Answer:
It will take Jake 0 hours and It will take Brianna 15 hours
Step-by-step explanation:
Let x be the no. of hours taken by Brianna to complete work alone
We are given that Jake does a job in 15 hours less time than Brianna
So,Jake work alone in hours =x-15
We are given that they can do the job together in 10 hours
So, [tex]\frac{1}{x-15}+\frac{1}{x}=\frac{1}{10}\\\frac{x+x-15}{(x-15)x}=\frac{1}{10}\\x=3,15[/tex]
So, Brianna complete work in 15 hours
So, Jake work alone in hours =x-15=15-15=0
So, It will take Jake 0 hours and It will take Brianna 15 hours
A water balloon is tossed vertically from a window at an initial height (s-sub zero) of 37 feet and with an initial velocity(v-subzero) of 41 feet per second. Answer the following using the fact that h(t)=-16T^2+v-sub zer0t+s sub zero. a) Determine a formula, h)t), for the function that models the height of the water balloon at time t . b)Plot the function in Desmos in an appropriate window. Use the graph to estimate the time the water balloon lands c)Use algebra to find the exact time the water balloon lands. Show your work. No decimals in your answer. d)Determine the exact time the water balloon reaches its highest point and its height at that time. e)4 pts] Compute the average rate of change of on the intervals . Include units on your answers and write a sentence to explain the meaning of the values you found. Arc{1.5,2}____________________________. Explanation: Arc{2,2.5}____________________________. Explanation: årc{2.5,3}____________________________. Explanation:
Answer:
a) h(t) = -16t^2 +41t +37
b) see attached (3.270 seconds)
c) (41+√4049)/32 seconds
d) 1.28125 seconds; 63.265625 feet
e) [1.5, 2]: -15; [2, 2.5]: -31; [2.5, 3]: -47
Step-by-step explanation:
a) The formula and initial values are given. Putting those values into the formula, we get ...
h(t) = -16t^2 +41t +37
__
b) The graph is attached. It shows the t-intercept to be about 3.270 seconds.
__
c) Using the quadratic formula, we can find the landing time as ...
[tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-41\pm\sqrt{41^2-4(-16)(37)}}{2(-16)}\\\\=\dfrac{41\pm\sqrt{4049}}{32}\qquad\text{only $t>0$ is useful}[/tex]
The exact landing time is (41+√4049)/32 seconds.
__
d) The highest point is at t=-b/(2a) = -41/(2(-16)) = 41/32 seconds.
The value of the function at that point is ...
h(41/32) = (-16(41/32) +41)(41/32) +37 = 41^2/64 +37 = 4049/64
The maximum height is 4049/64 = 63.265625 feet.
__
e) For a quadratic function, that average rate of change on an interval is the derivative at the midpoint of the interval. Here, the derivative is ...
h'(t) = -32t +41 . . . in feet per second
Then the average rates of change are ...
arc[1.5, 2] = h'(1.75) = -32·1.75 +41 = -15 ft/s
arc[2, 2.5] = h'(2.25) = -32(2.25) +41 = -31 ft/s
arc[2.5, 3] = h'(2.75) = -32(2.75) +41 = -47 ft/s
These are the average velocity of the water balloon over the given interval(s) in ft/s. Negative indicates downward.
Answer:
(a) h(t) = -16t² + 41t + 37
(b) About 3.3 s
[tex]\large \boxed{\text{(c) }\dfrac{41+ \sqrt{4049}}{32}\text{ s}}[/tex]
(d) -15 ft/s; -31 ft/s; -47 ft/s
Step-by-step explanation:
(a) The function
h(t) = -16t² + v₀t + s₀
v₀ = 41 ft·s⁻¹
s₀ = 37 ft
The function is
h(t) = -16t² + 41t + 37
(b) The graph
See Fig. 1.
It looks like the water balloon lands after about 3.3 s.
(c) Time of landing
h = -16t² + 41t + 37
a = -16; b = 41; c = 37
We can use the quadratic formula to solve the equation:
[tex]h = \dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}[/tex]
(i) Evaluate the discriminant D
D = b² - 4ac = 41² - 4(-16) × 37 = 1681 + 2368 = 4049
(ii) Solve for t
[tex]\begin{array}{rcl}h& = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-41\pm\sqrt{4049}}{2(-16)}\\\\ & = & \dfrac{41\pm\sqrt{4049}}{32}\\\\t = \dfrac{41- \sqrt{4049}}{32}&\qquad& t = \dfrac{41+ \sqrt{4049}}{32}\\\\\end{array}\\[/tex]
[tex]\text{The water balloon will land after $\large \boxed{\mathbf{\dfrac{41+ \sqrt{4049}}{32}}\textbf{ s}} $}[/tex]
(d) Time and maximum height
(i) Time
The axis of symmetry (time of maximum height) is at t = -b/(2a)
[tex]t = \dfrac{-41}{2(-16)} = \dfrac{41}{32} = \textbf{1.281 s}[/tex]
(ii) Maximum height
The vertex is at y = h(1.281) = h(t) = -16(1.281)² + 41(1.281) + 37 = 63.27 ft
(e) Average rate of change
(i) Arc{1.5,2}
h(1.5) = 62.5
h(2) = 55
m = (h₂ - h₁)/(t₂ - t₁) = (55 - 62.5)/(2 - 1.5) = -7.5/0.5 = -15 ft/s
The water balloon has started to fall after it has reached peak height, so it is not going very fast
(ii) Arc{2,2.5}
h(2.5) =39.5
m = (39.5 - 55)/(2 - 1.5) = -15.5/0.5 = -31 ft/s
The balloon is in mid-fall, so gravity has caused it to speed up.
(iii) Arc{2.5,3}
h(3) = 16
m = (16 - 39.5)/(2 - 1.5) = -23.5/0.5 = -47 ft/s
The balloon is about to hit the ground, so it is falling at almost its maximum velocity.
Fig. 2 shows the height of the balloon at the above times.
Find the equation of a line that passes through the point (3,2) and has a gradient of - 1/3
Leave your answer in the form y=mx + c
Answer:
y = -1/3x +3
Step-by-step explanation:
When given a point and slope, it is convenient to start with a point-slope form of the equation of a line.
y = m(x -h) +k . . . . . line with slope m through point (h, k)
y = (-1/3)(x -3) +2 . . . line with slope -1/3 through point (3, 2)
y = -1/3x +3 . . . . . . . simplified to slope-intercept form
What shape best describes the cross section cut at an angle to the base of a right rectangular prism? Trapezoid Parallelogram Square Rectangle
Answer:
Rectangle.
Step-by-step explanation:
The 2 dimensional section would be a rectangle.
Answer:
rectangle
Step-by-step explanation:
AC answers are
18.7
15.5
14.3
13.1
[tex]AB=8.391[/tex]
[tex]AC=13.05407[/tex]
Answer:
AB =8.4
AC = 13.1
Step-by-step explanation:
Use SOH CAH TOA, which means Sin= Opposite/Hypotenuse, Cosine= Adjacent/Hypotenuse, and Tangent= Opposite/Hypotenuse.
AB is the opposite compared to the angle, BC is the adjacent compared to the angle, and AC is the hypotenuse.
Write down what you know in the formulas:
theta = 40 degrees
BC = adjacent = 10
Plug them in to solve what you need:
AB is opposite, so use the tangent equation:
tangent (40 degrees) = AB / 10
AB =8.4
AC is the hypotenuse, so use the cosine equation:
cosine (40 degrees) = 10 / AC
AC = 13.1
What is the value of the power a if 5^a = 1/125
Answer:
a = -3
Step-by-step explanation:
5^a = 1/125
The fraction 1/125 can be written as a power with base 5.
5^a = 5^(-3)
Cancel the same bases on both sides.
a = -3
Answer:
a = -3.
Step-by-step explanation:
5^a = 1/125
1/125 = 1 / 5^3
= 5^-3
5^a = 5^-3
so a = -3.
Can anyone help me i am really confused
Answer:
125 cm³
Step-by-step explanation:
The volume (V) of a cube = s³ ( s is the length of the sides )
Since the shape is a cube then all sides are congruent, thus
V = 5³ = 5 × 5 × 5 = 25 × 5 = 125 cm³
Answer:
v=l×w×h 5×5×5=125cubedcm
Step-by-step explanation:
you see a cube has an equal length, width and height
Find the value of x.
Answer:
x= 42
Step-by-step explanation:
(2x +1)°= 85° (vert. opp. ∠s)
2x +1= 85
2x= 85 -1 (bring constant to 1 side)
2x= 84 (simplify)
x= 84 ÷2
x= 42
Which of the following equations is the translation 2 units up of the graph of y = |x|?
A. y = |x| - 2
B. y = |x| + 2
C. y = |x + 2|
D. y= |x - 2|
Answer:
its y = |x| + 2
Step-by-step explanation:
Q4. An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated.
(a) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw
(b) Use the possibility diagram to calculate the probability that the product of the two numbers is
I) A prime number
ii) Not a perfect square iii)
A multiple of 5 iv)
Less than or equal to 21
v) Divisible by 4 or 6
Answer:
B)
1.) 7/64 (2.) 27/32 (3.)15/64 (4.)5/8 (5.)21/32
Step-by-step explanation:
Given the following :
Two 8 - sided fair die (1, 2, 3, 4, 5, 6, 7, 8)
Total sample space = 8^2 = 64
B1)
Probability = (number of required outcome / number of total possible outcomes)
probability of getting a prime number:
number of prime numbers in possibility diagram = 7
1) P(getting a prime number) = 7/64
11) P(not a perfect square)
Not a perfect square values in the diagram = 54
= 54 / 64 = 27 / 32
111) a multiple of 5:
Multiple of 5 in the diagram = 15
= 15 / 64
IV) Less than or equal to 21:
= 40/64 = 5/8
V) divisible by 4 or 6:
Numbers divisible by four or 6 = 42
= 42 / 64 = 21 / 32
What is the slope of the line in the graph? On a coordinate plane, a line goes through points (negative 2, negative 1) and (0, 1). slope =
Answer:
1
Step-by-step explanation:
The slope is given by
m = (y2-y1)/(x2-x1)
= (1 - -1)/(0- -2)
= (1+1)/(0+2)
2/2
=1
Answer:
1
Step-by-step explanation:
by using rise over run
Multiply 8/11 by the reciprocal of -16/121
Answer: -11/2
Step-by-step explanation:
First, find the reciprocal of -16/121. Which is -121/16 (you can put the negative sign anywhere). Now, you must multiply the two fractions:
[tex]\frac{8}{11} *-\frac{121}{16}[/tex]
You can cross out the terms 8 and 16 because they can be simplified into 1 and 2. And you can cross out 11 and -121 because they can be simplified into 1 and -11:
= [tex]\frac{1}{1} * -\frac{11}{2}[/tex]
Now multiply the numerators together, and multiply the denominators:
= [tex]-\frac{11}{2}[/tex]
In 1995 the USPS approximated that they handled 1.8 x 10^11 pieces of mail. In 2010 the USPS reported that they handled 1.7x10^11 pieces. How many more pieces of mail were handled in 1995 than 2010
Answer:
[tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.
Step-by-step explanation:
We are given that in 1995, the USPS approximated that they handled [tex]1.8 \times 10^{11}[/tex] pieces of mail and in 2010, the USPS reported that they handled [tex]1.7 \times 10^{11}[/tex] pieces.
To find how many more pieces of mail were handled in 1995 than in 2010, we do subtraction of the pieces of mail that were handled in both the years.
Pieces of mail handled in 1995 = [tex]1.8 \times 10^{11}[/tex]
Pieces of mail handled in 2010 = [tex]1.7 \times 10^{11}[/tex]
As it is clear that more pieces of mail were handled in 1995.
So, Pieces of mail handled in 1995 - Pieces of mail handled in 2010 = [tex](1.8 \times 10^{11}) -(1.7 \times 10^{11})[/tex]
= [tex]10^{11} \times (1.8 -1.7)[/tex]
= [tex]10^{11} \times 0.1[/tex] = [tex]1 \times 10^{10}[/tex]
Hence, [tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.
Find the 75th term of the arithmetic sequence -21, -10,1, ...
Answer:
a(75) = 793
Step-by-step explanation:
Arithmetic Explicit Formula: an = a1 + (n-1)d
Step 1: Find equation
d = (1-(-10)) = 11
a1 = -21
an = -21 + 11(n-1)
Step 2: Plug in 75 as n
a(75) = -21 + 11(75-1)
a(75) = 793
And we have our final answer!
There are 8 times as many males as females on the maths course at university. What fraction of the course are female? Give your answer in its simplest form.
Answer:
⅑
Step-by-step explanation:
Let m represents number of males, and f represents number of females taking the maths course.
Given that number of males (m) taking the maths course is 8 times as much as number of females (f), total number of students taking the maths course (T).
Thus we can represent the information above with the following:
m = no. of males
f = no. of females
T = Total
m = 8f
T = m + f
Thus,
Total = 8f + f = 9f
==>The fraction of the course that are females = No. of females (f) ÷ Total no. of students (T)
= f/9f
Fraction of females in simplified form would be ⅑
How do you write this quadratic equation using substitution
Answer:
u^2 +7u -8=0 where u = 3x+2
Step-by-step explanation:
(3x+2)^2 + 7(3x+2) - 8=0
Let 3x+2 = u
u^2 +7u -8=0
Find the values of x and y in triangle ABCD
Answer:
x and y = 66.5
Step-by-step explanation:
180-47=133
133/2=66.5
Based on the given angle measures, which triangle has side length measures that could be correct? A right triangle is shown. The length of the hypotenuse is 16, the base is 8, and the other side is 13.9. The top angle is 60 degrees and the bottom right angle is 30 degrees. A right triangle is shown. The length of the hypotenuse is 13.9, the base is 8, and the other side is 16. The top angle is 60 degrees and the bottom right angle is 30 degrees. A right triangle is shown. The length of the hypotenuse is 13.9, the base is 16, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees. A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees.
Answer:
A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees.
Step-by-step explanation:
The measures of the angles of in a triangle should correspond to the length size of the side opposite each angle in a triangle.
In simple terms, this means that the larger the measure of an angle, the longer the length of the side opposite that angle. Therefore, the smallest measure of an the 3 angles in the triangle should correspond with the shortest length.
Therefore, the triangle with the correct side length would be "A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees." Check the attachment below to see how each side length corresponds with each angle opposite them.
Answer:
D
Step-by-step explanation:
your welcome
Brandee makes an hourly wage. In the last pay period, she earned $800 for regular hours and $240 for overtime hours. Her overtime rate of pay is 50% more than her regular rate of pay "r". Write and simplify an expression in terms of "r" that represents the number of hours "h" Brandee worked in the pay period. Show your work.
Step-by-step explanation:
Overtime rate= r+50%= 1.5r
Regular hours= 800/r
Overtime hours= 240/1.5r
Total hours worked
h=800/r+240/1.5rh= 800/r+160/rh=960/rr=960/hCan someone please help me with this geometry question
Answer:
A. q = 39
Step-by-step explanation:
Since the lines are parallel, their sides will be proportional,
So,
Taking their proportion
=> [tex]\frac{60}{40} = \frac{q}{26}[/tex]
Cross Multiplying
q × 40 = 26 × 60
q = [tex]\frac{1560}{40}[/tex]
q = 39
Z^5=-7776i
Find the solution of the following equation whose argument is strictly between 270 and 360 degrees
Answer:
Z=+6
Step-by-step explanation:
Z^5=-7776i
Let's note that i I mathematics means negative one i.e
i = -1
So the equation is equal to
Z^5=-*-(7776)
Z^5 = 7776
Z= 5√7776
Since it's a divisible by 6
It's giving us a clue that 6 it's the answer.
Ok let's check the 5th root of 7776 in our calculator.
Z=+6
+6 is the solution to the equation
Z^5=-7776i
PLEASE HELP, SOLVE THIS PROBLEM AND GIVE ME THE ANSWER!!!
Answer:
11 is the answer
Step-by-step explanation: i hope so cuz my calculations gives this answer
can someone help me please? thanks!
Answer:
V = 11/21
Step-by-step explanation:
Formula: V = 4/3πr³
Simply plug in r to find volume
V = 4/3π(1/2)³
V = 0.52381
And we have our answer!
What is the sign of the product (–5)(–3)(–8)(–6)? Positive, because the products (–5)(–3) and (–8)(–6) are negative, and the product of two negative numbers is positive Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive Negative, because the products (–5)(–3) and (–8)(–6) are negative, and the product of two negative numbers is negative Negative, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is negative
Answer:
Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive
Step-by-step explanation:
There are an even number of negative factors, so the product is positive:
Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive
Evaluate the expression \dfrac{7^2}{x^2-2} x 2 −2 7 2 start fraction, 7, squared, divided by, x, squared, minus, 2, end fraction for x=3x=3x, equals, 3
Answer:
7
Step-by-step explanation:
We want to evaluate the fraction below for x = 3. We will put the value of x to be 3:
[tex]\dfrac{7^2}{x^2-2}\\\\= \dfrac{7^2}{3^2-2}\\\\= \dfrac{49}{9-2}\\\\= \dfrac{49}{7} = 7[/tex]
The answer is 7.
Answer:
7Step-by-step explanation:
goodluck khan academy users
Solve the equation 4x2 – 27x – 5 = –10x to the nearest tenth.
Let A = {1, 2, 3, 4, 5} and B = {2, 4}. What is A ∩ B? (1 point)
A. {2, 4}
B. {1, 2, 3}
C. {1, 2, 3, 4}
D. {1, 2, 3, 4, 5}
Answer:
{2, 4}.
Step-by-step explanation:
A = {1, 2, 3, 4, 5} and B = {2, 4}.
A ∩ B?
This means intersection or what is in common
A ∩ B = {2, 4}.
When planning road development, the road commission
estimates the future population using the function
represented in the table, where x is the time in years and
f(x) is the total population.
What is the significance of 160,000 in the function?
the maximum population of the city
the expected population in 5 years
the initial population at the time of the estimation
the amount of increase in the population in years
Answer:
C
Step-by-step explanation:
Got 100% on edge.
What is the answer ?
Answer:
a rational number
Step-by-step explanation:
a rational number + a rational number will always be a rational number.
Ashley and Beth drove from city A to city B in exactly 5 hours, not taking rest stops. Ashley drove up to the area located halfway between the two cities at the average speed of 40 miles per hour and then Beth drove the other half at an average speed of 60 miles per hour. How many hours did Beth drive on their trip?
Answer:
2 hours
Step-by-step explanation:
Time= 5 hrs
Ashley's speed= 40 mph
Beth's speed= 60 mph
Beth's time in travel= x
Since they drove the same distance, we have this equation:
60x=40(5-x)60x=200-40x100x=200x=200/100x=2 hoursCan someone answer this question thanks
Answer:
80 = x
Step-by-step explanation:
The base angles are the same if the side lengths are the same
The unmarked angle is 50 degrees
The sum of the angles is a triangle is 180 degrees
180= 50+50+x
180 = 100 +x
180 -100 = 100+x-100
80 = x
Answer:
80°
Step-by-step explanation:
In an isosceles triangle, if the two sides are the same length, then the two angles formed on the base line are equal.
The other angle on the base line is also equal to 50°.
Angles in a triangle add up to 180°.
x° + 50° + 50° = 180°
x° + 100° = 180°
x° = 180° - 100°
x° = 80°