Write an equation for each line

Given:

The equation of the graph is x + y = 500.

The objective is to change the equation as inequality and to choose the correct region for shading.

Explanation:

As the equation is given as x + y = 500, the sum of the values of x and y lies within the 500. As its total sum is also equal to 500, the graph must lie with in the maximum range of 500 that is at A along with solid line. (If sum is not equal to 500, the graph will contain dotted line).

Representation of inequality:

The given equation can be represented in the form of inequality as,

Graph:

Then, the graph of the inequality will be,

Hence, the inequality is x + y ≤ 500 and the graph contains solid line with shaded region in A.

Answer:

[tex]y = \frac{3}{5} x + \frac{13}{5} [/tex]

Step-by-step explanation:

The equation of a line can be written in the slope-intercept form y= mx +c, where m is the slope and c is the y-intercept.

Let's rewrite the given equation into the slope-intercept form, so that we can identify its slope.

5x +3y= 15

3y= -5x +15

Divide both sides by 3:

[tex]y = - \frac{ 5}{3} x + 5[/tex]

Thus, the slope of the given line is [tex] - \frac{5}{3} [/tex]

The slope of a perpendicular line is the negative reciprocal of the given line. In simpler terms, the slope of the perpendicular line can be found by flipping the denominator and numerator, and by multiplying -1 afterwards.

Slope of perpendicular line= [tex] \frac{3}{5} [/tex]

Substitute the value of the slope into the equation:

[tex]y = \frac{3}{5} x + c[/tex]

To find the value of c, substitute a pair of coordinates the line passes through.

When x= -1, y= 2,

[tex]2 = \frac{3}{5} ( - 1) + c[/tex]

Solve for c:

[tex]c = 2 + \frac{3}{5} [/tex]

[tex]c = \frac{13}{5} [/tex]

Thus, the equation of the line described is [tex]y = \frac{3}{5} x + \frac{13}{5} [/tex].

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Answer: The correct answer is 62.5% and not 67.5 %

Step-by-step explanation: Yes you do 5 divided by 8 and then you move the decimal point two places to the right.

Hope this helped!!!!

the price of the ticket which Disney on ice would make no money at all is:

and here, are two posible solutions:

for the first one 1)

for the second one 2)

and in this problem the realistic answer is the first one, so the solution is $8 dollars

Based on the numbers that are all less than 496 and yet divide evenly into 496, the sum is 496

The numbers that are less than 496 and yet are able to divide evenly into it are known as the factors of 496. These numbers will not leave a reminder when they divide 496.

The factors of 496 include:

1, 2, 4, 8, 16, 31, 62, 124, 248, 496.

The sum of these numbers that are less than 496 is:

= 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248

= 496

In conclusion, the sum of all the numbers less than 496 that are able to divide it evenly is 496.

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Answer:

8%

Step-by-step explanation:

divide the after tax price by the before tax price

15.93/14.75=1.08

then subtract 1 from 1.08 (the 1 is the base price of the pizza) and convert the difference to percent to get the answer of 8% tax rate

47 had a finished basement with 0 three-car garage .

Thinking and cognition are related to reasoning, which requires using one's intellect. The study of logic focuses on how people can construct logically sound arguments using formal reasoning. Deductive, inductive, and abductive reasoning are three examples of logical reasoning that can be used to further break down reasoning. Aristotle distinguished between logical discursive reasoning (reason proper) and intuitive reasoning, noting that the former may lean toward the subjective and the personal, despite being correct. While logical and intuitive styles of reasoning might clash in certain social and political circumstances, in others they are considered as complimentary rather than competitive.

all the values are given that how many houses had a finished basement with no 3-car garage.

the no. of houses are = 47 .

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Value of x =5 and value of y =2

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 3^4 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. Exponents are necessary since, without them, it is highly challenging to express the product when a number is repeated several times by itself. For instance, it is much simpler to write 5^7 than it is to write 5 5 5 5 5 5.

[tex]3^{x}-3^{y}=234\\ 3^{x-y}.3^{y}-3^{y}=234\\ 3^{y}(3^{x-y}-1)=234\\ 3^{y}(3^{x-y}-1)=3^{2}.26\\[/tex]

Now, by comparison, we get:

[tex]3^{y}=3^{2}\\ y=2\\ Also, \\3^{x-y} -1=26\\ 3^{x-y}=27\\ 3^{x-y}=3^{3}\\ x-y=3\\ x-2=3\\x=5[/tex]

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It should be noted that the z-score for the sample mean that's given is 0.5.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

The following can be seen from the information illustrated:

Mean ( u ) =55

Standard Deviation ( sd )=12

Number ( n ) = 4

Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)

Z = (58-55)/12/ Sqrt ( 4 )

Z = 3/6= 0.5

Therefore, the z score is 0.5.

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An equation of the line that passes the through point (0, 9) and has slope m = [tex]\frac{2}{3}[/tex] is 3y-2x-27=0

What is point-slop equation of a line?

The point-slope equation of a line is

                      y - [tex]y_{1}[/tex] = m ( x  -[tex]x_{1}[/tex] )

The equation is useful when we know:

and want to find other points on the line.

Given that,

slope , m =  [tex]\frac{2}{3}[/tex]  and passing through the point is (0,9)

An equation of a line given the slope and a point is

             y - [tex]y_{1}[/tex] = m ( x  -[tex]x_{1}[/tex] )

or          y - 9 =  [tex]\frac{2}{3}[/tex] (x - 0)

or          y - 9 =  [tex]\frac{2}{3}[/tex] x

or          y =  [tex]\frac{2}{3}[/tex] x + 9

or          y = [tex]\frac{2x + 27}{3}[/tex]

or          3y = 2x + 27

or         3y - 2x - 27 = 0

Hence, an equation of the line that passes the through point (0, 9) and has slope m = [tex]\frac{2}{3}[/tex] is 3y-2x-27=0

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Answer:

n=2.4

Step-by-step explanation:

The value of n is ∛14.

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, known as the left-hand side (LHS) and the right-hand side (RHS), connected by an equal sign (=).

To solve the equation −8 + n³= 6

Add 8 to both sides of the equation to isolate the term with n:

−8 + n³ + 8 = 6 + 8.

Simplifying the equation gives: n³ = 14.

Take the cube root of both sides to solve for n.

Taking the cube root of n³ = 14

∛(n^3) = ∛14.

Therefore, n = ∛14.

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The equation of line passing through(4,-3) and perpendicular to x+3y=-15 is y = 3x - 15.

Using the slope formula, determine the slope.

To find the y-intercept, use the slope and one of the points (b).

You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).

Given,

coordinates = (4,-3)

equation of line = x+3y=-15

equation of line in standard form

⇒ y = -1/3x -5

Slope of line = -1/3

The slope of the line passing through (4,-3) and perpendicular to line x+3y=-15 is 3.

The equation of line becomes

(y + 3) = 3 (x - 4)

y + 3 = 3x - 12

y = 3x - 15

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Answer:

1 : Grouping Symbol

2 : Operator

3 : Order of Operations

4 : Exponent

5 : Variable

6 : Term

7 : Coefficient

8 : Constant

9 : Numerical Expression

10 : Variable Expression

11 : Equation

12 : Inequality

13 : Evaluate

14 : Open Sentence

we have that

the distance city B to city C is equal to

405+401=806 miles4

therefore

the answer is

Answer:

A

Step-by-step explanation:

The centroid cuts the median in a 2:1 ratio from vertex to side.

======================================================

Explanation:

x = width

2x = length, since it is twice as long as it is wide

area = length*width = 2x*x = 2x^2

Set this equal to the area of 450 sq ft and solve for x

2x^2 = 450

x^2 = 450/2

x^2 = 225

x = sqrt(225)

x = 15 feet is the width

2x = 2*15 = 30 feet is the length

Check:

area = length*width = 30*15 = 450

The answers are confirmed.

The zeros of the quadratic are (1 and 3), the vertex is (2, -1). Draw the parabola with a "solid" line. Shade the "interior" of the parabola.

For the given question;

The inequality of the function is given as;

= x² - 4x + 3

Find the factors;

(x - 3)(x - 1) = 0

x = 1 and x = 3 are the zeros of the equation.

Now, to graph the equation find the point;

Put x = 0; y = 3

Put x = 1; y = 0

Put x = 2, y = -1

Plot the points on the graph and join the points with solid line.

The vertex of the parabola is found at (2, -1).

Thus, the graph of the parabola is plotted.

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64 ^ (-2/3)

Rewrite 64 as 4^3

(4^3) ^ (-2/3)

Using the power rule a^b^c = a^(b*c)

4 ^(3*-2/3)

4^ -2

We know that a^ -b = 1/ a^b

1 / 4^2

1/16

Answer:

  an = 7 -3(n -1)

Step-by-step explanation:

You want the formula for the n-th term of the arithmetic sequence 7, 4, 1, -2, ....

An arithmetic sequence has a first term (a1) and a common difference (d) found by subtracting the previous term from the current term.

In the given sequence, the first term is a1=7, and the common difference is d=(a2 -a1) = 4 -7 = -3.

The n-th term of the given arithmetic sequence is ...

  [tex]a_n=a_1+d(n-1)\\\\\boxed{a_n=7-3(n-1)}[/tex]

__

Additional comment

The formula can be simplified to ...

  an = 10 -3n

i think 16? 1/2+1/2=1 so 8*2=16

Answer:

See below

Step-by-step explanation:

40 ÷ 50 =   40/50 = 4/5 = .8  

Answer: 68/5

Hope this helps! :)

Answer: f(-7)=-9

Step-by-step explanation:

For profit with the revenue of R=113.95x and cost of C=93x + 750 the value of x is 36units.

As given in the question,

Revenue for selling x units of a product is R = 113.95 x

Cost of producing x units is C = 93 x + 750

For profit, the revenue must be greater than the cost.

R > C

113.95x > 93x +750

Subtract 93x from both the sides

113.95x -93x >93x-93x +750

⇒20.95x > 750

Divide by 20.95

⇒x > 750/20.95

⇒x>35.7995

Nearest whole number is 36.

Value of x to produce a profit is 36units

Therefore, to make a profit with the revenue of R=113.95x and cost of

C =93x + 750 the value of x is 36units.

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9.16

1) Considering 14, and 6 the data. Let's calculate the Geometric Mean of it

2) To do that we just need to multiply those numbers, and since there are two of them take the square root of that product, between those 2 numbers

3) So the Geometric mean is 9.16 (approximately).

Answer:

Step-by-step explanation:

You want to find the rational function (f/g)(x) and its value for x=1 when f(x) = 4x^4−19x^3−10x^2+35x−50 and g(x) = x-5.

The ratio function is the ratio of the given functions, found by dividing f(x) by g(x). Since g(x) is a binomial with a leading coefficient of 1, synthetic division is recommended. The attachment shows the result.

  [tex](f/g)(x)=\dfrac{f(x)}{g(x)}=\dfrac{4x^4-19x^3-10x^2+35x-50}{x-5}\\\\\boxed{(f/g)(x)=4x^3+x^2-5x+10}[/tex]

The value of this function when x=1 is ...

  (f/g)(1) = 4·1³ +1² -5·1 +10 = 4 +1 -5 +10

  (f/g)(1) = 10

The fraction of counters Lesley get if Adam gives 10 counters out of 18 counters is 5/9.

The fraction of counters Adam have now is 4/9.

This is an expression which consists of a numerator and a denominator

A numerator is the upper of top value of a fraction

A denominator is the lower or bottom value of a fraction

Number of counters Adam has left = Number of counters Adam has - Number of counters Adam gave to Lesley

= 18 - 10

= 8

Fraction of the 18 counters Lesley get = Number of counters Adam gave to Lesley / Number of counters Adam has

= 10/18

= 5/9

Fraction of the 18 counters Adam have now = Number of counters Adam has left / Number of counters Adam has

= 8 / 18

= 4/9

In conclusion, the fraction of counters Adam have now after giving out 10 counters to Lesley is 4/9

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Answer:

y = -3/2x +11

Step-by-step explanation:

First you have to change the equation from standard form to slope form.

y = mx + b

2x-3y=7 --> subtract 2x from both sides

-3y = -2x + 7 --> now divide both sides by -3 to get y by itself

y = 2/3x - 7/3  --> the reason 2/3x is positive is because when there are two negatives it turns to a positive.

now you have to use point slope form y - y1 = m (x - x1)

x1 and y1 would be your point. 2 is x1 and 8 is y1

y - 8 = -3/2 (x - 2) --> the reason that m is -3/2 is because a perpendicular equation is the opposite reciprocal of the original slope

next distribute the -3/2

y-8 = -3/2x + 3 --> and now add 8 to 3 to get why by it self

now you have y = -3/2x + 11