6 sec can take penny to strike the ground.
Solution:
Given data:
[tex]H_0=288[/tex] feet
[tex]V_0=48[/tex] feet
[tex]h(t)=288+48t-16t^2[/tex]
Re-arrange the terms from greatest degree to smallest degree.
[tex]h(t)=-16t^2+48t+288[/tex]
We can solve it by applying quadratic formula,
[tex]$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here a = –16, b = 48, c = 288
[tex]$t=\frac{-48\pm \sqrt{48^2-4(-16)(288)}}{2(-16)}[/tex]
[tex]$t=\frac{-48\pm \sqrt{2304+18432}}{-32}[/tex]
[tex]$t=\frac{-48\pm \sqrt{20736}}{-32}[/tex]
[tex]$t=\frac{-48\pm144}{-32}[/tex]
Now, write find two t's using plus and minus operation.
[tex]$t=\frac{-48+144}{-32},\ \ t=\frac{-48-144}{-32}[/tex]
[tex]$t=\frac{96}{-32},\ \ t=\frac{-192}{-32}[/tex]
t = –3 (or) t = 6
We cannot write time is negative. so neglect t = –3.
Therefore t = 6.
Hence 6 sec can take penny to strike the ground.
What is the sum of 6 and g then g is added to 6
Answer:
12 + 2g ?
Step-by-step explanation:
6 + 6 = 12. g + g = 2g. So together you get 12 + 2g. I am not 100% sure.
What to decimals do you add to get 54.57
Answer:
[tex]Any\ two\ equations\ x,\ 54.57-x\\\\For\ example\ 23.37+31.20=54.57[/tex]
Step-by-step explanation:
[tex]Let\ first\ decimal=x\\\\Second\ decimal=y\\\\x+y=54.57\\\\y=54.57-x\\\\so\ any\ two\ decimal\ x\ and\ 54.57-x\ will\ give\ 54.57\\\\If\ we\ take\ first\ decimal(x)=23.37\\\\second\ decimal=54.57-23.37\\\\second\ decimal=31.20\\\\\Rightarrow 23.37+31.20=54.57[/tex]
Many of the colors in them were 'home dyed" although commercial dyes were unknown.
Read the passage. Look at the underlined section marked number 5. There may be a mistake in the way the sentence is written. If you
find a mistake, choose the answer that corrects the mistake. If there is no mistake, choose 'Correct as is.'
es )))
Correct as is
Many of the colors in them were 'home dyed, as commercial dyes were
unknown
Many of the colors in them were 'home dyed if commercial dyes were
unknown
Many of the colors in them were 'home dyed' whereas commercial dyes
were unknown
Answer:
b
Step-by-step explanation: i just know
Answer:
bb
Step-by-step explanation:
Many of the colors in them were "home dyed," as commercial dyes were unknown is the correct answer because "As" correctly begins the subordinate clause and shows the relationship to the main clause
Is y= -3x + 10 a linear function
Answer: yes
Step-by-step explanation:Can you brainless me
- What is the range of the following set of points: {(3, 4), (7, - 2), (11, – 8)}?
A {3, 7, 11}
B {-8, - 2, 3, 4, 7, 11}
c {-8, -2, 4}
Answer:
B) {-8,-2,3,4,7,11}
Step-by-step explanation:
range is y
Final answer:
The range of the set of points {(3, 4), (7, -2), (11, – 8)} is the set of their y-values, which are -8, -2, and 4. So the range is {-8, -2, 4}.
Explanation:
The range of a set of points in mathematics refers to the difference between the highest and lowest y-values (also known as the vertical coordinate) in the set. Looking at the provided set of points {(3, 4), (7, -2), (11, – 8)}, we identify the y-values as 4, -2, and -8. To find the range, we look for the highest and lowest y-values. The highest y-value among these points is 4, and the lowest is -8.
The range consists of all the y-values which the function or set of points may take. Consequently, within this set of points, the range encompasses all values from -8 up to 4. Therefore, the correct answer listing those y-values is Option C: {-8, -2, 4}
Archimedes went to sleep beside a big rock. He wanted to get up at 777 AM, but the alarm clock was yet to be invented! He decided to sleep at the spot where the rock's shadow should end when it's 777 AM so as to be awakened by the direct sunlight.
Archimedes knew that at 777 AM, the sunlight reaches the ground at an angle of 31^\circ31
∘
31, degrees. The rock beside which he slept was 555 meters tall.
How far from the rock did Archimedes go to sleep?
By using the tangent function tan(31°) = opposite/adjacent, and knowing the rock's height of 555 meters, we can find the distance from the rock that Archimedes should sleep to wake up with direct sunlight. The distance is calculated as the height of the rock divided by the tangent of the angle of the sun, which will give the desired result.
Explanation:To find out how far from the rock Archimedes went to sleep, we can use the concept of trigonometry. Specifically, we will use the tangent function, which relates the angle of the sun to the height of the rock and the distance of the shadow on the ground.
Given that the sunshine angle is 31 degrees and the rock is 555 meters tall, we can set up our equation using the tangent function: tan(31°) = opposite/adjacent, where the opposite side is the height of the rock, and the adjacent side is the distance from the rock where Archimedes slept.
The equation would look like this:
tan(31°) = 555 / distance
To solve for the distance, we rearrange the equation:
distance = 555 / tan(31°)
By calculating this, we would get the distance where Archimedes should sleep to be woken by the direct sunlight.
.There are 850 Douglas fir and Ponderosa pine trees in a section of forest bought by Karamazov Logging Co. The company paid an average of $300 for each Douglas fir and $225 for each Ponderosa pine. If the company paid $217,500 for the trees, how many of each kind did the company buy
The number of Douglas fir pine trees is 350, and the number of Ponderosa pine trees is 500
Applications of Simultaneous equationFrom the question, we are to determine the number of each kind of pine trees.
Let x represent Douglas fir pine trees
and y represent Ponderosa pine trees
From the first statement - There are 850 Douglas fir and Ponderosa pine trees
We can write that
x + y = 850 ------------- (1)
Also,
The company paid an average of $300 for each Douglas fir and $225 for each Ponderosa pine; and the company paid $217,500 for the trees.
From this statement, we can write that
300x + 225y = 217500 ---------------- (2)
Now, we will solve the equations simultaneously
From equation (1)
x + y = 850
Then,
x = 850 - y ------------ (3)
Substitute this into equation (2)
300x + 225y = 217500
300(850-y) + 225y = 217500
255000 -300y + 225y = 217500
255000 - 75y = 217500
255000 - 217500 = 75y
37500 = 75y
∴ y = 37500/75
y = 500
Substitute the value of y into equation (3)
x = 850 - y
x = 850 - 500
x = 350
∴ x = 350 and y = 500
Hence, the number of Douglas fir pine trees is 350, and the number of Ponderosa pine trees is 500
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[x^(-2)]^2 how do you simplify
Answer:
[tex](x^2)^2=x^4[/tex]
Step-by-step explanation:
Because of the power of a power property states that [tex]((x^n)^m)=x^{n\times{m}}[/tex], where n and m are real numbers, then, the expression you have just posted can be simplified by applying this property to [tex](x^2)^2=x^{2\times2}=x^4[/tex].
What is the value of 1/6^0?
1/6
0
1
undefined
Answer:
1
Step-by-step explanation:
Simplify the following:
(1/6)^0
Hint: | Any nonzero number to the zero power is one.
(1/6)^0 = 1:
Answer: 1
factor the expression below x^2-16x+64
Answer:
(x - 8)^2
Step-by-step explanation:
Factor the following:
x^2 - 16 x + 64
The factors of 64 that sum to -16 are -8 and -8. So, x^2 - 16 x + 64 = (x - 8) (x - 8):
(x - 8) (x - 8)
(x - 8) (x - 8) = (x - 8)^2:
Answer: (x - 8)^2
Allen and Beverly thought of the same number. Allen doubled the number and added 15 to the result. He got 51. Beverly performed the same operations with the number, but in reverse order. What did she get?
Allen and Beverly both thought of the number 18. When Allen doubled the number and added 15, he got 51. Beverly, in reverse order, subtracted 15 from the number and then doubled it to get 6.
Let the number that Allen and Beverly thought of be represented by 'x'.
Allen doubled the number and added 15 to the result, which gives us the equation:2x + 15 = 51
Now, we need to solve for 'x' to find the original number.
Subtract 15 from both sides of the equation: 2x = 51 - 15
2x = 36
Now, divide both sides by 2 to isolate 'x': x = 36 / 2
x = 18
So, Allen and Beverly both thought of the number 18.
Now, Beverly performs the same operations but in reverse order: 1. She starts with the number 18.
2. She subtracts 15 from it:18 - 15 = 3
3. Then, she doubles the result:2 * 3 = 6
So, Beverly gets the result of 6 by performing the same operations in reverse order.
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12 one half times one nine
Answer:
[tex]1\frac{7}{18}[/tex] or one seven eighteenths
Step-by-step explanation:
we know that
12 one half times one nine is the same that multiply 12 one half by one nine
so
[tex](12\frac{1}{2})(\frac{1}{9})[/tex]
Convert mixed number to an improper fraction
[tex]12\frac{1}{2}=12+\frac{1}{2}=\frac{12*2+1}{2}=\frac{25}{2}[/tex]
substitute
[tex](\frac{25}{2})(\frac{1}{9})=\frac{25}{18}[/tex]
Convert to mixed number
[tex]\frac{25}{18}=\frac{18}{18}+\frac{7}{18}=1\frac{7}{18}[/tex]
therefore
12 one half times one nine is one seven eighteenths
Which of the following is equivalent to 4x – 3y = -6?
Answer:
Hello, Subtract 4x 4 x from both sides of the equation. Divide each term by 3 3 and simplify. Divide each term in 3y=−4x+15 3 y = - 4 x + 15 by 3 3 . Use the slope-intercept form to find the slope and y-intercept.
Hope This Helps!
If f(x) = 10^x then what is the value of f(5)?
Answer:
100000
Step-by-step explanation:
f(5)=10^5
f(5)=100000
Answer:
100,000
Step-by-step explanation:
what is cos 0 if sec 0=2?
Step-by-step explanation:
[tex] \because \: \cos \theta = \frac{1}{\sec \theta} \\ \\ \therefore \: \cos \theta = \frac{1}{2} \\ \\ \therefore \: \cos \theta = \cos 60 \degree \\ \\ \huge \red{ \boxed{\therefore \: \theta = 60 \degree}}[/tex]
Answer:1/2
Step-by-step explanation:Plato
tina is a waitress that makes $10.40, but an average 8 hour shift for her brings in an additional $85 in tips. how much does tina make per hour as a waitress
Answer:
Tina makes per hours [tex]=\$11.925[/tex]
Step-by-step explanation:
Tina makes [tex]8[/tex] hours [tex]=\$10.40[/tex]
and additional tips [tex]=\$85[/tex]
total amount makes for [tex]8[/tex] hours [tex]= \$10.40+\$85[/tex]
total amount makes for [tex]8[/tex] hours [tex]=\$95.40[/tex]
total amount makes for [tex]1[/tex] hours [tex]=\frac{total\ amount}{total\ time}\\\\=\frac{\$95.40}{8}\\\\=\$11.925[/tex]
If there is a 60% chance of rain tomorrow and a 40% chance of wind and rain,
what is the probability that it is windy, given that it is rainy? Round your
answer to the nearest percent.
O A. 78%
O B. 71%
OC. 67%
O D. 33%
Answer:
67%
Step-by-step explanation:
we are given the probability of rain tomorrow of 60 % and a 40% chance of wind and rain. we are asked for the probability that it is windy, given that it is rainy. The formula that should be used is the quotient of the probability with "and" over the probability of the rain only. Hence, P[W U R ] / P [R] = 0.4 / 0.6 = 2/3 = 67%
:Answer: 67%
Step-by-step explanation:
APEX
There are 8 soccer matches per day at Greenville's annual soccer tournament, which lasts 17 days. Estimate the number of soccer matches during the tournament by rounding the larger number to the nearest ten.
The estimation of the total number of soccer matches in Greenville's annual tournament, with 8 matches each day for around 20 days, is approximately 160 matches.
Explanation:The student is asking for an estimation of the total number of soccer matches in Greenville's annual tournament. There are 8 matches each day, and the tournament runs for 17 days. The part of the question that asks you to round to the nearest ten refers to the 17 days, as this is the larger number. Rounding 17 days to the nearest ten would give us 20 days. Therefore, to estimate:multiply the rounded number of days (20) by the number of matches per day (8), yielding an estimate of 160 soccer matches during the tournament.
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Final answer:
The estimated number of soccer matches during Greenville's annual soccer tournament is 160 matches, calculated by rounding 17 days to 20 and multiplying by 8 matches per day.
Explanation:
To estimate the number of soccer matches during Greenville's annual soccer tournament, we round the larger number (17 days) to the nearest ten. Since 17 is closer to 20 than it is to 10, we round up to 20 days for our estimation. With 8 soccer matches per day, we then calculate the estimated number of matches as 8 matches/day × 20 days.
8 matches/day × 20 days = 160 matches
Therefore, an estimated 160 soccer matches will be played during the tournament.
-20-3x + 4) + 3x – 3 = -29
Answer:
look at the picture shown
WILL MARK BRAINLIEST!!!
What is the value of k?
A. −5
B. −3
C. 3
D. 5
Answer:
B. -3.
Step-by-step explanation:
If we take a look at the point (0, 1) in f(x), and compare it to the point (5, -2) in g(x), we can see that the point is simply moved to the right (translated horizontally) and moved down (translated vertically). Since k represents the vertical translation, the value must be -3.
1 -> -2
k = -3.
Answer:
B. -3
Step-by-step explanation:
Because I did the unit test
40 POINTS !!!A poll shows that 70% of teenagers in the United States use social media. A random sample of 30 teenagers showed that 90% of them use social media. A number generator was used to simulate 30 samples from a population in which 70% of teenagers use social media. The results are shown in the dot plot.
WHAT IS THE CHANCE OF GETTING A SAMPLE PROPORTION OF 90% OR GREATER
Answer:
0.20
Step-by-step explanation:
0.20
How to simplify (5+4)x2+4
AnsWER: 22
Step-by-step explanation: (5+4)X 2+4
9X2+4
18+4
22
what is the equation for 10x + 35
Answer:
5(2x + 7)
Step-by-step explanation:
8 1/5 + (4 2/5 + 3 3/10
Answer:
15 and 9/10 or 15.9
Step-by-step explanation:
4_2/5 + 3_3/10 = 4_4/10 + 3_3/10 = 7_7/10
8_1/5 = 8_2/10
8_2/10 + 7_7/10 = 15 9/10
or 15.9
Answer:15 and 9 10ths
Step-by-step explanation:
Find the value for the following determinant.
2
10
-2
Answer:
10
Step-by-step explanation:
1*4 -(3*(-2))=4-(-6)=4+6=10
5x + 2y = 8
x
+y=4
If you want to solve the system of equations by addition, which of the following could you do?
Multiply the second equation by 5 and add.
Multiply the second equation by 2 and add.
Multiply the second equation by -2 and add.
NEXTOUESTION
ASK FOR HEID
Answer:
you multiply the second equation by -2.
Step-by-step explanation:
to get rid of y and find x. Then you plug x into one of the equations to find y
A ladder on a fire truck has its base 8 ft. above the ground. The maximum length of the ladder is 100 feet. If the greatest acute angle the ladder can make with the ground is 70°, what is the highest it can reach?
Answer:
78 degrees
Step-by-step explanation:
It’s already above the grown by 8 feet 100 feet in the air but can only go 70
Dave works 5 hours at double time. He earns $98.00. Find his normal hourly rate?
Answer:
You just divide the numbers to get the hourly pay.
98÷5÷2
$9.80/hr
what is the slope of y=-5x-1
Answer:
5
Step-by-step explanation:
~Hope this helps!
Krystal~~
Let Y represent Jaron’s age in years. If Dawn were 5 years older, she would be Jaron’s age. Which expression represents Dawn’s age?
Answer:5-y=a
Step-by-step explanation: