A diver is jumping from a cliff into a river. The equation h(x)= -16x^2+20x+35 represents the divers height in feet over time in seconds.Based on the equation, the diver is blank feet above the water he jumps from the cliff
Answers
Step 1: Write out the equation and the given values.
\(\begin{gathered} h(x)=-16x^2_{}+20x+35 \\ \text{where} \\ h(x)\text{ is the height in f}eet\text{ above the river x seconds from the start} \\ x\text{ is the time in seconds} \end{gathered}\)Before the diver jumps from the cliff,
\(x=0s\)Step 2: Substitute the given value into the equation.
\(h(0)=-16(0)^2+20(0)+35=0+0+35=35\text{ ft}\)Therefore, the diver is 35 feet above the water before he jumps from the cliff
Related Questions
Which number line represents the solution to 5x < 30? F t 8 0 2 4 6 10 G =N + 4 H 8 0 6 10 H + 0 + 8 2 4 6 10 J + 2 + 4 0 6 8 10
Answers
Answer:
Line H, the third option
Step-by-step explanation:
First, find the value of x
5x < 30Divide both sides by 55x/5 < 30/5x < 6X is strictly less than 6, so the answer cannot include 6
This means the answer needs to have an open circle as an endpointThe less than sign (<) tells you the line should be pointing to the left
Multiply and simplify 24/7 and 9/16
Answers
Answer:
27/14 or 1 13/14
Step-by-step explanation:
First you simplify the problem to 3/7 × 9/2. then you multiply them to get 27/14 or 1 13/14.
Answer:
24/7 × 9/16
6/7 × 9/4
3/7 × 9/2
27/4
=6.75
Step-by-step explanation:
in dividing this equation, 4 can divide both 24 and 16 so 4 will divide 16 4 times and divide 24 6times. also 2 can divide 4 2times and divide 6 times so you will be having the third method. then you multiply them since you can have any number dividing them. your answer will be 27/4 which is an improper so you will either change it to decimals or mixed fraction
A marketing firm conducts a survey to determine the ages of their survey subjects who like a new health drink.
This is the resulting data from their survey:
49, 63, 78, 22, 41, 39, 75, 61, 63, 65,
58. 37. 45, 52, 81, 75, 78, 72, 68, 59,
72, 85, 63, 61, 75, 39, 41, 48, 59,55
61, 25, 61, 52, 58, 71, 75, 82, 49, 51
The mean age of the subjects who like the new health drink is (type your answer...)
and the median age of the subjects is (type your answer..)
Answers
Answer:
Mean = 59.1, Median = 61
(there might have been a mistake in calculation (a lot of numbers!))
Step-by-step explanation:
The sample size is 40,
Now, the formula for the mean is,
Mean = (sum of the sample values)/(sample size)
so we get,
\(Mean = (49+63+78+22+41+39+75+61+63+65+58+37+45+52+81+75+78+72+68+59+72+85+63+61+75+39+41+48+59+55+61+25+61+52+58+71+75+82+49+51)/40\\Mean = 2364/40\\Mean = 59.1\)
To find the median, we have to sort the list in ascending (or descending)order,
we get the list,
22,25,37,39,39,41,41,45,48,49,
49,51,52, 52,55,58, 58, 59, 59, 61,
61, 61, 61, 63, 63, 63, 65, 68, 71, 72,
72, 75, 75, 75, 75, 78, 78, 81, 82, 85
Now, we have to find the median,
since there are 40 values, we divide by 2 to get, 40/2 = 20
now, to find the median, we takethe average of the values above and below this value,
\(Median = ((n/2+1)th \ value + (n/2)th \ value )/2\\where, \ the\ (n/2)th \ value \ is,\\n/2 = (total \ number \ of \ samples) /2\\n/2=40/2\\(n/2)th = 20\\Hence\ the (n/2)th \ value \ is \ the \ 20th \ value\)
And the (n+1)th value is the 21st value
Now,
The ((n/2)+1)th value is 61 and the nth value is 61, so the median is,
Median = (61+61)/2
Median = 61
find the slope of the line thatpasses through these two points: (-3, 4): (2,-1)
Answers
Answer:
y=-x+1
Step-by-step explanation:
order these numbers from least to greatest 5 5/8, 5.684, 5.69, 111/20
Answers
Answer:
5/8 because the initial is invalid and the 1 output will only be the remaninging
Step-by-step explanation:
Answer:
111/20 < 5 5/8 < 5.684 < 5.69
Step-by-step explanation:
In decimal form
5 5/8 = 5.6255.6845.69111/20 = 5.5The highest mountain in earth is 29,028 ft. The lowest under sea trench is -35,840ft. Which has the highest absolute value
Answers
Answer:
undersea trench
Step-by-step explanation:
Absolute value is the distance from zero
The highest mountain trench is |29028| or 29028 ft from zero
The lowest under sea trench is | -35840| of 35840 ft from zero
The highest absolute value is the undersea trench
Height always be positive .
Highest mountain in earth=29028ftAbsolute value:-
\(\\ \sf\longmapsto |29028|=29028ft\)
Lowest undersea trench=-35840ftAbsolute value:-
\(\\ \sf\longmapsto |-35840|=35840ft\)
Find the volume of the composite solid (STEP BY STEP PLEASE) 25 POINTS
Answers
The volume of the composite solid is 5770.28ft³
How to determine the volume of the solid?The composite solid is made up of a cylinder and a hemisphere
The volume is the addition of the two solids
Volume=\(\pi\)r²h +2/3πr²
The given parameters are
π=22/7
h=22 ft
r=9 ft
Input the values to get
(22/7*9*9*22) + (2/3*22/7*9*9)
Simplifying the terms to get
5600.57+169.71
The volume is = 5770.28c
ft³
In conclusion, the volume of the solid is 5,770.28ft³
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In △ABC, m∠A=55°, c=11, and m∠B=19°. Find the perimeter of the triangle.law of sines 4A. 39B. 24C. 32D. 48
Answers
Solution: 24.096
Analysis:
We have a triangle and know two angles and one side of the triangle. According to the angle rule, a triangle's total intern angles equals 180 degrees. We have:
mm∠B=19°
∠A+∠B+∠C=180°
55°+19°+∠C=180°
∠C=180°-55°-19°
∠C=106°
\(\frac{a}{sin(A)}=\frac{b}{sin(B)}=\frac{c}{sin(C)}\)\(\begin{gathered} \frac{a}{sin(55)}=\frac{11}{sin(106)} \\ \\ a=\frac{11\ast sin(55)}{sin(106)}=\frac{11\ast0.82}{0.96}=9.37 \end{gathered}\)\(\begin{gathered} \frac{b}{sin(19)}=\frac{11}{sin(106)} \\ \\ b=\frac{11\ast sin(19)}{sin(106)}=\frac{11\ast0.325}{0.96}=3.726 \end{gathered}\)Perimeter=a+b+c
Perimeter=9.37+3.726+11
Perimeter=24.096
Objective 1.1 6. The graph below represents the equation y=1/2x+1. Which graph best represents the equation created when the slope of y= x + 1 is changed to 4?
Answers
Answer:
The correct answer is B
Step-by-step explanation:
When y=x+1is changed to 4 the slop changes too
3
Identify the segment bisector of RS
22
R
M
S
Answers
Answer:
M.
Step-by-step explanation:
I presume M is in the middle of line RS, so M is the segment bisector.
(hope this helps you <3)
Diego is at the batting cage where they are currently offering batting cage customers their choice of The Slow
Ball Challenge or The Fast Ball Challenge.
The Slow Ball Challenge: There will be 10 pitches, each at 60 mph. Diego estimates that he will hit each
individual pitch 95% of the time. If Diego can hit all 10 pitches, he will win a total of $25; otherwise he will lose
$5.
The Fast Ball Challenge: There will be 3 pitches, each at 90 mph. Diego estimates that he will hit each
individual pitch 60% of the time. If Diego can hit all 3 pitches, he will win a total of $60; otherwise he will lose
$10.
What are Diego's expected winnings from playing The Slow Ball Challenge? Round your answer to the nearest
dollar. $
What are Diego's expected winnings from playing The Fast Ball Challenge? Round your answer to the nearest
dollar. $
The batting cage is allowing customers to participate in their choice of either The Slow Ball Challenge or The Fast
Ball Challenge a total of 10 times.
If Diego wants to maximize his expected winnings, what should he do?
Answers
Answer:
The expected winnings from The Slow Ball Challenge rounded to the nearest dollar are $13
The expected winnings from The Fast Ball Challenge rounded to the nearest dollar are $5
Since The Slow Ball Challenge has higher expected winnings, Diego should play The Slow Ball Challenge all 10 times.
Step-by-step explanation:
khan academy
Given m∥n, find the value of x and y.
will give brainiest
Answers
Answer:
The value of x and y are x = 15 and y = 63
Step-by-step explanation:
If two adjacent angle formed a straight line, then the two angles formed a pair of linear anglesThe sum of the measures of the linear angles is 180°From the given figure
∵ The angles of measures (9x - 7)° and (4x - 8)° are adjacent angles
∵ The angles of measures (9x - 7)° and (4x - 8)° formed a line
∴ They formed a pair of linear angles
∵ The sum of the measures of the linear angles is 180°
→ That means add them and equate the sum by 180
∴ (9x - 7) + (4x - 8) = 180
→ Add the like terms
∵ (9x + 4x) + (-7 + -8) = 180
∴ 13x + (-15) = 180
→ Remember (+)(-) = (-)
∴ 13x - 15 = 180
→ Add 15 to both sides
∴ 13x - 15 + 15 = 180 + 15
∴ 13x = 195
→ Divide both sides by 13
∵ \(\frac{13x}{13}\) = \(\frac{195}{13}\)
∴ x = 15
∵ Lines m and n are parallels
∵ A line intersected them
∵ The angles of measures (2y + 2), (9x - 7) are interior alternate angles
∵ The interior alternate angles are equal in measures
∴ 2y + 2 = 9x - 7
∵ x = 15
→ Substitute the value of x
∴ 2y + 2 = 9(15) - 7
∴ 2y + 2 = 135 - 7
∴ 2y + 2 = 128
→ Subtract 2 from both sides
∴ 2y + 2 - 2 = 128 - 2
∴ 2y = 126
→ Divide both sides by 2
∴ \(\frac{2y}{2}\) = \(\frac{126}{2}\)
∴ y = 63
The values of x and y are 15 and 63, respectively
The angles in the figure are: (9x - 7)° and (4x - 8)°
These angles are adjacent angles.
So, we have:
\(\mathbf{9x - 7 + 4x - 8 = 180}\)
Collect like terms
\(\mathbf{9x + 4x = 180 + 8 + 7}\)
\(\mathbf{13x = 195}\)
Divide both sides by 13
\(\mathbf{x = \frac{195}{13}}\)
\(\mathbf{x = 15}\)
Also, we have:
\(\mathbf{2y + 2 = 9x - 7}\) -- interior angles
Subtract 2 from both sides
\(\mathbf{2y = 9x - 9}\)
Substitute 15 for x
\(\mathbf{2y = 9\times 15 - 9}\)
\(\mathbf{2y = 126}\)
Divide both sides by 2
\(\mathbf{y = 63}\)
Hence, the values of x and y are 15 and 63, respectively
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Solve the following inequality.
-22 < 4x + 6 < 50
[?]
х
![Solve the following inequality.-22 < 4x + 6 < 50[?]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/ynf76AySPASYJ11Z1zHacoDDcUpBoWGo.png)
Answers
Solution:
Let's simplify each inequality one by one.
-22 < 4x + 6 ≤ 50=> -22 - 6 < 4x => -28 < 4x => -7 < x => 4x + 6 ≤ 50=> 4x ≤ 50 - 6=> 4x ≤ 44=> x ≤ 11This means that...
-7 < x ≤ 11Hoped this helped!
4 times itself and plus 1 equals this number. What is the number?
Answers
Answer:
The number = -0.3
Step-by-step explanation:
Let the number equal x:
4x+1=x
4x=x-1
3x=-1
x=-1/3 or x=-0.3
Proof:
4(-0.3)=-1.3
-1.3+1=-0.3
The number = -0.3
Let the no be x
\(\\ \sf\longmapsto 4x+1=x\)
\(\\ \sf\longmapsto 4x-x=1\)
\(\\ \sf\longmapsto 3x=1\)
\(\\ \sf\longmapsto x=1/3\)
Need help with the 3rd one only. Will give brainliest and 5 star rating for fast replies.
Answers
Answer:
f^-1(0) = 4
Step-by-step explanation:
slope = -1/2 => y = -1/2x + 2
=> 1/2x = 2 - y
=> x = -2y + 4
=> f^-1(x) = -2x + 4
f^-1(0) = 4
Is (2, 3) a solution for the equation 2x + 3y = 6?
Answers
Answer:
No
Step-by-step explanation:
Input the values and see if the equation is true.
2x + 3y = 6
(2, 3) x = 2, y = 3
2(2) + 3(3) = 6
4 + 9 = 6
13 ≠ 6
Which graph represents the solution set of the compound inequality below?
x+3<= (4x-12) < 20
OH
4 5 6 7 8 9 10 11 12
4 5 6 7 8 9 10 11 12
6 7 8 9 10 11 12 13 14
6 7 8 9 10 11 12 13 14
Answers
A graph that represents the solution set of the compound inequality is: graph D.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).Next, we would solve the given compound inequality by making x the subject of formula as follows;
x + 3 < 1/2(4x - 12) < 20
Multiplying all through by 2, we have the following:
2x + 6 < 4x - 12 < 40
Next, we would solve the compound inequality in parts:
2x + 6 < 4x - 12
4x - 2x < 12 + 6
2x < 18
x < 18/2
x < 9.
4x - 12 < 40
4x < 40 + 12
4x < 52
x < 52/4
x < 13.
In conclusion, the line on a number line (graph) should be open when the inequality symbol is greater than (>) or less than (<).
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Keisha bought these supplies for school:
4 packs of pencils that cost $0.85 each
6 packs of pens for $1.25 each
5. What was the total cost of the pencils and pens, including a 6% tax?
A
$13.35
B
$10.90
C
$11.55
D
$2.23
.
Answers
Answer:
C. $11.55
Step-by-step explanation:
First, multiply 4 by $0.85 to get an answer of $3.40. Next, multiply 6 by $1.25 to get an answer of $7.50. Add up the cost of the pencils and pens by adding $3.40 and $7.50 to get $10.90. Next, we have to add the tax. Multiply $10.90 by 0.06 to get $.65. Add the $.65 to the $10.90 for a grand total of $11.55. Hope this helps!
What are the first three terms of the sequence modeled by the recursive function An=1/2a n-1 , when a1=1?
Answers
Answer:
A on edge trust
Step-by-step explanation:
The first three term of the sequence are,
⇒ 1/2 , 1/4, 1/8
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The recursive function is,
⇒ \(A_{n} = \frac{1}{2} a_{n - 1}\)
And, We have;
⇒ a₁ = 1
Now, The recursive function is,
⇒ \(A_{n} = \frac{1}{2} a_{n - 1}\)
Put n = 2;
⇒ \(A_{2} = \frac{1}{2} a_{2 - 1}\)
⇒ \(A_{2} = \frac{1}{2} a_{1}\)
⇒ \(A_{2} = \frac{1}{2}\ * 1\)
⇒ \(A_{2} = \frac{1}{2}\)
Put n = 3;
⇒ \(A_{3} = \frac{1}{2} a_{3 - 1}\)
⇒ \(A_{3} = \frac{1}{2} a_{2}\)
⇒ \(A_{3} = \frac{1}{2}\ * \frac{1}{2}\)
⇒ \(A_{3} = \frac{1}{4}\)
Put n = 4;
⇒ \(A_{4} = \frac{1}{2} a_{4 - 1}\\\)
⇒ \(A_{4} = \frac{1}{2} a_{3}\)
⇒ \(A_{4} = \frac{1}{2}\ * \frac{1}{4}\)
⇒ \(A_{4} = \frac{1}{8}\)
Thus, The first three term of the sequence are,
⇒ 1/2 , 1/4, 1/8
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A piece of material measures 38 inches. Courtney cuts the piece of material into two pieces. One piece measures 19 inches. Write an addition equation that could be used to find the length, m, of the other piece of material.
Answers
Answer:
As a whole, the piece first measured 38 inches. No matter how many times you cut it, all of the pieces will still add up to 38 inches. You know that 19 inches is the length of one of the two pieces, so all you need to find is the other unknown piece. Add the two together, with m being the unknown length.
19+m=38
If you want to solve the equation, just subtract 19 from both sides.
19+m=38
m=19
Consider the function shown on the graph.4512-299+6-3-¹3--6-9--12-15(8, 15)(3, 0)(7,0)1 2 3 4 5 6 7 8 9XWhich function does the graph represent?O f(x) = (x+3)(x + 7Of(x) = (x-3)(x-7)Of(x)= 3(x-3)(x-7)O f(x)= 11(x+3)(x + 7)
Answers
The intercept form of a quadratic equation is
\(\begin{gathered} y=a(x-p)(x-q) \\ where\text{ p and q are the roots of the function} \end{gathered}\)so
Step 1
find p and q values
\(\begin{gathered} p\text{ is the value for x where the function becomes zero, so check the graph} \\ (3,0) \\ so\text{ p=3} \\ and\text{ q} \\ (7,0) \\ so \\ q=7 \end{gathered}\)p=3
q=7
Step 2
now, to find the a value we need another point of the graph
check the vertex , it is
\((5,-12)\)so, replace
\(\begin{gathered} x=5 \\ y=-12 \\ y=a(x-p)(x-q) \\ replacing \\ -12=a(5-3)(5-7) \\ -12=a*2*-2 \\ -12=-4a \\ divide\text{ both sides by -4} \\ \frac{-12}{-4}=\frac{-4a}{-4} \\ 3=a \end{gathered}\)so
a=3
therefore, replacing in the formula we have the answer
\(f(x)=3(x-3)(x-7)\)I hope this helps you
Select the correct answer. Simplify the following algebraic expression. √45x^5 A. 9x²√5x OB. 91³√5x² О с. 3x²√5x OD. 3r³√5x²
please help me and can you explain how you got your answer
Answers
The simplified form of the given algebraic expression is 3x²√5x. The correct option is с. 3x²√5x
Simplifying an algebraic expressionFrom the question, we are to simplify the given algebraic expression.
The given expression is
√45x^5
First, we will write the given expression properly
The expression written properly is
√45x⁵
Simplifying
√45 × √x⁵
√9×5 × √x⁴×x
√9 × √5 × √x⁴ × √x
3 × √5 × x² × √x
3 × x² × √5 × √x
3x² × √5×x
3x² × √5x
3x²√5x
Hence, the simplified expression is 3x²√5x
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The equation y= 3×+5 represents a function. True or False PLEASE HURRY
Answers
Answer:
true
Step-by-step explanation:
First 5 represents the y-intercept and three represents the slope.
Find the dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2. (Let x, y, and z be the dimensions of the rectangular box.)(x, y, z) =
Answers
The dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.
Given that:
Total surface area of the rectangular box or cuboid = 100 cm²
A rectangular box with largest volume is a cube.
The total surface area of a cube = 6 times square of one edge length.
Let the edge length = given dimensions; x, y, z
So,
x = y = z
6x^2 = 100
x^2 = 100 / 6
x = √ 100 / 6
x = 10 / √ 6 cm
x = 2.449 cm
Hence, dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.
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Pankaj is a Biomedical Engineering student. He plans to deposit $600 that he earned as stipend, in
a bank account at 3% rate of interest compounded weekly for no more than 2 years. The total
amount of the money, A, that Pankaj will get back, is a function of time, t. Which is a reasonable
domain of the money that he may accumulate?
Answers
The correct answer is A: 600 <= money <= 2822.4.
This represents the range of possible values that Pankaj's accumulated money could fall into, given the specified conditions of the 3% interest rate compounded weekly for a maximum of 2 years. The lower bound, 600, represents the initial deposit amount, while the upper bound, 2822.4, represents the maximum amount of money Pankaj could earn after 2 years, assuming that interest is compounded every week.
40 is what percent of 320
Answers
Evaluate the integral using the indicated trigonometric substitution. sqrt(x2 − 81)/x dx, x = 9 sec()
Answers
Answer:
C
=
C
'
−
81
2
ln
9
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS RIGHT (NO LINKS)
Identify the three-dimensional figure that can be made from this net.
Answers
Answer:
The answer is D. Cone
Step-by-step explanation:
Lily invested $5000 at 3% interest componded annually. What is the balance in the
account after 8 years?
Answers
Answer:
Principal = 20833.334
Step-by-step explanation:
simple interest = $5000.
Rate = 3%
Time = 8 years.
Principal = ?
Principal =
\( = \frac{100 \times simple \: interest}{r \times t} \\ = \frac{100 \times5000 }{3 \times 8} \\ = \frac{500000}{24 \\ } \\ = 20833.334\)
Principal = $20833.334.
someone help me please
Answers
Answer:
A) The vertex of CDH would be point D.
B) The sides of CDH would be CD & HD.
C) Classify CDH as an acute angle.
Step-by-step explanation:
A) Those are just where they meet in the middle, and D is the middle point of CDH.
B) Those are literally just the sides.
C) There's acute, obtuse, right etc. angles. Acute angles are less than 90 degrees. And your angle is definitely less than 90.