Given the two equations below, determine which statement best describes the graph of the equations.
y=1/2x-3
y=-2x+16
Select answer A The two lines given by the above equations are perpendicular. Select answer
B The two lines given by the above equations coincide. Select answer
C The two lines given by the above equations are parallel.
D The two lines given by the above equations intersect (but are not perpendicular). ...?
Answer: Option A.
Step-by-step explanation:
The lines that we have is:
y = (1/2)x - 3
y = -2x + 16
Now, two lines of the shape y1 = a1*x + b1 and y2 = a2*x + b2 are parallel if both lines have the same slope, this means that a1 = a2.
Those lines are perpendicular if a1 = -1/a2
now, the slope in the first equation is (1/2) and in the second equation is -2.
so a1 = 1/2
-1/a1 = -(2) = a2
so the two lines are perpendicular, the correct option is A
A new savings account is opened with $300 and gains 3.1% yearly for 5 years
At the end of 5 years, with the 3.1% interest rate, your savings account will grow to $349.47.
Use the concept of percentage defined as:
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.
Given that,
A new savings account is opened with $300.
The account earns a 3.1% interest rate per year.
The interest is calculated yearly.
The duration of the investment is 5 years.
After the first year,
Savings will increase by 3.1% of $300, which is $9.30.
So, your balance at the end of the first year will be $309.30.
For the following years,
you will continue to earn 3.1% interest on the new balance each year. Here's a breakdown of your balance at the end of each year:
Year 1: $309.30
Year 2: $309.30 + 3.1% of 309.30 = $318.88
Similarly
Year 3: $328.77
Year 4: $338.96
Year 5: $349.47
Hence,
At the end of 5 years, with the 3.1% interest rate, your savings account will grow to $349.47.
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write 3 different improper fractions that equal 4 2/3
David wants to complete a hypothesis test with the least amount of probability for error. if he sets the significance level to 1%, assuming his sample is truly random, what else could he adjust in the test in order to reduce error?
The answer is B. He could increase the sample size.
You realize that more than 8000 gallons per year was a lot of water to waste with a leaky faucet. You fixed your faucet so that it now takes 11 minutes longer to fill a cup of water than it did when it leaked 1 fluid ounce 30 seconds. How many gallons will the faucet waste in 1 year?
Which of these can be a result of inflation?
Businesses grow cautious about spending
The government has to cut spending
The price of household items increases
Workers benefit from a lower cost of living
The price of household items increases is a result of inflation, option C is correct.
Inflation typically leads to a general rise in prices across the economy.
As the value of money decreases, it takes more money to purchase the same goods and services.
Therefore, the prices of household items, along with other consumer goods, tend to increase during periods of inflation.
However, it's important to note that inflation does not affect all goods and services uniformly.
Some prices may rise more rapidly than others, leading to changes in relative prices.
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A bedroom set lists for $12,000 and carries a trade discount of 30 percent. Freight (FOB shipping point) of $150 is not part of list price. Calculate the delivered price of the bedroom set including the freight. Assume a cash discount of 2 percent:
20% of what number is 47?
Need help
20% of 235 is the number 47.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Percentage is usually denoted by the symbol '%'.
Let x be the unknown number.
Given that 20% of the number x is 47.
Mathematically, this can be written as,
20% × x = 47
(20/100) x = 47
0.2x = 47
x = 47 / 0.2
x = 235
Hence the unknown number is 235.
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Which of the following has a graph that is a straight line?
Equation 1: y = 2x + 7
Equation 2: y2 = x − 1
Equation 3: y = 2x2 + 4
Equation 4: y = 3x3
41 2/3 divided by 4 1/4
What is 1 1/2 plus 2/3?
y = 2 x^2 + 4 linear or non i think its linear
2. Alice Hall, who loves to cook, makes an apple cake (serves 6) for her family. The recipe calls for 2 1/2 pounds of apples, 2 1/4 cups of flour, 1/5 cup of margarine, 1 1/4 cups of sugar and 4 eggs. Since guests are coming, she would like to make this cake so it will serve 24. How many pounds of apples should she use?
...?
Answer:
10 pounds
Step-by-step explanation:
We are given that Alice hall makes an apple cake (serves 6) for her family
Apples=[tex]2\frac{1}{2}=\frac{5}{2}[/tex]pounds
Flour=[tex]2\frac{1}{4}=\frac{9}{4}[/tex] cups
Margarine=[tex]\frac{1}{4}[/tex] cups
Sugar=[tex]1\frac{1}{4}=\frac{5}{4}[/tex] cups
Eggs=4
For 6 persons , apples required =[tex]\frac{5}{2}[/tex] pounds
For 24 persons=[tex]\frac{\frac{5}{2}}{6}\times 24[/tex]
For 24 persons=[tex]\frac{5}{12}\times 24=10[/tex] pounds
Hence, she should use 10 pounds of apples.
Rewrite the fractions with their LCD.
(1)/(3x-9y),(6)/(5x-15y)
A.
2/8x-21y and 2/8x-21y
B.
5(x-3y)/15(x-3y) and 18(x-3y)/15(x-3y)^2
C.
5/15(x-3y) and 18/15(x-3y)
D.
5/15x-135y and 18/15x-135y
make x the subject 6x+a=5(x+t)
To make x the subject of the equation, you can rearrange the equation x = 5t - a.
Explanation:To make x the subject of the equation, we need to isolate the variable on one side of the equation. Here's how:
Distribute 5 to both x and t: 6x + a = 5x + 5tSubtract 5x from both sides: 6x - 5x + a = 5tCombine like terms: x + a = 5tSubtract a from both sides: x + a - a = 5t - aCancel out a: x = 5t - aTherefore, to make x the subject, the equation is x = 5t - a.
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4. Which of the following sets of numbers is a Pythagorean triple?
A. 4, 5, 6
B. 8, 15, 17
C. 5, 12, 14
D. 8, 24, 25
Suppose a triangle has side lengths 6, 7, and 10. Which of the following best describes this triangle?
A. obtuse
B. acute
C. right
D. Cannot be determined.
The set 8, 15, 17 is a Pythagorean triple because 8^2 + 15^2 = 17^2. A triangle with sides of 6, 7, and 10 is an obtuse triangle, because 10^2 > 6^2 + 7^2.
Explanation:The set of numbers, 8, 15, 17, represents a Pythagorean triple. A Pythagorean triple consists of three positive integers a, b, and c, such that a^2 + b^2 = c^2. In this case, 8^2 + 15^2 = 64 + 225 = 289, and 17^2 = 289, so the equation is satisfied.
Furthermore, a triangle with sides 6, 7, and 10 would be described as obtuse. In any triangle, if the square of the length of the longest side is greater than the sum of the squares of the other two sides, then the triangle is obtuse. Thus, if 10^2 > 6^2 + 7^2, or 100 > 36 + 49, then the triangle is obtuse. Since this statement holds true, the triangle is indeed obtuse.
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The correct options are: B. 8, 15, 17 and A. obtuse
We can use the Pythagorean theorem to determine which set of numbers is a Pythagorean triple. The theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides (a and b): a2 + b2 = c2.
Option A: 4, 5, 6: [tex]4^2 + 5^2 = 16 + 25 = 41[/tex], and [tex]6^2=36[/tex], which is not equal to 41.Option B: 8, 15, 17: [tex]8^2 + 15^2 = 64 + 225 = 289[/tex], and [tex]17^2=289[/tex], equal.Option C: 5, 12, 14: [tex]5^2 + 12^2 = 25 + 144 = 169[/tex], and [tex]14^2=196[/tex], which is not equal to 169.Option D: 8, 24, 25: [tex]8^2 + 24^2 = 64 + 576 = 640[/tex], and [tex]25^2=625[/tex], which is not equal to 640.The correct Pythagorean triple is 8, 15, 17.
To determine the type of triangle with side lengths 6, 7, and 10, we use the idea that for a triangle with sides a, b, and c (where c is the longest side):
If [tex]c^2 = a^2 + b^2[/tex], the triangle is right.If [tex]c^2 < a^2+b^2[/tex], the triangle is acute.If [tex]c^2 > a^2+b^2[/tex], the triangle is obtuse.For the triangle with sides 6, 7, and 10:
[tex]6^2+7^2=36+49=85[/tex] and [tex]10^2=100[/tex].
Since 100 > 85, the triangle is obtuse.
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the first equation is substituted into the second equation.
8x – y = –9
4x – 3y = –22
4x – 3(–8x – 9) = –22
4x – 3(8x + 9) = –22
4(8x + 9) – 3y = –22
4(–8x – 9) – 3y = –22
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the first equation is substituted into the second equation.
8x – y = –9
4x – 3y = –22
4x – 3(–8x – 9) = –22
4x – 3(8x + 9) = –22
4(8x + 9) – 3y = –22
4(–8x – 9) – 3y = –22
Answer:
The answer is "4x - 3(8x +9) = -22."
Step-by-step explanation:
I just finished the test and got it right.
Find 3 consecutive odd integers whose sum is 225, explain please
Suppose R is a symmetric and transitive relation on a set A, and there is an element a in A for which aRx for every x in A. Prove that R is reflexive. ...?
what two numbers add to 7 and multiply to 10
Find the minimum, maximum, range, mean, and median for the data set.
2.4, 2.6, 7.2, 5.5, 4.1, 5.5, 6.1, 6.1
A.
minimum: 2.4
maximum: 7.2
range: 4.8
mean: 5.5
median: 4.9
B.
minimum: 2.4
maximum: 7.2
range: 9.6
mean: 4.9
median: 5.5
C.
minimum: 7.2
maximum: 2.4
range: 4.8
mean: 4.9
median: 5.5
D.
minimum: 2.4
maximum: 7.2
range: 4.8
mean: 4.9
median: 5.5
A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 45 dumpster loads of waste removed. In week 10, there were 30 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week.
f(x) = - 3x + 45
f(x) = 3x + 45
f(x) = - 3x + 60
f(x) = 3x + 60
The correct answer is:
[tex]\[\boxed{f(x) = -3x + 60}\][/tex]
To find the linear equation representing the amount of trash removed each week, we need to determine the slope and the y-intercept.
Given:
- In week 5, there were 45 dumpster loads.
- In week 10, there were 30 dumpster loads.
Step 1: Calculate the Slope
The slope m of a line is calculated by:
[tex]\[m = \frac{y_2 - y_1}{x_2 - x_1}\][/tex]
Here,[tex]\((x_1, y_1) = (5, 45)\) and \((x_2, y_2) = (10, 30)\).[/tex]
[tex]\[m = \frac{30 - 45}{10 - 5} = \frac{-15}{5} = -3\][/tex]
Step 2: Write the Equation in Point-Slope Form
Using the point-slope form of the equation [tex]\( y - y_1 = m(x - x_1) \):[/tex]
[tex]\[y - 45 = -3(x - 5)\][/tex]
Step 3: Convert to Slope-Intercept Form [tex]( \( y = mx + b \) )[/tex]
Simplify the equation:
[tex]\[y - 45 = -3(x - 5)\][/tex]
[tex]\[y - 45 = -3x + 15\]\[y = -3x + 15 + 45\]\[y = -3x + 60\][/tex]
Thus, the equation in function form that shows the amount of trash removed each week is:
[tex]\[f(x) = -3x + 60\][/tex]
Therefore, the correct answer is:
[tex]\[\boxed{f(x) = -3x + 60}\][/tex]
Where is the answer to the expression 3 − 6 located on a horizontal number line?
Mr. Thom makes $25,900/year salary as a document processor. He has made the following chart in order to divide his weekly paycheck into his accounts: Expense type Account Weekly deposits Essential (Fixed) 1st Checking account $219 Essential (Variable) 1st Checking account $115 Non-essential 2nd Checking account $40 Other (Unexpected) Emergency savings account $20 Other (Predictable) Education investment fund $10 Other (Predictable) Retirement investment fund $40 Other (Predictable) Emergency savings account $15 Total paycheck $498 Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. If he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings?
Answer:
C. 74
Step-by-step explanation:
NOTICE: Edge loves moving things around SO IT MIGHT NOT BE C FOR YOU But its fore sure 74
Final answer:
Mr. Thom can put $59 per week towards emergency savings.
Explanation:
To find the total amount that Mr. Thom can put towards emergency savings per week, we need to calculate the difference between his total paycheck and the sum of his weekly deposits into the other accounts. From the given information, his total paycheck is $498, and the sum of his weekly deposits into the other accounts is $219 + $115 + $40 + $10 + $40 + $15 = $439. We can subtract the sum of the weekly deposits from the total paycheck to find the difference, which is $498 - $439 = $59. This is the amount that Mr. Thom can put towards emergency savings per week.
A baseball bat manufacturing company needs to meet a daily target of producing 600 bats to 3,000 bats.
A single worker can complete 15 bats per day. The time taken to meet the daily target is inversely proportional to the number of workers. If t is the total time and n is the number of workers, then the function is represented by t(n)=k/n . Determine an appropriate domain to represent this function.
A. n<=15
B. n>=15
C. 600<=n<=3000
D. 40<=n<=200
A box has dimensions of 17 inches long, 1.3 feet wide, and 8 inches high. What is the volume of the box? The formula for the volume is V = l w h. (1 point)
2121.6 cubic inches (in3)
176.8 cubic inches (in3)
14.7 cubic inches (in3)
1.2 cubic inches (in3)
To find the volume of the box, convert all units to inches, then apply the formula for the volume of a rectangular prism, resulting in 2,121.6 cubic inches.
Explanation:To calculate the volume of the box with dimensions given in inches and feet, we first need to convert all units to the same system. Since the width is given in feet (1.3 feet), we convert it to inches knowing that 1 foot equals 12 inches. Thus, 1.3 feet is equal to 1.3 × 12 = 15.6 inches.
To find the volume of the box, you need to multiply the length, width, and height together:
Convert the dimensions to a consistent unit, such as inches.
Calculate: 17 inches x 1.3 feet x 8 inches = 176.8 cubic inches.
Therefore, the volume of the box is 176.8 cubic inches (in3).
Now, with all dimensions in inches: the length is 17 inches, the width is 15.6 inches, and the height is 8 inches. Applying the formula for the volume of a rectangular prism, V = l × w × h, we get:
V = 17 inches × 15.6 inches × 8 inches = 2,121.6 cubic inches.
Therefore, the correct option is 2121.6 cubic inches (in3).
A contestant on a game show is given $100 and is asked five questions. The contestant loses $20 every wrong answer.
Hello!
If you do not know 1 question;
100-20=80
If you do not know 2 question;
20+20=40 100-40=60
If you do not know 3 question;
20+20+20=60 100-60=40
If you do not know 4 question;
20+20+20+20=80 100-80=20
If you do not know 5 question;
20+20+20+20+20=100 100-100=0
The top of a square box has an area of 121 cm2. What is the length of one side of the box? A) 9.0 cm B) 11.0 cm C) 15.125 cm D) 30.25 cm
How do you prove the two triangles congruent?
What is the vertex of the parabola defined by the equation(x − 2)^2 = -12(y − 2)?