Answer:
(a) [tex]\sf -16r^2+20r-4=0[/tex]
(b) r = 1, r = 1/4
Step-by-step explanation:
Given equation: [tex]\sf h=-16r^2+20r-4[/tex]
where:
h = height (in feet)t = time (in seconds)Question (a)
The ball will hit the ground when h = 0
[tex]\sf \implies-16r^2+20r-4=0[/tex]
Question (b)
To factor [tex]\sf -16r^2+20r-4=0[/tex]
Divide both sides by 4:
[tex]\sf \implies-4r^2+5r-1=0[/tex]
Swap signs:
[tex]\sf \implies 4r^2-5r+1=0[/tex]
Split middle term:
[tex]\sf \implies 4r^2-4r-r+1=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\sf \implies 4r(r-1)-(r-1)=0[/tex]
Factor out common term (r - 1):
[tex]\sf \implies (4r-1)(r-1)=0[/tex]
Therefore:
[tex]\sf \implies (4r-1)=0 \implies r=\dfrac14[/tex]
[tex]\sf \implies (r-1)=0 \implies r=1[/tex]
320 people attended a rock concert how much money was taken?
rock concert £6 per person
Answer:
320 x 6 euros = 1920 Euros
Step-by-step explanation:
Simple multiplication :)
Hope this helps
Answer:
£1,920
Step-by-step explanation:
Multiply 320 by 6
320 • 6 = 1,920
And your answer will be 1,920
I hope it helps! Have a great day!
Muffin ^^
Express the trig ratios as fractions in simplest terms.
Answer:
See below
Step-by-step explanation:
[tex]\cos M=\frac{adjacent}{hypotenuse}=\frac{56}{70}=\frac{4}{5}\\\\\sin L=\frac{opposite}{hypotenuse}=\frac{56}{70}=\frac{4}{5}[/tex]
Hence, both ratios are equal to each other
Hi I just need quick answers !
⇒ Perimeter = 10 + 10 + 10 + 10 = 40 ft
Question 2: Find the slant height Definition of Slant Height: is the distance measured along a lateral face from the base to the center along the "center" of the faceTo understand the slant height, look at the diagram I attached
Slant height: 13 ft
Question 3: Find the Lateral AreaDefinition of Lateral Area: Area of the non-base faces only⇒ Lateral Area = 4 * (Area of Triangle)
= [tex]4*(\frac{1}{2} *10 * 13) = 4 * 5* 13 = 260ft^2[/tex]
= 260 ft^2
Question 4: Area of BaseArea of Base = 10 * 10 = 100ft^2
Question 5: Surface AreaDefinition of Surface Area: sum of the areas of surfaces of the figureSurface Area = Area of Base + Lateral Area
= 100 + 260 = 360 ft^2
Hope that helps!
The angle \theta_1θ 1 theta, start subscript, 1, end subscript is located in Quadrant \text{III}IIIstart text, I, I, I, end text, and \sin(\theta_1)=-\dfrac{\sqrt{3}}{2}sin(θ 1 )=− 2 3 sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, minus, start fraction, square root of, 3, end square root, divided by, 2, end fraction .
i need help with this i don't know how to do it.
Answer:
1935 were supporting the home team
Step-by-step explanation:
Since there are 4,500 people attending the game, we must find 43% of that. Doing this, we need to multiply 43% or .43 by 4,500.
After solving, you should get 1,935. There were 1,935 people supporting the home team.
each row in the table below shows one possible set of angle measurements for this drawing
find the missing angle measurements
Applying the definitions of angles on a straight line and vertical angles, the missing angle measurementts are given in the table atached below.
What are Angles on a Straight Line?Angles found on a straight line equals 180 degrees.
What area Vertcial Angles?Vertical angles are congruent angles that lie directly opposite each other.
Second Row:
m∠LGK = 45° (given in the diagram)
m∠IGH = 35° (given in the table)
m∠KGJ = m∠IGH (vertical angles)
m∠KGJ = 35°
m∠JGI = 180 - m∠KGJ (angles on a straight line)
m∠JGI = 180 - 35 = 145°
m∠HGL = 180 - m∠LGK - m∠IGH (angles on a straight line)
m∠HGL = 180 - 45 - 35 = 100°
Third Row:
m∠LGK = 45° (given in the diagram)
m∠HGL = 97° (given in the table)
m∠KGJ = 180 - m∠HGL - m∠LGK (angles on a straight line)
m∠KGL= 180 - 97 - 45 = 38°
m∠JGI = 180 - m∠KGJ (angles on a straight line)
m∠JGI = 180 - 38 = 142°
m∠IGH = m∠KGL (vertical angles)
m∠IGH = 38°
Thus, applying the definitions of angles on a straight line and vertical angles, the missing angle measurementts are given in the table atached below.
Learn more about straight line and vertical angles on:
https://brainly.com/question/14362353
Find the arc length of a central angle of 36° in a circle whose radius is 2 inches.
Answer:
y
Step-by-step explanation:
bc I told u to ..............
Given the function f(x)=3-2x^2, find k such that f(k)=-3
Answer:
k = ±√3
Step-by-step explanation:
Given :
f(x) = 3 - 2x²f(k) = -3To find the value of k, we need to equate both the functions to find the value of x such that it is equal to the value of k.
⇒ 3 - 2x² = -3⇒-2x² = -6⇒ x² = 3⇒ x = ±√3We already set a relation before, which is :
x = kTherefore, k = ±√3A group of coins is shown below. What is the probability and it's compliment of randomly selecting a nickel?
Answer:
Please post the full question.
Step-by-step explanation:
I am trying to help, but the question is missing some key info.
Please dont delete, as when he posts the full thing, I will reply to this answer with the answer and explanation.
NEED ANSWERS TO THESE PAGES!!!!!
Evaluate each algebraic expression.
3w + 4 ; w = 1/4, 7, -2
Please help me with this please and thank you
Answer:
L bozo
Step-by-step explanation:
ur whole life is an L
need it ASAP If a graph shows intersecting lines that represent a system of equations, how many solutions does that system of equations have?
Infinite solutions
No solution
Two solutions
One solution
Answer: Well, the answer really depends. But here are a few ways you can figure this out.
Step-by-step explanation:
If the two lines intersect once, then they have one solution.
If they intersect twice there are two solutions
If the lines never intersect, there are no solutions
And if the lines are identical, meaning that their equation is exactly the same. There are infinite solutions.
A solution with systems of equations is determined by the point of intersection. Your answer is the point of intersection
I hope this is helpful! : )
Answer:
no s
Step-by-step explanation:
What is the scale factor of this dilation?
Answer:
I am not sure but I thing it is -2.
Step-by-step explanation:
Hope it helps! (Please mark brainliest if it does!)
1.6667
Step-by-step explanation:
the lengths are the same on both sides which makes the triangles equilateral
therefore the scale=5/3
=1.6667
Does the graph represent a function? Why or why not?
What is the measure of \angle D∠Dangle, D?
Answer:
135⁰
Step-by-step explanation:
As in cyclic quadrilateral sum if opposite angles is equal to 180⁰
Explain the error and solve with correct step.
-5x + 9 - 9x < 21
-4x + 9 < 21
-4x < 12
x > -3
help me solve please show steps
There can be several possibilities and causes
y>2x-1
Then line will be dashed and solution region to be shaded.y<2x-1
Same like beforey≤2x-1
Solid line should be done and shading the solution regiony≥2x-1
Same like beforey=2x-1
A straight line and no shadingCredit: Mister Brainly
There can be several possibilities and causes:
y>2x-1
Then line will be dashed and solution region to be shaded.
y<2x-1
Same like before
y≤2x-1
Solid line should be done and shading the solution region
y≥2x-1
Same like before
y=2x-1
A straight line and no shading
A grain silo has a cylindrical shape. Its radius is 8ft, and its height is 36ft. What is the volume of the silo?
Use the value 3.14 for[tex]\pi[/tex], and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
The volume of a silo cylinder with radius of 8 feet and height of 36 feet is 7235 feet cube.
Volume of a cylinderThe volume of a cylinder can be calculated as follows;
Volume = πr²h
where
r = radiush = heightTherefore,
r = 8 ft
h = 36 ft
volume = 3.14 × 8² × 36
volume = 3.14 × 64 × 36
volume of the silo = 7234.56
Therefore, the volume of the cylindrical silo is 7235 ft³
learn more on volume here: https://brainly.com/question/27270919
What is the measurement of < F
Answer:
Option C - 65°
Step-by-step explanation:
Since the side lengths of this triangle are equal this triangle is an isosceles:
Because the triangle is an isosceles the base angles are equal so
∠G = ∠F = 65°
1) 3x + 6 - 2 + 5x
2) a bicycle is originally priced at 80$. The store owner gives a discount and the bicycle is now 60$. What percent discount was taken off?
Answer: ✨4(2+1)✨
Step-by-step explanation: ✨3+6−2+53x+6−2+5x3+4+53✨
Answer:
4(2x + 1)
---->
Step-by-step explanation:
1: 3x + 6 - 2 + 5x = 4(2x + 1)
2: Orignal Cost=80
Discounted Cost=60
Discount=80-60=20
Discount%=(20/80)*100=25%
Which of the following equations would describe the graph shown below?
Answer:
2
Step-by-step explanation:
WHOEVER ANSWERS THE QUESTION FIRST WILL GET 15 POINTS!!!!!
Answer:
b
Step-by-step explanation:
the answer is b
in the problem you can put the expression into a calculator and you will get the answer 3
in option b, y+2=3 bc a variable is always equal to one so your basically adding 1+2 which is equal to 3
I HOPE I HELPED A BIT<3
2x(5x-2)+(3x-0.5)*2=2x+3+10x-5+2x+3
Find X
(give step by step)
Answer:
x = 1.348331477 and 0.148331477
Step-by-step explanation:
TEPS USING THE QUADRATIC FORMULA2x(5x−2)+(3x−0.5)2=2x+3+10x−5+2x+3Use the distributive property to multiply 2x by 5x−2.10x2−4x+(3x−0.5)×2=2x+3+10x−5+2x+3Use the distributive property to multiply 3x−0.5 by 2.10x2−4x+6x−1=2x+3+10x−5+2x+3Combine −4x and 6x to get 2x.10x2+2x−1=2x+3+10x−5+2x+3Combine 2x and 10x to get 12x.10x2+2x−1=12x+3−5+2x+3 Subtract 5 from 3 to get −2.10x2+2x−1=12x−2+2x+3Combine 12x and 2x to get 14x.10x2+2x−1=14x−2+3Add −2 and 3 to get 1.10x2+2x−1=14x+1Subtract 14x from both sides.10x2+2x−1−14x=1Combine 2x and −14x to get −12x.10x2−12x−1=1Subtract 1 from both sides.10x2−12x−1−1=0Subtract 1 from −1 to get −2.10x2−12x−2=0This equation is in standard form: ax2+bx+c=0. Substitute 10 for a, −12 for b, and −2 for c in the quadratic formula, 2a−b±b2−4ac.x=2×10−(−12)±(−12)2−4×10(−2)Square −12.x=2×10−(−12)±144−4×10(−2)Multiply −4 times 10.x=2×10−(−12)±144−40(−2)Multiply −40 times −2.x=2×10−(−12)±144+80Add 144 to 80.x=2×10−(−12)±224Take the square root of 224.x=2×10−(−12)±414The opposite of −12 is 12.x=2×1012±414Multiply 2 times 10.x=2012±414Now solve the equation x=2012±414 when ± is plus. Add 12 to 414.x=20414+12Divide 12+414 by 20.x=514+3Now solve the equation x=2012±414 when ± is minus. Subtract 414from 12.x=2012−414Divide 12−414 by 20.x=53−14The equation is now solved.
x=514+3x=53−14
Help Needed. Please.....!
Answer:
1 7/8
Step-by-step explanation:
You just have to subtract 2 from 1/8.
What is the equation of the line passing through (0,2), with a slope of 5?
Answer:
y=mx+c
Finding the y-intercept by substituting the given points into the equation.
y=mx+c
2=5(0)+c
2-5=c
-3=c
Now, the equation is:
y=5x-3
what are the numbers for pie I need to know
Answer:
Pi is exactly [tex]3.1415926535897932384626433832795[/tex]
Pi is often used in mathematical expressions, calculating measurements, and finding circumference as well as volume.
65, 46, 78, 3, 87, 12, 99, 38, 71, 38
what is the median??
Answer:
median = 55.5
Step-by-step explanation:
Here we have 10 numbers which is an even number
then the median for the data set is the average of the two middle numbers
firstly ,we have to put the number of the set in order from least to greatest like this :
3 < 12 < 38 < 38 < 46 < 65 < 71 < 78 < 87 < 99
———————— ————————-
As you can see the middle two numbers are : 46 and 65
Now, we calculate their average :
[tex]\large \text Median = \frac{46+65}{2}= 55.5[/tex]
Tell whether each number is rational or irrational.0.121121112....
Last one, I promise!!! ._.
19x+28=20x-53
Answer:
x = 81
Step-by-step explanation:
Given:
[tex]\displaystyle \large{19x+28=20x-53}[/tex]
Subtract both sides by 28:
[tex]\displaystyle \large{19x+28-28=20x-53-28}\\\displaystyle \large{19x=20x-81}[/tex]
Subtract both sides by 19x:
[tex]\displaystyle \large{19x-19x=20x-81-19x}\\\displaystyle \large{0=x-81}[/tex]
Add both sides by 81:
[tex]\displaystyle \large{0+81=x-81+81}\\\displaystyle \large{81=x}\\\displaystyle \large{\therefore x=81}[/tex]
Therefore, the solution is x = 81
Let me know if you have any questions!
[tex]{\boxed{\mathfrak{✿ฺSolution :}}} [/tex]
[tex] \bold{ 19x+28 = 20 x - 53 }[/tex]
[tex] \bold{ 19x+28 - 28 =20x - 53 - 28}[/tex]
[tex]\bold{ 19x = 20x - 81 }[/tex]
[tex]\bold{ 19x - 20x = 20x - 81 - 20x }[/tex]
[tex]\bold{ -x = - 81 }[/tex]
[tex]\bold{ \frac{ - x}{ - 1} = \frac{ - 81}{ - 1} }[/tex]
[tex] \bold{ x = 81 }[/tex]