For f(x)=3x^2 – x+5, find the following 2f(–3) – f(4)=

Given:

A line passes through (1,-2) and is perpendicular to \(-4x+7y=21\).

To find:

The equation of that line.

Solution:

We have, equation of perpendicular line.

\(-4x+7y=21\)

Slope of this line is

\(m_1=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}\)

\(m_1=-\dfrac{-4}{7}\)

\(m_1=\dfrac{4}{7}\)

Product of slope of two perpendicular lines is -1.

\(m_1\times m_2=-1\)

\(\dfrac{4}{7}\times m_2=-1\)

\(m_2=-\dfrac{7}{4}\)

Now, slope of required line is \(-\dfrac{7}{4}\) and it passes through (1,-2). So, the equation of line is

\(y-y_1=m(x-x_1)\)

where, m is slope.

\(y-(-2)=-\dfrac{7}{4}(x-1)\)

\(4(y+2)=-7(x-1)\)

\(4y+8=-7x+7\)

\(4y+7x=7-8\)

\(7x+4y=-1\)

Therefore, the equation of required line is \(7x+4y=-1\).

Answer:

See below.

Step-by-step explanation:

4.

\( 15 - \sqrt{-32} = 15 - \sqrt{-1 \times 16 \times 2} = 15 - 4i\sqrt{2} \)

5.

\( \sqrt{-63} = \sqrt{-1 \times 9 \times 7} = 3i\sqrt{7} \)

6.

\( \sqrt{-100} + 26 = \sqrt{-1 \times 100} + 26 = 10i + 26 = 26 + 10i \)

In the given relationship, the independent variable is the number of books ordered, and the dependent variable is the cost to join the book club.

Now, let's answer the questions:

1. What is the independent variable in this relationship?

  Answer: The independent variable is the number of books ordered.

2. What is the dependent variable in this relationship?

  Answer: The dependent variable is the cost to join the book club.

3. What is the fixed cost in this relationship?

  Answer: The fixed cost is $5.00 per month, which is the cost to join the book club.

4. What is the variable cost in this relationship?

  Answer: The variable cost is $2.50 for every book ordered.

5. Write an equation to represent the relationship between the number of books ordered (x) and the cost to join the book club (y).

  Answer: The equation is y = 5 + 2.50x, where y represents the cost and x represents the number of books ordered.

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The value of x and y is (2, -2)

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

The equations are:

3x+y = 4 ----Equation 1

2x-y = 6 ----Equation 2

Eliminating Y Multiply negative both side

-[3x +y = 4 ] -

-3x-y = -4 ----Equation 3

From eq. (2) to eq. (3)

2x-y = 6

-3x-y = -4

=> 5x = 10

x =2

The value of x substitute in eq. (1)

3x+y=4

3(2) + y =4

6 + y = 4

y = -2

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The given question is incomplete, complete question is:

Puzzle Three Solve the to systems of equations. To unlock puzzle three find the product of solution (ordered pair - x and y value) and then find the mean of all five products.3x + y = 42 x - y = 6

Answer:

Please check the explanation.

Step-by-step explanation:

Given the decimal number

\(6.05\)

Rewrite as

\(=6+0.05\)

\(=6+\frac{5}{100}\)        ∵ 0.05 = 5/100

\(=6+\frac{1}{20}\)

\(=\:\frac{121}{20}\)

\(=6\frac{1}{20}\)

Given the decimal number

12.346

Rewrite as

\(=12+0.346\)

\(=12+\frac{173}{500}\)              ∵ 0.346 = 346/1000 = 173/500

\(=12\frac{173}{500}\)

Given the decimal number

7.5

Rewrite as

\(=7+0.5\)

\(=7+\frac{1}{2}\)                 ∵ 0.5 = 1/2

\(=7\frac{1}{2}\)

The given expression:

Apply BODMAS Rule : Brackets, Of, Division, Multiplication, Addition, Subtraction

According to BODMAS rule, we first simplify division:

Simplify multiplication:

Simplify addition:

Answer: -40

Step-by-step explanation:

you must have made a typo here.

none of the answer options are correct for the given problem.

let me just show you what you told me, and how I can solve at least this :

2a/4 = b/4

this simply means (multiply both sides by 4) :

2a = b

so, 5b is then (multiplying both sides by 5) :

5×2a = 5b

10a = 5b

but again, "10a" is not among the offered answers.

so, I don't know if you made a mistake with the basic problem or with the answer options.

Answer:

Option c- should have added from both sides

k= 9.7

Step-by-step explanation: I dont know if i am right but hope it is xd

The conversion rate will affect her budget as C. Kari has almost exactly enough left in her budget to see Genoa.

From the information given, it should be noted that a trip to Genoa will cost her €60.85.

This will be converted to dollars which will be:

= 60.85/0.6859

= 88.72

Therefore, out of the $585 budget, only $88.72 is used.

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The rate of change for the equation y - x = 10 is 1.

To find the rate of change for the equation y - x = 10, we need to determine how y changes with respect to x.

We can rewrite the equation as y = x + 10 by adding x to both sides.

Now, we can observe that the coefficient of x is 1. This means that for every unit increase in x, y will increase by 1. Therefore, the rate of change for this equation is 1.

In other words, as x increases by 1 unit, y will increase by 1 unit as well.

As a result, 1 represents the rate of change for the equation y - x = 10.

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Answer:

it's a and c

luk closely

Answer:

\(a^2=c^2-b^2\\b^2=a^2+c^2\\b^2=a^2-c^2\)

Step-by-step explanation:

I think these are antonyms because they don't follow the Pythagorean Theorem.

Answer:  A+B=C and this is the Pythagorean Theorem

Step-by-step explanation: I‘m his brother! He said I can have the free points! :)

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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Answer:

Step-by-step explanation:

Here we see regrouping of the multiplied numbers.

Relevant property is given below

Answer:

Your answer is C

Step-by-step explanation:

The equilibrium quantities are - The quantity demanded by the leader is qL = 19109/7 and the quantity demanded by the follower is qF = 14024/7.

The question requires us to find the inverse demand for a homogeneous-product Stackelberg duopoly, given the cost structures for the leader and follower are Cl(ql) = 4000ql and Cf(qf) = 6000qf respectively.T

he inverse demand for a homogeneous-product Stackelberg duopoly is p = 16000 - 4q where p is the price and q is the quantity.

Substituting the given value of inverse demand in the above equation we get:16000 - 4q = p... equation 1

Also, the total quantity demanded in the market is the sum of the quantity demanded by both the players.

Hence, we can say that,Total quantity demanded, Q = qL + qF, where qL is the quantity demanded by the leader and qF is the quantity demanded by the follower.

Now let us find the reaction function for the follower.

Follower's Reaction Function: We know that for a homogeneous-product Stackelberg duopoly, the leader decides its production quantity before the follower.

Hence, the leader's quantity is a fixed quantity.Using the leader's quantity the follower's best response function can be given as:qF = (p - CF(qF))/2 ... equation 2

Now let us find the leader's reaction function.

Leader's Reaction Function:For the leader, the best response function is obtained by maximising its profits.

The profit function for the leader can be written as:πL = (p - CL(qL))qL

Substituting the given values, we get:

πL = (16000 - 4qL - 4000qL)qL

= (12000 - 4qL)qL

= 3000 - 0.25qL ... equation 3

The total quantity demanded is given as Q = qL + qF

Substituting equation 2 and 3 in the above equation and solving for qL, we get:

qL + qF = qL + (p - CF(qF))/2

= 3000 - 0.25qLqL + (16000 - 4qF - 6000qF)/2

= 3000 - 0.25qL5qF + 0.5qL = 9000qF

= 1800 - 0.1qL ... equation 4

Substituting equation 4 in equation 2 and solving for qF, we get:

qF = (16000 - 4q - 6000(1800 - 0.1q))/2qF = 4800 - 0.05q ... equation 5

Substituting the value of qL in equation 1, we get:

16000 - 4q = 16000 - 4(26000 - 3.33Q)q

= 665Q + 8000

Now that we have found the reaction function for both the players, let's find their equilibrium quantities

Quantity demanded by the leader, qL = 26000 - 3.33Q

Quantity demanded by the follower, qF = 665Q + 8000

The total quantity demanded in the market is Q = qL + qF = 33133/7

The quantity demanded by the leader is qL = 19109/7 and the quantity demanded by the follower is qF = 14024/7.

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The equivalent expression for the derivative of f(g(x)) with respect to x is (f'(g(x))) (g'(x)), according to the chain rule.

Given that g(x) = 2ln(x+1) and f(x) is a differentiable function, we want to find the derivative of f(g(x)) with respect to x. We can use the chain rule to determine an equivalent expression for this derivative.

According to the chain rule, if we have a composite function y = f(g(x)), then the derivative of y with respect to x is given by the product of the derivative of f with respect to its argument multiplied by the derivative of g with respect to x.

In this case, g(x) is the inner function and f(u) is the outer function. Applying the chain rule, we have:

d/dx [f(g(x))] = f'(g(x))  g'(x)

Here, f'(u) represents the derivative of f with respect to its argument, and g'(x) represents the derivative of g with respect to x.

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To find the volume of the solid obtained by rotating the region R about the horizontal line y=1, we need to use the disk method. We need to integrate the area of the disks formed by slicing the solid perpendicular to the axis of rotation.

First, we need to find the limits of integration. The region R is bounded by the parabola y=5-x^2 and the horizontal line y=1. At the point where y=5-x^2 and y=1, we get:
5-x^2 = 1
x^2 = 4
x = ±2
So the limits of integration are -2 to 2.
Next, we need to find the radius of each disk. The distance between the axis of rotation (y=1) and the curve y=5-x^2 is:
r = 5-x^2 - 1
r = 4-x^2
Finally, we can integrate the area of the disks:
V = ∫[from -2 to 2] π(4-x^2)^2 dx
V = π ∫[from -2 to 2] (16 - 8x^2 + x^4) dx
V = π [16x - (8/3)x^3 + (1/5)x^5] [from -2 to 2]
V = π [(32/3) + (32/3) + (32/5)]
V = 192π/5

Therefore, the volume of the solid obtained by rotating the region R about the horizontal line y=1 is 192π/5, which is option b.

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Answer:

(8×6)+2×((14+6)×6)

=48+2×(20×6)

=48+240

=288

Step-by-step explanation:

please mark me as brainliest

Answer:

$62.50

Step-by-step explanation:

Answer:

$65.00

Step-by-step explanation:

Answer:

i dont understand it sorry

BStep-by-step explanation:

Answer:

Can you ask again with a picture? it's not clear with only text

Answer:

Step-by-step explanation:

Answer:

i think no 3 hasexactly one 0

The actual distance between the two cities is 288 miles.

A scale drawing is a smaller version of a larger image / city. The scale drawing is reduced by a constant ratio.  This means that the scale drawing of the two cities would be smaller than the actual cities.

The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. This means that the scale drawing of the two cities would be smaller than the actual cities.

The actual distance between the two cities = (3 x 24) ÷ 1/4

= 3 x 24 x 4 = 288 miles

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The volume of the figure, which is made up of 2 rectangular prisms, would be 276 cm ³.

The figure shown is made up of two rectangular prisms which means that we can find the volume of the entire figure by finding the volumes of the rectangular prisms and then adding up these volumes to find the total volume.

Volume of the first rectangular prism:

= Length x Width x Height

= 10 x 6 x 3

= 180 cm ³

Volume of the second rectangular prism:

= Length x Width x Height

= 4 x 6 x 4

= 96 cm ³

The total volume of the figure:

= 180 + 96

= 276 cm ³

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The slope of the line is -294/25 and the y-intercept is -294/25.

To find the equation of the line through (7,6) that cuts off the least area from the first quadrant, we need to minimize the product of the x and y intercepts.

Let the x-intercept be a and the y-intercept be b. Then the equation of the line is:

y = (-b/a)x + b

The product of the intercepts is ab = b(-6/b) = -6.

To minimize this product, we need to find the values of a and b that satisfy the constraint that the line passes through (7,6).

Substituting y = 6 and x = 7 in the equation of the line, we get:

6 = (-b/a)7 + b

Solving for b, we get:

b = 42/(a+7)

Substituting this value of b in the equation ab = -6, we get:

a(42/(a+7)) = -6

Simplifying, we get:

42a = -6(a+7)

48a = -42

a = -7/8

Substituting this value of a in the equation b = 42/(a+7), we get:

b = 294/25

Therefore, the equation of the line is:

y = (-294/25)x - 294/25

The slope of the line is -294/25 and the y-intercept is -294/25.

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Answer: 4 miles

Step-by-step explanation:

2.5x+4.7=14.7

        -4.7 -4.7

2.5x=10

2.5x=10

2.5    2.5

x=4

In other words...

Subtract 4.7 from both sides first. Then divide that answer on both sides by 2.5, and WALA!

Answer:

4 miles

Step-by-step explanation:

The statement "if s is a linearly dependent set, then each vector is a linear combination of the other vectors in s" is false.

A vector set's linear independence is an important attribute. If no vector in a set can be written as a linear combination of the other vectors in the set, the set is said to be linearly independent. The set is said to be linearly dependent if any of the vectors can be represented as a linear combination of the others.

If S is a linearly dependent set, then each vector in S is a linear combination of the others.

This is false.

For example, v₁ = (1,0), v₂ = (2,0), and v₃ = (1,1). Then v₂ = 2v₁ but v₃ is not a linear combination of v₁ and v₂, since it is not a multiple of v₁. But 2v₁ - 1v₂ + 0 v₃ = 0.

If an indexed set of vector S is linear dependent, then it is only necessary that one of the vectors is in the set.

Hence, the correct answer would be option (B).

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An equation of the question is 250 × 0.94^n = 150 and in approx 8 years it will have about 150 students.

The population of its high school decreases by 6% each year.

The senior class has 250 students now.

Each year decrease in population = 6% = 0.06

So it can be = 1 - 0.06 = 0.94

Total student now = 250

Let n be the number of years before the class will have  students.

So the equation should be = 250 × 0.94^n

After years left students = 150.

Now the equation should be

250 × 0.94^n = 150

Now solving the equation.

Divide by 250 on both side, we get

0.94^n = 150/250

0.94^n = 3/5

Taking log on both side, we get

log(0.94^n) = log(3/5)

Using the formula log(m^n) = n logm and log(m/n) = log m - log n

n log(0.94) = log3 - log5

Now finding the value of log using calculator

n (-0.062) = 1.099 - 1.61

(-0.062)n = -0.511

Divide by (-0.062) on both side, we get

n = 8.242

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The complete question is:

As a town gets smaller, the population of its high school decreases by 6% each year. The senior class has 250 students now. In how many years will it have about 150 students? Write an equation. Then solve the equation without graphing. Write an equation to represent this situation. Let n be the number of years before the class will have  students.

Answer:

the sum of two irrational numbers

Step-by-step explanation: