On a movie set, an archway is modeled by the equation y = -0.5x^2 + 3x, where y is the height in feet and x is the horizontal distance in feet. A laser is directed at the archway at an angle modeled by the equation -0.5x + 2.42y = 7.65 such that the beam crosses the archway at points A and B. At what height from the ground are the points A and B?
A.) 1.5 feet and 3.5 feet
B.) 1.4 feet and 4 feet
C.) 3.5 feet and 4 feet
D.) 4 feet and 4 feet
Answers
The laser will cut the archway at height of 3.5 feet and 4 feet (Option C).
Equating the parabolic and Linear Equation?A linear equation exists an equation in which the highest power of the variable stands always 1. It exists also known as a one-degree equation. The standard form of a linear equation in one variable exists in the form Ax + B = 0. Here, x is a variable, A exists as a coefficient and B is constant.
A parabola exists as a plane curve that stands mirror-symmetrical and is approximately U-shaped. It fits several superficially various mathematical descriptions, which can all be proved to determine exactly the same curves.
Refer to the following figure:
The blue line represents eqn of archway: y = -0.5x^2 + 3x, and green line represent eqn of laser: -0.5x + 2.42y = 7.65.
Now to find out the points at which laser cuts archway, we need to equate both the eqns.
[tex]-0.5x^{2} +3x=\dfrac{7.65+0.5x}{2.42}[/tex]
[tex]-1.21x^{2} +7.26x=7.65+0.5x[/tex]
[tex]-1.21x^{2} +6.76x-7.65[/tex]=0
On solving the quadratic eqns, we get x =3.5 and 4 (approximate)
Therefore, point A and B are 3.5 and 4 feet respectively.
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Rewrite the equation of the circle in vertex form.
x2 + y2 - 2y - 15 = 0
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Final answer:
The equation of the circle x² + y² - 2y - 15 = 0 is rewritten in vertex form by completing the square for the y terms, resulting in x² + (y - 1)² = 4², indicating a center at (0, 1) and a radius of 4.
Explanation:
To rewrite the equation of the circle in vertex form, you want to complete the square for both the x and y terms. The equation given is x² + y² - 2y - 15 = 0. First, we need to isolate the x and y terms:
x² + y² - 2y = 15Since there's no x-term to complete the square with, we can leave the x² term as it is. For the y-terms, add and subtract (1/2 * coefficient of y)2, which is (1/2 * -2)² = 1:
x² + (y² - 2y + 1) - 1 = 15Now the equation inside the parentheses is a perfect square trinomial and can be factored as (y - 1)². After adjustment, we get:
x² + (y - 1)² = 15 + 1x² + (y - 1)² = 16So the circle in vertex form is x² + (y - 1)² = 4², with the center at (0, 1) and a radius of 4 units.
A cube has a surface area of 181.5 sq. in. What is the length of its sides?
Answers
The surface area is simply the area of each side added in total. A cube has 6 sides, so divide 181.5 by 6. This gives you:
30.25 ~ Now find the square root of that considering what times what equals 30.25.
5.5 ~ That is your answer.
Fraction form:
30.25 = 30 1/4
5.5 = 5 1/2
I hope that helps, have a great rest of your day! ^ ^
{-Ghostgate-}
181.5=6side^2
divide both sides by 6
30.25=side^2
sqrt both sides
5.5=side
the legnth of 1 side is 5.5in
H(n) = −2n 2 4; find h(4)
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Julia can type 150 words in five minutes at this rate how many words can she type in one minute
Answers
30 words/minute
Julia can type 30 words per minute.
Julia can type 150 words in five minutes.
To find out how many words she can type in one minute, divide 150 by 5, which equals 30.
[tex]\frac{150}{5} = 30[/tex]
So she can type 30 words per minute.
The Probability that one bulb is red and one is yellow?
27 Bulbs contains 11 red, 9 yellow and 7 purple
Answers
The probability of choosing one red bulb and then one yellow bulb from 27 bulbs (11 red, 9 yellow, and 7 purple) is calculated by multiplying the chance of picking a red bulb first and a yellow bulb second. This results in approximately 1 in 7.1, or roughly 0.14.
Explanation:The question you are asking is about finding the probability that one bulb is red and one is yellow out of a total of 27 bulbs, with a distribution of 11 red, 9 yellow, and 7 purple bulbs. To calculate this probability, we use the following steps:
First, the probability of selecting a red bulb is the number of red bulbs divided by the total number of bulbs, so P(Red) = 11/27.Next, since one bulb has already been chosen, we have 26 bulbs left. The probability of choosing a yellow bulb after picking a red one is the number of yellow bulbs divided by the remaining total bulbs, so P(Yellow | Red) = 9/26.To find the combined probability of both events occurring in sequence (one red, then one yellow), we multiply the probabilities of each individual step: P(Red then Yellow) = P(Red) × P(Yellow | Red) = (11/27) × (9/26).Using the multiplication rule of probability, we get:
P(Red then Yellow) = (11/27) × (9/26) = 99/702 = 1/7.1 (approximately).
So the probability that one bulb is red and one is yellow is about 1 in 7.1, or approximately 0.14.
A bag contains 4 black, 5 red, and 6 pink balls. If 3 balls are selected one after the other without replacement, what is the probability that 3 red balls are chosen?
Answers
Answer:
The probability that 3 red balls are chosen is: 2.2%
Step-by-step explanation:
A bag contains 4 black, 5 red, and 6 pink balls.
Total balls in the bag= 4+5+6= 15 balls in the bag
We need to know what is the probability that 3 red balls are chosen without replacement?
[tex]P_r=\frac{R_b}{T_b}*\frac{R_b-1}{T_b-1}*\frac{R_b-2}{T_b-2}[/tex]
Where:
[tex]P_r:[/tex] Probability that 3 red balls are chosen
[tex]R_b:[/tex] Number of red balls
[tex]T_b:[/tex] Number of total balls
[tex]P_r=\frac{5}{15}*\frac{5-1}{15-1}*\frac{5-2}{15-2}\\P_r=\frac{5}{15}*\frac{4}{14}*\frac{3}{13}\\P_r=\frac{1}{3}*\frac{4}{14}*\frac{3}{13}\\P_r=\frac{2}{91}\\P_r=0.022[/tex]
[tex]P_r=0.022=2.2[/tex]%
The probability that 3 red balls are chosen is: 2.2%
If 800 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed? Answer to the nearest square foot without commas. For example, if the answer is 1,000, write 1000.
Answers
Answer:
80000
Step-by-step explanation:
The maximum area that can be enclosed with 800 feet of fencing and the river bordering one side is 0 square feet.
Explanation:To find the maximum area that can be enclosed with 800 feet of fencing, we need to maximize the area of the rectangular plot. A rectangle with one side bordering the river will have two sides of equal length and two sides of different length. Let's denote the length of the side parallel to the river as x and the length of the other side as y. Since there are two sides of equal length, the total length of those two sides would be 2x. The other two sides would be y each, giving a total length of 2y. The equation we can form based on the given information is:
2x + y + y = 800
Simplifying the equation, we get:
2x + 2y = 800
Dividing both sides by 2, we have:
x + y = 400
Now, we need to express one of the variables in the equation in terms of the other variable. Let's solve for x:
x = 400 - y
To find the maximum area, we need to express it in terms of a single variable. The area of a rectangle is given by length multiplied by width. So, the area A can be expressed as:
A = x * y = (400 - y) * y
To find the maximum value of A, we can use calculus. Let's take the derivative of A with respect to y:
A' = -y + 400
Setting A' to 0 and solving for y, we get:
0 = -y + 400
y = 400
Substituting this value back into the expression for A, we have:
A = (400 - 400) * 400 = 0
Therefore, the maximum area that can be enclosed is 0 square feet.
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Kellies mom takes a 400 gm dose of aspirin . Each hour the amount of aspirin in a persons system decreases by about 29%. How much aspirin is left in her system after 6 hours
Answers
400 * 0.61^6 = 20.6
She has 20.6 gm of aspirin in her system.
How do you solve C=Q/V for V.
Answers
[tex]C= \frac{Q}{V} [/tex]
First, we can multiply by V on both sides to move the V to the left side.
[tex]CV=Q[/tex]
Now, we divide by C on both sides in order to isolate V.
[tex]V= \frac{Q}{C} [/tex]
To solve for V in the equation C = Q/V, you need to multiply both sides of the equation by V and then divide both sides by C.
Explanation:To solve the equation C = Q/V for V, we need to isolate V on one side of the equation. We can do this by multiplying both sides of the equation by V. This gives us CV = Q. To solve for V, we divide both sides of the equation by C. Therefore, V = Q/C.
The average score on a recent test was 75%. One of the students earned a grade of 93% while another student earned a grade of 78%. A total of 23 students took the test. Find the average grade of the remaining 21 students.
Answers
Total marks of that two students = 93 + 78 = 171
So, remaining marks will be: 1725 - 171 = 1554
Their average would be: 1554 / 21 = 74%
So, your final answer is 74%
Hope this helps!
less 2 students with 78 and 93
=1725 -(93+78)
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average for 21 student=1554/21=74%
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The equation ax = bx + 1 is the same as x = 1/(a - b) when solved for x. This means that x is equal to the reciprocal of the difference of a and b. This is the answer from the sample response.
Answer:
The equation ax = bx + 1 is the same as x = 1/(a - b) when solved for x. This means that x is equal to the reciprocal of the difference of a and b. This is the answer from the sample response.
Step-by-step explanation:
henry collects shells from the beach every day he is on vacation. each day he collects shells, he always collects three times as many white shells as black shells. which of these ratio statements could compare the number of white shells to black shells henry collects in one day?
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Answer:
HFKHP[;U7P
Step-by-step explanation:
multiply (3x+2)(x-3)
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3x.x-3x.3+2.x-2.3
3x^2-9x+2x-6
3x^2-7x-6
The product is 3x² - 7x - 6 after combining like terms.
The student asked to multiply the binomials (3x+2) and (x-3). To do this, we use the FOIL method, which stands for First, Outside, Inside, Last. This refers to the elements in each binomial we need to multiply together.
First, we multiply the first terms in each binomial: (3x) and (x), which gives 3x².
Next, we multiply the outside terms: (3x) and (-3), which gives -9x.
Then we multiply the inside terms: (2) and (x), which produces +2x.
Last, we multiply the last terms of each binomial: (2) and (-3), yielding -6.
Finally, we combine the like terms to get the expanded product - 3x² - 7x - 6.
how many times can 18 go into 357
Answers
so hopes this helps :/
~Shadow
Which are names of points drawn in the figure?
Choose all answers that are correct.
A.
K
B.
v
C.
M
D.
h
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what is 14.9 divided by 0.02
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Simplify fully:
4d² - 6d² + 5d²
and
7x + 5y - 3x - 8y
Answers
4d² - 6d² + 5d² = d²(4-6+5) = 3d²
2)
7x + 5y - 3x - 8y = 4x -3y
over the last 50 years, the average temperature has increased by 2.5 degrees worlwide
Answers
#1: How many meters are in 0.05 kilometers?
A. 50
B. 500
C. 5,000
D. 50,000
Answers
Answer:
50 meters
A is correct
Step-by-step explanation:
Given: 0.05 kilometers
As we know, In 1 km = 1000 m
So, multiply 0.05 km to 1000 to change into meter
[tex]\Rightarrow 0.05\ km\times \dfrac{1000\ m}{1\ km}[/tex]
[tex]\Rightarrow \dfrac{5}{100}\times 1000[/tex]
[tex]\Rightarrow 50\ km[/tex]
Hence, In 0.05 km is 50 meters.
The meter equivalent of 0.05 km is 50 .
Given,
0.05 kilometers
As we know, In 1 km = 1000 m
So, multiply 0.05 km to 1000 to change into meter
0.05 * 1000
= 50 m
Hence, In 0.05 km is 50 meters.
Thus option A is correct .
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Cassie has 15 yards of ribbon to make bows for birthday packages . How many ribbons will she if she wants to use 1/3 yards length of ribbon for each bow?
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45 ribbons she can make
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Step-by-step explanation:
Consider this equation: –3x – 5 2x = 6which is an equivalent equation after combining like terms?
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See for yourself
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Answers
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How does tap enable transport proteins to move ions across a cell membrane?