How are the coordinates of the extreme value and the equation from part B in the form y=(x - h)² - Crelated? extreme value is at (1, -8)

we know that

inequality 1

The solution is the shaded area above the solid line x+y=10

Inequality 2

The solution is the shaded area below the solid line -x+y=-2

therefore

the solution of the system of inequalities is the region C

Answer:

Step-by-step explanation:

3x=27

The compound interest formula is:

Where:

C(n) is the interest generated after n periods

P is the principal value, the values deposited initially.

i is the annual interest rate in percentage terms.

n is the number of compounding periods.

In this case:

P = $600.00

i = 0.04 (converted from percentage to decimal by dividing by 100

n = 3 years

Then:

Then solve:

This is the amount of interest generated over 3 years. The total amount then will be the initial amount plus the interest generated:

Rounded up to the nearest cent, the amount she will be able to spend after 3 years is $674.91

And the cost is $29,40

To answer this question we need to understand the difference between discrete and continous data:

• Discrete data can only take certain values along some interval.

• Continuous data can take any value along some interval.

In this case we know that there will always be a integer number of people in the meeting, that is, we can only have certain values (we can't have 6.5 people in a meeting).

Therefore, this is a discrete data set.

The angle can be expressed as,

So, the angle can be drawn as,

To find the reference angle if the angles is greeter than 2π, we first subtract 2π from the angle(here 13π/6) until it is below 2π.

So, the reference angle is π/6.

The slope of a linear function can be obtained as:

Where (x1,y1) and (x2,y2) are points of the line.

For this problem we just have to pick 2 points from the table (they don't have to be consecutive). I'll pick:

• x1 = 0

• y1 = 4

• x2 = 2

• y2 = 14

And now we compute the slope:

The slope is 5 (third option)

Answer:

A. 12

Step-by-step explanation:

Answer:

The price decrease will be $1,674

The price of the next model will be $52,326

Explanation:

Given the cost of the current model as $54,000.

We're told that the next model of the car will cost 3.1% less than the current model, let's go ahead determine the price decrease as seen below;

We can see from the above that the price decrease is $1,674.

Let's go ahead and determine the price of the next model as seen below;

Therefore, the price of the next model will be $52,326

Answer:

x = 2, y = -1

Solve the following system:

{-y + x = 3 | (equation 1)

-y + 2 x = 5 | (equation 2)

Swap equation 1 with equation 2:

{2 x - y = 5 | (equation 1)

x - y = 3 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:

{2 x - y = 5 | (equation 1)

0 x - y/2 = 1/2 | (equation 2)

Multiply equation 2 by 2:

{2 x - y = 5 | (equation 1)

0 x - y = 1 | (equation 2)

Multiply equation 2 by -1:

{2 x - y = 5 | (equation 1)

0 x + y = -1 | (equation 2)

Add equation 2 to equation 1:

{2 x + 0 y = 4 | (equation 1)

0 x + y = -1 | (equation 2)

Divide equation 1 by 2:

{x + 0 y = 2 | (equation 1)

0 x + y = -1 | (equation 2)

Collect results:

Answer: |

| {x = 2

y = -1

I believe that this is truly the answer.

We are given the following functions;

We shall find the values of the following;

We substitute for the values of each function and we'll have;

Take note that the negative sign in front of the parenthesis affects both values. Hence negative +5 becomes -5. We now have;

(B):

Just like in part (a), we shall substitute for the value of each of the functions, as follows;

(C):

In this case, we calculate the product of both functions, and we start by substituting for the value of each;

We can now simplify the above and we'll have;

ANSWER:

we have the functions

Part A

Equate both equations

Solve for x

Solve the quadratic equation

using the formula

a=-1

b=9

c=-14

substitute

The values of are

x=2 and x=7

The answer Part A

The distances are x=2 units and x=7 units

Part B

f(x)=g(x)/h(x)

so

Rewrite in factored form

The given function has a discontinuity at x=7 (hole), a vertical asymptote at x=-3

and horizontal asymptote at y=2

Answer:

A

Y = -4|x+2|+3 

Step-by-step explanation:

we can see the graph is heading downwards -> it must be negative coefficient

The graph is going up 3 -> must have a plus 3 in formula outside absolute value

the graph is going to the left 2 -> must have a plus 2 in formula inside absolute value

Inverse variation:

k is a constant

Use the given information (when x=4 y=4) to find the value of the constant:

Then, the given relationship has the next equation:

Use the equation above to find y when x=2:

Answer:

Exponential decay

Explanation:

The exponential functions have the following form:

If b is a number greater than 1, the equation models exponential growth, and if b is lower than 1, the equation models an exponential decay.

Since the equation is:

We can say that the value of b is 0.5. 0.5 is lower than 1, so this equation models exponential decay.

Using linear programming, the amounts of each book that you should purchase are given as follows:

The maximum profit will be of $850.

To maximize the function, we have to find the numeric values at the intercepts of the most restrictive constraints, as the maximum value is the highest numeric value. This strategy is called linear programming.

In the context of this problem, the variables are given as follows:

The used book program makes a profit of $10 on each calculus text, $4 on each history text, and $8 on each marketing text, hence the profit function is defined as follows:

P(x,y,z) = 10x + 4y + 8z.

The constraint related to budget limitations, as an equality, is given by:

x + y + z = 1050.

The most restrictive constraint is from shelf-space limitations, and is given as follows:

2x + y + 5z = 1700.

Hence the intercepts are given as follows:

The numeric value of the profit function at each of these intercepts is:

Hence, due to the maximum numeric value, the maximum profit will be of $850, when 850 calculus books are purchased.

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The arc length, when the central angle is measure in degrees, is given by:

In this case the arc length is 19.6 cm and the angle is 130°, plugging these values we have that:

Therefore, the radius is 8.6 cm

y-intercepts of line y = -5x + 5 is greater then a line which passes through the points (5, 0) and (-5, 5)

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Here the points are (5, 0) and (-5, 5) and it is to find the equation of line passing through these points :

Now using slope formula to find the slope of line m :

m = (y₂-y₁)/ (x₂-x₁)

m = (5-0)/(-5-5)

m = 5/-10

m = -1/2

Let us first find the equation of the line using point-slope equation of line :

(y-y₁) = m(x-x₁)

Substituting all the values in above equation to get the equation of line :

(y-0) = -1/2(x-5)

2y = -x+5

2y = -x + 5

2y = -x +5

y = -x/2 + 5/2

Therefore, the equation of line passing through the points (5, 0) and (-5, 5) is y = -x/2 + 5/2 and its y-intercepts is 5/2

Now, the y-intercepts of line y = -5x + 5 is 5

That is, y-intercepts of line y = -5x + 5 is greater then a line which passes through the points (5, 0) and (-5, 5)

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ANSWERS

A. e(p) = 0.8p

B. a(p) = p - 10

C. e(a(p)) = 0.8p - 8

D. $312

EXPLANATION

A. The employee discount is 20%. To the total price, which is 100%, we have to subtract the 20% to find the final price of the product. If the price is p, then the price after the employee discount would be,

Hence, the function is e(p) = 0.8p

B. On Wednesdays, Erin gets a $10 discount on the price p of a product in the store, so if she buys on a Wednesday, she would pay a(p) = p - 10.

C. Now we have to find the function e(a(p)). This is a composition, where we have to replace p with a(p) in function e(p),

Hence, the function is e(a(p)) = 0.8p - 8

D. If Erin buys a $400 camera on a Wednesday she will get both discounts: the employee discount and the Wednesdays discount. To find the final price for a selling price of p = 400, we have to use the function found in part C,

Hence, the final price for the $400 camera is $312, after both discounts.

The value of differentiable function g(x)=x³ × f(x) if f(2)=-3 and f'(2)=-4 is -68.

If the derivative of a function exists at every point inside its domain, the function is said to be differentiable. In particular, f′(a) exists in the domain if a function f(x) is differentiable at x = a.

Given function

g(x)=x³ × f(x)

FInd out -

Value of g′(2) = ?

If f(2) = -3 and f'(2) = -4.

Let us apply the product rule of differentiation of a product of two functions. The product rule states that

d/dx (fg) = d/dx (f) × g + f × d/dx(g)

or

(fg)'(x) = f'(x) × g(x) + f(x) × g'(x).

Observe that if g(x) = x³ × f(x) then

g'(x) = 3x² × f(x) + x³ × f'(x).

Thus, g'(2) = 3 × 2² × f(2) + 2³ × f'(2)

Put the value of f(2) and f'(2)

= 3 × 4 × (-3) + 8 × (-4)

= -36 - 32

= - 68.

Therefore , If f(2)=-3 and f'(2)=-4, the value of the differentiable function g(x)=x³ × f(x) is -68.

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Answer: 287.&. Multiply 365 x 10 Great, you get 3650 . . . Multiply 287 by 3650 which then equals 1049375 . . . Wow! The interest will then be a total of 60929$ with the 8450 that she recieved that should equal 3 years total keeping it open . . .

Step-by-step explanation: Hope This Helps! Pls mark Branliest!

We will hve the following:

Explanation

The product-to-sum formula can be seen below.

Therefore, we can insert the values of the angles into the formula

Answer:

C or D pretty sure it's d

Answer:

C. 7/10 = 70 %

Explanation:

We are asked to find the total number of outcomes that give us at least 2 female puppies.

Now outcomes 1,2,4,5,7,9, and 10, which are 7 outcomes in total, give us at least two female puppies. Therefore, we can say 7 out of 10 times we get at least 2 female supplies and hence the probability is

Given the Infinite Geometric Series:

You can find its sum by using this formula:

Where "r" is the common ratio and the first term is:

In this case, you can identify that each term is obtained by multiplying the previous term by 4. Therefore:

You can identify that:

Therefore, you can substitute values into the formula and evaluate:

Hence, the answer is: Option B.

We know that O is midpoint of BF, which means OF is equal to OB by definition of midpoint.

Also, angles FOE and BOA are congruent by vertical angles theorem. Angles B and F are congruent by given, both are right angles.

We can deduct that triangles EFO and ABO are congruent by ASA postulate of congruence.

Answer:

6x+8

Step-by-step explanation:

2 x 2x+3 = 4x+6

2 x x+1 = 2x+2

4x+6 + 2x+2 = 6x+8

If the original price of suitcase is $62 and sale price is 51.99 amount of

markdown is $ 10.01 and markdown % is 16.14.

Mark down = original price -  sale price

                    =  62 -51.99

                    = $ 10.01

Mark down % =  [tex]\frac{mark down}{original selling price} \times 100[/tex]

                        =  [tex]\frac{ 10.01}{62} \times 100[/tex]

                        = 16.14%

markdown is the amount by which you reduce the selling price. The amount by which you reduce the price  can be expressed as a percentage of the sale price, or the discount rate.

To calculate markdown percentage  Divide the price difference  by the actual selling price. Then multiply that result by 100. The result is a markdown percentage.

For example, suppose a broker sells  XYZ stock to his clients at $20 per share. He originally bought the stock in the brokerage market at $0 per share. Therefore, the discount on the stock he sells is -$20 ($20 - $0)

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Notice that triangles NPQ and NRQ are similar, then:

Now, notice that:

Therefore:

Multiplying the above result by QR we get:

Substituting NR=125m, RP=65m, and QR=106.75m we get:

Simplifying the above result we get:

Answer: