Question 5 of 6Maximize the objective function P = 5x + 3y for the given constraints.
x ≥ 0
y ≥ 0
3x + 6y ≤ 48
2x + 8y ≤ 56

Answer:

Step-by-step explanation:

(1, 2), (3, 10)

(10 - 2)/(3 - 1) = 8/2 = 4

m = 4

The age of Nachelle would be 5 years and the age of Julian would be 7 years.

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Let's suppose the age of Nachelle is 'x' years then Julian's age would be 'x+2'.

              x² + [2(x + 2)]² = 139

             x² + 4x² + 8x + 16 = 139

             5x² + 8x - 123 = 0

Simplifying this, we get

       x = 4.22 and x = -5.82

Age cannot be a negative number so

         x ≈ 5.

x + 2 = 7 years

Hence the age of Nachelle would be 5 years and the age of Julian would be 7 years.

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Answer:

x        0     1     2    3    4

f(x)     4     5    6    7    8

Step-by-step explanation:

f(x) = x + 4

f(0) = 0 + 4 = 4

f(1) = 1 + 4 = 5

f(2) = 2 + 4 = 6

f(3) = 3 + 4 = 7

f(4) = 4 + 4 = 8

x        0     1     2    3    4

f(x)     4     5    6    7    8

Classification of given triangle is right angle triangle.

Let's suppose a, b and c are the sides of a triangle.

then we know that sum of 2 sides is always greater than third side.

a + b>c

b + c>a

c + a>b

a = 4.35, b = 5.8 , c = 7.25

a + b>c 4.35+5.8 = 10.15>7.25

b + c>a  5.8 + 7.25 =  13.05>4.35

c + a>b 7.25+4.35 = 11.60>5.8

So now we can say given side lengths are representing sides of a triangle.

It generalizes the Pythagorean Theorem, which states that for a right-angled triangle square of the hypotenuse is equal to the sum of squares of the base and height of the triangle, which is [tex]c^2 = a^2 + b^2[/tex]      

Similarly, It can be observed that

For acute-angled triangle

[tex]c^2 < a^2 + b^2[/tex]    

For Obtuse-angled triangle

[tex]c^2 > a^2 + b^2[/tex]

[tex]a^2 + b^2[/tex] = 18.9225 + 33.64 = 52.5625

[tex]c^2[/tex] = 52.5625

clearly we can see that [tex]a^2+b^2 = c^2[/tex]

So given triangle is Right-angled triangle.

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The table can be completed as follows x = 0, 2, 4 we get y = 1, 2, 3 for the linear equation [tex]y = \frac{1}{2}x + 1[/tex].

If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables.

Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalises the two sides of the equation.

A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.

Basically, there are infinitely many solutions to a linear equation with two variables.

The equation is :

[tex]y = \frac{1}{2}x + 1[/tex]

So, when x = 0

y = 1,

when x = 2

y = [tex]\frac{1}{2}*2 + 1[/tex] = 1 + 1 = 2

and , when x = 4

y = [tex]\frac{1}{2}*4 + 1[/tex] = 2+ 1 = 3

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If a boundary line is dashed, The ordered pairs are never part of the solutions of the inequality

Inequality, is a mathematical statement expressing an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

Solid line and dashed line in inequality

A region on one side of a line can be used to graphically show an inequality.

For the purpose of indicating that a line is not a part of the region, inequality plots that employ the < or > symbols have a dashed line.

Plotting a solid line indicates that an inequality that uses the symbol  ≤ or ≥ is included in the region.

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An effective claim in the essay is that; Chickens raised for-eggs should be allowed to roam free. Option A

The entire point of an argumentative essay is that the essay helps us to be able to bee able to make a point. It is the kind of essay in which we may be able to communicate our perspective about a matter.

In the argumentative essay, there could be a claim which is the main point that the essay is trying to address. The claim would thus provide the kernel of the essay. It is the point that the author wants to pass across to the readers.

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Answer: A: Chickens raised for eggs should be allowed to roam free.

Answer:

(0, 2 )

Step-by-step explanation:

If the dilatation is centred at the origin then the original coordinates are multiplied by the scale factor , that is

B (0, 4 ) → ( [tex]\frac{1}{2}[/tex] (0), [tex]\frac{1}{2}[/tex] (4) ) → (0, 2 )

Answer: (x-1) 3

Step-by-step explanation:

This is equation you want

x is unknown -1 in the mark and then times 3!

The two column proof is written as follows

Statement                                                           Reason

AD ≅ BD ≅ CD                                         given

ΔADB and ΔCDB are isosceles             Base angles are equal

< A =  < C = < ABD = < CBD = x              Definition of isosceles triangle.

< ABC =  < ABD + < CBD                         Adjacent angles

< ABC = x + x = 2x                                   Substitution property of equality

< ABC + < A + < C = 180                          Sum of angels of a triangle

2x + x + x = 180                                       Substitution property of equality

4x = 180                                                   Addition property of equality

x = 45 degrees                                        Division property of equality

< ABC = 2x = 2 * 45                                Substitution property of equality

< ABC = 90                                              Definition of right triangle

A triangle is said to be a right triangle if one of the angles is 90 degrees. Right angles are angles that are 90 degrees.

The proof required to proof that < B is 90

With the isosceles triangle giving and the equal sides the equation is written as

4x = 180

x = 45

< B has 2x (< ABD + < CBD) these are adjacent angles

< B = 2 * 45

< B = 90

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It will take 2 hours 24 minutes time to two trains to meet.

Let a train starts from A towards to B with velocity v1 = 90 miles/hour

and another train starts it's journey from B towars A with velocity               v2 = 110 miles/hour

Let after  time t hour they meet at C.

Hence, we get  AC + CB = AB

                    ⇒  v1t + v2t = 480

                    ⇒ (v1 + v2) t = 480

                    ⇒ (90 + 110) t = 480

                    ⇒ t = 480/200 = 48/20 = 12/5 hours

                     ∴ t = [tex]2\frac{2}{5}[/tex] hours

                          = 2 hour (2/5 × 60) mins

                    ∴ t  = 2 hours 24 minutes time

So, after 2 hours 24 minutes time they meet each otherv at C, where                 AC = v1t  = 90 × 12/5 = 216 miles.

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Answer: To find the tip amount in dollars for each order, you need to multiply the total bill amount by the tip percentage.

For the first order of 4 dishes, the total bill amount is $8 per dish * 4 dishes = $<<8*4=32>>32.

The tip amount is $32 * 20% = $6.40.

For the second order of 6 dishes, the total bill amount is $8 per dish * 6 dishes = $<<8*6=48>>48.

The tip amount is $48 * 14% = $6.72.

For the third order of 7 dishes, the total bill amount is $8 per dish * 7 dishes = $<<8*7=56>>56.

The tip amount is $56 * 11% = $6.16.

So, the tip amounts from least to greatest are $6.16, $6.40, and $6.72.

The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is wider than one other.

Confidence interval:

In statistics, confidence interval means  the probability that a population parameter will fall between two set values.

Given,

Here we need to find the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean.

According to the given question, the given confidence interval values are 90% and 95 %.

When we convert this percentage value into decimal, then we get the value as,

90% = 0.9

95% = 0.95

Here a 95 percent confidence interval, you have a 5 percent chance of being wrong.

And with a 90 percent confidence interval, you have a 10 percent chance of being wrong.

Therefore, 90 percent confidence interval would be wider than a 95 percent confidence interval.

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When a:3=12:a, then the positive of a will be 6.

Given, the  following quadratic equation

a : 3 = 12 : a

That is,

a/3 = 12/a

By cross- multiplication of the values, we will get

a * a = 12 *3

a ^ 2 = 36

From the above equation, we calculate the square root for the value a.

Therefore, we get the square root of,

a ^ 2 = 36

a = 6 ( as the square root of 36 is 6)

So, we can say that when a : 3 = 12: a the positive of a will be 6

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Amount Patrick has to pay back is $ 1680 and the simple interest is $ 280.

What is Simple Interest?

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) 100

Given data ,

Let the principal amount be = A

The value of A = $ 1400

Let the rate of interest be = r

The value of r = 10 %

Let the number of years = T

The value of T = 2 years

Now , the simple interest is calculated by the formula

Simple Interest = ( Principal Amount x Rate x Time Period ) 100

Substituting the values in the equation , we get

Simple Interest = ( 1400 x 10 x 2 ) / 100

Simple Interest = 14 x 20

Simple Interest = $ 280

Therefore , the simple interest in 2 years is $ 280

And , the total amount Patrick has to give back to the bank is given by the formula

Amount in 2 years = Principal + Interest

Amount in 2 years = 1400 + 280

Amount in 2 years = $ 1680

Therefore , the amount in 2 years is $ 1680

Hence , Amount Patrick has to pay back is $ 1680 and the simple interest is $ 280

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The measure of m∠x is 110°

What is the Isosceles Triangle?

Isosceles triangles are those triangles that have at least two sides of equal measure. We know that triangles are three-sided enclosed polygons and they are classified as equilateral, isosceles, and scalene, based on the length of their sides.

We have,

given the triangle Δwxy,

m∠y = 35°, and

there are two similar sides to the triangle wx ≅ xy,

Properties of an Isosceles Triangle are:

The two sides are congruent with each other.

The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle.

The two angles opposite to the equal sides are congruent with each other. That means it has two congruent base angles and this is called an isosceles triangle base angle theorem.

The angle which is not congruent to the two congruent base angles is called an apex angle.

The altitude from the apex of an isosceles triangle bisects the base into two equal parts and also bisects its apex angle into two equal angles.

The altitude from the apex of an isosceles triangle divides the triangle into two congruent right-angled triangles.

The two angles opposite to the equal sides are congruent with each other.

so, m∠w = m∠y = 35°

The sum of measure of the angles of the isosceles triangles is 180.

so,

m∠w + m∠x + m∠y = 180

35 + 35 + m∠x = 180

m∠x = 180 - 70

m∠x = 110°

Hence, the measure of m∠x is 110°.

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Therefore ,the volume of the block after cutting out the smaller cubes is  (8/25 cm^2)

Any three-dimensional solid's volume is just the amount of space it takes up. A cube, cuboid, cone, cylinder, or sphere can be one of these solids.

Volumes vary depending on the shape. We have examined different three-dimensional objects and shapes in geometry, including cubes, cuboids, cylinders, cones, and more. We will learn how to calculate the volume for each of these shapes.

Here,

volume = (8/25 cm2) represents the block's volume after the smaller cubes have been removed.

First, we must determine the volume of a cube with four or five centimeter sides, which is:

V = (4/5 cm)^2 = (16/25 cm^2)

The volume of each of the eight smaller cubes that was removed must now be subtracted.

v = (1/5 cm)^2 = (1/25 cm^2)

After the smaller cubes are removed, the block's volume is:

V - 8v = (16/25 cm^2) - 8*(1/25 cm^2) = (8/25 cm^2)

Therefore ,the volume of the block after cutting out the smaller cubes is  (8/25 cm^2)

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Step-by-step explanation:

As given in question that Skyler buys 8 T-shirts and 5 hats for $220.

The next day, he buys 5 T-shirts and 1 hat for $112.

We have to find the cost of T-shirt and hat each.

Let the cost of T-shirt and hat is x and y respectively.

According to the question,

8x + 5y = 220          ............(i)

5x + 1y = 112             ............(ii)

Multiply by 5 in eq. (ii)

25x + 5y = 560        ............(iii)

Now subtract eq. (iii) - eq. (i)

25x + 5y = 560

- 8x + 5y = 220

17x = 340

[tex]x = \frac{340}{17}[/tex]

∴ x = 20

Put the value of x in eq. (ii)

5 x 20 + y = 112

100 + y = 112

y = 112 - 100

∴ y = 12

The coordinates of A' and C' will not be the same. The perimeter and area of ΔA'B'C' will be the same. The measure of ∠B' and the slope of A'C' will be the same.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given translation,

2 units down and 3 units right

The coordinate will change as,(x,y) → (x+3,y-2) so it will change.

The transformation consists only of linear transformation no rotation exists thus area and perimeter will remain the same.

The slope and angle are unchanged irrespective of any transformation.

Hence "A' and C' will not have the same coordinates. The boundaries and surface area of ΔA'B'C' will be identical. The slope of A'C' and the measure of ∠B will be equal.".

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If Ann has 30% less money than mary, and jessica has 70% more money than mary and If the three of them have a total of $102, then Ann has $50.7, Mary has $51 and Jessica has $51.7

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It can be stated as a decimal or a fraction and is frequently represented by the sign "%". 50%, for instance, can be written as 0.5 or 1/2. A component or proportion of an entire is represented using percentages. For instance, if a student receives a 75% on an exam, it indicates that they correctly answered 75 out of 100 questions individually. Percentages are often used in everyday life to represent changes such as a rise or fall in pricing, an increase or reduction in population, or a growth or drop in sales. Percentages may be determined in mathematics using a variety of formulae and ideas including proportions, ratios, and decimals.

How to solve?

Ann has 30/100 * $x = $0.3x less money than Mary

Jessica has 70/100 * $x = $0.7x more money than Mary

Mary, Ann and Jessica have a total of $102

Mary + Ann + Jessica = $102

Mary + (Mary - $0.3x) + (Mary + $0.7x) = $102

3Mary = $102 + $0.3x + $0.7x

3Mary = $102 + $1x

3Mary = $102 + $x

3Mary - $x = $102

2Mary = $102

Mary = $102/2 = $51

Ann = Mary - $0.3x = $51 - $0.3x = $50.7

Jessica = Mary + $0.7x = $51 + $0.7x = $51.7

Ann has $50.7, Mary has $51 and Jessica has $51.7.

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If Ann has 30% less money than mary, and jessica has 70% more money than mary and If the three of them have a total of $102, then Ann has $50.7, Mary has $51 and Jessica has $51.7

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It can be stated as a decimal or a fraction and is frequently represented by the sign "%". 50%, for instance, can be written as 0.5 or 1/2. A component or proportion of an entire is represented using percentages. For instance, if a student receives a 75% on an exam, it indicates that they correctly answered 75 out of 100 questions individually. Percentages are often used in everyday life to represent changes such as a rise or fall in pricing, an increase or reduction in population, or a growth or drop in sales. Percentages may be determined in mathematics using a variety of formulae and ideas including proportions, ratios, and decimals.

Ann has 30/100 * $x = $0.3x less money than Mary

Jessica has 70/100 * $x = $0.7x more money than Mary

Mary, Ann and Jessica have a total of $102

Mary + Ann + Jessica = $102

Mary + (Mary - $0.3x) + (Mary + $0.7x) = $102

3Mary = $102 + $0.3x + $0.7x

3Mary = $102 + $1x

3Mary = $102 + $x

3Mary - $x = $102

2Mary = $102

Mary = $102/2 = $51

Ann = Mary - $0.3x = $51 - $0.3x = $50.7

Jessica = Mary + $0.7x = $51 + $0.7x = $51.7

Ann has $50.7, Mary has $51 and Jessica has $51.7.

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Answer:

Base is 5/2

Step-by-step explanation:

lets say that 2x = the base.

25/24 = 2( [tex]\frac{1}{2}[/tex]([tex]\frac{5}{6}[/tex])x)

[tex]\frac{25}{24}[/tex] = 2( [tex]\frac{5}{12}[/tex]x)

[tex]\frac{25}{24}[/tex] = [tex]\frac{5}{6}[/tex]x

[tex]\frac{25}{24}[/tex] times [tex]\frac{6}{5}[/tex]= x

5/4 =x

2x = 10/4

2x = 5/2

The interval at which the function f(x) = |4(x - 1)| + 2 is decreasing is (- ∞, 1).

We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.

In piecewise terms  | x | = x for x ≥ 0 and | x | = - x for x < 0.

We know in an absolute value function y = |x - h| + k, the vertex is (h, k) and it changes its direction from here.

Given, f(x) = |4(x - 1)| + 2 has a vertex at (1, 2).

Therefore the interval where the function is continuously decreasing is

( - ∞, 1).

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Answer:

There are no values of x

that make the equation true.

No solution

Step-by-step explanation:

Answer:

81.5%

Step-by-step explanation:

Note that 90 is 2 standard deviations away from 144, which accounted for 47.5% area

171 8 is 1 standard deviations away from the mean is which is 34% area.

So the total area is 81.5%

Answer: $28.79

Find 20% of $35.99.

Then subtract that answer (7.2) from $35.99

your answer is

The shoes where on sale for $28.79

Answer:

11 days

Step-by-step explanation:

y=24x+61

y=20x+105

(don't think I can solve this with elimination because there is no coefficient with a y-value.)

When looking for the interception you look for the point where both lines intercept. I graphed both equations online and looked for the point where they intercept, which is (11,325) meaning that in 11 days, both places will cost 325 dollars when you rent a car.

( I also looked for a calculator online that is especially used to find the interception between two points and it gave the same point, if wrong...I'm sorry)

A cylindrical vase with a curved surface area of 6.79 square metres will cost Rs. 8.14 to paint.

The area with just curved surfaces, leaving the circular top and base, is referred to as the curved surface area. Curved surface area is the amount of space left over after subtracting the cylinder's total circular area. The formula for curved surface area is 2 * pi * r * h.

Here,

We have to calculate the curved surface area of glass in which the flower basket is placed.

Glass is cylindrical,

Height of cylinder = 180cm = 1.8m

Radius of cylinder = 60cm = 0.6m

The curved surface area of the cylinder = 2πrh

The curved surface area of the cylinder = 2*22/7*0.6*1.8

The curved surface area of the cylinder = 6.78584 m²

Cost of painting the glass per m² = Rs. 1.2

Cost of painting 6.78584= 6.78584*1.2

Cost of painting 6.78584= Rs. 8.143

The cost of painting an cylindrical vase of curved surface area 6.79 m² will be Rs. 8.14.

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Answer:

The terms in Sequence 2 are four times as large as the terms in Sequence 1.

Step-by-step explanation:

If we take a look at the numbers,

Sequence 1: 0, 1, 2, 3, 4, 5

Sequence 2: 0, 4, 8, 12, 16, 20

We can see that 0 × 4 = 0,

1 × 4 = 4,

2 × 4 = 8,

And so on.

We can also see in sequence 2 that 4 is added to each of the numbers every time, whereas the first sequence is simply counting up.

Therefore, we can conclude that the terms in Sequence 2 are four times as large as the terms in Sequence 1.

Answer:

Step-by-step explanation:

the answer is A

Answer:

A.) [tex]\frac{-343}{27}[/tex]

Step-by-step explanation:

Looking at the available answers, I'm assuming the expression is [tex](-2-\frac{1}{3})^3[/tex].

So,

[tex](-2-\frac{1}{3})^3\\(-\frac{6}{3}-\frac{1}{3})^3\\(\frac{-7}{3})^3[/tex]

Use the exponent rule that states [tex](\frac{a}{b})^m=\frac{a^m}{b^m}[/tex]

So,

[tex](\frac{-7}{3})^3\\\frac{(-7)^3}{3^3}\\\frac{-343}{27}[/tex]

Equation for representing energy to the number of days E = P*( 1/d / 1000 )

This formula of energy is used to calculate the use of energy for a given period in a day . The consumption of energy is measured by multiplying the number of power units consumed in a given period.

E = P*(1/d/1000); where E = energy measured in Joules or kilowatt-hours (kWh), P = power units in watts,  and d = time over which the power or energy was consumed in a day  

Thus, whenever someone asks you how to calculate power consumption, you can calculate and answer using the above equation.

Energy consumption can be widely classified based on several factors such as worldwide energy consumption, its impact on the environment, etc.

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