5x + 6y = 18 and 18x -15y =36
// Solve equation [1] for the variable x
// Plug this in for variable x in equation [2]
// Plug this in for variable x in equation [3]
// Solve equation [2] for the variable y
// Plug this in for variable y in equation [3]
// Solve equation [3] for the variable z
// By now we know this much :
x = -6y-3z-18 y = -2 z = -1// Use the y and z values to solve for x
x = -6(-2)-3(-1)-18 = -3
Cindy has 26 nickels. She is getting rolls of nickels from the bank. She has enough money to get up to 10 rolls of nickels and each roll contains 40 nickels. The bank will not give partial rolls. The function that models the number of nickels Cindy will have after leaving the bank is f(r)=40r+26, where r is the number of rolls of nickels she gets. What is the practical domain of the function?
A) all real numbers
B) r>1
C) {66, 106, 146, 186, 226, 266, 306, 346, 386, 426}
D) all integers from 1 to 10, inclusive
Answer: Option D is the right answer. The practical domain of the function=all integers from 1 to 10, inclusive.
Step-by-step explanation:
Given function f(r)=40r+26, where r is the number of rolls of nickels she gets.
as it is already mentioned that she can get up to 10 rolls of nickels.
Therefore domain of function contains r ≤10,such that r is a natural number.
i.e.Domain of f(r)=all integers from 1 to 10, inclusive.
Domain of a f(x) is a set of values of x which make function f(x) well defined.
A frozen yogurt shop weighs customers' cups on a scale to determine how much they will pay for their yogurt. The scale rounds weights to the nearest tenth of an ounce. A weight of 10 ounces or more costs at least $3.
Final answer:
Leslie can find out which yogurt gives her more by converting pounds to ounces. A 2-pound container is equivalent to 32 ounces, which is more than the total of 30 ounces from five 6-ounce containers.
Explanation:
Comparing Yogurt Quantities
To determine which yogurt option provides more quantity, Leslie needs to convert the weights into the same units. This means converting pounds to ounces, or ounces to pounds. In this case, converting pounds to ounces is more straightforward because we deal with whole numbers.
There are 16 ounces in 1 pound, so a 2-pound container of yogurt is equivalent to 32 ounces (2 x 16 = 32). On the other hand, five 6-ounce containers of yogurt total 30 ounces (5 x 6 = 30). Therefore, the 2-pound container gives more yogurt since 32 ounces is more than 30 ounces.
Write the number 0.21212121.. as a fraction let x=
We know that numbers with periodic decimals (there are decimals that repeat infinitely) can be written as a fraction of two integer numbers.
Here we have the number:
0.212121...
Where the decimals "21" are repeating decimals, and we want to write this as a fraction.
And we will find that the fraction form of this number is: 21/99
To find it, first let's define:
x = 0.212121...
Now we need to multiply this by 10^n, where n is the number of repeating decimals, here we have two (2 and 1) then n = 2.
Now we need to multiply:
x×10^2 = x×100 = (0.2121...)×100 = 21.212121...
Now we can subtract the original number so we get:
x×100 - x = x×99 = 21.212121... - 0.212121... = 21
Then we just found that:
x×99 = 21
Solving for x, we get:
x = 21/99 = 0.212121...
Then the fraction that we want to find is 21/99
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Match the equation with its corresponding solution for x. 4x + 7 = 35
Circle P has a diameter of 20 feet. Circle Q has a diameter of 30 feet. What is the ratio of the circumference?
Answer:
The ratio of the circumferences of Circle P to Circle Q is [tex]\( \frac{2}{3} \).[/tex]
Explanation:
The circumference of a circle is given by the formula \(C = \pi \times d\), where [tex]\(d\)[/tex] is the diameter.
For Circle P with a diameter of 20 feet, the circumference is:
[tex]\[ C_P = \pi \times 20 \][/tex]
For Circle Q with a diameter of 30 feet, the circumference is:
[tex]\[ C_Q = \pi \times 30 \][/tex]
To find the ratio of the circumferences of Circle P to Circle Q, we divide the circumference of Circle P by the circumference of Circle Q:
[tex]\[ \text{Ratio} = \frac{C_P}{C_Q} = \frac{\pi \times 20}{\pi \times 30} \][/tex]
[tex]\[ \text{Ratio} = \frac{20}{30} = \frac{2}{3} \][/tex]
So, the ratio of the circumferences of Circle P to Circle Q is [tex]\( \frac{2}{3} \).[/tex]
Mr. Smith spent 6 hours hiking along a trail and back. He walked out at the rate of 4 miles per hour and walked back at the rate of 2 miles per hour. How long did it take Mr. Smith to get to the end of the trial?
Linear equations are algebraic equations which represents the value of variables. These equations have unique solutions or sometimes there may be a number of solutions. Linear equation may contain n number of variables.
Given:
[tex]\begin{aligned}\rm\:Total\: time\: taken\: by \:MR. Smith \: &= 6 hours\\\\\rm\:Speed\:while\:going &= 4 \:miles\:per\:hour.\\\\\rm\:Speed \:while\:coming\:back &= 2\: miles\:per \:hour \end[/tex]
CalculationsLet time taken to walk out be [tex]x[/tex] and time taken to walk back be [tex]2x[/tex]. The total time taken will be the summation of [tex]x[/tex] and [tex]2x[/tex] .
[tex]\begin{aligned}\rm\:Total\:time&= 6\:hours\\\\x+2x&= 6\: hours\\\\3x&=6\:hours\end[/tex]
Continuing further,
[tex]x=\dfrac{6}{3}\:hours \\\\x=2\:hours[/tex]
Therefore it can be said that the time taken by Mr. Smith to reach the end of the trial is 2 hours.
It is also observed that the speed while coming back was half of the speed of walking out. So it can be said that the time taken to walk back was twice the time Mr. Smith took to reach the end of the trail.
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A dolphin dove 31 meters below the surface of the water to reach a fish. It traveled 16% of the total distance every second.
What was the depth of the dolphin after 3 seconds?
A. –19.84 meters
B. –4.96 meters
C. –7.44 meters
D. –14.88 meters
Give the other person Brainliest, please...
PS: I know this question was asked back in 2017, but just want the other person to get brainliest :D
A water tank holds 18,000 gallons. How long will it take for the water level to reach 6000 gallons if the water is used at an average rate of 450 gallons per day?
Which equation is a point slope form equation for line AB ?
A.y−2=34(x−1)
B.y−1=34(x−2)
C.y−5=34(x−6)
D.y−6=34(x−5)
The required equation is C.) y−5 = 3/4(x−6)
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have to points (6,5) and, (-2,-1)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>(y-5)/(x-6)=(-1-5)/(-2-6)
=>4y-20=3x-18
=>y-5=3/4(x-6)
Hence, the required equation is, C.) y−5 = 3/4(x−6)
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Write each number in standard form 600 + 90 + 3
Need the complete Answer of this problemssssss.
A cylinder has a volume of 320 pi cu. in. and a height of 5". Find the radius of the cylinder.
Answer:
The radius of cylinder is 8 inches.
Step-by-step explanation:
We have given,
Volume of cylinder = 320π cubic inches
Height of cylinder = 5 inches
We know, Formula for volume of cylinder as : V =πr²h
where r is radius of cylinder and h is the height of cylinder.
So, We can plug values for V and h to get radius of cylinder.
i.e V = πr²h
320π = πr²* 5
Solving for r.
We get,
320 = r² * 5
320/5 = r²
64 = r²
or r = ±8 , Since radius of cylinder can not a negative number so we neglect -8.
Hence the radius of cylinder is 8 inches.
If 3/4 of the sections on a different spinner have stripes and there are 24 sections how many sections have stripes
17 times 59 distributive property