the question requires:
the time t required.
the equation of the inverse variation.
how do find t:
first we determine how much the tank holds by multiplying 120 by 40.
the tank holds 4800 gallons.
so now to find t we can use the formula v = d/t where d is the 4800 gallons.
so: t = d/v
t = 24 minutes
now for the equation of the inverse variation.
we can say that the equation is t = d/v since t and v are inversely proportional.
note that v and t stand for velocity and time respectively.
make sure to ask if you need any further guidance!!
Answer:
t = 24
Step-by-step explanation:
After trick-or-treating, Juan counted his candy. He collected 25 pieces of candy and noticed that 2/5 of the candy was chocolate. How many pieces of Juan’s candy were chocolate?
PLEASE HELP!!
Solve x^2=81 and x^2-18x=7.
Please show your work!
Answer:
x² = 81 , x = ± 9
x² - 18x = 7 : x = 9 ± √(22)
Step-by-step explanation:
x² = 81
simply take the square root of both sides
x = ± 9
x² - 18x = 7
This question is a bit more complicated as there is a variable with a power as well as a variable with no power. To solve for x we are going to have to put the equation in quadratic form then solve using the quadratic equation
x² - 18x = 7
put the equation in quadratic form by subtracting 7 from both sides so that the equation is equal to 0
x² - 18x - 7 = 0
we can now solve for x using the quadratic equation
recall the quadratic equation : [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]
where the value of a,b and c are derived from the equation
remember the equation is in quadratic form ax² + bx + c = 0
so ax² + bx + c = 0 : x² - 18x - 7 = 0
knowing this we can assign variables, a = 1 , b = -18 and c = -7
now we plug in the variables into the quadratic equation
recall equation : [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]
a = 1 , b = -18 and c = -7
plug in values
[tex]x=\frac{-(-18)+\sqrt{(-18)^2-4(1)(-7)} }{2(1)}[/tex]
remove parenthesis
[tex]x=\frac{18+\sqrt{(-18)^2-4(1)(-7)} }{2(1)}[/tex]
simplify exponent
[tex]x=\frac{18+\sqrt{324-4(1)(-7)} }{2(1)}[/tex]
simplify multiplication in square root and on denominator
[tex]x=\frac{18+\sqrt{324+28} }{2}[/tex]
simplify addition
[tex]x=\frac{18+\sqrt{352} }{2}[/tex]
simplify radical
[tex]x=\frac{18+4\sqrt{22} }{2}[/tex]
simplify fraction
[tex]x=9+or-\sqrt{22}[/tex]
and we are done!
Find the value of x in the equilateral triangle.
Х
3 in
Answer:
x≈3.35, or the square root of 11.
Step-by-step explanation:
Use the pythagorian therom. 3²+1.5²=x²
(Half of 3 is 1.5 and the line splits it in half)
Given line segment AB with endpoints A(-1, 7) and B(11, -1)
Find the length of AB
The length of the segment AB is the number of units on AB, and the length of segment AB is 14.4 units
How to determine the length of segment AB?The points are given as:
A = (-1,7)
B = (11,-1)
The length of the segment is then calculated using:
AB = √(x₁ - x₂)² + (y₁ - y₂)²
So, we have:
AB = √(-1 - 11)² + (7 + 1)²
Evaluate the exponent
AB = √144 + 64
Evaluate the sum
AB = √208
Evaluate the exponent
AB = 14.4
Hence, the length of segment AB is 14.4 units
Read more about length at:
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What is the value of the expression below?
56 +1/17
A1/952
B17/56
C35/17
D952
Answer:
[tex]56 \frac{1}{17} [/tex]
Step-by-step explanation:
[tex] 56 + \frac{1}{17} = \frac{56}{1} + \frac{1}{17} \\ \\ lcm \: of \: 17 \: and \: 1 \: = 17 \\ \\ \frac{952 + 1}{17} = \frac{953}{17} = 56 \frac{1}{17} [/tex]
Alex simplified the expression 7+(3x 1. 4)+5+2+(5x1. 4) to find the area of the figure on the grid.
What error did Alex make?
He found the perimeter of the figure instead of the area.
He added the lengths of the lines creating the indentation instead of subtracting them.
He used 5x1. 4 and 3 x 1. 4 as the length of each diagonal line instead of 5 and 3.
He added the five lengths together instead of multiplying them.
The error Alex made while simplifying the expression 7+(3x 1. 4)+5+2+(5x1. 4) is "he found the perimeter of the figure instead of the area".
How to find area of an object?The area of an object is the product of the length and width of the objects.
Alex added the dimensions of the grid instead of multiplying them.
7+(3x 1. 4)+5+2+(5x1. 4)
For instance,
Area of a rectangle = length × widthPerimeter of a rectangle = 2(length + width)Therefore, Alex found the perimeter of the figure instead of the area".
Learn more about area:
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f(x) = -2(3)^ x-2
Complete the following statements about f(x).
The y-intercept of f(x) is
The x-intercept of f(x) is_
The end behavior of f(x) is -
f(3) =
f(4) =
hi my name not Jeff. ok?
Step-by-step explanation:
hi im not jeff
Brahmagupta’s solution to a quadratic equation of the form ax2 bx = c involved only one solution. which solution would he have found for the equation 3x2 4x = 6?
The value of the quadratic equation is given by the formula. Then the value of x is 0.8968 and negative 2.23.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The equation for the expression is given below.
3x² + 4x = 6
3x² + 4x - 6 = 0
we know that the formula
[tex]\rm x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Then we have
[tex]x = \dfrac{-4 \pm \sqrt{4^2-4*4*(-6)}}{2*3}\\\\x = \dfrac{-4 \pm \sqrt{112}}{6}\\\\x = 0.8968, \ -2.23[/tex]
More about the factorization link is given below.
https://brainly.com/question/6810544
Which integer has the greatest value (-17,-7,-3,-23)
Answer:
that would be -3 becuase it's the least negative out of all the choices
Step-by-step explanation:
James and Sarah went out to lunch. The price of lunch for both of them was $60. They tipped their server 30% of that amount. How much did each person pay if they shared the price of lunch and the tip equally?
Answer:
The answer is that they both payed $9.00.
Step-by-step explanation:
The both payed $60.00, and 30% of that is $18.00.
( $60.00*.03=$18.00)
$18.00 divided by two (two people, James and Sarah) is $9.00.
So they both payed $9.00 individually.
Select the correct answer.
Sharla wanted to know how many minutes per hour a radio station typically plays music. She collected the following data from seven radio
stations
30,31,37,36,31,35, 34
By how many minutes would her median time change if she added another radio station playing 37 minutes?
a. 0.4
b. 0.5
c. 0.45
Answer:
b. 0.5
Step-by-step explanation:
Arranging the given data
30, 31, 31, 34, 35, 36, 37Median is the middle term⇒ Median = 34 minutesUpon adding 37 to the data set,
30, 31, 31, 34, 35, 36, 37, 37Median is the arithmetic mean of the middle two data pointsMedian = 34 + 35/ 2 = 34.5Change in Median
New Median - Original Median34.5 - 340.5If someone makes as many slices of toast as possible in 4 minutes and
40 seconds, how many slices do you think they can make?
Answer:
probably like 4 slices
Step-by-step explanation:
you figure if a toaster takes about 1-2 minutes to toast a piece of bread and a toaster usually can fit 2 slices at a time i would say 4.
Identify the correctly formulated null hypothesis:
A factory has a machine that dispenses 80 milliliters of fluid in a bottle. An employee believes the average amount of fluid is not 80 milliliters. Using 40 samples, he measures the average amount dispensed by the machine to be 78 milliliters with a standard deviation of 2. 5.
a
The machine dispenses 80 ml of fluid.
b
Ha: mu=80
c
H0: mu=80
d
The machine does not dispenses 80 ml of fluid
The stock market rose and fell over a
period of five days:
9. 8,-3. 5, 20. 5, 8. 6, -7. 7
Overall what was the net change in the
market?
Answer:
If your stock gains over 20% from the ideal buy point within 3 weeks of a proper breakout, hold it for at least 8 weeks.
Step-by-step explanation:
the money doesn't get redistributed to someone else.
can someone pls help me answer this question? hurry.
Answer:
12a −24b −4
Step-by-step explanation:
The diameter of a circle is 41 ft. Find its area to the nearest whole number.
Answer:A≈1320.25ft²
Step-by-step explanation:
A=1
4πd2=1
4·π·412≈1320.25431ft²
if a cars gas tank has 15 gallons of gas in it and the gauge says it the tank is 75% full how many gallons can the entire tank hold
use a proportion to change to the given unit
12kL = _____ L
28g = _____ mg
8 km = _____ m
2.2 g = ______ cg
7 dm = ______ m
5.5 cg = _____ dg
What is the coefficient of the x'y term in the expansion of (x – 2y)??
Answer:
2
Step-by-step explanation:
What is the solution to the system of equations?
4x+y=5
x-2y=6
O(2,-2)
O (-2,2)
O (1/2,4)
Answer:
(x, y) = (1 7/9, -2 1/9)
Step-by-step explanation:
If all you want is a solution, an appropriate calculator can provide that. The attachment shows the result of using a graphing calculator. (We have to know the fraction equivalents of the decimal values shown.)
The solution to the system is ...
(x, y) = (1 7/9, -2 1/9)
__
The solution is approximately (2, -2).
will make brainliest help please.
Answer:
D) As the amount of nutrients in the soil increases, the rate of plant growth increases.
Step-by-step explanation:
When there is more nutrients in the soil it makes the plant healthier and grow more. Also all of the other ones have no correlation to eachother or effect on another.
Express in simplest form.
Answer:
x-2/x
Step-by-step explanation:
¨/¨ means over
Answer:
(x-2)/x
Step-by-step explanation:
We can factor the numerator and denominator to see if anything simplifies.
[tex]\frac{(x-2) (x+5)}{x (x+5)}[/tex]
because (x-2)(x+5) = x² +5x-2x-10 = x² + 3x -10 and
x(x+5) = x² +5x
Simplify further
[tex]\frac{x-2}{x}[/tex]
because [(x+5) /(x+5)] = 1
Instructions: Use the image and your knowledge of the
isosceles triangle to find the value of x.
Answer:
Step-by-step explanation:
In Isosceles triangle base angles (angles oppoiste to equal sides) are congruent.
x + x + 98 = 180 {Angle sum proeprty of triangle}
2x + 98 = 180 {Subtract 98 from both sides}
2x = 180 - 98
2x = 82 {Divide both sides by 2}
x = 82/2
x = 41
Answer:
x = 41°
Step-by-step explanation:
An isosceles triangle has 2 opposite sides equal.
Therefore the angle opposite x is also x
Hence:
x + x + 98° = 180° (angles in a triangle add up to 180°)
2x + 98° = 180°
2x = 180° - 98°
2x = 82°
2x/2 = 82°/2
x = 41°
Johnny’s monthly expenses and income are listed below. calculate johnny’s debt-to-income (dti) ratio. johnny's monthly debt and income housing: rent $950.00 renter's insurance $25.00 credit: student $250.00 car $239.00 credit card
Answer:
c
Step-by-step explanation:
What is 2 log subscript 5 baseline (5 x cubed) one-third log subscript 5 baseline (x squared 6) written as a single logarithm?
The value of logarithm expression 2log₅(5x³) + (1/3)log₅(x² + 6) is simplified as log₅[{25x⁶}{∛(x² + 6)}].
What is a logarithm?Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.
The logarithmic expression is given as
[tex]2\log _55x^3 + \dfrac{1}{3} \log _5(x^2 +6)[/tex]
We know that formulas
[tex]a \log b = \log b^a\\\\\log a + \log b = \log ab[/tex]
Then we have
[tex]\rightarrow \log _5(5x^3)^2 + \log _5(x^2 +6)^{1/3}\\\\\rightarrow \log _525x^6 + \log _5\sqrt[3]{(x^2 +6)}\\\\\rightarrow \log _5 25x^6 (\sqrt[3]{(x^2 +6)})[/tex]
More about the logarithm link is given below.
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A single stem rose is $3.99. What would be the price of 36 roses?
What does folding paper have to do with exponents? (Currently struggling please help
Answer:
The thickness of the paper doubles each fold: it's an exponential growth.
Step-by-step explanation:
Solve this equation for
ab – ac = 1 for b
Answer:
a= 1/b-c
Step-by-step explanation:
Find the width of a cereal box that has a volume of 2,310 cm3 and is 22 cm long and 21 cm high.
breadth or width = 5cm
hope it helps...!!!
Simplify the following completely and show your work: -5x2(2x2 - 4x - 12)
Answer:
80+40x
Step-by-step explanation:
-5x2(2x2-4x-12)
-10(2x2-4x-12)
-20-20+40x+120
-40+120+40x
80+40x