Answer:
-5n + 2
Step-by-step explanation:
distribute 2 into (1 - 4n)
3n + 2 - 8n = -5n + 2
A carnival attraction tests your strength by how far in the air you can drive a weight with a hammer. If the weight reaches 15 feet, you win a prize. The equation h = -16t 2+ 31t + 2 gives the height, in feet, and time, in seconds of the weight after it is hit.
a. How long is the weight in the air?
b. What was the weight’s maximum height?
c. Did you win a prize? Why or why not?
Answer:
a. 2 secondsb. ~17 feetc. yesStep-by-step explanation:
Given function:
h(t) = -16t² + 31t + 2a.h(t) = 0 will give us the y-intercept of the graph. The greater value of t is the time the weight in the air
-16t² + 31t + 2 = 016t² - 31t - 2 = 0t = [31 + √(31²+4*16*2)]/32t = (31 + 33)/32t = 2 secondsb.Maximum height is reached at vertex.
The x coordinate of the vertex is determined as x = -b/(2a), considering the standard form of a quadratic function f(x) = ax² + bx + c
t = -31/(-16*2) = 31/32 = 0.96875h(0.96875) = -16(0.96875)² + 31*0.96875 + 2 = 17.015625 ftc.You win the prize as the maximum height is greater than 15 feetA game show is offering a prize of 1 cent on the first day , 3 cents on the second day 9 cents on the third day , etc. What is the total amount of money earned from this prize in two weeks ?
Answer:
$15943.23
Step-by-step explanation:
each day the total of the day before is multiplied by 3 so if you do that for 14 days you will get the answer
Answer:
2,391,4.84 dollars
Step-by-step explanation:
1, 3 , 9...
on the 1st day, 3^0
on the 2nd day, 3^1
on the 3rd day, 3²
:
one the 14th day, 3^(14-1)
=> 3^13
=> 1,594,323
"Total about of money" => have to add up the money from the 1st day to the 14th day:
1 + 3 + 9 + 27 + 81 + 243 + 729 + 2187 + 6561 + 19683 + 59049 + 177147 + 531441 + 1594323 = 2,391,484
Can anyone explain this question to me? My teacher solved it but I didn’t understand how she did it
Step-by-step explanation:
To find the space a figure takes, we need to find the volume. Volume of a rectangular prism can be found by multiplying the length, width, and height of the figure.
We can start with the green block. The dimensions of this figure are 6cm, 3cm, and 3cm. The 5cm at the bottom is not a dimension of the green figure. Instead, it shows the total width of both blocks. We will use this later.
Back to the first block, we will find its volume by multiplying its dimensions together.
3 · 3 · 6 = 54
So, the volume of the first block is 54 cm³.
To this, we will add the volume of the blue block. We can find its dimensions with some simple deduction.
The picture shows that the height of the figure is 4cm less than the height of the green one, 6cm.
6 - 4 = 2
The height, then, is 2cm.
The width can be found by subtracting the width of the green block from the total width of both figures, 5cm.
5 - 3 = 2
So, the width is also 2cm.
We can see that the length of the blue block is equal to that of the green one, so we know that the length is 3cm.
Now, multiply all the dimensions we have found together.
2 · 2 · 3 = 12
The volume of the blue block is 12cm³.
We have found the volumes of both figures, so now we can add them both together to find the total.
54 + 12 = 66
So, the total volume is 66cm³.
I hope this was a satisfactory explanation ^^ Good luck, mate
A college graduate is considering two different companies to apply to for a job. Acme Corp lists this sample of salaries on their website:
$45,000
$55,000
$140,000
$70,000
$60,000
$50,000
What typical salary would Summit Systems need to have to be meaningfully different from Acme Corp? Justify your reasoning using concrete details and domain specific vocabulary.
PLZ PLZ HELPP!!!!!
Please help me with this , I’m in desperate need of help.
Answer:
It will measure 30°. I hope it helps you
Which of the following graphs is the graph of a linear function?
Answer:
C
Step-by-step explanation:
A and B are not straight lines, so they are not linear functions.
C and D are straight lines, so they are linear. However, D fails the vertical line test, so it is not a function.
C and D are straight lines, they are linear. Then the linear graphs are represented by options C and D.
What is a graph?
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
A linear equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
A and B are not straight lines, they are not linear functions. Therefore,
C and D are straight lines, they are linear. Then the linear graphs are represented by options C and D.
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SohCahToa PLEASE HELP!!!
I don’t understand this
Answer:
57.99 °
Step-by-step explanation:
[tex]tan( x ) = \frac{16}{10} \\ x = arctan( \frac{16}{10} ) \\ x = 57.99 \: degrees[/tex]
Answer:
3) 57.99°
Step-by-step explanation:
16 is opposite of x° and 10 is adjacent to x°. Therefore, you use tangent because of SOHCAHTOA.
tan(x°)=opposite/adjacent
tan(x°)=16/10
tan⁻¹(tan(x°))=tan⁻¹(16/10)
x°=57.99461679°=58°
So the closest choice is 3) 57.99°
Olivia will deposit $1,530 in an account that earns 6% simple interest every year. Her sister
Melinda will deposit $1,500 in an account that earns 8% interest compounded annually. The
deposits will be made on the same day, and no additional money will be deposited or
withdrawn from the accounts. Which statement about the balances of Olivia's account and
Melinda's account at the end of 3 years is true?
A Olivia's account will have about $5.40 more than Melinda's account.
B Olivia's account will have about $84.17 more than Melinda's account.
C Melinda's account will have about $5.40 more than Olivia's account.
D Melinda's account will have about $84.17 more than Olivia's account.
D. Melinda's account will have about $84.17 more than Olivia's account.
Answer:
Olivia 275.4 and Melinda 360
Step-by-step explanation:
Olivia 1,530 x .06 = 91.8
91.8 x 3 = 275.4
Melinda 1,500 x .08 = 120
120 x 3 = 360
plz mark brainleist
what is 5 cm in mm. i need a simple answer. NO LINKS
50 millimeters
keystrokes
Someone answer this Please
Answer:
15 miles
Step-by-step explanation:
The Pythagorean theorem states that [tex]a^2+b^2=c^2[/tex] where a and b are the two legs (the sides of the triangle that are adjacent to the right angle) and c is the hypotenuse (the longest side). This only applies to right triangles.
Plug 12 mi and 9 mi into [tex]a^2+b^2=c^2[/tex] as a and b.
[tex]a^2+b^2=c^2\\12^2+9^2=c^2\\144+81=c^2\\225=c^2[/tex]
Take the square root of both sides
[tex]15=c[/tex]
Therefore, the length of the hypotenuse is 15 miles.
I hope this helps!
Birth control pills have a theoretical annual efficacy of 99.5%, but a real-worls efficacy of only 95%. If a college student takes the pill for the four years she is in college, what is the probability that she will become pregnant at least once using the real world efficacy rate?
A. 0
B. 0.005
C. 0.020
D. 0.185
Answer: In my opinion B. 0.005 is the correct answer
Step-by-step explanation:
hope it help youAnyone know the answer to this question?
For the plane curve defined by x = 7 cos t, y = 5 cos t, for t in [0, 2π] the ordered pair that corresponds to t = π/6 is ___
Answer:
The ordered pair is: [tex](\frac{7\sqrt{3}}{2},\frac{5\sqrt{3}}{2})[/tex]
Step-by-step explanation:
We are given the following plane curve:
[tex]x = 7 \cos{t}[/tex]
[tex]y = 5 \cos{t}[/tex]
Ordered pair for a value of t:
We find (x,y) for these values of t. So, when [tex]t = \frac{\pi}{6}[/tex]
[tex]x = 7 \cos{\frac{\pi}{6}} = 7\frac{\sqrt{3}}{2} = \frac{7\sqrt{3}}{2}[/tex]
[tex]y = 5 \cos{\frac{\pi}{6}} = 5\frac{\sqrt{3}}{2} = \frac{5\sqrt{3}}{2}[/tex]
The ordered pair is: [tex](\frac{7\sqrt{3}}{2},\frac{5\sqrt{3}}{2})[/tex]
The sum of ten and the quotient of a number x and 6 please help !
Answer:
10 + x/6
Step-by-step explanation:
10 + x/6 represents this phrase
pls help with this question
Answer:
We aren't going to do all your homework for you. That's why no one is answering. If you have one specific question, I can help
Step-by-step explanation:
. No one is going to do this whole assignment/homework.
rewarding 20 points pls help.
Which ordered pair is a solution of y = x+4
A.(0,0)
B.(5,54)
C.(7,28)
D.(9,13)
Use the cumulative normal distribution table to find the z-scores thqt bound the middle of 68% of theje area under the stanrard normal curve
Answer:
Z scores between -0.995 and 0.995 bound the middle 68% of the area under the stanrard normal curve
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Middle 68%
Between the 50 - (68/2) = 16th percentile and the 50 + (68/2) = 84th percentile.
16th percentile:
X when Z has a pvalue of 0.16. So X when Z = -0.995
84th percentile:
X when Z has a pvalue of 0.84. So X when Z = 0.995.
Z scores between -0.995 and 0.995 bound the middle 68% of the area under the stanrard normal curve
A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for pi , and round your answer to the nearest hundredth.
I need help like NOW pronto im confused HELP
ABC - DEF. what sequence of transformations will move ABC onto DEF
Answer:
A) A dilation by a scale factor of 2, centered at the origin, followed by a 180° clockwise rotation about the origin.
Step-by-step explanation:
a dilation by a scale factor of 2, centered at the origin will double its size and move point A from (-2,2) to (-4,4). Then the clockwise rotation of 180° degrees will rotate the figure so that it's point A (now called point D) will be at (4,-4).
Answer:
a pex
Step-by-step explanation:
What quadrilateral can be drawn that has exactly two pairs of perpendicular sides?
chris and Michelle are professional divers. During one of their dives, Chris goes 40 meters below the surface of the water, and Michelle dives 13 meters below Chris. What is Michelle’s position in meters?
Answer:
Michelle's position below the surface of water = 53 meter below water level
Step-by-step explanation:
Given:
Chris position in water = 40 meters below the surface of water
Michelle drive more than 13 meter below from Chris
Find:
Michelle's position below the surface of water
Computation:
Michelle's position below the surface of water = Chris position in water + Extra dive then Chris
Michelle's position below the surface of water = 40 meter + 13 meter
Michelle's position below the surface of water = 53 meter below water level
PLEASE HELP !! ILL GIVE BRAINLIEST !!
What is the area of the triangle. Side a=24cm b=30cm h=18cm
Answer:
a=270cm^2
Step-by-step explanation:
a= HbB/2
18×30/2
270cm^2
Answer:
Area =(H×B)÷2
=(18x30)÷2
=54O ÷2
=27O
The range of the numbers 34 32 12 65 and 45 is
Answer:
53
Step-by-step explanation:
Range is found by subtracting the largest number in a set by the smallest number.
Set: {12, 32, 34, 45, 65}
Largest number: 65
Smallest number: 12
65 - 12 = 53
hope this helps and is right :)
Use the graph to write a linear function that relates y to x
y=
What is the value of the function f(x)= 1/4 x-3 when x=12
Answer:
0
Step-by-step explanation:
f(x)=1/4x-3
f(12)=(1/4 times 12) -3
f(12)=(3)-3
0
What is the solution to the linear equation?
2/3x-1/2=1/3+5/6x
Answer:
x = -5
Step-by-step explanation:
2/3x - 1/2 = 1/3 + 5/6x
add 1/2 to each side of the equation:
2/3x = 5/6 + 5/6x
subtract 2/3x from both sides:
0 = 5/6 + 1/6x
subtract 5/6 from both sides:
1/6x = - 5/6
multiply both sides by 6:
x = -5
What does it mean to do something 4.5 times?
Answer:
This is a standard notation used by many computer programs including Excel. Entering a value in this form is not the same as entering the logarithm of a number. This is simply a shortcut way to enter very large values, or tiny fractions, without using logarithms.
Step-by-step explanation:
f(x) = 5x^2 + 9x – 4
g(x) = – 8x^2 – 3x – 4
Find (f + g)(x).
Answer:
(f + g)(x) = – 3x^2 + 5x - 8
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
= 5x^2 + 9x – 4 + (– 8x^2 – 3x – 4)
= 5x^2 + 9x – 4 – 8x^2 – 3x – 4
Combine
= – 3x^2 + 5x - 8
The sum of the given functions is defined as the expression (f + g)(x) which is equal to -3x² + 6x – 8.
Use the concept of quadratic function defined as:
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:
ax² + bx + c = 0
The given functions are:
f(x) = 5x² + 9x – 4
g(x) = – 8x² – 3x – 4
Since (f + g)(x) = f(x) + g(x)
Then put the functions,
(f + g)(x) = (5x² + 9x – 4) + ( – 8x² – 3x – 4)
Rearranging like terms,
(f + g)(x) = 5x²– 8x² + 9x – 3x – 4 – 4
Simplifying it,
(f + g)(x) = -3x² + 6x – 8
Hence,
The expression for (f + g)(x) is -3x² + 6x – 8.
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Select the correct answer.
Two friends are sitting on a seesaw at the park. The height, h(t), of the left seat, in inches above the ground, is modeled by a sine function. Let
trepresent the time, in seconds, since the friends started seesawing.
t
0
1
2.
3
4
5
6
ht)
24
48
24
0
24
48
24
If the friends start seesawing with the plank in a level position, how long does it take for the friend in the left seat to move upward, downward,
and then back to the initial position?
Answer:
Correct Answer 4 Secs
Step-by-step explanation:
#Platolivesmatter
Hope this helped :)
The time it takes for the friend in the left seat to move upward, downward, and then back to the initial position is 4 seconds.
What is a function?A relation is a function if it has only One y-value for each x-value.
Two friends are sitting on a seesaw at the park.
The height, h(t), of the left seat, in inches above the ground, is modeled by a sine function.
Let t represent the time, in seconds, since the friends started seesawing.
t 0 1 2 3 4 5 6
h(t) 24 48 24 0 24 48 24
The friends start see sawing with the plank in a level position.
The initial position at 0 of them is at 24.
The group has to come back to this position after moving upward and downward.
The time it takes to reach upward is,
f(48)=1
The time it takes to reach downward after going upward is,
f(0)=3
Coming back to initial potion,
f(24)=4
Hence, the time it takes for the friend in the left seat to move upward, downward, and then back to the initial position is 4 seconds.
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