Answer:
a) The equation of the arch is [tex]y = -10\cdot x^{2}[/tex].
b) The height of the arch from the ground is 810 feet.
Step-by-step explanation:
Statement is incomplete. Complete statement is:
An archway in front of a school is in the shape of a parabola. The top of the arch is the vertex (0,0). The school seal is at the focus, 2.5 feet below the vertex, and the arch is 18 feet wide at the ground.
Write an equation that represents the arch.
What is the height from the top of the arch to the ground?
a) Write an equation that represents the arch.
According to the statement, the archway is a vertical downward parabola. From Analytical Geometry we know that parabolas are represented by the following equation in standard form:
[tex]y-k = 4\cdot p\cdot (x-h)^{2}[/tex] (Eq. 1)
Where:
[tex]p[/tex] - Distance between vertex and focus, measured in feet.
[tex]x[/tex] - Independent variable, measured in feet.
[tex]y[/tex] - Dependent variable, measured in feet.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex, measured in feet.
If we know that [tex]p = -2.5\,ft[/tex], [tex]h = 0\,ft[/tex] and [tex]k = 0\,ft[/tex], then the equation that represents the arch:
[tex]y = -10\cdot x^{2}[/tex]
The equation of the arch is [tex]y = -10\cdot x^{2}[/tex].
b) What is the height from the top of the arch to the ground?
Given that parabola is a symmetrical curve, we determine the vertical position at the base of the arch ([tex]x = 9\,ft[/tex]):
[tex]y_{min} = -10\cdot (9\,ft)^{2}[/tex]
[tex]y_{min} = -810\,ft[/tex]
Then, the height of the arch from the ground is given by this difference:
[tex]h = 0\,ft-(-810\,ft)[/tex]
[tex]h = 810\,ft[/tex]
The height of the arch from the ground is 810 feet.
which posture or theorem proves that these two triangles are congruent
ASA Congruence
AAS Congruence Theorem
HL Congruence Theorem
SAS Congruence postulate
Answer:
AAS Congruence Theorem
Solve for c.
2c^2 = 338
c = ?
c = ?
Answer:
C=13, -13
Have a wonderful day!!!
What is the value of x
Answer:
98 degrees
Step-by-step explanation:
First calculate the entire triangles angles:
180 - 53 - 45 = final angle of triangle
82 = final angle of triangle
Using the straight line rule for angles, x and the inner angle must equal to 180 degrees:
180 - 82 = x
98 = x
Angle x is 98 degrees.
264 equals the sum of 96 and t
Write the sentence as an equation.
Answer:
96+t=264
Step-by-step explanation:
I want the answer PLZ
Answer:
3
Step-by-step explanation:
They have the same side length and its shown
Help me please !!!!!!!!
Answer: Since x is 157 degrees the missing value,m, is 23 degrees because a line is 180 degrees, n is also 23 degrees so it would be the same
Step-by-step explanation:
please help 8(10+8)
Answer:
its 180.... that's the answer
Answer:
it is 80 + 64
Step-by-step explanation:
All you have to do is multiply 8 by the numbers inside the parenthesis
Simplify 4/9 - 5/12 + 1/4
Answer:
5/18
Step-by-step explanation:
The simplified answer is 5/18
Step-by-step explanation:
the answer is
0.27777777777
brainliest and 60 points ;)
8 * 65 * 7 * 321 * 0 * 1=??
Answer: 0
Step-by-step explanation:
Any expression multiplied by 0 = 0
x+6y=-36 solve for y
Answer:
y=−1/6x−6
Step-by-step explanation:
How do you work out 3^2+2^3 indices
3^2 +2^3
9+2^3
9+8
Answer : 17
Jenni works at a salon and earns a 15% commission on her total sales. How much
must she sell in total in order to earn $90 in one day?
Answer:
$600
Step-by-step explanation:
90/0.15
please help me with this! thank you so much!
Answer: Look at the photo
Step-by-step explanation:
[tex](3x + 3) + (4x + 2) = 180\\7x + 5 = 180\\[/tex]
Substract 5 from both sides
[tex]7x = 175[/tex]
Divide by 7 from both sides
x = 25
Please help me find the domain and range
Answer:
Domain: (-∞,-1) U (-1,∞)
Range: (-∞,1) U (0,∞)
find x
3x
2x+40
x+50
4x
Answer:
27
Step-by-step explanation:
The sum of all exterior angles of any quadrilateral= 360°
3x+2x+40+x+50+4x = 360°
11x + 90 = 360°
11x = 360 - 90
10x = 270
x = 270/10
x = 27
Solve the system of equations using substitution.
- 4x + 4y= 8
y= -2x – 10
-
O (4, -18)
O (12, -34)
o(-4,-2)
O (-2,-6)
Answer:
(- 4, - 2 )
Step-by-step explanation:
Given the 2 equations
- 4x + 4y = 8 → (1)
y = - 2x - 10 → (2)
Substitute y = - 2x - 10 into (1)
- 4x + 4(- 2x - 10) = 8 ← distribute and simplify left side
- 4x - 8x - 40 = 8
- 12x - 40 = 8 ( add 40 to both sides )
- 12x = 48 ( divide both sides by - 12 )
x = - 4
Substitute x = - 4 into (2) for corresponding value of y
y = - 2(- 4) - 10 = 8 - 10 = - 2
Solution is (- 4, - 2 )
Consider a geometric sequence with a first term of 4 and a fourth term of -2.916.
a) Find the common ratio of this sequence.
b) Find the sum to infinity of this sequence.
Answer:
a) Find the common ratio of this sequence.
Answer: -0.82
b) Find the sum to infinity of this sequence.
Answer: 2.2
Step-by-step explanation:
nth term in geometric series is given by [tex]4\ th \ term = ar^n-1\\-2.196 = 4r^{4-1} \\-2.196/4 = r^{3} \\r = \sqrt[3]{0.549} \\r = 0.82[/tex]
where
a is the first term
r is the common ratio and
n is the nth term
_________________________________
given
a = 4
4th term = -2.196
let
common ratio of this sequence. be r
[tex]4\ th \ term = ar^n-1\\-2.196 = 4r^{4-1} \\-2.196/4 = r^{3} \\r = \sqrt[3]{-0.549} \\r = -0.82[/tex]
a) Find the common ratio of this sequence.
answer: -0.82
sum of infinity of geometric sequence is given by = a/(1-r)
thus,
sum to infinity of this sequence = 4/(1-(-0.82) = 4/1.82 = 2.2
A scale drawing of an office space uses a scale of 1 in. : 4 yd. The scale drawing has an area of 12 square inches. What is the area of the actual office space?
Answer: 48 yards
Step-by-step explanation:
From the question, we are informed that a scale drawing of an office space uses a scale of 1 in. : 4 yd.
When the scale drawing has an area of 12 square inches, to get the area of the actual office space, we multiply the given number by 4 since the actual office space is 4× the scale drawing. This will be:
= 12 × 4 yards
= 48 yards
What is x equal to? And what is the scale factor?
Answer:
1. 225 km
2. 95 km
3. 412.5 km
Step-by-step explanation:
For this one, it is saying that for every 2 cm, that is 50 km. So if you look at 9 cm, you can divide that by 2 cm to get 4.5 cm, this is what you can multiply by 50 km to get 225. Or you can look at it this way, for every 1 cm, the actual distance is 25 km. Then you can multiply each value by 25 to get your answer. Whichever one works for you.
the population of China is about 1.4 x 10 ^ 9 people. Julie grew up in a town with a population of about 7,000 people. How many times greater is the population of China than Julies town? Please answer this in scientific notation
Answer:
200000
Step-by-step explanation:
I believe that 200000x7000 = 1400000000 (The answer to the China population equation), therefore should be correct. Hope this helped.
Simplify (1/2)^4.......................................................................
Answer:
[tex]-1/16[/tex]
Step-by-step explanation:
Answer:
1/16
Step-by-step explanation:
(1/2 × 1/2 × 1/2 × 1×2)
(1/4 × 1/4)
(1/16)
Does anyone know this!? Pick the one the correctly describes it!
If its correct ill mark you as the best answer!
Answer:
d- the slope is undefined
Step-by-step explanation:
I WILL BRAINLEIST PLEASEMegan earned $4 an hour for babysitting. She earned $16 on Saturday. How many hours did she babysit?
Answer:
4 hours
Step-by-step explanation:
16/4= 4
values of x and y
to
135°
Step-by-step explanation:
Answer:
xy/100=135
xy=13500
x=13500/y
Solve by substitution
Answer:
(1,4)
Step-by-step explanation:
Answer: x = 1, y = 4
Steps: 3y + 4x = 16, -2x + y = 2
Isolate y for 3y + 4x = 16: y = (16 - 4x ÷ 3)
Substitute y into the other equation (-2x + y = 2): -2x + (16 - 4x ÷ 3) = 2
Simplify: 16 - 10x ÷ 3 = 2
Isolate x for 16 - 10x ÷ 3 = 2: x = 1
Substitute x = 1 into y = (16 - 4x ÷ 3): y = 16 - 4x · 1 ÷ 3
y = 4, x = 1
Plz mark brainliest:)
Plz help I don’t get what this is
Answer:
A) 98.94 sq. meters
B) 42 sq. meters
Step-by-step explanation:
A) So first we calculate the area for the square which is 15*20 = 300. Then we calculate the area of the circle which is pi*r^2 and in this case the radius is 4 which is 1/2 of 8. The area is approx. 201.06. Then we subtract that from 300. 300-201.06 = 98.94. The answer for A) is approx. 98.94
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
B)First we calculate the area of the whole square which is 8*6 = 48. Then the area of the garden which is 2*3 = 6. 48-6 = 42. The answer is B) is 42 then.
What is the slope of the line that passes through the points (4, 6) and
(-16, -18)?
Answer:
-3 / 5
Step-by-step explanation:
18-6 / -16-4
12 / -16-4
12 / -20
-3 / 5
5.6 divided by 7
A:8
B:7
C.8
D.7
Other:
Answer:
C
Step-by-step explanation:
Dude, just look it up.
Please help me :( someone anybody just once I won’t ask again
Answer:
1) 77
2) -11
3) -11
4) 7
5) 29
Step-by-step explanation:
Just sub the x into the equation.
*I recommend checking my answers, but this is what I would put/
What is the y-intercept in this problem?
Answer:
(0, -1) I think
Step-by-step explanation:
I have not done this in a while
Hope this helps, though.