Answer:
A) the diving board is 1m high.
B) maximum height of the diver is 3.25 meter(s)
C)i)the diver is a ascending from 0 metres to 0.5 metres.
II) the diver descends from 0.5 metres to 1 m
Step-by-step explanation:
A) We are given the function;
f(x) = −9x² + 9x + 1
Now, the height of the diving board will be when x = 0 metres. This is because at x = 0, the driver didn't jump.
Thus;
f(0) = -9(0²) + 9(0) + 1
f(0) = 1 m
Thus, the diving board is 1m high.
B) From quadratic equations, we can say that in the given function, we have as follows;
a = -9
b = 9
c = 1
Now, a < 0
This means that the parabola opens down and it's vertex formula will be used and value of x plugged into the given function to get the maximum height.
Thus, vertex is;
x = -b/2a
x = -9/(2 × -9)
x = 1/2
x = 0.5 m
Thus;
Max height = -9(0.5²) + 9(0.5) + 1
Max height = 3.25 m
The maximum height of the diver is 3.25 meter(s)
C) Since the parabola opens down, the diver is ascending from 0 metres to 0.5 metres.
Similarly, the diver descends from 0.5 metres to 1 m
The path of the diver is an illustration of a quadratic function.
The height of the diving board is 1 meterThe maximum height of the diver is 3.25 mThe diver ascends from 0 meters to 0.5 metersThe function is given as:
[tex]\mathbf{f(x) = -9x^2 + 9x + 1}[/tex]
(a) The height of the diving board.
This is represented by the constant term in the function.
So, we have:
[tex]\mathbf{Height = 1}[/tex]
Hence, the height of the diving board is 1 meter
(b) The maximum height of the diver
We have:
[tex]\mathbf{f(x) = -9x^2 + 9x + 1}[/tex]
Differentiate
[tex]\mathbf{f'(x) = -18x + 9}[/tex]
Set to 0
[tex]\mathbf{-18x + 9 = 0}[/tex]
Collect like terms
[tex]\mathbf{18x = 9}[/tex]
Divide through by 18
[tex]\mathbf{x = 0.5}[/tex]
Calculate f(0.5)
[tex]\mathbf{f(x) = -9x^2 + 9x + 1}[/tex]
[tex]\mathbf{f(0.5) = -9(0.5)^2 + 9(0.5) +1}[/tex]
[tex]\mathbf{f(0.5) = 3.25}[/tex]
Hence, the maximum height of the diver is 3.25 m
(c) The depth, the diver ascends to
In (b), we have:
[tex]\mathbf{x = 0.5}[/tex]
This means that, the diver ascends from 0 meters to 0.5 meters
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The graph shows the distances traveled by two runners over several minutes.
A graph measuring distance and time. Two lines, labeled Runner A and Runner B, exit the origin to show that distance increases as time increase
Which runner is moving at a slower rate?
Select from the drop-down menu to correctly complete the statement.
Runner
Choose...
is moving at a slower rate.
(3x-2)(3x-5) expand
explain step-by-step
Step-by-step explanation:
[tex](3x - 2)(3x - 5) = \\ 3x(3x - 5) - 2(3x - 5) = \\ 3x \times 3x - 3x \times 5 - 2 \times 3x - 2 \times ( - 5) = \\ 9 {x}^{2} - 15x -6 x + 10 = \\ 9 {x}^{2} - 21x + 10[/tex]
Which of the following could be a function? Select three that apply.
Answer:
For this one I think the answer would be A and E
Step-by-step explanation:
when seeing if the coordinates represent a function, make sure none of the inputs repeat and none of the outputs repeat.
hope this helps
y=4x-7 how do i identify the slope and Y intercept?
Answer:
The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Using the slope-intercept form, the slope is 4 .
Step-by-step explanation:
Determine if 0.828228222822228222228... is rational or irrational and give a reason for your answer.
Answer:
irrational
Step-by-step explanation:
it cannot be written as a ratio
The given decimal number is a nonterminating and non-repeating decimal it is irrational.
The given decimal number is 0.828228222822228222228...
We need to identify whether the given decimal number is rational or irrational.
What are rational numbers and irrational numbers?Rational Numbers
The term ratio came from the word ratio which means the comparison of any two quantities and is represented in the simpler form of a fraction. A number is considered a rational number if it can be expressed in the form of a/b where both a (numerator) and b(denominator) are integers. The denominator of a rational number is a natural number(a non-zero number). Integers, fractions including mixed fractions, recurring decimals, finite decimals etc all come under the category of rational numbers.
Irrational Numbers
A number is considered an irrational number if it cannot be able to simply further to any fraction of a natural number and an integer. The decimal expansion of irrational numbers is neither finite nor recurring. Irrational numbers include surds and special numbers such as π. The most common form of an irrational number is pi (π). A surd is a non-perfect square or cube which cannot be simplified further to remove the square root or cube root.
Since the given decimal number is a nonterminating and non-repeating decimal it is irrational.
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where would 0.015 go?
Answer:
Right after 0.05
Step-by-step explanation:
I think
Help me plzzzzzzz need and answer as fast as you can plzz
Answer:
9
Step-by-step explanation:
count the places (vote me brainiest)
PLZ HELP IMAGE BELOW THXS
-98 = 14m
112
-7
7
-112
Answer:
[tex]\boxed {m = -7}[/tex]
Step-by-step explanation:
Solve for the value of [tex]m[/tex]:
[tex]-98 = 14m[/tex]
-Switch:
[tex]14m = -98[/tex]
-Divide both sides by [tex]14[/tex]:
[tex]\frac{14m}{14} = \frac{-98}{14}[/tex]
[tex]\boxed {m = -7}[/tex]
Therefore, the value of [tex]m[/tex] is [tex]-7[/tex].
Can someone please help me
Answer:
1/3
Step-by-step explanation:
Take two points and do the y2 - y1 over x2 - x1 method.
A website gives the population of a European country as 16,714,683. What is this population to three significant digits
Answer: 16.7m
Step-by-step explanation:
A students that 42% of 78 is 45
Answer:
this is incorrect. 42% of 78 is actually 32.76
what is 7+1+5
A.13
B. 24
C.14
D.21
Answer:
13
Step-by-step explanation:
7 plus 1 is 8
8 plus 5 is 13
Answer:
A.13
Step-by-step explanation:
7+1=8
8+5=13
WILL MARK BRAINLIEST!!
simplify (√5)(3√5)
A) 5 5/6
B) 5 1/6
C) 5 2/3
D) 5 7/6
which pair or pars of polygons are congruent
A. 3 and 4
B. 1 and 3
C. 1, 3, and 4
D. 2, 3, and 4
E. 1, 2, 3, and 4
Answer:
B. 1 and 3
Step-by-step explanation:
pair 2 the green one is a bit bigger than the the red one
pair 4 the red one is a bit bigger than the the green one
I got 1 minute to do this dude
Answer:
Y=30x
Step-by-step explanation:
Y-total cost, so make everything equal to that. 30 is the amount she makes each month so multiply that with x.
If the regular price of a new T-shirt is $13.95 and its on sale for 25% off. what is 25% of the price rounded to the nearest cent?
Answer:
3.49
Step-by-step explanation:
288 miles on 12 gallons of fuel; 240 miles on 10 gallon of fuel
Answer: 1: 24 miles per gallon (mpg)
2: 24 miles per gallon (mpg)
Step-by-step explanation: PLEASE GIVE BRAINLIEST IT HELPS ALOT. THANKYOU.
A number has a 6 in the tenths place. The number also has a digit whose value is 1/10 the value of the 6 in the tenths place. Which could be the expanded form of the number?
Answer:
The expanded form of the number is
= 6 × 1/10 + 6 × 1/100
= 6/10 + 6/100
= 0.6 + 0.06
The number is = 0.66
Step-by-step explanation:
A number has a 6 in the tenths place. The number also has a digit whose value is 1/10 the value of the 6 in the tenths place. Which could be the expanded form of the number?
We are told that a number has 6 in its tenth place
This means
6/10 = 0.6
The number also has a digit whose value is 1/10 the value of the 6 in the tenths place.
This means
= 6/10 × 1/10 = 6/100
0.6 × 1/10
= 0.06
Hence, the expanded form
= 6 × 1/10 + 6 × 1/100
= 6/10 + 6/100
= 0.6 + 0.06
= 0.66
What is the length of each leg of the triangle below?
45
26
90°
45
A. 132
B. V13
C. 1
D. 18
E. 13
OF /26
Answer:
Option (A)
Step-by-step explanation:
From the triangle ABC given in the picture,
Since, ∠BAC and ∠BCA are equal in measure, opposite sides of these angles will be equal.
AB = BC
Therefore, ΔABC is an isosceles triangle.
By applying Pythagoras theorem in ΔABC,
AB² + BC² = AC²
AB² + AB² = AC² [Since, AB = BC]
2(AB)² = AC²
2(AB)² = (26)²
AB² = [tex]\frac{676}{2}=338[/tex]
AB = [tex]\sqrt{338}[/tex]
AB = [tex]\sqrt{169\times 2}[/tex]
= [tex]13\sqrt{2}[/tex] units
Therefore, Option (A) will be the answer.
Answer:
A: 13 times the square root of 2.
Step-by-step explanation:
eudora got it right
what is the difference between 1.28 x 10^5 and 3.2 x 10^4
Answer:
1.92 x 10
Step-by-step explanation:
3.20-1.28=1.92
10^5-10^4=10
=1.92 x 10
Correct me if I'm wrong
Help I will give you brainliest if it’s correct
Answer:
The second answer choice
Step-by-step explanation:
All of the other answers keep the shape the same when transforming them
Answer:
the 3rd one
Step-by-step explanation:
How many square feet of outdoor carpeting will we need for this hole 3ft 2ft 1ft 2ft 12ft 4ft
Answer:
40
Step-by-step explanation:
which decimal number shows two and one tenth in standard form
A 0.21
B 2.01
C 2.1
D 20.1
Hi! I believe your answer is C- 2.1 because the number 2 is in the whole number spot and the first number after the decimal is the tenth. So, it's 2 and one-tenth, because there's a one. I hope this helps you! Good luck and have a great day. ❤️
How do you tell if an equation, table, graph, and word problem are all related to the same situation?
PLZ help me I need help on this is a grade today
If it took eight men ten hours to build a wall, how long will it take four men?
Answer:
I want to say 20
Step-by-step explanation:
4 is half of 8, so double the time and its 20.........
Since it took 10 hours for 8 men to build a wall. If you had 4 men build a wall it would most likely take twice as long than if there were 8 men due to less people.
So it would take 20 hours for 4 men to build a wall.
Roxanne is going to build a rectangular prism out of 36 one- inch cubes. She wants the height of the rectangular prism to be 3 inches, and she wants the width to be shorter than the length. How many rectangular prisms with different dimensions can she build?
Answer:
3
Step-by-step explanation:
Since Roxanne has 36 one inch cubes, the maximum volume of rectangular prism she can have is 36 in³ = 1 in × 1 in × 36 in.
Now, if Roxanne wants a rectangular prism with height 3 inches, this implies that the area of its base is 36 in³/3 in = 12 in².
We now find all the factors of 12 = 1 × 12, 2 × 6, 3 × 4.
So, we have 3 different areas of base of rectangular prism in which the width is shorter than its length the width being the smaller dimension.
So, the different rectangular prisms in which the volume = 36 in³ in which the width is shorter than its length and has a height of 3 in is
1 × 12 × 3, 2 × 6 × 3, 3 × 4 × 3.
So we have 3 different rectangular prisms
how to find the area of a generic quadrilateral
Answer:
Area = base × height, or A = b × h for short. Example: If the base of a rectangle has a length of 10 inches and the height has a length of 5 inches, then the area of the rectangle is simply 10 × 5 (b × h) = 50 square inches.
Step-by-step explanation:
Find the X and Y intercepts of the equation y = 3/2 x - 9
Yoshio has three peices of fabirc. Each piece of fabric has the same length. The total length of the fabric is 2 1/4 yards. What is the legth of each pice of fabric?
Answer:3/4
Step-by-step explanation:2 1/4/3=3/4
Length of each piece of fabric is [tex]\boldsymbol{\frac{3}{4}}[/tex] yards.
Define length.The term "length" involves the measurement of distance. Length is a variable with the value distance in the International System of Quantities.
Number of pieces of fabric [tex]=3[/tex]
Total length of a fabric [tex]=2\frac{1}{4}[/tex] yards
[tex]=\boldsymbol{\frac{9}{4}}[/tex] yards
Therefore,
Length of each piece of fabric [tex]=\frac{9}{4}\div 3[/tex]
[tex]=\boldsymbol{\frac{3}{4}}[/tex] yards
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