Answers
Answer:
Given as steps.
Step-by-step explanation:
Step 2: Opposite angles of a parallelogram are Equal
Step 4 ( After " Definition of a parallelogram"): Given
Step 5: ASA congruency Property / Therom
Step 6: CPCTC
P.S: It is ASA congruency Therom as both angles are adjacent to the side they are trying to prove.
Hope It Helps!
Related Questions
what conclusions can you draw about the sugar content of the cereals at Supermarket Eats? Which of the cereals would you be willing to purchase and which ones would you avoid? Explain your reasoning below.
Answers
When choosing cereals at Supermarket Eats, it is important to read the nutrition labels and choose cereals that are lower in added sugars and higher in fiber.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants
Based on general nutrition guidelines, it is recommended to choose cereals that are lower in added sugars and higher in fiber.
If the cereals at Supermarket Eats have nutrition labels, it is important to read them carefully to determine the sugar content per serving size. According to the American Heart Association, it is recommended that men limit their intake of added sugars to no more than 9 teaspoons per day, and women limit their intake to no more than 6 teaspoons per day. Choosing cereals that have less than 5 grams of added sugars per serving is a good rule of thumb.
In terms of fiber content, it is recommended to choose cereals that have at least 3 grams of fiber per serving. This will help to keep you feeling full and satisfied, and promote healthy digestion.
Therefore, When choosing cereals at Supermarket Eats, it is important to read the nutrition labels and choose cereals that are lower in added sugars and higher in fiber.
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Use the properties of exponents to rewrite y = 5e-0. 7t in the form ya(1 + r)' or y = a(1-r). Round the value of r to the
nearest thousandth. Then find the percent rate of change to the nearest tenth of percent
Answers
The percent rate of change to the nearest tenth of a percent is approximately 30.0% for both forms.
Starting with [tex]Y=5e^{-0.7}[/tex] we can rewrite it using the property that [tex]e^{In(x)} = x[/tex]:
[tex]y=5e^{0.7t} = 5e^{ine^{in-0.7t} } =5e^{ln(5)}e^{-0.7t}[/tex]
Using the property that e^(ln(x)) = x again, we can simplify further:
[tex]y = 5e^{(ln(5)} e^{-0.7t} = 5(5^{1/In(5)}e^{-0.7t})[/tex]
Let [tex]a = 5^{1/ln(5)}[/tex]and r = 0.7, then we have:
[tex]y = 5a(1 + r)^{-t} ; y = a(1 - r)^t[/tex]
Rounding r to the nearest thousandth, we have:
r ≈ 0.700
To find the percent rate of change, we can use the formula:
percent rate of change = (1 ± r) * 100%
For the first form, we have:
percent rate of change = (1 - 0.700) * 100% ≈ 30.0%
For the second form, we have:
percent rate of change = (1 - 0.700) * 100% ≈ 30.0%
Therefore, the percent rate of change to the nearest tenth of a percent is approximately 30.0% for both forms.
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On a coordinate plane, a parabola with a solid boundary line opens down. It goes through (negative 2, 0), has a vertex at (2, 12), and goes through (6, 0). Find the symbol and coefficients for the standard form of the inequality represented by the graph. y the boundary line. a = b = c =
Answers
Therefore , the solution of the given problem of inequality comes out to be y - 12 = -(3/4)(x - 2)².
What is an inequality?Without the equal sign, an association or collection of numbers can be a disparity in mathematics. Equity always comes after equilibrium. When standards are still incompatible, inequality results. Fairness and disparity have different variable characteristics. Because parts aren't always similar or close to one another, we decided to select the most common symbol (). It is also possible to use disparities of any size to assess values.
Here,
We must recast the parabola's equation in this form in order to determine the inequality's standard form. The vertex version of a quadratic equation is as follows:
=> y = a(x - h)² + k
where (h, k) is the parabola's apex. Inputting the numbers provided yields:
=> y = a(x - 2)² + 12
We can use the information that the parabola passes through (-2, 0) and to determine the value of a. (6, 0). When we enter these values into the formula, we obtain:
=> 0 = a(-2 - 2)² + 12
=> 0 = 16a + 12
=> a = -3/4
The parabola's solution is as follows:
=> y = -(3/4)(x - 2)²
We need to separate y on one side in order to determine the inequality's standard form:
=> y - 12 = -(3/4)(x - 2)²
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Exhibit 3-2 A researcher has collected the following sample data. The mean of the sample is 5. 3 5 12 3 2 Refer to Exhibit 1. Rhe variance is"
a. 80
b. 4.062
c. 13.2
d. 16.5
Answers
The variance of the sample is 17.05. However, none of the given options matches with this value. The closest option is option (d) 16.5.
What is variance?Variance is a measure of the spread or variability of a set of data. It is the average of the squared differences from the mean. The formula for variance is:
Variance = (sum of squared deviations from the mean) / (number of observations - 1)
where the squared deviation from the mean is the difference between each data point and the mean of the data set, squared. The variance is useful in statistical analysis and can provide information about the distribution of the data. A higher variance indicates that the data is more spread out, while a lower variance indicates that the data is clustered more closely around the mean.
In the given question,
To find the variance of the sample, we can use the formula:
Variance = [(sum of squared deviations from the mean)/ (number of observations - 1)]
First, we need to find the squared deviation of each observation from the mean, which is the difference between each observation and the mean, squared:
(3-5.4)² = 5.76
(5-5.4)² = 0.16
(12-5.4)² = 43.56
(3-5.4)²= 5.76
(2-5.4)²= 12.96
Next, we need to sum up these squared deviations:
5.76 + 0.16 + 43.56 + 5.76 + 12.96 = 68.2
Then, we divide the sum of squared deviations by the number of observations minus 1:
Variance = 68.2/(5-1) = 17.05
Therefore, the variance of the sample is 17.05. However, none of the given options matches with this value. The closest option is option (d) 16.5.
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A physics exam consists of 9 multiple-choice test that has 7 questions. Each of the questions has 5 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions?
A.) 78,125
B.) 16,807
C.) 35
D.) 12
Answers
Using expression 5⁷ x 9, there are 59,049,125 ways to answer all 9 tests if you select one option per question and leave nothing blank.
What exactly are expressions?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, and exponentiation) that represents a value or a quantity.
Expressions can be simple or complex, and they can contain one or more variables. For example, "2x + 3" is a simple expression that contains the variable x.
Now,
To solve this problem, we can use the multiplication principle of counting, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things.
For each of the 9 tests, there are 5 choices for each of the 7 questions. Therefore, there are 5 x 5 x 5 x 5 x 5 x 5 x 5 possible ways to answer the questions on each test. Using the multiplication principle, we can find the total number of ways to answer all 9 tests by multiplying the number of ways to answer each test together:
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 5⁷ x 9 = 59,049,125
Therefore,
there are 59,049,125 possible ways ways to answer all 9 tests if you select one option per question and leave nothing blank.
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Isaac walks 6/10 of a mile in 1/5 of an hour. If Isaac’s walking rate remains constant, what is Isaac’s walking rate in miles per hourur
Answers
Answer: 3 mph
Step-by-step explanation:
I did it in mah brain
A firm has classified its customers in two ways: according to whether the account is overdue and whether the account is new (less than 12 months) or old. An analysis of the firm's records provided the input for the following table of joint probabilities: One account is selected at random. If the account is overdue, what is the probability that it is new? If the account is new, what is the probability that it is overdue?
Answers
The probability that it is new is 0.0833.
The probability that it is overdue is 0.25.
How to calculate conditional probability?To solve this problem, use conditional probability.
Let A be the event that the account is new, and B be the event that the account is overdue.
A) To find the probability that an account is new given that it is overdue, calculate:
P(New | Overdue) = P(New and Overdue) / P(Overdue)
P(New | Overdue) = 0.05 / (0.05 + 0.55) = 0.0833 or 8.33%
So the probability that the account is new, given that it is overdue, is 8.33%.
B) To find the probability that an account is overdue given that it is new, calculate:
P(Overdue | New) = P(Overdue and New) / P(New)
P(Overdue | New) = 0.05 / (0.05 + 0.15) = 0.25 or 25%
So the probability that the account is overdue, given that it is new, is 25%.
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The complete question is:
A firm has classified its customers in two ways: according to whether the account is overdue and whether the account is new (less than 12 months) or old. An analysis of the firm's records provided the input for the following table of joint probabilities: One account is selected at random. If the account is overdue, what is the probability that it is new? If the account is new, what is the probability that it is overdue?
Find an expression which represents the difference when (−5x+7) is subtracted from (9x+5) in simplest terms.
Answers
14x - 2
To find the difference between (−5x+7) and (9x+5), we need to subtract the first expression from the second.
(9x+5) - (-5x+7)
= 9x + 5 + 5x - 7 [Distribute the negative sign to (-5x+7)]
= 14x - 2
Therefore, the difference between (−5x+7) and (9x+5) is 14x - 2.
Help with work shown all of them
Answers
The expression are simplified to ;
7. 16 + 8g
8. 4h - 20g
9. -35 + 7n
10. 16m + 8
13. -56n + 7m
14. -36 - 6d
15. -8c - 4d
16. -6f + 10g
What are algebraic expressions?Algebraic expressions are defined as expressions that are usually made up of terms, variables, constants, factors and coefficients.
These expressions are identified with mathematical or arithmetic operations, such as;
AdditionMultiplicationSubtractionBracketDivisionParentheses, etcFrom the information given, we need to expand the bracket to determine the expressions, we have;
a. -7(8n - m)
expand the bracket
-56n + 7m
b. (6+d)(-6)
expand the bracket
-36 - 6d
c. (4c + 2d) - 2
expand the bracket
-8c - 4d
d. -2(3f - 5g)
expand the bracket
-6f + 10g
e. (2 + g) 8
expand the bracket
16 + 8g
f. 4(h - 5g)
expand the bracket
4h - 20g
g. -7(5 - n)
expand the bracket
-35 + 7n
h. 8(2m + 1)
expand the bracket
16m + 8
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Step-by-step explanation:
13. -7(8n-m)= -56n+7m
14. (6+d)(-6)= -36-6d
15. (4c+2d)(-2)= -8c-4d
16. -2(3f-5g)= -6f+10g
7. (2+g)8= 16+8g
8. 4(h-5g)= 4h-20g
9. -7(5-n)= -35+7n
10. 8(2m+1)= 16m+8
Cual expresion algebraica representa la siguiente frase? N aumetado en un 25% A. 0. 25N
B. N + 0. 25N
C. 25N
D. N + 25
Answers
The algebraic expression that represents the sentence "N increased by 25%" is 0.25N.
Hence the correct option is A.
This means that N is multiplied by 0.25 or 1/4. To find the result of N increased by 25%, you simply need to multiply N by 0.25 and add the result to the original value of N. The option A, 0.25N, represents this concept in a clear and concise manner.
The other options (B, C, and D) are either incomplete or incorrect. It is important to understand the concept of percentage increase and how it is represented algebraically, as it is a common operation in many mathematical and real-life scenarios, such as calculating interest rates, growth rates, and inflation rates.
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There are 150 players on the high school football team. 30% of the players are on the freshman team, and the rest of them are on either JV or varsity.
How many players are on the freshman team?
Answers
Write a word problem involving percents for which the percent is about one half and the whole is known. Write a percent equation for the problem and then use it to solve the problem
Answers
The purchase cost is $40. Question: What is the discount price of shoes if they were originally $80 and are currently on sale for 50% off. % formula: Sale price equals 50% of $80.
The word puzzle asks you to determine the sale price of shoes that are being offered at a 50% discount. The percent equation, which asserts that the percent of the whole is equal to the part over the entire, or percent = part/whole, may be used to solve this problem. In this instance, the sale price is the component we are interested in, the initial price of $80 is the component as a whole, and 50% is the percentage. With these numbers as inputs, we can calculate the sale price as 50% of $80. When we solve for the sale price, we arrive at $40. Hence, the sneakers are $40 on sale.
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Write a word problem involving percents for which the percent is about one half and the whole is known. Write a percent equation for the problem and then use it to solve the problem. If a store has a sale on shoes for 50% off and the original price is $80, what is the sale price?
A bicycle wheel make five rotations. The bicycle travel 30. 09 find the diameter
Answers
The diameter of the wheel is approximately 1.918 meters.
We can use the formula:
distance traveled = circumference of wheel x number of rotations
The circumference of the wheel is equal to the distance traveled in one rotation, which is equal to the diameter of the wheel times pi (π). So we can rewrite the formula as:
distance traveled = (diameter of wheel x π) x number of rotations
where d is the diameter of the wheel.
We are given that the bicycle travels 30.09 meters and the wheel makes five rotations, so we can plug in these values:
30.09 = (d x π) x 5
Solving for d, we get:
d = 30.09 / (π x 5)
d ≈ 1.918 meters
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the measure of three interior angle of a triangle are in the ratio 2፡3፡4. what is the measure of the smallest and largest interior angles of triangle?
Answers
Answer:
Below
Step-by-step explanation:
The interior angles of ANY triangle add up to 180 degrees
you want to divide this 180 into 2 + 3 + 4 = 9 parts
180 / 9 = 20 degrees for each part
2 parts = 2 * 20 = 40 °
4 parts = 4 * 20 = 80 °
28 students are divided into
7 groups for a party game.
32 students would create
how many groups of the
same size?
Answers
Answer:
If 28 students are divided into 7 groups, then each group will have 28/7 = 4 students.
To find out how many groups would be created if there were 32 students, we can use the same ratio:
32 students divided into groups of 4 students each would give us:
32/4 = 8 groups.
Therefore, if there were 32 students, they would be divided into 8 groups of the same size.
write the ratio in the simplest form ;120mimutes:4hours:6hours
Answers
[tex]f(x) = \frac{ {x}^{3} + 1 }{ {x}^{3} - 2} [/tex]
Find the inverse
Answers
Answer:
Step-by-step explanation:
[tex]f^-1[/tex][tex]\sqrt[3]{1/-1+x | + | 2x/-1+x}[/tex]
The length of a rectangle is 1 ft more than double the width, and the area of the rectangle is 28 ft². Find the dimensions.
Answers
28= (1+2x)(x)
28=x+2x²
2x²+x-28 = 0
2x²+8x-7x-28 =0
2x(x+4) -7(x+4) =0
(x+4)(2x-7) = 0
x = -4 and 7/2
dimensions can't be negative
length=1+2×7/2 =1+7 = 8ft
width= 7/2ft
The net of a right circular cylinder is shown.
net of a cylinder where the radius of each circle is labeled 4 meters and the height of the rectangle is labeled 8 meters
What is the surface area of the cylinder? Use π = 3.14 and round to the nearest whole number.
251 m2
301 m2
502 m2
804 m2
Answers
The area of each circular base is πr^2, where r is the radius. In this case, the radius is 4 meters, so the area of each circular base is:
π(4)^2 = 16π
The lateral surface area is the area of the rectangle that forms the curved surface of the cylinder. The height of the rectangle is the same as the height of the cylinder, which is 8 meters, and the base of the rectangle is the circumference of the circle, which is 2πr. So, the lateral surface area is:
8(2πr) = 16πr
Substituting r = 4, we get:
16π(4) = 64π
Adding the areas of the two circular bases and the lateral surface area, we get:
16π + 16π + 64π = 96π
Using π = 3.14 and rounding to the nearest whole number, the surface area of the cylinder is:
96π ≈ 301 square meters
Answer:
The first person to answer was correct, the answer is 301 m squared.
Step-by-step explanation:
I took the quiz so you don't have to! <3
exponential law of heating and cooling
Answers
Part A: k = 8.4, to find the value of k, we must solve for k in the equation.
Part B: 193°F is the temperature of the water after 4.5 minutes.
What is initial temperature?Initial temperature is the temperature of a system before it undergoes a change. It can be calculated by subtracting the change in temperature from the final temperature.
Part A: k = 8.4
To find the value of k, we must solve for k in the equation.
We are given the temperature of the room (67°F) and the initial temperature of the water (208°F).
We are also given the temperature of the water after 3 minutes (193°F). We can plug these values into the equation and solve for k:
T-Ta = k(To-T)
193-67 = k(208-193)
126 = 15k
k = 126/15
k = 8.4
Part B: 193°F
To find the temperature of the cup of water after 4.5 minutes, we can plug the k-value we found in Part A into the equation, along with the given temperature of the room (67°F) and the initial temperature of the water (208°F).
T-Ta = k(To-T)
T = Ta + k(To-T)
T = 67 + 8.4(208-T)
T = 67 + 1747.2 - 8.4T
9.4T = 1814.2
T = 193
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Part A: k = 8.4, to find the value of k, we must solve for k in the equation.
Part B: 193°F is the temperature of the water after 4.5 minutes.
What is initial temperature?The temperature of a system at the start of a shift is called the initial temperature. You can figure it out by deducting the final temperature from the temperature difference.
Part A: k = 8.4
We must answer for k in the equation in order to determine its value.
We are informed of the room's temperature (67°F) and the water's starting temperature (208°F).
After three minutes, we are also told the water's temperature (193°F). We can solve for k by entering these numbers into the equation:
T-Ta = k(To-T)
193-67 = k(208-193)
126 = 15k
k = 126/15
k = 8.4
Part B: 193°F
We can enter the k-value we discovered in Part A, the given room temperature (67°F), and the starting temperature of the water (208°F) into the equation to determine the temperature of the cup of water after 4.5 minutes.
T-Ta = k(To-T)
T = Ta + k(To-T)
T = 67 + 8.4(208-T)
T = 67 + 1747.2 - 8.4T
9.4T = 1814.2
T = 193
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The complete question is,
EXIT TICKET
After heating up in a teapot, a cup of hot water is poured at a temperature of 208^0F . The cup sits to cool in a room at a temperature of 67^0 F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between temperature of the water and the temperature of the room, as given by the formula shown below.
Part A: If the cup of water reaches the temperature of 193^0 F after 3 minutes. Find the value of k, to the room, as given by the formula shown below. nearest thousandth.
Part B: Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.
342×38 without using a calculator
Answers
Answer:
12996
Step-by-step explanation:
342
× 38
-----
2052 (2 x 342)
13680 (3 x 342, plus a zero)
-----
12996
Therefore, 342 × 38 = 12,996.
PLSSSSSSSSSS HELPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!
How is the quotient of 8,552 and 16 determined using an area model?
Enter your answers in the boxes to complete the equations.
8,552 ÷ 16 = (___÷ 16) + (480 ÷ 16) + (___ ÷ 16) + (8 ÷ 16)
8,552 ÷ 16 = ___ +30 + ___ + 8/16
8,552 ÷ 16 = ___ 1/2
Answers
Answer:
Step-by-step explanation:
Hi there I am able to help so when you do 8,552/16 it is best to reverse it then add the expression, what I mean by that is translating expressions. the answer would be 444.23 then you would want to add (480/16) no mental math how you would do this is the recalabric way, take 480/16 and put in an a fraction to make it work easier than the rest of your problems you would do the same things its simple, just repeat what I did to all the other problems,
regards, me
at a local book store, fiction books were on sale. Some were priced at $6 and some at $8. Marci bought 10 books and spent a total of $68.00. How many $6 books did she buy?
Answers
Answer:
6 $6 books
Step-by-step explanation:
Using the information, we can create a system of equations.
We can let x represent the total number of $6 Marci bought and y represent the total number of $8 books she bought.
Because the total number of books is 10, one equation we have is x + y = 10.
Because the total cost of both types of books is $68, our other equation is 6x + 8y = 68.
We can solve with substitution by isolating y in the first equation and plugging it into the second equation:
[tex]x+y=10\\y=-x+10\\\\6x+8(-x+10)=68\\6x-8x+80=68\\-2x+80=68\\-2x=-12\\x=6[/tex]
Thus, the total number of $6 books Marci bought was 6.
an
How was Malaka's father finally able to move to the
United States?
O He saved enough money to afford the cost of moving.
He was accepted to UCLA's School of Management.
He studied and was able to pass the TOEFL.
He received a teaching job at UCLA.
Answers
Answer:
B
Step-by-step explanation:
He was accepted to UCLA's School of Management
The Angler's Club requires that members spend at least $250 per month at their restaurant. Mr. Donovan has spent $179. 85 so far this month. Write an inequality to describe the situation, then complete the sentence.
Answers
Mr. Donovan still needs to spend at least $70.15 in the restaurant this month to meet the Angler's Club requirement.The inequality that describes the situation is:250 - 179.85 ≤ x
where x represents the amount of money Mr. Donovan still needs to spend in order to meet the Angler's Club requirement.
To solve for x, we first subtract 179.85 from 250 to get:
70.15 ≤ x
Therefore, Mr. Donovan still needs to spend at least $70.15 in the restaurant this month to meet the Angler's Club requirement.
In summary, Mr. Donovan's spending so far this month is less than the minimum required by the Angler's Club, and he needs to spend at least $70.15 more to meet the requirement.
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Ariana has a deck that measures 16 feet by 24 feet. She wants to increase each
dimension by equal lengths so that its area is doubled. By how much should she
increase each dimension?
Can anyone help plss:)
Answers
Answer:
The answer would be 80.
Step-by-step explanation:
First you want to add 16 and 24.
Next you want to multiply that answer by 2.
Then you have your answer and I hope this helps
a square fits exactly inside a circle with each of its vertices being on the circumference of the circle.
the square has side lengths of xcm
the area of the circle is 56cm squared.
work out the value of x to 3 significant figures.
Answers
After addressing the issue at hand, we can state that As a result, the square value of x to three significant figures is 5.03 cm.
what is a square?According to Euclidean geometry, a square is an equilateral quadrilateral with four equal sides and four equal angles. It is also referred to as a rectangle with two neighbouring sides of equal length. A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles. Furthermore, the diagonals of the square are evenly spaced and split at a 90-degree angle. a neighbouring rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.
The Pythagorean theorem can be used to find the square's diagonal:
2x2 = diagonal2 = x2 + x2 = 2x2[tex]x * \sqrt = diagonal = sqrt(2x2) (2)[/tex]
Because the diagonal equals the circle's diameter, the radius is half of the diagonal:
x * \sqrt(2) / 2 = radius
We can now use the formula for the area of a circle to calculate x:
[tex]\pi * radius2 = area[/tex]
[tex]\Pi * (x * sqrt(2) / 2)2 = 56[/tex]
[tex]56 = pi * (x^2 / 2)[/tex]
[tex]x^2 = 112 / pi[/tex]
x = 5.027 (rounded to 3 significant figures) (rounded to 3 significant figures)
As a result, the value of x to three significant figures is 5.03 cm.
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A parallelogram of base 12cm has an area 108sq. Cm. Find the height
Answers
The height of the parallelogram is 9 cm.
To find the height of a parallelogram with a given base and area, we can use the formula:
Area = base x height
In this case, we are given that the base of the parallelogram is 12 cm and the area is 108 sq. cm. Substituting these values into the formula, we get:
height = 108/12
Simplifying this expression, we get:
height = 9cm
A parallelogram is a four-sided polygon with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure, meaning that the adjacent angles are supplementary (their sum is 180 degrees).
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Demonstrate your knowledge by giving clear, concise solutions to each problem. Be sure to include all
relevant drawings and justify your answers (show all your work). You may show your solution in more
than one way to investigate beyond the requirements of the problem. (21 pts)
1. a. Tell how you know that a system of linear equations has no solutions. (3 pts)
b. Write a system of two linear equations that has no solution. (3 pts)
c. Tell how you know that a system of two linear equations has more than one solution. How
many solutions will such a system have? Justify your answer. (3 pts)
d. Write a system of two linear equations that has more than one solution. (3 pts)
e. Write a system of linear equations that has only one solution. (3 pts)
f. Solve the system of equations in part e in at least two ways. (3 pts)
g. Write a word problem that can be solved using a system of two linear equations. Solve the
problem and give the meaning of the answer. (3 pts)
Answers
The solutions of a system of linear equations are as follows;
1. Their slope is the same but their y-intercept are different
b. y = 3·x + 2 and y = 3·x + 5
c. The equations are the same
d. y = 3·x + 2 and y = 9·x + 15
e. y = 3·x + 2, and y = 8·x + 5
f. x = 0, y = 0
g. Please see the following section
What is a system of linear equations?A system of linear equations are equations that have the same variables.
1. a. A system of linear equations have no solution if the equations in the system of equations have the same slope
b. y = 3·x + 2, and y = 3·x + 5
c. A system of two linear equations has more than one solution if the equations in the system are the same
The number of solutions = Infinite number of solutions
d. y = 3·x + 5, 3·y = 9·x + 15
e. y = 3·x + 5, y = 8·x + 5
f. y = 3·x + 5, y = 8·x + 5
Therefore; 3·x + 5 = 8·x + 5
3·x = 8·x
3·x - 8·x = 0
-5·x = 0
x = 0/(-5) = 0
x = 0
y = 3·x + 5
y = 3 × 0 + 5 = 5
y = 5
The solution is therefore;
x = 0, y = 5
g. A customer wants to spend a total of ¢50 to buy drawing pads and pencils. The cost of the pencil the customer intends to buy is ¢2, and the cost of each drawing pad is ¢8. The number of pencils and the number of drawing pads the customer buys are the same.
How many drawing pads and pencils does the customer buy.
Let x represent the number of drawing pad the customer buys and let y represent the number pencils the customer buys, we get;
8·x + 2·y = 50
x = y
Therefore;
8·x + 2·x = 50
10·x = 50
x = 50/10
x = 5
Therefore; y = 5
The number of drawing pads and pencils the customer buys are 5 each.
Learn more on linear system of equations here: https://brainly.com/question/30586361
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Arthur is building a rectangular sandbox for his son. The area of the sandbox is 17 23/32 square feet. If the length of the sandbox is 3 3/8 feet, what is the width of the sandbox?
Answers
Answer:
5 1/4 feet----------------------------------
Area of a rectangle is the product of it width and length:
A = wlGiven the length and area of a rectangle, find the missing width:
w = A/lw = 17 23/32 : 3 3/8 = (17*32 + 23)/32 : (3*8 + 3)/8 = 567/32 : 27/8 =567/32 * 8/27 = 21/4 = 5 1/4