The quadratic equation with roots -1 and 3 and a leading coefficient of 1 is: [tex]f(x) = x^2 - 2x - 3[/tex]
To write a quadratic equation with roots -1 and 3, we can use the factored form of a quadratic equation:
A quadratic equation in factored form looks like this:
[tex]f(x) = a(x - r1)(x - r2)[/tex]
where:
f(x) is the quadratic function,
a is the leading coefficient,
r1 and r2 are the roots of the quadratic equation.
Given the roots -1 and 3, the factored form of the quadratic equation is:
[tex]f(x) = a(x - (-1))(x - 3)[/tex]
Now, you mentioned that the leading coefficient (a) is 1. So we can rewrite the equation as:
[tex]f(x) = 1(x + 1)(x - 3)[/tex]
Now, we can expand the equation to its standard form:
[tex]f(x) = (x + 1)(x - 3)[/tex]
Using the FOIL method (First, Outer, Inner, Last):
[tex]f(x) = x^2 - 3x + x - 3[/tex]
Simplify:
[tex]f(x) = x^2 - 2x - 3[/tex]
So, the quadratic equation with roots -1 and 3 and a leading coefficient of 1 is: [tex]f(x) = x^2 - 2x - 3[/tex]
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The first recorded tempature is 109F. Four hours later the second tempature is 58F . What is the change in tempature
Carl’s Cable Company charges $55 for monthly service plus $4 for each pay-per-view movie. Teleview Cable Company charges $110 per month with no fee for movies. For what number of movies is the cost of Carl’s Cable Company less than the cost of Teleview?
The number of movies for which the cost of Carl's Cable Company is less than the cost of Teleview is about 13.
What is inequality?The relation between two unequal expressions is defined as inequality.
Given, Carl's Cable Company charges $55 for monthly service and $4 for each movie.
Let the number of movies be x, then the total charge for Carl's Cable Company is:
Carl's Cable = 55 + 4x
The cost of Teleview Cable Company is $110.
Therefore, the cost of Carl's Cable Company is less than the cost of Teleview if:
55 +4x < 110
4x < 110 - 55
4x < 55
x < 55/4
x < 13.75
Hence, the number of movies for which the cost of Carl's Cable Company is less than the cost of Teleview is about 13.
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Final answer:
Carl's Cable Company is cheaper than Teleview Cable Company when the number of pay-per-view movies watched is less than 14. As we can't watch a fraction of a movie, Carl's Cable is less expensive for up to 13 movies.
Explanation:
To determine for what number of movies is the cost of Carl's Cable Company less than the cost of Teleview, we set up an inequality based on the cost structures provided. Let m represent the number of pay-per-view movies.
Carl's Cable Company: $55 + $4m
Teleview Cable Company: $110
To find the number of movies where Carl's is cheaper, we want to find when:
$55 + $4m < $110
Now we solve for m:
Subtract $55 from both sides to isolate the variable term: $4m < $110 - $55
Simplify the right side: $4m < $55
Divide both sides by $4 to solve for m: m < $55 / $4
Simplify: m < 13.75
Since m must be a whole number (you can't watch a fraction of a movie), Carl's Cable is cheaper for up to 13 movies.
Inverse Distributive property of 6x + 108
Julia spends $2.25 on gas for her lawn mower. She earns $14.00 mowing her neighbor's yard. What is Julia's profit?
what is the LCM of 3 and 8
the length of the kitchen counter of Sal's house is 9 times the length of a book. The length of a book is 8 inches. What is the length, /, of the kitchen counter? Draw a picture and write an equation to solve
wildlife protection groups buld bat houses to help sve bate one bat house holds about 300 bats larry says 12 bat houses hold about 4500 bats do you agree
What is the value of 0 in 601,199
The drag force F on a boat varies jointly with the wet surface area A of the boat and the square of the speed s of the boat. A boat with a wet surface area of 50ft2 traveling at 7mph experiences a drag force of 98N . Find the wet surface area of a boat traveling 7.5mph and experiencing a drag force of 135N .
Final answer:
The wet surface area of the boat is approximately 69.7ft^2.
Explanation:
The drag force on a boat varies jointly with the wet surface area and the square of the speed of the boat. This can be represented by the equation:
F = k · A · s^2
where F is the drag force, A is the wet surface area, s is the speed, and k is a constant of variation.
To find the wet surface area of a boat traveling at 7.5mph and experiencing a drag force of 135N, we can set up the following proportion:
(98N) ÷ (50ft^2) = (135N) ÷ (x ft^2)
Cross-multiplying and solving for x, we find that the wet surface area of the boat is approximately 69.7ft^2.
DIVIDING ALGEBRAIC FRACTIONS
a^2-7a-18/4a^3 divided by a^2-4a-45/2a^3-4a^2 multiplied by a^2+3a-10/a^2-4+4
Answer:
a+2/2a
Step-by-step explanation: this is the correct answer
A seller has a house that is 1700 ft^2. The neighborhood comps show the line of best fit to be y=0.074x + 50.48. What is a fair price for this house?
Using the line of best fit, it is found that a fair price for the house is of $176,280.
What does the line of best fit states?It states that the fair price for a house of x square feet, in thousands of dollars, is given by:
y = 0.074x + 50.48.
In this problem, we have a house of 1700 ft^2, hence the fair price in thousands of dollars is given by:
y = 0.074(1700) + 50.48 = 176.28.
Which is a fair price of $176,280.
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Answer:199,000
Step-by-step explanation:
A certain brand of coffee comes in two sizes. An 11.3 -ounce package costs $2.88 . A 27.8 -ounce package costs $6.48 . Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
To calculate the unit price for each coffee package, you divide the total cost by the number of ounces. The 11.3-ounce package has a unit price of about $0.255 per ounce, and the 27.8-ounce package has a unit price of about $0.233 per ounce. The 27.8-ounce package is the better buy with a lower unit price.
Explanation:To find the unit price for each size of coffee package, you divide the cost by the number of ounces.
For the 11.3-ounce package:
Unit price = Total price / Number of ouncesUnit price = $2.88 / 11.3 ouncesUnit price ≈ $0.255 cents per ounce (rounded to the nearest cent)For the 27.8-ounce package:
Unit price = Total price / Number of ouncesUnit price = $6.48 / 27.8 ouncesUnit price ≈ $0.233 cents per ounce (rounded to the nearest cent)Comparing the unit prices, the 27.8-ounce package is the better buy based on the lower unit price.
To find the unit price, divide the cost by the number of ounces. The 27.8-ounce package is the better buy based on a lower unit price.
Explanation:To find the unit price for each size of the coffee, we divide the cost by the number of ounces. The unit price of the 11.3-ounce package is $2.88 divided by 11.3, which is approximately $0.255.
The unit price of the 27.8-ounce package is $6.48 divided by 27.8, which is approximately $0.233.
Based on the unit price, the 27.8-ounce package is the better buy as it has a lower unit price than the 11.3-ounce package.
After a lesson on exponents,Tia went home and said to her mom,"I learned that 10 to the power of 4 is the same as 40,000." She has made a mistake in her thinking. Use words,numbers, or a place value chart to help Tia correct her mistake. Please show the actual solution
The perimeter of a trapezoid is 39 – 7. Three sides have the following
lengths: 9, 5 + 1, and 17 – 6.
What is the length of the fourth side?
Leon evaluated the expression (–4a – 6) + a2 for a = 8. (-4(8) - 6) + 82 (-32-6) + 82 (-38) + 82 (-38) + 16 –19 + 16 –3 Analyze Leon's work. Check all that apply. Leon should have subtracted inside the parentheses before he multiplied. The expression inside the parentheses should be simplified to –26 instead of –38. Leon multiplied 8 by 2 when he should have raised 8 to a power of 2. The multiplication of two negative values in step 4 should result in a positive value. The correct answer should be 35.
Answer:
c,d,e
Step-by-step explanation:
Final answer:
Leon should have simplified the expression inside the parentheses before adding -38 and 64.
Explanation:
Leon evaluated the expression (–4a – 6) + a2 for a = 8.
Substituting a = 8 into the expression, we get (-4(8) - 6) + 82.
Simplifying the expression, we have (-32 - 6) + 64.
Combining like terms, we get -38 + 64.
Finally, adding -38 and 64 gives us 26.
Can you state the exact probability that y will fall between 195 and 205
The final answer is that there's a 38.29% probability that [tex]\( y \)[/tex] will fall between 195 and 205.
Let's break down the calculation step by step.
1. First, we need to determine the mean (average) and standard deviation of the data set. Let's assume we have a normal distribution with a mean (μ) of 200 and a standard deviation (σ) of 10.
2. Next, we'll use the Z-score formula to standardize the values of 195 and 205.
[tex]\( Z = \frac{{X - \mu}}{\sigma} \)[/tex]
[tex]For \( X = 195 \):[/tex]
[tex]\( Z_{195} = \frac{{195 - 200}}{10} = -0.5 \)[/tex]
[tex]For \( X = 205 \):[/tex]
[tex]\( Z_{205} = \frac{{205 - 200}}{10} = 0.5 \)[/tex]
3. After standardizing, we can look up the corresponding probabilities in the standard normal distribution table (Z-table) or use a calculator/tool that provides this information.
4. The Z-table shows that the probability of Z being between -0.5 and 0.5 (inclusive) is approximately 0.3829 (or 38.29%).
So, the exact probability that [tex]\( y \)[/tex] will fall between 195 and 205 is 38.29%.
Explanation:
1. We started by identifying the mean and standard deviation of the data set, which are essential parameters for working with normal distributions.
2. Using the Z-score formula, we standardized the values of 195 and 205 to Z-scores, allowing us to compare these values on a standard normal distribution.
3. By referencing the Z-table or using a tool, we found that the probability of Z falling between -0.5 and 0.5 is 0.3829 (38.29%).
4. Therefore, the final answer is that there's a 38.29% probability that [tex]\( y \)[/tex] will fall between 195 and 205.
Complete Question:
Can you state the exact probability that y will fall between 195 and 205?
Find the zeros of the function
f(x)=2x^2-4x-2.9 to the nearest hundredth
What is the greatest common factor of 28, 48, and 64?
The greatest common factor of 28, 48, and 64 is, 4
We have to given that,
To find the greatest common factor of 28, 48, and 64
Now, We can find prime factor all of the numbers.
Then, collect the factors which appear in all three lists:
28 = 2 x 2 x 7
48 = 2 x 2 x 2 x 2 x 3
64 = 2 x 2 x 2 x 2 x 2 x 2
Here, The only factor which appears in all lists is 2.
It appears twice in the first number,
So, the greatest common factor of 28, 48, and 64 is 2 x 2 = 4
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Which is the graph of a logarithmic function?
A B C or D
Answer-
The D plot represents the logarithmic function.
Solution-
1st plot represents the rectangular hyperbola (with vertical asymptote at x=3 and horizontal asymptotes at y=0),
[tex]f(x) =\frac{1}{x-3}[/tex]
2nd plot represents the straight line (passing through origin and slope 1/5),
[tex]f(x)=\frac{x}{5}[/tex]
3rd plot represents the parabola (vertex at 3, 0),
[tex]f(x)=\frac{1}{c} (x-3)^{2}[/tex] (where c is a constant)
4th plot represents the logarithmic curve,
[tex]f(x)=c\log x[/tex] (where c is a constant)
∴ The 4th graph is a graph of a logarithmic function.
Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.
Megan solved a similar equation below. Is Megan's solution correct? Explain why or why not.
3(2x − 4) = 5x − 1
6x − 12 = 5x − 1
11x − 12 = –1
11x = 11
x = 1
can someone do it step by step?
When you use the Distributive Property, we will find...
5x - 4 = -6x - 4
Eliminate 4 by adding it to both sides.
5x = -6x
Add 6x to both sides and we get 11x = 0.
11x = 0
Divide both sides by 11.
x=0
The only mistake Megan made was when adding 5x with Megan accidentally subtracting 5x from the other side.
For this problem:
3(2x − 4) = 5x − 1
Distribute
6x - 12 = 5x - 1
Add 1 to both sides
6x - 11 = 5x
Subtract 6x from both sides
-11 = -x
Divide both sides by -1.
x = 11.
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A 15 foot ladder is leaning against a wall. if the foot of the ladder is sliding away from the wall at a rate of 10 ft/sec, at what speed is the top of the ladder falling when the foot of the ladder is 9 feet away from the base of the wall?
A baseball player went up to bat 250 times in a season. He hit the ball 100 times. Find the rate of balls hit to times at bat. Express as a simplified fraction.
a. 2/5 b.5/2 c. 2/3 d. 3/5
Final answer:
To find the rate of balls hit to times at bat, divide 100 hits by 250 at bats, simplifying the fraction by dividing both numerator and denominator by 50, resulting in a simplified fraction of 2/5.
Explanation:
The rate of balls hit to times at bat can be found by dividing the number of hits by the number of times at bat. In this case, the baseball player hit the ball 100 times out of 250 times at bat.
To find the simplified fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 50:
100 ÷ 50 = 2 and 250 ÷ 50 = 5.
Thus, the simplified fraction of the rate of balls hit to times at bat is 2/5.
Currently, the area of Oak Park is represented by (9x2 + 6x + 9). The city will be expanding the park this summer. The area of the expansion is represented by 8x − 7. Which polynomial expression represents the total area of Oak Park after the expansion?
Answer:
9x2 + 14x + 2
Step-by-step explanation:
Combine like terms
(9x2 + 6x + 9) + (8x −7)
9x2 + 14x + 2
Does this table represent a function?
Marty is selling her 2,950 square foot house and wants to list it for the average price per square foot for houses stills in her area. Based on the table that shows the last five houses sold, at what price will Marty list her house? (Round to nearest hundreds)
Answer:
516
Step-by-step explanation:
If six different chips are to placed on the board, how many different layouts are possible?
A long year-end status report for work is 80 pages long. You need to print 14 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.66 each.
To print 14 copies of an 80-page report, you would need 3 reams of paper, costing a total of $10.98.
To calculate the cost of the paper for printing reports, we will need to determine the total number of pages being printed, how many reams that equates to, and then calculate the cost based on the price per ream. First, we calculate the total pages: 80 pages per report imes 14 copies = 1120 total pages. Next, we determine how many reams of paper are needed: 1120 total pages ÷ 500 pages per ream = 2.24 reams. Since paper is sold by whole reams, we will need to purchase 3 reams to have enough paper.
The cost of the paper will be 3 reams x $3.66 per ream = $10.98. Therefore, the cost for the paper needed to print the 14 reports will be $10.98.
the scores on an exam are normally distributed with a mean of 74 and a standard deviation of 7. what percent of the score are less than 81?
A. 50%
B. 84%
C. 13.5%
D. 16%
Your answer is B. 84% :)
You know that a number 8 less than 60 is the number 52. so, you could write your answer from the previous part as, "what number can you multiply by 4 to get 52
a spider is 6mm long. what fractional part of 1 centimeters is 6 millimeters