Answers
Given:
The function is
[tex]h=3+25t-5t^2[/tex]
To find:
The values of t where h is 8 meters.
Solution:
We have,
[tex]h=3+25t-5t^2[/tex]
Putting h=8, we get
[tex]8=3+25t-5t^2[/tex]
[tex]0=3+25t-5t^2-8[/tex]
[tex]0=-5+25t-5t^2[/tex]
[tex]0=-5(1-5t+t^2)[/tex]
Dividing both sides by -5 and interchanging the sides, we get
[tex]1-5t+t^2=0[/tex]
[tex]t^2-5t+1=0[/tex]
Here, [tex]a=1,b=-5,c=1[/tex].
Using quadratic formula, we get
[tex]t=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]t=\dfrac{-(-5)\pm \sqrt{(-5)^2-4(1)(1)}}{2(1)}[/tex]
[tex]t=\dfrac{5\pm \sqrt{25-4}}{2}[/tex]
[tex]t=\dfrac{5\pm \sqrt{21}}{2}[/tex]
It can be written as
[tex]t=\dfrac{5-\sqrt{21}}{2}[/tex] and [tex]t=\dfrac{5+\sqrt{21}}{2}[/tex]
[tex]t=0.20871215[/tex] and [tex]t=4.7912878[/tex]
[tex]t\approx 0.21[/tex] and [tex]t\approx 4.79[/tex]
Therefore, the required values of t are 0.21 and 4.79.
Related Questions
Help pls for brainlest and extra points i need done soon
Answers
Answer:
5/6= 10/12
12/100<10/12
6. What percentage of the children in class 5 is a member of a sports club? 3
Result sports questionnaire
for: class 5
“Are you a member of a
sports club?
yes: 15
no:5”
Answers
Answer:
75%
Step-by-step explanation:
Let x be the percentage for sports club members.
x% of 20 = 15
x/100 x 20 = 15
x/5 = 15
x = 75
3y (3x - 1) - ( 3x - 1) tama "termino común"
Answers
Answer:
9xy-3x-3y+1
Step-by-step explanation:
3y(3x-1)-1(3x-1)
PLEASE HELP I AM ABOUT TO FAILL
Suppose that a plano cost 5,000 and loses 20% of its value oach year. table shows the value, of a piano after years.
1. 5000
2. 4000
3. 3200
write an equation that can be used to find the value of the piano, v, after t years.
Answers
Answer:
Step-by-step explanation:
90
Based on the information, the value of the piano after 16 years is $140.74.
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
Using this formula to find the value of the piano, v, after t years.
CP = Principal(1-rate)[tex]^t[/tex]
Where:
Principal=$5,000
Rate=20%
Number of year = 16 years
Let plug in the formula;
=5,000(1-0.20)^16
=5,000(.80)^16
=$140.737
= $140.74 (Approximately)
Hence, the value of the piano after 16 years is; $140.74.
Learn more about interest here;
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(-1)^2 × (-1)^3 × (-1)^5
Answers
Answer:
1
Step-by-step explanation:
(-1)^2 = 1
(-1)^3 = -1
(-1)^5 = -1
(1) (-1) (-1) = 1
Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is 37%. If they have six children, what is the probability that at most one of their six children will have that trait? Round your answer to the nearest thousandth.
Answers
Answer:
Yes
Step-by-step explanation:
Answer:
Sum: 0.78619≈0.786
Step-by-step explanation:
n=4
r=1, 2, 3, 4
r=1,2,3,4
"At least" counts up.
p=32\%=0.32
p=32%=0.32
q=1-0.32=0.68
q=1−0.32=0.68
The chance a success does NOT occur.
_{n}C_{r}p^rq^{n-r}
The probability that at most one of their six children will have that trait is 0.68
How to determine the probability?From the question, the given parameters are
Number of children, n = 6
Probability of a child with the trait, p = 37%
The required probability that at most one will have that trait is represented as P(x ≤ 1)
This probability is calculated ;
P(x ≤ 1) = P(0) + P(1)
Where
P(x) = ⁿCₓ * pˣ (1 - p)ⁿ⁻ˣ
So, we have
P(x ≤ 1) = ⁷C₀ (37%)⁰ (1 - 37%)⁷⁻⁰ + ⁷C₁ (37%)¹ (1 - 37%)⁷⁻¹
Evaluate;
P(x ≤ 1) = ⁷C₀ * 1 * (63%)⁷ + ⁷C₁ * (37%) * (63%)⁶
So, we have;
P(x ≤ 1) = 1-0.32= 0.68
Hence, the probability is 0.68
Read more about probability at
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In a recent survey of 700 people, 15% said that red was their favorite color. How many people said that red was their favorite color?
Answers
Answer:
Answer: 105
Step-by-step explanation:
In a recent survey of 700 people, 15% said that red was their favorite colour. 105 people said read was their favorite colour.
Answer:
105
Step-by-step explanation:
I need help with this plz
Answers
Answer: B
Step-by-step explanation:
.Mr. Morrison can do 120 jumping jacks in two minutes. Write an equation to represent how many jumping jacks Mr. Morrison can do in 5 minutes.
Answers
Use special right triangle find the exact value of x.
X=?
Answers
Answer: 12
Step-by-step explanation:
What is another way of writing 5(6+3) using to distribute property
Answers
Answer:
The multiplication of 5(6) and 5(3) will each be done before you add.
5(6) + 5(3) = 30 + 15 = 45. Note that the answer is the same as before.
Step-by-step explanation:
hope this helps...
have a nice weekend ヽ(ヅ)ノ
oh and if i was supposed to follow something sorry cuz i can't see the pic...
Kamogelo walks 1.25 km in 25 minutes and Masego walks 1.44 km in 30 minutes. If these are
their travelling times and distance to school then, who walks faster.
Answers
Answer:
Kamogelo walks Faster
Step-by-step explanation:
1.25 km is less distant and in twenty five minutes it is fast enough.
Jenny used the expression –16x2 + 38x + 5 to determine the height of an object x seconds after it was hit into the air. How long does it take the object to hit the ground?
Answers
Answer:
0<x<2.5
Step-by-step explanation:
-16x^2+38x+5 = 0
-16x^2+40x-2x+5 = 0
ROUGH WORK
[Product=-16×5=-80, Sum=38. (Product=40×-2, Sum=40-2) (40&-2)]
BACK TO EXPLAINATION
-8x(2x-5)-1(2x-5) = 0
x = -1/8, 2.5
0<x<2.5
Aaron saw it was 86° Fahrenheit, F, in Australia in January. Aaron used the formula C=5/9(F−32) to find the temperature in degrees Celsius, C. What temperature, in degrees Celsius, did Aaron find?
Answers
Answer:
[tex]30^{\circ}\text{C}[/tex]
Step-by-step explanation:
The temperature that Aaron saw was [tex]86^{\circ}\text{F}[/tex]
The formula to convert Fahrenheit to Celsius is
[tex]C=\dfrac{5]{9}(F-32)[/tex]
[tex]\Rightarrow C=\dfrac{5}{9}\times (86-32)[/tex]
[tex]\Rightarrow C=30^{\circ}\text{C}[/tex]
The given temperature in Celsius that Aaron found would be [tex]30^{\circ}\text{C}[/tex].
2. Find the missing side length.
Round answers to the nearest tenth.
13
29°
Х
Answers
Answer:
50
Step-by-step explanation:
Since it's a right angle, it's automadically 90 degrees. Add 29 + 13 which gives you 42. 90 - 42 gives you 48. Rounded to the nearest 10th is 50. Here's what I explained in numerical form:
29 + 13 = 42
90 - 42 = 48
Five or more raise the score. For or less turn to zero:
48
8 is larger than 5 so you add "plus 1" to the next number:
50
The relationship between income (I), in dollars, and the time (h), in hours, for 2 different jobs is represented. Compare the hourly rates of Job A and Job B.
Answers
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete. However, I will solve using the following assumptions.
Job A:
[tex]y = 2x + 5[/tex]
Job B
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} \ \\ y & {6} & {10} & {14} & {18} & {22} \ \end{array}[/tex]
The first step is to calculate the rate of Job B using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex](x_1,y_1) = (1,6)[/tex]
[tex](x_2,y_2) = (2,10)[/tex]
So, we have:
[tex]m = \frac{10 - 6}{2 - 1}[/tex]
[tex]m = \frac{4}{1}[/tex]
[tex]m = 4[/tex]
So, the hourly rate of job B is $4/hr
For Job A:
[tex]y = 2x + 5[/tex]
A linear equation has the form:
[tex]y = mx + b[/tex]
Where m is the rate
By comparison:
[tex]m = 2[/tex]
So, the hourly rate of Job A is $2/hr
Comparing both rates, we can draw the following conclusions;
The hourly rate of Job A is greater than the hourly rate of Job BThe hourly rate of Job A is twice the hourly rate of Job B.a polygon has perimeter 15 units.it is dilated with a scale factor of 3/5.what is the perimeter of its image
Answers
Given what we know, we can confirm that the perimeter of the image is 9 units.
Perimeter and Scale factor.To calculate the perimeter of a shape, we must add the length of all of its sides. When we dilate a shape, we multiply each of its sides by our scale factor.Our scale factor is [tex]\frac{3}{5}[/tex], which corresponds to 0.6 in decimal form Taking the sum of 15 as the perimeter of the preimage and multiplying by 0.6 gives us the perimeter of the image which is 9 units.Therefore, given that [tex]15units * \frac{3}{5} = 9 units[/tex], we can confirm that the perimeter of the image is 9 units.
To learn more about Scale factors visit:
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There are two mystery numbers. The sum of 2 times the first number and 5 times the second number is -5. The sum of 3 times the first number and 10 times the second number is -5. What are the two numbers?
Answers
Answer:
the two numbers are -5 and 1
Step-by-step explanation:
Let x and y be the first number and second number respectively.
According to the question, we can find 2 equations:
2x + 5y = -5
3x + 10y = -5
On solving,
x = -5
y = 1
Answer:
X=-5,Y=1
Step-by-step explanation:
First equation: 2X+5Y=-5
Second equation:3X+10Y=-5
If we subtract the first from the second equation
(3X+10Y)-(2X+5Y)= 0 so, X+5Y= 0
So X= -5Y .then substitute in the second equation
So ,3(-5Y)+10Y= -5 , therefore -15Y + 10Y=-5 so, -5Y=-5 which means that Y=1
Then substitute with that in the first equation so 2X+5= -5
2X= -10 therefore X=-5
I need help on this right now please help ASAP!!!
Answers
Answer:
C would be your answer
Step-by-step explanation:
X to the fourth power minus Y to the fourth power
Answers
Answer:
[tex](x - y) \times (x + y)( {x }^{2} + {y}^{2} )[/tex]
Step-by-step explanation:
[tex](x ^{2} - y ^{2} ) \times (x ^{2} + y ^{2} )[/tex]
[tex] ({x} - y) \times (x + y) \times {x }^{2} + y ^{2} )[/tex]
fish swims at an altitude of -20.2 meters. A bird flies at an altitude of 38.1 meters. Which of the following statements are true? PLZ HEPPO
Answers
Answer:
D and e
Step-by-step explanation:
Side c on a right triangle is ALWAYS the longest.
O No answer text provided.
O No answer text provided.
O True
O False
Answers
Answer:
the answer should be false..
I NEED HELP PLZZ THE IS DUE TODAY PLZZ thank you
Answers
The height is 2 cubes, the length is 5 cubes, and the width is 3 cubes. Now you can just plug it into the formula.
V=lwh
V= 5x3x2
V=30
Hope this helps!! :)
HELLLLLP MEEEE IDENTIFY THE HEIGHT
Answers
Answer:
11
Step-by-step explanation:
The height is 11 inches.
i need help with this lol
Answers
Answer:
Answer is A
Step-by-step explanation:
you first take the same like terms
8c+6-3c-2
8c and -3c are like terms 8c-3c=5c
+6 and -2 are like terms 6-2=4
5c+4
What is the volume of this sphere rounded to the nearest hundredth?
Answers
Answer:
2144.7
Step-by-step explanation:
Volume of a sphere is V= [tex]\frac{4}{3} \pi r^{3}[/tex]
V= [tex]\frac{4}{3} \pi 8^{3}[/tex]
V=(4 /3)·π·8^3≈2144.66058 --> 2144.7
Your employer tells you that the salary for your new job will be less than $484 per week but not less than $396 per week. Which inequality describes your salary, S?
Answers
I think the inequality is less than or equal to (here what the sign looks like ≤ )
Trying again, but im attaching the screenshot this time!
Answers
Answer:
the area of a triangle is 9 because 4.24 times 4.24 equals 17.9776 estimated is 18 divided by 2 is 9 times 4 is 36. Now we divide 36 by 2 so we know what the area of the two trapezoids so we know the top and the bottom which is 18. The area of the square in between the triangles is 4.24 times 6 which is 25.22 estimated is 26. Now we add 26 with 18 which is 34. Now we have to find the area of the rectangle to do this we need to multiply 7.24 and 2 we need to do this so we know the length of the rectangle which is 14.48 estimated is 14. Now that we know the length we multiply it with the height which is 6, 14 times 6 equals 84.
84 is the rectangles area and the area for the trapezoids is 36.
84 plus 18 plus 18 equals 120 squared
Alaina bought a square frame for her desk that has an area of 81 square inches. What is the perimeter of the frame?
Answers
Square has 4 equal sides
Which means the length and width are the same number
x^2= 81
X=9
9+9+9+9=36
Perimeter=36
A fitness trainer sets the incline on a
treadmill to 7º. The walking surface is 5
feet (60 inches) long. Approximately how
many inches did the trainer raise the
end of the treadmill from the floor?
Answers
Answer:
Step-by-step explanation:
sin Ф equal the opposite leg of the triangle dividend by the hypotenuse
sin Ф = opp / hyp
the problem gave you the Ф (the angle 7°)
and the length of the hypotenuse (the walking surface 60 inches)
You want to use the inches since the question wants to know how many inches off the floor is the end of the walking surface
sin 7 = opp / 60 solve for opp
60 × sin(7) = opp use your calculator, I don't have one handy