Answers
For a system of linear equations to have a solution, it means that they would cross over at some point, thus if we are looking for a system of linear equations that do not have a solution (ie. they do not cross over), we are looking for two parallel lines.
Now for two lines to be parallel, they must have the same gradient. Thus, we must find the value of a for which both the equations have the same gradient. In order to do this, we should first write both equations in the form y = mx + c, where m is the gradient and c the y-intercept.
1) Equation 1:
(1/2)x - (2/3)y = 7
(3/4)x - y = 21/2 (Multiply both sides by 3/2)
(3/4)x = 21/2 + y (Add y to both sides)
(3/4)x - 21/2 = y (Subtract 21/2 from both sides)
Thus, the first equation may be written as y = (3/4)x - 21/2
2) Equation 2:
ax - 8y = -1
(a/8)x - y = -1/8 (Divide both sides by 8)
(a/8)x = -1/8 + y (Add y to both sides)
(a/8)x + 1/8 = y (Add 1/8 to both sides)
Thus, the second equation may be written as y = (a/8)x + 1/8
Now that we know the equations of the two lines, we can compare their gradients.
Equation 1: m = 3/4
Equation 2: m = a/8
Remember, for the two lines to be parallel, their gradients must be the same. Thus, we must equate the two gradients above to find the value of a:
3/4 = a/8
24/4 = a (Multiply both sides by 8)
6 = a
Therefor, if the system of linear equations has no solution, and a is a constant, the value of a is 6 (answer D).
Related Questions
PLEASE HELP ASAP 40 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answers
Answer: The answer is D
Step-by-step explanation:
Factor and set each set equal to zero to get x=0,2,-1,1
Answer:
D
Step-by-step explanation:
x¹³ - 2x¹² - x¹¹ + 2x¹⁰ = 0
x¹⁰(x³ - 2x² - x + 2) = 0
x¹⁰ [x²(x - 2) - (x - 2)] = 0
x¹⁰(x² - 1)(x - 2) = 0
x = 0 (multiplicity 10)
x = 1
x = -1
x = 2
Simplify the expression.
the quantity x to the three halves power end quantity to the power of 6
A. x to the power of one ninth
B. x to the power of one sixth
C. x to the power of six
D. x to the power of nine
Answers
Answer:
D. x to the power of nine
Step-by-step explanation:
The applicable rule of exponents is ...
(x^a)^b = x^(ab)
You have a=3/2, b=6, so ab = 3/2·6 = 9.
(x^(3/2))^6 = x^(3/2·6) = x^9
Please help me with this proof
Answers
5. Next time include the entire page in the photo. I'm guessing it's U at the top right and O at the bottom right.
First box.
SE ≅ SU
Given
Second box
angle 1 ≅ angle 2
Those are vertical angles, which are always congruent
Third box
angle E = angle U
Given
Next box, three arrows in.
triangle MES ≅ triangle OUS
Angle - Side - Angle
Last box:
MS ≅ SO
Corresponding parts of congruent triangles.
-----------
6.
First box:
angle E ≅ angle U
Given
Second box:
NS ≅ NS
reflexivity (aka it's the same segment)
Third box:
angle 1 = angle 2
Definition of angle bisector
Next box:
triangle WNS ≅ triangle ENS
Angle - Side - Angle
Next:
WN ≅ EN
Corresponding parts of congruent triangles.
Answer:
5. Next time include the entire page in the photo. I'm guessing it's U at the top right and O at the bottom right.First box. SE ≅ SUGivenSecond boxangle 1 ≅ angle 2Those are vertical angles, which are always congruentThird boxangle E = angle UGivenNext box, three arrows in.triangle MES ≅ triangle OUSAngle - Side - AngleLast box:MS ≅ SOCorresponding parts of congruent triangles.-----------6.First box:angle E ≅ angle UGivenSecond box:NS ≅ NSreflexivity (aka it's the same segment)Third box:angle 1 = angle 2 Definition of angle bisectorNext box:triangle WNS ≅ triangle ENSAngle - Side - AngleNext: WN ≅ ENCorresponding parts of congruent triangles
Pasion wants to rent a car to take a trip and has a budget of $75. There is a fixed rental fee of $25 and a daily fee of $10. Write an inequality that would be used to solve for the maximum number of days for which Pasion can rent the car on her budget.
Answers
Answer:
The maximum number of days is 5
Step-by-step explanation:
Let
x ----> the number of days
y ---> the total cost to rent a car in dollars
we know that
The fixed rental fee plus the daily fee multiplied by the number of days must be less than or equal to Pasion's budget
so
The inequality that represent this situation is
[tex]25+10x\leq 75[/tex]
Solve the inequality for x
Subtract 25 both sides
[tex]10x\leq 75-25[/tex]
[tex]10x\leq 50[/tex]
Divide by 10 both sides
[tex]x\leq 5\ days[/tex]
therefore
The maximum number of days is 5
Which set of points contains the solutions to the inequality y ≥ 1⁄4x + 5?
A. {(–3,–17), (4,11), (7,19)}
B. {(4,6), (8,8), (–3,6)}
C. {(3,4), (2,3), (8,27)}
D. {(–2,–1), (4,–7), (5,1)}
Answers
Answer:
B. {(4,6), (8,8), (–3,6)}
Step-by-step explanation:
You can graph the equation and plot the points, or you can try the points algebraically. For the latter, it is convenient to rearrange the inequality a bit.
y ≥ 1/4x + 5 . . . . . given
4y ≥ x + 20 . . . . . multiply by 4
You can use this form, or you can subtract x to get ...
4y -x ≥ 20
Trying the offered points, we want 4y-x to be at least 20. We get ...
A: 4(-17) -(-3) = -65 . . . . less than 20
B: 4(6)-4 = 20 . . . a solution
4(8) -8 = 24 . . . a solution
4(6)-(-3) = 27 . . . a solution . . . . set B contains solutions to the inequality
C: 4(4)+3 = 19 . . . . less than 20
D: 4(-1)-(-2) = -2 . . . . less than 20
Find the sun and express it in simplest form.(-3s-4c+1)+(-3s+3c)
Answers
Answer:
-6s-c+1
Step-by-step explanation:
(-3s-4c+1)+(-3s+3c)
We have been given the above expression. To find the sum, we simply collect the like terms and combine them;
(-3s-4c+1)+(-3s+3c) = -3s + -3s -4c + 3c + 1
-3s + -3s -4c + 3c + 1 = -3s - 3s + 3c - 4c + 1
-3s - 3s + 3c - 4c + 1 = -6s - c + 1
Therefore;
(-3s-4c+1)+(-3s+3c) = -6s-c+1
Sara had some candy in her pocket. She first kept 2 pieces herself and then gave her 5 children 3 pieces each. If she didn't have any candy left over, how many pieces of candy did she start with
Answers
17 pieces. She had two and she had to have 15 to give to the children. If each child got 3 and there is 5. This turns into 3*5=15. Then you would add 15+2 to get 17
Sara initially had 17 candies. This computation is based on the 2 pieces she kept for herself and the three pieces of candy each of her five children received.
Explanation:The subject of this question is mathematics, specifically it deals with basic arithmetic and problem solving. According to the problem, Sara kept 2 pieces of candy for herself and then gave each of her 5 children 3 pieces. In mathematical terms, this can be represented as an equation: 2 (pieces Sara kept) + 5 (children) * 3 (pieces each child received) = Total pieces of candy Sara had initially.
To solve this equation, first multiply the number of children by the pieces each received: 5 * 3 = 15. Then add the pieces Sara kept: 2 + 15 = 17. Therefore, Sara initially had 17 pieces of candy.
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Last week the price of oranges at the farmers market was 1.75 per pound.This week the price has decreased by 20%.What is the price of oranges this week.
Answers
Answer:
1.40
Step-by-step explanation:
Last week, the price of oranges at the farmers market was 1.75
This week, the price has reduced by 20%
20% of 1.75 = 0.2 × 1.75 = 0.35
The price of the oranges this week is 1.75 - 0.35 = 1.40
A data value is considered _______ if its z-score is less than minus2 or greater than 2.
Answers
Answer:
Unusual
Step-by-step explanation:
we know that
The z-score is a measure of how close the given data point is to the mean of the values given with the standard deviation
so
if its z-score is greater than or equal to -2, or less than or equal to 2., then the data value is considered ordinary
if its z-score is less than -2 or greater than 2, then the data value is considered unusual
A data value is considered an outlier if its z-score is less than -2 or greater than 2.
Z-scores are a statistical measure that standardizes data, enabling comparisons across different datasets.
A z-score tells us how many standard deviations a data point is from the mean.
When a z-score is below -2 or above 2, it suggests that the data point is significantly distant from the mean of the dataset.
This indicates that the data point is an extreme observation, differing substantially from the rest of the data.
Outliers can be caused by various factors, such as measurement errors, data entry mistakes, or genuine anomalies in the underlying data. Identifying and handling outliers is crucial for robust statistical analysis and modeling.
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What's the difference between:
x≥0
And
Nonnegative integer.
?
Answers
Answer:
none, if x is an integerx may be a real number, hence not necessarily an integerStep-by-step explanation:
x ≥ 0 means x is non-negative, but it does not mean x is an integer. An additional restriction would need to be applied for x to be a non-negative integer.
Please answer this question for 25 points and brainliest!!
Answers
Answer:
64 cm²
Step-by-step explanation:
Suppose the original paper was x cm on a side. Then the original perimeter was 4x.
When the square is folded in half, two of the sides are now x/2, so the perimeter is ...
x + x/2 + x + x/2 = 3x
If 3x = 24 cm, then x = 8 cm.
The area of the original paper is ...
A = x² = (8 cm)² = 64 cm²
Francine Flicka found a bargain when she bought a lawn mower. She paid the store's clerk three $20 bills and received him $7.45 in change. If the sales tax is 7.3%, what was the selling price of the mower before taxes?
$56.39
$53.55
$52.55
$48.97
Answers
Answer:
$48.97
Step-by-step explanation:
Let p represent the marked price of the mower. Then the price with tax is ...
with tax = p + 7.3%×p = 1.073p
The amount Flicka paid is the amount tendered less the change she received, so is ...
3×$20 - 7.45 = with tax = 1.073p
To find p, we can divide by its coefficient:
(3 × $20 - 7.45)/1.073 = p ≈ $48.97
The selling price before taxes was $48.97.
_____
Comment on the problem
If you check the answer, you find the amount with tax is ...
$48.97 × 1.073 ≈ $52.54481 ≈ $52.54
so the change Flicka would have received would have been $7.46, not $7.45. If the price were $48.98, then the change would have been $7.44. There is no price at which the mower can be marked that will make the total with tax come to $52.55. There is no solution to this problem.
Answer:
$48.97
Step-by-step explanation:
She paid three $20 bills
3 × 20 = $60
She received $7.45 change
60 - 7.45 = $52.55
The mower was for $52.55 with sales tax.
The sales tax is 7.3%.
Before the sales tax (reduce tax).
52.55 × (1-7.3%)
= $48.97
Two linear equations are shown. What is the solution to the system of equations? (7, 4) (9, 7)
Answers
Answer:
[7, 13/3]
Step-by-step explanation:
Can someone help please
Answers
ANSWER
[tex]3 \: radians[/tex]
EXPLANATION
The formula for the calculating the length of an arc is
[tex]l = r \theta[/tex]
where theta is in radians.
From the diagram
[tex]l = 12cm[/tex]
[tex]r = 4cm[/tex]
We substitute the values to obtain;
[tex]4\theta = 12[/tex]
Divide both sides by 4 to get;
[tex]\theta = \frac{12}{4} [/tex]
[tex]\theta = 3 \: radians[/tex]
Which relationship describes angles 1 and 2?
Select each correct answer.
complementary angles
supplementary angles
vertical angles
adjacent angles
Answers
Answer:
complementary angles
Step-by-step explanation:
∠1 and ∠2 form a right angle and are complementary, that is they sum to 90°
please help asap urgent
brainliest
Answers
Answer:
6 unit cubesStep-by-step explanation:
Look at the picture.
What is the factorization of the polynomial below?
4x^2 - 25
Answers
[tex]4x^2 - 25=(2x-5)(2x+5)[/tex]
The angle between a 180-pound force F and AB= 5i + 2j is 30.Find the work done by F in moving and object from A to B.
Answers
Answer:
[tex]W=839.464\ ft*lbf[/tex]
Step-by-step explanation:
The work done is the product of the magnitude of the force applied to the object by the magnitude of the displacement of the object by the cosine of the angle between the force and direction of the displacement. This is:
[tex]W=|F|*|r|cos(\theta)[/tex]
In this case
[tex]\theta=30\°[/tex]
|F|=180 pound force
The magnitude of vector AB is:
[tex]|r|= \sqrt{5^2 + 2^2}\\\\|r|= \sqrt{29}\ fr[/tex]
Finally the work is:
[tex]W=180*\sqrt{29}*cos(30\°)[/tex]
[tex]W=839.464\ ft*lbf[/tex]
Answer:
the answer is option 1, A
Step-by-step explanation:
What is magma? a. The molten mixture of rock-forming substances, gases, and water from the mantle.. c. Hardened lava on the surface of the Earth. b. Liquid rock that reaches the surface. d. All of the above Please select the best answer from the choices provided A B C D
Answers
Answer: A. The molten mixture of rock-forming substances, gases, and water from the mantle
Magma is a mass of molten rock that is found in the deepest layers of the Earth at high temperature and pressure, and that can flow out through a volcano.
The composition of this mass is a mixture of liquids, volatile and solids that when they reach the surface in an eruption becomes lava, which when cooled crystallizes and gives rise to the formation of igneous rocks.
How many cans of paint are needed to cover an area of 2200 square units if one can of paint covers in area 400 square units
Answers
The cans of paints and areas are illustrations of equivalent ratios.
5.5 cans are needed to paint an area of 2200 units square
The given parameter is:
[tex]\mathbf{Cans : Area = 1 : 400}[/tex]
Express as fraction
[tex]\mathbf{\frac{Cans }{ Area }= \frac{1 }{ 400}}[/tex]
Multiply both sides by Area
[tex]\mathbf{Cans= \frac{1 }{ 400} \times Area}[/tex]
When the area is 2200, we have:
[tex]\mathbf{Cans= \frac{1 }{ 400} \times 2200}[/tex]
[tex]\mathbf{Cans= 5.5}[/tex]
Hence, 5.5 cans are needed to paint an area of 2200 units square
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5.5 cans of paint are required to cover an area of 2200 square units, but since you can't have half a can, you would actually need 6 cans of paint.
Explanation:This problem can be solved using simple division, which is a common concept in Mathematics. Given that one can of paint covers 400 square units, to find out how many cans of paint are needed to cover an area of 2200 square units, we need to divide the total area by the area that one can covers. So, 2200 ÷ 400 = 5.5.
However, you cannot have half a paint can, so you would need 6 cans of paint to fully cover the area. Here, we apply the mathematical principle of rounding up because you can't use half a can of paint.
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Raymond took out a 25-year loan for $135,000 at an APR of 3.6% compounded monthly. If his bank charges a prepayment fee of 6 months' interest on 80 % of the balance, what prepayment fee would he be charged for paying off the loan 5 years early?
A. 683.10
B 546.08
C. 695.49
D. 543.46
Answers
Answer:
D. 543.46
Step-by-step explanation:
The formula for the remaining balance on the loan is ...
A = P(1 +r)^n +p((1 -(1 +r)^n)/r)
where P is the principal, p is the monthly payment, r is the monthly interest rate, and n is the number of months.
We have P=135,000, p = TBD, r = 3.6%/12 = .003, n = 20×12 = 240.
___
The monthly payment is given by the same formula by setting A=0. In this case, n is 25 years, or 300 payments. Solving for p, we get, ...
p = Pr(1 +r)^n/((1 +r)^n -1) = Pr/(1 -(1 +r)^-n)
So, the monthly payment is ...
p = 135,000×0.003/(1 -1.003^-300) = 683.10
Using this value in the formula for remaining balance, we get ...
A = 135000(1.003^240) +683.10((1 -1.003^240)/0.003) = 37,459.20
___
80% of this balance is 29,967.36. The answer choices only make sense if we assume the interest penalty is equivalent to the interest being compounded monthly:
$29,967.36 × (1.003^6 -1) = $543.47
The closest match among answer choices is ...
D. 543.46
Select the correct answer
What is the 10th term of the geometric sequence 3,6, 12, 24,48 ...?
A. 512
B. 3,072
C. 768
D. 1,536
Answers
Answer:
hey mate.
Step-by-step explanation:
Select the correct answer
What is the 10th term of the geometric sequence 3,6, 12, 24,48 ...?
A. 512
B. 3,072
C. 768
D. 1,536
is ... 768
Answer:
D
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r is the common ratio
r = 6 ÷ 3 = 12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 2
Using a₁ = 3 and r = 2, then
[tex]a_{10}[/tex] = 3 × [tex]2^{9}[/tex] = 3 × 512 = 1536 → D
How many lines of symmetry does a 15 sided polygon have?
Answers
Answer: 15 lines of symmetry.
Step-by-step explanation:
There are 15 lines of symmetry does a 15 sided polygon have.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
We have to given that;
Number of lines of symmetry does a 15 sided polygon have
Since, We know that;
Number or line of symmetry is equal to number of sides of polygon.
Here, Number of side = 15
Hence, There are 15 lines of symmetry does a 15 sided polygon have.
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The area of a rectangle is 38.25 square yards and its base is 9 yards. What is the height? Do not round your answer.
h = ________ yd
Answers
Answer:
4.25 yards
Step-by-step explanation:
Area of rectangle = Base x Height
or
Height = Area of Rectangle ÷ Base
In this case, Area =38.25 sq yards and Base = 9 yards
Height = 38.25 ÷ 9 = 4.25 yards
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The given line passes through points (-4,-3) and (4,1). What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4,3)?
y - 3 = __________ (x+4)
Answers
Find the missing factor. Write your answer in exponential form.
1^9 = 1^7 • = _
Answers
Answer:
[tex]1^2[/tex]
Step-by-step explanation:
The number 1 is called the base. When we multiply like bases, we add the exponents. So in order to get 1^9, we will multiply 1^7 by 1^2 because 7+2=9.
Answer:
The answer is [tex]1^{2}[/tex]
Step-by-step explanation:
Using the formula: [tex]a^{m}+a^{n}= a^{m+n}[/tex]
[tex]1^{9}=1^{7}*1^{2}=1^{7+2=9} =1^{9}[/tex]
Which of the following statements is true concerning triangle XYZ below?
Answers
Answer:
The correct answer to this problem is the second option: YZ is the longest side.
Step-by-step explanation:
In order to solve this problem, we need to understand the relationship between angle measure and side lengths in a triangle.
In a triangle, the longest side is located across from the largest angle measure, the smallest side is located across from the smallest angle, and the middle length side is located across from the medium sized angle.
Using this knowledge, we can conclude that since XYZ is the smallest angle, XZ must be the smallest side. We can also state that since YXZ is the largest angle, YZ is the longest side.
Looking at the answer options, the only choice that aligns with this information is the second option: YZ is the longest side, and thus we can conclude that this is the correct answer.
Hope this helps!
YZ is the longest side
Step-by-step explanation:
Simplify the expression. the quantity x to the three halves power end quantity to the power of 6
Answers
Answer:
x^9
Step-by-step explanation:
The rule of exponents that applies is ...
(a^b)^c = a^(b·c)
For your problem, you have a=x, b=(3/2), c=6, so ...
(x^(3/2))^6 = x^(3/2·6) = x^9
Answer:
[tex]x^9[/tex]
Step-by-step explanation:
We are given that an expression
[tex]\left\{(x)^{\frac{3}{2}\right\}^6[/tex]
We have to simplify the given expression
In order to simplify the expression we will use given below rule
We know that [tex](a^b)^c= a^{b\cdot c}[/tex]
Using this rule
[tex](x)^{\frac{3}{2}\cdot 6}[/tex]
[tex](x)^{3\cdot 3}[/tex]
[tex]x^9[/tex]
[tex]\left\{(x)^{\frac{3}{2}\right\}^6=x^9[/tex]
I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS ALL CORRECTLY
Q1: What is an outlier? What is a cluster?
Q2: How do you determine the equation of a line of best fit for data?
Q3: Explain the difference between frequency and relative frequency.
Answers
Answer:
Ans1.
Outlier
A value that "lies outside" (is much smaller or larger than) most of the other values in a set of data.
Cluster
When data seems to be "gathered" around a particular value.
For example: for the values 2, 6, 7, 8, 8.5, 10, 15, there is a cluster around the value 8.
Ans.2
A line of best fit (or "trend" line) is a straight line that best represents the data on a scatter plot.
This line may pass through some of the points, none of the points, or all of the points.
i will explain through an example
1. Prepare a scatter plot of the data on graph paper.
2. Using a strand of spaghetti, position the spaghetti so that the plotted points are as close to the strand as possible.
3. Find two points that you think will be on the "best-fit" line.
4. We are choosing the points (9, 260) and (30, 530).
You may choose different points.
5. Calculate the slope of the line through your two points (rounded to three decimal places).
6. Write the equation of the line.
7. This equation can now be used to predict information that was not plotted in the scatter plot.
Question: Predict the total calories based upon 22 grams of fat. ANS: 427.141 calories
Ans.3
1.Frequency is the number of times a result occurs, while “relative frequency” is the number of times the result occurs divided by the number of times the experiment is repeated.
2.Frequency can easily be determined by conducting a simple experiment and noting how many times the event in question occurs; no calculations are needed. On the other hand, relative frequency is determined by using simple division.
An arrow is shot vertically upward at a rate of 180ft/s. Use the projectile formula h=?16t2+v0t to determine at what time(s), in seconds, the arrow is at a height of 420ft. Round your answer(s) to the nearest tenth of a second.
Answers
The answer is:
[tex]t_1=3.60s\\t_2=7.94s[/tex]
Time equal to 3.30 seconds when the arrow was going up.
Time time equal to 7.94 seconds when the arrow was going down.
Why?To solve the problem, we need to solve the quadratic equation and find the value of values of time where the height of the arrow is 420 feet.
Also, we are given some information, we need to substitute it and then use the quadratic equation.
The equation is:
[tex]h=-16t^{2}+vot\\\\-16t^{2}+vot-h=0[/tex]
Substituting the given information we have:
[tex]-16t^{2}+vot-h=0[/tex]
[tex]-16t^{2}+180\frac{ft}{s} t-420=0[/tex]
We have a quadratic equation where:
[tex]a=-16\\b=180\\c=-420[/tex]
Now, using the quadratic equation to find the value or values of "t", we have:
[tex]\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]\frac{-180+-\sqrt{180^{2}-4*-16*-420 } }{2*-16}=\frac{-180+-\sqrt{32400-26880 } }{-32}\\\\\frac{-180+-\sqrt{32400-26880}}{-32}=\frac{-180+-\sqrt{5520}}{-32} \\\\\frac{-180+-\sqrt{5520}}{-32}=\frac{-180+-(74.29)}{-32}\\\\t_1=\frac{-180+(74.29)}{-32}=3.30\\\\t_2=\frac{-180-(74.29)}{-32}=7.94[/tex]
Hence, we have two positive values of time, it means that there are two moments of time where the height of the arrow is equal to 420 feet, those times are:
[tex]t_1=3.60s\\t_2=7.94s[/tex]
Time equal to 3.30 seconds when the arrow was going up.
Time equal to 7.94 seconds when the arrow was going down.
Have a nice day!
Answer:
3.3secs, 7.9secs
Step-by-step explanation:
We are looking for the number of seconds it takes the arrow to reach a height of 420ft. We are given the projectile formula h=−16t2+v0t, where h is the height, in feet, and t is the time, in seconds. We can substitute the initial velocity v0=180 and desired height h=420 to find
420=−16t2+180t
Rewriting this quadratic equation in standard form, we have
16t2−180t+420=0
Now that the equation is in standard form, at2+bt+c=0, we can identify the coefficients a=16, b=−180, and c=420. Substituting these into the quadratic formula, we have
t=−b±b2−4ac‾‾‾‾‾‾‾‾√2a=−(−180)±(−180)2−4(16)(420)‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√2(16)=180±5520‾‾‾‾‾√32
The approximate values for t are
t=≈180+5520‾‾‾‾‾√327.9andt=≈180−5520‾‾‾‾‾√323.3
The arrow will go up and then fall down. As the arrow goes up, it will reach 420ft after approximately 3.3s. It will also pass that height on the way down at approximately 7.9s.