(8.2 x 10^-3) and write answer in scientific notation.

Solving,

= 0.3(8.2 x 10^-3)

= 0.3 * 0.0082

= 0.00246

Writing in scientific notation

= 2.46 X 10 ^ -3

So, after solving the expression 0.3(8.2 x 10^-3) the result is 2.46 X 10 ^ -3.

What is the end behavior of the graph of f(x) = x5 – 8x4 + 16x3?
Answer: B.) f(x) => -∞ as x => -∞; f(x) => +∞ as x => +∞
The graph touches, but does not cross, the x–axis at x =__
The graph of the function crosses the x–axis at x = ___

Answers

Answer: End behaviour is,

f(x) => -∞ as x => -∞;

f(x) => +∞ as x => +∞

The graph touches, but does not cross, the x–axis at x = 4

The graph of the function crosses the x–axis at x = 0

Step-by-step explanation:

Given function is,

[tex]f(x)=x^5-8x^4+16x^3----(1)[/tex]

The degree of f(x) is 5 ( odd ) with positive leading coefficient,

Hence, the end behaviour of f(x) is,

f(x) => -∞ as x => -∞;

f(x) => +∞ as x => +∞

Now, from equation (1),

[tex]f(x)=x^3(x^2-8x+16)[/tex]

If f(x) = 0,

[tex]x^3(x^2-8x+16)=0[/tex]

[tex]\implies x^3=0\text{ or }x^2-8x+16=0[/tex]

[tex]x^3=0\text{ or }(x-4)^2=0[/tex]

[tex]x^3=0\text{ or }x-4=0[/tex]

[tex]\implies x=0\text{ or }x=4[/tex]

Now, the multiplicity of 4 is 2 ( even )

Thus, the graph touches, but does not cross, the x–axis at x = 4

Also, the multiplicity of 0 is 3 ( odd )

Hence, the graph of the function crosses the x–axis at x = 0

By using the concept of end behavior of a function, the result is

f(x) [tex]\rightarrow[/tex] [tex]-\infty[/tex] as x [tex]\rightarrow -\infty[/tex] and f(x) [tex]\rightarrow[/tex] [tex]\infty[/tex] as [tex]x \rightarrow[/tex] [tex]\infty[/tex]

The graph touches, but does not cross the x - axis at x = 4 as the multiplicity of 4 is even

The graph of the function crosses the x - axis at x = 0 as the multiplicity of 0 is odd.

What is end behavior of a function?

Let the function be f(x). End behavior of a function f(x) indicates how will the function behaves as x tends to +[tex]\infty[/tex] and [tex]-\infty[/tex]

Here,

f(x) = [tex]x^5 - 8x^4 + 16x^3[/tex]

[tex]\lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} x^5 - 8x^4 + 16x^3\\\\= -\infty[/tex]

[tex]\lim_{x \to \infty} f(x) = \lim_{x \to \infty} x^5 - 8x^4 + 16x^3\\\\= \infty[/tex]

So f(x) [tex]\rightarrow[/tex] [tex]-\infty[/tex] as x [tex]\rightarrow -\infty[/tex] and f(x) [tex]\rightarrow[/tex] [tex]\infty[/tex] as [tex]x \rightarrow[/tex] [tex]\infty[/tex]

f(x) = [tex]x^5 - 8x^4 +16x^3[/tex]  

     = [tex]x^3(x^2 - 8x +16)\\[/tex]

     = [tex]x^3(x - 4)^2[/tex]

[tex]x^3 = 0[/tex] or [tex](x - 4)^2 = 0[/tex]

[tex]x = 0[/tex] (Multiplicity 3 which is odd)

[tex]x = 4[/tex] (Multiplicity 2 which is even)

So The graph touches, but does not cross the x - axis at x = 4 as the multiplicity of 4 is even

The graph of the function crosses the x - axis at x = 0 as the multiplicity of 0 is odd.

To learn more about end behavior of a function, refer to the link-

https://brainly.com/question/1365136

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What does it mean to be a unit of account

Answers

Final answer:

A unit of account is a standardized metric for determining the worth of items and services in an economy, facilitating comparisons, trade-offs, and accounting. It eliminates the inefficiencies of barter by providing a common denominator for value.

Explanation:

Unit of account is one of the fundamental functions of money, serving as a standardized metric for determining the worth of items and services in an economy. This function allows for the assignment of prices and the performance of accounting, which is vital for making rational economic decisions. In essence, it provides a common denominator by which value can be measured, allowing for easier comparison and exchange. For instance, if an accountant charges $100 to file a tax return, this monetary amount can also represent the value of other goods, such as two pairs of shoes priced at $50 each. This facilitates trade-offs and helps to calculate revenue, expenditure, and savings, among other economic activities.

Without a unit of account, the economic system would likely rely on barter, which is significantly less efficient due to the necessity for a double coincidence of wants. Modern economies use fiat money as their unit of account, which has no intrinsic value but is declared legal tender by the government.

A car has a length of 193.2 inches. A scale drawing is made using a ratio of 20:1 . What is the length of the scale drawing?

Answers

The ratio of 20:1 means for every 20 inches the car is in real life, the drawing will be 1 inch.

To find the length of the drawing, divide the length of the real car by 20.

193.2 / 20 = 9.66 inches.

3 tons of compost cost $8,280.00. What is the price per pound?

Answers

Answer:

$1.38 per pound

Solution:

1 ton = 2,000 pounds

2,000 * 3 = 6,000 pounds

8,280 / 6,000 = $1.38 per pound.

Hope This Helps ;)

Answer: 8,280 divided by 6,000   is 1.3,

Step-by-step explanation: there are 2,000 pounds in one ton so 3 tons would be 6,000 pound so divivde the pounds from the price

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