Answer: The coordinates where the two lines intersect are (-5, -8).
Step-by-step explanation:
To find the coordinates where the two lines intersect, we need to solve the system of equations simultaneously. We can do this by substitution or elimination, but we'll use substitution here:
First, we set the two equations equal to each other:
x - 3 = 2x + 2
Next, we solve for x:
x - 2x = 2 + 3
-x = 5
x = -5
Now that we have the value of x, we can substitute it into one of the original equations to find the corresponding value of y. Let's use the first equation:
y = x - 3
y = (-5) - 3
y = -8
Triangle Similarity
To answer problem 1.) a. and b.
Refer to the attached image.
a. Triangles ABC and EDC are similar based on the AA similarity theorem used as justification.
b. Length of AB is: 703 ft.
What is the AA Similarity Theorem?According to the AA similarity theorem, two triangles are similar if two of their angles are congruent to each other. If two triangles are similar, then their corresponding sides will have proportional lengths.
a. Since m<D = m<B = 91°, and angles DCE and BCA are vertical angles that are congruent, then triangles ABC and EDC are similar to each other according to the AA similarity theorem.
b. DE = 222 ft
DC = 24 ft
BC = 76 ft
AB = ?
Using the proportion formed by the corresponding lengths of the similar triangles, AB/DE = BC/DC, plug in the values and find the length of AB:
AB/222 = 76/24
Cross multiply:
AB * 24 = 222 * 76
AB = 703 ft
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Charlotte is enjoying a sunny day in the garden on the top of her apartment building. She hears a siren and
is curious where it is coming from. She looks over the edge of the roof and spots an ambulance stopped at
the park down the street from her apartment building. The angle of depression to the ambulance is 3.4°
and her apartment building is 40 feet tall. How far away is the ambulance from the front door of her
apartment building? Round your answer to the nearest tenth. Draw a picture to help you solve the problem.
?
Solving the provided question we can say that by Pythagorean theorem the ambulance from the front door of her apartment building is [tex]YT^2 = -252[/tex] .
what is Pythagorean theorem?The Pythagorean Theorem, often known as the Pythagorean Theorem, is the fundamental Euclidean geometry relationship between the three sides of a right triangle. The area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the right angle equals the sum of the squares that span its sides. It is sometimes written as the general algebraic notation a2 + b2 = c2.
Since XY is tangent to circle O at T, we know that angle OYT is a right angle.
Using the Pythagorean theorem in triangle OYT
[tex]YT^2 = OT^2 - OY^2 \\YT^2 = 18^2 - 24^2\\YT^2 = 324 - 576\\YT^2 = -252[/tex]
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What is the slope of the line that passes
through the points (5, -6) and (9, -6)?
Write your answer in simplest form.
the slopes would look like this
what is 14/20 equivalent to
The expression 14/20 is equivalent to 7/10
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
Given the expression:
14/20
The common term between the numerator and denominator is 2. Hence:
= 7/10
The expression 14/20 is equivalent to 7/10
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Question 29 of 40
Does this graph show a function? Explain how you know.
9
A. Yes; the graph passes the vertical line test.
OB. No; there are y-values that have more than one x-value.
C. No; the graph fails the vertical line test.
D. Yes; there are no y-values that have more than one x-value.
The graph represents a function because the graph passes the vertical line test option (A),
Yes, the graph that passes the vertical line test is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Here, The graph is attached to the picture, please refer to the picture.
Now, We have a graph shown in the picture.
The graph represents the parabola.
As we know, if the graph passes the vertical line test then it can be a function.
Thus, the graph represents a function because the graph passes the vertical line test option (C) Yes, the graph that passes the vertical line test is correct.
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3 out of every 7 workers in a factory are male. How many male workers are there if there are 24 female workers?
Answer: I guess its 10?
Step-by-step explanation:
Answer:28
Step-by-step explanation:
4x/7=24
x=42(total workers)
male workers=42-24=28
You randomly shuffle a deck of cards and deal two cards from the top. What is the probability that you deal the 7 of Spades followed by a King?
The probability that you deal the 7 of Spades followed by a King is 0.1.
What is a probability? Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.Given is that you randomly shuffle a deck of cards and deal two cards from the top.
We can write the probability as -
P{E} = 1/52 + 4/51
P{E} = 0.02 + 0.08
P{E} = 0.1
Therefore, the probability that you deal the 7 of Spades followed by a King is 0.1.
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How do you display a variable in MATLAB?
By using the "disp" function, we can show the value of a variable on the screen.
With MATLAB's "disp" function, you can show the value of a variable on the screen. The "disp" function prints the variable's or expression's value as text on the screen. The syntax for employing the "disp" function is as follows: CSS copy code displayed (variable)
The variable that you want to display is called "variable" in this case. MATLAB will show the value of the variable in the Command Window when the "disp" function is called with the variable as an argument.
Assume, for instance, that you've created the variable "x" and given it the value of 5. The following code can be used to show the value of "x": scss Coding example: x = 5; disp(x); When this code is executed, MATLAB will show that.
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Juan lives in a state where sales tax is 6%. This means you can find the total cost of an item, including tax, by using the expression c + 0.06c, where c is the pre-tax price of the item.
Use the expression to find the total cost of an item that has a pre-tax price of $72.00.
The total cost is $76.32.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Juan lives in a state where sales tax is 6%.
The modeled Equation is:
c + 0.06c, where c is the pre-tax price of the item.
If we have the pre-tax price of $72.00.
Total cost = 1.06 c
= 1.06 x 72
= $76.32
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Kendra's aunt sent her $50 for her birthday 10 years ago. At the time,
Kendra wasn't sure what she wanted to do with the money so she put
it in a piggy bank and forgot about it. She just found this $50 in the
piggy bank when she was cleaning her room. Over the past ten years
yearly inflation has averaged 2.46%. How much is Kendra's birthday
money worth now?
Because of the inflation of 2.46%, the $50 of Kendra is not worth of $62.3 after 10 years.
What is inflation?The amount that a collection of products and services have increased in price during a specific time frame, typically a year, is measured by inflation. One of the most well-known words in economics, perhaps.
Countries have experienced protracted periods of instability due to inflation.
Prices for goods and services are always subject to change in a market economy.
Some prices increase while others decrease.
When prices of products and services grow broadly rather than just for a few specific items, it is said to be inflation.
This means that today, for the same amount of money, you can buy less than you could yesterday.
So, we have: $50
Now, the inflation rate is 2.46%.
Then, 50/100 * 2.46
1.23
1.23 * 10
12.3
12.3 + 50 = $62.3
Therefore, because of the inflation of 2.46%, the $50 of Kendra is not worth of $62.3 after 10 years.
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Bria and April were comparing text messages during lunch. April sent 20 text messages today. April sent one-fourth of the amount of text messages sent by Bria.
Write an equation to determine how many text messages Bria sent.
t divided by 4 equals 20
4t = 20
t + 4 = 20
t − 4 = 20
The equation that determines how many text messages Bria sent is given as follows:
t/4 = 20.
How to determine the number of messages that Bria sent?The number of messages that Bria sent is obtained applying the proportions in the context of the problem.
The amount sent by April is given as follows:
20 messages.
20 is one fourth of the amount t sent by Bria, hence the equation is given as follows:
t/4 = 20.
The number of messages sent by Bria is then given as follows:
t = 20 x 4
t = 80 messages.
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The volume of a solid hemisphere is 1152π cm 3 . Find its curved surface area.
The curved surface area of the hemisphere is 864π cm².
What is a hemisphere?When a sphere is cut into two equal parts a hemisphere is formed.
The volume of a hemisphere is (2/3)πr³ and the area surface area of a hemisphere is 2πr².
Given, The volume of a solid hemisphere is 1152π cm³.
Therefore, (2/3)πr³ = 1152π.
r³ = 1728.
Now, 2×2×2 = 8 so 12³ is 1728.
r = 12 cm.
Now, The surface area is 2×π×144 cm².
= 864π cm².
If a circle is cut into two equal parts we call them each a semicircle.
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Small airplanes weigh both passengers and bags to make sure the plane can hold all the weight aboard. Crew members also use this information to make sure the weight is evenly distributed across the plane. One such airline requires that each passenger and his bag weighs no more than 330 lbs. On this airline, each passenger is allowed to bring exactly one bag that weighs at most 30 lbs. Write and graph a system of inequalities to represent possible combinations of the weight of the passenger, x, and the weight of the bag, y that would fit this airline’s requirements.
The solution is, a system of inequalities to represent possible combinations of the weight of the passenger, x, and the weight of the bag, y that would fit this airline’s requirements are,
x+ y ≥ 330
y≥ 30
What is inequality?
An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
given that,
One such airline requires that each passenger and his bag weighs no more than 330 lbs.
On this airline, each passenger is allowed to bring exactly one bag that weighs at most 30 lbs.
let, the weight of the passenger, x, and the weight of the bag, y that would fit this airline’s requirements.
so, a system of inequalities to represent possible combinations of the weight of the passenger, x, and the weight of the bag, y that would fit this airline’s requirements are,
x+ y ≥ 330
y≥ 30
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State the degree of the polynomial.
x²y + x²y² − xy
Enter your answers in the boxes.
Answer:
Factor:
[tex]xy(xy+x-1)[/tex]
Evaluate:
[tex]xy(xy+x-1)[/tex]
This polynomial is a quadratic polynomial.
Step-by-step explanation:
Six guests invited by Mr. And Mrs. Bernardo to dinner. They are to be all
seated around a
circular table. How many ways can they be seated?
1. If the couple must sit together?
2. If the couple must not be together?
1) If the couple must sit together, there are 240 ways that they can be seated.
2) If the couple must not be together, there are 720 ways that they can be seated.
1) If the couple must sit together, we can think of them as one unit. So, there are 5 units to be seated around the table. We can choose any one of these units to be the starting point, and then arrange the other units clockwise around the table.
The couple can be arranged in two different ways within their unit. So, the total number of ways they can be seated is: 5! × 2 = 240.
2) If the couple must not sit together, we can think of them as separate units. So, there are 6 units to be seated around the table. We can choose any one of these units to be the starting point, and then arrange the other units clockwise around the table.
The couple cannot be seated next to each other, so there are 3 possible units where they cannot be seated next to each other. Once we have chosen one of these units for the starting point, there are 2 ways to arrange the couple within their unit. Therefore, the total number of ways they can be seated is: 5! × 2 × 3 = 720.
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A sketch of y= cos x° for-360 ≤x≤ 360 is shown.
a) State the coordinates of A.
A00
b) State the coordinates of B.
B(00
B
Y₁
Ax
The Coordinates for A is (π/2, 1).
and, the Coordinates for B is (-π, 0).
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
We have y= cos x.
So, when x = π/2 sin x have the maximum value which equals to 1.
Then ,the coordinates is (π/2, 1).
and, when x=π or x=-π then sin x =0
Then ,the coordinates is (-π, 0).
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How many 750ml to ounces ?
There are 25.36 fluid ounces in 750 milliliters (mL). To convert mL to fluid ounces, multiply the volume in mL by the conversion factor of 0.033814.
There are 25.36 fluid ounces in 750 milliliters (mL).
To convert mL to fluid ounces (fl oz), you can use the conversion factor of 0.033814, which is the number of fluid ounces in one milliliter. Multiplying the volume in mL by this conversion factor gives the result in fluid ounces.
So, to convert 750 mL to fluid ounces, you can multiply 750 by 0.033814, which gives:
750 mL * 0.033814 = 25.36 fl oz
Therefore, 750 mL is equivalent to 25.36 fluid ounces.
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An airplane climbs at an angle of 40 degrees with the ground. What is the ground distance it has traveled (to the nearest 100 ft) when it has attained an altitude of 2400ft
The airplane has traveled a ground distance of 2900 ft when it has attained an altitude of 2400 ft at an angle of 40 degrees with the ground.
Determine ground distanceThe ground distance that the airplane has traveled can be found using the trigonometric function of tangent. The tangent of an angle is the ratio of the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the altitude (2400 ft) and the adjacent side is the ground distance we are trying to find.
We can use the formula:
tan(angle) = opposite/adjacent
Plugging in the given values:
tan(40) = 2400/adjacent
Solving for the adjacent side (ground distance):
adjacent = 2400/tan(40)
Using a calculator, we can find the value of tan(40) and then divide 2400 by that value to get the ground distance:
adjacent = 2400/0.8391
adjacent = 2860.67 ft
Rounding to the nearest 100 ft, the ground distance is 2900 ft.
Therefore, the airplane has traveled a ground distance of 2900 ft when it has attained an altitude of 2400 ft at an angle of 40 degrees with the ground.
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Line segment A B is reflected across a line to form line segment A prime B prime. Points M and N are halfway between points A and A prime and B and B prime.
A reflection line is equidistant from a pre-image point and its image.
Therefore, in segment AA’, point M is the
PLS HELP ME
The equation of the line segment A'B' will be ax + by + d√(a² + b²) + c₁ = 0.
What is the distance between two parallel lines?Let the two lines be ax + by + c₁ = 0 and ax + by + c₂ = 0. Then the distance between the lines is given as,
d = |c₂ - c₁| / √(a² + b²)
Let the distance between Line AB and A'B' be d and the equation of the line AB be ax + by + c₁ = 0. Then the value of c₂ is given as,
d = |c₂ - c₁| / √(a² + b²)
d√(a² + b²) = c₂ - c₁
c₂ = d√(a² + b²) + c₁
Then the equation of the line A'B' is given as,
ax + by + c₂ = 0
ax + by + d√(a² + b²) + c₁ = 0
The equation of the line segment A'B' will be ax + by + d√(a² + b²) + c₁ = 0.
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A guy wire runs from the top of a cell tower to a metal stake in the ground. Jacob places a 9-foot tall pole to support the guy wire. After placing the pole, Jacob measures the distance from the stake to the pole to be 1 ft. He then measures the distance from the pole to the tower to be 11 ft. Find the length of the guy wire, to the nearest foot.
The length of the guy wire, to the nearest foot, is 109 feet.
What is Pythagoras' theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
From the diagram.
ΔABE is similar to ΔCDE.
CD = 9 ft
DE = 1 ft
BD =11 ft
And we know,
ΔABE ~ ΔCDE.
So, the corresponding sides of similar triangles,
AB/CD = BE/DE
AB/9 = (11 + 1)/1
AB/9 = 12
AB = 12 x 9
AB = 108 feet.
To find AE:
Applying Pythegoras' theorem,
we get,
AE = √(AB² + BE²)
AE = √(108² + 12²)
AE = 108.67
Therefore, AE = 109 feet.
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Fabian is 3 years younger than twice Yemia's . If Fabian is 27 years old how old is Yemia?
Answer:
Yemia is 60
Step-by-step explanation:
Answer:
Yemia is 60
Step-by-step explanation:
(27 + 3) x 2 = 60
I NEED HELP AND FAST PLEASE HELP !!!!
The solution for f the angle ∠DEF will be 122°.
What is geometry?Geometry is the study of two- and three-dimensional figures such as quadrilaterals, triangles, circles, their sides, and angles.
Symmetry is defined as if the object is cut by its centre line the two cut parts should be the mirror image of each other so that we can call them symmetric to each other.
Given that the angles are:-
∠DCE = (3x + 16)°
∠DEF = (6x - 10)°
∠CDE = (2x - 4)°
In the triangle ΔCDE,
∠DEC = 180 - 3x - 16 - 2x + 4
∠DEC = (-5x + 168)°
∠DEC + ∠DEF = 180
5x + 168 + 6x - 10 = 180
x = 180 - 158
x = 22
The value of the ∠DEF is,
∠DEF = 6x - 10
∠DEF = 6 x 22 - 10
∠DEF = 122°
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What score would a student need to have a 30th percentile score on the SAT? Recall that the mean score was 1509, and the standard deviation of the scores is 312.
Group of answer choices
a. 1244
b. 1345
c. 1456
d. 1673
Rounding to the nearest whole number, we get that the score a student would need to have a 30th percentile score on the SAT is 1345. Correct option is B.
To find the score corresponding to the 30th percentile, we need to use the standard normal distribution with a mean of 0 and a standard deviation of 1. We can convert the SAT score to a standard normal score using the formula:
z = (x - μ) / σ
where x is the SAT score, μ is the mean score (1509), and σ is the standard deviation (312).
To find the score corresponding to the 30th percentile, we need to find the z-score that has an area of 0.30 to its left. Using a standard normal table or calculator, we can find that the z-score corresponding to a 30th percentile is approximately -0.52.
Now we can use the formula to find the corresponding SAT score:
-0.52 = (x - 1509) / 312
Solving for x, we get:
x = -0.52 * 312 + 1509 = 1345.36
Therefore, the answer is (b) 1345.
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Write an equivalent equation to AB = AC using A^-1 such that, when it is simplified, the resulting equation will simplify to B = C. What property should be used to continue simplifying the above equation? A. (AB)^-1 = B^-1A^-1 B. (A^-1)^T = (A^T)^-1 C. A-^1A = 1 D. (A^-1)^-1 = A
The property that should be used to continue simplifying the above equation is A-^1A = 1. So, correct option is C.
We can start with the equation AB = AC and multiply both sides by A^-1 on the left:
A^-1(AB) = A^-1(AC)
Using the associative property of matrix multiplication, we can simplify the left-hand side:
(A^-1A)B = (A^-1A)C
Using the fact that A^-1A = I (the identity matrix), we get:
IB = IC
Simplifying further using the fact that I times any matrix is that matrix itself, we obtain:
B = C
Therefore, the equivalent equation to AB = AC using A^-1 that simplifies to B = C is A^-1(AB) = A^-1(AC), and the property used to continue simplifying the equation is A^-1A = I.
The correct option is (C) A^-1A = 1, which is equivalent to A^-1A = I, since the identity matrix is denoted as 1 in some contexts.
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The cost of an air conditioner is $110. The cost to run the air conditioner is $0.35 per
minute.
What is the range of the situation above?
A function that models the total cost of running the air conditioner for the first 400 minutes is .
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Let the number of minutes be m.
Let the total cost be T.
Given the following data:
Cost of air conditioner = $130
Running cost = $0.25 per minute
Time = 400 minutes.
To write a function that models the total cost of running the air conditioner for the first 400 minutes:
How to solve a word problem.
First of all, we would write an equation to models the total cost of running the air conditioner for the first 400 minutes:
For the total time:
0.25m
For the total cost:
T= 130 + 0.25m
For the domain:
The value of m is the domain and it can be chosen from 0 to 130.
Domain (m) = [0, 130].
For the range:
A range represents the minimum and maximum value of a data set.
Thus, the value of T would be between 130 and 230.
Range = [130, 230].
For the intercept:
when x = 0, we have:
y = 130 + 0.25(0)
y = 130.
Intercept = [0, 130]
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How do I need to work this the answer at the bottom is 160
Answer:
178ft
Step-by-step explanation:
Split the shape up into pieces. If you make an invisible cut vertically from the 14 ft length you will realise you have a small triangle attached to a rectangle.
You can assume that the height of the triangle is equal to the 20 - 14 as the left side must equal the right side for this shape thus this invisible length is equal to 6 ft
Area of triangle: (6ft x 6ft)/2 = 18 ft^2
Area of rectangle: 20ft x 8ft = 160 ft^2
Area of total shape = 160 + 18 = 178ft
So you're correct
If 5x+2=52, then what does x equal?
Answer:
x=10
Step-by-step explanation:
If we subtract 2 from 52 we get 50 and ten mutiplys into 50.
What is JK flip-flop and its truth table?
In the JK Flip-Flop truth table, when both inputs of the JK Flip-Flop are set to 1 and the clock input is also set to "High," the circuit is toggled from the SET to the RESET state.
Similar in operation to the SR flip flop is the JK flip flop. The JK flip flop is marked with the letters "J" and "K" rather than "S" and "R." When both inputs are set to 1, SR flip flips yield incorrect states as outputs, while JK flip flops do not, even when both "J" and "K" flip flops are set to 1. The only distinction between JK and SR flip flops is this. The JK Flip Flop is an additional clock input circuitry-equipped gated SR flip-flop. The presence of a clock input circuit prevents the invalid or unlawful output situation from occurring when both inputs are set to 1. The JK flip-flop hence has four input combinations that are possible: 1, 0, "no change," "toggle," and With the exception of the clock input, the JK flip flop's symbol is identical to that of the SR bistable latch.
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What is the equation of this graph
Use the x-values: 1, 2, 3, and 4 to write solutions of the equation y = 13x + 5 as ordered pairs.
O (1, 18), (2, 31), (3, 44), (4, 57)
O (19, 1), (20, 2), (21, 3), (22, 4)
O (1, 19), (2, 20), (3, 21), (4, 22)
O (18, 1), (31, 2), (44, 3), (57, 4)
The solutions of the equation as ordered pairs is:
(1, 18), (2, 31), (3, 44), (4, 57)
How to use the x-values: 1, 2, 3, and 4 to write solutions of the equation y = 13x + 5 as ordered pairs?
In order to use the x-values: 1, 2, 3, and 4 to write solutions of the equation y = 13x + 5 as ordered pairs, substitute the values of x into the equation and calculate y. That is:
when x = 1:
y = 13(1) + 5 = 18
when x = 2:
y = 13(2) + 5 = 31
when x = 3:
y = 13(3) + 5 = 44
when x = 4:
y = 13(4) + 5 = 57
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