Step-by-step explanation:
At t = 20 min, V = 45,000 L.
At t = 70 min, V = 0 L.
a) The rate is the slope:
m = ΔV/Δt
m = (0 L − 45,000 L) / (70 min − 20 min)
m = -900 L/min
b) Using the slope to find V when t = 0 min:
m = ΔV/Δt
-900 L/min = (V − 0 L) / (0 min − 70 min)
V = 63,000 L
c) Use slope-intercept form to find the equation.
V = -900t + 63,000
d) At t = 62 min:
V = -900(62) + 63,000
V = 7200
Answer:
a. -900 L/min
b. Vo = 63,000 Liters
c. V ( t ) = 63,000 - 900*t
d. 7,200 Liters
Step-by-step explanation:
Solution:-
We have a swimming pool which is drained at a constant linear rate. Certain readings were taken for the volume of water remaining in the pool ( V ) at different instances time ( t ) as follows.
t = 20 mins , V = 45,000 Liters
t = 70 mins , V = 0 Liters
To determine the rate ( m ) at which water drains from the pool. We can use the linear rate formulation as follows:
[tex]m = \frac{V_2 - V_1}{t_2 - t_1} \\\\m = \frac{0 - 45000}{70 - 20} \\\\m = \frac{-45,000}{50} = - 900 \frac{L}{min}[/tex]
We can form a linear relationship between the volume ( V ) remaining in the swimming pool at time ( t ), using slope-intercept form of linear equation as follows:
[tex]V = m*t + V_o[/tex]
Where,
m: the rate at which water drains
Vo: the initial volume in the pool at time t = 0.
We can use either of the data point given to determine the initial amount of volume ( Vo ) in the pool.
[tex]0 = -900*( 70 ) + V_o\\\\V_o = 63,000 L[/tex]
We can now completely express the relationship between the amount of volume ( V ) remaining in the pool at time ( t ) as follows:
[tex]V ( t ) = 63,000 - 900*t[/tex]
We can use the above relation to determine the amount of volume left after t = 62 minutes as follows:
[tex]V ( 62 ) = 63,000 - 900*(62 )\\\\V ( 62 ) = 63,000 - 55,800\\\\V ( 62 ) = 7,200 L[/tex]
Help me with these 2 questions please
Answer:
1st one= B 25 cents
2nd one= D 2 miles
Step-by-step explanation:
1.
8x3=24
6/24=25
= 25 cents
2.
1.6 km= 1 mile
so 1/2 of a mile =
0.8 km
1/4 of an hour = 15 minutes
0.8km= 15 minutes
15x3= 45 minutes
0.8km x 3= 2.4km
2.4km = 2 miles
hope it helps hunney xx
Brock wants to compete for the featherweight boxing title, but the upper limit for that weight class is 126 pounds. He currently weighs 134 pounds. Brock can lose 3 pounds per day if he does vigorous workouts. The number of days, d, that Brock will need to work out to compete at the featherweight level is represented by the inequality 134 – 3d < 126. Select the fewest number of days he would have to work out to compete at the featherweight level. A. 1 B. 2 C. 3 D. 4 E. 5
Answer:
C. 3
Step-by-step explanation:
Brock weighs 134 pounds, he will lose 3 pounds a day until he is 126 pounds
D will represent the number of days he will work out.
134 - 3d < 126
134 - 3(3) < 126
134 - 9 = 125
125 < 126
3 days
We can say that Brock needs to workout for minimum 3 days to compete at feather weight level.
winthrop has $4.40 worth of nickles and dimes. If winthrop has 3.5 times as many nickles as he has dimes, how many dimes does he have?
Answer:
16
Step-by-step explanation:
If n is number of nickles and d is number of dimes:
5n + 10d = 440
n = 3.5d
Substitute:
5(3.5)d + 10d = 440
17.5d + 10d = 440
27.5d = 440
d = 16
2) The senior classes at High School A and High School B planned separate trips to the local
amusement park. The senior class at High School A rented and filled 2 vans and 14 buses with
294 students. High School B rented and filled 3 vans and 7 buses with 161 students. Each van
and each bus carried the same number of students. Find the number of students in each van and
in each bus.
A) Van: 9, Bus: 28 B) Van: 11, Bus: 27
C) Van: 20, Bus: 7 D) Van: 7, Bus: 20
Answer:
D) Van: 7, Bus: 20
Step-by-step explanation:
Add the amount of students together (455 students in total)
Then I added the amount of buses and vans together (5 Vans and 21 Buses)
Then I plugged in each answer
5 x 7 = 35
455 - 35 = 420
420 / 21 = 20
What is the simplified expression for 3 y squared minus 6 y z minus 7 + 4 y squared minus 4 y z + 2 minus y squared z? y squared minus y squared z minus 10 y z minus 5 y squared minus y squared z minus 5 y z minus 5 7 y squared minus y squared z minus 10 y z minus 5 7 y squared minus y squared z minus 2 y z minus 5
Answer:
7y^2 - y^2z - 10yz-5
C. 7 y squared minus y squared z minus 10 y z minus 5
Step-by-step explanation:
A. y squared minus y squared z minus 10 y z minus 5
B. y squared minus y squared z minus 5 y z minus 5
C. 7 y squared minus y squared z minus 10 y z minus 5
D. 7 y squared minus y squared z minus 2 y z minus 5
Given:
3y^2 - 6yz - 7 + 4y^2 - 4yz + 2 - y^2z
Collect like terms in the expression
3y^2 + 4y^2 - 6yz - 4yz - y^2z - 7 + 2
Simplify
7y^2 - 10yz - y^2z - 5
Rewritten as
7y^2 - y^2z - 10yz-5
Option C. 7 y squared minus y squared z minus 10 y z minus 5
Is the answer
Answer:
C. 7 y squared minus y squared z minus 10 y z minus 5
Step-by-step explanation:
I took the cumulative exam...
Also I want the person above me to get brainliest... :)
Please help me with this question regarding TRIGONOMETRY!
Answer:
The answer is option 2.
Step-by-step explanation:
First, you have to find the length of CD using Tangent Rule, tanθ = opposite/adjacent:
[tex] \tan(θ) = \frac{oppo.}{adj.} [/tex]
[tex]let \: θ = 48[/tex]
[tex]let \: oppo. = cd[/tex]
[tex]let \: adj. = ad = 110[/tex]
[tex] \tan(48) = \frac{cd}{110} [/tex]
[tex]cd = 110 \tan(48)[/tex]
[tex]cd = 122.17 \: feet[/tex]
Next, you have to find the length of BC using Sine Rule:
[tex] \sin(θ) = \frac{oppo.}{hypo.} [/tex]
[tex]let \: θ = 65[/tex]
[tex]let \: oppo. = cd = 122.17[/tex]
[tex]let \: hypo. = bc[/tex]
[tex] \sin(65) = \frac{122.17}{bc} [/tex]
[tex]bc = \frac{122.17}{ \sin(65) } [/tex]
[tex]bc = 134.8 \: feet \: (near.tenth)[/tex]
Answer:
[tex]\boxed{134.8 \: \mathrm{ft}}[/tex]
Step-by-step explanation:
Let’s take triangle ACD.
Find length CD.
tan θ = [tex]\frac{opposite}{adjacent}[/tex]
tan (48) = [tex]\frac{CD}{110}[/tex]
110 tan (48) = CD
CD ≈ 122.167
Let’s take triangle BCD.
Find length BC.
sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
sin (65) = [tex]\frac{122.167}{BC}[/tex]
BC = [tex]\frac{122.167}{sin(65)}[/tex]
BC ≈ 134.796
Calcule o valor dos produtos a) (-4). (-7/8) b) (-4). (-7/8) n sei pq tá repetido tá aqui na folha ;-; c) (-4).(+ 3,5) d) (-2).(-3/4). (-1/7) PRA HOJEE
Answer:
a) (-4). (-7/8) = 28/8
b) (-4). (-7/8)= 28/8
c) (-4).(+ 3/5) = -12/5
d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28
Step-by-step explanation:
a) (-4). (-7/8) = 28/8
b) (-4). (-7/8)= 28/8
c) (-4).(+ 3/5) = -12/5
d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28
É repetido talvez com sinal alterado para mostrar a diferença na resposta. Se o sinal for alterado, a resposta também se tornará negativa. Seria - 28/8.
Quando um número negativo é multiplicado por um número negativo, obtém um número positivo. Mas quando um número positivo é multiplicado por um número negativo, dá uma resposta negativa.
Sempre se lembre
negativo * negativo = positivo
positivo * negativo = negativo
negativo * positivo = negativo
positivo * positivo = positivo
Em palavras simples, dois sinais diferentes dão um sinal negativo e dois sinais semelhantes dão um sinal positivo na multiplicação.
English
a) (-4). (-7/8) = 28/8
b) (-4). (-7/8)= 28/8
c) (-4).(+ 3/5) = -12/5
d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28
Its repeated maybe with a changed sign to show the difference in the answer. If the sign is changed the answer would also become negative . It would become - 28/8.
When a negative number is multiplied with a negative number it gives a positive number. But when a positive number is multiplied with a negative number it gives a negative answer.
Always remember
negative * negative= positive
positive *negative=negative
negative *positive =negative
positive * positive = positive
In simple words two unlike signs give a negative sign and two similar signs give a positive sign in multiplication.
Decide whether the data table represents a linear function or an exponential function
Answer:
A
Step-by-step explanation:
Answer is a because the common difference is -9
Answer:
the data represent a linear function because there is a common difference of -9
Step-by-step explanation:
Find the product of additive inverse and multiplicative inverse of 3/2
Answer:
Additive inverse = -3/2
Multiplicative inverse = 2/3
Step-by-step explanation:
To find Additive inverse, just change the sign.
Additive inverse of 3/2 = -3/2
If we add a number and its additive inverse, we will obtain 0.
Multiplicative inverse of number a is 1/a and multiplicative inverse of a fraction a/b is b/a.
When we multiply a number & its inverse, we will get 1
Multiplicative inverse of 3/2 = 2/3
What is the approximate angle between two position vectors if their terminal points are (5, -2) and (7, 3)?
Hi,
Answer:
[tex]Angle=\frac{pi}{4}[/tex] = π/4 = 45°
Have a good day.
determine (a) the volume and (b) the surface area of the three-dimensional figure. when appropriate, use the pi key on your calculator.
a) the volume is _____
b) the surface area is ____
Step-by-step explanation:
The figure above is a cube since all it's sides are equal
Volume of a cube = l³
where l is the length of one side
From the question
l = 3yd
So the volume of the cube is
Volume = 3³
Volume = 3yd³
Surface area of a cube = l²
Surface area = 3²
= 9yd²
Hope this helps you
The graph of the function f(x) = −3x2 − 3x + 6 is shown. Which statements describe the graph? Select three options. On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (negative 0.5, 6.75), and goes through (1, 0). The vertex is the maximum value. The axis of symmetry is x = negative one-half. The domain is all real numbers. The range is all real numbers. The function is decreasing from (−∞, 6.75).
Answer:
On a coordinate plane, a parabola opens down
has a vertex at (negative 0.5, 6.75)
The vertex is the maximum value. The axis of symmetry is x = negative one-half.
The domain is all real numbers
Step-by-step explanation:
Answer:
The vertex is the maximum value.
The axis of symmetry is x = negative one-half.
The domain is all real numbers.
Step-by-step explanation:
The answer above is correct.
what is the 8th term of the geometric sequence with this explicit formula ?
Answer: C.) - 896
Step-by-step explanation:
Given the explicit formula :
An = 7 × (-2)^(n-1)
The 8th term of the geometric sequence using the formula will be :
n = 8
A8 = 7 × (-2)^(8-1)
A8 = 7 × (-2)^7
A8 = 7 × (-128)
A8 = - 896
HELLLPPPP I need a explication on whether or not these angle relationships are possible
Answer:
Step-by-step explanation:
5x+30 is a corresponding angle with 4x-9 so set them equal to each other. 4x-9+2x+3 will equal 180
Answer:
no, the values would be above 180º
Step-by-step explanation:
if...
(4x - 9) + (2x + 3) + y = 180
(5x + 30) + y = 180
then...
(4x - 9) + (2x + 3) = 5x + 30
so...
6x - 6 = 5x + 30
x = 36
plug it in.
4(36) - 9 = 135
2(36) + 3 = 75
already you can see the sum of these two angles surpasses 180 which is not possible for a triangle.
Which table represents a function?
Answer:
Table 4 represents a function.
Step-by-step explanation:
Functions require that each x-value has a unique y-value. In the other tables you see a value repeated in the x column, with a different value in the y column.
If it rains, I do not go sailing. It rains 10 % 10\% 10% of days; I go sailing 3 % 3\% 3% of days. If it does not rain, what is the (conditional) probability that I go sailing? Written "p(I go sailing | it does not rain)''
Answer:
0.03333 or 1/30
Step-by-step explanation:
Let A =" I go sailing" and B = "it does not rain"
P(A) = 0.03
P(B) =0.90
Since I never go sailing when it rains, P(A and B) =0.03.
Therefore, the (conditional) probability that I go sailing, given that it does not rain is:
[tex]P(A|B)=\frac{P(A\ and\ B)}{P(B)} \\P(A|B)=\frac{0.03}{0.90}=0.033333[/tex]
The probability is 0.03333 or 1/30.
answer pls in the pic
Answer:
Hey there!
6 increased by a scale factor of 1.5 is 9.
9 increased by a scale factor of 1.5 is 13.5.
Thus, the area would be 9 times 13.5, or 121.5
Hope this helps :)
Answer:
121.5 [tex] {in}^{2} [/tex]Step-by-step explanation:
Let's find the enlarged area:
[tex] = {(scale \: factor)}^{2} \times original \: area[/tex]
Plug the values
[tex] = {(1.5)}^{2} \times 6 \times 9[/tex]
Evaluate the power
[tex] = 2.25 \times 6 \times 9[/tex]
Calculate the product
[tex] = 121.5 \: {in}^{2} [/tex]
Hope this helps...
Best regards!!
4. If and β are zeroes of the polynomial x²+4x+3, find the polynomial whose zeroes are 1+/ and 1+/ β
Answer:
(1+β)/α = 2
(1+α)/β = 0
Step-by-step explanation:
We need to determine the zeros of the polynomial. This would be done by equating the polynomial to zero and using factorization method to find the variables
x²+4x+3 = 0
x²+x+3x+3=0
x(x+1) +3 (x+1) = 0
(x+1)(x+3) = 0
(x+1)= 0 or (x+3) = 0
x= -1 or -3
If α = -1, and β=-3
(1+β)/α = (1-3)/-1 = -2/-1
(1+β)/α = 2
(1+α)/β = (1-1)/-3 =0/-3
(1+α)/β = 0
What is the value of r? What is the length of EB?
Answer:
r=9
EF = 55
Step-by-step explanation:
CF = ED
9r - 6 = 8r+3
Subtract 8r from each side
9r-8r - 6 = 8r-8r+3
r-6 =3
Add 6 to each side
r-6+6 = 3+6
r = 9
EF= CD = 4r+19
= 4*9+19
=36+ 19
=55
HELP! 8TH GRADE MATH. I WILL NAME BRAINLIEST!!!
Answer:
Step-by-step explanation:
y = -|x| + 1
Start with the absolute value function: y = |x|. Reflect it over the x-axis by making it y = -|x|. Finally, shift up 1 unit by adding one, getting a final answer of y = -|x| + 1.
Which of these r-values represents the strongest correlation?
A. -0.7
B. -0.8
C. -0.6
D. -0.5
I guess the answer is D because it is the most far from -1 rather than the other
Answer: The answer should be D.-0.5
What is the function rule for the line
If 300men can do a piece of work in 16days,how many men would do 1/5 of the work in 15days?
Answer:
60men
Step-by-step explanation:
300 men - 15 days - 1 work
men? - 15 days - 1/5 of work
When 1 man does 1/5 of work,
how many days needed = (15 × 1/5) × 300 = 900days
Men needed to complete 1/5 work in 15 days = 900 ÷ 15 = 60men
According to a commercial, 4 out of 5 dentist recommend a certain brand of toothpaste. Suppose There are 120 dentist in your area. What is the expected number of dentist who recommend the brand? What is the standard deviation?
4/5 recommend, so about 4/5(120) = 96 doctors recommend the brand.
Pleas answer it now in two minutes
Answer:
30
Step-by-step explanation:
cos^-1(square root of 3 divided by 2)
Mrs.joshi bought a saree for Rs 1750.she sold it at a profit of 4%.what would be her profit or loss percent ?
Answer: Rs 1820
Step-by-step explanation:
This is profit, thus is it a percentage increase of 4%. Thus, she sold the saree for 104% of what she bought it for, Rs 1750. Thus, simply do 1.04*1750 to get 1820.
Hope it helps <3
GRADE
Perimeter: Change in Dimensions
A rectangle ABCD has a width of 3 inches and a length of 7 inches.
a) What is the Perimeter of the rectangle?
BINDEX
b) What is the Perimeter of the new rectangle if you double the width of rectangle ABCD? How did you find
it? How many times bigger or smaller did the new Perimeter get? (You can divide the new Perimeter over the
old one to find the times of increase/decrease)
c) What is the Perimeter of the new rectangle if you double the width and length of rectangle ABCD? How did
you find it? How many times bigger or smaller did the new Perimeter get compared to the perimeter of
rectangle ABCD?
d) Now choose a different shape of your liking and give it your own dimensions. Answer questions a), b), c)
and d) for the shape you chose.
e) Can you generalize what happens to the Perimeter if you change one of the dimensions of a shape and
what happens when you change both dimensions of the shape?
lick "Create lournal Fntn" tn antar un
Answer:
A) 20 in
B) 26 in and it got bigger by 1.3 times
C) 40 in and it got bigger by 2 times
Step-by-step explanation:
A) so the formula for finding perimeter is P= 2(L+W) so its (3+7)*2 = 20
B) if you double 3, 3*2=6 then it is 2*(6+7) = 26. 26/20= 13/20= 1.3 times more
C) if you double 3, 3*2=6 and 7, 7*2= 14 then it is (14+6)*2 = 40. 40/20=2/1 = 2 times more.
Also i couldnt solve D for you but try to solve it using what I wrote below.
Hope it helps :)
The area of a rectangle is 42 ft squared, and the length of the rectangle is 5 ft more than twice the width. Find the dimensions of the rectangle. length and width.
Answer:
Length = 12 ftWidth = [tex] \frac{7}{2} ft[/tex]
Step-by-step explanation:
Given,
Area of rectangle = [tex]42 \: {ft}^{2} [/tex]
Width = X
Length = 2x + 5
Now,
[tex]x(2x + 5) = 42[/tex]
[tex]2 {x}^{2} + 5x = 42[/tex]
[tex]2 {x}^{2} + 5x - 42 = 0[/tex]
[tex]2 {x}^{2} + 12x - 7x - 42 = 0[/tex]
[tex]2x(x + 6) - 7(x + 6) = 0[/tex]
[tex](2x - 7)(x + 6) = 0[/tex]
Either
[tex]2x - 7 = 0[/tex]
[tex]2x = 0 + 7[/tex]
[tex]2x = 7[/tex]
[tex]x = \frac{7}{2} [/tex]
Or,
[tex]x + 6 = 0[/tex]
[tex]x = 0 - 6[/tex]
[tex]x = - 6[/tex]
Negative value can't be taken.
So, width = [tex] \frac{7}{2} ft[/tex]
Again,
Finding the value of length,
Length = [tex]2x + 5[/tex]
[tex]2 \times \frac{7}{2} + 5[/tex]
[tex]7 + 5[/tex]
[tex]12[/tex]
Length = 12 ft
Answer:
length = 12 ft, width = 3.5 ft
Step-by-step explanation:
w = width
l = length = 2w + 5
A = wl = w(2w + 5) = 42
2w² + 5w - 42 = 0
(w + 6)(2w - 7) = 0
w + 6 = 0, w = -6 (dimension cannot be negative)
2w - 7 = 0, w = 3.5
l = 2(3.5) + 5 = 12
What type of right triangle would you use this formula for and why?
c=2a
Answer:
30 60 90 triangle
the hypotenuse is twice the length of the shorter leg length.
Compare the functions shown below: f(x) x y −3 −27 −2 −8 −1 −1 0 0 1 1 2 8 3 27 4 64 g(x) linear graph with y intercept of negative 1 and x intercept of negative 2 h(x) = (x + 4)2 + 2 What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = 0 to x = 4? f(x), g(x), h(x) g(x), f(x), h(x) h(x), g(x), f(x) g(x), h(x), f(x)
Hey There!!
To get the average rate of change, we simply have to use this formula:
ARC = (y2 -y1) / (x2 - x1)
For the first function:
ARC = (64 - 0) / (4 - 0) = 16
For the second function, since it's a line, the ARC would just be equal to the slope
m = ARC = (-1 - 0) / (0 - (-2)) = -0.5
For the third function:
h(0) = 18
h(4) = 66
ARC = (66 - 18) / (4 - 0) = 12 Therefore, the order of the functions from lest to greatest according to the average rate of change on the interval from x= 0 to x = 4 is:
g(x)
h(x)
f(x)
Hope This Helps!!
By ☆Itsbrazts☆
Answer:
slope of f(x) is 16 slope of g(x) is -1/2 and tho slope of h(x) 12.5
Step-by-step explanation: