If ABCD is a parallelogram, AD = 14, EC = 11, mZABC = 64°, mZDAC = 71°, and mZBDC = 25,
find each measure.
А
a) BC =
d) mZABD =
B
b) AC =
e) m ACD =
E
D
С
c) m DAB
f) mZADB =
Answers
Find attached to this answer the diagram of the Quadrilateral
Question:
If ABCD is a parallelogram, AD = 14, EC = 11, m∠ABC = 64°, m∠DAC = 71°, and m∠BDC = 25, find each measure.
a) BC =
b) AC =
c) m∠DAB =
d) m∠ABD =
e) m∠ACD =
f) m∠ADB =
Answer:
a) BC = 11
b) AC = 22
c) m∠DAB = 116°
d) m∠ABD = 39°
e) m∠ACD = 45°
f) m∠ADB = 25°
Step-by-step explanation:
a) BC
In the question above, EC = 11
We can see that EC and BC are equal sides of a diagonal line that has been divided into two equal parts in a Quadrilateral.
Hence, In a quadrilateral ABCD,
EC = BC
Hence BC = 11
b) AC
AC is one of the diagonal lines that divided parallelogram ABCD
AC = BC + EC
AC = 11 + 11
AC = 22
c) m∠DAB
m∠ABC = 64°
m∠ADC = 64°
For the two angles above, a diagonal bisects through those angles.
Also the sum of angles in a triangle = 180°
Hence,
180° = 1/2m∠ABC + 1/2m∠ADC +
m∠DAB
m∠DAB = 180° - ( 1/2 (64) + 1/2(64))
m∠DAB = 180 ° - 64°
m∠DAB = 116°
d) m∠ABD
Since,
m∠ABC = 64° and m∠BDC = 25
m∠ABC = m∠BDC + m∠ABD
64 = 25+ m∠ABD
m∠ABD = 64° - 25°
m∠ABD = 39°
e) m∠ACD
In the above question,
m∠ABC = 64°,
m∠ADC = m∠ABC, this is because, opposite angles in a quadrilateral are congruent and equal to each other.
Hence, m∠ADC = 64°
m∠DAC = 71°,
In a triangle , all the angles in a triangle = 180°
Hence,
180° = m∠DAC + m∠ADC + m∠ACD
180° = 71° + 64 ° + m∠ACD
m∠ACD = 180° -(71 + 64)°
m∠ACD = 180° - 135°
m∠ACD = 45°
f) m∠ADB
Since
m∠DAB = 116°
m∠ABD = 39°
The sum of angles in a triangle = 180°
180° = m∠ABD + m∠DAB + m∠ADB
180° = 39 ° + 116° + m∠ADB
m∠ADB = 180° - ( 116 + 39)°
m∠ADB = 25 °
a) BC = 11
b) AC = 22
c) m∠DAB = 116°
d) m∠ABD = 39°
e) m∠ACD = 45°
f) m∠ADB = 25°
Given : AD=14 , EC=11, m∠ABC= 64°, m∠DAC=71° and m∠BDC=25°
To find: BC =? , AC =? , m∠DAB =?, m∠ABD =? ,m∠ACD =? ,m∠ADB =?
Consider the figure given below ABCD is a parallelogram
To find a) BC
Given, EC = 11
As seen in figure that EC and BC are equal sides of a diagonal line that has been divided into two equal parts in a Parallelogram.
Hence, In a Parallelogram ABCD,
EC = BC
Hence BC = 11
To find b) AC
AC is one of the diagonal lines that divided parallelogram ABCD
AC = BC + EC
AC = 11 + 11
AC = 22
To find c) m∠DAB
Given, m∠ABC = 64°
m∠ADC = 64°
(For the two angles above, a diagonal bisects through those angles)
Also From Angle sum property;
Hence,
180° = 1/2m∠ABC + 1/2m∠ADC + m∠DAB
m∠DAB = 180° - ( 1/2 (64) + 1/2(64))
m∠DAB = 180 ° - 64°
m∠DAB = 116°
To find d) m∠ABD
Since,
m∠ABC = 64° and m∠BDC = 25
m∠ABC = m∠BDC + m∠ABD
64 = 25+ m∠ABD
m∠ABD = 64° - 25°
m∠ABD = 39°
To find e) m∠ACD
Given, m∠ABC = 64°;
m∠ADC = m∠ABC, this is because, opposite angles in a quadrilateral (here parallelogram) are congruent and equal to each other
Hence, m∠ADC = 64°
m∠DAC = 71°,
In a triangle , all the angles in a triangle = 180°(Angle sum property)
Hence,
180° = m∠DAC + m∠ADC + m∠ACD
180° = 71° + 64 ° + m∠ACD
m∠ACD = 180° - (71 + 64)°
m∠ACD = 180° - 135°
m∠ACD = 45°
To find f) m∠ADB
Since ,m∠DAB = 116° and m∠ABD = 39°
From Angle sum property;
180° = m∠ABD + m∠DAB + m∠ADB
180° = 39 ° + 116° + m∠ADB
m∠ADB = 180° - ( 116 + 39)°
m∠ADB = 25 °
Learn more:
https://brainly.com/question/23163052
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Answer:
y=2x-4
Step-by-step explanation:
Add -2x to both sides.
-y=-2x+4
divide each side by -1 to get y=mx+b.
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Answer:
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Step-by-step explanation:
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Help please! Your effort is appreciated!
Answers
Answer:
[tex]a^1[/tex]
Step-by-step explanation:
We want to rewrite [tex]\frac{a * a * a * a * a * a * a}{a * a * a* a * a * a}[/tex] in index form. That is:
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Part A Each time you press F9 on your keyboard, you see an alternate life for Jacob, with his status for each age range shown as either alive or dead. If the dead were first to appear for the age range of 75 to 76, for example, this would mean that Jacob died between the ages of 75 and 76, or that he lived to be 75 years old. Press F9 on your keyboard five times and see how long Jacob lives in each of his alternate lives. How long did Jacob live each time? Part B The rest of the potential clients are similar to Jacob, but since they’ve already lived parts of their lives, their status will always be alive for the age ranges that they’ve already lived. For example, Carol is 44 years old, so no matter how many times you press F9 on your keyboard, Carol’s status will always be alive for all the age ranges up to 43–44. Starting with the age range of 44–45, however, there is the possibility that Carol’s status will be dead. Press F9 on your keyboard five more times and see how long Carol lives in each of her alternate lives. Remember that she will always live to be at least 44 years old, since she is already 44 years old. How long did Carol live each time? Part C Now you will find the percent survival of each of your eight clients to the end of his or her policy using the simulation in the spreadsheet. For each potential client, you will see whether he or she would be alive at the end of his or her policy. The cells in the spreadsheet that you should look at to determine this are highlighted in yellow. Next, go to the worksheet labeled Task 2b and record either alive or dead for the first trial. Once you do this, the All column will say yes if all the clients were alive at the end of their policies or no if all the clients were not alive at the end of their policies. Were all the clients alive at the end of their policies in the first trial? Part D Next, go back to the Task 2a worksheet, press F9, and repeat this process until you have recorded 20 trials in the Task 2b worksheet. In the Percent Survived row at the bottom of the table on the Task 2b worksheet, it will show the percentage of times each client survived to the end of his or her policy, and it will also show the percentage of times that all of the clients survived to the end of their respective policies. Check to see whether these percentages are in line with the probabilities that you calculated in questions 1 through 9 in Task 1. Now save your spreadsheet and submit it to your teacher using the drop box. Are your probabilities from the simulation close to the probabilities you originally calculated?
Answers
Step-by-step explanation:
brain list me please......
Answer:
Jacob:
Alive 69-70
alive 79-80
alive 62-63
alive 73-74
alive 78-Died 79
Carol:
alive 88-89
alive 67-68
alive 99-100
alive 73-74
alive 94- Died 95
Step-by-step explanation:
Both the red and blue line segments stretch from the center of the circle to a
point on the circle. The length of the blue line segment is 5. How long is the
red line segment?
5
Center
O A. 10
O B. 2.5
O c. 5
O D. 7.5
Answers
Answer:
C. 5
Step-by-step explanation:
The circle has point in the center from where two line blue and red are stretched to the point on the circle. The blue line is 5 in length and the red line length is not known. The circumference of the circle is equal on all the area around the origin. Therefore the red line must also be 5 in length as of blue line.
In the diagram what is the measure of WRS
Answers
Step-by-step explanation:
in the diagram what is the value of WRS
Find the exact values of sin 2θ and cos 2θ for cos θ = 6/13
Answers
Answer:
Step-by-step explanation:
cos^-1(6/13)=62.5136°
sin(2*62.5136°)=0.8189
cos(2*62.5136°)=-0.5740
Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $775 from a combination of $5.00 quick washes and $8.00 premium washes. This system of equations models the situation. x + y =125 5x + 8y = 775
Answers
Answer:
[tex] x+y = 125[/tex] (1)
[tex] 5x+8y = 775[/tex] (2)
We can solve for y from equation (1) and we got:
[tex] y = 125-x[/tex] (3)
And replacing (3) into (2) we got:
[tex] 5x +8(125-x) = 775[/tex]
And solving for x we got:
[tex] 1000-3x = 775[/tex]
[tex] 3x= 225[/tex]
[tex] x=75 [/tex]
And solving for y from (3) we got:
[tex] x= 125-75 =50[/tex]
And the solution would be x = 50 and y =75
Step-by-step explanation:
For this problem we have the following system of equations:
[tex] x+y = 125[/tex] (1)
[tex] 5x+8y = 775[/tex] (2)
We can solve for y from equation (1) and we got:
[tex] y = 125-x[/tex] (3)
And replacing (3) into (2) we got:
[tex] 5x +8(125-x) = 775[/tex]
And solving for x we got:
[tex] 1000-3x = 775[/tex]
[tex] 3x= 225[/tex]
[tex] x=75 [/tex]
And solving for y from (3) we got:
[tex] x= 125-75 =50[/tex]
And the solution would be x = 50 and y =75
What is the solution to the equation -0.2(x - 20) = 44 - x? x = -90 x = 50 x = -50 x = 90
Answers
Answer:
x= 50
Step-by-step explanation:
First, simplify the equation
Expand the terms on the left hand side to make it easier to rearrange
-0.2(x-20) =44-x
-0.2x+4 =44-x
Rearrange the equation by moving the numbers to one side and the variables to the other
-0.2x +x= 44-4
0.8x = 40
Isolate for x
x= 40/0.8
x= 50
A political analyst predicts Mr. Smith will only get 122 votes for mayor. If Mr. Smith only gets 57 votes, what is the political analyst's percent error?
Answers
Answer:
65%
Step-by-step explanation:
WHat is the answer to this?
Answers
Answer:
0.9
Step-by-step explanation:
First, convert them all into fractions:
[tex]2\frac{1}{3}=\frac{7}{3}[/tex]
[tex].5=\frac{1}{2}[/tex]
Now, we have:
[tex]\frac{4x+9}{\frac{7}{3} } =\frac{3x}{\frac{1}{2} }[/tex]
Cross multiply:
[tex]\frac{1}{2} (4x+9)=\frac{7}{3} (3x)[/tex]
On the left, distribute. On the right, notice that the 3 in the denominator and the coefficient 3 cancel:
[tex]2x+4.5=7x[/tex]
[tex]4.5=5x[/tex]
[tex]x=0.9=9/10[/tex]
Answer and step-by-step explanation:
Photo
a lottery game has balls numbered 1 through 21. what is the probability of selecting a ball with a prime number on it or a 10
Answers
Answer:
3/7
Step-by-step explanation:
The prime numbers that lie between 1 and 21 are 2,3,5,7,11,13,17, and 19. These 8 balls, plus the 10-ball comes to a total of 9 balls that could be picked out of the 21. Therefore, the probability of picking one of these balls is 9/21 or 3/7
Answer:
[tex]\frac{9}{21}[/tex]
Step-by-step explanation:
→ List the prime numbers between 1 and 21
2, 3, 5, 7, 11, 13, 17 and 19
→ Count how many ball that is
8 balls
→ Remember in the question it says "what is the probability of selecting a ball with a prime number on it or a 10"
8 balls + 1 ball (the one with the number 10)
→ 9 balls overall over a total of 21
consider the distribution of monthly social security (OASDI) payments. Assume a normal distribution with a standard deviation of $116. if one-fourth of payments are above $1214,87 what is the mean monthly payment?
Answers
Answer:
[tex]\mu = x - z(\sigma)[/tex]
[tex]\mu = 1214.87 - 0.67(116) \\\\\mu = 1214.87 - 77.72 \\\\\mu = \$1137.15[/tex]
Therefore, the mean monthly payment is $1137.15.
Step-by-step explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
We are asked to find the mean monthly social security (OASDI) payment.
Mean monthly payment = μ = ?
We are given that the standard deviation is $116
One-fourth of payments are above $1214.87
One-fourth means 25%
[tex]P(X > x )= P(Z > z ) = 0.25\\\\P(X < x )= P(Z < z) = 1 - 0.25\\\\P(X < x )= P(Z < z) = 0.75\\\\[/tex]
From the z-table, the z-score corresponding to 0.75 is found to be 0.67
[tex]z = 0.67[/tex]
The mean is found by
[tex]x = \mu + z(\sigma)[/tex]
[tex]\mu = x - z(\sigma)[/tex]
Where
x = $1214.87
z = 0.67
σ = $116
[tex]\mu = 1214.87 - 0.67(116) \\\\\mu = 1214.87 - 77.72 \\\\\mu = \$1137.15[/tex]
Therefore, the mean monthly payment is $1137.15.
Brainliest for the correct awnser!! Multiply each side by the common denominator to find the quadratic equation equivalent to this equation.
Answers
Answer:
B.
Step-by-step explanation:
You can cross multiply or multiply by the common denominator. The common denominator in this case is [tex]5\cdot x=5x[/tex]
[tex]5x(\frac{6}{x})=5x(\frac{2x+4}{5})[/tex]
[tex]30=2x^2+4x[/tex]
[tex]2x^2+4x-30=0[/tex]
Note that [tex]x\neq 0[/tex]
Answer:
B
Step-by-step explanation:
Well the common denominator of 5 and x is 5*x=5x.
[tex]5x(\frac{6}{x} )=5x(\frac{2x+4}{5} )\\\\30=2x^{2} +4x\\\\2x^2+4x-30=0[/tex]
Copy the problem, mark the givens in the diagram, and write a Statement/Reason proof. Given: MN ≅ MA ME ≅ MR Prove: ∠E ≅ ∠R
Answers
Answer:
Step-by-step explanation:
Given: MN ≅ MA
ME ≅ MR
Prove: ∠E ≅ ∠R
From the given diagram,
YN ≅ YA
EY ≅ RY
<EMA = <RMN (right angle property)
EA = EY + YA (addition property of a line)
NR = YN + RY (addition property of a line)
EA ≅ NR (congruent property)
ΔEMA ≅ ΔRMN (Side-Side-Side, SSS, congruence property)
<MNR ≅ MAE (angle property of congruent triangles)
Therefore,
<E ≅ <R (angle property of congruent triangles)
let f(x) = 2x^2 + x - 3 and g(x) = x+ 2. Find (f • g) (x)
Answers
Answer:
(f • g) (x) = 2x² + 9x + 7Step-by-step explanation:
f(x) = 2x² + x - 3
g(x) = x + 2
To find (f • g) (x) substitute g(x) into every x in f (x)
That's
(f • g) (x) = 2(x + 2)² + x + 2 - 3
Expand and simplify
(f • g) (x) = 2( x² + 4x + 4) + x - 1
= 2x² + 8x + 8 + x - 1
Group like terms
= 2x² + 8x + x + 8 - 1
We have the final answer as
(f • g) (x) = 2x² + 9x + 7Hope this helps you
a scale drawing of a rectangular playground has a length of 20 inches and a width of 10 inches as shown below. the scale is 1 inch = 4 feet. what is the area of the actual playground? *
Answers
Answer:
3,200 ft²
Step-by-step explanation:
first you want to convert the sides from inches to feet so 20* 4= 80, and 10* 4= 40 then you multiply the sides to get the area which is 80*40= 3,200 ft²
An architect needs to consider the pitch, or steepness, of a roof in order to ensure precipitation runoff. The graph below shows
the vertical height, y, versus the horizontal distance, x, as measured from the roof peak's support beam.
Roof Steepness
y
14
12
10
8
Vertical Height (feet)
4
2
+X
10 12 14
0
2
4
6
8
Horizontal Distance (feet)
Determine the equation that could be used to represent this situation.
Answers
Answer:
The third answer (C).
Step-by-step explanation:
This graph starts at 10. So it needs the +10 at the end.
Also the slope is -1/2 because the graph goes down one, right two. Rise/run.
Answer:
y= -1/2x+10
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
For the the given graph, the y-intercept is 10. The slope can be determined by finding the rate of change between any two points on the graph, such as (2,9) and (8,6).
2. Suppose that the mean salary in a particular profession is $45,000 with a standard deviation of $1,500. What percentage of people in that profession earn less than $48,000
Answers
Answer:
93%
Step-by-step explanation:
mean=45,000 standard deviation=2000 value of concern=48,000
We can easily see that since the value of concern (48,000) is GREATER than the mean, we can rule out the last two choices.
There is no possible way a number can be greater than the mean, but less than the 50th percentile.
convert 48,000 into a z-score, which is given as:
(x-mean)/standard deviation
or in this case:
(48000-45000)/2000=1.5
using my z-score table or calculator, I can see that a z-score of 1.5 corresponds to about the 93th percentile
An ancient Sicilian legend says that the barber in a remote town who can be reached only by traveling a dangerous mountain road shaves those people, and only those people, who do not shave themselves. Can there be such a barber
Answers
Answer:
No there cannot be.
Step-by-step explanation:
In explaining this question, I would like us to take into account who the barber is,
" the barber is the one who shaves all those, and those only, who do not shave themselves".
This barber cannot be in existence because who would shave him? If he should shave himself then there is a violation of the rule which says he shaves only those who do not shave themselves. If he shaves himself then he ceases to be a barber. And if he does not shave himself then he happens to be under those who must be shaved by the barber, because of what the rule says. But then he is the barber.
This lead us to a contradiction.
Neither is possible so there is no such barber.
Fundamental Theorem of Algebra...
(x+7)^5
1. Using the Fundamental Theorem of Algebra explain how many roots your expression can have. How many real roots and how many complex roots are possible?
Answers
Answer:
A real root of fifth-grade multiplicity/No complex roots.
Step-by-step explanation:
The Fundamental Theorem of Algebra states that every polynomial with real coefficients and a grade greater than zero has at least a real root. Let be [tex]f(x) = (x+7)^{5}[/tex], if such expression is equalized to zero and handled algebraically:
1) [tex](x+7)^{5} = 0[/tex] Given.
2) [tex](x+7)\cdot (x+7)\cdot (x+7)\cdot (x+7)\cdot (x+7) = 0[/tex] Definition of power.
3) [tex]x+7=0[/tex] Given.
4) [tex]x = -7[/tex] Compatibility with the addition/Existence of the additive inverse/Modulative property/Result.
This expression has a real root of fifth-grade multiplicity. No complex roots.
Change 3Y - 2X = -6 to the slope-intercept form of the equation of a line.
Answers
Answer:
y = 2/3x -2
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
3y -2x = -6
Solve for y
Add 2x to each side
3y = 2x-6
Divide by 3
3y/3 = 2x/3 -6/3
y = 2/3x -2
Identify the CRITICAL VALUES(S) used in a hypothesis test of the following claim and sample data:
Claim: "The proportion of defective tablets manufactured in this factory is less than 6%."
A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective. Test the claim at the 0.05 significance level.
a. -1.883
b. -1.645
c. -1.96
d. -0.102
Answers
Answer:
-1.96
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis. In this question the sample of 500 defective tablets is under test. 20 tablets found to be defective so the null hypothesis is accepted as less than 6% of tablets are defective.
Datguy323 is going to complain again. What's the variables for: [tex]x^2+y^2=29\\x+y=7[/tex]
y<4
Answers
Answer: :o I FINALLY MADE IT
(5, 2)
x = 5
y = 2
Step-by-step explanation:
First, I graphed both equations. They meet at the points (5,2) and (2,5). Because y < 5, the solution is (5, 2)
Hope it helps <3
Answer:
[tex]x=5\\y=2[/tex]
Step-by-step explanation:
[tex]x^2 +y^2 =29[/tex]
[tex]x+y=7[/tex]
Solve for x in the second equation.
[tex]x+y=7[/tex]
[tex]x+y-y=7-y[/tex]
[tex]x=7-y[/tex]
Plug in the value for x in the first equation and solve for y.
[tex](7-y)^2 +y^2 =29[/tex]
[tex]y^2-14y+49+y^2 =29[/tex]
[tex]2y^2-14y+20=0[/tex]
[tex]2(y-2)(y-5)=0[/tex]
[tex]2(y-2)=0\\y-2=0\\y=2[/tex]
[tex]y-5=0\\y=5[/tex]
[tex]y<4[/tex]
[tex]y=2[/tex]
[tex]y\neq 5[/tex]
Plug y as 2 in the second equation and solve for x.
[tex]x+y=7[/tex]
[tex]x=7-y[/tex]
[tex]x=7-2[/tex]
[tex]x=5[/tex]
Answer the following questions: 2/3 is what percent of 1/4?
Answers
Answer:
1/2 or 0.5
Step-by-step explanation:
To find out what 2/3 is out of 3/4, we just have to multiply them together to get our exact answer.
[tex]\frac{2}{3} *\frac{3}{4}=\frac{6}{12}=\frac{1}{2}[/tex]
Our final answer is 1/2 or 0.5.
Which of the following best describes so ?
A.
Center
B.
Radius
C.
Diameter
D.
Chord
Answers
Step-by-step explanation:
D.
chord
hope you like this
stay at home stay safe
Answer: d
Step-by-step explanation:
please help it's Factorisation with Numbers
Answers
Answer:
C.
6a + 18x + 18p
Step-by-step explanation:
3(2a + 6 (x + p)) firs multiply (x + p) with 6
3 (2a + 6x + 6z) now multiply inside the parenthesis with 3 and the answer would be 6a + 18x + 18p
In the triangles, QR = DE and SR = FE. Triangles S Q R and F D E are shown. Angle S R Q is 62 degrees. Angle D E F is 50 degrees. Sides Q R and D E are congruent. Sides S R and F E are congruent. Which statement about the sides must be true? QS = DF DF < QS QS < DE SR = DE
Answers
Answer:
b
Step-by-step explanation:
The sides must be true DF < QS
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
ΔSQR and ΔFDE
QR = DE and SR = FE
∠SQR =62°, ∠DEF =50°
QR ≅ DE and SR ≅ FE
∵ ∠DEF > ∠SQR
So, side DF < QS
Hence, DF < QS
Learn more about of congruent triangles
brainly.com/question/4364353
#SPJ2
Ellie can edit an average of 160 pages of text in an 8 hour work day. What is her unit rate for the number of pages edited per hour?
Answers
[tex]\text{We need to find how many pages she can edit in 1 hour}\\\\\text{We know that she can average 160 edits in 8 hours}\\\\\text{With this data, we can find the unit rate}\\\\\text{To get the unit rate, we would divide 160 by 8. This will get us the pages}\\\text{per hour}\\\\160\div8=20\\\\\text{She can edit 20 pages per hour}\\\\\boxed{\text{20 pages}}[/tex]
A ball is thrown from an initial height of 2 feet with an initial upward velocity of 33/fts. The ball's height h (in feet) after t seconds is given by the following. =h+2−33t16t2 Find all values of t for which the ball's height is 18 feet. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)
Answers
Answer:
t=1.283 seconds and
0.779 seconds
Step by step Explanation:
Given: h=18 ft
The given equation is h=2+33t-16t²
Then if we substitute the value of given h, h=18 ft into the given equation we have,
18=2+33t-16t²
Then if we re- arrange we have
16t²−33t+16=0
We can see that the above quadratic equation is in standard form, with a=16, b=33 and c=16 then we can use quadratic formula in solving it which is
t= −(−33±√[(−33) ²−4×16×16)]/(2×16)
= [33±√[1089−1024]/(32)
= [33±√[65]/(32)
=1.283 or 0.779 seconds
the two real roots , of the quadratic are:
1.283 and
0.779 seconds
t= 1.283 or 0.779 seconds
Hence, the ball is at 18 feet with height 0.779seconds after it has been thrown up and,
and is at 21 feet with height 1.283 seconds after after thrown down