. A bridge over a river is built in the shape of a parabolic arch. The bridge has a span of 100 feet. The height of the arch is 10 feet at a point 40 feet from the center. Find the height of the arch at its center.
Answer:
The height of the arch at its center is 250/9 or about 27.78 feet.
Step-by-step explanation:
We can write an equation to model the parabolic arch.
Let the left-most point of the arch be the origin (0, 0).
Since the bridge has a span of 100 feet, the right-most point must be (0, 100).
We can use the factored form of a quadratic:
[tex]y=a(x-p)(x-q)[/tex]
Where p and q are the x-intercepts.
Our x-intercepts are x = 0 and x = 100. Hence:
[tex]y=ax(x-100)[/tex]
At a point 40 feet from the center, the height of the arch is 10 feet.
The center is x = 50. So, a point 40 feet from the center can be either x = 10 or x = 90.
So, for instance, when x = 10, y = 10. Substitute and solve for a:
[tex]10=10a(10-100)[/tex]
So:
[tex]\displaystyle a=-\frac{1}{90}[/tex]
The same value will result if we let x = 90 and y = 10.
Hence, our equation is:
[tex]\displaystyle y=-\frac{1}{90}x(x-100)[/tex]
The height of the arch at its center will be when x = 50. Hence:
[tex]y(50)=\displaystyle -\frac{1}{90}(50)((50)-100)=\frac{250}{9}\approx 27.78\text{ feet}[/tex]
3n - (2 +n)
plz help me I need help I’m stuck
Answer:
if you are factoring the answer is 2(n-1)
if simplifying the answer is 2n-2
Step-by-step explanation:
See image below:)
A triangular prism is 33 meters long and has a triangular face with a base of 20 meters and a height of 24 meters. The other two sides of the triangle are each 26 meters. What is the surface area of the triangular prism?
Answer:
7920
Step-by-step explanation:
Answer:
V = 6196.62 m³
Step-by-step explanation:
Given: A triangular prism; 33 meters long, a base of 20 meters, a height of 24 meters. The other two sides of the triangle are each 26 meters
To find: What is the surface area of the triangular prism?
Formula: [tex]A = 12bh[/tex]
Solution: Triangular prisms have their own formula for finding surface area because they have two triangular faces opposite each other. The formula is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height.
I need help ..................
Answer:
Step-by-step explanation:
hi
convert standard form to factored form
f(x)=x^+5x+6
(LT 5.6)
Answer:
(x+3)(x+2)
Step-by-step explanation:
f(x)=x²+5x+6=x²+2x+3x+6=x(x+2)+3(x+2)=(x+3)(x+2)
[tex] {x}^{2} + 5x + 6[/tex]
[tex] {x}^{2} + 2x + 3x + 6[/tex]
[tex]x(x + 2) + 3(x + 2)[/tex]
[tex](x + 3)(x + 2)[/tex]
How would you simplify this? Please help
[tex]8^{\frac{4}{3}} = \sqrt[3]{8^4} = \sqrt[3]{(2^3)^4} = \sqrt[3]{2^{3*4}} = 2^4 = 16[/tex]
Answer: C (16).
[tex]2\sqrt{6} - 6\sqrt{54} = 2\sqrt{6} - 2 * 3 * \sqrt{6} * \sqrt{9} = 2\sqrt{6}(1-3\sqrt{9}) = 2\sqrt{6}(1-3*3) = 2\sqrt{6}(1-9)=2*\sqrt{6}*(-8) = -16\sqrt{6}[/tex]
1.
[tex] \sqrt[3]{8^{4} } [/tex]
2.
[tex]2 \sqrt{6} - 6 \sqrt{54} \\ 2 \sqrt{6} - 6 \sqrt{9 \times 6} \\ 2 \sqrt{6} - 18 \sqrt{6} \\ - 16 \sqrt{6} [/tex]
Function g can be thought of as a scaled version of f(x) = x^2
write the equation for g(x)
Answer:
g(x) = - x^2
Step-by-step explanation:
The negative sign flips the f(x) graph across the x-axis.
Answer:
The first guy is right
Step-by-step explanation:
At a coffee shop, the first 100 customers'
orders were as follows.
Small
Medium Large
Hot
5
48
22
8
12
5
Cold
What is the probability that a customer ordered
a hot drink given that he or she ordered a large?
Answer:
Step-by-step explanation:
What is the probability that a customer ordered
a hot drink given that he or she ordered a large?
So we are looking for the percentage of a hot drink and a Large.
Our list:
Small
Medium Large
Hot
5
48
22
8
12
5
Cold
He can tell there is 10% atleast for hot and 0% for a large
The probability that a customer ordered a hot drink given that he or she ordered a large is 22%
What is probability?Probability denotes the possibility of the outcome of any random event.
Given that a table of the first 100 customers' orders at a coffee shop.
We need to find the probability that a customer ordered a hot drink given that he or she ordered a large,
= 22 / 100
= 22%
Hence, the probability that a customer ordered a hot drink given that he or she ordered a large is 22%
Learn more about probability, click;
https://brainly.com/question/30034780
#SPJ7
How many ways can 3 different flags be hung in a row if there are 8 flags to choose from?
Answer:
8 flags can be chosen for the first position
7 flags are left for the second position
6 flags are left for the third position
8 * 7 * 6 = 336
solve it pleeeease
will give you brainliest
Answer:
Step-by-step explanation:
I m sorry if i m wrong.
e no is 100% correct
A classroom has a length of 20ft. And a width of 30ft. The flooring is to be replaced by tiles. If each tile has a length of 24 in and a width of 36 in, how many tiles are needed to cover the classroom?
Answer:
100
Step-by-step explanation:
first we need to turn the feet into inches
20x12=240
30x12=360
now to get the area of the floor we need to do 360x240=
86,400
now the area of each tile is 24x36=864
now to find out how many tiles fit on the floor we need to do 86,400 divided by 864 which = 100
Tell whether the function table represents a linear or exponential relationship.
Answer: Linear
Step-by-step explanation: When determining whether the function table represents a linear or exponential relationship, we are checking to see if the rate of change is constant or increasing. If we look at the table, when x increases by 1, y increases by 3. This means that on that interval, the average rate of change is 3/1 = 3. When we increase x by 1 again, we see that y increases by 3 again. This means that the rate of change is constant for the function, so it must be linear.
Find the value of x
a) 57
b) 60
c) 69
d) 63
Answer:
b
Step-by-step explanation:
The tangent- secant angle 55° is equal to half the difference of its intercepted arcs, that is
[tex]\frac{1}{2}[/tex] (170 - x) = 55 ( multiply both sides by 2 to clear the fraction )
170 - x = 110 ( subtract 170 from both sides )
- x = - 60 ( multiply both sides by - 1 )
x = 60 → b
What is the sum of ⅔+
1/5
Step-by-step explanation:
1. make the denominators the same.
10/15+3/15= 13/15
About how many hours will it take to travel 410 miles at an average speed of 50 miles per hour? Use D=r•t
Answer:
Step-by-step explanation:
The first thing to notice about this problem is that you have a mixture of Metric and English units. The first thing that I would recommend is to convert 410 miles into Kilometers
1 mile = 1.61 km
410 miles = (410*1.61) = 660 km (rounded to the nearest km)
Now you need to know the time. The formula for travel is d=rt. You know the distance, and you know the rate, solve the formula for time.
t=d/r.
t=660km/120km/k
t=5.5 hours. Plus add the 2 15 minutes breaks. 2*15=30 minutes. 60 minutes in an hour means that you add 30/60 hours to the trip, or another .5 hours.
Therefore the answer is 5.5+.5 hours.
The answer is: time=6 hours.
Find the mean of the data set {4.5,5, 3.5, 2, 2.5}.
So what is the answer ;, I nordeste im
Answer:
Mean = 3.5
Step-by-step explanation:
The given data is :
4.5,5, 3.5, 2, 2.5
We need to find the mean of the given data.
We know that,
Mean = sum of observations/total no. of observations
Here,
Total no. of observations = 5
Sum of observations = 4.5 + 5+ 3.5+ 2+ 2.5 = 17.5
Mean,
[tex]m=\dfrac{17.5}{5}\\\\m=3.5[/tex]
Hence, the mean of the data set is equal to 3.5.
∠A and \angle B∠B are complementary angles. If m\angle A=(2x-4) ∘ and m\angle B=(5x+17) ∘ , then find the measure of \angle A∠A.
Answer: 18°
Step-by-step explanation:
Complementary angles are the angles that when we add them together, the value will equal 90°.
In this question, we've to add both angles and equate them to 90°. This will be:
(2x - 4) + (5x + 17) = 90
2x - 4 + 5x + 17 = 90
Collect like terms
2x + 5x = 90 + 4 - 17
7x = 77
x = 77/7
x = 11
Angle A will be:
= (2x-4)
= 2(11) - 4
= 22 - 4
= 18°
C.P. = Rs400, Loss = 12% , Find S.P
Answer:
Step-by-step explanation:
CP= Rs 400
loss%=12%
let sp be x
SP=CP-loss%*CP
x=400-12/100*400
x=40000-4800/100
x=35200/100
x=352
therefore sp =Rs 352
Answer:
S.P. = ₹352
Step-by-step explanation:
UNITARY METHOD:
If C.P. = ₹100
Then SP = ₹(100-12) = ₹88
If C.P. = ₹1
S.P. = ₹(88/100)
Then, as given: C.P. = Rs 400
S.P. = ₹( 88/100)*400
= ₹352
Therefore, S.P. = ₹352
A farmer is monitoring the water content of the soil during a dry summer. The water content of the soil is decreasing at a rate of 2.5% per week. If a certain soil sample contains 200 grams of water on July 1st, which equation describes the relationship between y, amount of water in grams, and t, time in weeks after July 1st?
Every 2 days, Marina spends a total of 5.25 hours baking cupcakes and 4.75 hours decorating the cupcakes. At this rate, what is the total number of hours that Marina will spend baking and decorating cupcakes in 7 days?
PLS HELP!!! I HAVE A TIME LIMIT
Answer:
70
Step-by-step explanation:
Ok so we first add 4.75 and 5.25. 4.75+5.25=10. So 10 hours each day so 10 x 7 = 70. 70 hours in 7 days
Answer:
i would say it is either 30 or 35
Step-by-step explanation:
7/2=3.5
so you would round it down to 3 or keep it that
and 4.75+5.25=10
3(10)=30 and 3.5(10)=35
If it's every two days.
Elizabeth buys to red cans of tomato juice and three blue cans of tomato juice in all how many cups of tomato juice does she by
I need help with this
Answer:
D.
Step-by-step explanation:
You pass 3x to the other side so you get 4y = -16 - 3x
to clear y you divide both sides by 4
y = (-16-3x )/ 4
you can simplify this so it so it gives us
y = -4 - 3/4x
Jackson is building a bookshelf and has a piece of wood that is 5/8 long. He needs to cut pieces that are 1/16 foot long. How many pieces can Jackson cut?
Answer:
6 is the Answer.Step-by-step explanation:
A fraction consists of two parts the top number and the bottom one.
Think of the top number as the count and the bottom as the size indicator. So you have:
countsize indicator −−−−−−−−−−→proper names numeratordenominator
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the action example of dividing 3 into 6.
We can do this division directly because their size indicators are the same. That is, we have: 61÷31. People do not normally write it this way but it is correct.
To directly divide the counts the size indicator must be the same
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So we need to see how many of 18 will fit into 34
We can not do this directly in one operation as the size indicators are not the same.
Lets make the size indicators (denominators) the same
Multiply by 1 and you do not change the value but
1 comes in many forms.
[34×1]÷18 → [34×22]÷18
[3×24×2]÷18 → 68÷18
Now that the size indicators (denominators) are the same we can just divide the counts (numerators)
countsize indicator→[68÷18]=6÷1=6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I could explain more showing the connection between this and the shortcut method but what I have shown you will do for now.
Aldo needs 46 cookies for a party.
The cookies he wants come in packs of 8.
How many packs should he buy?
Answer:
6 Packs
Step-by-step explanation:
Since he needs 46 cookies, he will have to buy 46/8 which is 5.75 packs. But since the packs are sold in whole, not fractions, he buys a ceil approximation of the packs which is 6, because if he buys 5, it will not be enough.
Find from first principles, the derivative
3x+5/root x
Answer:
look at the picture
Step-by-step explanation:
What does difference of squares mean? How can you recognize it when looking at an expression?
A pyramid. This shape has faces. This shape has vertices. This shape has edges.
Answer:
5 faces 5 vertices 8 edges
Step-by-step explanation: i just finished it.
Answer:
This shape has
✔ 5
faces.
This shape has
✔ 5
vertices.
This shape has
✔ 8
edges.
Step-by-step explanation:
Trust me on this, also can I have brainiest please?
Hope you do well! :D
I did the instruction, and I got it correct.
PLSS answer
The graph below can be used to solve which equation?
Answer:
Ix + 2I - 5 = -(x - 1)*(x - 3)
Step-by-step explanation:
In the graph, we can see two functions a red one, f(x), and a blue one, g(x)
And the equation would be f(x) = g(x)
The red one is an absolute value function, we can see that the vertex is at x = -2 and at y = -5, and it has a slope equal to 1.
Remember that for an absolute value equation with a vertex (a, b) is:
f(x) = Ix - aI + b
Then in this case, the absolute value equation is:
f(x) = Ix - (-2)I - 5
f(x) = Ix + 2I - 5
The blue equation is a quadratic equation, with roots 1 and 3, and we can see that it opens down, so the leading coefficient is negative.
Remember that for a quadratic equation with roots a and b, with leading coefficient A is:
g(x) = A*(x - a)*(x - b)
Then in this case the quadratic equation is something like:
g(x) = -N*(x - 1)*(x - 3)
Then the equation will be something like:
f(x) = Ix + 2I - 5 = g(x) = -N*(x - 1)*(x - 3)
Ix + 2I - 5 = -N*(x - 1)*(x - 3)
The only option that has this shape is the first option (the top one) such that N = 1, then:
Ix + 2I - 5 = -(x - 1)*(x - 3)
is the correct option.
Tickets are arranged from 1 to 25 at a ticket counter. if one of the tickets is drawn at random whag is the probability that the chosen ticket is a multiple of 5. and what is the probability that the chosen ticket is a multiple of 6?
Answer:
The probability of choosing a ticket thats a multiple of 5 is 5/25
The probability of choosing a ticket thats a multiple of 6 is 4/25
Step-by-step explanation:
multiples of 6 are 6, 12, 18, and 24
multiples of 5 are 5, 10, 15, 20, and 25
The probability of choosing a ticket thats a multiple of 5 is 5/25
The probability of choosing a ticket thats a multiple of 6 is 4/25
2.1x10^6
______
7x10^3
answer in standard form
...................10^......
Given:
The expression is:
[tex]\dfrac{2.1\times 10^6}{7\times 10^3}[/tex]
To find:
The simplified form of the given expression in standard form.
Solution:
We have,
[tex]\dfrac{2.1\times 10^6}{7\times 10^3}[/tex]
It can be written as:
[tex]\dfrac{2.1\times 10^6}{7\times 10^3}=\dfrac{21\times 10^5}{7\times 10^3}[/tex]
[tex]\dfrac{2.1\times 10^6}{7\times 10^3}=\dfrac{21}{7}\times \dfrac{10^5}{10^3}[/tex]
[tex]\dfrac{2.1\times 10^6}{7\times 10^3}=3\times 10^{5-3}[/tex] [tex][\because \dfrac{a^m}{a^n}=a^{m-n}][/tex]
[tex]\dfrac{2.1\times 10^6}{7\times 10^3}=3\times 10^2[/tex]
Therefore, the required value is [tex]3\times 10^2[/tex].