A zip line steel cable is being constructed for a reality television competition show. The high end of the zip line is attached to the top of a 50-foot pole, while the lower end is anchored at ground level to a stake 50 feet from the base of the pole. (See figure.) Find exact values for all your answers below.
Answer:
find the value of 8x³-y³
A ball was thrown off a bridge. The table relates to the height of the ball above the ground in feet to the time in seconds after it was thrown. Use the data to enter a quadratic model in vertex form and convert it to standard form. Use the model to find the height of the ball at 1.5 seconds.
The peak height reached at 144 feet, and the graph passing through points (0, 120), (1, 144), (2, 120), gives;
1. The vertex form of a quadratic equation is f(x) = a•(x - h)² + k
Where;
a = The leading coefficient
(h, k) = The coordinates of the vertex.
Let t represent the time of travel of the ball and let h represent the height.
From the given table, we have;
f(t) = a•(t - h)² + k
f(0) = 120 = a•(0 - h)² + k = a•h² + k
120 = a•h² + k
f(1) = 144 = a•(1 - h)² + k = a•(h² - 2•h + 1) + k
f(1) = a•(h² - 2•h + 1) + k
f(1) - f(0) = 144 - 120 = 24 = -((2•h - 1)•a
24 = -((2•h - 1)•a
f(2) = 120 = a•(2 - h)² + k
f(2) - f(1) = -24 = -((2•h - 3)•a
(f(1) - f(0)) - (f(2) - f(1)) = 48 = -2•a
Therefore;
a = -24
24 = -((2•h - 1)•a
24 = -((2•h - 1)×(-24)
-1 = -((2•h - 1)
2•h - 1 = 1
h = 2/2 = 1
h = 1
120 = a•(2 - h)² + k
120 = (-24)•(2 - 1)² + k
k = 120 + 24 = 144
k = 144Which gives;
The vertex form is y = -24•(x-1)² + 144
From the vertex form, we have;
y = -24•(x-1)² + 144 = -24•(x²-2•t+1) + 144
y = -24•(x²-2•tlx+1)+ 144 = -24•x²+48•x - 24 + 144
y = -24•x²+48•x + 120
y = -24•x² + 48•x - 24 + 144 = -24•x²+ 48•x + 120
y = -24•x² + 48•x + 120
The height of the ball after 1.5 seconds is
y = -24×1.5² + 48×1.5 + 120 = 138
The height of the ball at t = 1.5 seconds is 138 feetLearn more about quadratic equations here:
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Oscar is building a fence and purchases three boards that each measure
2.91 meters long. How many meters of fence board did Oscar purchase?
Oscar bought 8.73 meters of fence board to build the fence.
The metric system and the International Systems of Units both use the metre (m), also spelt as meter, as the basic unit of length (SI). In the British Imperial and American Customary systems, it is equivalent to roughly 39.37 inches.
A fence is a building used to enclose a space, usually outdoors. It is often made of posts joined by boards, wire, rails, or nets.
Oscar purchases three boards that measure 2.91 meters long each to build a fence.
Let say the length of one board be x = 2.91 meters.
Then the total length of fence board Oscar purchases is:
= 3x = 3 × 2.91 meters = 8.73 meters
Hence Oscar purchased 8.73 meters of fence board.
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Which of the following must be a factor of the function
Answer:
(A) (x -2)
Step-by-step explanation:
You want to know a factor of the function whose values given in the table include (x, y) = (2, 0).
Polynomial zerosA polynomial function y = p(x) will have a factor of (x-a) if and only if p(a) = 0.
The table shows y=0 for x=2, so this polynomial function will have a factor of (x -2).
__
Additional comment
The function shown in the table is ...
y = (x -2)²
so it actually has two factors that are (x -2).
You can tell this is a polynomial function of degree 2 because the 2nd differences are constant.
First differences between successive y-values: -7, -5, -3, -1, 1, 3
Second differences between successive first differences: 2, 2, 2, 2, 2.
11. -7.5 -2.75 help me and make sure you simpfily
Answer:
-10.25
Step-by-step explanation:
I'm not sure if this is what you want, but -7.5-2.75= -10.25
Estimate √15 to the nearest tenth. Then locate √15 on a number line.
√15~ (Round to the nearest tenth as needed.)
Answer:
3.9 It would be between the numbers 3 and 4 on a number line, but closer to 4
Step-by-step explanation:
If you put this in your calculator hit the square root button and then the number 15, your calculator will spit out 3.87298334621 then round this to the nearest tenths place. Look at the digit 7 to decide to round up for down. This number would be closer to 3.9 than 3.8
what is the direction of vector v if it ends at (-3,-10)
The direction of the vector v in standard position is approximately 253.301°.
What is the direction of a given vector?
Vectors in rectangular form present the change of each of the two variables parallel to orthogonal axes. Each point is described by the following definition:
v = (Δx, Δy) (1)
And the direction of a vector is equal to this inverse trigonometric function:
θ = tan⁻¹ (Δy / Δx) (2)
If we know that Δx = - 3 and Δy = - 10, then the direction of the vector is:
θ = tan⁻¹ (- 10 / - 3)
θ = tan⁻¹ (10 / 3)
θ ≈ 253.301°
The direction of the vector v in standard position is approximately 253.301°.
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simplified fraction 8b+3b-2=6+8b+4
Answer:
b=4
Step-by-step explanation:
it works
Use the fact that 1 kilometer = 0.62 miles to convert 3,070 meters to miles.
Round to the nearest hundredth
Answer: 1.90 miles
Step-by-step explanation:
The conversion rate for meters to kilometers is 1 meter for 0.001 kilometers. Using this rate you can do, [tex]3070m*\frac{0.001km}{1m}[/tex]. The m units cancel and you're left with 3.07km. Since we are given the conversion rate of 1 kilometer = 0.62 miles, we can do, [tex]3.07km*\frac{0.62mi}{1km}[/tex]. again the km units cancel and you're left with 1.9034 mi. Rounded to the nearest hundredth to get 1.90.
what integer would be added to 4 to result in a sum of zero
Answer:
-4
Step-by-step explanation:
4+(-4) =
4-4 =
0
(a) Find the slope of the line through (-6, -13) and (-10,- 29).
(b) Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is
vertical.
Answer:
a) 2
b) left to right
Step-by-step explanation:
a) slope= (y2 -y1)/(x2-x1)
(-13-(-21))/(-6-(-10))
8/4
2
b) left to right
Can you explain this to me?
1. Rewrite Divide
2. Rewrite Simplify
3. Rewrite Simplify Expressions
4. Simplify Fractions
5. and Solve
How many degrees must figure A be rotated counterclockwise around the origin in order to line up with Figure B?
Answer:
270
Step-by-step explanation:
One turn would put you in quadrant 2 and would be 90. A second turn would put you in quadrant 3 and that would be 180. A third turn would put you in quadrant 4 and that would be 270. I know that it is hard to see what I mean by a turn. It would be if you had a piece of tracing paper with the figure drawn on it and you turn the paper at the origin so that the lines at the corners would like up, each turn would be 90 more degrees.
Nigel is going from London, UK, to Moscow, Russia, by train. He goes 296 miles on a train from London to Paris, France. He takes another train 500 miles to Munich, Germany, and switches trains in Munich to ride 256 miles on a train to Vienna, Austria. His last train ride carries him 1,298 miles from Vienna to Moscow. Find his total distance by first rounding each distance to the nearest hundred miles before adding.
Answer: 2400 miles
Step-by-step explanation:
Round;
256 to 300
500 to 500
296 to 300
1,298 to 1,300
Add; 300 + 300 + 500 + 1,300 to get your 2,400 miles.
In March, Mrs. Anderson's students read 2,489 pages. In April, they read 3,052 pages. What is the total
number of pages read for the two months? Enter your answer in the box.
Answer: 5541 pages
Step-by-step explanation:
2489+3052= 5541 pgs
Tristan used his graduation money of $2000 to set up a savings account. He wants to determine which investment would make the most money.
Find the amount of money each investment would yield after 5 years.
How much would Tristan earn with Account A: 5.7% interest compounded monthly
The amount that Tristan would earn in 5 years is $657.30.
How much would Tristan earn?When an amount is compounded monthly, it means that both the amount invested and the interest that has already accrued increases in value every month or 12 times in a year.
The first step is to determine the future value of the investment.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate : 5.7% / 12 = 0.475%m = number of compounding = 12N = number of years$2000 x (1.00475)^(12 x 5)
$2000 x (1.00475)^60
= $2,657.30
Amount he would earn = $2,657.30 - $2,000 = $657.30
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What fractions is in simplest form? 4/10, 15/18, 17/51, 9/21
Step-by-step explanation:
2/5
5/6
1/3
3/7
...........
Pablo received a gift card of $100 for a pizza restaurant .The restaurant charges $15 per pizza. Teresa received a gift card of $70 for a different pizza restaurant .the restaurant charges $10 per pizza .let X be the number of pizzas purchase. for each card write an expression for the amount of money left on the card after purchasing X pizzas.
a)Amount of money left on Pablo's card in dollars = $100 - $15x
= $(90 - 15x)
b) Amount of money left on Teresa's card in dollars= $70 - $10x
= $(70 - 10x)
c) Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.
$100 - 15x = $70 - 10x
Let x be the number of pizzas purchased. For each card, write an expression for the amount of money left on the card after purchasing x pizzas.
For Pablo
Keith received a gift card of $100 for a pizza restaurant. The restaurant charges $15 per pizza.
x numbers of pizza costs = $15x
Hence, the amount of money left on Pablo's card after purchasing x pizzas = $100 - $15x
For Teresa,
Mary received a gift card of $70 for a different pizza restaurant. The restaurant charges $10 per pizza.
Hence, x number of pizzas cost =$10 × x
= $10x
Therefore, the amount of money left on Mary's card after she buys x pizzas =
$70 - $10x
Amount of money left on Pablo's card in dollars = __________
Amount of money left on Teresa's card in dollars=____________
Write an equation to show that the two cards have the same amount of money left on them.
To find the equation that shows that the two cards have the same amount of money =
Equation 1 = Equation 2
$100 - 15x = $70 - 10x
Collect like terms
-15x + 10x = $70 - $100
-5x = -30
x = 30/5
x = 6
Hence, anytime Pablo and Teresa buys ,6 pizzas their gift card will have the same amount of money left on them.
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Carlos find the absolute value of -5.3 and then if I the opposite of an answer. Jason find the opposite of -5.3 and then find the absolute value of his answer. Who’s final value is greater? Explain.
The person who has a greater number will be Carlos since 5.3 is more than -5.3.
How to illustrate the information?It should be noted that Carlos find the absolute value of -5.3. This will be - (-5.3) = 5.3.
On the other hand, Jason find the opposite of -5.3 and then find the absolute value of his answer. This will still be -5.4
Therefore, the person who has a greater number will be Carlos.
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whats the simplest form of b⁴ b²?
Answer:
Step-by-step explanation:
Simplify ((b^4)^4) / ((b^2)^3).First lets simplify the numerator. ((b^4)^4). The notation is b to the fourth power, to the fourth power, which is multiplying sixteen b’s. That explains why we multiple the exponents, to get b^(16) for the numerator.Similarly we simplify the denominator by multiplying the exponents for ((b^2)^3) = b^6.Putting the simplified numerator and denominator together is (b^(16))/(b^6).The six b’s in the denominator cancel six b’s in the numerator for (b^(16))/(b^6) = b^(10). Final answer b^(10).Note, another way to view (b^(16))/(b^6) = (b^(16)) * (b^(-6)) then add the exponents to have the same answer (b^(10))
simplify (3 * -8) plus (2x+5)-(4x-8)
The simplified value of the given expression is -11 - 2x.
BODMAS stands for Brackets of Division, Multiplication, Addition and Subtraction.
Here, we are given an expression as follows-
(3 * -8) + (2x+5) - (4x-8)
According to the rules of BODMAS, brackets must be solved first. Hence, we simplify the terms in brackets first as given below-
(-24) + (2x + 5) - (4x - 8)
Opening up the brackets we get-
-24 + 2x + 5 - 4x + 8
= -24 + 5 + 8 + 2x - 4x
= -24 + 13 -2x
= -11 - 2x
Thus, the simplified value of the given expression is -11 - 2x.
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Question is in the picture attached. Thank you kindly
Answer: C, B, D, A
Step-by-step explanation:
[tex]\ln(xy)=\ln x+\ln y\\\\\ln(x/y)=\ln x-\ln y\\\\\frac{\ln y}{\ln x}=\log_{x} y\\\\\ln (x^y)=y \ln x[/tex]
These are all standard logarithm rules.
Translate (in terms of x) then solve the algebraic equation: Ten is subtracted from twice some number and the result is the sum of the number and 2.
Answer:
2x-10=x+2
x = 12
Step-by-step explanation:
Let's solve your equation step-by-step.
2x−10=x+2
Step 1: Subtract x from both sides.
2x−10−x=x+2−x
x−10=2
Step 2: Add 10 to both sides.
x−10+10=2+10
x=12
2,720 divided by 20 what’s the answer
Answer:
136
Step-by-step explanation:
2720 / 20 = 136
order from least to greatest:
-4.2 -4.6 -14.4 14.7
14.7
Submit Answer
-8.1
-8.1 -7.5
The order from least to greatest is -14.4 < -4.6 < -4.2 < 14.7
Given sequence of numbers is -4.2, -4.6, -14.4, 14.7
Negative numbers:
A negative number is a number that is less than zero which is often used to represent the magnitude of a loss. It can be written from highest to lowest in magnitude.
So the given sequence can be written from least to greatest as
-14.4 < -4.6 < -4.2 < 14.7
Therefore, The order from least to greatest is -14.4 < -4.6 < -4.2 < 14.7
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Wharton, Inc., pays income taxes on capital gains (including gains on marketable securities) at a rate of 30 percent. At December 31, year 1, the company owns marketable securities that cost $180,000 but have a current market value of $220,000. b. As of December 31, year 1, what income taxes has Wharton paid on the increase in value of these investments? c. Prepare a journal entry at January 4, year 2, to record the cash sale of these investments at $220,000. d. What effect will the sale recorded in part c have on Wharton’s tax obligation for year 2?
The sale of investments at a price above cost is 102,000 units.
What are Marketable Securities?Any unrestricted financial instrument that can be bought or sold on a public stock exchange or a public bond exchange is defined as marketable security. As a result, marketable securities are either marketable equity securities or marketable debt securities. Marketable securities include stocks, bonds, preferred shares, and exchange-traded funds (ETFs). Marketable securities can also include money market instruments, futures, options, and hedge fund investments. The most important feature of marketable securities is their liquidity.To record the sale:
(Refer to the table shown below)
To document the sale of the security:
850k market price - 180k cost = 340k profit on the sale(Refer to the table shown below)
Record the income tax payable for the security gain:
Gain of 340,000 × 30% tax rate = 102,000Therefore, the sale of investments at a price above cost is 102,000 units.
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The correct question is given below:
Wharton, Inc. pays income taxes on capital gains at a rate of 30 percent. On December 31, 2015, the company owns marketable securities that cost $180,000 but have a current market value of $520,000. Record the sale of investments at a price above cost.
What is the smallest prime number that divides evenly into 45?
Answer: It's 3, because 3 is a prime number and divides evenly into 45.
Step-by-step explanation:
45 / 3 = 15
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
A binomial experiment has the given number of trials and the given success probability n=2 p=0.2
The mean of binomial experiment has the given number of trials and the given success probability n=2 p=0.2 is 0.2
Bernoulli distribution may be a distinct likelihood distribution wherever the Bernoulli variate will have solely zero or one because the outcome.p is that the likelihood of success and one - p is that the likelihood of failure.The mean of a distribution is E[X] = p and also the variance, Var[X] = p(1-p).Bernoulli distribution may be a special case of statistical distribution once just one trial is conducted.It is given that probability of success is 0.2.
According to Bernoulli distribution
Mean = probability of success
= 0.2
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The complete question is given below :
A binomial experiment has the given number of trials and the given success probability n=2 p=0.2 then find mean
What is the quotient of 6.208 x 10^9 and 9.7 x 10^4 expressed in scientific notation?
It should be noted that 6.208 x 10^9 and 9.7 x 10^4 expressed in scientific notation will be 0.64 × 10^5.
How to calculate the value?It should be noted that quotient simply means that we've to divide the numbers that are given.
This will be 6.208 x 10^9 and 9.7 x 10^4 expressed in scientific notation will be:
=(6.208 × 20^9) / (9.7 ×10^4)
= 0.64 × 10^5
The value is 0.64 × 10^5.
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the equation sin(40)=b/20can be used to determine the length of segment ac . what is the length of ac? round to the nearest tenth
If the equation [tex]sin(40)=\frac{b}{20}[/tex] can be used to determine the length of segment AC, then the length of AC is 12.85 units
Given,
The equation,
sin 40 = [tex]\frac{b}{20}[/tex]
We know,
According to trigonometric equation
sin θ= Opposite side / Hypotenuse.
Length of the segment AC = b
Then,
sin 40 = [tex]\frac{b}{20}[/tex]
b= sin 40 × 20
b= 12.85 units
Hence, if the equation [tex]sin(40)=\frac{b}{20}[/tex] can be used to determine the length of segment AC, then the length of AC is 12.85 units
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