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]
A cube has a side length of 5x cm. What is the volume of the cube?
Answer:
125x^3 cm^3
Step-by-step explanation:
The volume of a cube of side length s is V = s^3.
If the side length is 5x cm, then V = (5x cm)^3 = 125x^3 cm^3
Find the missing side. Round to
the nearest tenth.
10
33°
Х
X = ?
Given:
A right angle triangle with legs x and 10.
The angle opposite to the side with measure 10 is 33 degrees.
To find:
The value of x.
Solution:
We know that, in a right angle triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
In the given triangle,
[tex]\tan 33^\circ=\dfrac{10}{x}[/tex]
[tex]x=\dfrac{10}{\tan 33^\circ}[/tex]
[tex]x=15.39864[/tex]
[tex]x\approx 15.4[/tex]
Therefore, the value of x is 15.4 units.
The sum of three numbers is fifty-four. The second number is four times the first number, and the third number is six more than the first number. What are the three numbers?
Answer:
8 , 32 AND 14
Step-by-step explanation:
The price of a cake of radius r сm and height h cm is given by the formula
P=
[tex] \frac{1}{25} {r}^{2} h[/tex]
If the price of cake is $240 and the height is 15 cm, calculate the radius
of the cake.
pls provide step-by-step explanation, final ans is 20 cm. tysm <33
Answer:
20 cm
Step-by-step explanation:
Given that :
P = 1/25 r²h
P = price = 240 ; h = height = 15cm
Inputting values into the equation :
240 = 1/25 * r² * 15
25 * 240 = 15r²
6000 = 15r²
6000 / 15 = r²
400 = r²
Square root of both sides
20 = r
Radius = 20cm
A 12 foot ladder is leaning up against the side of a building. The bottom of the ladder is 4 feet away from the bottom of the building Approximately how high up the side of the building does the ladder reach? 8 ft 10 ft 11 ft 12 ft
You can use the Pythagoras theorem for this since a right triangle is formed.
[tex]c^2 = a^2 + b^2[/tex]
C = 12
A = 4
B = x
Input values:
[tex]12^2 = 4^2 + x^2[/tex]
[tex]144 = 16 + x^2[/tex]
[tex]128 = x^2[/tex]
[tex]x = \sqrt{128}[/tex]
[tex]x = 11.3137...[/tex]
So, about 11ft.
what is 1 x (a + 3) = a + 3
Answer:
[tex]\huge\boxed{a\in\mathbb{R}}[/tex]
The solution is the set of all real numbers.Step-by-step explanation:
[tex]1\times(a+3)=a+3\\\\a+3=a+3\\\\a-a+3=a-a+3\\\\3=3\qquad\bold{TRUE}[/tex]
Answer:
See the Image below:)
ITS TRUE
SOLUTION ALL REAL NUMBERS
Step-by-step explanation:
The radius of a circle is 75 centimeters.
Enter the circumference of the circle, in centimeters. Round your answer to the nearest hundredth.
Answer:
The circumfrence is 150pi.
Step-by-step explanation:
While a circle, symbolically, represents many different things to many different groups of people including concepts such as eternity, timelessness, and totality, a circle by definition is a simple closed shape. It is a set of all points in a plane that are equidistant from a given point, called the center. It can also be defined as a curve traced by a point where the distance from a given point remains constant as the point moves. The distance between any point of a circle and the center of a circle is called its radius, while the diameter of a circle is defined as the largest distance between any two points on a circle. Essentially, the diameter is twice the radius, as the largest distance between two points on a circle has to be a line segment through the center of a circle. The circumference of a circle can be defined as the distance around the circle, or the length of a circuit along the circle. All of these values are related through the mathematical constant π, or pi, which is the ratio of a circle's circumference to its diameter, and is approximately 3.14159. π is an irrational number meaning that it cannot be expressed exactly as a fraction (though it is often approximated as 22/7) and its decimal representation never ends or has a permanent repeating pattern. It is also a transcendental number, meaning that it is not the root of any non-zero, polynomial that has rational coefficients. Interestingly, the proof by Ferdinand von Lindemann in 1880 that π is transcendental finally put an end to the millennia-old quest that began with ancient geometers of "squaring the circle." This involved attempting to construct a square with the same area as a given circle within a finite number of steps, only using a compass and straightedge. While it is now known that this is impossible, and imagining the ardent efforts of flustered ancient geometers attempting the impossible by candlelight might evoke a ludicrous image, it is important to remember that it is thanks to people like these that so many mathematical concepts are well defined today.
The mean of six numbers is 10. When
mother number is added the new mean is
9. Find the number added.
Answer:
3
Step-by-step explanation:
If 6 numbers have a mean value of 10, it means that the sum of the numbers divided 6 is equal to 10. This can be expressed as:
x÷6=10
x=60
The new number added will be the 7th number and now the mean is 9. You have to ask what number divided by 7 is equal to 9? This can be expressed as:
y÷7=9
y=63
63-60=3
So the new number added is 3
Answer:
3
Step-by-step explanation:
Mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
Given the mean of 6 numbers is 10, then
[tex]\frac{sum}{6}[/tex] = 10 ( multiply both sides by 6 )
sum = 60
When another number x is added then count is 7
[tex]\frac{60+x}{7}[/tex] = 9 ( multiply both sides by 7 )
60 + x = 63 ( subtract 60 from both sides )
x = 3 ← the number added
What is the value of h?
Answer:
6.
Step-by-step explanation:
626×10−34
Answer:
h= 5.7
Step-by-step explanation:
trust me pls ill show work if u need me to
Use this set of number to answer the question.
4, 11, 6, 9, 23, 34, 6, 19,
What is the median for this set of numbers?
A. 6
B. 10
C. 14
D. 16
Answer:
10
Step-by-step explanation:
arrange the number in order from smallest to largest, 4, 6, 6, 9, 11, 19, 23, 34. you then find the middle number, in this case there is no middle number, but 9 and 11 are the closest, so you add those to together to get 20, then divide by 2. this gives you ten
if you have any questions, leave them in the comments and i will try to answer them, if this helped pls give brainliest
Answer:
Hello There!!
Step-by-step explanation:
Median is ordering the numbers from smallest to biggest.
Ordered: 4,6,6,9,11,19,23,34
And there is no middle number so you have two add the two middle numbers 9+11=20 then divide by 2 which equals 10.
hope this helps,have a great day!!
~Pinky~
What is the angle relationship between c and d?
Also what is the relationship between c and f?
(could be Vertical, alternate exterior, alternate interior, corresponding, same-side interior, same-side exterior, or linear pair.)
Answer:
1. linear pair (c and d)
2. alternate interior angles (c and f)
Step-by-step explanation:
Here, we want to get the relationship between angles
From what we have , we can see that angle d and angle c lie on a straight line
Thus, we have that angle c and angle d are supplementary angles since they will add up to give 180 degrees . So we can call the two a linear pair
For c and f, we can notice a z-like angle between the two
In this case, when we have a z-like angle, the relationship that exists between the two angles is that they are alternate interior angles
Use the law of cosines to write an expression equivalent to b
Given:
A triangle ABC.
The given expression for b is:
[tex]b=\sqrt{m+n-pq}[/tex]
To find:
The expression that is equivalent to b.
Solution:
According to the Law of Cosines,
[tex]b^2=a^2+c^2-2ac\cos B[/tex]
It can be written as:
[tex]b=\sqrt{a^2+c^2-2ac\cos B}[/tex] ...(i)
We have,
[tex]b=\sqrt{m+n-pq}[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]m=a^2[/tex]
[tex]n=c^2[/tex]
[tex]p=2ac[/tex]
[tex]q=\cos B[/tex]
Therefore, the required values are [tex]m=a^2,n=c^2,p=2ac,q=\cos B[/tex].
What value of x makes this equation true? 4x – 10 = 18
Answer:
7 is the correct answer. brainliest plese
Answer: x=7
4,7=28
28-10 =
18
THIS IS RIGT I PROMIS
or to do it yourself do
10 plus 18
then divide it by 4
Write the sentence as a conditional statement.
Two parallel lines lie in the same plane.
Help me and show work plz <3
Answer:
0.8^4
Step-by-step explanation:
Write the expression using exponents.
[tex]0.8 \: · \: 0.8 \: · \: 0.8 \: · \: 0.8 \: = \boxed { ? }[/tex]
___________________Solution :-Given Information :-Expression ➢ 0.8 · 0.8 · 0.8 · 0.8 To Find :-The value of the expression using exponents. Calculation :-Since, the expression is actually the repetition of 0.8, so we can write this as,
⇒ 0.8 · 0.8 · 0.8 · 0.8 = ( 0.8 )⁴
Calculating further, We get,
⇒ ( 0.8 )⁴ = [tex] \sf \frac{8 \times 8 \times 8 \times 8}{10 \times 10 \times 10 \times 10} = \frac{8⁴}{10⁴} [/tex]
⇒ ( 0.8 )⁴ = [tex] \frac{4096}{10000} [/tex]
Calculating further, We get,
⇒ ( 0.8 )⁴ = 0.4096
∴ 0.8 · 0.8 · 0.8 · 0.8 = ( 0.8 )⁴ = 0.4096
____________________Final Answer :-0.8 · 0.8 · 0.8 · 0.8 = ( 0.8 )⁴ = 0.4096____________________The graphs below have the same shape. What is the equation of the blue
graph?
Answer:
G(x) = (x^2 +2)
Step-by-step explanation:
The graph moved to the left 2 units, therefor that is the equation :)
The equation of the blue graph will be G(x) = (x² +2).
What is a qudratic function?In mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is a polynomial function defined by a quadratic polynomial.
A parabola is the shape of a quadratic function's graph. The "width" or "steepness" of a parabola can vary and it can expand upward or downward.
The given equation of the red graph is,
F(x) = x²
The graph moved to the left 2 units, hence the equation can be written as,
G(x) = F(x) + 2
G(x) = x² + 2
To know more about quadratic function follow
https://brainly.com/question/25841119
#SPJ7
I will mark you brainlist!
1 Mr. Ruiz made a map of his ranch on the grid shown below.
Cattle
Horses
Sheep
What percent of the ranch is used for sheep?
A 33%
B 25%
C 20%
D 16%
Each month Elizabeth budgets $760 for fix expenses, $620 for living expenses, and $80 for annual expenses. Her annual net income is $35,040. Which sentence best describes her monthly budget.
It shows a Deficit of $1255
It shows a surplus of $1255
It shows a surplus of $1460
It is balanced
Answer:
Step-by-step explanation:
760+620+80=1460 total monthly expenses.
$32,580 annually divided by 12 months = monthly income of $2,715
2,715-1460=1,255
Her budget shows a surplus of $1,255
please include work
Answer:
[tex] \frac{ \sqrt{3} }{2} x = 15 \\ x = \frac{30}{ \sqrt{3} } = 10 \sqrt{3} \\ \\ area = \frac{3 \sqrt{3} }{2} {x}^{2} = 15 \times 3 \times 10 \sqrt{3} = 450 \sqrt{3} [/tex]
Help plz..And No links!! I repeat No links!!
This is Right answer....
I hope you understand....
give me Brainliest.....
Thanks....
I need help with this
Answer:
look at s d g
Step-by-step explanation:
[tex] \frac{1}{x^{2} - 1 } - \frac{1}{x - 1} [/tex]
Answer:
-x/x^2-1
Step-by-step explanation:
-x^2+x/x^3-x^2-x+1
x(-x+1)/(x+1)(x-1)(x-1)
-x/x^2-1
plz help 12 points !!! it's l due in a hourPIL Assessment 0 Stephan has a piece of wood that measures 18 inches long and 12 inches wide. He wants to make a tray with sides 2 inches high. Maurice says that he can make a tray that has a base measuring 10 inches by 10 inches. Is he correct? Use the drop-down menus to explain your answer. Stephan Choose... have enough wood to make the tray because he has Choose... square inches, which is Choose... than he needs to make the tray, Choose... square inches.
Answer:
No, because he needs to make a 18 by 12 base. Not enough wood, (area)..... square inches
URGENT PLEASE HELP!!
What is the equation of the linear function?
A. y = 1/2x + 3 B. y = -1/2x + 6 C. y = 2x + 3 D. y = -1/2x + 3
Answer:
y = -1/2x + 3
Step-by-step explanation:
(6，0) is on the linear function, 0= -1/2 × 6 + 3
I WILL GIVE YOU BRAINLIEST ANSWER IF YOU GET IT CORRECT!
Laura is donating two boxes of books
to the library. One box has a mass of
9 kilograms. The other box has a mass
of 7 kilograms. What is the total mass
of the two boxes in grams?
Answer:
16000 grams
Step-by-step explanation:
9(1000) + 7(1000) = 16000
someone help me please i have 20 minutes left to finish this
Answer: 17. is A and 18 is most likely G
Step-by-step explanation:
I need the answer ...
what is 625.842 rounded to the nearest tenths
Answer:
625.8
Step-by-step explanation:
your welcome
Answer:
625.8
Step-by-step explanation:
a tenth is the first decimal place after the decimal, if there's a five next to it then you can add a number to that place, but since both of the numbers next to the tenth are under 5, we don't add an extra number to it, making the answer 625.8
(HELP ASAP)In the figure, if OQ is the angle bisector of ∠POR, find m∠POQ.
Answer:
61°
Step-by-step explanation:
[tex]9x+7=13x-17[/tex], QO Bisector
[tex]x=6\\[/tex], Algebra
[tex]m<POQ = 60[/tex], Algebra/Sub