What is the equation of the line that passes through the point ( − 3 , 1 )and has a slope of 2/3

To find the maximum profit, we can look for the vertex of the parabolic function representing the profit.

The given profit function is:

\(Z = -3x^2 + 12x + 25\)

We can see that the coefficient of the \(x^2\) term is negative, which means the parabola opens downwards. This indicates that the vertex of the parabola represents the maximum point.

The x-coordinate of the vertex can be found using the formula:

\(x = \frac{-b}{2a}\)

In our case, a = -3 and b = 12. Plugging these values into the formula, we get:

\(x = \frac{-12}{2 \cdot (-3)}\\\\x = \frac{-12}{-6}\\\\x = 2\)

To find the maximum profit, we substitute the x-coordinate of the vertex into the profit function:

\(Z = -3(2)^2 + 12(2) + 25\\\\Z = -12 + 24 + 25\\\\Z = 37\)

Therefore, the maximum profit is 37.

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The equation of the tangent line to f(x) at the point (4, 35) is y = (9/2)x + 17

First, we need to find the slope of the tangent line at the point (4, 35). The slope of the tangent line is equal to the derivative of the function f(x) at x=4.

f(x) = 4x + x/2 + 1

Taking the derivative of f(x) with respect to x:

f'(x) = 4 + 1/2

Evaluating f'(4)

f'(4) = 4 + 1/2 = 9/2

So the slope of the tangent line at x=4 is 9/2.

Now we use the point-slope form of a line to find the equation of the tangent line.

y - y₁ = m(x - x₁)

where (x₁, y₁) is the point (4, 35) and m is the slope we just found:

y - 35 = (9/2)(x - 4)

Expanding and simplifying

y - 35 = (9/2)x - 18

y = (9/2)x + 17

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The linear equation that shows how many packages of breadsticks Dirk bought as (1/4)b.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have Dirk who brought [b] breadsticks to a potluck. The breadsticks are packaged in bags of 4.

Assume that he bought [x] bags of breadsticks. Then, we can write the linear equation that shows how many packages of breadsticks Dirk bought as -

x = (1/4)b

Therefore, the linear equation that shows how many packages of breadsticks Dirk bought as (1/4)b.

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Answer:

a^2+2ab = 21

(a+b)^2= 25

Step-by-step explanation:

(a+b)^2 = a^+2ab+b^2

sub a=3 and b=2 and simplify  

Answer: 52

Explanation:

You need to replace the x-values with 8 to solve this. So, the equation would look like this. f(8)= 7 x 8 - 5

7 times 8 is 56. 56 minus four is 52 which is your answer.

If you needed to graph this then it would look like this... (8, 52)

The 8 is in the input because it is the x-value (we replace x with 8) and 52 is output/range/y-value because it is the answer.

Answer:

Step-by-step explanation: the distance is 6 but if you're talking decimal then the distance is 1.4142

Answer:77

Step-by-step explanation:

6*12+5

72+5

77

the answer is simply 77

Answer:

Surface area = 2,160 in²

Step-by-step explanation:

Given:

Length of box = 15 in

Width of box = 30 in

Height of box = 24 in

Find:

Surface area

Computation:

Surface area = 2h[l+b]

Surface area = 2(24)[30 + 15]

Surface area = 48 x 45

Surface area = 2,160 in²

Answer:a

Step-by-step explanation:

10 ( N+14)= 9(N)

Answer:

x = 18.45

Step-by-step explanation:

Given that,

Chipper Jones get paid = \(1.23\times 10^6\)

Alex get paid = \(2.27\times 10^7\)

Let Alex get x times paid than chipper i.e.

\({x}=\dfrac{A}{C}\\\\x=\dfrac{2.27\times 10^7}{1.23\times 10^6}\\\\x=18.45\)

Hence, Alex gets paid 18.45 times than the Chipper.

Answer:

1.59x + 11.49

your graphs y int is 11.49.

graphing topping price up to 10:

0topping- 11.49

1topping- 13.08

2top- 14.67

3top- 16.26

4top- 17.85

5top- 19.44

6top- 21.03

7top- 22.62

8top- 24.21

9top- 25.80

10top- 27.39

Step-by-step explanation:

1.59x determines cost for toppings. 1.59 is flat rate of 1 topping, x is with multiple toppings. 11.49 is the cost of one plain pizza. flat rate

Answer:

Transversal line

Step-by-step explanation:

That is a picture of a Transversal line, a Transversal line intersects 2 or more parallel lines.

Answer:

ok that is so hard I CAN not do it

Answer:

i am tired of being single but i do not no at all that seems really hard i feel bad for u

Step-by-step explanation:

So, the CDF of the minimum of x and y is given by Fmin(z) = Fx(z) * Fy(z).

If x and y are independent random variables with cumulative distribution functions (CDFs) Fx(x) and Fy(y), respectively, the CDF of the minimum of x and y, denoted as Fmin(z), can be obtained by multiplying the individual CDFs.

To find the cumulative distribution function (CDF) of the minimum of two independent random variables x and y, we can use the concept of order statistics.

Let Fx(x) and Fy(y) be the CDFs of x and y, respectively. The CDF of the minimum, denoted as Fmin, can be calculated as follows: Fmin(z) = P(min(x, y) ≤ z)

Since x and y are independent, the event min(x, y) ≤ z occurs if and only if both x ≤ z and y ≤ z. Therefore, we can express Fmin(z) as the product of the individual CDFs: Fmin(z) = P(x ≤ z, y ≤ z) = P(x ≤ z) * P(y ≤ z) = Fx(z) * Fy(z)

So, the CDF of the minimum of x and y is given by Fmin(z) = Fx(z) * Fy(z).

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Given the image of the ice cream cone.

The image is a combination of a cone and a hemisphere.

The volume of the ice cream is the sum of the volume of the cone and the hemisphere.

From the figure, it is clear that the radius of the cone and the hemisphere is 6 in and the height of the cone is 17 in.

The volume of the ice cream is:

Thus, the volume of the ice cream is 1093.7143 in^3.

Answer:

The number of possible numeric value for SAT are 8 possible numeric values

Step-by-step explanation:

A cryptarithm is a form of mathematical game where unknown numbers represented by letters of the alphabet are used to form mathematical equations

The given cryptarithm is SAT + SUN = 700

The parameters are;

The digits represented by the letters are different

Non of the digits represented by the letters equals 7 or 0

We have;

T + N = 10

1 + A + U = 10

1 + S + S = 7

Therefore, S = (7 - 1)/2 = 3

S = 3

A + U = 10 - 1 = 9

A + U = 9

Therefore, A = 4 or 5 (2 choices)

From T + N = 10

T = 1, 2, 8, or 9 (4 choices) similarly, N = 1, 2, 8, or 9 (4 choices)

Therefore, the number of numeric values that SAT represent is given as follows;

(S = 1 choice) × (A = 2 choices) × (T = 4 choices) = 1 × 2 × 4 = 8 numeric values

SAT has 8 possible numeric value

The answer that refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time is prevalence.

Prevalence is the total number of cases of a disease or disorder in a population at a given point in time, and does not include cases that have been resolved or previously diagnosed cases. It is an important measure of the health of a population, as it allows researchers to identify patterns in the distribution of a disease or disorder and helps inform public health strategies.

Prevalence is calculated by dividing the total number of cases of a disease or disorder in a population at a given point in time, by the size of the population. For example, if a population of 100,000 people has 500 cases of a particular disease, the prevalence would be 0.005 or 0.5%.

Prevalence is an important metric in epidemiology and public health, and is often used in combination with incidence rates to measure the health of a population. Incidence rates measure the number of new cases of a disease or disorder that occur in a population over a certain time period, whereas prevalence is a snapshot of the total number of cases of a disease or disorder in a population at a given point in time.

Knowing the prevalence of a disease or disorder in a population helps public health practitioners understand the magnitude of a health issue, inform public health strategies, and identify risk factors and trends in the distribution of a disease or disorder.

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The diagonals AC and EC of the pentagon forms two right

triangles and on isosceles triangle, together which gives the

area of the pentagon.

Correct response:

The area of the convex polygon is found by the sum of the

areas of the three triangles that are formed by drawing two

diagonals facing the two 90° angles.

The given parameters are;

AB = 5

BC = 12

AE = 13

DE = 8

CD = 6

m∠B = m∠D = 90°

Required:

The area of the convex pentagon ABCDE

Solution:

The area of pentagon ABCDE = Right ΔABC + Right ΔCDE + ΔACE

Area of right triangle ΔABC = \(\frac{1}{2}\) × 5 × 12 = 30

Area of right triangle ΔCDE = \(\frac{1}{2}\) × 6 × 8 = 24

Length of AC = \(\mathbf{\sqrt{\overline{AB}^2 + \overline{BC}^2}}\)

Which gives; AC = \(\mathbf{\sqrt{5^2 + 12^2}}\) = 13

Length of EC = \(\mathbf{\sqrt{\overline{CD}^2+ \overline{DE}^2}}\)

Which gives; EC = \(\mathbf{\sqrt{6^2 + 8^2}}\) = 10

Therefore, ΔACE is an isosceles triangle

Base of ΔACE = EC

Therefore;

Height of isosceles triangle ΔACE = \(\mathbf{\sqrt{13^2 - 5^2}}\) = 12

Area of ΔACE = \(\mathbf{\frac{1}{2}}\) × 10 × 12 = 60

Therefore;

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Answer:

b

Step-by-step explanation:

3 times 10 is 30

3 times 1 is 3

3 times 1 tenth is .3

3 times 1 onethousandth is .003

add them all up to get 33.303

To determine the local behavior of the function f(x) = -4x(x^2)(x-4), we can examine the signs and multiplicity of the factors involved.

This will help us identify the intervals where the function is increasing or decreasing, as well as locate any local extrema (maximum or minimum points).

Let's analyze the factors of the function:

x:

The factor x appears once, so it changes signs at x = 0.

It is a linear factor, so it has a slope of 1 and passes through the origin.

(x^2):

The factor (x^2) appears with an even power, which means it is always non-negative.

It is a quadratic factor, so its graph is a parabola that opens upwards.

(x-4):

The factor (x-4) appears once, so it changes signs at x = 4.

It is a linear factor, so it has a slope of 1 and passes through the point (4, 0).

Now, let's consider the local behavior of the function:

At x = 0:

The factor x is zero, so f(0) = 0.

Since (x^2) and (x-4) are non-zero, their effect does not change the sign of the overall function.

Therefore, we have a potential local minimum at x = 0.

Between x = 0 and x = 4:

The factor x remains non-zero and positive in this interval.

The factor (x-4) changes signs from negative to positive.

The overall function f(x) will be negative in this interval.

At x = 4:

The factor (x-4) is zero, so f(4) = 0.

Since x and (x^2) are non-zero, their effect does not change the sign of the overall function.

Therefore, we have a potential local maximum at x = 4.

For x > 4:

The factor (x-4) remains non-zero and positive in this interval.

The factor x changes signs from positive to negative.

The overall function f(x) will be positive in this interval.

Based on this analysis, we can summarize the local behavior of the function f(x) = -4x(x^2)(x-4) as follows:

There is a potential local minimum at x = 0.

There is a potential local maximum at x = 4.

The function is negative between x = 0 and x = 4.

The function is positive for x > 4.

Please note that these conclusions are based on the factors and their signs, and additional analysis might be necessary to confirm the nature of the local extrema.

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To access the first element of an array of integers called "numbers," you can use the expression:
numbers[0]`
This expression uses the array name "numbers" and the index "0" to access the first element.

To access the last element of "numbers," assuming it contains 10 elements, use the expression:

`numbers[9]`

Here, we use the index "9" since arrays are zero-indexed, meaning the last element in a 10-element array has an index of 9.
To access the first element of the array called numbers, we would use the expression "numbers[0]."

To access the last element of the array, assuming it contains 10 elements, we would use the expression "numbers [9]" since arrays are zero-indexed in most programming languages.

To access the last element of the array regardless of its length, we can use the expression "numbers [numbers.length-1]," which subtracts 1 from the length of the array to access the last element.
To access the last element, regardless of its length, use the expression:

'numbers [numbers. length - 1]'

This expression uses the "length" property of the array to find the total number of elements and subtracts 1 to get the correct index for the last element.

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Answer:

x = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Step-by-step explanation:

Step 1: Set up Equation

(7x - 1) + 80 + (6x - 3) = 180

Step 2: Solve for x

Answer: x = 8

Step-by-step explanation:

Hoped this helped

Answer:

\(p=\frac{16}{9}\)

Step-by-step explanation:

\(6(3p-2)=20\)

Distribute the brackets.

\(6(3p)+6(-2)=20\)

\(18p-12=20\)

Add \(12\) on both sides.

\(18p-12+12=20+12\)

\(18p=20+12\)

\(18p=32\)

Divide \(18\) on both sides.

\(\frac{18p}{18}=\frac{32}{18}\)

\(p=\frac{16}{9}\)

Answer:

\(p = \frac{16}{9} \\ \)

Step-by-step explanation:

\(6(3p - 2) = 20 \\ 18p - 12 = 20 \\ 18p = 32 \\ \frac{18p}{18} = \frac{32}{18} \\ p = \frac{16}{9} \)

According to given information, the volcanic eruption occurred about 11,400 years ago.

The half-life information from the given table can be used to estimate the time since the volcanic eruption. Geologists determined that a crater was formed by a volcanic eruption.

A wood chip from a tree that died during the eruption has been analyzed chemically. The analysis has shown that it contains approximately 300 of its original carbon-14.

It is required to estimate how long ago the volcanic eruption occurred.

Carbon-14 has a half-life of 5,700 years. This means that after every 5,700 years, half of the carbon-14 atoms decay. So, the remaining half of the carbon-14 will decay after the next 5,700 years.

Therefore, it can be inferred that after two half-lives (2 x 5,700 years), only one-fourth of the carbon-14 will remain in the wood chip.

Let's assume that initially, the wood chip contained 100% of the carbon-14 atoms. But after the first half-life (5,700 years), only 50% of the carbon-14 atoms will remain.

After the second half-life (another 5,700 years), only 25% of the carbon-14 atoms will remain in the wood chip. But the given problem states that approximately 300 of its original carbon-14 remains in the wood chip.

This means that there is one-fourth (25%) of the original carbon-14 atoms in the wood chip. This implies that the eruption happened two half-lives (2 x 5,700 years) ago.

Now, we can calculate the time since the volcanic eruption occurred using the formula:

t = n x t1/2 where,

t = time elapsed since the volcanic eruption

n = number of half-lives

t1/2 = half-life of carbon-14

From the above discussion, it is inferred that n = 2.

Also, t1/2 = 5,700 years.

Substituting the given values in the formula: t = 2 x 5,700t = 11,400 years

Therefore, the volcanic eruption occurred about 11,400 years ago.

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The function graph for each of the cases with the description of the graph is plotted.

a. The ratio of the height of such a baseball thrown across outfield to home plate to the distance from centerfield.

This, will a parabolic graph as shown.

b. The volume of people who visit the mall per hour during regular business hours on such a particular day.

Thus, this graph will be step wise function as the value of people visiting the mall varies with the time.

c. A cup of coffee's temperature x minutes after it has been poured.

This, will be decreasing graph as the temperature of the coffee will keep on decreasing.

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