Graph the linear inequality y < 1/2x + 2 using slope-intercept form.

Answer:

Step-by-step explanation:

Lets simplify this step by step

5(2x+2)+3x+6

Distribute:

=(5)(2x)+(5)(2)+3x+6

=10x+10+3x+6

Combine Like Terms:

=10x+10+3x+6

=(10x+3x)+(10+6)

=13x+16

13x+16

The constant of variation for the given graph is 1/4.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.

Given that the equation of the line in the graph is a direct variation equation.

Direct variation equations are of the form,

y = k x, where k is a constant number called constant of variation.

We have to find the value of k.

y = k x is an equation in slope intercept form where k is the slope and the value of y intercept is 0, since the line passes through origin (0, 0).

It is enough to find the slope of the given line.

Take two points from the graph, let it be (4, 1) and (-4, -1).

Slope = (-1 - 1) / (-4 - 4) = -2 / -8 = 1/4

The value of k is 1/4.

Hence the value of constant of variation is 1/4.

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Answer: 70

Step-by-step explanation: First, let's find how many are worth each in numbers. Use this formula:

Part Percent * Whole number / 100

Plug in the numbers:

Red = 12 * 250 / 100

3000/100

= 30 red marbles

Blue = 16* 250 / 100

4000 / 100

= 40 blue marbles

40 + 30 = 70

White = 250 - 70

= 180 white marbles

We can check our answer by adding 12 + 16. That's 28. So by multiplying 250 by 28, we get 7000. 7000 divided by 100 = 70

70 = 70

Therefore, both statements are true

I hope this helped!

The optimal production of wind and solar that will maximize overall power output is 3 units/day of solar power and 2 units/day of wind power.

To solve this question, we use the following representations

So, the objective function is to maximize z = x + y, which represents the overall power output.

From the question, we have the following constraints:

Using the Lagrangian function, we have:

L(x,y,λ1,λ2,λ3) = x + y + λ1(6-x) + λ2(y-1) + λ3(2x-y-1)

To find the optimal solution, we need to find the values of x, y, λ1, λ2, and λ3 that will make the partial derivatives of L equal to zero:

∂L/∂x = 1 + λ3 = 0

∂L/∂y = 1 - λ1 + λ2 + λ3 = 0

Using the variables x and y, we have

∂L/∂λ1 = -x + 6 = 0

∂L/∂λ2 = y - 1 = 0

∂L/∂λ3 = 2x - y - 1 = 0

Using a graphing calculator, the points that maximize the objective function are:

x = 3 and y = 2

i.e.

Power output is 3 units/day of solar power and 2 units/day of wind power.

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From the table given a linear function that relates y to x  is y = -7.

What is point - slope form of line?

The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

The point - slope form of line is y - y1 = m(x - x1).

From the given table of values we have to find the linear function that relates y to x.

First to find the slope.

Slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-7-(-7)}{0-(-2)} = \frac{0}{2} = 0[/tex]

Now consider the point - slope form of line,

 y - y1 = m(x - x1).

y - (-7) = 0(x - 0)

 y + 7 = 0

       y = -7

Hence, from the table given a linear function that relates y to x  is y = -7.

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It is TRUE that the given image represents the function.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.

The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Initially, functions represented the idealized relationship between two changing quantities.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

So, the given image represents a function and it is a kind of many-to-one function.

Therefore, it is TRUE that the given image represents the function.

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Answer:

you forgot the question

Step-by-step explanation:

By solving the equation The answer is  -27+17r .Because the Given question is a Equivalent Equation

3+4(r-6)= 3(2+2r)+7r

3+4r-24=6+6r+7r

3-6-24+4r+6r+7r

-24+17r

Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.

If two equations have the same solution, they are equivalent.

Equations that are equivalent can be created by adding, subtracting, multiplying, and dividing by the same number on either side of the equal sign.

Finding the value of the variable that makes the equation's condition true is the goal of equation solving. The subsequent actions are carried out while keeping the equation balanced on both sides in order to isolate the variable. By repeating this, LHS and RHS finally remain equal, and the equilibrium is maintained throughout.

We separate the variable on one of the sides of the equation after applying this approach of systematic balancing, which entails a series of identical mathematical operations on both sides of the equation. The final step is the solution of the equation.

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The statement that a rate is a type of ratio that has both terms expressed in different units is true.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

A rate is a type of ratio that has both terms expressed in different units.

This is true.

Example:

The unit rate of running a distance of 5 km in 4 hours.

Rate = 5km/4 hours

Unit rate = (5/4) km / 1 hour

Thus,

A rate is a type of ratio that has both terms expressed indifferent unit is true.

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Answer:

[tex]x^2+7x-9+\dfrac{12}{x-7}[/tex]

Step-by-step explanation:

The detailed explanation is in the attached image. It is a real pain to type this in the brainly equation editor so I just used LateX and printed out the result in case you are interested.

I may have made typos in the detailed explanation, if so, let me know

Answer:

[tex]y-4=-2(x-0)[/tex]

Step-by-step explanation:

We are given that a line has a slope (m) of -2, and contains the point (0,4).

We want to write the equation of the line in point-slope form.

Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.

Since we are already given the slope, we can immediately plug it into the formula.

Substitute -2 as m.

[tex]y-y_1=-2(x-x_1)[/tex]

Now, let's label the values of our points to avoid confusion and mistakes.

[tex]x_1=0\\y_1=4\\[/tex]

Substitute into the formula.

[tex]y-4=-2(x-0)[/tex]

Topic: point-slope form

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The relationship between the green highlighted segment in triangle 2 and the blue highlighted segment in triangle 1 is D. The highlighted segments are congruent.

Congruent segments are segments in different shapes that have the same length and angle. In other words, they are identical to each other even though they are in different shapes.

The green highlighted segment in triangle 2 and the blue highlighted segment in triangle 1 are congruent segments because the blue highlighted segment was segment the green highlighted segment was derived from which is why they are the same.

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The store had $0 profit first in month 4 and then in month 10

The maximum profit of $1000 occurred in month 7

The function is given as

p(z) = -z² + 14z - 40

Next, we set p(z) = -z² + 14z - 40 = 0 and then solve for z.

So, we ha

-z² + 14z - 40 = 0

Rewrite as

z² - 14z + 40 = 0

Factorize

(z - 10)(z - 4) = 0

Solve for z

z = 10 and z =4

So the store had a profit of zero dollars in month 4 and then in month 10

Here, we calculate the vertex using

x = -b/2a = -14/2*-1 = 7

Plugging this value into the function, we get:

p(7) = -7² + 14*7 -40 = 49-98+40 = 1

so the maximum profit was $1000 and it occurs in the month 7.

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The solution is greater than -1.5 and less than -1.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

convert mixed fractions into improper fractions, then to decimal

14 2/5 = 72/5 = 14.4

11 1/8 = 89/8 = 11.125

Thus, the equation becomes:

14.4x+6.55= -11.125x-2.45 + 17 x

=>  14.4x + 11.125x - 17x = -6.55 -2.45

=>  8.525x = -9

=> x =  -9 / 8.525 = -1.055

solution of the equation rounded to the nearest tenth = -1.1

Thus, The solution is greater than -1.5 and less than -1.

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Answer:

279.05649m³

Step-by-step explanation:

Circumference = 2πr

6 = 2πr

6/2π = r

r = 9.424777961

Area = πr²

Area = π(9.424777961²)

Area = 279.05649m³

Answer:

the answer I got was 18 over 1657

Step-by-step explanation:

its a fraction so the numerator is 18 and the denominator is 1657

He must get at least 97% on the final examination to earn an A in the course.

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Answer: [tex]B. \frac{2}{7} -\frac{2}{k}[/tex]

Step-by-step explanation:

The statement about probability that is true is that the probability of landing on purple is equal to the probability of landing on yellow. That is option D

Probability is defined as the possible outcome of an event which may likely or unlikely occur.

The total number of sections with different colours = 8

Sections 1 and 8 are purple.

Sections 2 and 3 are yellow.

Sections 4, 5, and 6 are blue.

Section 7 is orange

The probability of landing on purple is equal to the probability of landing on yellow. That is;

probability of landing a purple = 2/8 = 1/4

Probability of landing a yellow = 2/8 = 1/4

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Answer:

A) 270

Step-by-step explanation:

Interest = principle x time x rate

Interest = 3000 x 2 x .045   4.5% = .045 as a decimal

Interest = 270

The length of the longest side of ∆XYZ will be 40 cm. Then the correct option is A.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The sides of triangle ∆ABC have lengths of 3 cm, 8 cm, and 10 cm. If the smallest side of a similar triangle ∆XYZ has a length of 12 cm.

Let 'x' be the length of the longest side. Then the equation is given as,

x / 10 = 12 / 3

Simplify the equation, then we have

x / 10 = 12 / 3

x / 10 = 4

x = 40 cm

The length of the longest side of ∆XYZ will be 40 cm. Then the correct option is A.

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Using PEDMAS the value of 1×(-0.3÷0.5-0.9) is -0.3

PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete.

In the expression 1×(-0.3÷ -0.5-0.9) we solve what is in the parentheses first and we must follow the rules in the parentheses.

So we deal with the division first

1× ( 0.6-0.9)

1× -0.3 = -0.3

Therefore the value of the expression 1×(-0.3÷0.5-0.9) is -0.3.

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The interpretation of the likelihood of randomly selecting a terrier from the dog shelter where terriers are 85% is A. Likely.

Probability refers to the chance or likelihood of an expected event occurring when there are many possible chances.

Probability is depicted as a fractional value lying between zero and one when it is not 100% uncertain or certain.

Thus, since the percentage of terriers in the dog shelter is 85%, it is 85% likely that one selects a terrier.

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Answer: A: Likely.

Step-by-step explanation:

Our velocity is said to be 10% of the speed of light. Therefore, we need to multiply by 10% the speed of light. As a result, our speed is three times 10 to 7 m/s. Our diameter is 500 metres.

Thus, our radius is 250 metres. It goes through a volume of space equal to pi r squared times V times T in one second. We then multiply 5.8, 8 times 10 to the 12 m3 by pi times 2, 50 squared times three times 10, and seven times one second. Our density is 10 to 6 atoms per cubic metre, or one atom per cubic centimetre.

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The null hypothesis is true for an analysis of variance -MS (between) should be about the same size as MS within. Option (d) is the correct answer.

If the null is true, MS between and MS within should be about the same since they are both estimates of the same quantity (variance).

The null hypothesis is a characteristic arithmetic theory that suggests that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

The null hypothesis in statistics defines that there is no difference between groups or no relationship between variables.

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The solution to the equation 7x² - 10 = -17 is x = i

From the question, we have the following parameters that can be used in our computation:

7x^2-10=-17

Express the equation properly

So, we have the following representation

7x² - 10 = -17

Add 10 to both sides of the equation

This gives

7x² = -7

Divide both sides by 7

x² = -1

Take the square roots

x = √-1

Rewrite as

x = i

Hence, the solution is x = i

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The correct option is a. Bias from undercoverage, is best description of the term bias.

When you remove a portion of the population from your sample, undercoverage bias develops.

Undercoverage bias as well as nonresponse bias may appear to be identical, but they differ greatly.

For the stated question-

Roosevelt received support from lower-income voters and ultimately won with 62% of the vote, one of the biggest margins of victory in US presidential election history.

Thus, this clearly shows the bias from undercoverage.

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The complete question is-

Before the 1936 US presidential election, a popular poll predicted that Alfred Landon would comfortably win against Franklin D. Roosevelt. The poll randomly sampled people from sources like telephone and car registration records, but the country was in an economic crisis, so many voters without those luxuries were not included in the poll. Voters with lower incomes favored Roosevelt, who ultimately won with 62%, percent of the vote—one of the largest margins of victory ever in a US presidential election. Which type of bias does this scenario best describe?

a. Bias from undercoverage

b. Bias from using voluntary response

c. Response bias

d. Nonresponse bias

Answer:2

Step-by-step explanation:1+1=2

Answer: 2

Step-by-step explanation:

1

+

1

____

2

The given function expressions is  24f + 14g

Given,

-3 × f (-8) + 7 × g(2)

= -3f (-8) + 7g (2)

Simplifying the above equation,

= -3f (-8) = 24f

= 7g (2) = 14g

Then we get,

= 24f + 14g

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According to the line-plot Sofia needed 10(3/4) more feet of bricks.

What is the line-plot?

A line plot is a graph that shows data as checkmarks or dots across a number line, indicating the frequency of each value.

In the line plot the horizontal line is showing the values of the size in feet of the bricks say 'l'.

The number of vertically aligned crosses at a given value of  'l', indicates the length of bricks for which the 'l' is needed in the project.

Follow the formula - l × n (number of crosses) = total bricks in feet

0/4 × 0 = 0

1/4 × 2 = 2/4

2/4 × 4 = 8/4

3/4 × 3 = 9/4

1 × 6 = 6

To obtain the total size in feet add all the values -

L = 2/4 + 8/4 + 9/4 + 6

L = (2 + 8 + 9 + 24)/4

L = 43/4

L = 10(3/4)

Therefore, the feet of bricks required is 10(3/4).

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