Answer: To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations:
y = -3x + 8
y = -2x^2 + 7x
We can set the two equations equal to each other and solve for x:
-3x + 8 = -2x^2 + 7x
This simplifies to:
2x^2 - 10x + 8 = 0
Dividing both sides by 2, we get:
x^2 - 5x + 4 = 0
Factoring the left side, we get:
(x - 1)(x - 4) = 0
So the solutions for x are x = 1 and x = 4.
To find the corresponding values of y, we can substitute these values of x into either equation. Let's use y = -3x + 8:
When x = 1, y = -3(1) + 8 = 5
When x = 4, y = -3(4) + 8 = -4
Therefore, the two skaters might collide at the points (1, 5) and (4, -4).
Step-by-step explanation:
- Given a parallelogram has a 78 and sides of 21 cm and 15 cm. Find the length of the longest diagonal.
PLEASE PLEASE HELP ME!!!!!!!!
The parallelogram H’I’J’K is a dilation of the parallelogram HIJK. What is the scale factor of the dilation?
Simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.
PLEASE LOOK AT PICTURE!!!!!!
Answer: 1/3, proper, 1 1/3, not proper.
HELPPPPP PLEASEEEEEE
18. A business invests $10,000 in an
account that earns 3.2% interest
that is compounded quarterly.
What type of function best
represents the growth of the
investment?
◻ linear
◻ quadratic
◻ exponential
19. What is the value of the account
described in Item 18 after 5 years?
Round to the nearest cent.
Answer: Exponential & $11,709.83
Step-by-step explanation:
The growth of the investment can be represented by an exponential function because the interest is being compounded quarterly, which means that the interest is being added to the account balance and the account balance is growing exponentially over time.
The formula for the future value of an investment with continuous compounding is:
A = P e^(rt)
Where A is the future value, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years.
In this case, the principal investment is $10,000, the annual interest rate is 3.2%, and the interest is compounded quarterly, so the quarterly interest rate is 3.2%/4 = 0.8%. The time period is 5 years, so t = 5.
The formula for the future value of an investment with quarterly compounding is: A = P (1 + r/n)^(nt)
Where n is the number of compounding periods per year, which is 4 in this case.
Substituting the values, we get:A = $10,000 (1 + 0.032/4)^(4*5) = $11,709.83
Therefore, the value of the account after 5 years is $11,709.83 rounded to the nearest cent.
If sin a = -1/4 and π < a <3pi/2 and cos b= 5/9 and 0 < b < pi/2, find the exact value of the following. Show all your work and simplify your answers.
sin(a + B) =
Answer:
Step-by-step explanation:
Read the story. A group of sixth-grade students volunteered to pick up garbage at Elver Park for Earth Day. To make it more fun, they set up a contest to see whether girls or boys could pick up the most garbage. The girls won, picking up 8 pieces of garbage for every 5 pieces the boys picked up. Pick the diagram that models the ratio in the story.
We may conclude after answering the presented question that This ratio indicates that the guys picked up 5 pieces of rubbish for every 8 pieces of rubbish picked up by the girls.
what is ratio?In mathematics, ratios demonstrate how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit plate, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, whereas the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of integers a and b represented as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one male and three girls (for every boy she has three daughters), 3/4 are girls and 1/4 are boys.
The ratio in the narrative is represented by the following diagram:
Girls : Boys=8:5
This indicates that the guys picked up 5 pieces of rubbish for every 8 pieces of rubbish picked up by the girls.
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Grace The Brand Jewelry generated the following information from its financial statements:
Earnings after interest and taxes R600 000
Earnings per share R2,50 per share
Shareholder equity R1000 000
Market to book ratio 2,60
What is the company’s market price per share?
Answer:
Step-by-step explanation:
We can use the market-to-book ratio to calculate the company's market price per share.
Market-to-book ratio = Market value per share / Book value per share
Book value per share = Shareholder equity / Number of shares outstanding
We are given the market-to-book ratio as 2.60, and the shareholder equity as R1000 000. We can calculate the book value per share as follows:
Book value per share = R1000 000 / Number of shares outstanding
To calculate the number of shares outstanding, we can use the earnings per share (EPS) formula:
EPS = Earnings / Number of shares outstanding
We are given the earnings per share as R2.50, and the earnings after interest and taxes as R600 000. Substituting these values, we get:
R2.50 = R600 000 / Number of shares outstanding
Solving for Number of shares outstanding:
Number of shares outstanding = R600 000 / R2.50 = 240,000 shares
Now, we can calculate the book value per share:
Book value per share = R1000 000 / 240,000 = R4.17 per share
Finally, we can calculate the market value per share using the market-to-book ratio:
Market-to-book ratio = Market value per share / Book value per share
2.60 = Market value per share / R4.17
Market value per share = 2.60 x R4.17 = R10.83 per share
Therefore, the company's market price per share is R10.83.
Y=3x^2-4x-1 what is the sign of leading coefficient
Answer:The leading term in a polynomial is the term with the highest degree.
Step-by-step explanation:
Step-by-step explanation:
y = 3 x^2 - 4 x - 1
leading coefficient is 3 and its sign is ' + ' or positive
Elena drinks 9 glasses of water during the day. Each glass is 250 milliliters. How many
liters of water does Elena drink during the day? Explain or show your reasoning.
Spar
Answer:
2.25
Step-by-step explanation:
9 × 250 m = 2250 mL
1 L = 1000 m
2250 mL × (1 L)/(1000 mL) = 2.25 L
evaluate [(- 5/4) ^ - 2] ^ 3
Answer:
4096/15625 or
0.262144 or
(4/5)^6
I need to know how to solve this problem and the answer of it.
Answer:
P = 8g⁵ - 15g + 14
Step-by-step explanation:
This question has expressions to represent the side lengths of a triangle.
The side lengths are:
-8g⁵ - 7g
10g⁵ - 8g
6g⁵ + 14
They ask for a simplified expression for the perimeter. The purpose of this question is to combine like terms.
P = s₁ + s₂ + s₃ where s is a side length of the triangle.
P = (-8g⁵ - 7g) + (10g⁵ - 8g) + (6g⁵ + 14)
P = 8g⁵ - 15g + 14
Un cilindro cuya altura es de 1 pie tiene un volumen de 10 pies". ¿Cuál sería el volumen en pies cúbicos para un cilindro con la misma altura pero tres veces el diámetro?
The volume of the second cylinder is 90 square feet.
How to find the volume of the larger cylinder?Here we know that a cylinder whose height is 1 ft has a volume of 10 ft², remember that the volume for a cylinder of radius R and height H is:
V =pi*R²*H
Where p = 3.14
Then the radius here is:
10 = 3.14*R²*1
√(10/3.14) = R
If we triple the diameter we also triple the radius, then the volume of the other cylinder will be:
V = 3.14*(3*√(10/3.14))²*1
V = 90
The volume is 90 square feet.
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K
The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rater.
P = $7000.00, A = $7280.00, t = 1 year
The loan's simple interest rate is 4%.
What is simple interest ?
Simple interest can be defined as a technique used to calculate the proportion of interest paid on a sum over a set time period at a set rate.
To determine the loan's simple interest rate, we can use the simple interest formula:
A = P(1 + rt)
Where
A is the future valueP is the principal r is the interest rate t is the time periodWe can rearrange this formula to solve for the interest rate r:
r = (A/P - 1) / t
Plugging in the given values, we get:
r = ($7280.00/$7000.00 - 1) / 1
r = 0.04 or 4%
Therefore, the loan's simple interest rate is 4%.
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What is the GCF in simplify form
Answer: 9x^2y
the gcf of -63 , 9 and 90 is 9
And the gcf of the variables is x^2 and y
So, 9x^2y
54,825,638 rounded to the nearest ten million
Answer: 50,000,000
Step-by-step explanation:
Given number is 54825638
The number at the tens place is 4 which is less 5. So, round down the value.
rounded value of 54825638 is 50000000.
Therefore, 54825638 rounded to the nearest Hundreds is 50000000.
Write down the equations of the asymptotes of the functions below g() = 3tan (2x) where x = [-90°; 90°]
The equatiοns οf the asymptοtes fοr g(x) = 3tan(2x) x = -π/8, π/8, 3π/8, 5π/8, and 7π/8.
What are asymptοtes?The asymptοte is a line οr curve that a functiοn apprοaches but never crοsses as the independent variable gets clοser tο a specific number οr infinity. A line οr curve that the graph οf a functiοn apprοaches steadily but never meets is referred tο as an asymptοte.
The fοllοwing is the expressiοn fοr the vertical asymptοtes οf the functiοn g(x) = 3tan(2x):
x = (2n + 1)π/4
where n is an integer.
This is because the tangent function approaches infinite when 2x is an odd multiple of [tex]\pi[/tex]/2,
The tangent function, on the other hand, has vertical asymptotes at odd multiples of [tex]\pi[/tex]/2.
So the vertical asymptotes of g(x) in the range of x = [-90°; 90°] are:
x = -π/8, π/8, 3π/8, 5π/8, and 7π/8.
Examining the behavior of the tangent function as x approaches positive or negative infinity can reveal the horizontal asymptotes of the function g(x) = 3tan(2x).
As x approaches odd multiples of /2, the tangent function oscillates between positive and negative infinity, so no horizontal asymptotes exist.
As a result, in the given range, the formulae for the vertical asymptotes of the function g(x) = 3tan(2x) are:
x = -π/8, π/8, 3π/8, 5π/8, and 7π/8.
Therefore, no horizontal asymptotes exist.
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each classroom has 6 rows of 5 desks. how many desks are thre in 45 classrooms?
There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Each classroom has 6 rows of 5 desks.
So the total number of desks in one classroom.
= 6 rows x 5 desks per row
= 30 desks
To find the total number of desks in 45 classrooms, we can multiply the number of desks in one classroom by the number of classrooms.
= 30 desks per classroom x 45 classrooms
= 1,350 desks
Therefore,
There are 1,350 desks in 45 classrooms that each have 6 rows of 5 desks.
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Please help i’ll give brainlist!!
Solve each proportion.
Answer: 12, 32/11
Step-by-step explanation:
3 12
4 32/11
What is the length of the circle's radius (r) if the circle's area is
approximately 400m yd²?
Answer:
11.28m
Step-by-step explanation:
Area = πr^2
Area = 400 = πr^2
r =sqrt ([tex]\frac{400}{\pi }[/tex]) = 11.28
r = 11.28m
or
A line has a slope of 1 and passes through the point (6,10). Write its equation in slope-intercept form.
Answer:
[tex]\huge\boxed{\sf y = x + 4}[/tex]
Step-by-step explanation:
Slope = m = 1
Point = (x,y) = (6,10)
Here, x = 6 and y = 10
Slope-intercept equation:y = mx + c
Where m is slope and c is y-intercept.
Put x, y and m in the above equation.
10 = (1)(6) + c
10 = 6 + c
Subtract 6 from both sides10 - 6 = c
c = 4So,
The slope-intercept form is:y = (1)x + (4)
y = x + 4[tex]\rule[225]{225}{2}[/tex]
Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 145 subjects with positive test results, there are 21 false positive results; among 156 negative results, there are 4 false negative results. If one of the test subjects is randomly selected, find the probability that the subject tested negative or did not use marijuana. (Hint: Construct a table.)
Question content area bottom
Part 1
The probability that a randomly selected subject tested negative or did not use marijuana is enter your response here.
(Do not round until the final answer. Then round to three decimal places as needed.)
Answer:
The probability that a randomly selected subject tested negative or did not use marijuana is 0.589.
Step-by-step explanation:
Trevor used about half of a 5-lb bag of potatoes (2 lb 6 oz). How much did the remaining potatoes weigh?
Answer:
Step-by-step explanation:
f Trevor used 2 lb 6 oz of a 5-lb bag of potatoes, then the weight of the remaining potatoes is:
5 lb = 80 oz (since 1 lb = 16 oz)
Remaining potatoes = Total potatoes - Used potatoes
Remaining potatoes = 80 oz - 2 lb 6 oz
Remaining potatoes = 80 oz - (2 × 16 oz + 6 oz)
Remaining potatoes = 80 oz - 38 oz
Remaining potatoes = 42 oz
Therefore, the remaining potatoes weighed 2 lb 10 oz (or 42 oz).
Lola hosts a podcast about computers, and Franco hosts a podcast about parenting. Both podcasts have a set duration for each episode. Last year, Lola released 17 episodes and Franco released 43 episodes, for a total of 5,645 minutes of content. This year, Lola released 36 episodes and Franco released 43 episodes, which lasted a total of 6,956 minutes. How long is each episode?
Answer:
Let's denote the duration of each episode of Lola's podcast by "L" and the duration of each episode of Franco's podcast by "F".
From the information given, we can write two equations based on the total duration of content for the two years:
17L + 43F = 5,645 (equation 1)
36L + 43F = 6,956 (equation 2)
To solve for L and F, we can eliminate F by subtracting equation 1 from equation 2:
(36L + 43F) - (17L + 43F) = 6,956 - 5,645
Simplifying, we get:
19L = 1,311
Therefore, the duration of each episode of Lola's podcast (L) is:
L = 1,311 / 19
L ≈ 69.0 minutes
To find the duration of each episode of Franco's podcast (F), we can substitute the value of L into either equation 1 or 2:
17L + 43F = 5,645
17(69.0) + 43F = 5,645
1,173 + 43F = 5,645
43F = 4,472
F = 4,472 / 43
F ≈ 104.0 minutes
Therefore, each episode of Lola's podcast is approximately 69.0 minutes long, and each episode of Franco's podcast is approximately 104.0 minutes long.
Investing $1,000 at a 5% annual interest rate for 6 years, compounded every two months,
yields $1,348.18. Without doing any calculations, rank these four possible changes in order
of the increase in the interest they would yield from the greatest increase to the least
increase:
• Increase the starting amount by $100.
• Increase the interest rate by 1%.
• Let the account increase for one more year.
• Compound the interest every month instead of every two months.
Once you have made your predictions, calculate the value of each option to see if your
ranking was correct.
Answer:
Step-by-step explanation:
Ranking:
Compound the interest every month instead of every two months.
Increase the interest rate by 1%.
Let the account increase for one more year.
Increase the starting amount by $100.
Calculations:
If the interest is compounded monthly instead of every two months, the final value would be $1,357.36, which is an increase of $9.18 compared to the original value.
If the interest rate is increased to 6%, the final value would be $1,411.58, which is an increase of $63.40 compared to the original value.
If the account increases for one more year at the same interest rate, the final value would be $1,435.09, which is an increase of $86.91 compared to the original value.
If the starting amount is increased by $100, the final value would be $1,421.61, which is an increase of $73.43 compared to the original value.
2. Natasha interviewed with 5 companies this week because she is planning on switching companies. Her projected earnings per hour from the companies are written below. 25.13 42 53.5 35.7 47.8 Which inequality represents her earnings, e, from any of the companies she interviewed with? a. e < 53 b. e < 56.7 c. e < 38 d. e< 53.57
the correct option for this question is (a) e < 53.
Why it is?
The inequality that represents Natasha's earnings, e, from any of the companies she interviewed with is:
e < 53.5
This is because her projected earnings per hour range from $25.13 to $53.5, and the maximum value is $53.5. So, her earnings from any of the companies cannot be greater than $53.5 per hour. Therefore, the correct answer is option (a) e < 53.
Earnings are the amount of money that a person earns from their work, business, investments, or other sources of income. This can include salaries, wages, commissions, bonuses, and profits, among others.
Earnings are typically reported as gross income, which is the total amount earned before taxes and other deductions are taken out. It is an important measure of a person's financial well-being and is often used to determine eligibility for credit or loans. Earnings can vary widely depending on a person's job, level of experience, education, and industry, among other factors.
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Complete the following table:
Note: Do not round intermediate calculations. Round your final answers to the nearest cent.
Chain discount is a type of discount offered by a seller to a buyer for purchasing a certain amount of goods or services in a series of transactions. The discount is applied incrementally as the buyer meets specific purchasing thresholds.
What is the chain discount?Chain discounts are often used to encourage larger purchases and build customer loyalty. They can be beneficial for both the buyer and the seller, as the buyer receives a discount and the seller increases their sales volume.
Item: Trotter treadmill
List price: $ [tex]3,000[/tex]
Chain discount: [tex]9/4[/tex]
To calculate the net price, we first need to determine the amount of the chain discount.
Chain discount = List price x Chain discount rate
Chain discount = $ [tex]3,000 \times 9/4[/tex]
Chain discount = $ [tex]6,750[/tex]
The net price is the list price minus the chain discount:
Net price = List price - Chain discount
Net price = $ [tex]3,000[/tex] - $6,750
Net price = -$3,750
Therefore, The Net price is = -$3,750
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Need help with the questions
1. Calculating the output when using -6 as the input, we have:
Rule 1: subtract 7 = -13
Rule 2: square the input = 36.
Rule 3: divide by 3 = 12
Rule 4: divide the input into 3 = -2
Rule 5: write π = -2π
Rule 6: volume of a cube = -216cm³
What is function rule?A function rule is a mathematical expression that describes how to calculate the output value of a function based on its input value. It can be thought of as a set of instructions that tell you what to do with the input value to get the output value.
2. a. True. Speed is the ratio of distance traveled to the time taken to travel that distance. In this case, the distance is fixed at 100 meters, so speed is solely dependent on time. For each value of time, there is only one corresponding value of speed, making it a function.
b. False. While time and distance are related in the formula for speed, time is not a function of distance in this case. Each student's time is independent of the distance they cover, and the same distance is covered by all students (100 meters). Therefore, for any given distance, there are multiple possible values of time, making it not a function.
c. False. The number of students racing is not related to their speed. Each student's speed depends solely on their individual time, which is not affected by the number of other students racing.
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What is the value of x in the solution to this system of equations?
5x−5y=120
y=−7x+8
Enter your answer in the box.
x =
Answer:
X is 4.
Step-by-step explanation:
Hope this helps!
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Answer:
There is 5% of the juice left.
Step-by-step explanation:
We know that originally, the container had 80 oz of orange juice, this is 100% in our case.
Then we can write a relation:
80 oz = 100%
Now there are 4 ounces left, in the same way as before, we can write this as:
4 oz = X%
We want to find X%
First, let's write our equations:
4 oz = X%
80 oz = 100%
We can take the quotient between these two equations to get:
(4oz/80oz) = (X%/100%)
We need to solve this for X%, then we get:
(4oz/80oz)*100% = X% = 5%
This means that 4 oz is 5% of the initial volume of the juice container.
Then we can conclude that there is 5% of the juice left.
the soccer team manager plans to have 2 gallons of water for every 4 players on the team during practice. determine whether the statements about ratios are true or false.
A. The team manager needs 1 gallon of water for every 1 player
` true or false
B. The ratio of number of players to gallons of water is 2:1
` true or false
C. The team manager ould need 4 gallons of water for 10 players
` true or false
D. For 30 players, the team manager would need 15 gallons of water ` true or false
Answer:
A.=False
B.=True
C.=False
D.=True
Step-by-step explanation:
The original ration is 2 gallons of water for 4 players.
Each player requires 1/2 gallon of water.
To get the amount of water needed multiply 1/2 by the amount of players.
1*(1/2) does not equal 1
2*(1/2) equals 1
10*(1/2) does not equal 4
30*(1/2) equals 15
PLEASE ANSWER ASAP THIS QUESTION IS ALOT OF POINTS
The graph is increasing from 0 minutes to 40 minutes, decreasing from 40 minutes to 80 minutes, and constant from 80 minutes to 200 minutes.
What is increasing?The rate of global warming is increasing. Every year, average global temperatures continue to rise, leading to more extreme weather events and disruptions to the environment. This has been caused by human activities, such as burning fossil fuels, which release carbon dioxide and other greenhouse gases into the atmosphere. These gases trap heat, leading to a rise in temperatures.
The domain of the relation is the set of all time values, ranging from 0 minutes to 200 minutes. The range of the relation is the set of all depth values, ranging from 0 feet to 8 feet.
The graph represents a function because for every value of time, there is exactly one corresponding value of depth.
The graph shows the depth of water in a horse trough over a certain amount of time. The graph starts at 0 feet and increases to a maximum of 8 feet over the first 40 minutes. After 40 minutes, the depth of the water starts to decrease until it reaches a minimum of 2 feet at 80 minutes. After 80 minutes, the depth of the water remains constant at 2 feet until the end of the graph at 200 minutes.
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