Graph this system of inequalities. Identify the solution region on the graph.
y<-x+4, y>-x 2

Answer:

The third one

Step-by-step explanation:

It cannot be the first 2 as the corners wouldn't line up. It cannot be the last one as B and R are not the same angles

The volume of the rectangular box is the product of the base area and the height 3x - 1

The given parameters are:

Length = 3x + 4

Width = 3x

Height = 3x - 1

The base area of the rectangular box is calculated as

Base area = Length * Width

Substitute the known values in the above equation

Base area = 3x(3x + 4)

This means that the volume of the rectangular box is the product of the base area and the height 3x - 1

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Answer:

y = -0.6x^2 + 5x + 6

Step-by-step explanation:

First, find the equation of a linear line that passes through the points (0,6) and (3, 15.6) in the slope intercept form, y = mx + b. We know that the line has a y-intercept of 6, so b = 6. Substitute 3 for x, 15.6 for y, and 6 for b to find m.

y = mx + b

15.6 = 3m + 6

9.6 = 3m

m = 3.2

y = 3.2x + 6

y = a(x - 0)(x - 3) + 3.2x + 6

y = a(x)(x - 3) + 3.2x + 6

Finally, substitute 10 for x and -4 for y in the equation above to find a.

-4 = a(10)(10 - 3) + 3.2*10 + 6

-4 = a(10)(7) + 32 + 6

-4 = 70a + 38

-42 = 70a

a = -0.6

Simplify to write in standard form.

y = -0.6(x)(x - 3) + 3.2x + 6

y = -0.6x^2 + 5x + 6

An example of an exponential graph function has been attached and its' properties are as below.

The general formula for exponential functions is: f(x) = aˣ, a > 0, a ≠ 1.

The reasons for the restrictions are because;

If a ≤ 0, then when you raise it to a rational power, you may not get a real number.

The graph of an exponential function y = 2ˣ is shown in the attached file. Here are some properties of the exponential function when the base is greater than 1.

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The system of inequalities be

3x+2y ≤ 25, 4x+6y ≤ 37

1) Maximum number of sundaes possible exists 9.

2) Maximum number of milkshakes possible exists 6.

3) Combination that uses the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.

A system of inequalities exists the system where the set of more than one inequalities in more than or equivalent to one variable.

Given: A sundae needs 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries.

Ramses have to create sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries.

Let x represent the number of sundaes he creates and y the number of milkshakes he creates.

We represent in tabular form,

                    Sundae(x)      Milkshake(y)     Total

Ice-cream          3                         2             3x+2y

Strawberries      4                        6             4x+6y

System of inequalities:

Sundaes and milkshakes with at most 25 ice-cream scoops exist

33x+2y ≤ 25.

Sundaes and milkshakes with at most 37 strawberries exist 4x+6y ≤ 37.

1) Maximum number of sundaes possible:

Maximum number of sundaes possible when y = 0

From the graph y = 0 at x = 9.25

Therefore, the maximum number of sundaes possible exists at 9.

2) Maximum number of milkshakes possible:

Maximum number of milkshakes possible when x = 0

From the graph x = 0 at y = 6.167

Therefore, the maximum number of milkshakes possible exists at 6.

3) Combination that utilizes the most of both Ice-cream and Strawberries:

A combination of both is possible there exists an intersection of both the equation.

From the graph, the intersection point exists x = 7.6 and y = 1.1.

Therefore, the Combination that utilizes the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.

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Answer:

Step-by-step explanation:

The borrower owes $14,760.82  at the end of 8 years

What is compounding interest?

Compounding interest means that earlier interest would earn more interest in the future alongside the loan principal.

Note that in this case the loan continues to accumulate interest because there no repayments, in other words, the loan balance after 8 years, which comprises of the principal and interest for 8 years can be computed using the future value formula of a single cash flow(the single cash flow is the principal) as shown thus:

FV=PV*(1+r/n)^(n*t)

FV=loan balance after 8 years=unknown

PV=loan amount=$5,000

r=annual interest=14%

n=number of times in a year that interest is compounded=2(twice a year)

t=loan period=8 years

FV=$5000*(1+14%/2)^(2*8)

FV=$5000*(1.07)^16

FV=$5000*2.95216374856541

FV=loan balance after 8 years=$14,760.82

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The book value of the fixed assets for the current year and the preceding year is: $1,442,587; $926,368.

Current year book value

Land and buildings $707,150

Machinery, equipment, and internal-use software $671,793

Office furniture and equipment $106,073

Other fixed assets related to leases $855,652

Less Accumulated depreciation and amortization ($898,081)

Book value $1,442,587

Preceding year book value

Land and buildings $410,147

Machinery, equipment, and internal-use software  $530,363

Office furniture and equipment $91,930

Other fixed assets related to leases $643,507

Less Accumulated depreciation and amortization  ($749,579)

Book value $926,368

Therefore the book value of the fixed assets for the current year and the preceding year is: $1,442,587; $926,368.

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The total company fund before any bonuses were paid is $995 and there were 20 staffs.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Let y represent the total company fund and x represent the number of staffs.

From the first statement:

y - 50x = -5  (1)

Also:

y - 45x = 95    (2)

From equation 1 and 2:

x = 20, y = 995

The total company fund before any bonuses were paid is $995 and there were 20 staffs.

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Answer:

A)

Step-by-step explanation:

3+3=6 6>5

3+5=8 3<8

A)

Option A is correct. The gross profit that has been calculated for this year is given as 17545

22050 × 97.5%(100-2.5%) = 21498.75

= 21498.75 × 0.975 = 20961.28

= 20961.28 x 0.975 = 20437.24

= 20437.24 x  0.975  = 19926.31

= 19926.31 ×  0.975  = 19428.15

= 19428.15 x  0.975  = 18942.45

= 18942.45 x  0.975  = 18468.80

= 18468.89 ×  0.975  = 18017

= 18007 × 0.975  = $17545

Hence we can see at the end of the solution that the value of the gross profit in 2028 = $17545

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46) True

47) False

These are true by definition.

The base of the exponential function model in order to get 15% decay should be 0.85

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.

The first step would be figuring out the function's base.

The function's form should be, [tex]y=a*b^{t}[/tex]

Here,

'a' denotes the starting value.

'b' denotes the decrease rate.

't' denotes time.

According to the question, the exponential function model is,

[tex]y=b^{\frac{t}{12} }[/tex]

In order to get a 15% decay,

The base of the function should be (100-15)/100 = 0.85

Thus, Base of function(b) = 0.85

The exponential function model is written as:

[tex]y=0.85^{t/12}[/tex]

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Using the probability concept, we have that:

a) The experimental probability is of 0.75 = 75%.

b) The theoretical probability is of 0.5 = 50%.

c) As the number of trials increases, the probabilities are expected to get closer, though they might not be equal.

A probability is given by the number of desired outcomes divided by the number of total outcomes. For an experimental probability, these number of outcomes are taken from previous trials. A theoretical probability is calculated before any trial, and as the number of trials increase, the experimental and theoretical probabilities get closer.

From the table, there were 20 trials, and 2 + 3 + 4 + 4 + 2 = 15 resulted in even numbers, hence the experimental probability is:

p = 15/20 = 0.75 = 75%.

For a fair machine, even and odd numbers should be equally as likely, hence the theoretical probability is of 0.5 = 50%.

For item c, we have that as the number of trials increases, the probabilities are expected to get closer, though they might not be equal.

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Answer: [tex]\Large\boxed{A.~y=3x+4}[/tex]

Step-by-step explanation:

Given information

Slope = 3

Point = (-3, -5)

Given the format of the equation

Slope-intercept form: y = mx + b

Substitute values into the equation

y = (3)x + b

y = 3x + b

Substitute the given point into the equation to get the value of [ b ]

(-5) = 3(-3) + b

-5 = -9 + b

b = -5 + 9

b = 4

Therefore, the equation of the line is [tex]\Large\boxed{y=3x+4}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

72 Degrees

Step-by-step explanation:

10 / 50 = 0.2

A circle has 360 degrees.

0.2 X 360 = 72

Using the Fundamental Counting Theorem, the number of possible telephone numbers is given by:

a) 900,000.

b) 78,125.

c) 10,000.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For item a, a multiple of 100 means that the last two digits are 00, hence the parameters are:

[tex]n_1 = 9, n_2 = n_3 = n_4 = n_5 = 10, n_6 = n_7 = 1[/tex]

Hence the number is:

N = 9 x 10^5 = 900,000.

For item b, odd digits are 1, 3, 5, 7 and 9, hence the parameters are:

[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = n_7 = 5[/tex]

Hence the number is:

N = 5^7 = 78,125.

For item c, if the first 3 digits are 277, the parameters are:

[tex]n_1 = n_2 = n_3 = 1, n_4 = n_5 = n_6 = n_7 = 10[/tex]

Hence the number is:

N = 10^4 = 10,000.

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The inequality system that has the solution set shown will be C. x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2.

It should be noted that inequalities are simply used to compare two expressions that are unequal.

It can be seen that the solution set that's illustrated is:

x² + y² <= 16

-1/4x² + 2 <= y

Therefore, the inequality system that has the solution set shown will be option C.

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Answer:

5w^2 + 6w - 32

Step-by-step explanation:

Subtract as needed and combine like terms

(-2w^2 + 6w - 19) - (-7w^2 +13) dont forget to distribute the negative

so you get this:

-2w^2 + 7w^2 = 5w^2

6w

-19 - 13 = - 32

your answer is 5w^2 + 6w - 32

hope this helps :)

Hi :)

Let's solve by combining like terms

Combining like terms means you add or subtract

Solve by combining like terms

[tex]\implies\darkblue\sf{-2w^2+6w-19-(-7w^2+13)}\\\implies\darkblue\sf{-2w^2+6w-19+7w^2-13}\\\implies\darkblue\sf{-2w^2+7w^2+6w-19-13}\\\implies\darkblue\sf{\underline{5w^2+6w-32}}[/tex]

[tex]\tt{Learn\:More;Work\:Harder}[/tex]

:)

Answer:

The answer to that question depends

beacuse where ever you are it changes like uk you can pay 100€

or japan it can be around 1000¥

Answer:

the total new area is 2800 ft²

Step-by-step explanation:

original area: 1600 ft²

new expanded area: 1600 ft² + 75% of 1600 ft²

new expanded area = 1600 ft² + 0.75 × 1600 ft²

new expanded area = 1600 ft² + 1200 ft²

total new area = 2800 ft²

The striped rectangle has a total area of 69,375 cm².

To find the area of the striped rectangle we must carry out the following procedures.

Find the area of each segment of the rectangle, that is, what is the area of each of the 24 squares that make up the rectangle, for that we divide the 111cm² of the total area into 24.

According to the above, we infer that each square has an area of 4.625cm².

On the other hand, to find the area of the striped rectangle we must take into account that it is 5 squares long by 3 squares high, that is, its area is 15 squares.

Finally, each square has an area of 4.625cm², so to find the total area of the striped area we must multiply the area of each square by the number of squares.

15 × 4.625cm² = 69.375cm²

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The equation for the horizontal asymptote will be y = -2.

Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:

y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)

= y = -2/1

= y = -2

The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0

= x + 3 = 0

= x = -3

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The resulting value of the function when the values of t is 2 and 6 are 3.5 and 6.5 respectively

Functions are expressions in form of variables. Given the following quadratic equation expressed as:

f(t) = 0.25t^2 − 0.5t + 3.5

We can find the equivalent value of the function when the value of t a re 2 and 6.

If the value of t is 2. hence;

f(2) =  0.25(2)^2 − 0.5(2) + 3.5

f(2) = 1 - 1 + 3.5

f(2) = 3.5

If the value of t is 6, hence;

f(6) = 0.25(6)^2 − 0.5(6) + 3.5

f(6) = 9 - 3 + 3.5

f(6) = 6.5

Hence the resulting value of the function when the values of t is 2 and 6 are 3.5 and 6.5 respectively

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The equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256

The given parameters are:

Rate, r = doubles every two days

Initial number of strain, a = 1

This means that the function is an exponential function.

An exponential function is represented as:

A(d) = a * r^d

Since the strain doubles every two days, we have:

A(d) = a * r^(d/2)

Substitute the known values in the above equation

A(d) = 1 * 2^(d/2)

Evaluate the product

A(d) = 2^(d/2)

When there are 256 bacterial cells, the equation becomes

2^(d/2) = 256

Hence, the equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256

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The best approach to calculating the stipulated 20% tip by means of fractions is to note that the tip is one-fifth of the total amount charged on the bill.

The percentage represented as; 20% can be expressed as a fraction.

This follows from the fact that the percentage, % symbol translates to divided by 100.

Consequently, we must note that the 20% translates to; 20/100 = 1/5.

Hence, the 20% tip is one-fifth of the total amount.

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Answer:

11 and 2/3

Step-by-step explanation:

The given expression be [tex]$(5)^{7/3[/tex] then the value exists ³√5⁷.

The base number exists raised to a power of the exponent numerator and estimated to the root of the exponent denominator.

Given: [tex]$(5)^{7/3[/tex]

The given expression contains an exponent of (7/3)

When we exist transforming from exponential form to radical form you always place the numerator as our constant's exponent in the radical ( [tex]$5^{\frac{7}{3} }$[/tex] exists named the radicand because it exists found in the radical) and the denominator in front of the radical, where it would be named the index.

The formula would be: [tex]$(\sqrt[n]{x})^{q}=x^{\frac{p}{q}}$[/tex]

Therefore, the correct answer is ³√5⁷.

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