Find the equation of the line that passes through point (6,1) with the x-intercept of 2.

The factor of the polynomial function 2x^3 - 3x^2 - 5x + 6 is (b) x -2

The polynomial is given as:

2x^3 - 3x^2 - 5x + 6

Next, we test the factors

Option A. x + 6

Set the factor to 0

x + 6 = 0

Solve for x

x = -6

So, we set up the division as follows:

-6  l   2    - 3     -5      6

Bring down the leading coefficient

-6  l   2    - 3     -5      6

        2

Multiply 2 and -6

-6  l   2    - 3     -5      6

                -12

        2

Add -3 and -12

-6  l   2    - 3     -5      6

                -12

        2      -15

Repeat this process

-6  l   2    - 3     -5      6

                -12    72    -402

        2      -15    67    -396

-396 is the remainder of the above division.

This means that x + 6 is not a factor of the polynomial

Option B. x - 2

Set the factor to 0

x - 2 = 0

Solve for x

x = 2

So, we set up the division as follows:

2  l   2    - 3     -5      6

Bring down the leading coefficient

2  l   2    - 3     -5      6

        2

Multiply 2 and 2

2  l   2    - 3     -5      6

                4

        2

Add -3 and -12

2  l   2    - 3     -5      6

                4

        2      1

Repeat this process

2  l   2    - 3     -5      6

                4      2      -6

        2      1       -3     0

0 is the remainder of the above division.

This means that x - 2 is a factor of the polynomial

There is no need to check for the remaining options

Hence, the factor of the polynomial function 2x^3 - 3x^2 - 5x + 6 is (b) x -2

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The exponential function that represent the concentration of algae cells per milliliter in d days is [tex]C(d) = 10(2)^d[/tex]

An equation is an expression that shows the relationship between two numbers and variables.

The standard form of an exponential funtion is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

Let C(d) represent the concentration of algae cells per milliliter in d days

At point (1, 20)

20 = ab   (1)

At point (2, 40)

40 = ab²     (2)

From equations 1 and 2:

b = 2, a = 10

The exponential function that represent the concentration of algae cells per milliliter in d days is [tex]C(d) = 10(2)^d[/tex]

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Answer:

  $264.78

Step-by-step explanation:

The government pays the interest on Briana's loan while she is in school. Her monthly payments will be for a loan of $26,000. The amount of the payment can be found from the amortization formula, or using a calculator or spreadsheet.

For a loan of principal amount P at annual rate r for t years, the monthly payment is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t)) = $26000(0.04125/12)/(1 -(1 +0.04125/12)^(-120)) = $264.78

Briana's monthly payment after she graduates is $264.78.

The total distance Ramiro travelled is 380 miles.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side).

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.

let x be the first day hours

let y be the second day hours.

now,

x = y + 2

40x = 60y + 20

Putting x= y+2

40(y + 2) = 60y + 20

40y + 80 = 60y + 20

60 = 20y

y = 3 hours

For, first day

x = y + 2

x = 3 + 2

x = 5 hours

Thus,

Total distance = 40(5) + 60(3)

=200 + 180

=380 miles

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Yes, the mean is 26.4 and the standard deviation is 3

We are given;

n = 40, p = 66% = 0.66, and  q = 1 – 0.66 = 0.34

If np ≥ 5 and np ≥ 5, then the binomial random variable, x is approximately normally distributed, then;

Mean; µ = np

Standard deviation; σ = √npq

where;

n is the sample size.

p is the population proportion.

q = 1 – p.

Calculating np and nq gives;

np = (40)(0.66) = 26.4

nq = (40)(0.34) = 13.6

Both np and nq are greater than 5, the normal distribution can be used to approximate the binomial distribution.

Thus, µ = np

µ = 40(0.66) = 26.4

Standard deviation;

σ = √(40 * 0.66 * 0.34)

σ = 3

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Answer: B) m∠3 + m∠5 = 180°

Step-by-step explanation:

Concept:

For this question, we will be looking at each answer choice and eliminating the incorrect ones

A) ∠1 ≅ ∠6

∠1 is an exterior angle

∠6 is an interior angle

They are in an alternative position

Since they are neither both exterior nor interior, they are not congruent

[tex]\large\boxed{FALSE}[/tex]

B) m∠3 + m∠5 = 180°

∠3 is an interior angle

∠5 is an interior angle

They are in a same-side position

Since they are both interiors, they fulfill the same-side interior angle theorem, which states: that if a transversal cuts two parallel lines, then the interior angles on the same side of the transversal are supplementary, which means their sum adds up to 180°.

[tex]\Huge\boxed{TRUE}[/tex]

C) m∠2 + m∠6 = 180°

∠2 is an exterior angle

∠6 is an interior angle

They are in a same-side position

Since they are on the same side, they fulfill the corresponding angle theorem which states: the angles that occupy the same relative position at each intersection are congruent to each other.

However, they are only congruent, they don't add up to 180°

[tex]\large\boxed{FALSE}[/tex]

D) ∠4 ≅ ∠8

∠4 is an interior angle

∠8 is an exterior angle

They are in an alternative position

Since they are neither both exterior nor interior, they are not congruent

[tex]\large\boxed{FALSE}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: Just guessing, try.. or dont.

Step-by-step explanation:

There are 3 seniors. To make up 100% we would have to do 33.33%. I would say that the probabilty is around 33.33, and don't know the different orders possible.

The best approach to calculating the stipulated 20% tip by means of fractions is to note that the tip is one-fifth of the total amount charged on the bill.

The percentage represented as; 20% can be expressed as a fraction.

This follows from the fact that the percentage, % symbol translates to divided by 100.

Consequently, we must note that the 20% translates to; 20/100 = 1/5.

Hence, the 20% tip is one-fifth of the total amount.

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The reverse number of the three-digit number is 732

Let the three-digit number be xyz.

So, the reverse is zyx

This means that

Number = 100x + 10y + z

Reverse = 100z + 10y + x

From the question, we have the following parameters:

y = x + 1

z = 1 + 2y

The sum is represented as:

100x + 10y + z + 100z + 10y + x = 10^3 - 31

100x + 10y + z + 100z + 10y + x = 969

Evaluate the like terms

101x + 101z + 20y = 969

Substitute y = x + 1

101x + 101z + 20(x + 1) = 969

101x + 101z + 20x + 20 = 969

Evaluate the like terms

101x + 101z + 20x = 949

121x + 101z = 949

Substitute y = x + 1 in z = 1 + 2y

z = 1 + 2(x + 1)

This gives

z = 2x + 3

So, we have:

121x + 101z = 949

121x + 101* (2x + 3) = 949

This gives

121x + 202x + 303 = 949

Evaluate the sum

323x = 646

Divide by 323

x = 2

Substitute x = 2 in z = 2x + 3 and y = x + 1

z = 2*2 + 3 = 7

y = 2 + 1 = 3

So, we have

x = 2

y = 3

z = 7

Recall that

Reverse = 100z + 10y + x

This gives

Reverse = 100*7 + 10*3 + 2

Evaluate

Reverse = 732

Hence, the reverse number of the three-digit number is 732

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The average rate of change obtained from the ratio of change in y to the change in x is 27

The average rate of change can be obtained using the relation :

Rate of change = (y2 - y1) ÷ (x2 - x1)

at; x1 = -3

y1 can be calculated from the function ;

y1= 3(-3³)-1

y1=-82

At ; x2 = 3

y2 can be calculated from the function ;

y2 = 3(3³)-1

y2=80

The rate of change can be calculated thus : (y2 - y1) ÷ (x2 - x1)

[80-(-82)]/[3-(-6])

162/6

27

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The maximum volume of the cylinder in exact form is; V_max = 2560π/27

Let us define the variables as:

Radius of cone = r

Radius of cylinder = x

Height of Cone = h

Height of Cylinder = y

The general equation for volume of the cylinder is;

V = πx²y  

Taking a strip of both figures and relating x, y, r & h as well as using ratios of similar triangles, we have:

Height of triangle above cylinder/Base of Triangle above cylinder   =   Height of full triangle/Base of full triangle

This gives;

(h - y)/2x  = h/2r

Making y the subject gives us;

h – y = hx/r

y =  h – hx/r

y = h(1 – x/r)

Plug in y into our Volume equation:

V(x) = πx²h(1 – x/r)

V(x) = πh(x²  - x³/r)

To get maximum volume, find the derivative of the volume and solve for when the derivative equals zero:

V'(x) = πh(2x  - 3x²/r)

V'(x) = 0

Thus;

(2x  - 3x²/r) = 0

x( 2r – 3x) = 0

Thus;

x = 0 or x = 2r/3

Put x = 2r/3 in our volume equation to find V_max

V_max  = πh((2r/3)² – (2r/3)³/r)

V_max = πh(4r²/9 - 8r²/27)

V_max = πh(12r²/27 - 8r²/27)

V_max = 4πhr²/27

Thus, at r = 8 and h = 10, we have;

V_max = 4π(10)8²/27

V_max = 2560π/27

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Answer: B. All real numbers

Step-by-step explanation:

See attached image.

Answer:

1/4 cups of milk and 1 1/3 Tbsp of butter.

Step-by-step explanation:

Milk : 3/4 multiplied by 1/3 = 3/12 = 1/4
Butter : 4 multiplied by 1/3 = 4/3 = 1 1/3

The critical value for the given confidence level, c = 0.90 and n = 21 is [tex]t_c=1.725[/tex].

The critical value is calculated as follows:

It is given that,

confidence level c = 0.90

sample size n = 21

Then,

degree of freedom,

(d.f) = n - 1 = 21 - 1 = 20

So, from the t-distribution table,

at d.f = 20 and the confidence level 0.90, the critical value is 1.725.

I.e., [tex]t_c[/tex] = 1.725

For this, α = (1 - 0.90)/2 = 0.05

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Answer:

x = 6

Step-by-step explanation:

the tangent- tangent angle UVW is half the difference of the intercepted arcs, that is

∠ UVW = [tex]\frac{1}{2}[/tex] (UW - WU ) , then

5x + 17 = [tex]\frac{1}{2}[/tex] (37x + 5 - (23x - 5) ) ← multiply both sides by 2

10x + 34 = 37x + 5 - 23x + 5

10x + 34 = 14x + 10 ( subtract 14x from both sides )

- 4x + 34 = 10 ( subtract 34 from both sides )

- 4x = - 24 ( divide both sides by - 4 )

x = 6

Based on the data presented, it can be concluded out of the 52 females 26 prefer cats.

To read the graph we must take into account that the rows refer to the preference of men, preference of women and those who have no preference.

On the other hand, the columns refer to the number of students of both genders who prefer or do not prefer each animal. Additionally, adding all the students of each gender we have the total of the sample.

According to the above, the total sample of female students would be 52.

According to the above, the fraction that expresses this relationship correctly is:

[tex]\frac{26}{52}[/tex]

Note: This question is incomplete because the graph is missing. Here is  the graph.

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The graph is shown in the attached image.

Answer:

32: X=54

31: Xx54+74

Answer:

[tex]2x+5y=41[/tex]

Step-by-step explanation:

Median of a triangle:  A line segment that connects a vertex of a triangle to the midpoint of the opposite side.

Vertex:  The point where any two sides of a triangle meet.

Given vertices of a triangle:

Find the midpoint of BC (Point D) by using the Midpoint formula.

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Define the endpoints:

Substitute the defined endpoints into the formula:

[tex]\textsf{Midpoint of BC}=\left(\dfrac{-21-33}{2},\dfrac{25+13}{2}\right)=(-27,19)[/tex]

Therefore, D = (-27, 19).

Find the slope of the median (line AD) using the Slope formula.

Define the points:

Substitute the defined points into the Slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{19-9}{-27-(-2)}=-\dfrac{2}{5}[/tex]

Therefore, the slope of the median is -²/₅.

Substitute the found slope and one of the points into the Point-slope formula to create an equation for the median.

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-9=-\dfrac{2}{5}(x-(-2))[/tex]

Simplify and rearrange the equation so it is in standard form Ax+By=C:

[tex]\implies 5(y-9)=-2(x+2)[/tex]

[tex]\implies 5y-45=-2x-4[/tex]

[tex]\implies 2x+5y-45=-4[/tex]

[tex]\implies 2x+5y=41[/tex]

Therefore, the equation of the median is:  

2x + 5y = 41

The monthly payment is $796.40.

The total amount she would deposit is $286,705.51

The total interest earned is $513,294.49

The payments made by Jessica are known as deferred annuities. Deferred annuities are when a series of payments are made in exchange for an amount of money in the future.

The formula that can be used to determine the amount of monthly deposit is: future value / annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

r = interest rate = 6%/12 = 0.5%

n = number of years = 30 x 12 = 360

Annuity factor = ](1.005^360) - 1] / 0.005 = 1004.515

Monthly payments = 800,000 / 1004.515 = $796.40

Total amount she would deposit = monthly payment x number of years x number of months in a year

$796.40 x 30 x 12 = 286,705.51

Total interest earned = value of the retirement account - total amount deposited

800,000 - 286,705.51 = 513,294.49

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The required coordinates of the unit circle for s = -11π/6 is (√3/2, 1/2). Using trigonometric functions, the required answer is calculated.

There are six trigonometric functions.

They are sin θ, cos θ, tan θ, sec θ, cosec θ, and cot θ.

Where θ - 0 to 360° or 0 to 2π

For a unit circle, the coordinates are given in the form of trigonometric functions as below:

x = cos θ and y = sin θ

Here it is given that s = θ = -11π/6

So, on substituting,

x = cos θ = cos (-11π/6)

⇒ x = √3/2

y = sin θ = sin (-11π/6)

⇒ y = 1/2

Thus, the required coordinate pair is (√3/2, 1/2).

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The value of sin 0 in quadrant 2 is 4/5

Given that cos 0 = -3/5

We have;

Let's find the opposite side, using Pythagorean theorem

5^2 = x^2 + (-3)^2

25 = x^2 + 9

collect like terms

x^2 = 25 - 9

x^2 = 16

x = √ 16

x = 4

We have that

sin 0 = opposite/hypotenuse

sin 0 = 4/5

It is important to note that the trigonometric identity 'sine' is positive in quadrant 2

sin 0 = 4/5

Hence, the value of sin 0 in quadrant 2 is 4/5

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Answer:

Step-by-step explanation:

An equation can be set up and solved based on the relation between the two speeds and the relation between time, speed, and distance.

  time = distance/speed

Let x represent the (slower) speed on the way home. Then the total time for the round trip was ...

  time going + time coming home = total time

  270/(x +11) +270/x = 9

  30x +30(x +11) = x(x +11) . . . . . . multiply by x(x+11)/9

  x^2 -49x -330 = 0 . . . . . . . .  rewrite in standard form

  (x -55)(x +6) = 0 . . . . . . . . factor

x = 55 or x = -6 . . . . . . . solutions to this equation; x < 0 is extraneous

Justin's rate on the way there was 66 mph; on the way home, it was 55 mph.

Answer:

1,680

Step-by-step explanation:

8 positions with basically 8 choices.

that is 8! arrangements.

but 2 is there 2 times.

8 is there 2 times.

5 is there 3 times.

only 3 is a single digit.

so, we need to eliminate every arrangement, where the 2s trade places, where the 5s trade places, and where the 8s trade places, because they are the same numbers.

that means we have to divide the 8! by 2!, then again by 2!, and again by 3!.

8! / (2! × 2! × 3!) = 8! / 24 = 1,680

The Average number of sheep grazed in per acre is 6 approx. in rancher’s herd.

According to the statement

We have given that the A rancher’s herd of 250 sheep grazes over a 40-acre pasture.

And we have to find the how many sheep are grazing on each acre.

So, For this purpose If we assume that the sheep are equally distributed, to see how many sheep there are in each acre we just divide the number of sheep by the number of acres. So,

we have to find the average of number of sheep in per acre.

We know that

The total area of the rancher’s herd = 40 acre

The number of sheep grazes in the land = 250 sheep

Now, we have to find the Average number

Average number of sheep grazed in per acre = 250/40

Average number of sheep grazed in per acre = 6 approx.

So, The Average number of sheep grazed in per acre is 6 approx. in rancher’s herd.

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Answer:

Step-by-step explanation:

a-b=21

5a-2b=18

Using elimination, we have

5a-5b=105

5a-2b=18

So:

3b=-87 so b=-29

Substituting, a=-8

(a,b)=(-8,-29)

Answer:

18 miles

Step-by-step explanation:

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