Answer:
x= 13
Step-by-step explanation:
3x-4+20= 55
combine like terms:
3x+16= 55
subtract 16 from both sides:
3x = 39
divide 3 to both sides:
x= 13
Jake dives from a diving board that is 18 feet off the ground. He reaches a maximum height of 26 feet after 2 seconds. What is the standard and vertex formula of this quadratic equation and in how many seconds with Jake hit the water?
Answer:
The time it will take Jake to hit the water ia approximately 4.46 seconds
Step-by-step explanation:
The given parameters in the question are; feet
The height off the ground, of the diving board from which Jake dives, h₀ = 18 feet
g = The acceleration due to gravity
The maximum height Jake reaches, h = 26 feet
The time Jake takes to reach maximum height = 2 seconds
We have;
h = h₀ + u·t + 1/2·g·t²
v² = u² - 2·g·(h - h₀)
v = u - gt
u = gt
Where;
v = The final velocity
u = The initial velocity
t = The time taken
u = 9.81 × 2 = 19.62 m/s
The vertex form of a quadratic equation is f(x) = a(x - h)² + k², with the vertex = (h, k)
Substituting the values, gives;
26 = 18 + u·t - 1/2 × 9.81 × t²
8 = 19.62·t - 1/2 × 9.81 × t² = 19.62·t - 4.905·t²
19.62·t - 4.905·t² - 8 = 0
Therefore, the standard form is -4.905·t² + 19.62·t - 8 = 0
The coordinate of the vertex, is (2, 8), the vertex form is therefore;
-4.905(t - 2)² + 8
2) The time it will take Jake to hit the water is given as follows;
The height at which Jake meets the water = -18 feet from initial height
∴ -4.905·t² + 19.62·t - 8 = -18
-4.905·t² + 19.62·t - 8 + 18 = 0
-4.905·t² + 19.62·t + 10 = 0
t² - 4·t - 2.04 = 0
By the quadratic formula, we have;
t = (4 ± √((-4)² - 4 × 1 × -2.04))/(2×1)
t ≈ 4.46 seconds or t ≈ -0.46 seconds
∴ t ≈ 4.46 seconds
The time it will take Jake to hit the water ≈ 4.46 seconds.
* Practice Buddy
* Some balls are in the closet. Mr. Thomas takes
out 14 balls for class. Now there are 64 balls in
the closet. How many balls were in the closet in
the beginning?
There were
balls in the closet.
Done
Answer:
78 balls buddy
Step-by-step explanation:
Help me out please its with triangles and stuff
Answer:
11 in = 33 in.
Step-by-step explanation:
6 in. = 18 in.
the second triangle is 3 times bigger than the smaller one.
Which of the following situations represent inductive reasoning? Select all that apply.
A. Harriet notices that her friend eats an apple for lunch every Monday, Wednesday, and Friday. Since today is Friday, Harriet makes a conjecture that her friend will eat an apple for lunch.
B. You notice that all butterflies in your yard are blue and black. Therefore, you decide that all butterflies are blue and black.
C. Terance adds the sides of an equilateral triangle and finds the length of the perimeter to be 3 times the length of one side. He guesses that the perimeter of every equilateral triangle will be three times the length of a side.
D. Kiana is writing a list of numbers 4, 8, 12, 16, ____. Her friend Freddy says the next number will be 20.
Wayne walked from the car dealership to the post office and then from the post office to the garbage dump. How far did Wayne walk in all? garbage dump car dealer .
Answer:
I want to say seven units
Step-by-step explanation:
I believe he went 4 units up and 3 units left if he went to just the car dealership , post office and Garbage dump .
Hope I could help -
Sleepy~
Mrs. Sung gave a test in her trignonmetry class. The scores were normally distributed with a mean of 85 and a standard deviation of 3.
What percent would you expect to score between 88 and 91? Round answer to the nearest tenth.
Answer and explanation:
67% as it's +/- one standard deviation from the mean
-qx + p = r. Slove for X.
Answer:
x=-r-p/q
Step-by-step explanation:
Evaluate the expression 2/3 x−12 if x=18
Answer:
Step-by-step explanation:
Given equation is 2/3 x−12
Given x=18
Putting X=18 in given equation we get
2/3x-12= 2x18/3-12=
=12-12 =0 is the answer
E
What is the value of d to the nearest hundredth?
d
7.2
D
42°
d
The triangle has 3 sides and angles. The measure of "d" from the given diagram is 6.48
Application of SOH CAH TOAThe given diagram is a triangle. According to the SOH CAH TOA identity;
tan theta= opp/adj
Given the following
opp = d
adj = 7.2
Substitute
tan 42 = d/7.2
d = 7.2tan42
d = 6.48
Hence the measure of "d" from the given diagram is 6.48
Learn more on SOH CAH TOA here:https://brainly.com/question/20734777
#SPJ1
Each day a carwash used 4 2/3 gallons of soap. After 2 days, how much soap would they have used?
Answer:
9 1/3
Step-by-step explanation:
PLSSS HELP PLSSSS IM SUFFERING IM NOT A LAZY NOR BAD STUDENT BIT THIS IS HARD FOR MEEE PLSSS HELPPP
Answer:
OOP
Step-by-step explanation:
oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop oop!
2x - 5y + 3z = 27
4x + 3y - 7z=-37
x - 2y + 5z = 30
I need help solving this with cramers rule
Step-by-step explanation: answer {x,y,z} = {1,-2,5}
/ Solve equation [3] for the variable x
[3] x = 2y - 5z + 30
// Plug this in for variable x in equation [1]
[1] 2•(2y-5z+30) - 5y + 3z = 27
[1] - y - 7z = -33
// Plug this in for variable x in equation [2]
[2] 4•(2y-5z+30) + 3y - 7z = -37
[2] 11y - 27z = -157
// Solve equation [1] for the variable y
[1] y = -7z + 33
// Plug this in for variable y in equation [2]
[2] 11•(-7z+33) - 27z = -157
[2] - 104z = -520
// Solve equation [2] for the variable z
[2] 104z = 520
[2] z = 5
// By now we know this much :
x = 2y-5z+30
y = -7z+33
z = 5
// Use the z value to solve for y
y = -7(5)+33 = -2
// Use the y and z values to solve for x
x = 2(-2)-5(5)+30 = 1
which shape is similar to shape l?
Answer:
pentagon
Step-by-step explanation:
got 5 sides
which of the following pairs of functions are inverses of each other
Answer:
c would be the answer you are looking for and please mark brainliest
Step-by-step explanation:
Options A and D have functions that are inverses of each other.
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function.
To check whether two functions are inverses of each other, we need to check if the composition of the functions in both orders results in the input value.
Here, we need to check if f(g(x))=x and g(f(x))=x for all values of x in their domains.
A. f(x) = 7/(x-9) and g(x) = (x+9)/7
f(g(x)) = f((x+9)/7) = 7/((x+9)/7 - 9) = 7/(x/7) = x, so f and g are inverses of each other.
B. f(x) = x/6 + 8 and g(x) = 6x - 8
f(g(x)) = f(6x-8) = (6x-8)/6 + 8 = x/6 + 8/6 = x/6 + 4/3, which is not equal to x. Therefore, f and g are not inverses of each other.
C. f(x) = 2 + ∛x and g(x) = 2 - x³
f(g(x)) = f(2 - x³) = 2 + ∛(2 - x³) ≠ x, so f and g are not inverses of each other.
D. f(x) = 5x - 11 and g(x) = (x+11)/5
f(g(x)) = f((x+11)/5) = 5((x+11)/5) - 11 = x, and g(f(x)) = g(5x-11) = (5x-11+11)/5 = x/5, so f and g are inverses of each other.
Therefore, only options A and D have functions that are inverses of each other.
Learn more about inverse functions here:
brainly.com/question/2541698
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If the sales tax for the city of Los Angeles is 9.75%.how much tax would you pay for an item that costs $200.00
The table represents some points on the graph of a linear function. What is the slope of the line?
Answer:
-9/2!
Step-by-step explanation:
For this one, It's a bit hard! But, using the process of elimination, you can tell, that since the Y's are going down, this is a negative slope. Since there was only two answers, and only one was negative, it's -9/2!
I really hope this helped... I know it wasn't the best, but I graphed it for you!
Identify the function that fits the following table
x y
3 12
5 25
7 37
9 49
find the function
A. f(x) = 5x + 4
B.f(x) = 6x + 5
C.f(x) = 5x - 4
D.f(x) = 6x - 5
What are all the ways to multiply
Answer:
multiplying :v
Step-by-step explanation:
................
The greatest common factor of 4xy and -6xy
Answer:
The greatest common factor is 2x
G
Which number line can be used to find the distance between (-1, 2) and (-5, 2)?
--7-6-5
-3-2
0
1
2
3
-2 -1 0
1
2
3
5
6 7
8
-7 -6 -5 4 3 - -
0 1
2
3
1
2
3 4 5
9514 1404 393
Answer:
see below
Step-by-step explanation:
The y-coordinates of the points are the same, so the distance between those points will be the difference of the x-coordinates. The first number line shows those x-coordinates plotted properly. It can be used to find the difference between them.
72 times what gives you 6834
Answer:
94.917
Step-by-step explanation:
6834/72 = 94.916666
Round off 13,486 to the nearest hundred.
Answer:
13,500
Step-by-step explanation:
Answer: 13,500
Step-by-step explanation:
So the 4 is in the hundred place than u look to the right where the next digit is which is 8. If its 5 or more u round up but if its 5 or less it stays the same. So 8 is 5 or more than u round up the 4 to 5 and leave the rest of the digit 0's. but u leave the 13 the same. If that makes sense.
−8⋅f(1)−4⋅g(4)= Help me ASAP
Answer:
sorry I can
Step-by-step explanation:
why wala pa kame jan sorry wait kalang
1. Name the quadrant or axis containing the point (-1, 2)
A
V-axis
B
x-axis
с
quadrant II
D
quadrant III
Answer:
Can u put a pic 9f the question
It took 45 minutes to jog 5 miles. At this rate, how long did it take to jog 1
mile? *
Answer:
9 minutes
Step-by-step explanation:
45 ÷ 5 = 9
Therefore, it was 9 mins / mile
Hopefully this helped! :D
-LavenderVye
Answer:
9 minutes to jog 1 mile
Step-by-step explanation:
Time = 45
Distance = 5
Speed = [tex]\frac{Distance}{Time}[/tex]
= [tex]\frac{45}{5}[/tex]
= 9
The supermarket has 48 aisles. 12 of the aisles are empty. What percentage of the aisles are empty
Answer:
25% of the isles are empty
Step-by-step explanation:
48/12 is 25%
Answer:
25%
Step-by-step explanation:
12 + 12 + 12 + 12= 48
if 12 isles are empty, then that is 1/4 of 48 aka 25%
find the value of 1/3^-2
Answer:
9
Step-by-step explanation:
just reciprocate and change the negative sign to positive
Write the slope intercept form of the equation of the line through the given points.
through: (-4,2) and (0,3)
y= 3x +1/4
y= -5/4x +3
y= 1/4x +3
y= -1/4x +3
Answer:
y= 1/4x + 3
Step-by-step explanation:
Answer:
y= 1/4x +3
Step-by-step explanation:
I used a graph
I need to have this done by tonight and I don’t know what to put
Answer:
A. Option 1
Sign up cost = 0
1 Month = 125
2 Months = 150
3 Months = 175
4 Months = 200
Step-by-step explanation:
For every option simply write what the starting cost is in the top box for every option. Then multiply the monthly cost by how many months for each box and then add the starting cost. The result of the multiplication and addition will be what you put in each box.
Find the solutions to the equation below 9x^2 -81=0
Step-by-step explanation:
=
−
±
2
−
4
√
2
x=2a−b±b2−4ac
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
9
2
−
8
1
=
0
9x^{2}-81=0
9x2−81=0
=
9
a=
a=9
=
0
b={\color{#e8710a}{0}}
b=0
=
−
8
1
c={\color{#129eaf}{-81}}
c=−81
=
−
0
±
0
2
−
4
⋅
9
(
−
8
1
)
√
2
⋅
9
x=2⋅9−0±02−4⋅9(−81)