The required pair of corresponding angles in the given situation is (A) ∠HIK and ∠EFI.
What are corresponding angles?In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.
In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.
Angles that are equal in size and are found on the same side as the transversal line are called corresponding angles.
Either both are acute or both are obtuse.
By creating an F shape, we can typically identify comparable angles.
So, now after reading the description we know exactly what are corresponding angles.
Now, we can easily tell that the pair of corresponding is:
∠HIK and ∠EFI
Therefore, the required pair of corresponding angles in the given situation is (A) ∠HIK and ∠EFI.
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Change 0.182 0.005 0.050 0.174 Table 10-3. Regression results for predicting depression at wave 2 Predictor Variable b Beta P R? Depression Score Wave 1 0.267 0.231 0.000 0.182 Sociodemographic Age -0.014 -0.024 0.538 0.187 Sex 0.165 0.034 0.370 Psychologic Health Neuroticism, wave 1 0.067 0.077 0.056 0.0237 Past history of depression 0.320 0.136 0.000 Physical Health ADL, wave 1 -0.154 0.103 0.033 0.411 ADL, Wave 2 0.275 0.283 0.012 ADL?, wave 2 -0.013 --0.150 0.076 Number of current 0.115 0.117 0.009 symptoms, wave 2 Number of medical 0.309 0.226 0.000 conditions, wave 2 BP, systolic, wave 2 -0.010 -0.092 0.010 Global health rating 0.284 0079 0.028 change Sensory impairment -0.045 -0.064 0.073 change Social support inactivity Social support-friends, -1.650 -0.095 0.015 0.442 wave 2 Social support-visits, -1.229 -0.087 0.032 wave 2 Activity level, wave 2 0.061 0.095 0.025 Services (community residents 0.207 0.135 0.001 0.438° only), wave 2 Abhreviation: BP = blood pressure 0.031 0.015€ Based on above MLRA summary Table, which of following independent variables is the strongest predictor (or factor)?
Number of medical conditions, wave 2
Number of current symptoms, wave 2
Global health rating change
Past history of depression
ADL, wave 2
The regression result of 0.320, the beta of 0.136, and the p-value of 0.000.
The strongest predictor in the MLRA summary Table is past history of depression. This is shown by the regression result of 0.320, the beta of 0.136, and the p-value of 0.000. This means that past history of depression has a strong and statistically significant influence on predicting depression at wave 2.
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BP = FC + VCM
The fixed costs associated with the fundraiser include: one-time charges of art ($45), screen and set-up ($60),
and advertising ($50 for a newspaper ad). In addition, the unit cost of the sweatshirt will be $16.50 per sweatshirt, with an additional charge of $.50 per shirt for shipping and individual plastic wrap. You plan to sell the sweatshirts for a retail price of $22.
A. Calculate breakeven in units.
B.calculate breakeven in dollars
1. The breakeven in units equals 31 units.
2. The dollar amount to breakeven is
What is the breakeven in units?The variable cost per unit includes the cost of the sweatshirt ($16.50) and the additional charge for shipping and plastic wrap ($0.50), so the total variable cost per unit is:
= $16.50 + $0.50
= $17.00
The contribution margin per unit is:
= 22.00 - $17.00
= $5.00
The fixed costs include the one-time charges of art ($45), screen and set-up ($60), and advertising ($50), so the total fixed costs are:
= $45 + $60 + $50
= $155
Using the breakeven formula, we can calculate the number of units required to break even:
= Fixed costs / Contribution margin per unit
= $155 / $5.00
= 31 units
What is the breakeven in dollars?To calculate the breakeven in dollars, we need to multiply the breakeven in units by the selling price per unit:
The breakeven in dollars equals to:
= Breakeven in units x Selling price per unit
= 31 x $22.00
= $682.00
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Environment An accident at an oil drilling platform is causing a circular oil slick. The slick is 0.08 foot thick, and when the radius of the slick is 150 feet, the radius is increasing at the rate of 0.5 foot per minute. At what rate (in cubic feet per minute) is oil flowing from the site of the accident?
The rate of oil flowing from the site of the accident is 47123.74 cubic feet per minute.
To find the rate at which oil is flowing from the site of the accident, we need to determine the rate of change of the volume of oil in the slick with respect to time.
We know that the slick is circular with a thickness of 0.08 feet and a radius that is increasing at a rate of 0.5 feet per minute. Let's call the radius of the slick at time t "r" and the volume of oil in the slick at time t "V".
The volume of a cylinder (which the slick approximates) is given by the formula V = πr^2h, where π is the constant pi and h is the height or thickness of the cylinder.
Differentiating both sides with respect to time, we get:
dV/dt = 2πrh(dr/dt) + πr^2(dh/dt)
We know that the thickness of the slick is constant at 0.08 feet, so dh/dt = 0. We also know that the radius is increasing at a rate of 0.5 feet per minute, so dr/dt = 0.5. Finally, we know that the radius of the slick is currently 150 feet, so r = 150.
Substituting these values into the formula, we get:
dV/dt = 2π(150)(0.5) + π(150)^2(0)
dV/dt = 47123.74 cubic feet per minute
Therefore, the rate at which oil is flowing from the site of the accident is approximately 47123.74 cubic feet per minute.
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ASA, SSS, SAS
Define each postulate and give a well written and visual example of each term.
Include as much detail as possible
Answer:
In geometry, postulates are statements that are accepted as true without proof. The three postulates for congruent triangles are ASA, SSS, and SAS. These postulates are used to prove that two triangles are congruent.
ASA Postulate:
ASA stands for "Angle, Side, Angle." This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have ∠A ≅ ∠D, ∠B ≅ ∠E, and AB ≅ DE. Therefore, we can conclude that ΔABC ≅ ΔDEF by ASA postulate.
SSS Postulate:
SSS stands for "Side, Side, Side." This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and AC ≅ DF. Therefore, we can conclude that ΔABC ≅ ΔDEF by SSS postulate.
SAS Postulate:
SAS stands for "Side, Angle, Side." This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and ∠B ≅ ∠E. Therefore, we can conclude that ΔABC ≅ ΔDEF by SAS postulate.
Overall, the ASA, SSS, and SAS postulates are important tools in proving the congruence of triangles in geometry. They allow us to make logical deductions about the properties of triangles based on their corresponding angles and sides.
Answer:
They are different because ASA means that the two triangles have two angles and the side between the angles congruent. SAS means that two sides and the angle in between them are congruent
Step-by-step explanation:
and sss If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.
Armando opened a new savings account with an initial deposit if $250. Which combination will result in a zero balance in armandos account?
A zero balance in Armando's account can be achieved by subtracting $250 from the account balance. This can be done through a combination of withdrawals and/or transfers out of the account.
What is subtracting?Subtracting is a mathematical operation that involves taking one number away from another. It is the inverse of addition, and is represented by the minus sign (-). Subtracting is used to determine the difference between two numbers, or to reduce a number by a given amount. In algebraic terms, subtracting is represented by the equation: a - b = c, where a is the starting number, b is the number to be subtracted, and c is the resulting difference. Subtracting can also be used on fractions, decimals, and other forms of numbers.
For example, Armando could make a $250 withdrawal from the account or transfer $250 to another bank account.
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The coordinates below represent points that were translated.Draw a line to connect the coordinates with the correct description and algebraic representation of the translation.
(x-11, y+14) = (-4-7, 7+7) = (-11,14) which matches the new coordinates T(-11,14).
The coordinates' meaning is unclear?In this sense, coordinates are the points where a grid system intersects. GPS coordinates are typically created by combining latitude and longitude. The distance of north and the south from the equator, which is 0 degrees iof north and south, is measured by lines of latitude.
COORDINATES DESCRIPTION ALGEBRAIC REPRESENTATION8. T (-4,7) 7 units right, 7 units up (x-11, y+14)
9. U (3,-4) 7 units left, 7 units up (x+7, y+7)
10. V (-2,-10) 7 units right, 7 units down (x+7, y-7)
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*CORRECT AND FASTEST ANSWER GETS BRAINLIEST!!!*
A greengrocer buys fruit and vegetables from the market and sells them at a 25% mark up. On one particular moring her fruit and vegetables cost her €500. If she sells all of her produce, find:
A) her profit
B) her total income
Answer: Below :)
Step-by-step explanation:
A) To find the profit, we first need to calculate the cost of the produce plus the 25% markup.
The markup is 25% of the cost, which is 0.25 * 500 = €125.
So the total cost of the produce plus markup is €500 + €125 = €625.
Now, if the greengrocer sells all the produce, the total revenue will be 100% plus the 25% markup, which is 125% of the original cost.
125% of €500 is 1.25 * 500 = €625, which is the same as the cost plus markup.
Therefore, the profit is the markup, which is €125.
B) To find the total income, we add the profit to the total cost:
Total income = €500 + €125 = €625
Answer:
A) €125
B) €625
There are 30 students in Mr. Hall class. 1/3 of the students are traveling somewhere this summer. Of those traveling, 1/5 are going out of the country. How many students are traveling out of the country?
The number of students traveling are 2 students out of the 30 who are traveling out of the country this summer. If 1/3 of the students are traveling somewhere this summer, then we can calculate the number of students who are traveling by multiplying the total number of students by 1/3:
Number of students traveling = 30 x 1/3 = 10
Now, we need to find out how many of these 10 students are traveling out of the country. We know that 1/5 of the students who are traveling are going out of the country, so we can find the number of students who are traveling out of the country by multiplying the total number of traveling students by 1/5:
Number of students traveling out of the country = 10 x 1/5 = 2
Therefore, there are 2 students out of the 30 who are traveling out of the country this summer.
It's important to note that fractions can be converted to decimals or percentages to make them easier to work with. For example, 1/3 can be written as 0.33 or 33%, and 1/5 can be written as 0.20 or 20%. This can be particularly useful when dealing with more complex problems or when working with larger numbers.
In summary, by using the information given, we can determine that out of the 30 students in Mr. Hall's class, 10 are traveling somewhere this summer, and out of those 10 students, 2 are going out of the country. This type of problem-solving helps build math skills that are applicable in real-world scenarios, such as budgeting and planning for travel.
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Suppose you have a certain amount of money in a savings account that earns compound monthly interest, and you want to calculate the amount that you will have after a specific number of months. The formula is as follows: f=p*(1 + i)^t f is the future value of the account after the specified time period. p is the present value of the account. i is the monthly interest rate. t is the number of months. Write a program that takes the account's present value, monthly interest rate, and the number of months that the money will be left in the account as three inputs from the user. The program should pass these values to a function that returns the future value of the account, after the specified number of months. the program should print the account's future value. SAMPLE RUN #2: python3 FutureValue.py None Show Highlighted Only Interactive Session Hide Invisibles Highlight: Enter current bank. balance: 35.72 Enter.interest rate:0 Enter the amount of time that passes: 100 35.7
Answer:
Step-by-step explanation:
Hi there! Just multiply by x and find the value of f=p. Good luck!
Megan's standard pay is £17.70 per hour. She gets paid 1.5 times this rate for working overtime. How much will Megan get paid for working 11 hours of overtime? Give your answer to the nearest pound.
Answer:
Step-by-step explanation:
Overtime Rate = [tex]17.70 \times 1\frac{1}{2}[/tex]
[tex]= 17.70 \times \frac{3}{2}[/tex]
[tex]=\frac{53.10}{2}[/tex]
[tex]=\pounds26.55[/tex]
Pay [tex]=11*26.55=\pounds 292.05[/tex] (I assume you can use a calculator for this)
Solution: [tex]\pounds 292[/tex]
Use the table to answer the following question. The table shows pairs of values for a linear function. A different function is defined by the equation y = 4x. Which of the following statements is TRUE? The functions both have a slope of 4. The functions are both proportional. The functions have opposite slopes. The functions both have a y-intercept of 4.
A statement which is true include the following: C. The functions have opposite slopes.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial number.Based on the information provided above, an equation that models one of the function is given by;
y = 4x
mx = 4x
Slope, m = 4.
For the other function, the slope can be calculated as follows;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (0 - 4)/(1 - 0)
Slope (m) = -4/1
Slope (m) = -4.
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Identify and name congruent triangles
The answers are a) ASA congruence rule b) SSS congruence rule c) it is not necessary congruent.
What is Congruence ?Congruent refers to having the same height and shape. Congruent therefore involves comparing two numbers, and equivalent denotes the equality of two expressions. Therefore, to state two line segments are congruent implies that the two lines have equal measures.
According to question:a) ∠GIH is corresponding to ∠LJK
GH = KL
∠IHG = ∠KLJ
By ASA congruence rule
ΔGIH ≅ ΔJKL
b) AB = DF
AC = DE
BC = EF
By SSS congruence rule
ΔABC ≅ ΔDEF
c) Two Corresponding sides are congruent, which is not enough to make them congruent.
So, it is not necessary congruent.
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Elena and Jada were racing on their bikes. Elena started 15 meters ahead of Jada. Elena biked at a rate of 20 meters per second. Jada biked at a rate of 22 meters per second. Let x represent time in seconds and y represent distance in meters. After how many seconds will Jada pass Elena?
Jada overtakes Elena after 7.5 seconds.
The set of equations that best captures the scenario is =y=15+20x.
Let's establish a coordinate system with Elena's starting point as the origin. Elena's separation from the origin at time x is given by: y=15+20x
y1 = 15 + 20x
Jada's distance from the origin at time x is determined similarly by:
y2 = 22x
Finding the moment x at which Jada overtakes Elena and their distances from the origin are equal is our goal.
y1 = y2
With the formulas for y1 and y2 substituted, we obtain:
15 + 20x = 22x
When we simplify this equation, we obtain:
2x = 15
x = 7.5
Jada therefore overtakes Elena after 7.5 seconds.
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The equation y = 8x represents the
relationship between the amount of
time Shanay takes to weave thread
into fabric and the number of rows.
How long will it take Shanay to weave
72 rows of fabric at this constant rate?
Write the percent as a decimal.
95%
Answer:
9.5 decimal
espero y te ayude
please help ill give brainliest to the first correct answer.
i really dont understand this question
The required time is mathematically given as
t-150 minutes.
This is further explained below.
What is the time?We know that the volume of the prism is given by.
[tex]\text{Volume}=\text{(Base Area)}\times\text{height}[/tex]
[tex]\text{Base Area}=\dfrac{1}{2}\times(1.4+0.6)\times2[/tex]
[tex]\text{Base Area}=2\ \text{m}^2[/tex]
Now,
[tex]\text{Volume}=2\times1=2\ \text{m}^3[/tex]
Given that there is a twenty percent drop in the level of the pond during the first thirty minutes.
Because of this, the volume increases.
[tex]\text{Volume}=2\times0.8=1.6\ \text{m}^3[/tex]
Now, the rate of emptying the tank is,
[tex]=\dfrac{2-1.6}{30} =\dfrac{1}{75} \ \text{m}^3/ \text{min}[/tex]
In conclusion, We also know that,
$$
[tex]\text{time}=\dfrac{\text{volume}}{\text{rate}}[/tex]
[tex]\text{time}=\dfrac{2}{\frac{1}{75} } =150 \ \text{min}[/tex]
Therefore, Colin must wait for the pond to drain for a total of 150 minutes.
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Write a formula for f(t) as a sum of Heaviside functions. Type uc for the Heaviside function that jumps at c (don't type uc(t) ). F(t) = t, 0 ≤ t ≤ 3 2t−3, 3 < t ≤ 4 5, 4 < t
The formula for f(t) as a sum of Heaviside functions is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4).
To express f(t) as a sum of Heaviside functions, we break down the function into its respective intervals and use the unit step function or Heaviside function to represent the function in each interval.
f(t) = t, 0 ≤ t ≤ 3
f(t) = 2t - 3, 3 < t ≤ 4
f(t) = 5, 4 < t
Using the Heaviside function uc for the jump at c, we can represent each interval as follows:
f(t) = tuc(t) - tuc(t-3), 0 ≤ t ≤ 3
f(t) = (2t-3)uc(t-3) - (2t-3)uc(t-4), 3 < t ≤ 4
f(t) = 5uc(t-4), 4 < t
Therefore, the formula is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4)
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Expand and simplify (3x - 1)(9x² + 3x + 1)
Stanley is making trail mix out of 10 bags of nuts and 20 bags of dried fruits. He want each new portion of trail mix to be identical, containing the same combination of dried fruits with no bags left over. What is the greatest number of portions of trail mix Stanley can make?
To solve this problem, we can use the Greatest Common Factor (GCF) of 10 and 20.
The GCF is the largest number that divides evenly into both 10 and 20. To find the GCF, we can use a factor tree.
We start with 10 and 20 as our starting numbers.
10 = 2 * 5
20 = 2 * 2 * 5
We can see that both 10 and 20 have a factor of 2 and a factor of 5. The Greatest Common Factor between 10 and 20 is 2 * 5, or 10.
Therefore, the greatest number of portions of trail mix Stanley can make is 10.
What method could have been used to collect the data
The method used to collect data will depend on the specific research question being asked and the resources available to the researcher.
One common method for collecting data is through experimentation. This involves designing a controlled experiment that allows researchers to manipulate one or more variables while keeping all other factors constant.
Observational data can be particularly useful when it is not possible or ethical to manipulate variables in an experiment.
Surveys and questionnaires are another way to collect data. These methods involve asking people to provide information about their attitudes, beliefs, and behaviors.
Other methods for collecting data include case studies, in which researchers closely examine a single individual or group, and archival research, in which data is collected from existing records, such as census data or medical records.
By carefully selecting the right method for their research, scientists can gather accurate and reliable data that can help to advance our understanding of the world around us.
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PLEASE HELP ME!
i have no clue what to do
Answer:
Step-by-step explanation:
you are going to give more info ?????
Someone please help me ASAP!! It’s due today!! Show work please! I will mark brainliest if it’s done correctly
Answer:
D
Step-by-step explanation:
First set up the fraction [tex]\frac{9}{40}[/tex] , and next divide 9 ÷ 40 = 0.225. Lastly, multiply 0.225 × 100 = 22.5%.
Hope this helps.
Suppose a product's revenue function is given by R(q) = - 7q + 600qr. Find an expression for the marginal revenue function, simplify it, and record your result in the box below. Be sure to use the proper variable in your answer. (Use the preview button to check your syntax before submitting your answer.) Answer: MR(q) =
The expression for the marginal revenue function is MR(q) = 600r - 7.
The given product's revenue function is R(q) = - 7q + 600qr.
To find an expression for the marginal revenue function, we can use the following steps:
Step 1: Take the first derivative of the revenue function with respect to q to obtain the marginal revenue function MR(q).
Step 2: Simplify the expression for MR(q) to record the final result.
In other words, the marginal revenue function MR(q) is the derivative of the revenue function R(q) with respect to q. Here, R(q) = - 7q + 600qr.
So, we have to differentiate R(q) with respect to q to get MR(q).
The derivative of - 7q with respect to q is - 7.
The derivative of 600qr with respect to q is 600r because the derivative of q with respect to q is 1.
MR(q) = dR(q) / dq
= (d/dq)(- 7q + 600r)
= (- 7) + (600r)
= 600r - 7
The equation that represents the marginal revenue function is MR(q) = 600r - 7.
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graph of 12x+6y=432 & 9x+3y=270
The line [tex]12x + 6y = 432[/tex] is represented by the red line, and the line equation [tex]9x + 3y = 270[/tex]is represented by the blue line. The point where these two lines intersect is (36,0).
What is equation?In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion [tex]"2x + 3 = 9"[/tex]states that the word "2x + 3" corresponds to the number "9". The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components. For example, in the equations" [tex]x^2 + 2x - 3 = 0[/tex]," the variable x is lifted to the powercell. Lines are utilised in many areas of mathematics, include algebra, arithmetic, and geometry.
To plot these lines on a graph, we first need to solve for y in terms of x for each equation.
can plot these lines
[tex]12x+6y 4326y=-12x+432y = -2x+729x+3y=2703y=9x+270y=-3x+90[/tex]
[tex]|100|_ | . | . 90|_ . | . | .80|_ . | . | .70|_ . | . | .60 |___________________________________________ 0 30 60 90 120 150 180 210 240 270 300[/tex]
The line[tex]12x + 6y = 432[/tex]is represented by the red line, and the line 9x + 3y = 270 is represented by the blue line. The point where these two lines intersect is (36,0).
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Write the linear equation of a line going through (-2,7) with a y-intercept of -3.
Answer:
y = -5x - 3
Step-by-step explanation:
A linear equation is y = mx + b
m = the slope
b = y-intercept
We know
Points (-2,7) (0,-3)
Slope = rise/run or (y2 - y1) / (x2 - x1)
We see the y decrease by 10 and the x increase by 2, so the slope is
m = -10/2 = -5
Y-intercept is located at (0, -3)
So, the equation is y = -5x - 3
Benito made a wooden box to grow herbs on his patio. The box is 16 inches wide, 12 inches tall, and 28 inches long. He plans to fill the box exactly two-thirds full with potting soil. What volume of soil does Benito need? I know how to do this I just need to know if the two-thirds part is trying to throw me off
To fill the wooden box with potting soil precisely up to two-thirds of its capacity, Benito requires a volume of 3,584 cubic inches.
The volume of soil that Benito needs to fill the box two-thirds full can be calculated by finding two-thirds of the total volume of the box.
The volume of the box can be calculated by multiplying the width, height, and length:
16 inches (width) x 12 inches (height) x 28 inches (length) = 5,376 cubic inches.
Two-thirds of this volume can be found by multiplying the total volume by 2/3:
5,376 cubic inches x 2/3 = 3,584 cubic inches.
Therefore, Benito needs 3,584 cubic inches of potting soil to fill the box exactly two-thirds full.
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List all prime numbers in the 2023 February calendar
Answer:
6 29 25
Step-by-step explanation:
those are the prime numbers on the 2023 feb calendar
from a survey involving 1,000 university students, a market research company found that 750 students owned laptops, 450 owned cars, and 350 owned cars and laptops. if a university student is selected at random, what is the (empirical) probability that
The probability that a student selected randomly owns either a laptop or a car is 85%.
Given a survey with a total of 1000 students, the following data was obtained: 750 students own laptops450 students own cars350 students own laptops and cars a university student is selected at random, what is the (empirical) probability that the student owns either a laptop or a car?
For two events A and B, the union of A and B is the probability that event A or event B occurs. It is the addition of the probabilities of each event minus the intersection of the two events. So in this case, the probability of a student owning either a laptop or a car is P(A∪B) = P(A) + P(B) - P(A∩B) where:
P(A) = probability of owning a laptop = 750/1000 = 0.75
P(B) = probability of owning a car = 450/1000 = 0.45
P(A∩B) = probability of owning both a laptop and a car = 350/1000 = 0.35
Now, substituting values into the formula:
P(A∪B) = 0.75 + 0.45 - 0.35= 0.85
Therefore, the probability that a university student selected randomly owns either a laptop or a car is 85%.
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2x+2y= 24
x=3y
What is the value of x+y? I WILL MARK BRAINLIEST AND GIVE 20 POINTS
Answer:
x + y = 12
Step-by-step explanation:
Pre-SolvingWe are given the following system of equations:
2x + 2y =24
x = 3y
We want to find the value of x + y.
SolvingWe first need to find the values of x and y, which we will do by solving the system.
We can solve this system by substitution.
We know that x = 3y, so we can substitute 3y as x in 2x+2y=24.
This gives us:
2(3y) + 2y = 24
Multiply.
6y + 2y = 24
Add the terms together.
8y = 24
Divide both sides by 8.
y = 3
We found the y value, now let's find the value of x.
The second equation is x=3y, so if we plug the value of y in there, we can find the value of x.
Substitute 3 as y.
x = 3(3) = 9
The value of x is 9.
So, to find x+y, we substitute the values we found.
x + y = 3 + 9 = 12
A line passes through the point (-4,4) and has a slope of -3