For linear function f, f(2)=0 and f(4)=-6.
Write function f in slope-intercept form.
Hint
Examples:
f(5)=0 means (5,0) is a point on the line.
f(3)=-2 means (3,-2) is a point on the line.
How do you find the slope of the line when you have 2 points?

Answer:

Its the 3rd one

Step-by-step explanation:

The value of x in . (4x-101)° = (2x+3) is 52°.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

The value of x. (4x-101)° = (2x+3)

Collect the like terms

4x - 2x = 3 + 101

2x = 104

Divide

x = 104 / 2

x = 52°

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Complete question

Find the value of x. (4x-101)° = (2x+3)

Answer:

92 apples remaining

Step-by-step explanation:

2 * 69 = 138 apples

138 * (3/9) =

138 * (1/3) =

138 * 1/3 =

138/3 = 46 apples

138 - 46 = 92 apples remaining

Answer:

you have 2 apples

then you got it 69 times= 2×69 = 138

then you give 3 ninths to a friend

138/9 = 15.33

you gave it 3 one-ninths = 3× 15.33 = 46

so must be left with 138-46 = 92

Answer:

Step-by-step explanation:

986

the Discriminant will always be greater than or equal to zero. This means that the polynomial has at least one real root.

Let f(x) = a0 + a1x + a2x2 + a3x3 be a polynomial function of odd degree 3.

We know that the degree of a polynomial is the highest power of the variable in the equation. Since the degree of f(x) is 3, then a3 ≠ 0.

Now, consider the Discriminant of the polynomial, which is defined as the expression below:

Discriminant = b2 - 4ac

In this case, b2 = a2^2, c = a0 and a = a3, thus the Discriminant is:

Discriminant = a2^2 - 4a0a3

Since a3 ≠ 0 (as mentioned before), the Discriminant will always be greater than or equal to zero. This means that the polynomial has at least one real root.

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Yes, it is possible to use the law of cosines to solve for one angle in a triangle.

The law of cosines states that in any triangle, the square of the length of any side (c) is equal to the sum of the squares of the lengths of the other two sides (a and b) minus twice the product of those sides and the cosine of the angle between them (C):

c^2 = a^2 + b^2 - 2ab * cos(C)

If you know the lengths of all three sides of a triangle (a, b, and c), you can use the law of cosines to solve for the cosine of one of the angles (C). Once you have the cosine of the angle, you can use the inverse cosine function (also known as the arccosine) to find the measure of the angle in degrees.

For example, if you know the lengths of sides a and b and the measure of angle C in a triangle, you can use the law of cosines to find the length of side c:

c = sqrt(a^2 + b^2 - 2ab * cos(C))

Alternatively, if you know the lengths of sides a and c and the measure of angle B in a triangle, you can use the law of cosines to find the length of side b:

b = sqrt(c^2 - a^2 - 2ac * cos(B))

In both cases, once you have found the value of one of the sides, you can use the law of sines to find the measure of the remaining angle in the triangle.

The graph of the Line Segment BC with the endpoints B(8,9) and C(-4,5) is shown below.

In the question ,

it is given that ,

the end points of the line segment is B(8,9) and C(-4,5) .

we have to graph the line segment BC.

first we mark the point on the coordinate plane , with point B and point C .

after that we join the points .

and the equation of the line segment is

(y - 5) = (9-5/8+4)*(x + 4)

(y - 5) = (1/3)*(x + 4)

3y - 15 = x + 4

x - 3y + 19 = 0

Therefore, the graph of the line segment BC is shown below.

The given question is incomplete , the complete question is

Graph line segment BC with endpoints B(8,9) and C(-4,5) and label the points.

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Answer:

  (a)  3m +4 = 6m

Step-by-step explanation:

You want to know which of the equations is false when the value of the variable is 5.

  3(5) +4 = 19 ≠ 6(5) . . . . . the given equation is false for m=5

  -5(5 -7) = -5(-2) = 10 . . . . true

  17 = 4(5) -3 = 20 -3 . . . . true

  5 +9 = 14 . . . . true

The area bounded by f(x)=3x³-3x²-x+8, g(x) = 2x³- 10x² + 29x+8

over the interval [1, 5] is 164 square units.

Exactly one element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The domain and codomain of the function are, respectively, the sets X and Y as a whole.

The first presentation of the idea of function that is known about was developed by two Persian mathematicians, Al-Biruni and Sharaf al-Din al-Tusi. Originally, functions were used to depict the desired relationship between two varying values. For example, time affects the position of a planet. Up to the 19th century, the functions that were taken into consideration were differentiable.

Given,

f(x)=3x³-3x²-x+8

g(x) = 2x³- 10x² + 29x + 8

And the interval is  [1, 5].

By using area formula,

A=[tex]\int\limits^a_b {f(x)-g(x)} \, dx[/tex]

A=[tex]\int\limits^a_b[/tex](Upper function-Lower function)dx

A=[tex]\int\limits^3_1[/tex][g(x)-f(x)]dx+[tex]\int\limits^5_3[/tex][f(x)-g(x)]dx

A=[tex]\int\limits^3_1[/tex](-x³-7x²+30x)dx+[tex]\int\limits^5_3[/tex](x³+7x²-30x)dx

A= (118/3)+(374/3)

A=164 square units.

Therefore, the area bounded by f(x)=3x³-3x²-x+8, g(x) = 2x³- 10x² + 29x+8

over the interval [1, 5] is 164 square units.

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As per the least-squares regression,

a) The residual for the high school senior with a foot length of 20cm and a height of 160cm is 2.94

b) As per the given standard deviation, the value of the context 5.9

The term standard deviation in math is defined as a measure of how dispersed the data is in relation to the mean.

Here we have given that the random sample of 65 high school seniors was selected from all high school seniors at a certain high school.

And we need to find following.

While we looking into the given question, as per the least-squares regression line, here the estimated height for a high school senior with a foot length of 20 cm is calculated as,

=> y = 2.599x + 105.08

Now, we have to apply the value of x as 20, then we get,

=> y = 2.599(20) + 105.08

=> y = 157.06

Therefore, the residual is calculated as,

=> 160 − 157.06 = 2.94

b) As per the given standard deviation, here the differences between each data point and its corresponding estimate varies with a standard deviation of 5.9 cm.

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The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the degrees of freedom.

How are the degrees of freedom determined?

Hence, the t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the degrees of freedom.

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Answer:

[tex]\textsf{System of equations: \quad }\begin{cases}x=\dfrac{1}{2}y\\\\2x+2y=360\end{cases}[/tex]

[tex]\begin{aligned} \textsf{Solutions}: \quad x &= 120^{\circ}\\y &= 60^{\circ}\end{aligned}[/tex]

Step-by-step explanation:

An obtuse angle is greater then 90° and less than 180°.

An acute angle is less than 90°.

Therefore, from inspection of the given diagram:

If the measures of the acute angles are one-half times the measures of the obtuse angles:

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

Angles in a quadrilateral sum to 360°.

[tex]\implies 2x+2y=360[/tex]

Therefore, the system of equations is:

[tex]\begin{cases}x=\dfrac{1}{2}y\\\\2x+2y=360\end{cases}[/tex]

Substitute the first equation into the second equation and solve for y:

[tex]\implies 2\left(\dfrac{1}{2}y\right)+2y=360[/tex]

[tex]\implies y+2y=360[/tex]

[tex]\implies 3y=360[/tex]

[tex]\implies \dfrac{3y}{3}=\dfrac{360}{3}[/tex]

[tex]\implies y=120[/tex]

Substitute the found value of y into the first equation and solve for x:

[tex]\implies x=\dfrac{1}{2} \cdot 120[/tex]

[tex]\implies x=60[/tex]

Answer:

-7 - 4/4

= -7 - 1

= -8

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

-7 - 4/4= -7 - 1= -8

Let f(t) be 51000+ (2100)t which represent Chelsea's salary at Company A and g(t) be 45000(1.041)t which Chelsea salary at Company B.

Chelsea's offer from company A includes a raise of $2100 annually and a starting salary of $45,000.

Since the increase is constant, the salary of Chelsea from Company A is a linear function, as can be seen here.

f(t) is salary of chelsea from company A after t years.

f(t) = 45000+ (2100)t

The offer made to Chelsea by company B includes a starting salary of $45,000 and an annual raise of 4.1%.

we can see here that raise is exponential, so raise is:

(1+4.1/100) = (1+0.041) = (1.041) per year.

Consequently, the salary of Chelsea from Company B is a function that is exponential.

g(t) is salary of chelsea from company B after t years.

g(t) = 45000(1.041)t

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The number of sticks in pattern 6 is; 26

The nth term of the sequence formed is; aₙ = 4n + 2

From the attached image, we see that;

Number of sticks in pattern 1 is 6

Number of sticks in pattern 2 is 10

Number of sticks in pattern 3 is 14

Thus, the sequence will be;

6, 10, 14, ...

This is an AP because the difference is 4.

The formula for the nth term of an AP is;

aₙ = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

In our sequence, first term; a = 6

Common difference; d = 10 - 6 = 4

Thus, the equation for the nth term is;

aₙ = a + (n - 1)d

aₙ = 6 + (n - 1)4

aₙ = 6 + 4n - 4

aₙ = 4n + 2

Now, substitute n = 6 in the above equation to find the number of sticks in pattern 6. This gives;

a₆ = 4(6) + 2

a₆ = 26

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No, the lines are not perpendicular because Line m has a slope of 2/3 and line n has a slope of 3/5.

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

For two lines to be perpendicular if the slopes are reciprocal of each other.

line m: 2/3

line n: 3/5

Therefore,

n ⊥ p is False.

The slopes are not negative reciprocal of each other. so the lines are not perpendicular.

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For the proportion of all hometowners in the united states that hold a home equity loan, confidence interval is (0.0992, 0.1508).

We have given that in a recent poll of 1000 homeowners in the United states, one in eight homeowners reports havinf a home equity loan that he or she is curently paying off.

If one in eight reports having a home equity loan then for 1000 hometowners = 1000/8 = 125.

Sample proportion p = 125/1000 = 0.125

given that confidence coefficient = 0.99

α = 1 - confidence coefficient = 1 - 0.99

α = 0.01    

z₀.₀₁ / 2 = 2.58

Therefore the interval estimate for the proportion of all homeowners in the United states that hold a home equity

                        = p ± z₀.₀₁/2 √p(1-p)/n

                        = 0.125 ± 2.58 √0.125(0.875)/1000

                        = 0.125 ± 2.58 √0.0001

                        = 0.125 ± 0.0258

                        = (0.125 - 0.0258,0.125 + 0.0258)

                        = (0.0992, 0.1508)

Hence (0.0992, 0.1508) is the confidence interval.

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The correct expression to model the cost of manufacturing b basketballs in 1 day is:

O $5.25b-$1,400.00

The fixed costs of manufacturing the basketballs are $1,400.00 per day, and the variable costs are $5.25 per basketball. To find the total cost of manufacturing b basketballs in 1 day, you need to add the fixed costs and the variable costs for each basketball.

The variable costs for b basketballs would be $5.25 * b. To find the total cost, you need to subtract the fixed costs of $1,400.00 from this amount. This can be represented by the expression $5.25b - $1,400.00.

The other expressions do not correctly represent the cost of manufacturing b basketballs in 1 day because they do not correctly account for both the fixed costs and the variable costs.

Answer:

Deepak have taken 5 days leave from the start of the work.

The answers to both subparts are shown:

(A) The derivative of f'(5) means the pace at which the price per pound changes in relation to the weight of coffee sold at $5 per pound.

(B) The unit of f'(5) is pounds/dollar.

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument.

Calculus's core tool is the derivative.

We may find the slope of a function at any point by using its derivative. We can find numerous derivatives by adhering to certain rules.

For instance: A constant value, such as 3, always has a slope of 0.

(A) Meaning of derivative of: f'(5)

We have: Q = f(p) ...(1)

Differentiating Q in relation to p results in:

qQ/dp = f'(p) ...(2)

The rate of change of the price per pound in relation to the volume of coffee sold is implied by equation (2).

If p = 5, we get:

qQ/dp = f'(5) ...(3)

The rate at which the price per pound changes in relation to the amount of coffee sold at $5 per pound is implied by equation (3).

(B) Unit of f'(5):

Equation (3)'s result that qQ/dp = f'(5) suggests that f'(5) units are pounds/dollar.

Therefore, the answers to both subparts are shown:

(A) The derivative of f'(5) means the pace at which the price per pound changes in relation to the weight of coffee sold at $5 per pound.

(B) The unit of f'(5) is pounds/dollar.

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Correct question:
The quantity (in pounds) of gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q = f(p). (a) What is the meaning of the derivative f '(5)? The rate of change of the price per pound with respect to the quantity of coffee sold. The supply of coffee needed to be sold to charge $5 per pound. The rate of change of the quantity of coffee sold with respect to the price per pound when the price is $5 per pound. The rate of change of the price per pound with respect to the quantity of coffee sold when the price is $5 per pound. The price of the coffee as a function of the supply. What are the units of f '(5)? dollars dollars/pound pounds/(dollars/pound) pounds dollars/(pound/pound) pounds/dollar

Answer:

x = 7/3.

Step-by-step explanation:

DE is parallel to BC and AD= DB and AD = EC.

So, AD/DB = (x+1)/(4x-6)

(x + 1)/(4x - 6) = 1

x + 1 = 4x - 6

1 + 6 = 4x - x

3x = 7

x = 7/3.

A study about the diet of undergraduate students,

5) Chi-square statistic test , would use to determine if the observed and expected frequencies of diets are consistent. With null hypothesis as the observed and expected frequencies of diets are consistent.

6) The excepted students to eat

meat = 165

exclusively vegetarian= 6

strict vegetarian= 1

7) Chi-square statistic value is 62.755 and degree of freedom are 2 . The critical value for Chi-square statistic is 0.00001

8) P-value< 0.05, so reject the null hypothesis.

Therefore there is no sufficient evidence to support that the observed and expected frequencies of diets are consistent.

A random sample of undergraduates in the University of Virginia dining hall.

Sample size , n = 175

Three categories are given as shown in above table with percentage of report eating a diet.

Report also consists observed values about the number of students diet including the three different categories

5) The Chi-square test would use to determine the required result. Consider Null and alternative hypothesis as :

H₀ : the observed and expected frequencies of diets are consistent

Hₐ : the observed and expected frequencies of diets are not consistent

χ² =∑(Oᵢ - Eᵢ)²/Eᵢ

where, χ² --> chi-square cofficient or value

Oᵢ --> observed values which are provided

Eᵢ --> excepted values

Excepted values , Eᵢ = n× p

here we assume that,

6) The number of students would you expect to eat meat = 168

The number of students would you expect to eat exclusively vegetarian

= 6.125 ~ 6

The number of students would you expect to eat strict vegetarian = 0.875 ~ 1

7) Degree of freedom,df = k - 1 = 2, where k denotes total number of categories here

Chi-square statistic, χ² = ∑(Oᵢ - Eᵢ)²/E

χ² = 62.755

Using chi-square table, the critical chi-square value for χ² = 62.755 and degree of freedom 2 is 0.00001 ..

8) Significance level, alpha = 0.05

As we see that p-value = 0.00001< alpha = 0.05

So, we reject the null hypothesis.

Thus, there is no sufficient evidence to support null hypothesis.

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The dimensions giving the minimum surface area are  r = 0.98 cm approx. and h = 1.998 cm .

What is surface area?

The surface area of a solid object could be a live of the full area that the surface of the article occupies.

Main body:

The surface area of the closed cylinder is given by,

S = 2πr²+2πrh

And volume is given by,

V = πr²h

Where, R is radius and h is height of cylinder.

Volume is given to be  6 cm³.

V = πr²h = 6

h = 6/πr²

Inserting this value of h in Surface area equation, we get,

S = 2πr²+ 2πr ( 6/πr²)

S = 2πr² + 12 /r

Now differentiating wrt x to find minimum, inserting ds/dr = 0 , we get,

4πr = 12/r²

r = (3/π)¹/³

r = 0.98 cm approx.

h = 6/π *(0.98)²

h = 6/3.017

h = 1.998 cm

Hence ,the dimensions giving the minimum surface area are  r = 0.98 cm approx. and h = 1.998 cm .

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Answer isn't one of your options, it is 34.

[tex]f(9) = (3(9)+7)[/tex]

[tex]f(9) = (27+7)\\ \\f(9) = 34[/tex]

[tex]f(9) = 34[/tex].

The probability of rolling a six on any given roll is constant, so the probability distribution is a geometric distribution.

What is a probability distribution?

A probability distribution is a function that describes the probabilities of different outcomes in a random event or experiment. It is used to represent the likelihood of different outcomes occurring in a given situation.

In the case of rolling a die until the first time that a six turns up, the probability distribution for t (the number of rolls it takes to get a six) would describe the probability of getting a six on each roll.

The probability of getting a six on the first roll is 1/6, since there is a 1 in 6 chance of rolling a six on any given roll. The probability of getting a six on the second roll is 1/6, since there is still a 1 in 6 chance of rolling a six on any given roll. The probability of getting a six on the third roll is also 1/6, and so on.

The probability distribution for t in this case can be represented by the following table:

t Probability

1 1/6

2 1/6

3 1/6

4 1/6

5 1/6

... ...

This probability distribution indicates that the probability of getting a six on the first roll is 1/6, the probability of getting a six on the second roll is 1/6, and so on.

Hence, the probability of rolling a six on any given roll is constant, so the probability distribution is a geometric distribution.

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The exact amounts for each category are given as follows:

The exact amounts for each category are obtained applying the proportion  relative to the percentage of each category, that is, multiplying the decimal equivalent of the percentage by the total amount of $800.

Hence the amounts are given as follows:

The pie chart with the categories and their percentages is given by the image shown at the end of the answer.

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The lower estimate and upper estimate of the erupted materials of total q(6) quantity after 6 seconds is equal to 160 metric tons and 218 metric tons respectively.

As given in the question,

Reading of the rate is represented by r(t) in metric tons

Time interval in seconds:

t :       0     1     2       3      4       5       6

r(t) :  2     10    18     32    44     54     60

Lower estimate for the q(6) quantity of the erupted material after 6 seconds.

= r(0)(1) + r(1)(1) + r(2)(1) + r(3)(1)+ r(4)(1) + r(5)(1)

= 2 + 10 + 18 + 32 + 44 + 54

= 160

Upper estimate for the q(6) quantity of the erupted material after 6 seconds.

=  r(1)(1) + r(2)(1) + r(3)(1)+ r(4)(1) + r(5)(1) + r(6)(1)

=  10 + 18 + 32 + 44 + 54 + 60

= 218

Therefore, the lower estimate and upper estimate of the total q(6) quantity after 6 seconds is equal to 160 metric tons and 218 metric tons respectively.

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Answer: b. radius of the cone = 5; height of the cone = 12

Step-by-step explanation:

The volume of the cylinder is [tex]\pi (5^2)(4)=100\pi[/tex].

The only option that makes the same volume is option b. In this case, the volume is [tex]\frac{\pi}{3}(5^2)(12)=100\pi[/tex].

Answer:

Step-by-step explanation:

Part 1: true

(-4, -1) and (0, 2)

m = 2+1/0+4

m = 3/4

(0, -3) and (4, 0)

m = 0+3/4+0

m = 3/4

Part 2: true

It intercepts at (0, -3)

Part 3:

I can't really see what slope it says but if it says -3/5, then its true, otherwise it's false.

(5, -1) and (0, 2)

m = 2+1/0-5

m = 3/-5

m = -3/5

Part 4: false

Graph A would have 2 and Graph C would have different intersecting points.