The function, f(x), describes the height of a dome on top of a building, where f(x) is the height from the base of the dome and x is the horizontal distance from where the dome meets the building.
The domain of the function is __ ≤ x ≤ ___
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Answers
The height of the dome of the building is given by
[tex] f(x)=2\sqrt{-x^2+10x} [/tex]. The quantity in the square root should be greater than or equal to 0. We need
[tex] -x^2+10x\geq 0\\
x(10-x)\geq 0\\
0\leq x\leq 10 [/tex].
So the domain is [tex] 0\leq x\leq 10 [/tex]
Answer:
0 ≤ x ≤ 10
Step-by-step explanation:
We cannot take the square root of a negative number. This means we cannot use negative numbers in this equation; this means the lower end is 0.
We can only use x values until the value of the negative square is greater than the value of 10 times the x.
10(1) = 10, which is greater than -(1(1)) = -1.
10(2) = 20, which is greater than -(2(2)) = -4.
10(3) = 30, which is greater than -(3(3)) = -9.
10(4) = 40, which is greater than -(4(4)) = -16.
10(5) = 50, which is greater than -(5(5)) = -25.
10(6) = 60, which is greater than -(6(6)) = -36.
10(7) = 70, which is greater than -(7(7)) = -49.
10(8) = 80, which is greater than -(8(8)) = -64.
10(9) = 90, which is greater than -(9(9)) = -81.
10(10) = 100, which is equal to -(10(10)) = -100. This means this is the cutoff point for this function.
Related Questions
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Mr. McClellan compared the weights (in pounds) of pairs of elk antlers dropped at Mount St Helens NVM and Rocky Mountain NP. He tabulated them in the following data table.
Weight of elk antler pairs at Mount St Helens NVM:
{34, 34, 30, 30, 30, 28, 28, 26}
Weight of elk antler pairs at Rocky Mountain NP:
{40, 38, 36, 36, 36, 36, 34, 32}
(a) Create a line plot for each data set.
(b) Calculate the mean and MAD for each area of collection.
(c) Calculate the means-to-MAD ratio for the two areas of collection.
(d) What inference can be made about the areas in regard to weight of dropped elk antlers? Explain
Answers
B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:
m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8
= 240 ÷ 8
= 30
m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8
= 288 ÷ 8
= 36
In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:
MSH = {|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}
= {4, 4, 0, 0, 0, 2, 2, 4}
RM = {|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}
= {4, 2, 0, 0, 0, 0, 2, 4}
Therefore,
MAD(MSH) = (4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8
= 16 ÷ 8
= 2
MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8
= 12 ÷ 8
= 1.5
C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:
r(MSH) = 30 ÷ 2 = 15
r(RM) = 36 ÷ 1.5 = 24
D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).
A) The two line plots are attached.
B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:
m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8
= 240 ÷ 8
= 30
m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8
= 288 ÷ 8
= 36
In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:
MSH = {|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}
= {4, 4, 0, 0, 0, 2, 2, 4}
RM = {|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}
= {4, 2, 0, 0, 0, 0, 2, 4}
Therefore,
MAD(MSH) = (4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8
= 16 ÷ 8
= 2
MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8
= 12 ÷ 8
= 1.5
C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:
r(MSH) = 30 ÷ 2 = 15
r(RM) = 36 ÷ 1.5 = 24
D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).
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Which measure is equivalent to 2.5 liters? A)2.5 mL B)250 mL C) 2500 mL D)25,000 mL
Answers
we know that
[tex] 1L=1000mL [/tex]
we are given 2.5L
so, to find 2.5L into mL, we will have to multiply both sides by 2.5
[tex] 2.5*1L=2.5*1000mL [/tex]
now, we can simplify it
[tex] 2.5L=2500mL [/tex]
so, option-C.............Answer
What conclusions can you make about numbers in scientific notation with negative exponents?
Answers
Graph the data from the table below. Describe the parent function as linear, square root, cube root, cubic, or quadratic.
Answers
The g(x) function has been scaled by a factor of 2. In other words, each point on g(x) is twice as high as its corresponding point on f(x). Specifically for example, the point (1,1) has been doubled to (1,2). Overall, this vertically stretches out the parent function graph.
Both the parent function f(x) and the other g(x) curve are square root functions.
See the attached image. The blue curve goes through the given points from the table. The red curve is the parent function.
THIS IS SUPER EASY I NEED HELP
Answers
[tex]2^5=2\cdot2\cdot2\cdot2\cdot2=32[/tex]
Answer: [tex]\left(\dfrac{1}{2}\right)^5=\dfrac{1}{32}[/tex]
(1/2) x (1/2) x (1/2) x (1/2) x (1/2)
The answer is .03125 or 1/32
Jess is building a skateboarding ramp in the shape of a triangular prism with the dimensions shown. If Jess wants to cover all faces of the ramp with plywood, how much plywood will he need?
96 square feet
144 square feet
156 square feet
168 square feet
Answers
surface area of the triangular prism=2*area of the base+perimeter of base*height
area of the base=b*h/2
b=3 ft
h=4 ft
area of the base=3*4/2----> 6 ft²
perimeter of the base=3+4+5-----> 12 ft
height of the prism=12 ft
surface area of the triangular prism=2*6+12*12-----> 12+144---> 156 ft²
the answer is
156 ft²
Answer:
C) 156
Step-by-step explanation:
The diameter of a circular placemat is 15 inches. Devon wants to sew a border of lace around the placemat. If the lace he wants is sold by the foot, how many feet of lace will he need to purchase?
Answers
Answer: 47 feet
Write the vertex form of the equation of the parabola which has a vertex of (0,0) and contains the point (1,2). A. Y=2x^2. B. Y=2(x-1)^2. C. Y=x^2. D. Y=(x+1)^2+1
Answers
Here the vertex is at (0,0), so we have y-0 = a(x-0)^2, or y = ax^2
All we have to do now is to find the value of the coefficient a.
(1,2) is on the curve. Therefore, 2 = a(1)^2, or 2 = a(1), or a = 2.
The equation of this parabola is y = 2x^2.
The vertex form of the equation of a parabola with a vertex at (0,0) and passing through the point (1,2) is [tex]y=2x^2.[/tex]
The vertex form of a parabola is given by: [tex]y = a(x - h)^2 + k[/tex] where (h, k) is the vertex of the parabola.
In this case, the vertex is (0, 0), so h = 0 and k = 0.
Therefore, the equation becomes: [tex]y = a(x - 0)^2 + 0.[/tex] Simplifying further, the equation becomes: [tex]y = ax^2[/tex].
Now, we need to find the value of 'a.' To do this, we can use the given point (1, 2). Substitute these values into the equation:
[tex]2 = a(1)^2[/tex].
Therefore, 'a' is 2. So, the final equation in vertex form is: [tex]y = 2x^2.[/tex]
So, the correct answer is A. [tex]Y = 2x^2.[/tex]
Solve the system of equations. y = 7x + 43 y = 2x + 13 a. ( -6, 1) c. ( 6, 1) b. ( 6, -1) d. No solution
Answers
y = 7x + 43
y = 2x + 13
We wanna solve y = 7x + 43 for y in y = 2x + 13
What does that even mean? Well it simply means that we gonna replace y by 7x + 43.
y = 2x + 13
7x + 43 = 2x + 13
Subtract 2x on both sides
7x + 43 - 2x = 2x + 13 - 2x
5x + 43 = 13
Now we can subtract 43 on both sides
5x + 43 - 43 = 13 - 43
5x = -30
Then divide both sides by 5
5x/5 = -30/5
x = -6
Now since we have the value for x, we gonna use that value to find y.
We can do that by substituting -6 for x in y = 7x + 43
But what does that mean? It means that in y = 7x + 43, we gonna replace the x by -6
y = 7x + 43
y = 7(-6) + 43
y = -42 + 43
y = 1
Thus,
The answer is: x = -6 and y = 1
The correct answer is option A (-6,1).
Let me know if you have questions about the answer. As always, it is my pleasure to help students like you.
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Jack needs to save $125 to go to a concert. He has saved $35. He makes $7.50 an hour at his job. With x representing the number of hours, which equation and solution can be used to show how many hours Jack must work in order to have enough money to go to the concert?
A. 125x + 35 = 750; x = 5.75
B. 35x + 125 = 750; x = 18
C. 7.5x + 35 = 125; x = 12
D. 35−7.5x=125;x=6
Answers
He makes $7.50 an hour at his job.
With x representing the number of hours
so equation
7.5x + 35 = 125
7.5x = 90
x = 12
answer
C. C. 7.5x + 35 = 125; x = 12
there are 54 people at the party. 18 of them are wearing red, what percent of them are not wearing red
Answers
54-18 = 36 not wearing red
36 out of 54 = 36/54
36/54 = 0.6666
0.6666 * 100 = 66.67%
Percent wearing red is 66.67%
There are 54 people at the party.
18 people are wearing red which means that 36 people are not wearing red
54 - 18 = 36
The fraction [tex]\frac{36}{54}[/tex] represents the 36 people at the party that are wearing no red. We can find what percent of the people at the party are not wearing red by turning [tex]\frac{36}{54}[/tex] into a percent.
[tex]\frac{36}{54}[/tex] can be reduced to [tex]\frac{2}{3}[/tex] by dividing both the numerator and denominator by the greatest common factor of 36 and 54.
2 ÷ 3 = 0.667
0.667 × 100 = 66.67%
Therefore, 66.67% of the people at the party are not wearing red
Mrs. Sloan is purchasing 3.4 pounds of trail mix that costs $4.25 per pound. How much change will Mrs. Sloan receive if she gives the cashier $20.00.
a. $14.45 b. $5.55 c. $12.55 d. $7.45
Answers
multiply number of pounds purchased by price per pound
= 3.4 pounds * $4.25 per pound
= $14.45 total cost
STEP 2:
subtract total cost of purchase (step 1) from amount she gave cashier ($20.00)
= $20.00 - $14.45
= $5.55 amount received back from cashier
ANSWER: (B) $5.55 received back
Hope this helps! :)
the number of people who attended the spring festival is 799 more than 8 thousands. how many people attended the festival?
Answers
In this question, we are given the information about total number of people but in word equation.
We are given that, 799 more from 8 thousand attend the festival.
When we are given more, we add the number to the number from which it is more.
Here, we will add 799 to 8,000 in order to calculate total number of people who attended the festival
Thus, total number of people who attended the festival = 8,000 people + 799 people = 8,799 people.
Diane is baking cookies. She bakes four dozen sugar cookies, three dozen butter cookies, and two dozen chocolate chip cookies. She gives away 2 dozen sugar cookies, 2.5 dozen butter cookies, and 1.5 dozen chocolate chip how many cookies does she have left? ( Give an exact number of cookies).
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What is the size of the angle in the shaded triangle marked by the arrow
Answers
What do you call a person who makes face all day long
Answers
A clockmaker is the answer
which is a ABBC pattern?
Answers
Answer:
90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you
Step-by-step explanation:
What method could have been used to collect the data?
Answers
Answer: Observation.
12. Other data that could be recorded from the students that could be used to make a box plot include:
-age of the students
-weight of the students
-exam scores
-grades in which they belong to
A probability close to 1/2 indicates a chance event is ________ to occur
Likely, unlikely, or neither likely nor unlikely
Please help
Answers
Which of the binomials below is a factor of this trinomial ? X^2 + x + 12
Answers
x² + x + 12 = 0
x² + x = - 12
x² + x + 1/4 = - 12 + 1/4
x² + x + 1/4 = - 11 3/4
x² + x + 1/4 = - 47/4
(x + 1/2)² = - 47/4
x + 1/2 = +/- √(- 47/4)
x + 1/2 = +/- [tex] \frac{47}{4}i [/tex]
x = 1/2 +/- [tex] \frac{47}{4}i [/tex]
If the constant was a negative, it would be factor-able (is that a word?).
how do i solve 3 (2y-4)=8y+9-9y
Answers
Distribute 3:
6y - 12 = 8y + 9 - 9y
Combine like terms:
6y - 12 = -y + 9
Add y to both sides:
7y - 12 = 9
Add 12 to both sides:
7y = 21
Divide both sides by 3:
y = 3
6y - 12 = 8y + 9 - 9y
Collect the like terms with y.
6y - 12 = -y + 9
Move the variable to the left side and then change its sign.
6y + y - 12 = 9
Now move the constant to the right side and change its sign.
6y + y = 9 + 12
Add the terms on the left side of the equation.
7y = 9 + 12
Add the numbers on the right side.
7y = 21
Lastly,, divide both sides of the equation by 7 to find your final answer.
y = 3
This means that y = 3 is the correct answer to your question.
Let me know if you have any further questions.
:)
Two numbers multiply to be -15 and adds to be 2 what are the numbers?
Answers
[tex]x + y = 2 \\ x \times y = - 15[/tex]
[tex]x + y = 2 \\ x = 2 - y[/tex]
Substitute that into
[tex](2 - y) \times y = - 15 \\ 2y - {y}^{2} = - 15 \\ {y}^{2} - 2y - 15 = 0 \\ (y - 5)(y + 3) = 0 \\ y = 5[/tex]
Substitute that into
[tex]x = 2 - 5 \\ x = - 3[/tex]
Answer : The two numbers are 5 and - 3.
Hope this helps. - M
What is the slope of this line?
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The sum of the ages of two people is 32. The difference is their ages is 4. What is the age of the younger person ?
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Solving for Circumference of a Penny A penny is 1.9 cm wide. What is the circumference of a penny? Approximate using mc001-1.jpg = 3.14 and round the answer to the nearest tenth if necessary.
Answers
Rounding to the nearest tenth, the circumference of a penny is approximately 6.0 cm.
To find the circumference of a penny, we use the formula for the circumference of a circle:
Circumference = π * diameter
Since the penny's width is given (which is the same as the diameter), we can plug in the values:
Circumference = 3.14 * 1.9 cm
Now, calculate the circumference:
Circumference ≈ 5.966 cm
Rounding to the nearest tenth, the circumference of a penny is approximately 6.0 cm.
To know more about circumference:
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write the worlds as an algebraic expression. the width plus twelve. how do i do it?
Answers
Reason/Explanation:
It's asking us to write the words as an algebraic expression. "The width plus twelve." For starters, we don't know what the width is, so we use a variable, X. Now we add 12. So we use X + 12. The width is X, plus twelve.
-DustinBR
You have to find x then add 13
Need Help ASAP..GIVING 15 POINTS TO WHO ANSWERS.IF YOU COPY AND NOT ANSWER YOU WILL GET REPORTED
The original price for a clothes washer and dryer is $999. Which coupon is a better deal? A) SAVE 20% ON ANY WASHER/DRYER COMBO B) SAVE $200 ON ANY WASHER/DRYER COMBO C) SAVE $75 PLUS 5% OFF ON ANY WASHER/DRYER COMBO D) SAVE $50 PLUS 20% OFF ON ANY WASHER/DRYER COMBO
Answers
Mitch does not know the correct answer to two multiple choice questions. The choices are A,B,C, and D. If Mitch just guesses, what is the probability that Mitch will guess both answers correctly?
Answers
1/4 * 1/4 = 1/16
Final answer:
Mitch has a 1/16 probability of guessing both multiple-choice answers correctly when randomly guessing among four options.
Explanation:
If Mitch guesses on two multiple-choice questions with choices A, B, C, and D, the probability of guessing both correctly is calculated as follows: The probability of correctly guessing one question is 1/4 (since there are 4 possible choices, and only one is correct). To find the probability of guessing both correctly, we multiply the probabilities of each independent event. Thus, the probability of guessing the first question correctly AND the second question correctly is 1/4 × 1/4 = 1/16.
7.Kristy baked 18 cookies. She took 2/3 of the cookies to work. How many cookies did she NOT take to work? 4 6 8 12
Answers
2/3 of 18 = 12
18-12=6
18 - 18 * 2/3
18 - 36/3
18 - 12
6
She didn't take 6 cookies to work.
solve the exponential equation
[tex] {10}^{ - x} = {7}^{4x} [/tex]