Answer:
Addition property of equality formula
Lesson Summary
We learned that the addition property of equality tells us that if we add the same quantity to both sides of an equation, then our equation remains the same. The formula is if a = b, then a + c = b + c.
Step-by-step explanation:
The height of a tennis ball tossed into the air is modeled by h(x) = 40x â€" 16x 2, where x is elapsed time in seconds. During what time interval will the tennis ball be at least 15 feet above the ground? x > 0. 5 seconds and x > 2. 04 seconds x > 0. 5 seconds and x ≤ 2. 04 seconds x ≥ 0. 5 seconds and x > 2. 04 seconds x ≥ 0. 5 seconds and x ≤ 2. 04 seconds.
The time interval x >0.5 and x > 2.04 will the tennis ball be at least 15 feet above the ground.
Given that,
The height of a tennis ball tossed into the air is modeled by,
[tex]\rm h(x) = 40x - 16x^2[/tex]
Where x is elapsed time in seconds.
We have to determine,
During what time interval will the tennis ball be at least 15 feet above the ground?
According to the question,
The height of a tennis ball tossed into the air is modeled by,
[tex]\rm h(x) = 40x - 16x^2[/tex]
Where x is elapsed time in seconds.
Then,
When the tennis ball be at least 15 feet above the ground,
[tex]h(x) = 15[/tex]
Substitute the value of h(x) in the equation,
[tex]\rm h(x) = 40x - 16x^2\\\\ 15 = 40x - 16x^2\\\\ 16x^2-40x+15=0[/tex]
Factorize the equation for finding the time interval will the tennis ball be at least 15 feet above the ground is,
[tex]\rm 16x^2-40x+15= 0\\\\x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\x = \dfrac{-(-40)\pm \sqrt{(-40)^2-4 \times 16 \times 15}}{2 \times 16}\\\\x = \dfrac{-(-40)\pm \sqrt{1600- 960}}{32}\\\\x = \dfrac{40\pm \sqrt{640}}{32}\\\\x = \dfrac{40 + 25.29}{32} \\\\x = \dfrac{40 + 25.29}{32} \ and \ x = \dfrac{40 - 25.29}{32}\\\\x = \dfrac{65.29}{32} \ and \ x = \dfrac{14.71}{32}\\\\x = 2.04 \ and \ x = 0.45[/tex]
Hence, The time interval x >0.5 and x > 2.04 will the tennis ball be at least 15 feet above the ground.
For more details about Inequality refer to the link given below.
https://brainly.com/question/17177510
Which of the following represents the zeros of f(x) = 6x3 − 31x2 + 4x + 5?
If any doubt leave a comment
CAN SOMEONE HELP ME PLEASE ASAP!?
Answer:
C
Step-by-step explanation:
Daniela listened to a popular radio station for 1 hour. Then she made a circle graph to summarize what she had heard.
Complete the table to show the angle measure for each section and the number of minutes that section represents.
Answer:
1.50
Step-by-step explanation:
divide 2 add 5 divide 2 again
8
Find the arc length of the partial circle.
units
Answer:
How to solve ???Arc Length = θ × (π/180) × r, where θ is in degree.
Radius and the sector area:-Multiply the sector area by 2.Then divide the result by the radius squared (the units should be the same) to get the central angle in radians.Multiply the central angle by the radius to get the arc length.Let's solve ur question :- Answer :-The Arc length of the given partial circle is 4π units or 12.56 units .
Used formulae :- The length of the Arc is "I" units , the radius "I" units and the angle subtended by the Arc at the center is "X" is ( X° / 360° ) x 2πr units .Circumference of the circle = 2πr units .π = 3.14Step-by-step explanation:
Ur answer with proof refer to above attachments .Hope this helps you XD ✌️Answer:
4π
Step-by-step explanation:
Hope this helps!
please helppp !
whats the measure of angle 1
Answer:
1 = 70
Step-by-step explanation:
The triangle is an isosceles.
Subtract the angle 40 from 180 (all angles in a triangle add up to 180
The bottom two angles are the same, so dividing the number given by 180 - 40 by 2
180 - 40 = 140
140 / 2 = 70
The area of a rectangle is greater than or equal to 42 square centimeters. The width of the rectangle is 6 centimeters and the length is
centimeters. Select the possible value(s) of a.
7
Answer:
≥7
Step-by-step explanation:
6x7=42
Hope that helps
Answer:
x≥7
Step-by-step explanation:
It costs Chevy $20,000,000 to develop and market a new model of a car. The company sells each car for $25,000, How many cars
must Chevy sell to make more than
$5,000,000 in profits?
Answer:
I believe it to be 1000 cars. Please look at solution to check if I did it the way your problem wants you to do it.
Step-by-step explanation:
Since Chevy needs to make 5,000,000 in profits, earns 25,000 per car, and had invested 20,000,000, we can set an equation with x being the number of cars:
5,000,000 = 25,000x -20,000,000
Notice how 20,000,000 is negative. This is because chevy starts with a negative amount of money (as they just spent it) and are wanting to earn it back. Anyway, lets solve this.
25,000,000=25,000x
x=1,000
we can see that chevy needs to sell more than 1000 cars to make a profit, however I'm unsure of the 25,000 part. This answer is assuming that they make 25,000 profit for each car.
what is an equation in slope-intercept form for the line (-5, 2) and (5,-3)?
Answer:
y = [tex]-\frac{1}{2} x[/tex] [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
solved using point-slope form
points given: (-5, 2) and (5, -3)
slope: [tex]\frac{-3-2}{5-(-5)} =\frac{-5}{10} =-\frac{1}{2}[/tex]
y = [tex]-\frac{1}{2}[/tex] x + b
insert x- and y- values of (-5, 2) and solve for b
2 = [tex]-\frac{1}{2}[/tex] (-5) + b
2 = 2.5 + b
subtract 2.5 from both sides
2 - 2.5 = 2.5 + b - 2.5
-0.5 = b
insert b- value
y = [tex]-\frac{1}{2} x[/tex] [tex]-\frac{1}{2}[/tex]
Write 32 as a product of primes. Use index notation when giving your answer.
Answer:
[tex]2^{5}[/tex]
Step-by-step explanation:
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
Then
32 = 2 × 2 × 2 × 2 × 2 = [tex]2^{5}[/tex]
Solve for y. -6y-31= 5 and thank you
[tex]-6y -31 =5\\\\\implies -6y = 5+31 = 36\\\\\implies y = -\dfrac{36}6 = -6[/tex]
Step-by-step explanation:
...........y=-6.........
find the side of square whose perimeter. is 24.8cm.
Answer:
6.2
Step-by-step explanation:
Jennie has $200 and spends $30. What percent did Jennie spend?
Answer:
30$ is 15% of 200$
Step-by-step explanation:
To find how much percent Jennie spent let's first find how much one percent of $200 is.
∴200/100=2
so one percent of 200 is 2
now let's find how much percent 30$ is of 200$
∴30/2=15
meaning that 30$ is 15% of 200$
What is the initial value of the exponential function shown on the graph?
A : 0
B : 1
C : 2
D : 4
Combine like terms to create an equivalent expression.
Enter any coefficients as simplified proper or improper fractions or integers.
6(1/2w -3/4)
Answer:
Y= 3w-4.5
Step-by-step explanation:
What point located in quadrant IV has an x-value that is 3 units from the origin and a y-value that is 4 units from the origin?
ANYBODY HELP. EXPERTS HELP!!!!!!!!!!
Answer:
Question 1 Between 3 - 4 hrs
Question 2 Between 1 - 3 hrs
Question 3 Between 4 - 8 hrs
Question 4 Between 2 - 3 hrs
Question 5 Represents the starting position
Step-by-step explanation:
Two consecutive whole numbers is 57. What are the two numbers?(hint: Let n represent the first number. Then n + 1 is the next consecutive whole number.
28+29 = 57
=======================================================
Explanation:
n = first number
n+1 = second number
Add up those two items and set the result equal to 57. Solve for n.
first+second = 57
(n) + (n+1) = 57
2n+1 = 57
2n = 57-1
2n = 56
n = 56/2
n = 28
n+1 = 28+1 = 29
The two consecutive whole numbers are 28 and 29
28+29 = 57
Answer:
28 and 29
Step-by-step explanation:
Given values:
1st number = n
2nd number = n+1
n + n + 1 = 57
2n + 1 = 57
2n = 56
n = 28
n+1 = 29
Answer: 28 and 29
I NEED HELP PLEASE AND THANK YOU (asap)
Which relation represents a linear function?
A) (5,6), (3,8), (1,10), (-1, 12)
B) (-3,1), -1,4), (1,9), (3,16)
C) (-2,0), (0,1), (2,3), (4,6)
D) (7,-1), (4,-3), (1,-6), (-2,-9)
14x-21y
factorise this equation
Answer:
7(2x - 3y)
Step-by-step explanation:
Take out what they both have, put it on the outside.
Put the rest on the inside.
Answer:
7 (2 x - 3y)
Step-by-step explanation:
if rs=44 and qs=68 find qr.
Answer:
qr=68r/s
Step-by-step explanation:
rs=44
s=44/r
qs=68
q(44/r)=68
44q/r=68
44q=68r
q=68r/44
rs=44
r=44/s
qr=(68r/44)(44/s)=68r/s
Write the first three terms of the sequence defined by the recursive formula if a1=2.
a_n= a_n-1 / 4 - 2
The first three terms of the sequence defined by the recursive formula are 2, -7/2 and -3/2
Given:
[tex]an = \frac{an - 1}{4} - 2[/tex]
where,
n = number of terms
First term, a1 = 2
Second term, a2
[tex]an = \frac{an - 1}{4} - 2[/tex]
a2 = {(2 - 1)/ 4} - 2
= 1/4 - 2
= (1-8) / 4
= - 7/4
Third term, a3
= {(3-1) / 4} - 2
= 2/4 - 2
= 1/2 - 2
= (1-4) / 2
= -3/2
Therefore, the first three terms of the sequence defined by the recursive formula are 2, -7/2 and -3/2
Learn more about sequence:
https://brainly.com/question/6561461
Answer:
a1 = 2
a2 = -3/2
a3 = -19/8
Explanation:
a_n-1 means the last term.
So if a1 = 2, a2-1 is the same thing as a1, which is 2. So a2 = 2/4 - 2. a2 = -3/2
It's the same thing for a3. a3-1 is just the last term, which is a2, -3/2. So a3 = (-3/2) / 4 - 2. a3 = -19/8
I need helpppoppppppppppppp
Answer:
Step-by-step explanation:
2 1
Jeremy brought a sandwich and a drink that cost him $7. His drink cost $1.75. Solve the equation 7=s + 1.75 to find s, the cost of Jeremy’s sandwich.
Answer:
the answer is 5.25
Step-by-step explanation:
subtract the amount from the drink and should give you the cost of the sandwich
What is f(5) for the function f(x) = 7x + 1
7 (5) + 1 = 35 + 1 = 36
So, f(5) = 36
Solve for p if L = 2 1/2 ft and W = 3 2/5 ft. P = 2L + 2W
Answer:
[tex]\frac{59}{5}[/tex] or 11 [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
hope this helps :)
Jeremy brought a sandwich and a drink that cost him $7. His drink cost $1.75. Solve the equation 7=s + 1.75 to find s, the cost of Jeremy’s sandwich.
Answer:
s= $5.25
Step-by-step explanation:
7-1.75=5.25
7=5.25+1.75
s=$5.25
a. How do you identify the boundary line?
Answer:
Find your property line by visiting your local county recorder or assessor's office. You can access public maps of your street and locate your boundaries. Many counties also let you access property lines online. If your property is on platted land, you may be able to access the plat maps online.
Step-by-step explanation:
Factors of 2x^2-13x+21
Answer:
(2x-7)(x-3)
Step-by-step explanation:
a train is leaving the station and goes from 3m/s to 30 m/s in 12 s. The acceleration of the train is
Answer:2.25 m/s^2
Step-by-step explanation:
a = (v-u)/t = 27/12 = 2.25 m/s^2