three water reservoirs are connected to each other with galvanized iron pipes. free surface height of the reservoir 1 is at 15 ft, the reservoir 2 is at 110 ft and the reservoir 3 is at 55 ft. each reservoir is connected to others via a pipe, and the three pipe meet each other at one node.
Answers
Water flows from reservoir 2 (110 ft) to reservoir 1 (15 ft) and reservoir 3 (55 ft) due to the pressure difference created by the varying water levels, with the flow rate determined by the magnitude of the pressure difference.
The three water reservoirs are connected to each other with galvanized iron pipes. Reservoir 1 has a free surface height of 15 ft, reservoir 2 has a height of 110 ft, and reservoir 3 has a height of 55 ft. Each reservoir is connected to the others via a pipe, and the three pipes meet at one node.
To understand how the water flows between the reservoirs, we can use the concept of water pressure. Water always flows from areas of higher pressure to areas of lower pressure.
In this case, reservoir 2 has the highest water level at 110 ft, so it has the highest pressure. Water will flow from reservoir 2 to reservoir 1 and reservoir 3 because their water levels are lower.
The water flow between the reservoirs is determined by the difference in their water levels. For example, the water level in reservoir 2 is 110 ft, and the water level in reservoir 1 is 15 ft. This means there is a pressure difference of 110 ft - 15 ft = 95 ft between the two reservoirs.
Water will flow from reservoir 2 to reservoir 1 until the pressure is equalized. Similarly, water will flow from reservoir 2 to reservoir 3, but the pressure difference will be different because the water level in reservoir 3 is 55 ft.
The pipe connecting reservoir 2 to reservoir 1 will have a higher flow rate compared to the pipe connecting reservoir 2 to reservoir 3 because the pressure difference is greater between reservoir 2 and reservoir 1.
In summary, the water will flow from reservoir 2 to reservoir 1 and reservoir 3 due to the difference in their water levels. The flow rate will depend on the pressure difference between the reservoirs.
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Related Questions
How to convert nm to cm
Answers
Express the formula d=rt in terms of the time,t. Use your formula to find the time when the distance is 40 and the rate is 8.
Answers
The expression for d=rt in terms of the time is t = d/r; t = 5.
What is time? Time can be defined as a continuous and ongoing sequence of events that occur consecutively from the past to the present to the future. Time is used to measure, measure or compare the duration of events or the intervals between them, and even the sequence of events. Time is a useful concept that we use in our daily life. We have to watch when we cook, play, study, go to school, meet someone, etc. So knowing the right time is very important. Time is usually the answer to when an event happens or happened. The concept of time determines when a certain event occurs, has occurred or will occur. Time is a measurable quantity and is also infinite. The time is calculated in seconds, minutes, hours, days, months and years.Therefore,
In the equation d=rt
t = d/r
when distance is 40 and the rate is 8
t = d/r
Replace d with 40 and rate with 8
t = 40/8
t = 5
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I seem to be stuck on these few questions, could anyone help me?? ty
Answers
Answer:
4x
3x
Step-by-step explanation:
1.)
we see that when x=0 y=0 which means that our equation
y=mx+b
b=0
(this is shown if we plug in 0 for x)
0= 0x+b
0=b
Next, we notice that each time it's increasing by four which means our slope is just 4
the answer is 4x
The y intercept (or b) is the same deal as question one
we can also see that when x=1 y=3 which means that
3=x+0
3=x
our slope is 3
The diagram shows a square with a perimeter of 20cm. What is the perimeter of the rectangle?
Answers
Answer:
Answer
Step-by-step explanation:
so the squars perimiter is 20cm and the square has 4 sides so 20/4 is 5 so each side of the square is 5cm long
so if you add all the sides together on the rectangle (only the ones on the perimiter) you get
5 x 12 = 60
so 60cm is the perimiter
Answer:
p = 60cm
Step-by-step explanation:
20 / 4 = 5cm
whole thing = 5 x 12 = 60cm
Please write a persuasive essay on why parents are more important than peers.
Answers
Disclaimers: some of these points count if everyone has good parents
Parents always have their child’s best interest in mind (not always but for this scenario well imagine)
Parents can help counteract peer pressure
Parents will always be there for their child
Parents influence a child’s values
if p(a) = 0.38, p(b) = 0.83, and p(a ∩ b) = 0.57; then p(a ∪ b) =
Answers
The value of the union of sets A and B is, P(A ∪ B) is 0.64.
The union of two sets means the total elements in both the sets combined.
Given: sets P(A) = 0.38, P(B) = 0.83, and intersection P(A ∩ B) = 0.57
We need to find the union of P(A ∪ B).
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Let us substitute the given values in the formula.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
=0.38+0.83-0.57
=1.21-0.57
=0.64
Therefore, the value of union of sets P(A ∪ B) is 0.64.
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A new car is available in a sedan model and
a hatchback model. It is available in eight
different colors. Customers can choose to
add any combination of four optional
features.
A) 308 B) 369
C) 256
D) 358
Answers
The correct answer for the total number of configurations is not listed among the options A, B, C, or D. Customers can choose any combination of four optional features.
In the given scenario, we have a new car that comes in two models: sedan and hatchback. Additionally, there are eight different colors to choose from, and customers have the option to add any combination of four optional features. The question asks for the total number of possible configurations considering all these choices.
To find the total number of configurations, we need to consider the choices for each category and multiply them together.
Model:
Since the car is available in two models (sedan and hatchback), we have 2 choices for the model.
Color:
There are eight different colors available for the car. Since the color choice is independent of the model, we still have 8 choices for the color.
Optional features:
Customers can choose any combination of four optional features. Since there are no restrictions on the selection, we can consider it as a combination problem. The number of ways to choose r items from a set of n items is given by the formula nCr = n! / (r!(n-r)!). In this case, we want to choose 4 features from a set of available features. So, we have 4C4 = 4! / (4!(4-4)!) = 1.
To find the total number of configurations, we multiply the number of choices for each category together:
Total configurations = (Number of models) x (Number of colors) x (Number of optional features)
= 2 x 8 x 1
= 16.
Therefore, there are a total of 16 possible configurations for the new car, considering the choices for the model, color, and optional features.
Based on the options provided, none of them matches the correct answer. The correct answer for the total number of configurations is not listed among the options A, B, C, or D.
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find a1 in a geometric series for which sn = 93, r = 2, and n = 5
Answers
The first term, a1, in the geometric series is -3.
What is Geometric Series?
A geometric series is a series for which the ratio of two consecutive terms is a constant function of the summation index. The more general case of a ratio and a rational sum-index function produces a series called a hypergeometric series. For the simplest case of a ratio equal to a constant, the terms have the form
To find the first term, a1, in a geometric series given the sum, Sn = 93, the common ratio, r = 2, and the number of terms, n = 5, we can use the formula for the sum of a geometric series:
Sn = a1 * (1 - r^n) / (1 - r)
Plugging in the given values, we have:
93 = a1 * (1 - 2^5) / (1 - 2)
Simplifying the expression:
93 = a1 * (1 - 32) / (-1)
93 = a1 * (-31)
Now we can solve for a1 by dividing both sides of the equation by -31:
a1 = 93 / -31
a1 = -3
Therefore, the first term, a1, in the geometric series is -3.
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In Exercises 12, describe the transformation of f represented by g. Then graph
each function.
12. f(x)=3|x|-2; g(x) = -f(x-6)
Answers
The functions are f(x) = 3 · |x| - 2 and g(x) = - 3 · |x - 6| + 2 and their graphs are shown in the image attached aside.
What is the transformation of a given function?
In this problem we have two functions defined in the statement, the first involves an absolute value function and the second function represents the first function after being reflected around the x-axis and translated horizontally in + 6 units. Now we proceed to derive the expression of the function g(x):
g(x) = - (3 · |x - 6| - 2)
g(x) = - 3 · |x - 6| + 2
Finally, we proceed to graph the two functions, whose picture is attached aside. The function f(x) is the red one and the function g(x) is the blue one.
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1. Priya is buying raisins and almonds to make trail mix. Almonds cost $5.20 perpound and raisins cost $2.75 per pound. Priya spent $11.70 buying almondsand raisins. The relationship between pounds of almonds a, pounds of raisinsr,and the total cost is represented by the equation 5.20a - 2.75r = 11.70.
Answers
The variables are:
• a: pounds of almonds
,• r: pounds of raisins
The total cost is represented by the equation:
\(5.20a+2.75r=11.70\)a. Substituting into the above equation with a = 2, and solving for r:
\(\begin{gathered} 5.20\cdot2+2.75r=11.70 \\ 10.40+2.75r=11.70 \\ 10.40+2.75r-10.40=11.70-10.40 \\ 2.75r=1.30 \\ \frac{2.75r}{2.75}=\frac{1.30}{2.75} \\ r\approx0.47 \end{gathered}\)Priya bought approximately 0.47 pounds of raisins
b. Substituting into the above equation with a = 1.06, and solving for r:
\(\begin{gathered} 5.20\cdot1.06+2.75r=11.70 \\ 5.512+2.75r=11.70 \\ 5.512+2.75r-5.512=11.70-5.512 \\ 2.75r=6.188 \\ \frac{2.75r}{2.75}=\frac{6.188}{2.75} \\ r\approx2.25 \end{gathered}\)Priya bought approximately 2.25 pounds of raisins
c. Substituting into the above equation with a = 0.64, and solving for r:
\(\begin{gathered} 5.20\cdot0.64+2.75r=11.70 \\ 3.328+2.75r=11.70 \\ 3.328+2.75r-3.328=11.70-3.328 \\ 2.75r=8.372 \\ \frac{2.75r}{2.75}=\frac{8.372}{2.75} \\ r\approx3.04 \end{gathered}\)Priya bought approximately 3.04 pounds of raisins
d. Isolating r from the equation, we get:
\(\begin{gathered} 5.20a+2.75r=11.70 \\ 5.20a+2.75r-5.20a=11.70-5.20a \\ 2.75r=11.70-5.20a \\ \frac{2.75r}{2.75}=\frac{11.70-5.20a}{2.75} \\ r=\frac{11.70}{2.75}-\frac{5.20a}{2.75} \\ \text{ Simplifying} \\ r=\frac{234}{55}-\frac{104}{55}a \end{gathered}\)The graph shows the growth rate of a certain bacteria in a lab, where the number of bacteria depends on the number of hours since the start of the experiment. Based on the graph, what is the approximate number of bacteria after 16 hours? 6 bacteria 8 bacteria 60 bacteria 80 bacteria
Answers
Answer:
Step-by-step explanation:
The graph shows the growth rate of a certain bacteria in a lab, where the number of bacteria depends on the number of hours since the start of the experiment. C 60 bacteria.
Answer:
60 Bacteria
Step-by-step explanation:
C on Edge. Good Luck!
what is the volume of the parallelepiped with sides i, 8j − k, and 9i + 7j − k?
Answers
The volume of a parallelepiped is a scalar quantity that represents the amount of space enclosed by its sides. In this case, the volume is given as 1,
To find the volume of a parallelepiped, we can use the scalar triple product of the vectors representing its sides. In this case, the sides of the parallelepiped are given by the vectors i, 8j - k, and 9i + 7j - k.
Using the scalar triple product formula, the volume V is given by:
V = |i ⋅ (8j - k) × (9i + 7j - k)|
Expanding the expression, we have:
V = |i ⋅ (8j - k) × (9i + 7j - k)|
= |(8i ⋅ (9i + 7j - k)) - ((8j - k) ⋅ (9i + 7j - k))|
Simplifying further:
V = |(72i ⋅ i) + (56i ⋅ j) - (8i ⋅ k) - (72j ⋅ j) + (8j ⋅ k) - (k ⋅ k)|
= |72 + 0 - 0 - 72 + 0 - 1|
= | -1 |
Therefore, the volume of the parallelepiped is 1.
it means that the parallelepiped has a volume of 1 unit. It is important to note that the volume of a parallelepiped can be negative if the orientation of the sides is such that they form a left-handed coordinate system. In this case, the volume is positive, indicating a right-handed coordinate system.
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An element e in a ring R is said to be idempotent if e² = e. An element of the center of the ring R is said to be central. If e is a central idempotent in a ring R with identity, then
(a) 1Re is a central idempotent;
(b) eR and (1R - e)R are ideals in R such that R = eR X (1R - e)R.
Answers
If e is a central idempotent in a ring R with identity, the following statements hold: (a) 1Re is a central idempotent. (b) eR and (1R - e)R are ideals in R such that R = eR × (1R - e)R.
(a) To show that 1Re is a central idempotent, we can verify that (1Re)^2 = 1Re. Since e is idempotent, we have e^2 = e. Multiplying both sides by 1R, we get (1R)(e^2) = (1R)e. Using the distributive property, this simplifies to e(1Re) = (1Re)e. Since e is central, it commutes with all elements of R, and thus we have (1Re)e = e(1Re). Therefore, (1Re)^2 = e(1Re) = (1Re)e = 1Re, showing that 1Re is idempotent.
(b) To prove that eR and (1R - e)R are ideals in R, we need to show that they are closed under addition and multiplication by elements of R. Since e is idempotent and central, we can verify that eR is closed under addition and multiplication. Similarly, (1R - e)R is closed under addition and multiplication. Furthermore, the sum of eR and (1R - e)R is the whole ring R because any element in R can be written as the sum of an element in eR and an element in (1R - e)R. Therefore, eR and (1R - e)R are ideals in R. Moreover, since e is central and idempotent, eR and (1R - e)R are also central idempotents.
Hence, we can conclude that if e is a central idempotent in a ring R with identity, the statements (a) and (b) hold.
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compare −114 and −1 greater than or less than
Answers
Answer:
-114 is less than -1
Answer:
-114 < -1
Step-by-step explanation:
When dealing with two negative numbers, always remember that the larger the number the smaller it is, the smaller the number the larger it is
Joey and his band have just recorded 14 new songs. The band decides that they want the new songs to form an album. How many ways can the 14 new songs be arranged on the album?
Answers
Answer:
87,178,291,200 ways
Step-by-step explanation:
Number of songs = 14
To Form an album with the 14 songs, the number of ways at which the 14 songs can be arranged is obtained by calculating the factorial of the number of songs ;
Number of ways in which the 14 songs can be arranged :
14! = (14 * 13 * 12 * 11* 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) = 87178291200 ways
an uber charges a flat fee of $15 then charges $4 per mile write an equation for the total cost of ur ride? identify the m, b, & Equation
Answers
Answer:
Step-by-step explanation:
A cereal box in the shape of a rectangular prism has a volume of 18x^3 - 3x^2 - 6x. What are three possible linear expressions for the dimensions of the cereal box?
Answers
From factoring, the volume of a rectangular prism can be written as:
3x * (2x+1) * (3x-2).
FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
The question gives: 18x³-3x²-6x. You can see that, initially, 3x is a common term. Therefore, you can write: 3x * (6x²-x-6) . Nonetheless, the question also asks 3 linear expressions, here only you have one (3x).
Thus, you should factor the expression (6x²-x-6) into two linear expressions: (2x+1)* ( 3x-2).
Thus, the volume of a rectangular prism can be written as:
3x * (2x+1) * (3x-2)
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Patrick raced round a 440 metre circular track and stopped suddenly after 900 metres . How far was she from the starting point at the 900 metre mark ? Solve
Answers
Answer:
20 meters
Step-by-step explanation:
The track is circular so it means that after Patrick raced the entire track he is back at the starting point. In other words, every 440 meters he is back to the beginning.
So we would have that, if he races round the track twice, he would run 440(2) = 880 meters and he would be back at the starting point.
The problem asks us how far is he from the starting point at the 900 meter mark. If at 880 meters he is at the starting point, then at 900 meters he would be \(900-880=20\) meters from the starting point.
If a rectangle measures 12 meters by 16 meters, what is the length, in meters, of the diagonal of the rectangle?
Answers
Answer:
20 meters
Step-by-step explanation:
use the Pythagorean theorem:
\(a^2+b^2=c^2\\\\12^2 + 16^2 = c^2\\\\144 + 256 = c^2\\\\c^2 = 400\\\\c = 20\)
A bond with face value $1,000 has a current yield of 7.0% and a coupon rate of 9.0%.
Answers
The bond's coupon payment is $90 and the current market price is approximately $1,285.71.
To determine the current yield and coupon payment for a bond, to understand the definitions of these terms:
Current Yield: The current yield of a bond is calculated by dividing the annual coupon payment by the bond's current market price and expressing it as a percentage.
Coupon Rate: The coupon rate of a bond is the annual interest rate specified by the bond when it was issued. It represents the percentage of the bond's face value that will be paid as a coupon payment each year.
Given that the bond has a face value of $1,000, a current yield of 7.0%, and a coupon rate of 9.0%, we can calculate the coupon payment and the current market price of the bond.
Coupon Payment: The coupon payment is calculated by multiplying the face value of the bond by the coupon rate. In this case:
Coupon Payment = $1,000 ×9.0% = $90
Current Market Price: To find the current market price of the bond, we can use the formula for current yield and rearrange it as follows:
Current Yield = (Coupon Payment / Current Market Price) × 100
7.0% = ($90 / Current Market Price) × 100
Dividing both sides by 100 and rearranging the equation:
Current Market Price = $90 / (7.0% / 100)
Current Market Price = $90 / 0.07
Current Market Price ≈ $1,285.71
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Explain why ac is equal to
Bc
Answers
Answer:
because length is same I hope it will help you please follow me
Translate the expression with rational exponents into a radical expression. Simplify if necessary.
2
(
(-343)
Answers
Answer:
-686
Step-by-step explanation:
2 x -343 = -686
mount everest begins on a plain that is 14,000 feet high, then the summit sits at 29,028 feet. the difference between the height of these two areas is called the .
Answers
The elevation gain of Mount Everest is 15,028 feet, a very impressive feat considering it is the highest elevation gain of any mountain in the world.
The difference between the height at the base of Mount Everest, which is 14,000 feet and the summit, which is 29,028 feet is 15,028 feet. This is also known as the elevation gain. It can be calculated using the following formula:
Elevation Gain = Summit Height - Base Height
So in this case, Elevation Gain = 29,028 ft - 14,000 ft
Which gives us: Elevation Gain = 15,028 ft
The elevation gain of Mount Everest is 15,028 feet, a very impressive feat considering it is the highest elevation gain of any mountain in the world. It is also the highest mountain in the world, with the summit standing at an impressive 29,028 feet. This is a testament to the power of nature and the sheer scale of Mount Everest.
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3x +y = 3
2y = 10-6x
On a graph
Answers
Answer:
GRAPH OF 3x + y = 3 (written on attachment)
GRAPH OF 2y = 10 - 6x (written on attachment)
helium is pumped into a spherical balloon at a rate of 3 cubic feet per second. how fast is the radius increasing after 3 minutes? note: the volume of a sphere is given by . rate of change of radius (in feet per second)
Answers
The rate of change of radius of spherical balloon is 0.00418 feet per second.
First, we need to find an equation that relates the radius and the volume of the balloon. We can use the formula for the volume of a sphere
V = (4/3)πr^3
To solve for the rate of change of the radius, we can use the chain rule of differentiation
dV/dt = dV/dr * dr/dt
where dV/dt is the rate of change of the volume, dV/dr is the derivative of the volume with respect to the radius (which is 4πr^2), and dr/dt is the rate of change of the radius.
We know that the helium is pumped into the balloon at a rate of 5 cubic feet per second, so dV/dt = 5. We want to find the rate of change of the radius after 3 minutes, which is equivalent to 180 seconds.
Substituting these values into the equation above and solving for dr/dt, we get:
5 = 4/3 * π * r^2 * dr/dt
dr/dt = 5 / (4/3 * π * r^2)
We don't know the radius of the balloon, but we can use the fact that the volume of the balloon increases at a constant rate of 5 cubic feet per second to find it. After 3 minutes (180 seconds), the volume of the balloon will have increased by:
ΔV = 5 * 180 = 900 cubic feet
Using the formula for the volume of a sphere, we can solve for the radius:
V = (4/3)πr^3
r = (3V/4π)^(1/3)
Substituting ΔV = 900, we get:
r = (3*900/4π)^(1/3) ≈ 7.91 feet
Now we can substitute this value into the equation for dr/dt
dr/dt = 5 / (4/3 * π * (7.91)^2) ≈ 0.00418 feet/second
Therefore, the radius is increasing at a rate of approximately 0.00418 feet per second after 3 minutes.
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--The given question is incomplete, the complete question is given
" Helium is pumped into a spherical balloon at a rate of 5 cubic feet per second. How fast is the radius increasing after 3 minutes?
Note: The volume of a sphere is given by V=(4/3)pi*r^3
Rate of change of radius (in feet per second) = "--
Question 4.
In the third month of a study, a sugar maple tree is 86 inches tall. In the seventh month, the tree is 92 inches tall. Assuming the tree grows at a constant rate every month, what is the rule for the height of the tree during the nth month?
an = 83 + 1.5(n – 1)
an = 83 + 1.5(n + 1)
an = 86 + 2(n – 1)
an = 86 + 2(n + 1)
Answers
The arithmetic sequence formula for the height of the tree during the nth month is option A: an = 83 + 1.5(n – 1).
What is arithmetic sequence?
The nth term of an arithmetic progression is determined using the arithmetic sequence formula. The series where the common difference between any two next words stays constant is known as an arithmetic sequence.
In the third month, the height of a sugar maple tree is = 86 inches
In the seventh month, the height of a sugar maple tree is = 92 inches
The arithmetic sequence is given as -
an = a1 + (n - 1)d.
The first equation is an = 83 + 1.5(n – 1).
Here, a1 = 83, d = 1.5.
Substitute the value of n = 3 to get 86.
an = 83 + (3 - 1)1.5
an = 83 + (2)1.5
an = 83 + 3
an = 86
Now, substitute the value of n = 7 to get 92.
an = 83 + (7 - 1)1.5
an = 83 + (6)1.5
an = 83 + 9
an = 92
Therefore, the equation obtained is an = 83 + 1.5(n – 1).
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find the value of x
93
109
46
Answers
Answer:
109 °
Step-by-step explanation:
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akqnajjsjajqjajqjwjwwujwjsw akqnajjsjajqjajqjwjwwujwjsw
akkaskakk akqnajjsjajqjajqjwjwwujwjsw snsjjjaja la snsnjJaan
smsnsnsnsnskskksksakksksksksjsjsjsjsksksbnnjbnjjj
Answer:
i think it's 68 because all the angle have to add up to 180 degrees and if you add
68+93+109+46
you will get 180
Please solve and give me the correct answer :)
Answers
Answer:
hello.
i believe this is the answer.
To three decimal places, what is the volume of a cube (cm3) with an edge length of 0.843 cm?
Answers
The volume of cube whose edge length is 0.843 is 0.599 cubic centimeters.
According to the given question.
Length of the edge of the cube = 0.843 cm.
As we know that, a cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.
And the volume of cube is calcualted by the formula
V = a^3
Where,
V is the volume of cube
And, a is the length of the edge of cube
Therefore,
The volume of the cube whose edge length is 0.843 cm
= (0.843cm)^3
= 0.599 cubic centimeters
Hence, the volume of cube whose edge length is 0.843 is 0.599 cubic centimeters.
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a line passes through the point (-9,-8) and is parallel to the line with equation y=5x-7. what is the slope of this line?
Answers
Answer:
5
Step-by-step explanation:
slopes of the parallel lines are always same this line has slope five
because equation in y intercept form is y=mx+b
where m is the slope.
so the slope of the new line will be five