Finding the equation of the parabola, it is found that the height of the diving board is of 24 feet.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
From the maximum height, it is found that the vertex is at (1,25), hence:
h = 1, k = 25.
Hence:
y = a(x - 1)² + 25.
You hit the water 6 feet from the diving board, hence y(6) = 0, meaning that we use it to find a as follows:
0 = a(6 - 1)² + 25
25a = -25.
a = -1.
Hence:
y = -(x - 1)² + 25.
The height of the diving board is y(0), hence:
y = -(0 - 1)² + 25 = -1 + 25 = 24 feet.
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(1, 3) and (-8,-6)
Answer:
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What is the perimeter, in feet, of a rectangle whose length is four times its width
which is 8 feet?
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
4,12,36
Answer:
Step-by-step explanation:
this is clearly not a linear sequence (the terms don't have the same difference).
so, it has to be a geometric sequence.
the common ratio is r.
s2 = s1 × r
16 = 64 × r
r = 16/64 = 1/4
control :
s3 = s2×r
4 = 16 × 1/4 = 4
correct.
Step-by-step explanation:
solve for x 34=-2x need help asap
34 = -2x
Divide through by -2
x = -17
The greatest integer less than or equal to
[tex] \rm \int_{1}^2 log_{2}( {x}^{3} + 1 ) dx + \int_{ 1 }^{log_{2}(9)} ( {2}^x - 1) {}^{ \frac{1}{3} } \: dx \: is \\ [/tex]
We use a property from an earlier question of yours [27174924], that
[tex]\displaystyle \int_a^b f(x) \, dx + \int_{f(a)}^{f(b)} f^{-1}(x) \, dx = b\,f(b) - a\, f(a)[/tex]
Note that
[tex]f(x) = \log_2(x^3+1) \implies f^{-1}(x) = \left(2^x - 1\right)^{1/3}[/tex]
[tex]a = 1 \implies f(a) = \log_2(1^3 + 1) = \log_2(2) = 1[/tex]
[tex]b = 2 \implies f(b) = \log_2(2^3 + 1) = \log_2(9)[/tex]
so that the exact value of the integral is
[tex]\displaystyle \int_1^2 \log_2(x^3 + 1) \, dx + \int_1^{\log_2(9)} \left(2^x - 1\right)^{1/3} = 2\log_2(9) - 1[/tex]
Now, observe that
[tex]8 = 2^3 < 9 < 2^{7/2} = 8\sqrt2 \approx11.3 \\\\ \implies 3 < \log_2(9) < \dfrac72 \\\\ \implies 6 < 2\log_2(9) < 7 \\\\ \implies 5 < 2\log_2(9) - 1 < 6[/tex]
so that
[tex]\left\lfloor 2\log_2(9) - 1 \right\rfloor = \boxed{5}[/tex]
The nearest star to us, Alpha Centauri, is 4.3 light years away. A light year is 5, 865,696,000,000 miles. How far away is Alpha Centauri in miles? Express your a swer in scientific notation?
Answer:
Step-by-step explanation: 18,612,464,000,000 or 1.8612464 × 10^13
chapter 8
Find the area of each. Use your calculator's value of [pi]. Round your answer to the nearest tenth.
Given the radius in the diagram, the area of the circle to the nearest tenth is 116.9m².
What is the area of the given circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
Where r is radius and π is constant pi.
Given the data in the question;
Radius of the circle r = 6.1mArea A = ?Plug the given value into the area of circle formula and solve for A.
A = πr²
A = π × 37.21m²
A = 116.9m²
Given the radius in the diagram, the area of the circle to the nearest tenth is 116.9m².
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\Find the equation of a line that contains the points (−8,−1) and (−1,−2).
The correct answer is 1x+7y=-15.
Finding an equation in standard form for a line with the points (-8, -1) and (-1, -2) is what we're after.
Since a, b, and c are integer coefficients in standard form, a and b CANNOT equal 0 or be negative.
It is helpful to first put the line in a different form, such as slope-intercept form, which is represented by the equation y=mx+b, where m is the slope and b is the y intercept.
Let's start by calculating the slope using the equation, which can be done from two points.
(y_2-y_1)/(x_2-x_1)
x1 = -8
y1 = -1
x2 = -1
y2 = -2
Substituting the value = (-2-(-1 ))/((-1-(-8))
= -2+1/-1+8
= -1/7
Thus the slope is -1/7
y=mx+b
y=(-1/7)x+b
-1=(-1/7)(-8)+b
-1=8/7+b
-1-8/7=b
-7-8/7=b
-15/7 = b
substituting the value in equation,
y = (-1/7)x-15/7
7y=-1x-15
Thus the equation is,
1x+7y=-15
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Donna is going to swim 17 laps. She has completed 8 laps. What fraction of laps has she completed?
What fraction of her swim remains?
What fraction of her swim has she completed?
What fraction of her swim remains?
Answer:
She has completed [tex]\frac{8}{17}[/tex] laps.
She has [tex]\frac{9}{17}[/tex] laps remaining
Hope that helps
If the sum of a number and seven is tripled, the result is four less than twice the number. Find the number.
Answer:
-25
Step-by-step explanation:
3(x+7)+4=2x
3x+25=2x
x= -25
Three-tenths of the books in the school library are how-to books. Of these, 0.2 deal with carpentry and 0.4 deal with electronics. Interpret what the figure 0.12 represents in this context. (1 point)
the fraction of books in the library that are how-to books on carpentry
the fraction of books in the library that are how-to books
the fraction of the how-to books that are about elther carpentry or electronics
the fraction of the books in the library that are how-to books on electronics
The figure 0.12 represents in this context the D. the fraction of the books in the library that are how-to books on electronics.
How to illustrate the information?From the information, three-tenths of the books in the school library are how-to books and 0.2 deal with carpentry and 0.4 deal with electronics.
Therefore, the figure 0.12 represents in this context the fraction of the books in the library that are how-to books on electronics.
This was calculated as:
= 0.4 × 0.3
= 0.12
Therefore, the correct option is D.
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What is a power that is unique to (only held by) the United States Senate?
declare war
initiate (begin) impeachment proceedings
create courts
approve Presidential appoitments
Which number sentence is true?A.-3 + 5 = -8B.-3 – (-5) = -8C.3 – 5 = 2D.3 – (-5) = 8
Answer:
D) 3 - (-5) = 8
Step-by-step explanation:
A. [tex]-3 + 5 \to 5 - 3 \to 2[/tex]
B. [tex]-3 - (-5) \to -3 + 5 \to 5 - 3 \to 2[/tex]
C. [tex]3 - 5 \to -2[/tex]
D. [tex]3 - (-5) \to 3 + 5 \to 8[/tex]
Translate the given quadrilateral to the left 6 units and down 5 units. please show work
Answer:
A wouldn now be at -4, -1
B would be at -1, -1
C would be placed at -1, -5
D would be located at -2, -2
Step-by-step explanation:
Hope it helps!
Answer:
5
Step-by-step explanation:
Factor- 5
[tex]Domain: x - R[/tex]
[tex]Range : y - R[/tex]
[tex]Zeros - 0[/tex]
[tex]Y - intercept \: \: y = 5[/tex]
[tex]Horizontal \: asmptotes \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 5, x > + \infty [/tex]
[tex]Parity : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: The \: function \: is \: even[/tex]
[tex]Monotonicity : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( - \infty , \: \infty \: \: ) constant[/tex]
.
.
In an examination for the final students of a school, 60 offered History, 50 for Economics 48 for Literature ,30 History and Economics, 16 History and literature, 22 Economics and Literature. If 10 offered candidates offered all the three subjects. How many candidates sat for the exam, assuming that each candidate sat for at Least one Subject. ?
There are total 100 candidates that sat for the exam.
What are sets?A set is a group of items (referred to as members or elements) that are taken to be one object. Writing x A denotes that an item x is a member of the set A, whereas writing x A denotes that x is not a member of A.
Using the formula of sets,
n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C),
n(A) = 60 n(B∩C) = 16
n(B) = 50 n(C∩A) = 22
n(C) = 48 n(A∩B∩C) = 10
n(A∩B) = 30
The total students sat for the class are -
n(A∪B∪C) = 60 + 50 + 48 - 30 - 16 - 22 + 10
n(A∪B∪C) = 100
So, In total 100 candidates appeared for the exam.
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what is the interest of rs 2500 for 5 years at the rate of 2 paisa per 2 months of rs 2?
Answer:
First, converting R percent to r a decimal
r = R/100 = 3.875%/100 = 0.03875 per year,
then, solving our equation
I = 10000 × 0.03875 × 5 = 1937.5
I = $ 1,937.50
The simple interest accumulated
on a principal of $ 10,000.00
at a rate of 3.875% per year
for 5 years is $ 1,937.50.
Step-by-step explanation:
The diameter of each wheel of a bicycle is 26 inches. If you are traveling at a speed of 30 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning?
30 ÷ 60 = .5 mile per minute
the diameter of the wheel is 26 inches
circule perimeter = 2 pi r
r = 1/2 d = 13 inch
circule perimeter = 81.7 inches
half mile = 31680 inch
31680 ÷ 81.7 = 387. 76 revolutions per minute
16051 to the nearest thousand
Answer:
16,000
Step-by-step explanation:
Because,
I know it :)
What is the Roman numeral for 824
Answer:
Step-by-step explanation:
DCCCXXIV
A bird was perched on a tree at a height of 15 feet. The bird then saw food on a branch below and dropped down 6 1/3ft
What is the current height of the bird?
The current height of the bird is 8 2/3 feet.
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example:
2 1/3 is a mixed fraction.
where,
2 =quotient
1 = remainder
We have,
Bird initial height = 15 feet.
The bird drops down to 6 1/3 feet.
The current height of the bird is:
= 15 - 6 1/3
We can write the mix fraction 6 1/3 in a proper fraction
6 1/3 = 19 / 3
= 15 - 19/3
= (45 - 19) / 3
= 26 / 3
= 8 2/3 feet
Thus the current height of the bird is 8 2/3 feet.
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Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the most accurate rate of speed Morris is traveling?
answer:
48 miles per hour
the sum of a number and 5 is between 0 and 12. write the compound inequality and solve
The inequality will be given by 0 < x + 5 < 12 or -5 < x < 7 which meant value of number x will lie between -5 and 7.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
It is given that the sum of a number and 5 is between 0 and 12. This can be represented by an inequality.
Let's assume the number is x.
So , the sum of number x and 5 will be :
= x + 5
Also , given that, this value is between 0 and 12 .
This meant the inequality will be given by :
0 < x + 5 < 12
Let's subtract 5 from every term of inequality.
0 - 5 < x + 5 - 5 < 12 - 5
or
-5 < x < 7
The value of x lies between -5 and 7.
Therefore , the inequality will be given by 0 < x + 5 < 12 or -5 < x < 7 which meant value of number x will lie between -5 and 7.
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If m < CDF = (3x + 14), m < FDE = (5x -2), and m < CDE = (10x - 18), find x.
The value of x in the angle is 15
How to determine the value of x?The given parameters are
m < CDF = (3x + 14), m < FDE = (5x -2), and m < CDE = (10x - 18)
The above means that
Line FD divides angle CDE
So, we have
CDE = CDF + FDE
This gives
10x - 18 = 3x + 14 + 5x - 2
Evaluate the like terms
2x = 30
Divide both sides by 2
x = 15
Hence, the value of x in the angle is 15
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Using the diagram below, state the exact value of sin 8.m
Give your answer as a fraction in its simplest form..
5cm
4cm
0
3cm
The diagram is
Answer:
if ur adding them that would be 12cm for all
Step-by-step explanation:
hope it helped
What is the value of x if 25 = 5x + 35?
[tex] \bf\implies x = - 2 \\ [/tex]
Step-by-step explanation:[tex]25 = 5x + 35 \\ 25 - 35 = 5x \\ - 10 = 5x \\ - \frac{ \cancel{10}}{ \cancel5} = x \\ - 2 = x \\ \implies \boxed{ x = - 2} \: ans.[/tex]
Answer:
35.45
Step-by-step explanation:
PLS HELP ME I ONLY HAVE 2 MINS!!!
Complete the following sentence with the correct symbol. Select all that apply
|-1| ___ 1
≥
≤
≠
<
>
=
helpppppp ur gurlllll out
Answer:
see below
Step-by-step explanation:
When evaluating functions, what is f(x) = x + 7
The value of the function is f(−1)=6.
A function is defined as a relation between a set of inputs having one output each.
In this problem, we are given a function f(x) = x+7 and we are asked to evaluate f(-1)
Recall that f(x) = y.
When we evaluate functions, we substitute the given x-value to find the corresponding y-value of the functionWhen evaluating functions using function notation the number in place of the "x" in "f(x)" is the number that you plug into the x of your function.
So, if f(x)=x+7 then
f(−1)=(−1)+7
Therefore, f(−1)=6
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FInd the equation of the line that passes through (1,3) and is perpendicular to y=1-2x. Leave your answer in the form ax+by=c Where a,b and c are integers.
Answer:
[tex]y = \frac{x}2 + 2.5[/tex]
Step-by-step explanation:
Step 1) Finding the slope
The line is perpendicular to [tex]y = 1 - 2x[/tex], therefore, its slope is equal to the negative invert of [tex]y[/tex]'s slope.
[tex]y[/tex]'s slope is -2 (the coefficient to [tex]x[/tex]), and, therefore, the line's slope is [tex]m = [-(-2)]^{-1} = 2^{-1} = \frac12[/tex]
Step 2) Building the Equation
We can now substitute the slope, along with the given point's coordinates, into the formula [tex]y - y_1 = m(x - x_1)[/tex] :
[tex]y - 3 = \frac12(x - 1)\\\to y - 3 = \frac{x}2 - \frac12\\\to y = \frac{x}2 + 2.5[/tex]
Between 9:00am and 4:00 pm the temperature rose from 68° to 85°. What was the percent increase in temperature between 9:00am and 4:00 pm?
The percent increase in temperature between 9:00 am and 4:00 pm is 25%
The percent increase can be calculated as follows ?The first step is calculate the percentage change
= 85-68
= 17
The percent increase can be calculated as follows
= 17/68 × 100
= 0.25 × 100
= 25%
Hence the percent increase is 25%
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