Answer:
The arrow will take 4.19 seconds to hit the ground
The arrow will go 24 feet to reach its maximum height and it takes 2 seconds to reach this height
Step-by-step explanation:
The quadratic function is f(t) = -5t² + 20t + 4, where
f(t) is the height in feet
t is the time in seconds
If the arrow hit the ground that means h(t) = 0
→ Substitute h(t) by 0 and use the quadratic formula to find t
∵ h(t) = 0
∴ 0 = -5t² + 20t + 4
→ Switch the two sides
∴ -5t² + 20t + 4 = 0
→ Multiply all terms by -1 to make the coefficient of t² positive
∴ 5t² - 20t - 4 = 0
→ The quadratic formula is [tex]t=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex] , where
a is the coefficient of t²b is the coefficient of tc is the numerical term∵ a = 5, b = -20, c = -4
∴ [tex]t=\frac{-5+-\sqrt{(-20)^{2}-4(5)(-4)}}{2(5)}[/tex]
∴ [tex]t=\frac{-5+-\sqrt{400+80}}{10}[/tex]
→ Find the values of t in decimal
∴ t = 4.19 seconds OR t = -0.19 ⇒ refused because it is negative
∴ The arrow will take 4.19 seconds to hit the ground
The graph of this quadratic function is a parabola with maximum vertex (h, k), where
h = [tex]\frac{-b}{2a}[/tex]k = f(h)To find the maximum height and the time taking for this to occur find h and k where k is the maximum height and h is the time for this to occur
∵ f(t) = -5t² + 20t + 4
∵ a = -5 and b = 20
∴ h = [tex]-\frac{20}{2(-5)}=-\frac{20}{-10}=2[/tex]
∴ The time for the maximum height is 2 seconds
→ Now use it to find k
∵ k = f(h)
∴ k = f(2)
∵ f(2) = -5(2)²+ 20(2) + 4
∴ f(2) = -5(4) + 40 + 4
∴ f(2) = -20 + 40 + 4
∴ f(2) = 24
∴ k = 24
∴ The maximum height is 24 feet
The arrow will go 24 feet to reach its maximum height and it takes 2 seconds to reach this height
What is an equation of the line that passes through the points (-3, -2)(−3,−2) and (3, 6)(3,6)? Put your answer in fully reduced form.
Answer:
The equation of the line is y = [tex]\frac{4}{3}[/tex] x + 2
Step-by-step explanation:
The form of the equation that passes through two points (x1, y1) and (x2, y2) is y = m x + b, where
m is the slope of the line whose rule is [tex]m=\frac{y2-y1}{x2-x1}[/tex] b is the y-intercept, you can find it by substituting x, y in the equation by (x1, y1) OR (x2, y2)Let us solve the question:
∵ The line passes through the points (-3, -2) and (3, 6)
∴ x1 = -3 and x2 = 3
∴ y1 = -2 and y2 = 6
→ Use the rule of m to find it
∵ [tex]m=\frac{6-(-2)}{3-(-3)}=\frac{6+2}{3+3}=\frac{8}{6}[/tex]
→ Simplify it by dividing up and down by 2
∴ m = [tex]\frac{4}{3}[/tex]
→ Substitute its value in the form of the equation above
∴ y = [tex]\frac{4}{3}[/tex] x + b
→ To find b substitute x and y by x1 and y1
∴ -2 = [tex]\frac{4}{3}[/tex] (-3) + b
∴ -2 = -4 + b
→ Add 4 to both sides
∴ -2 + 4 = -4 + 4 + b
∴ 2 = b
→ Substitute it in the form of the equation
∴ y = [tex]\frac{4}{3}[/tex] x + 2
∴ The equation of the line is y = [tex]\frac{4}{3}[/tex] x + 2
8
The first term of an arithmetic sequence is 5. The third term of the sequence is 13.
Which of the following expressions represents the nth term of the sequence?
A 4n +1
B) 4n + 5
5n+1
D) 5n + 5
Answer:A 4n+1
Step-by-step explanation: found the answer key
If the first term of an arithmetic sequence is 5 and the third term of the sequence is 13 then the nth term is A) 4n +1.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference(d).
aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
Given, The first term of an arithmetic sequence is 5.
The third term of the sequence is 13.
As we can conclude that for 2 terms the common difference is increased by 8.
∴ Common difference (d) = 8/2 = 4.
Now, we know the nth term of an arithmetic sequence is,
aₙ = a₁ + (n - 1).d.
aₙ = 5 + (n - 1)×4.
aₙ = 5 + 4n - 4.
aₙ = 4n + 1.
learn more about arithmetic sequence here :
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Find the total cost to the nearest cent.
$16 haircut; 15% tip
please answer fast
Choose the point-slope form of the equation below that represents the line that passes through the points (-3, 2) and (2, 1).
y + 3 = -5(x - 2)
y-2--5(x + 3)
y+3 -- - 2)
y-2-(x+3)
the expression below gives the cost of green beans(x) and cucumbers (y). what is the cause of 6 bunches of green beans and 4 cucumbers? .79x+0.99y
This is my explanation thus sucks and half the timem you guys dont even have the right answer . So this is my answer for you at leatst try to get it tight because if you dont try you wont suceed
Find the surface area of this rectangular solid.
7cm 5cm 4cm
A. 138
B. 166
C. 168
D. 16
E. 140
E:The answer is 140 because seven times five times four equals 140.
Whats 2 + 6? If the 2 is really a 7?
Answer:
13
Step-by-step explanation:
7 + 6 = 13
Help0oejelensb skeidnekendidne helps 10101
Answer:
b = (looks to be) -3.5
m = [tex]\frac{1}{2}[/tex]
Type of Slope = Positive, linear
Equation = y = [tex]\frac{1}{2}[/tex]x - 3.5
CHOP CHOP PLZ HURRRYYYYY I WILL POST ONE MORE QUESTION FOR 20 POINTS AND BRAILY CHOP CHOP PLZ
Answer:
given, verticals angle thm, definition of supplementary, {you need to see the pic for it}, substitution, and you need to see the pic for the rest so i can’t help
can you go answer my question tho
Step-by-step explanation:
6th grade mathematics
Answer:
and?
Step-by-step explanation:
ANSWER WILL GET BRAINLIEST!!!!!!!!!!!!!!!!
Answer:
C. The two lines have the same slope
Step-by-step explanation:
If two lines are parallel, then they are both going in the same direction forever. If two lines go in the same direction forever, then they have the same slope.
which statement correctly describes the relationship between the graph of f(x) and the graph of g(x)=f(x)+3? read answers above
Answer:
the first one
Step-by-step explanation:
g(x) is f(x) plus 3, so it is being translated up
Just solve for 50 points and brainliest!
10-5+3=
6-4+10=
Answer:
(1) 8 (2) 12
Step-by-step explanation:
PEMDAS
HELP ME PLZZZZZZZZZZZZZZZZZ!!!!!!!!!!
Answer:
45
Step-by-step explanation:
I multiplied 7 x 9 and got 63 so I figure 5 x 9 is right.
Solve the following system using substitution.
6x + 3y= - 12
y= -2x -6
(3,-12)
no solution
infinitely many solutions
(2,0)
Answer:
No solution
Step-by-step explanation:
if you replace the y with -2x-6 into the first equation, you will get rid of the x's which it gives you the hint that there is no solution.
Help math question 1 ,2 ,3 grade 12
Answers:
1.
a. 20%
60/300 × 100/100
= ( 60 × 100 / 300 ) × 1/100 = 20/100
Calculator: 60 ÷ 300 × 100
b. 90%
270/300 × 100/100
270/300 × 100/100= ( 270 × 100 / 300 ) × 1/100 = 90/100
Calculator: 270 ÷ 300 × 100
c. 58.33%
175/300 × 100/100
100/100= ( 175 × 100 / 300 ) × 1/100 = 58.33/100
Calculator: 175 ÷ 300 × 100
2.
a. 35 Students
Calculator: 10 × 350 / 100
b. 93
Calculator: 10 × 930 / 100
c. 118
Calculator: 10 × 1180 / 100
d. 1036
Calculator: 10 × 10,360 / 100
3.
a. 11.1 (Repeated)
Calculator: 50 / 450 × 100%
b. 6.67 (6 Repeated)
Calculator: 50 / 750 × 100%
c. 4.167 (6 Repeated)
Calculator: 50 / 1200 × 100%
Hopefully this helps:)
The point (5, -6) is reflected over the x-axis. What are the new coordinates of the reflection?
Answer:
(5,6)
Step-by-step explanation:
since it is reflected over x axis, y value will flip sign
hey i need help with a math question thank you :)
Answer:
y = 60x + 20
y = 65x
0 = 5x - 20
5x = 20
x = 4 ---> 4 hours
Substitute x as 4:
y = 65 x 4
y = 260 ---> 260 miles
So the answer is A
What is the final price of a $125 jacket that is on sale for 35% off?
Answer:
$81.25
Step-by-step explanation:
first change the percent into a decimal by moving the point 2 spaces to the left. then multiply that decimal by the asnwer to see how muhc money she's getting off. Finally subtract the total by that number.
{(-2, 6), (2, 0), (3, 6), (4, -1), 5, 3)}
Dom:
Range:
Function?
Answer:
Domain = {-2, 2, 3, 4, 5}
Range= {6, 0, 6, -1, 3)
It is a function
Step-by-step explanation:
It is a function because there is only one y value for each x value
what is the slope of this line ?
Answer:
1 I think
Step-by-step explanation:
Change in y
--------------------
Change in x
The highest temperature recorded in the town of Westgate this summer was 100°F. Last
winter, the lowest temperature recorded was -1°F. Find the difference between these
two extremes.
Answer:
101
Step-by-step explanation:
100- (-1) NEGATIVE MINUS NEGATIVE CANCEL OUT ON EACH OTHER AND GIVE POSITIVE: 100 + 1 = SO THE ANSWER IS 101^F
The difference between these two extreme temperatures is of
101° F.
We have the highest temperature recorded in the town of Westgate which is equal to 100°F. Last winter, the lowest temperature recorded was -1°F.
We have to find the difference between these two extremes.
What is Temperature ?Degree of hotness or coldness measured on a definite scale is called Temperature. When the temperature of the body is high it is called hot body and when it is low it is called cold body.
According to question, we have -
Highest temperature recorded = 100°F
Lowest temperature recorded = -1°F
Let the the difference between these two extreme temperatures be x. Then -
x = Highest temperature recorded - Lowest temperature recorded
x = 100 - (- 1) = 101° F
Hence, the difference between these two extreme temperatures is of
101° F.
To solve more questions on Temperature variations, visit the link below-
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Find the LCM.
5, 20, 68
Find the unit rate. Round to the nearest hundredth, if necessary. $130 for 17 ft2. The unit rate is $ /ft2.
Answer:
201
Step-by-step explanation:
I'm smart ok trust me ON this one if I'M wrong at least I tried
Town M is 282 feet below sea level. Town R is 679 feet above sea level. How much higher, in feet is Town R than M?
Given parameters:
Elevation of Town M = 282ft
Elevation of Town R = 679ft
Unknown:
How much higher is Town R than M = ?
Solution:
Town M lies below the sea level whereas Town R is above the sea level.
Graphically:
Town R 679ft
↑
↑
↑
↑
↔↔↔ Sea level
↓
↓
Town M 282ft
Town R is 282ft + 679ft higher than Town M = 961ft
Find the value of x in the triangle shown below.
Choose 1 answer:
Answer:
D
Step-by-step explanation:
you already have the hypotenuse, you're looking for a way to find one of the sides. well 7 squared is 49 and 2 squared is 4. 49-4 is 45 and you can't take the square root of 45 evenly so you leave it under the radical, aka D, your answer.
For what values of x is the equation true? (Form 1st!)
x^2-4x=32
Answer:
It can be solved in many forms
one by replacing each point to see which one satisfy the equation or by using quadratic formula
so the right answer is the fourth one
Please help me with this! Legitimate answers only please!
Fill in the blanks with the proper/right options for the problem.
Answer:
x = $80 rate of change
y = total amount the store earns
m = the amount of hours store is open
b = $150 starting point when x is 0
Step-by-step explanation:
y=8x-150
how did you get the product of sum and differences of terms?
Answer:
Step-by-step explanation:
The the terms be x and y
The sum of the terms = x+y
Difference of terms = x-y
Product of the sun and differences will be expressed as:
(x-y)(x+y) = x²-xy+xy-y²
(x-y)(x+y) = x²-y²
Hence the product of the terms is equivalent to the difference of two squares of the terms
Examine the intersection of these two lines:
Which of the following pairs of angles are
supplementary? Select all that apply.
Answer:
You can't answer this question since there is no picture. Remember though the any 2 angles that make 180 degrees or resembles a line is 180 degrees.