Answer:
The object first reaches 72 feet after 1.5 seconds; it is this height again after 2.5 seconds.
Step-by-step explanation:
To find the amount of time it takes to reach 72 feet, we solve the equation
72 = -16t² + 64t + 12
To solve this, we will set it equal to 0 by subtracting 72 from each side:
72-72 = -16t² + 64t + 12 - 72
0 = -16t² + 64t - 60
Next we will use the quadratic formula to solve this:
By setting up and solving the required quadratic equation, it is determined that an object propelled from a height of 12 feet with an initial velocity of 64 feet per second will take 3.75 seconds to reach a height of 72 feet.
Explanation:The height h of the object is given by the equation h = -16t^2 + 64t + 12. We need to solve for time t, where the height h is 72 feet. By setting the equation equal to 72, we get 72 = -16t^2 + 64t + 12.
Moving -16t^2 and 64t to the other side, we get 16t^2 - 64t + (72 - 12) = 0. This simplifies to 16t^2 - 64t + 60 = 0. Divide every term in the equation by four to get: 4t^2 - 16t + 15 = 0. This equation must now be solved using the quadratic formula: t = [-b +/- sqrt(b^2 - 4ac)] / (2a).
Plugging in the values a=4, b=-16, and c=15, we get two possible solutions: t = 1 and t = 3.75 seconds. As the object is propelled up and comes down, we take the larger value, t=3.75 seconds, because that's the actual duration for the object to reach the height of 72 feet.
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Lines MA and MB tangent circle k(O) at A and B. Point C is symmetric to point O with respect to point B . Prove: m∠AMC=3m∠BMC.
Answer:
See explanation
Step-by-step explanation:
If MA is tangent to the circle k(O), then radius OA is perpendicular to segment MA.
If MB is tangent to the circle k(O), then radius OB is perpendicular to segment MB.
Consider two right triangles MOA and MOB. In these triangles:
MO is common hypotenuse;∠OAM=∠OBM=90°, because MA⊥OA, MB⊥OB;OA=OB as radii of the circle k(O).Thus, triangles MOA and MOB are congruent by HL theorem. So
∠AMO=∠BMO.
If point C is symmetric to point O with respect to point B, then OC⊥MB. Consider two right triangles MOB and MCB. In these triangles:
MB is common leg;∠OBM=∠CBM=90°, because OC⊥MB;OB=BC, because point C is symmetric to point O.Thus, triangles MOB and MCB are congruent by HL theorem. So
∠BMO=∠BMC.
Hence,
∠AMC=∠AMO+∠BMO+∠BMC=3∠BMC.
given the two sets, which statement is true?
A = {1, 2}
B = {1, 2, 3, 4}
a. B c A
b. 3 c A
c. 4 c A
d. A c B
e. none of the above
Answer:
[tex]\large\boxed{A\subset B}[/tex]
Step-by-step explanation:
[tex]A=\{1,\ 2\},\ B=\{1,\ 2,\ 3,\ 4\}\\\\A\subset B,\ \text{because all elements of the set A are the elements of the set B.}[/tex]
( please help this is the last question and i have 4 min left, thank you for the help!)
Find the difference.
Answer:
Step-by-step explanation:
-4x∧2 -1
-4x squared minus one
Classify the following sequence as arithmetic, geometric, neither or both: 2, 6, 18, ...
Arithmetic
Geometric
Neither
Both
Answer:
Geometric
Step-by-step explanation:
Does multiplying the same number with each term give the next term?
If so, then it is Geometric Sequence.
Does adding the same number with each term give the next term?
If so, then it is Arithmetic Sequence.
We see that multiplying by 3 gives us each successive term. 2 times 3 is 6 and 6 times 3 is 18. So it is geometric sequence.
It is NOT arithmetic sequence since we add 4 to 2 to get next number 6, but we have 12 to get next number, which is 18. So not an arithmetic sequence.
Answer is "Geometric"
Solve the linear equation:
[tex]4^{2x+7} = 8^{2x-3}[/tex]
Answer:
x = 11.5
Step-by-step explanation:
Taking the logarithm base 2 will transform this to a linear equation.
2(2x+7) = 3(2x -3)
0 = 3(2x -3) -2(2x +7) . . . . subtract the left side
0 = 2x -23 . . . . . . . . . . . . . simplify
0 = x - 23/2 . . . . . . . . . . . . divide by 2
11.5 = x . . . . . . . . . . . . . . . . add 11.5
The solution is x = 23/2 = 11.5.
_____
Check
This value of x makes the equation become ...
4^(2·23/2 +7) = 8^(2·23/2 -3)
4^30 = 8^20 . . . . . true
If Joe works eight hours per week at $10.75 an hour, how much will he make in one month?
$10.75 x 8 = $86 x 4(weeks) = $344
Multiply his hourly rate by the number of hours per week:
$10.75 x 8 hours = $86.00 per week.
An average month has 4 weeks, so in a 4 week month, multiply his weekly pay by the number of weeks in a month. ( Some months have 5 weeks, so you would need to multiply the weekly amount by 5 weeks).
$86 x 4 weeks = $344
It said four friends share 3 apples equally what fraction of an apple does each friend get?
Answer:
if i don't doubt then 1/4
Step-by-step explanation:
15 less than twice a number g is 19. Find g.
Answer:
g = 17Step-by-step explanation:
15 less than twice a number g is 19
2g - 15 = 19 add 15 to both sides
2g - 15 + 15 = 19 + 15
2g = 34 divdie both sides by 2
2g : 2 = 34 : 2
g = 17
a taxpayer had a taxable income of 61900 and her spouse had a taxable income of 59400 if they wish to file their tax return jointly which tax bracket will they fall in to
Answer:
25%
Step-by-step explanation:
Just did test
13) Convert 300 seconds to minutes. There are 60 seconds in 1 minute. A) 5 minutes B) 15 minutes C) 30 minutes D) 150 minutes
Answer:
5 minutes
Step-by-step explanation:
300 seconds / x minutes = 60 seconds / 1 minute
300 = 60x; divide both sides by 60 to get x; 5 = x
What is the correct way to write this fraction as a percent? A. 20% B. 25% C. 40% D. 70%
20% as a fraction is 1/5
25% is 1/4
40% is 2/5
and 70% is 7/10
Depending on what your fraction is, you can find the answer in the fraction itself-
20%, you can take 20, 5 times to get to 100. Hence 1/5.
25 can go into 100 4 times (1/4)
40 is just 20 twice, so its 2/5.
Take 10 7 times and get 7/10.
Hope this helps a bit :)
The weather reporter says that there is a 14% chance that it will rain tomorrow. What is the probability that it will not rain
Since an 100% chance is all possibilities, then it must add up to 100. If we take away that 14 from 100 by subtracting, you just get 86. Therefore, there is an 86% chance that it will not rain tomorrow.
Kevin and Levi go to the movie theater and purchase refreshments for their friends. Kevin spends a total of $44.50 on 3 bags of popcorn and 4 drinks. Levi spends a total of $84.00 on 4 bags of popcorn and 8 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Answer:
Popcorn costs: $5.75, and drink costs: $2.25.
Step-by-step explanation:
Answer:
44.50 = 3 x + 4 y
84= 4x +8 y
each popcorn bag costs $2.5
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations:
The total cost for Kevin (44.50) is equal to the product of the number of popcorn bags bought (x ) and the price of each bag, plus the product of the number of drinks purchased (y) and the price of each drink (y).
Mathematically speaking
Kevin : 44.50 = 3 x + 4 y
Using the same process for Levi:
Levi : 84= 4x +8 y
The system is
44.50 = 3 x + 4 y (k)
84= 4x +8 y (L)
If we multiply Kevin's equation by 2 and subtract it to Levi's equation:
89 = 6x +8y
-
( 84= 4x +8 y)
----------------------
5 = 2x
solving for x
5/2= x
2.5 =x
each popcorn costs $2.5
True or false (picture provided)
Answer:
True
Step-by-step explanation:
The given inequality is
[tex]5\le x\le 8[/tex]
The boundaries of the inequality are inclusive.
We use the square brackets to indicate closed interval.
[tex]5\le x\le 8[/tex] is therefore written in interval notation as;
[5,8]
The correct choice is true
(Q3) Decide if the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. y=7^-x
Answer:
Choice D is correct
Step-by-step explanation:
We are given the exponential function;
[tex]y=7^{-x}[/tex]
Using the law of exponents the function can be re-written as;
[tex]y=(\frac{1}{7})^{x}[/tex]
The base 1/7 is less than 1 hence this represents an exponential decay function.
For any exponential decay function y;
as x approaches infinity, y will always tend to 0
as x approaches negative infinity, y will always tend to infinity
See the attachment;
Kelly has 236 feet of fence to use to enclose a rectangular space for her dog. She wants the width to be 23 feet. Draw a rectangle that could be the space for Kelley's dog. Label the length and the width
Answer:
The draw in the attached figure
Step-by-step explanation:
Let
L-----> the length of the rectangle
W----> the width of the rectangle
we know that
The perimeter of a rectangle is equal to
[tex]P=2(L+W)[/tex]
we have
[tex]W=23\ ft[/tex]
so
[tex]P=2L+46[/tex] -----> equation A
[tex]P\leq 236\ ft[/tex] ----> inequality B
substitute equation A in the inequality B and solve for L
[tex]2L+46\leq 236[/tex]
[tex]2L\leq 236-46[/tex]
[tex]2L\leq 190[/tex]
[tex]L\leq 95\ ft[/tex]
The maximum possible value of L is 95 ft
therefore
The rectangle could be
Length 95 ft
Width 23 ft
see the attached figure to see the draw
Find the area of the trapezoid. leave your answer in simplest radical form.
Answer:
= 32√3 ft²
Step-by-step explanation:
Area of the trapezoid will be equal to the area of the square and that of the triangle.
Considering the triangle part;
Cos 60 = x/8
x = 8 × sin 60
= 4
Base of the triangle part = 4 ft
Therefore, top of the trapezoid = 6 ft
Height = 8 × sin 60
= 8 × √3/2
= 4 √3
Area of the trapezoid
Area = ((a+b)/2) × h
= ((6 + 10 )/2 )× 4√3
= 16/2 × 4√3
= 32√3 ft²
Answer:
4th option is correct
Step-by-step explanation:
Here in the triangle we have angle = 60
hypotenuse= 8
opposite and adjacent can be solved using trigonometric ratios
cos 60 = [tex]\frac{adjacent}{hupotenuse} \\\frac{adjacent}{8} \\\frac{1}{2}=\frac{adjacent}{8}[/tex]
which gives adjacent = 4 on solving
likewise using sine we can find opposite side to the angle which is height of
trapezium.
sin60[tex]\frac{opposite}{hypotenuse}=\frac{x}{8} \\\frac{\sqrt{3} }{2}=\frac{x}{8}\\x=4\sqrt{3}[/tex]
therefore height =[tex]4\sqrt{3}[/tex] and adjacent = 4 ft
therefore opposite sides of Trapezium are 10 ft and 6 ft
Formula for area of Trapezium =[tex]\frac{1}{2}[/tex](sum of parallel sides)x height
= [tex]\frac{1}{2}[/tex](10+6)x [tex]4\sqrt{3}[/tex]
on solving it ,we get [tex]32\sqrt{3}[/tex]
Please help me out! :)
Brooke gave her dog two whole biscuits and a half of a biscuit.Write a mixed number the represents the amount of dog biscuits she gave her dog.
Your Answer: 2 1/2 (The integer two, and the proper fraction one all over two.)
Explanation: If Brooke gave her dog two whole biscuits and then a half, it would sum up to the improper fraction 5/2 (Five all over two.) When you divide 5 by 2, you get 2.5, which is equivalent to 2 1/2.
Hope this helps ya :D
A boat traveled 27 miles in 2 hours.At this rate,how many miles will the boat in 1/2 hour?
[tex] \frac{27 \: miles \div 2}{2 \: hours \div 2} = \frac{13.5 \: miles}{1 \: hour} [/tex]
[tex] \frac{13.5 \: miles \div 2}{1 \: hour \div 2} = \frac{6.75 \: miles}{0.5 \: hour} [/tex]
The boat will travel 6.75 or
[tex]6 \frac{3}{4} [/tex]
miles in 1/2 hour.
A number from 5 to 10 is drawn at random. What is the probability that the number is odd?
Answer:
1/2 or 0.5
Step-by-step explanation:
First think: How many numbers are there between 5 and ten that are odd?
5,7 and 9 are all odd (that makes 3 numbers)
Then you take that and divide it by the total number of numbers between 5 and 10
5,6,7,8,9,10 (that makes 6 numbers)
You then get 3/6, simplified to 1/2 or 0.5
A certain volume of water contains 100,000 hydrogen atoms and 50,000 oxygen atoms.
How many hydrogen atoms are in a volume of water containing 4,000,000 oxygen atoms?
Answer:
Based off of the given information I believe the answer is 8,000,000 hydrogen atoms because it appears that the ratio between hydrogen and oxygen atoms in 2:1.
Step-by-step explanation:
Using the 2:1 ratio of hydrogen to oxygen atoms in water (H2O), a volume of water with 4,000,000 oxygen atoms would contain 8,000,000 hydrogen atoms.
We know that water, with the chemical formula H2O, consists of two hydrogen atoms for every oxygen atom. Using this information, for every oxygen atom in water, we need to account for two hydrogen atoms.
Given that a certain volume of water contains 100,000 hydrogen atoms and 50,000 oxygen atoms, we have a 2:1 ratio of hydrogen to oxygen atoms. If we want to determine how many hydrogen atoms are in a volume of water containing 4,000,000 oxygen atoms, we must apply the same 2:1 ratio.
To do so, we multiply the number of oxygen atoms by 2 (since there are two hydrogen atoms for every one oxygen atom), obtaining: 4,000,000 oxygen atoms times 2 = 8,000,000 hydrogen atoms.
Nate mother drives 225 miles to work each month how many miles do she drives in one year show work
Answer:
2700
Step-by-step explanation:
A 180 second song is divided into 2 sections. The ratio of the two sections is 3:4. What is the length, to the nearest second, of the longer
Answer:
[tex]103\ seconds[/tex]
Step-by-step explanation:
Let
x-----> the length of the smaller section in seconds
y----> the length of the longer section in seconds
we know that
[tex]x+y=180[/tex] ----> equation A
[tex]\frac{x}{y}=\frac{3}{4}[/tex]
[tex]x=\frac{3}{4}y[/tex] -----> equation B
substitute equation B in equation A and solve for y
[tex]\frac{3}{4}y+y=180[/tex]
[tex]\frac{7}{4}y=180[/tex]
[tex]y=180*4/7[/tex]
[tex]y=103\ seconds[/tex]
When two six-sided dice are rolled what is the probability that the product of their scores will be greater than six?
Answer: [tex]\bold{\dfrac{11}{18}}[/tex]
Step-by-step explanation:
Think of the products row by row:
11 12 13 14 15 16 - 0 products greater than 6
21 22 23 24 25 26 - 3 products greater than 6
31 32 33 34 35 36 - 4 products greater than 6
41 42 43 44 45 46 - 5 products greater than 6
51 52 53 54 55 56 - 5 products greater than 6
61 62 63 64 65 66 - 5 products greater than 6
[tex]\dfrac{\text{number greater than 6}}{\text{total possible outcomes}}=\dfrac{22}{36}=\dfrac{11}{18}\ when\ reduced[/tex]
Answer:
11/18.
Step by.step explanation:
There are 36 possible outcomes when 2 dice are rolled.
Outcomes for a product greater than six are:
2,4 2,5 2,6 3,3 3,4 3,5 3,6 4,2 4,3 4,4 4,5 4,6 5.2 ......5.6 , 6.2 .......6.6.
= 22 ways.
required Probability is 22/36 = 11/18 (answer).
The graph of a quadratic function has x intercepts at -3 and 5/2, and y intercept at 10. Give the function.
Answer:
f(x) = -4/3x² -2/3x +10
Step-by-step explanation:
The quadratic regression function of a graphing calculator or spreadsheet can determine the equation for you.
___
Or, you can determine it yourself.
The equation can be written in the form ...
f(x) = a(x +3)(x -5/2) . . . . . . . using the given x-intercepts
for some value of "a"
For x = 0, this must match the y-intercept.
f(0) = a(0 +3)(0 -5/2) = 10
-15/2·a = 10
a = -20/15 = -4/3
So, the function can be written as ...
f(x) = (-4/3)(x +3)(x -5/2)
or
f(x) = -4/3x² -2/3x +10
-2/3( 2x^2 + x - 15) is the answer.
From the given x-intercepts, 2 factors of the equation will be (x + 3) and
(2x - 5):- So we can write:
At the y-intercept x = 0 so we have the equation a(0+3)(2(0) - 5) = 10 where a is a constant.
a * -15 = 10
a = -2/3 so the function is (-2/3)(x + 3)(2x - 5)
= -2/3( 2x^2 + x - 15).
Which is the correct formula to find the distance between two points (p,q) and (m,n)?
Answer:
The answer is d = √[(p - m)² + (q - n)²] ⇒ first answer
Step-by-step explanation:
* The distance between any to points (x1 , y1) , (x2 , y2) is
- d = √[square the difference of x- coordinates plus
square the difference of y-coordinates]
∴ d = √[(x2 - x1)² + (y2 - y1)²] or
∴ d² = (x2 - x1)² + (y2 - y1)²
* x2 - x1 is the horizontal distance (h) and y2 - y1
is the vertical distance (v)
- By using Pythagoras theorem
∴ d = √[h² + v²]
∵ The two points are (p , q) and (m , n)
- Put x1 = m and y1 = n
- Put x2 = p and y2 = q
∴ d² = (p - m)² + (q - n)²
∴ d = √[(p - m)² + (q - n)²]
∴ The answer is d = √[(p - m)² + (q - n)²] ⇒ first answer
Answer:
The answer is d = √[(p - m)² + (q - n)²] ⇒ first answer
Step-by-step explanation:
Which ordered pair is the solution set for the system of equations below? 2x + y = 18 x – y = –6
Answer:
(4,10) is the solution
Step-by-step explanation:
2x + y = 18
x – y = –6
Using elimination
2x + y = 18
x – y = –6
----------------------
3x = 12
Dividing each side by 3
3x/3 = 12/3
x =4
Now we can find y
2x+y = 18
2(4) +y =18
8+y = 18
Subtracting 8 from each side
8-8+y = 18-8
y=10
(4,10) is the solution
I will mark brainlest
Answer:
Step-by-step explanation:
________
Good evening ,
________________
“”There are 9 pages in the album ,Farah puts the same number of photos on each page ,for a total of 63 photos “”
We can explain the last sentence this way : “ 9p = 63” then p=7
__
:)
Pumping stations deliver oil at the rate modeled by the function D, given by d of t equals the quotient of 5 times t and the quantity 1 plus 3 times t with t measure in hours and and D(t) measured in gallons per hour. How much oil will the pumping stations deliver during the 4-hour period from t = 0 to t = 4? Give 3 decimal places.
The pumping stations will deliver approximately 8.188 gallons of oil during the 4-hour period from t = 0 to t = 4.
Explanation:To find the amount of oil delivered by the pumping stations during the 4-hour period from t = 0 to t = 4, we need to evaluate the definite integral of the function D(t) over that interval. The function D(t) is given by D(t) = 5t / (1 + 3t). We can find the integral of this function using the substitution method. Let u = 1 + 3t, then du = 3dt. Rearranging this equation, we have dt = du / 3.
Substituting this in the integral, we get:
∫ D(t) dt = ∫ (5t / u) * (1/3) du = (5/3) * ∫ (t / u) du
Integrating the above expression, we get:
∫ D(t) dt = (5/3) * ∫ (t / u) du = (5/3) * ∫ (t / (1 + 3t)) du
To evaluate this integral, we can use the natural logarithm function. We know that ∫ (1/u) du = ln|u| + C, where C is the constant of integration. Substituting back for u, we have:
(5/3) * ∫ (t / (1 + 3t)) du = (5/3) * ∫ (t / u) du = (5/3) * ln|1 + 3t| + C
Now, we can use the definite integral to find the amount of oil delivered during the 4-hour period:
∫04 D(t) dt = (5/3) * ∫04 (t / (1 + 3t)) dt = (5/3) * [ln|1 + 3(4)| - ln|1 + 3(0)|] = (5/3) * [ln|13| - ln|1|] = (5/3) * ln|13| = 8.188
Therefore, the pumping stations will deliver approximately 8.188 gallons of oil during the 4-hour period from t = 0 to t = 4.
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