Consider the following linear program.
Min 3A + 4B
s.t.
1A + 3B ≥ 9
1A + 1B ≥ 7
A, B ≥ 0

Answer:

∠ EBF = 47°

Step-by-step explanation:

since BE bisects ∠ ABF , then

∠ ABE = ∠ EBF = 2(w + 11) = 2w + 22

∠ ABF = ∠ ABE + ∠ EBF ( substitute values )

8w - 6 = 2w + 22 + 2w + 22

8w - 6 = 4w + 44 ( subtract 4w from both sides )

4w - 6 = 44 ( add 6 to both sides )

4w = 50 ( divide both sides by 4 )

w = 12.5

Then

∠ EBF = 2w + 22 = 2(12.5) + 22 = 25 + 22 = 47°

If a company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. The implied valuation of the business is: $4,533,333.

First step is to calculate the equity valuation

Using this formula

Equity valuation=Amount invested/Equity rate

Let plug in the formula

Equity valuation=$800,000/.15

Equity valuation=$5,333,333

Second step is to calculate the implied valuation

Implied valuation=Equity valuation-Amount invested

Let plug in the formula

Implied valuation=$5,333,333-$800,000

Implied valuation=$4,533,333

Therefore If a company asks an investor for an investment of $800,000 in exchange for 15% equity in the business. The implied valuation of the business is: $4,533,333.

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(A∩B)∪(A∩C) using roster method is as follows:

(A∩B)∪(A∩C)  = {a, e, f}

Sets are an organized collection of objects that can be represented in set-builder form or roster form.

Therefore,

The universal sets is as follows:

U = {a, b, c, d, e, f, g, h}

The subsets are as follows:

A = {c, e, f}

B = {a, e, f}

C = {a, b, d, g, h}

Therefore, let's find (A∩B)∪(A∩C) using roster method.

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.

Hence,

(A∩B) = {e, f}

(A∩C) = {a}

Finally,

(A∩B)∪(A∩C) = {a, e, f}

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a) "how many quarters you have is a function of how many times you paid for the parking meter."

b) y = 10 - x

domain: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

range: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

c) table:

x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

y: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0

Here we know that you have a total of 10 quarters, and the parking meter costs 1 quarter.

Then, each time if we define two variables:

y = how many quarters you have.

x = how many times you paid for the parking meter.

We can write:

"y is a function of x"

Or:

"how many quarters you have is a function of how many times you paid for the parking meter."

b) The rule is really simple, it would be a linear relation:

y = 10 - x

The domain (the set of possible values of x) is:

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

You can't use less than 0 quarters and you can't use more than 10.

c) The range is also:

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Which represents the possible numbers of quarters that you can have.

And the table will be:

x: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

y: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0

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Answer:

(-2[tex]x^{2}[/tex]+3x+1)

Step-by-step explanation:

f(x) = -2x² + 4  g(x) = 3x - 3 find f (4) + g(-6).

f(x)+g(x)

(-2[tex]x^{2}[/tex]+4) +(3x-3)

(-2[tex]x^{2}[/tex]+3x+4-3)

(-2[tex]x^{2}[/tex]+3x+1)

Domain: (−∞,∞) , {x|x ∈ R}

Range: [0,∞) , {y|y ≥ 0}

Continuity: y=3x^2 is a parabola opening upwards, the vertex is at (0,0) and the focus is (0,1/12)

Max's and Min's: the minimum and maximum x value goes to infinity while for the y value the minimum is 0 and goes up to infinity.

Intervals: both x and y start to increase from the origin

Symmetry: the axis of symmetry is x=0 so therefore there the parabola is symmetrical

Answer:

Step-by-step explanation:

Given function:

[tex]y=3x^2[/tex]

The domain is the set of all possible input values (x-values).

The domain of the given function is unrestricted.

Therefore, the domain is (-∞, ∞).

The range is the set of all possible output values (y-values).

As x² ≥ 0, the range of the given function is [0, ∞).

A function f(x) is continuous when, for every value [tex]c[/tex] in its domain:

[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]

Therefore, the function is continuous on its domain (-∞, ∞).

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

[tex]\begin{aligned}y & = 3x^2\\\implies \dfrac{\text{d}y}{\text{d}x} & = 6x\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies 6x & = 0\\x & = 0\end{aligned}[/tex]

[tex]\textsf{When} \:x = 0 \implies y=3(0)^2=0[/tex]

Therefore, the stationary point of the given function is (0, 0).

To determine if a stationary point is minimum or maximum, differentiate the function again and substitute the x-value of the stationary point:

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 6x\\\implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6 \end{aligned}[/tex]

As the second derivative is positive regardless of the x-value of the stationary point, the stationary point is a minimum.

[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]

[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]

Increasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies 6x & > 0 \\ x & > 0\end{aligned}[/tex]

Decreasing

[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies 6x & < 0 \\ x & < 0\end{aligned}[/tex]

Therefore:

[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]

[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]

As x² ≥ 0 and there is symmetry about the y-axis,

[tex]\textsf{then $f(x)=f-x)$ for all $x$,}[/tex]
so the function is even.

Answer:

4.61

Step-by-step explanation:

4.00 is the same as 4

4.00

0.61

--------+

4.61

Answer:

22

Step-by-step explanation:

The ratio tells us 2/5 of the swimmers are indoor swimmers.

55(2/5)=22

Answer:  15 + |−6| = 21 steps

Its stated that Joy walked 15 steps forward, meaning it would be a positive value. Shaunte walking backwards would give a negative value.

Value of the given expression j³k/h0 is 12

h = 8

j=-1

h = 8

In order to do this, we need to change the values of h, j, and k in the given statement = (-1)^3 (-12) / 8^0  ....(1)

Find the denominator by using (1)

(-1)³ (-12) / 1

Analyze each exponent.

= 12/1

Hence, j³k/h0 = 12

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Complete Question -

What is the value of this expression if h=8 ,j= -1 , and k= -12? j³k/h0

Answer: A.   {3, 4, 5}

Explanation:

Write out the whole numbers from 2 to 6 to get 2,3,4,5,6

But we erase the first and last values since we aren't including those endpoints. So we end up with 3,4,5

Answer:

B

Step-by-step explanation:

Capitals represents countries as the function

The sale price before taxes and after discount is $1,430.

Given that A couch with a list price of $2200 will be discounted 35 % at the time of purchase and asked to find the sale price before taxes.

The original cost of the couch=$2200

The discount percentage=35 %

I.e. 35 % of $2200 is $770

The discount given to the customer will be 35% i.e. $770

⇒The selling price will be $770 less than the original cost price.

As a result, the selling price will be =$2200-$770

The Selling price of the couch is $1,430

Therefore,The sale price before taxes and after discount is $1,430.

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Answer:

Omar can ride the roller coaster 4 times and will have 4 tickets leftover.

Step-by-step explanation:

For a more simple problem like this, long division is not necessary.

You may have learned the technique of finding how many times a divisor can "go in" to the dividend.

In this case, 5 (the cost of riding the coaster) can go into 24 (the amount Omar has) 4 times, because 5, 10, 15, 20. However, going in one more time puts us at 25, which Omar does not have, so 5 can only go into 24 5 times.

Since there is still 4 tickets leftover, Omar can ride the coaster 4 times, and will have 4 tickets left.

Answer:

$675.00

Step-by-step explanation: The chart says it all

The classification within the real number system that describes all numbers in the set -1, 1, 0, 14/2, square root 25 is; Rational Numbers

Real numbers can be defined as the union of both rational and irrational numbers.

Rational numbers are numbers that can be represented by fractions, such as exact roots and repeating decimals.

Irrational numbers cannot be represented by fractions, such as non-repeating decimals and non-exact roots.

Now;

-1 is a rational number

1 is a rational number

14/2 is a rational number

The square root of 25 is equal to 5 as 25 is a perfect square of 5. Hence, as 5 is an integer and can be expressed in the form of p/q root, then we say that 25 is rational number

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Answer: y=1

Step-by-step explanation:

Slope formula: m=(y2-y1)/(x2-x1)

m=(1-1)/(0-8)

m=0/(-8)

m=0

y=mx+b

1=0(0)+b

b=1

y=0x+1

y=1

The number in each of the set of blank boxes is 10

From the first number set of stamps, we see that the sum of each row is;

5 + 5 + 5 + 5 = 20

There are four rows. Thus;

Total sum of set of stamps = 20 + 20 + 20 + 20

Total sum of set of stamps = 80

Now, for the blank set of stamps, we see that there are 8 boxes which are al equal. Now, for this 8 boxes t have same sum as that of the initial set of stamps, it means they must sum up to 80.

If the number in each box is x, then;

8x = 80

x = 80/8

x = 10

Thus, the number in each of the set of blank boxes is 10

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Answer:

56 degrees

22 minutes

48 seconds

In linear equation , length of each car =.375 feet.

What in mathematics is a linear equation?

Rack of the cars on the train were the same length = 8

train was 3 feet long.

length of each car = 3/8 = .375 feet

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The liquidity premium for the corporate bond is 0.25%.

Any additional compensation needed to stimulate investment in assets that cannot be quickly and effectively converted into cash at fair market value is known as a liquidity premium. For instance, due to its relative illiquidity, a long-term bond will have a higher interest rate than a short-term bond.

Liquidity premium for corporate bond will be:

= 5.25 - 3.5 - 1.5

= Interest - Treasury - Default risk

= 0.25%.

Therefore, the liquidity is 1.25%.

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Answer:

y = - 2x + 2

Step-by-step explanation:

[tex]y-8=-2(x-(-3))\\y-8=-2(x+3)[/tex]

[tex]y-8=-2x-6[/tex]

[tex]y=-2x-6+8[/tex]

[tex]y=-2x+2[/tex]

Hope this helps

Answer: 697

Step-by-step explanation:

17 * 41=

17 * (40+1)=

17 * 40 + 17 * 1=

17 * 10 * 4 + 17=

170 * 4 + 17=

680+17=697

Answer:

22.5

Step-by-step explanation:

∠EAB=2x (alternate interior angles)

∠AEB=180°-4x (linear pair)

The 17th term of the sequence is 289

The nth term is given as

Sn = n^2

The 17th term of the sequence implies that

n = 17

So, we have

S17 = 17^2

Evaluate

S17 = 289

Hence, the 17th term of the sequence is 289

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Answer:

bca

Step-by-step explanation:

5x5=25 5 to the power of 2 is 25 plus the power of x on all of them

The correct option is D: k/2 is the expression that is equivalent to the expression, K/2.

In response to the question;

We must determine the expression that is equivalent to k/2.

Among the options, Option D: k/2 is same as expression K/2.

Choice C, when written as (1/2)k, is equivalent to k/2 since they both imply half of k.

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Integer addition is the addition of integers with the same signs, whereas integer subtraction is the addition of integers with the opposite signs.

Are there any consistent rules for adding and subtracting integers?

What in math is an integer?

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