Answers
Answer:
Step-by-step explanation:
In the standard form of a quadratic,
[tex]h(x)=-x^2+v_0x+h_0[/tex],
that last term, the h0, is the initial height off the ground that the object is. That means that for the first question, the irrigation system is initially 9.5 feet off the ground.
In order to answer the next question, we need to find the vertex of the parabola, because this is where the max height will occur and at how many feet away from the system. The max height is the k of the vertex and the horizontal distance away is the h of the vertex: (h, k). Thankfully, we have simple formulas to find those:
[tex]h=-\frac{b}{2a}[/tex] and [tex]k=c-\frac{b^2}{4a}[/tex] where a, b, and c come from the coefficients in the equation. For us, a = -1, b = 10, and c = 9.5. Finding h first:
[tex]h=-\frac{10}{2(-1)}=\frac{-10}{-2}=5[/tex]
and now k:
[tex]k=9.5-(\frac{10^2}{4(-1)})=9.5-(\frac{100}{-4} )=9.5-(-25)=9.5+25=34.5[/tex]
Summing it up, the vertex is at (5, 34.5), The interpretation of that is that "The spray reaches a max height of 34.5 feet at a horizontal distance of 5 feet away from the sprinkler head."
Next we are asked how far away from the sprinkler head the water hits the ground. To do this we factor the expression to find the zeros. The zeros tell us where the water will hit the ground after it reaches its max height and then falls back down to earth.
I used my calculator to factor this for me to get that the water will hit the ground 10.87 feet away from the sprinkler head.
Related Questions
Use the graph that shows the solution to f(x) = g(x).
f(x) = 1+2x/x
g(x) = 2+x
What is the solution to f(x) = g(x)?
Select each correct answer:
X = -2
X = -1
X = 1
X = 2
Answers
Answer:
B and C
Step-by-step explanation:
The equation intersects each other at x=-1 and x=1
Justin is saving money to buy a stereo. He has $25 saved in the bank right now. He earns $40 each week delivering newspapers.
Let y = the total amount of money Justin has, and x is in weeks.
Answers
B. Jennifer needs new trim around the base boards.
How much trim does she need?
What assumptions do you make?
Answers
binomial expansions for clever cookies
Answers
The answers are in the red rectangles with the work.
Let me know if something is unreadable.
pls pls pls help me answer this quickly
Answers
Answer:
768
Step-by-step explanation:
(8×8×10)+(8×8×6/3)
= 640+128
= 768
Answered by GAUTHMATH
Find area of the cross section of the dam pictured below
Answers
Answer:
(w + h cotθ)hStep-by-step explanation:
Cross section is the isosceles trapezoid.
Area of trapezoid:
A = 1/2(a + b)hWe have one of the bases and the height.
Let the difference of the base lengths is x.
We have:
(x/2)/h = cot θ ⇒ x = 2h cot θThe area is:
A = 1/2(w + w + 2h cot θ)h = (w + h cotθ)hFind the area of given figure: 6cm 2cm 3cm 1cm
Answers
Answer:
12cm²
Step-by-step explanation:
separate it to two parts, rect and square
rect- 3cm×1cm =3cm²
square- 3cm×3cm =9cm²
then, 3cm²+9cm²=12cm²
Understanding Transversals
Use the diagram to complete the statements. (please helpp)
Answers
Answer:
Step-by-step explanation:
1. Determine the measure of the unknown angles indicated by letters. Justify your answers with
the properties or theorems you used
Answers
Answer:
hello,
Step-by-step explanation:
a)
In an isocele triangle, base's angles have the measure:
42+2a=180
2a=180-42
a=69(°)
b)
in a triangle, an external angle has for measure the sum of the angles not adjacents.
55+b=132
b=77 (°)
c)
in a quadrilater the sum of the (interior) angles is 2*180=360 degrees.
90+90+68+c=360
c=360-90-90-68
c=112 (°)
1. Determine the measure of the unknown angles indicated by letters. Justify your answers with
the properties or theorems you used.
Answers
Answer:
110
Step-by-step explanation:
we use the sum of 3 angles in a triangle is 180
and sum of 2 adjacent angles is 180 too
180= (180-d)+)+(180-85)+(180-165)
so d=110
Step-by-step explanation:
video do oo so do to go do go to
Two walls of a canyon form the walls of a steady flowing river. From a point on the shorter wall, the angle of elevation to the top of the opposing wall is 20° and the angle of depression to the bottom of the opposing wall is 320 feet. Using the appropriate right triangle solving strategies, solve for the following: (Do not round intermediate calculated values. Only the final answer should be rounded to one decimal place.)
Answers
Answer:
x is approximately 226.3 feet
y is approximately 308.6 feet
z is approximately 226.3 feet
Step-by-step explanation:
The given parameters of the walls are;
The angle of elevation from the top of the shorter wall to the top of the opposing wall, θ₁ = 20°
From the diagram, the angle of depression from the top of the shorter wall to the bottom of the opposing wall, θ₂ = 45°
The distance from the bottom of the shorter wall to the base of the opposing wall, l = 320 feet
x = The height of the shorter wall = l × sin(θ₂)
∴ x = 320 feet × sin(45°) = 320 feet × (√2)/2 = 160·√2 feet ≈ 226.3 feet
∴ x ≈ 226.3 feet
By observation, we have;
y = x + z × tan(θ₁)
Where;
z = l × cos(θ₂)
∴ y = 160·√2 + 320 × cos(45°) × tan(20°) ≈ 308.6
y ≈ 308.6 feet
z = l × cos(θ₂)
∴ z = 320 × cos(45°) = 160·√2 ≈ 226.3
z ≈ 226.3 feet.
What are the solutions to the system of equations graphed below?
Answers
Answer:
The answer is B (4, 8) and (0, -8)
Name the quadrant or axis where the point (4.-6) is located.
Answers
Answer:
Step-by-step explanation:
(4, -6) is in quadrant IV , (quadrant 4)
PLEASE HELP, solve for X
Answers
Answer:
27
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
(48+x) * 48 = 60^2
(48+x)48=3600
Divide each side by 48
48+x =75
Subtract 48
48+x-48 = 75-48
x =27
( a ) 2x + 3y − 5z ( ) 32
( b ) x + y + z ( ) 8
( c ) x
2 + 2xy + z
2
( ) 36
( d ) (x + y)(x + z) ( ) −1
( e ) −(x
2 − y
2
) ( ) −16
Answers
Answer:
Step-by-step explaWe are losing Earth's greatest biological treasures just as we are beginning to appreciate their true value. Rainforests once covered 14% of the earth's land surface; now they cover a mere 6% and experts estimate that the last remaining rainforests could be consumed in less than 40 years.
One and one-half acres of rainforest are lost every second with tragic consequences for both developing and industrial countries.
Rainforests are being destroyed because the value of rainforest land is perceived as only the value of its timber by short-sighted governments, multi-national logging companies, and land owners.
Nearly half of the world's species of plants, animals and microorganisms will be destroyed or severely threatened over the next quarter century due to rainforest deforestatioue to rainforest deforestation. That equates to. As the rainforest species of tesrees anddisappear, so do many possible that 1% plants have been tested by sciMost rainforests are cleared by chainsaws, bulldozers and fires for its timber value and then are followed by farming and ranching operations, onian Rainforest five centuries ago. Today there are less than 200,000.
In Brazil alone, European colonists have destroyed more than 90 indigenous tribes since the 1900's. With them have gone centuries of
nation:
please help! i have no idea
Answers
Answer:
θ = 51.7
SOH-CAH-TOA
CAH: COS = ADJ/HYP cos(θ) = 19.4/29.3
θ = 48.5
93.2 + 48.5 + x = 180
x = 38.3
90 + 38.3 + θ = 180
θ = 51.7
Step-by-step explanation:
The price of an item increased by 25 percent. if the price of the item after the increase is 2.00. What was the original price? (Show your work)
A. 1.50
B. 1.60
C. 1.75
D. 2.50
E. 3.20
Answers
Let the original price = x
From X to get the new price you multiply by 1 + the percent of the increase which is 25%
1,25X = 2.00
Divide both sides by 1.25:
X = 1.60
The original price was B. 1.60
Answer:
x=1.60
Step-by-step explanation:
Let x be the original price
We increase by 25%
x+ .25x = new price
1.25x = 200
Divide each side by 1.25
x = 2.00/1.25
x=1.60
what is percent of a number
Answers
Step-by-step explanation:
a fraction of a number out of 100%
Answer and step-by-step explanation:
Percent (%) means per 100
A percentage is a number or ratio expressed as a fraction of 100
Example 50% of 8 = 8*50/100 = 4
Solve for x.
A) - 9
C) -5
B) -11
D) 10
Answers
Answer: D) 10
Step-by-step explanation:
All angles in a triangle adds up to 180°
60° + 50° + 7x = 180°
7x = 180° - 60° - 50° = 180°- 110° = 70°
x = (70 ÷ 7)° = 10°
please help, is associated with angles. thank u :)
Answers
Answer:
Step-by-step explanation:
Because those lines are parallel, that means that the angle measuring 75 and the angle measuring 4x + 7 are alternate interior and by definition are congruent. Therefore,
75 = 4x + 7 and
68 = 4x so
x = 17
A package of 3 pairs of insulated gloves costs $26.07. What is the unit price of the pairs of
gloves?
Answers
Answer:
8.69 per pair
Step-by-step explanation:
Take the total cost and divide by the number of pairs
26.07 /3
8.69 per pair
Please help me answer it right
Answers
Answer: B
Step-by-step explanation:
3/4 x 4/4 = 12/16
Answer:
12/16
Step-by-step explanation:
16 is a multiple of 4, so using the scale factor of 16 and 4, you can solve to find the numerator.
16 / 4 = 4
3 × 4 = 12
The answer is 12/16.
Hope this helps.
In a carnival drawing, a yellow ticket wins $1, a green ticket wins $5, and a blue ticket wins $10. There are 20 green tickets, 25 yellow tickets and 5 blue tickets. In simplest form, what are the odds in favor of winning $5 or more?
A. 1:1
B. 1:2
C. 2:1
D. 1:3
Answers
Answer: B. 1:2
Step-by-step explanation: Since there are 20 green tickets and 5 blue tickets that means there are 25 tickets that could win $5 or above and the total number of tickets are 50. That means there is a 25/50 chance you could win a ticket above $5. If you simplify the ratio you will get 1/2 or 1:2
The odds in favor of winning $5 or more is 1:2.
In a carnival drawing, a yellow ticket wins $1, a green ticket wins $5, and a blue ticket wins $10. There are 20 green tickets, 25 yellow tickets and 5 blue tickets.
What is the odd?
Odd refers to a number that will have a remainder of 1 when divided by 2. Odd also describes something that is unusual or weird. Odd has many other senses.
Since there are 20 green tickets and 5 blue tickets that means there are 25 tickets that could win $5 or above and the total number of tickets are 50. That means there is a 25/50 chance you could win a ticket above $5. If you simplify the ratio you will get 1/2 or 1:2.
To learn more about the odds visit:
https://brainly.com/question/79151
#SPJ2
Joan is cutting a roll of ribbon to be used as bows on gifts. If each bow takes 7/8 of a metre of ribbon and Joan has 7 m total of ribbon, how many bows can be made?
Answers
a) 61°
b) 29°
C) 40°
d) 50°
Answers
Answer:
29 degrees (~0.506 rad)
What is the main purpose of closing entries for revenues and expenses into Profit and Loss Summary? a. To determine the profit for period. b. To transfer the journalised entries to relevant ledger account. c. To check the accuracy of journal entries. d. To provide information of business ability to repay for the debt.
Answers
Answer:
A
Step-by-step explanation:
Revenues and expenses are closed every year so that the profit or loss can be determined for the yearly period.
A carpenter is making a backyard deck. In the measurements, he has determined that he needs to make a support triangle with an area 46m2. He knows that the base must be 1 less than 2 times the height. If the base is represented by 2x-1 and height equals x. Find the equation that correctly shows the area of the triangle.
Answers
Answer:
base = 3x - 1
height = x
area of triangle = (1/2)bh
22 = (1/2)(3x-1)(x)
44 = (3x-1)(x)
44 = 3x^2-x
0 = 3x^2-x-44
0 = 3x^2-12x+11x-44
0 = (3x^2-12x)+(11x-44)
0 = 3x(x-4)+11(x-4)
0 = (x-4)(3x+11)
x = {-11/3, 4}
throw out the negative solution (extraneous) leaving
x = 4 m (height)
.
Base:
3x - 1 = 3(4) - 1 = 12 - 1 = 11
Step-by-step explanation:
I hope it will help you
Find the value of the trigonometric ratio.simply the fraction if needed.
Answers
Answer:
Cos A = Adjacent / hypochondrium
Cos A= 9/ 41
Terri is buying some candy at the corner store. There, small candies cost 10 1 point cents each and large ones cost 25 cents each. Terri bought 52 candies and spent $8.05. A system of equations describing this situation could be written in the form below where S represents the number of small candies and L represents the number of large candies. What is the sum of A, B, C and D? *
Answers
hi my name how are you home work sind
Find the length of the side and area ot the square whose perimeter is given below a)44cm b)80cm
Answers
9514 1404 393
Answer:
a) 11 cm
b) 20 cm
Step-by-step explanation:
A square has four equal-length sides, so the perimeter is 4 times the side length. Then the side length is 1/4 of the perimeter.
a) s = (1/4)(44 cm) = 11 cm
b) s = (1/4)(80 cm) = 20 cm
