Use the rational root theorem to list all possible rational roots for each equation. Then find any actual rational roots. X^3-4x+1=0

Option B:

Equation of the line of best fit in slope-intercept form is [tex]y=\frac{1}{2}x+1[/tex].

Solution:

Take two points on the line (0, 1) and (4, 3).

So, [tex]x_1=0, y_1=1, x_2=4, y_2=3[/tex].

Slope of the line:

[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]$m=\frac{3-1}{4-0}[/tex]

[tex]$m=\frac{2}{4}[/tex]

[tex]$m=\frac{1}{2}[/tex]

y-intercept means the point which crosses at y-axis.

Here the point on the y-axis is (0, 1).

y-intercept (b) = 1

Slope-intercept form:

y = mx + b

[tex]$y=\frac{1}{2}x+1[/tex]

Equation of the line of best fit in slope-intercept form is [tex]y=\frac{1}{2}x+1[/tex].

Option B is the correct answer.

Answer:

3.5 alligators

Step-by-step explanation:

i did khan academy

Answer:

3.5

Step-by-step explanation:

I just answered it :) it was correct btw

Answer:

The diameter of the smaller can is ≅ 9.14 cm

Correct statement and question:

Two cylindrical cans are mathematically similar.

The larger can has a capacity of 1 liter and a diameter of 12 cm and the smaller can has a capacity of 440 ml.

Calculate the diameter, d, of the 440 ml can.

Source:

Previous question that can be found at brainly

Step-by-step explanation:

Let's recall that:

A. The formula of the volume of a cylinder is π*r²*h, where:

r is the radius of the cylinder (half of the length of the diameter) and h, represents the height of the cylinder.

B. 1 liter = 1,000 milliliters = 1,000 cubic centimeters

Therefore, we can find the height of the larger can, this way:

V = π*r²*h

Replacing with the value we know:

d = 12 ⇒ r = 6

1,000 = 3.1416 * 6² * h

1,000 = 113.0976h

h = 1,000/113.0976

h = 8.84 cm (rounding to the next hundredth)

Now we can find the ratio of the radius to the height of the larger can to find the measures of the smaller can, this way because the cylinders are mathematically similar:

Ratio = Radius/Height

Ratio = 6/8.84

Ratio = 0.6787

It means the radius of the smaller can is 0.6787 multiplied by the value of the height of the smaller can. Let x represent the height h of the smaller can, we can write this equation to solve for x:

V = π*r²*h

Replacing with the values we know:

height = x

radius = 0.6787x

440 = π * (0.6787x)² * x

440 = 3.1416 * 0.4606x² * x

440 = 1.4471x³

x³ = 440/1.4471

x³ = 304.06

∛x = ∛304.06

x = 6.73 ⇒ height of the smaller can = 6.73 cm and radius of the smaller can = 6.73 * 0.6787 = 4.57

If radius = 4.57 cm ⇒ diameter = 2 * 4.57 = 9.14 cm

The diameter of the smaller can is ≅ 9.14 cm

The diameter of the 440 ml can is approximately 9.12 cm.

To determine the diameter of the smaller can, we use the fact that the two cans are mathematically similar. This means that their dimensions have a constant ratio, known as the scale factor.

The capacity of the larger can is 1 liter (1000 ml), and the capacity of the smaller can is 440 ml.

The scale factor for volumes is given by:

Scale Factor (Volume) = (Volume of smaller can) / (Volume of larger can) = 440 ml / 1000 ml = 0.44

Since the cans are similar, the scale factor for the linear dimensions (such as diameter) is the cube root of the volume scale factor:

Scale Factor (Diameter) = ∛(Scale Factor (Volume)) = ∛(0.44)

Using a calculator, we find:

∛(0.44) ≈ 0.76

Now, we multiply the diameter of the larger can by this scale factor to find the diameter of the smaller can:

Diameter of the smaller can = Diameter of the larger can × Scale Factor (Diameter) = 12 cm × 0.76 ≈ 9.12 cm

Therefore, the diameter of the 440 ml can is approximately 9.12 cm.

Complete question:

Two cylindrical cans are mathematically similar.

The larger can have a capacity of 1 liter and the smaller can have a capacity of 440 ml.

Calculate the diameter, d, of the 440 ml can if the diameter of the larger can is 12 cm.

Final answer:

The store sold 1 and 2/5 more cases of juice on Friday than on Saturday.

Explanation:

To determine how many more cases of juice the store sold on Friday than on Saturday, we need to subtract the number of cases sold on Saturday from the number of cases sold on Friday.

Friday's sales: 6 and 1/5 cases
Saturday's sales: 4 and 4/5 cases

We convert these mixed numbers to improper fractions to make the subtraction easier:

Now we subtract the two fractions:

(31/5) – (24/5) = 7/5 cases

Convert the improper fraction back to a mixed number:

7/5 = 1 and 2/5 cases

So, the store sold 1 and 2/5 more cases of juice on Friday than on Saturday.

Answer: 3% (3/100), 4% (1/25), and 5% (1/20)

Step-by-step explanation:

So, there are 100 recordable DVDs, and 5 are defective. The way you find the answer is by dividing 100 by 100, which equals one. That means you have a one percent chance to select one random DVD. But, since you need to find the probability of selecting at least three non-defective DVDs, you would need to multiply 1 by 3, 4 or 5 to get the percentages for you probability.

Final answer:

The probability of selecting at least three non-defective disks from a pack with 5 defective ones among a total of 100 is found by summing the probabilities of selecting exactly three non-defective disks plus the probability of selecting all four non-defective disks.

Explanation:

The question asks for the probability of selecting at least three non-defective disks from a pack that contains 100 recordable DVDs, with 5 being defective. To solve this, we consider the scenarios where 3 or 4 non-defective disks are chosen out of the 4 disks we pick. We will calculate these probabilities using the hypergeometric distribution, which is apt for scenarios where we have a finite population without replacement.

Calculating the Probability:

Let X represent the number of non-defective disks selected.

There are two outcomes where at least three disks are non-defective: when exactly 3 are non-defective (one is defective) or when all 4 are non-defective.

Probability of selecting 3 non-defective disks and 1 defective disk (X = 3):
P(X = 3) = [number of ways to choose 3 non-defective from 95]
imes [number of ways to choose 1 defective from 5] / [number of ways to choose 4 from 100].

Probability of selecting 4 non-defective disks (X = 4):
P(X = 4) = [number of ways to choose 4 non-defective from 95] / [number of ways to choose 4 from 100].

The total probability of selecting at least three non-defective disks is the sum of these two probabilities: P(X = 3) + P(X = 4).

Answer:

A. 1

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The other dude did have the right answer, but for an explanation, you:

1. Take the 51,000 and multiply it by 22.65% (The sum of taxes for this job). You get 39448.5. You take 39448.5 and divide it by 12 (for monthly net income) and you get 3287.375 a month.

Then you:

2. Take 54,000 and multiply it by 28.65 (the sum of taxes for this job (remember that this job has an extra tax of 6%)). You get 38529. You take 38529 and divide it by 12 (for monthly net income) and you get 3210.75 a month.

Finally:

3. You just compare the monthly net incomes and see that marketing manager job pays around 70 more dollars a month. Hope that helped!

Answer:

Therefore,

[tex]\textrm{Volume of Ball}=14130\ inches^{3}[/tex]

Step-by-step explanation:

Given:

Spherical Shape Ball

[tex]Radius =15\ inches[/tex]

pi = 3.14

To Find:

Volume of Ball= ?

Solution:

Formula for Volume of Sphere is given by

[tex]\textrm{Volume of Sphere}=\dfrac{4}{3}\pi (Radius)^{3}[/tex]

Substituting the given values we get

[tex]\textrm{Volume of Ball}=\dfrac{4}{3}\times 3.14\times 15^{3}=14130\ inches^{3}[/tex]

Therefore,

[tex]\textrm{Volume of Ball}=14130\ inches^{3}[/tex]

Answer:

average = sum of observations/number

80=400/5

Therefore, the sum of the scores has to equal 400.

Step-by-step explanation:

400-(82+77+75+84)=x

400-(318)=x

x=82

That is the minimum score needed.

Answer:

60

Step-by-step explanation:

Step 1:  Solve for x

x + 3x + 2x = 180

6x / 6 = 180 / 6

x = 30

Step 2:  Find the measure of angle C

Angle C = 2x

Angle C = 2(30)

Angle C = 60 degrees

Answer:  60

Answer:

Therefore,

2²+5² = c² will be matched.

The equation that could be used to find the length of the hypotenuse is 2²+5² = c².

Pythagorean theorem is a fundamental relation in between the three sides of a right triangle.

It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

Given is right triangle we need to find an equation to determine the length of the hypotenuse,

To find the length of the hypotenuse of a right triangle you can use the Pythagorean theorem, that can be written as:

(base)² + (altitude)² = (hypotenuse)²

In this case, a=2, b=5 and c=c, so according to the Pythagorean theorem:

2²+5²=c²

Hence the equation that could be used to find the length of the hypotenuse is 2²+5² = c².

Learn more about Pythagoras theorem, click;

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Answer:

I = 130

Step-by-step explanation:

The sum of all four angles in a four-sided closed shape will ALWAYS be equivalent to 360 degrees. Also, the opposite angles of a parallelogram will ALWAYS be equivalent. This means F = H.

To begin, the measure of F, y + 7, and the measure of H, 3y - 79, are equal. This equation looks like: y + 7 = 3y - 79

Now subtract y from both sides: 7 = 2y - 79

Add 79 to both sides: 86 = 2y

And divide both sides by 2: 43 = y

Now that you have the value of y, plug 43 into y and solve for both equations:

43 + 7 = 3(43) - 79

50 = 129 - 79

50 = 50

So now we know that  the measure of angles F and H are 50. 50 + 50 is 100.

Since we know that the sum of all four sides must be equivalent to 360. subtract 100 from 360 to get the sum of the measures of angles I and G:

360 - 100 = 260

So now 260 must equal I + G. Since I and G must be equivalent, just divide 260 by 2 and you have your answer: 260/2 = 130

Answer:

Y=1/3x

Step-by-step explanation:

1) there is no y intercept as x=0 when y=0 so that rules out y=x-2

2) next, we will use the formula for slope to find the value of m

Y2-Y1/X2-X1

Where y2=-1

Y1=0

X2=-3

X1=0

So

-1-0/-3-0=-1/-3

Aka 1/3

So y=1/3x

Hope this helps!

Answer:

This is a statement not a question

Answer: 4*p=8

Step-by-step explanation:

You can use inverse operation to answer this equation.

Answer:

4*p=8

Step-by-step explanation: I took the test

Answer:

4 and -3

Step-by-step explanation:

4-3=1

4(-3)=-12

The two numbers that have a sum of 1 and a product of -12 is -4 & 3

From the question, we are determine the two unknown numbers by solving the quadratic equation

The given quadratic equation is

n² + n -12 = 0

The quadratic equation can be solved as follows

n² + n -12 = 0

By factorizing

n² +4n -3n -12 = 0

n(n+4) -3(n+4) = 0  

(n+4)(n-3) = 0

Then,

n+4 = 0 OR n -3 = 0

∴ n = -4 OR n = 3

Hence, the two numbers that have a sum of 1 and a product of -12 are -4 & 3

Learn more on Solving quadratic equations here: https://brainly.com/question/2320567

Answer:

3600

Step-by-step explanation:

960*3=2880

To find how many per hour: 960/24= 40

40*18=720

720+2880=3600

Answer:

3600 watts

Step-by-step explanation:

960 multiplied by 3 , then divide 18 by 24. Multiply 0.75 by 960, and then add 2880 and 720.

Good morning

Answer:

Step-by-step explanation:

56 increased by 25% = 56+25%

                                    = 56 + 56×(25÷100)

                                    =70

________________________________

:)

Answer: /2 is not greater than 6/8 and the answer to the question "Is 1/2 greater than 6/8?" is no. Note: When comparing fractions such as 1/2 and 6/8, you could also convert the fractions (if necessary) so they have the same denominator and then compare which numerator is larger.

Answer:

6/8 is greater than 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the image attached you can notice that line ZY is tangent at point Y.

Remember that the radius is always perpendicular to tangents, by definition, that means [tex]XY \perp ZY[/tex].

That means [tex]\triangle XYZ[/tex] is a right triangle where [tex]\angle Y = 90\°[/tex].

All these facts are deducted form having ZY as a tangent.

We know by given that

[tex]XZ=8+9=17[/tex]

[tex]XY=8[/tex], becaus it's the radius.

Using Pythagorean Theorem

[tex]17^{2} =8^{2}+ZY^{2}[/tex]

Solving for [tex]ZY[/tex]

[tex]ZY=\sqrt{17^{2} -8^{2} } \\ZY=\sqrt{289-64}\\ ZY=\sqrt{225}\\ ZY=15[/tex]

Therefore, the length of ZY must be 15 units to be tangent to circle X.

Answer:

15 units

Step-by-step explanation:

The guy above me has got it right! :D

Answer:

This is false

Step-by-step explanation:

xy is one term, x+y would be two terms

Answer:

False

Step-by-step explanation:

In an algebraic expression with terms, the terms are added together. Here all you have is x multiplied by y. xy is a single term. Since no term is being added to the term xy, all you have is one term, not two.

Value of x is 5. I remember doing this last year..

35a+45b=80

then we would do 99-80, and that gives us the value of c, 19

Answer:

x= −6−2y

Step-by-step explanation:

Subtract 2y from both sides of the equation x= −6−2y

Answer:-6-2y

Step-by-step explanation:

X+2y=-6

subtract 2y from both sides

X+2y-2y=-6-2y

X=-6-2y

Here we need to solve some expressions. Remember the following rules:

[tex](+)(+)=+ \\ \\ (-)(-)=+ \\ \\ (+)(-)=- \\ \\ (-)(+)=-[/tex]

Then, from the left side:

[tex]5-2\cdot 7=5-14=\boxed{-9} \\ \\ 5-2\cdot 4=5-8=\boxed{-3} \\ \\ 5-2\cdot 0=5-0=\boxed{5} \\ \\ 5-2\cdot -3=5+6=\boxed{11} \\ \\ 5-2\cdot 10=5-20=\boxed{-15} \\ \\ 5-2\cdot -8=5+16=\boxed{21} \\ \\[/tex]

from the right side:

[tex]-(-4)+3=4+3=\boxed{7} \\ \\ -(6)+3=-6+3=\boxed{-3} \\ \\ -(-8)+3=8+3=\boxed{11} \\ \\ -(-5)+3=5+3=\boxed{8} \\ \\ -(2)+3=-2+3=\boxed{1} \\ \\ -(15)+3=-15+3=\boxed{-12} \\ \\ -(-6)+3=6+3=\boxed{9}[/tex]

The equation of the line perpendicular to y = -2x + 8 is y = 1/2x + 8.

A line is perpendicular to another line if their slopes are negative reciprocals of each other. The slope of the line y = -2x + 8 is -2, so the slope of a line perpendicular to it would be 1/2.

Of the above choices, only line (C) has a slope of 1/2. Therefore, the equation of the line perpendicular to y = -2x + 8 is y = 1/2x + b, where b is the y-intercept.

To find the value of b, we can substitute a point on the line y = -2x + 8 into the equation y = 1/2x + b. For example, the point (0, 8) lies on the line y = -2x + 8. Substituting this point into the equation y = 1/2x + b, we get:

8 = 1/2 * 0 + b

b = 8

Therefore, the equation of the line perpendicular to y = -2x + 8 is y = 1/2x + 8.

for such more question on perpendicular

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Answer:

Step-by-step explanation:

bruh

Answer:

I need more information

Answer:

p = - 3

Step-by-step explanation:

Given

x² - 6x = 12

To obtain the required form use the method of completing the square

add ( half the coefficient of the x- term )² to both sides, thus

x² + 2(- 3)x + 9 = 12 + 9

(x - 3)² = 21

Thus p = - 3

Given the quadratic functions expressed as;

x² - 6x = 12

The value of p given the quadratic expression is -3

Complete the square at the left hand side of the equation.

Add the square of the half of coefficient of x to both sides.

coefficient of x = -6

Half of coefficient of x = -6/2 = -3

Square of the result = (-3)² = 9

Add 9 to both sides of the equation

x² - 6x + 9 = 12 + 9

Factoring the left hand side

(x-3)² = 21

Comparing the result with (x+p)² = q

The value of p wil be -3

Learn more here: brainly.com/question/13981588

Answer:

maybe just 41?

Step-by-step explanation:

It's asking for the small arc XY, so that would just be 41. Correct me if i'm wrong

The scale factor of the dilation from ABCD to A′B′C′D′ is 3.

Step-by-step explanation:

Step 1:

In the pre-image ABCD, the length of one of the sides is given as 14 units.

For the other shape A′B′C′D′, the same side as the previous shape is given as 8 units.

Step 2:

To determine the scale factor, we divide the measurement after scaling by the same measurement before scaling.

In this case, it is the given length of the sides CD and C′D′.

So the scale factor = [tex]\frac{C^{1} D^{1} }{CD} = \frac{8}{14} = \frac{4}{7} .[/tex]

So the shape ABCD is dilated by a scale factor of [tex]\frac{4}{7}[/tex] to produce the shape A′B′C′D′.

Answer: The answer is 4/7

Step-by-step explanation: the other persons work was correct!! so i got 100%