Solve the linear programming problems: (find the constraints, objective function, feasible region, and the minimumand maximum values)12. A small business produces oak chairs and walnut chairs. The business can make at most 20 chairs per week.Materials cost $100 per oak chair and $150 per walnut chair. The business has a budget of $2400 per week formaterials. Each oak chair sells for $400 and each walnut chair sells for $500. What are the number of oak and walnutchairs that the small business should produce in order to maximize / minimize sales?

Answer:

Since two angles of the triangle have the same measure, the triangle is an isosceles triangle.

Let one angle be a variable (eg: x) so we can form expressions and solve.

Let the first and second angle be x°.

Form an expression for the third angle using the information given.

Third angle = (x + 21)°

Since sum of angles in a triangle is 180°, we can form an equation.

x + x + (x + 21) = 180

Simplify and solve for x.

3x + 21 = 180

3x = 159

x = 53

Largest angle is the third angle.

Substitute x into the expression to find the value.

Third angle = 53 + 21

= 74°

The sequence of transformations is:

Reflection across the x-axis followed by a translation of 5 units to the left.

We start with the red figure, the first thing we should apply is a reflection across the x-axis.

Doing this, we will see that both figures are in the same orientation, while in different positions.

At this point, we should do a translation to the left of 5 units, this will move the whole red figure 5 units to the left and that will map the red figure into the blue one.

Notice that if the transformations are applied in the other order (first the translation and then the reflection) we will get the same outcome.

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Hello! So...

We are given the following to solve:

Solve for x.

[tex]\frac{2}{3} (2x-\frac{1}{2})=13[/tex]

_______________________________________

1. Multiply both sides by 3.

[tex]3[/tex] × [tex]\frac{2}{3}(2x-\frac{1}{2})=13[/tex] × [tex]3[/tex]

_______________________________________

2. Simplify.

[tex]4x-1=39[/tex]

_______________________________________

3. Add 1 to both sides.

[tex]4x-1+1=39+1[/tex]

_______________________________________

4. Simplify.

[tex]4x=40[/tex]

_______________________________________

5. Divide both sides by 4.

[tex]\frac{4x}{4} =\frac{40}{4}[/tex]

_______________________________________

6. Simplify.

[tex]x=10[/tex]

^Hence, our solution.

__________________________________________________

Hope this helps! If you need anything else, don't hesitate to comment below and I'll see what else I can do for you. Thanks and good luck!

The number of weeks for your friend's savings to be same as your savings does not exist

The given parameters are:

Your savings account

Initial amount = $100

Weekly savings = $40

Your friend's savings account

Initial amount = $80

Weekly savings = $10

The equation that represents the amount in the account after w weeks is represented as

Amount = Initial amount + Weekly savings x Number of weeks

This gives:

You: Amount = 100 + 40x

Your friend = 80 + 10x

The above equations are linear equations

When the amounts are equal, we have

100 + 40x = 80 + 10x

This gives

30x = -20

Divide

x = -2/3

The number of weeks cannot be negative

Hence, your friend's savings will never be up to your savings

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Possible question

You have $100 in a savings accoun and save an additional $40 each week. Your friend has $80 in a savings account and saves and addtional $10 each week.

When will you and your friend have the same amount?

The bottle of 40 tablets will contain 420 milligrams of tablets.

Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.

Given that a multivitamin tablet contains 10.5 mg of calcium and there are 40 tablets in the bottle. The total amount of the tablets in the bottles will be calculated as:-

Total tablets = 10.5 mg x 40

Total tablets = 420 mg

Therefore, a bottle of 40 tablets will contain 420 milligrams of tablets.

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The most appropriate choice for function, domain and range of a function will be given by

Domain of the given function is [tex]\mathbb{R}[/tex], the set of real numbers

Range of the given function is [tex]\mathbb{Z}[/tex], the set of integers.

What is Function, Domain and Range of a function?

Function

A function from A to B is a rule that assigns to each element of A a unique element of B

Domain of a function

Domain of a function is the set of  values for which the function is defined.

Range of a function

The set of values obtained on putting the values of the domain is called the range of a function.

Here,

Domain of [tex]y = [x] + 2[/tex]

[tex][x][/tex] is defined for all [tex]x[/tex] ∈ [tex]\mathbb{R}[/tex], the set of real numbers

Domain of the given function is [tex]\mathbb{R}[/tex], the set of real numbers

[tex][x][/tex] is the greatest integer not exceeding [tex]x[/tex]

So [tex][x][/tex] [tex]+ 2[/tex] gives only integer values

So Range of the given function is [tex]\mathbb{Z}[/tex], the set of integers.

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Answer: 80.7%

Step-by-step explanation: COGS (beverage and food costs) = $68,555

$68,555 is 80.6529412% of $85,000 rounded to the nearest tenth is 80.7%

Answer:

11 nickels . Are in a doldollar

Step-by-step explanation:

The answer is letter B. Zero.

The solution is the point in which two lines cross, but here we observe to parallel lines, there is no intersection. So there is no solution.

From the question, we were asked that how many 42 inches wide panels must be bolted together to create a 28 feet wall.

First let's covert the two measurement to same unit.

So, lets convert 42 inches into feet.

Recall, 1 foot will give 12 inches

42 inches will be:

42/12 = 3.5 feet

Therefore, the wide wall that must be bolted together to create a 28 feet wall is:

= 28/3.5

= 8 feet.

The number of dollars Jada and Kelly each have now is $18 and $15.

Given:

Ratio of the number of dollars Jada has to the number of dollars Kelly has = 4:7

Changed ratio after Kelly gives Jada $6.00 = 6:5

Let the number of dollars Jada and Kelly have be 4x and 7x.

Kelly gives Jada $6.00,

So,

Number of dollars Jada has now is $(4x + 6).

Number of dollars Kelly has now is $(7x - 6).

The ratio of the number of dollars is changed to 6:5.

⇒ [tex]\frac{4x + 6}{7x -6} = \frac{6}{5}[/tex]

⇒ 5(4x + 6) = 6(7x - 6)

⇒ 20x + 30 = 42x - 36

⇒ 42x - 20x = 30 + 36

⇒ 22x = 66

⇒ x = 3

Number of dollars Jada has now = (4x + 6) = $18

Number of dollars Kelly has now = (7x - 6) = $15

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Ratio of A to B = 3/4

Ratio of B to C = 12/5

Multiply the ratio of A to B by 3/3

Comparing the ratio of A to B and the ratio of B to C:

Ratio of A to B to C = 9 : 12 : 5

Total ratio = 9 + 12 + 5 = 26

Value of C = (5/26) x Total value

60 = (5/26) x Total value

Total value = (60 x 26)/5

Total value = 312

Value of A = (9/26) x Total value

Value of A = (9/26) x 312

Value of A = 9 x 12

Value of A = 108

We can replace x with any real number, positive or negative. We can also plug in x = 0. There aren't any restrictions to worry about with the input.

Examples:

Plug in x = 2 to get f(2) = 2(1/10)^2 = 0.02

Plug in x = -2 to get f(-2) = 2(1/10)^(-2) = 200

Plug in x = 0 to get f(0) = 2(1/10)^(0) = 2

The domain of the given function is "All real numbers". So, option D is correct.

The domain of a function is the set of possible values as inputs to the function. The Domain of the exponential function is the set of all real numbers represented by R.

here, we have,

Finding the domain of the given function:

The given function is f(x) = 2×

Since this function has the variable x in the exponent, this is an exponential function.

So, its inputs are of all real numbers. And the domain is {x:x ∈ R}.

Thus, option D is true.

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Answer:

217°

Step-by-step explanation:

the tangent ratio is positive in the first and third quadrants.

37° is the angle in the first quadrant

then the angle in the third quadrant is

180° + 37° = 217°

Given

Point A = (25, 98)

Point B = (55, 92)

Procedure

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

Now, what about b, the y-intercept?

The equation of the line that passes through the points

(25,98) and (55,92)

Answer:

264

Step-by-step explanation:

0.75x352

Answer:

Step-by-step explanation:

First we have to consider the initial and final velocities to calculate the average acceleration:

v_i= - \Big[ 1.10\frac{m}{s}\Big]\widehat{i} \\ v_f= \Big[ 11.5\frac{m}{s}\Big]\widehat{j} \\ \implies \Delta v=v_f-v_i \\ \implies \Delta v= [ 1.10\frac{m}{s}]\widehat{i} +[ 11.5\frac{m}{s}]\widehat{j} \text{ in an average time } \Delta t=1.40\,s.v

i

​

=−[1.10

s

m

​

]

i

v

f

​

=[11.5

s

m

​

]

j

​

⟹Δv=v

f

​

−v

i

​

⟹Δv=[1.10

s

m

​

]

i

+[11.5

s

m

​

]

j

​

 in an average time Δt=1.40s.

With the information we can calculate the average acceleration in terms of the x- and y-components:

a=\Delta v/\Delta t= \dfrac{[ 1.10\frac{m}{s}]\widehat{i} +[ 11.5\frac{m}{s}]\widehat{j}}{1.40\,s} \\ \text{ } \\ \implies a= \big[ 0.786\frac{m}{s^2}\big]\widehat{i} + \big[ 8.214\frac{m}{s^2} \big]\widehat{j}a=Δv/Δt=

1.40s

[1.10

s

m

​

]

i

+[11.5

s

m

​

]

j

​

​

⟹a=[0.786

s

2

m

​

]

i

+[8.214

s

2

m

​

]

j

​

Answer:Explanation:

(a)$10,488

(b)$12,218.

• ric;' Monthly Salary = $1,730

• Percentage commision = 12%

Part A

f Eric 's sales were $87,400 for last month, his amount of commission will be:

Eric's amount of commission is $10,488.

art B

Eric's gross pay will be the sum of his monthly salary and commission.

Eric's gross pay is $12,218.

⇒2 will multiply everything in the brackets.

[tex]2(p)+2(19)=8\\2p+38=8\\[/tex]

⇒Now I will group like terms to solve for p. Note those that cross the equal sign change sign

[tex]2p=8-38\\2p=-30\\\frac{2p}{2} =\frac{-30}{2} \\p=-15[/tex]

We found that p=-15

Answer:

1) 29 equals n over 3

2) x + 4 = 6

3) p − 53 = 118

4) L over 4 equals 24

Step-by-step explanation:

1) twenty-nine is one-third of the number n is

29 = 1/3 • n

29 = 1/3 • n/1

29 = n/3

So, the answer is 29 equals n over 3

2) The song was 6 minutes long and she has already sung 4 minutes

Let's find the equation to be used to see how much longer she will have to sing?

? + 4 = 6

x + 4 = 6

3) The equation to be used to find the pencils left according to the question is p − 53 = 118 since he has 118 pencils left out of collecting 53 pencils so the remaining pencil would be 118 - 53

Where, p is representing the pencil remaining

So, the answer is p − 53 = 118

4) I think you made a typo in this question

Correction

Julia has a square poster of a puppy on her bedroom wall. The length is one-fourth the width of the picture. If the width is 24 inches, write and solve an equation to determine the length

Answer

so the answer to this question is L over 4 equals 24

L/4 = 24

L = 24*4

L = 96

so, the length is equal to 96 inches and the equation is L over 4 equals 24

First I will define what prime factor means

Prime factors of 42 are the factors of 42 that are prime

Prime numbers are those numbers that have two factors; 1 and itself

Factors of 42 are those numbers that can go into 42 without remainder

So let's list out the factors of 42, they are;

Factors of 42 = 1, 2, 3, 6, 7, 14, 21 and 42

Now among these factors, we will list out the ones that are prime, they are the prime factors

That is;

Prime factors of 42 = 2, 3, and 7

To express 42 as a product of it's prime factors, we have 2 ways of doing this

The first method is; To keep dividing 42 by the smallest prime factors

42 = 2 x 3 x 7

The second method is;

Therefore, the prime factorization of 42 = 2 x 3 x 7

The prime factorization of 42 is 2 × 3 × 7.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

The positive pair factors of 42 are (1, 42), (2, 21), (3, 14), and (6, 7).

The negative pair factors of 42 are (-1, -42), (-2, -21), (-3, -14), and (-6, -7).

The 42 factors that are prime are known as the prime factors of 42.

Prime numbers are those with just themselves and factor 1 as their factors.

The numbers that can round to 42 without leaving a remainder are known as 42 factors. Let's enumerate the 42 factors, which are as follows:

1, 2, 3, 6, 7, 14, 21, and 42 are factors of 42.

We shall now list the prime factors among them, they are the prime factors. which is;

42 has prime factors of 2, 3, and 7.

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In the class, there is a total of 42 students.

25 take biology.

15 take history.

18 take biology but not history.

There are four situations that you have to include in the Venn diagram:

"The students take only biology"

"The students take only history"

"The students take biology and history"

"The students take neither classes"

To draw the Venn diagram, you have to make one circle for each subject, i.e. one circle for biology and one for history, and label them.

Then you have to enter the similarities between both subjects, this means, where the circles overlap, you will find the students that take both subjects.

Finally, outside the circles, you will find the students that take neither subject:

Now, you have to determine how many students are included in each part of the Venn Diagram.

1) You know that 25 students take biology and that 18 take biology but not history, to determine the number of students that take both subjects, you have to calculate the difference between both values:

7 students take biology and history.

2) 15 students take history out of these you know that 7 take also biology. To determine the number of students that take only history, you have to calculate the difference between both values:

8 students take history but not biology.

3) To determine the number of students that take neither class, you have to subtract to the total number of students, those who take only biology plus those who take only history plus those who take both classes:

9 Students of the class take neither class.

Finally, you can write each value in the corresponding part of the Venn diagram:

• Inside the green circle, you have to include the 18 students that take only biology.

• Inside the blue circle, you have to include the 8 students that take only history.

• Where both circles overlap, you have to include the 7 students that take both classes.

• Outside the circles, you have to include the students that take neither.

The product of any two negative numbers is positive.

Consider a positive number to be something as a gift, and a negative number to be something you give to me.

So, let's say you get 4 laptops from me, and - 4 means you give away 4 laptops to me.

Now when you say - 4 + - 4 + - 4 + - 4 + - 4.

This means that you are giving away 4 laptops 5 times to me, so basically you have given away 20 laptops, which means I have 20 laptops and you have - 20.

Now, - 4 * - 5 means, you give away 5 laptops, for - 5 times to me. But the second number is - 4, so the receiver, that is me, is giving it back to you. Thus indirectly, you gave away 4 chocolates to yourself 5 times. Thus you have 20 laptops.

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Answer:

9

Step-by-step explanation:

sostrict 16 4fg _d-5=9

Answer:

-11.8684210526

Step-by-step explanation:

Deon served 16 orders. Pablo served 32 orders. Teresa served 7 orders.

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

Let Deon order be x , since Teresa served 9 fewer orders than Deon.  , then Teresa order is x - 9,

since Pablo served 2 times as many orders as Deon, it means Pablo's order is 2x . combining all

Deon 's orders = x

Pablo's order = 2x

Teresa 's order = x - 9

Total order = 55

Then

x + 2x + x - 9 = 55

4x - 9 = 55

4x = 55 + 9

4x = 64

x = 16

Therefore :

Deon served 16 orders

Pablo served orders = 32 orders

Teresa served 16 - 9 orders = 7 orders

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The change between the morning and afternoon temperature is 2.7.

It should be noted that temperature simply means the degree of hotness as well as the coldness that is in a particular body

In this case, the temperature was -2 1/2 in the morning . by the afternoon the temperature was 0.2.

The change between the temperature will be:

= 0.2 - (- 2 1/2)

= 0.2 + 2.5

= 2.7

The temperature change is 2.7.

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Answer:

A. 8

Step-by-step explanation:

Geometric mean= √(4×16) = √64 = 8

Answer: b

Step-by-step explanation: