An arch is in the shape of a parabola. It has a span of 96 feet and a maximum height of 8 feet.Find the equation of the parabola. ______________Determine the distance from the center at which the height is 2 feet. ___________
Answers
We know the equation of a parabola can be written as
y = a(x-b1) (x-b2) where a is a constant and b1 and b2 are the zeros
y = a ( x - 48) ( x - -48)
y = a ( x-48) (x+48)
Now when x = 0 y = 8
8 = a ( 0-48) ( 0+48)
8 = a (-2304)
-8/2304 = a
-1/288 = a
y = -1/288 ( x-48) (x+48)
This is the equation for the parabola
Now let y = 2
2 = -1/288 ( x-48) (x+48)
Multiply each side by -288
-576 = (x-48)(x+48)
FOIL
-576 = x^2- 2304
ADD 2304 to each side
1728=x^2
Take the square root of each side
24 sqrt(3) = x
24 sqrt(3) ft
41.569 ft
Related Questions
(4+3i)-(2-i)Simplify, leave in a+bi form
Answers
The given expression is
(4 + 3i) - (2 - i)
We would simplify the terms inside the parentheses. The negative sign(- 1) outside the second parentheses would be used to multiply each term inside. We have
4 + 3i + - 1 * 2 + - 1 * - i
4 + 3i - 2 + i
By collecting like terms, we have
4 - 2 + 3i + i
2 + 4i
Thus, the answer in a + bi form is
2 + 4i
Leila drove to the mountains last weekend. There was heavy traffic on the way there and the trip took 7 hours. When Leila drove home, there was no traffic and the trip only took 4 hours. If her average rate was 27 miles per hour faster on the trip home, how far does Leila live from the mountains
Answers
We have the next formula
[tex]d=r\cdot t[/tex]where d is the distance, r is the rate and t is the time.
For the trip going
d=r*7
For the trip returning
d=(r+27)*4
Then we solve
7r=4r+108
We solve for r
7r-4r=108
3r=108
r=36
Then for d
d=36*7
d=252 miles
ANSWER
she lives 252 miles far from the mountains
Need help. Not understanding how to start with each of these
Answers
Given
mean = 84 pounds
standar deviation = 13 pounds
Procedure
a. New hippo weighs between 90 and 109 pounds
Areas under portions of a normal distribution can be computed by using calculus. Since this is a non-mathematical treatment of statistics, we will rely on computer programs and tables to determine these areas.
[tex]\begin{gathered} \mu=84 \\ \sigma=13 \\ \end{gathered}[/tex]Between 90 and 109
Results:
Area (probability) = 0.295
b. What weight corresponds with the 6th percentile?
The score you have entered means that the hippo is at the sixth percentile – their percentile rank is 6%
Given P(xZ = -1.555
The value of the z-score tells you how many standard deviations you are away from the mean.
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ x=z\sigma+\mu \\ x=-1.555\cdot13+84 \\ x=63.785 \end{gathered}[/tex]63.785 is the weight for the 6th percentile
c. What percentages of hippos are born weighing 27 pounds or less?
Z = (27 - 84)/13
Z-score = -4.38462
0% of hippos are born at 27 pounds or less
The sum of two numbers is 26. The larger number is one less than twice the smaller number. Find the numbers.
Answers
Answer:7,9
Step-by-step explanation: The smallest number is 7 and the biggest number is 9
HELP PLEASE and please give out a good answer. Which ones are right? Or wrong?
Answers
You have the following equation for model the amount of money raised by selling concessions related to the number of fans:
y = 5.2x - 20
The previous equation has the form of a line y =mx + b, where m is the unit rate of change and b a constant value.
The first sentence is true because in the given situation m = 5.2 and it is the unit rate of change.
The second sentence is false because the constant -20 is independent of the number of fans.
The third sentence is true because if no fans are attended, then x=0 and
y = 5.2*0 - 20
y = -20
that is, there is a loss of money.
Use the information from the previous question to answer this question now that you know the length of the missing side of the triangle, find the actual distance. Since each unit on the grid is zero. 5 mile, the ferry will travel about blank miles
Answers
Solution
find the actual distance. Since each unit on the grid is 0.5 mile, the ferry will travel about
Length of the missing side of the triagle = 10.2
Unit on the grid = 0.5mile
[tex]\begin{gathered} 1\text{unit -}\longrightarrow\text{ 0.5 mile} \\ 10.2\text{unit}--\longrightarrow x \\ x=\frac{10.2\times0.5}{1} \\ x=5.1 \end{gathered}[/tex]Hence the correct answer is Option C
Which of the following functions best models the data shown in the scatterplot below? y=3x+5y=x2+10y=x+8y=2x+
Answers
Given:
a graph is given
Required:
To simplify which option is correct
Explanation:
From the graph we know the model should be line. And it passes through (15,60)
if the model is y=x+8 , y =15+8=23
there is too much difference between 23 and 60, so y=x+8 is wrong
and y=3x+5 is right
Required answer:
y=3x+5
Which point is a solution to the system of inequalities below?A. (1,2)B. (4,7)C. (0,3)D. (-1,1)
Answers
For this problem we have the following two inequalities given:
[tex]x+2y\ge4\text{, y}-2x<0[/tex]And we want to find the point of solution to the system of inequalities and for this case we can work with equations
[tex]x+2y=\text{4 (1) }[/tex][tex]y-2x=\text{ 0 (2)}[/tex]If we solve for x from equation (1) we got:
[tex]x=\text{ 4}-2y\text{ (3)}[/tex]And replacing equation (3) into equation (2) we got:
[tex]y-2(4-2y)=\text{ 5y}-8=\text{ 0}\rightarrow y=\text{ }\frac{8}{5}=\text{ 1.6}[/tex]And solving for x we got:
[tex]x=\text{ 4}-(2\cdot1.6)\text{ = 0.8}[/tex]So then the intersection point between the two lines is (0.8,1.6). If we analyze all the possible options we have this:
(1,2)
Determine if the two triangles are congruent.• If they are, complete the congruence statement; and identify how they are congruent.• Otherwise, select "Not Congruent" for BOTH drop downs.Be sure to identify any corresponding angles or sides that you know are congruent!AniBby[ Select ]AACB ZA [Select ]
Answers
Triangle ACB is congruent with triangle DCB by SAS
Because they have two sides of equal lenght (AC - DC and common side CB) and an agle of equal measure (A - D)
a card is from a standard deck of cards is chosen at random, then a coin is tossed. what is the probability of getting ace and tails!?
Answers
A standard deck of cards consists of 52 cards with 4 aces.
The probability of getting an ace in a pack of the standard deck is;
[tex]P_1=\frac{4}{52}=\frac{1}{13}[/tex]Find two solutions for the equation 4x+3y=24 , draw it's graph .
Answers
The equation of consideration is:
[tex]4x\text{ + 3y = 24}[/tex]Since two unknowns ( x and y) are given in just one equation, to get each set of the solutions, we are going to choose a value of x and get a corresponding value of y
Let x = 0, to get the value of y at point x = 0, substitute this value of x into the given equation:
[tex]4(0)\text{ + 3y = 24}[/tex][tex]3y\text{ = 24}[/tex][tex]y\text{ = }\frac{24}{3}\text{ = 8}[/tex]The first set of solutions is therefore:
[tex]x\text{ = 0, y = 8}[/tex]To get the second set of solution, let us choose x = 3 and substitute this value into the given equation:
[tex]4(3)\text{ + 3y = 24}[/tex][tex]12\text{ + 3y = 24; 3y = 24 - 12; 3y = }12;\text{ y = 12/3; y = 4}[/tex]The second set of equation is:
[tex]x\text{ = 3, y = 4}[/tex]The above is the graph showing the two sets of solutions
Point M is located at (-4,-6)What is located 4units from point M?
Answers
We have a point M located at (-4,-6).
We have to identify what is located 4 units from point M.
We can draw a circle with center at M with a radius of 4 units.
The circumference will include all the points that are 4 units away from M.
We can draw them as:
We can see that none of the points listed is 4 units from M.
The y-axis is located 4 units away from M.
Other point that is 4 units from M is for example (-4,-2).
bill:$42,tax 9%,tip,18%
Answers
We have the next information
Bill $42
tax 9%
tip 18%
if the total is 42
the tax will be
42*.09=$3.78
the tip will be
42*.18=$7.56
Fill in the missing number to complete the pattern.18, 12, _ , 0
Answers
The given pattern starts with an 18, then we have a 12, we can go from 18 to 12 by subtracting 6 from the initial number. By subtracting 6 from 12, we get the number that goes on the right side of 12, that is:
12 - 6 = 6
Then, fill the missing number with a 6.
18, 12, 6, 0
The wholesale price for a pillow is $4.50 . A certain department store marks up the wholesale price by 90% . Find the price of the pillow in the department store. Round your answer to the nearest cent, as necessary.
Answers
The wholesale price for a pillow is $4.50 .
The store marks up the wholesale price by 90%.
That is, 90% of $4.50 has been aadded with the wholesale price as the store price (SP).
Therefore we have, '
[tex]Sp=4.50+\frac{90}{100}\times4.50=8.55[/tex]Thus, the store price is $8.55
Find the area of the shaded region in the figure. Use the pi key for pi.The area of the shaded region in the figure is approximately: (Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
Hello there. To solve this question, we'll need to remember some properties on geometry and areas of figures.
First, the area of a square is equal to the square of its side length.
The area of a circle is given by pi * the square of its radii, being this radii half of the diameter:
In this case, the side of the square is 1.5' and the diameter of the circle is 5.8'.
Finding the radii of the circle:
r = d/2 = 5.8'/2 = 2.9'
Calculating the area of the square and the circle
Asquare = 1.5² = 2.25 and Acircle = pi * 2.9² = pi * 8.41
The area of the shaded region is calculated by the difference between the area of the circle and the square
Ashaded = Acircle - Asquare
Ashaded = 8.41pi - 2.25
This is the area of the region we've been looking for.
what is the minimum amount of shrink wrap she will need?
Answers
we know that
To find out the minimum amount of shrink, you need to calculate the surface area
The surface area of the figure is equal to the area of its two triangular faces and its three rectangular faces
so
SA=2[(1/2)(4)(2.2)]+(3)(4)+(2.2)(3)+(3)(4.6)
SA=8.8+12+6.6+13.8
SA=41.2 in^2
answer is option Cin a class, 2/3 of the pupils are boys. If there are 15 more boys than girls, how many pupils are there in the class (use equation method)
Answers
Solution
Step 1:
Let the number of pupils = n
[tex]\begin{gathered} Number\text{ of boys = }\frac{2}{3}n \\ Number\text{ of girls = }\frac{2}{3}n\text{ - 15} \end{gathered}[/tex]Step 2:
Write an equation to find the value of n
[tex]\begin{gathered} \frac{2}{3}n\text{ + }\frac{2}{3}n\text{ - 15 = n} \\ \frac{4n}{3}\text{ - n = 15} \\ \frac{4n\text{ - 3n}}{3}\text{ = 15} \\ \frac{n}{3}\text{ = 15} \\ \text{n = 15 }\times\text{ 3} \\ \text{n = 45} \end{gathered}[/tex]Final answer
There are 45 pupils in the class.
Hi can you help me with this question real quick please
Answers
The volume of a sphere is given by
[tex]V=\frac{4}{3}\pi r^3[/tex]where V denotes the volume and r the radius. In our case,
[tex]r=\frac{3}{2}in[/tex]Then, by substituting this value into the formula, we have
[tex]V=\frac{4}{3}\pi(\frac{3}{2})^3[/tex]which gives
[tex]\begin{gathered} V=\frac{4}{3}\pi\frac{3^3}{2^3} \\ V=4\pi\frac{3^2}{8} \\ V=\pi\frac{9}{2} \end{gathered}[/tex]By taking Pi as 3.14, we get
[tex]V=14.13in^3[/tex]So , by rounding to the nearest tenth, the answer is 14.1 cubic inches.
Heather invested $19,400 in a growth fund at 3.16% compounded quarterly for 9 years and 6 monthsA) calculate the maturity value of this amount at the end of the termB) Calculate the amount of compounded interest earned
Answers
GIVEN:
We are given the details of an investment as follows;
Initial investment = $19,400
Interest rate = 3.16%
Period of investment = 9 years and 6 months
Required;
To use the information given to calculate
(a) The maturity value at the end of the term
(b) The amount of compound interest earned.
Step-by-step solution;
The formula applied in calculating the maturity value is as follows;
[tex]A=P(1+r)^t[/tex]Where the variables are;
[tex]\begin{gathered} A=Maturity\text{ }value \\ \\ P=Initial\text{ }investment\text{ }(19400) \\ \\ r=rate\text{ }of\text{ }interest\text{ }(0.0316) \\ \\ t=time\text{ }in\text{ }years\text{ }(9.5) \end{gathered}[/tex]However, for an investment whose interest is compounded at different intervals within 1 year, the formula becomes modified as shown below;
[tex]A=P(1+\frac{r}{n})^{tn}[/tex]Where the variable n is the number of times interest is compounded annually. For an investment whose interest is compounded quarterly, that is, four times a year, the formula becomes;
[tex]A=P(1+\frac{r}{4})^{4t}[/tex]We can now calculate as follows;
[tex]\begin{gathered} A=19400(1+\frac{0.0316}{4})^{4\times9.5} \\ \\ A=19400(1+0.0079)^{38} \\ \\ A=26161.6208681 \\ \\ A\approx26161.62 \end{gathered}[/tex]We can now determine the amount of compound interest earned by deducting the initial amount invested from the maturity value. Thus we have;
[tex]\begin{gathered} Interest=A-P \\ \\ Interest=26161.62-19400 \\ \\ Interest=6761.62 \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} Maturity\text{ }value=26,161.62 \\ \\ Interest=6,761.62 \end{gathered}[/tex]I was out for quarantine and teacher won’t help, I need help!
Answers
A linear equation can be written as:
[tex]y=mx+b[/tex]Let:
y = c = Cost
x = h = Hours
Using the data, we can create a 2x2 system of equations. So:
[tex]\begin{gathered} x=2,y=20 \\ 20=2m+b_{\text{ }}(1) \\ ---------- \\ x=8,y=50 \\ 50=8m+b_{\text{ }}(2) \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} (2)-(1) \\ 50-20=8m-2m+b-b \\ 30=6m \\ m=\frac{30}{6} \\ m=5 \\ so\colon \\ 20=2(5)+b \\ b=10 \end{gathered}[/tex]Therefore,the linear equation is given by:
[tex]y=5x+10[/tex]For a equation of the form y = mx + b
m = Slope (rate)
b = y-intercept (Initial value)
Therefore the hourly rate for renting a bicycle is $5 and the deposit is $10
Aubrey spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -4.6°F. Between 9am and noon, the temperature increased by 4.2°F. Between noon and 3pm, the temperature went down 8.3°F. Between 3pm and 6pm, the temperature decreased by 6.9°F. What was the temperature at 6pm?
Answers
The temperature at 6pm is 15. degrees F if Aubrey spends a winter day recording the temperature once every three hours for science class.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
It is given that:
Aubrey spends a winter day recording the temperature once every three hours for science class.
The temperature between 9 am and noon:
= -4.6 + 4.2
= -0.4 degree F
Between noon and 3pm, the temperature went down 8.3°F.
= -0.4 - 8.3
= -8.7 degrees F
Between 3pm and 6pm, the temperature decreased by 6.9°F.
= -8.7 - 6.9
= 15. degrees F
Thus, the temperature at 6pm is 15. degrees F if Aubrey spends a winter day recording the temperature once every three hours for science class.
Learn more about the sequence here:
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Use the graph of the function to estimate the interval on which the function is decreasing.Enter your answer in interval notation.Enter any values to one decimal place.
Answers
The Solution:
Given:
Required:
To determine the interval in which the function is decreasing.
From the given graph, the interval in which the function is decreasing is:
[tex](-2.5,1)[/tex]
Therefore, the correct answer is (-2.5, 1)
Which of the following polynomial has roots at 3, -4, and a double root at-2?
Answers
The second polynomial [tex]f(x) = (x - 3)(x+4)(x+2)^2[/tex] has roots 3, -4 and a double root at -2.
What is root of polynomial?
The values of a variable for which the provided polynomial equals zero are referred to as a polynomial's roots. P(a) = 0 if an is the polynomial's root for x.
Since, if x is a root of the polynomial then x is a zero of the polynomial.
That means f(x) = 0
Consider, the first polynomial, [tex]f(x) = (x+3)(x-4)(x-2)^2[/tex]
plug x = 3, [tex]f(3) = (9)(-1)(1)^2 = -9[/tex] ≠ 0
Plug x = -4, [tex]f(-4) = (-1)(-8)(36) = 368[/tex] ≠ 0
Plug x = -2, [tex]f(-2) = (1)(-6)(16) = -96[/tex] ≠ 0
Therefore, 3, -4 and -2 are not the roots of the first polynomial.
Now consider the second polynomial, [tex]f(x) = (x-3)(x+4)(x+2)^2[/tex]
Plug x = 3, [tex]f(3) = 0[/tex]
Plug x = -4, [tex]f(-4) = 0[/tex]
Plug x = -2, [tex]f(-2) = 0[/tex]
Therefore, x = 3, -4, -2 are the roots of the second polynomial.
To know more about the roots of polynomial, click on the link
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Due 05/05/200:00Tickets to a school play cost $3 for students and $8 for adults. On opening night, $1,000 was collected and 150 tickets sold Use substitution to solvea system of equations to find how many of each kind of ticket were sold? Enter your answers in the boxesstudent ticketsadult tickets
Answers
We will use the next variables
x is the number of tickets sold for students
y is the number of tickets sold for adults
First equation
x+y=150
Second equation
3x+8y=1000
we isolate the x of the first equation
x=150-y
we substitute the equation above in the second equation
3(150-y)+8y=1000
450-3y+8y=1000
we sum like terms
5y=1000-450
5y=550
y=550/5
y=110
Then we substitute the value of y in the equation with x isolate
x=150-y=150-110=40
x=40 and y=110
The students sold
40 tickets for students
110 tickets for adults
Hi so sorry i need help in geometry i think its asking if the two given angles are coterminal or not
Answers
Given these two angles:
[tex]\frac{5\pi}{4}[/tex][tex]-\frac{3\pi}{4}[/tex]You need to remember that, by definition, two angles are coterminal if the Difference (the result obtained by subtracting them) is:
[tex]360\text{\degree or }2\pi[/tex]Then, you need to set up:
[tex]\frac{5\pi}{4}-(-\frac{3\pi}{4})[/tex]Solving the Subtraction, you get:
[tex]=\frac{5\pi}{4}+\frac{3\pi}{4}[/tex][tex]=\frac{8\pi}{4}[/tex][tex]=2\pi[/tex]Hence, the answer is: They are Coterminal Angles.
2.Evaluate the following mixed numbers, then simplify.7 1/2 divide 1 1/8
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Given the numbers : 7 1/2 and 1 1/8
We will divide them
so,
[tex]\begin{gathered} 7\frac{1}{2}\div1\frac{1}{8} \\ \\ =\frac{15}{2}\div\frac{9}{8} \\ \\ =\frac{15}{2}\times\frac{8}{9} \\ \\ =\frac{8}{2}\times\frac{15}{9}=4\times\frac{5}{3}=\frac{20}{3}=6\frac{2}{3} \end{gathered}[/tex]Mauricio is buying his wife flowers for their anniversary. The florist has 5 red roses, 4 yellow roses, and 3 pink roses. What is the probability he will select 1 yellow rose the 2 red rose. Independent or Dependent
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We will have the following:
The probability will be given by:
[tex]p=(\frac{1}{12})(\frac{5}{11})(\frac{4}{10})\Rightarrow p=\frac{1}{66}[/tex][tex]\Rightarrow p=0.01515151515\ldots\Rightarrow p\approx0.015[/tex]So, the probability of that happening is approximately 15%.
It is dependent.
main and Range HAMAD SALIM 12 Range 12 The graph below represents the function y = f(x). State the domain and range of this function. 1 I US
Answers
Remember that the domain is the data set of all possibles values of x and the range is the data set of all possibles values of y
so
Looking at the graph
Domain is the interval for x
[-5,8}
All real numbers greater than or equal to -5 and less than or equal to 8
Range is the interval for y
[-3,2]
All real numbers greater than or equal to -3 and less than or equal to 2
Linda Davis agreed to lend money to Alex Luciano at a special interest rate of 7% per year, on the condition that he borrow enough that would pay her $500 in interest over a four-year period. What was the minimum amount Alex could borrow?
Answers
It is given that,
[tex]\begin{gathered} Rate(R)\text{ = 7\%} \\ I\text{ = \% 500} \\ T\text{ =3 years} \end{gathered}[/tex]Interest is given by the formula,
[tex]I\text{ = }\frac{PRT}{100}[/tex]Substituting the value in the formula,
[tex]\begin{gathered} 500\text{ = }\frac{P\times7\times4}{100} \\ 50000\text{ = 28P} \\ P\text{ = }\frac{50000}{28} \\ P\text{ = 1785.71 } \end{gathered}[/tex]Thus the minimum amount to be borrowed is $ 1785.71.