Answers
Related Questions
Melissa and Emily are playing at the pool.They have three different measuring jars for; liters, cups, and pints. They find that 7 cups of water and 3 liters of water filled 9.8 pints. Later, they find that if they start with 5 liters of water and remove 9 cups of water, they end up with 6 pints of water. Model the given two situations as a system of linear equations. Based on your equations, determine the relationship between;
●cups and liters,
●cups and pints,
●and pints and liters.
Show all your work and submit your work along with the resulting relationships.
Answers
[tex]7c+3l=9.8p[/tex] ⇒ Equation 1
5 litres - 9 cups = 6 pints
[tex]5l-9c=6p[/tex] ⇒ Equation 2
Relationship between cups and litres
Rearranging equation 1 to make pints the subject
[tex]7c+3l=9.8p[/tex]
[tex]p= \frac{7c+3l}{9.8} [/tex] ⇒ substitute this into Equation 2
[tex]5l-9c= \frac{7c+3l}{9.8} [/tex]
[tex]49l-88.2c=7c+3l[/tex]
[tex]49l-3l=7c+88.2c[/tex]
[tex]46l=95.2c[/tex]
[tex]l=2.1c[/tex]
Hence, 1 litre = 2.1 cups
Relationship between cups and pints
Rearrange equation 1 to make litres the subject
[tex]7c+3l=9.8p[/tex]
[tex]3l=9.8p-7c[/tex]
[tex]l= \frac{9.8p-7c}{3} [/tex] ⇒ Substituting this into Equation 2
[tex]5( \frac{9.8p-7c}{3})-9c=6p [/tex]
[tex] \frac{49p-35c}{3}-9c=6p [/tex]
[tex] \frac{49}{3}p- \frac{35}{3}c-9c=6p [/tex]
[tex] \frac{49p}{3}-6p= \frac{35}{3}+9c [/tex]
[tex] \frac{31}{3}p= \frac{62}{3}c [/tex]
[tex]p=2c[/tex]
Hence, 1 pint = 2 cups
Relationship between pints and litres
Rearranging equation 1 to make cup the subject
[tex]7c=9.8p-3l[/tex]
[tex]c= \frac{9.8p-3l}{7} [/tex] ⇒ subsitute this into equation 2
[tex]5l-9( \frac{9.8p-3l}{7})=6p [/tex]
[tex]5l- \frac{63}{5}p+ \frac{27}{7}l=6p [/tex]
[tex]5l+ \frac{27}{7}l=6p+ \frac{63}{5}p [/tex]
[tex] \frac{62}{7}l= \frac{93}{5}p [/tex]
[tex]l=2.1p[/tex]
Hence, 1 litre = 2.1 pints
Here's work you can copy and paste:
7 cups + 3 liters = 9.8 pints
7c+3l=9.8p
5 liters - 9 cups = 6 pints
5l+9c=6p
Cups and Liters
7c+3l=9.8p
p= 7c+3l/9.8 (put in equation 2)
5l-9c= 7c+3l/9.8
49l-88.2c=7c+3l
49l-3l=7c-88.2c
46l=45.2c
1Liter = 2.1 Cups
Cups and Pints
7c+3l=9.8p
3l=9.8p-7c
l=9.8p-7c/3 (put in equation 2)
5(9.8p-7c/3)-9c=6p
(49p-35c/3)-9c=6p
49/3p-35/3c-9c=6p
49/3p-6p=35/3c+9c
31/3p=62/3c
1 Pint = 2 Cups
Pints and Liters
7c=9.8p-3l
c=9.8p-3l/7 (put in equation 2)
5l-9(9.8p-3l/7)=6p
5l-63/5p+27/7l=6p
5l+27/7l=6p+63/5p
62/7l=93/5p
1 Liter = 2.1 Pints
3x-2y=13 2x+3y=-16 are these lines parallell or perpendicular or neither
Answers
-2y = -3x + 13
y = 3/2x - 13/2...slope is 3/2, y int is -13/2
2x + 3y = -16
3y = -2x - 16
y = -2/3x - 16/3...slope = -2/3, y int is -16/3
perpendicular lines will have negative reciprocal slopes. To find the negative reciprocal of a number, flip the number and change the sign.
On the 1st equation, the slope was 3/2....find its negative reciprocal.....flip it, making it 2/3....change the sign...making it -2/3. So the negative reciprocal of 3/2 is -2/3.
So if one equation has a slope of 3/2 and another equation has a slope of -2/3, then these lines are perpendicular <==
Which expression is equal to x + (f + g)?
xf + g
x + fg
(x + f) ⋅ g
(x + f) + g
Answers
Last choice
The answer is (x + f) + g
simplify square root of 1.69
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In the given problem, the square root of 1.69 is 1.3.
The square root of a non-negative real number is a value that, when multiplied by itself, results in the original number. In mathematical notation, the square root of the number "x" is represented by the symbol "√x."
The square root is an inverse operation of squaring, which means that if one squares a number and then take its square root, he or she gets back to the original value. The concept of the square root is nearly related to obtaining the side length of a square with a given area or obtaining the magnitude of a vector in mathematics.
1.69 also can be written as [tex]\dfrac{169}{100}[/tex] in fraction form.
[tex]\sqrt{\dfrac{169}{100}} = \sqrt{\dfrac{13^2}{10^2} }[/tex]
[tex]= \sqrt{(\dfrac{13}{10} )^2}\\= \dfrac{13}{10} \\= 1.3[/tex]
Thus, 1.3 is the square root of 1.69.
Learn more about square roots here:
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Find the circumference of a circle whose area is 24pi ft^2
Answers
This gives r = root24
Circumference = 2pi * r
= 2pi * root24
= 4pi * root6
Hope I'm able to help you.
Answer:
30.76 [tex]ft^{2}[/tex]
Step-by-step explanation:
To calculate the circumference of a circle you just have to multiply the diameter by pi.
C= D*[tex]\pi[/tex]
And in order to calculate the value of the diameter you have to clear the formula for the area.
A= [tex]r^{2} *\pi[/tex]
r=[tex]\sqrt{\frac{24 \pi }{\pi } }[/tex]
r=[tex]\sqrt{24}[/tex]
r=4,89
Once we get the radius, we only have to calculate the diameter:
D=2r=9,79
now we just calculate the circumference:
C=D*[tex]\pi[/tex]= (9.79)(3.14)= 30.76
A realtor listed a house that was 45 yards by 10 yards. What is the total square footage of the house?
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and 10 yds would be (10 * 3) = 30 ft
A = L * W
A = 134 * 30
A = 4050 sq ft <==
Answer: There is 1500 squared feet of the house.
Explanation:
Since we have given that
Dimensions of a house is given by
[tex]45\ yards\ and\ 10\ yards[/tex]
So, we need to find the square footage of the house ,
Area of house is given by
[tex]Length\times Breadth\\=45\times 10=4500\ yards^2[/tex]
Now, we'll change it into feet ,
As we know that
[tex]1\ yard=3\ feet[/tex]
So, total squared footage of the house is given by
[tex]\frac{4500}{3}=1500\ feet^2[/tex]
Hence, there is 1500 squared feet of the house.
Twice a number decreased by 15 is equal to -27 . What is the number ?
Answers
2x = -27 + 15
2x = - 12
x = -12/2
x = -6 <==
A dogs weight increased by 50% in 3 years . By the end of the 3years , the dog weighed 45 pounds . How much did the dog weigh 3 years ago
Answers
Then, it would be: x * 150/100 = 45
x * 1.5 = 45
x = 45/1.5
x = 30
So, your final answer is 30 Pounds
Goodluck
Final answer:
To calculate the dog's weight from three years ago, we take the current weight and divide it by 1.50 since the weight increased by 50%. The equation 1.50 * x = 45 pounds results in x = 30 pounds, indicating the dog weighed 30 pounds three years ago.
Explanation:
The question concerns the original weight of a dog whose weight increased by 50% over a period of three years, bringing its weight to 45 pounds at the end of that period. To determine the dog's weight from three years ago, we use the following steps:
Understand that a 50% increase implies that the final weight is 150% of the original weight (100% + 50%).
Represent the original weight as 'x'.
Set up the equation: 1.50 * x = 45 pounds.
Divide both sides by 1.50 to solve for 'x': x = 45 / 1.50.
Calculate 'x' to find that 'x' equals 30 pounds.
Therefore, the dog weighed 30 pounds three years ago.
Create a set of data that contains 11 test scores and satisfies each condition below:
Mean: 83
Median: 81
Mode: 80
Range: 26
Answers
Answer:
An example of a data set that satisfies each of these conditions is:
[72, 75, 79, 80, 80, 81, 82, 84, 88, 94, 98]
Step-by-step explanation:
Let's start by defining the terms:
Mean: Average of all numbers
Median: Middle score in a set of given numbers
Mode: Most frequently occuring number
Range: Difference between the lowest and highest number
There are many possible data sets for these conditions, but these are the numbers I found work. I'm sure there is a simpler way to figure this out, but this way makes the most sense to me. This was my process.
We know that all of our numbers need to add up to 913. We know this because our mean is 83 and there are 11 numbers (83X11=913). We can check this by taking 913/11 (the number of scores)=83 (mean)
We know that the median needs to be 81. When the numbers are in order lowest to highest, we would need to have 5 numbers below 81 and 5 numbers above 81. The sixth number in the set should be 81.
We know the mode is 80, so 80 has to be in our data set at least twice with all other numbers appearing less often. This is why I put two 80s and one of every other number in my data set.
I then picked the lowest number in my data set, ensuring that a range of 26 would allow me enough space on both sides of the median. Since I have my lowest number, I can add 26 and get the highest number in my data set.
Once I have the main numbers, I just need to put other numbers before and after the median that would give me a sum of 913 (see the section about the mean). These can be any numbers that go in the right order as long as they don't change any of the numbers we've already established and they total 913.
How do you tell if the shape on a data distribution is symmetric or not symmetric?
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A circle is increased to have a circumference that is 4 times larger than the original. Which of the following options best describes the change in the radius of the original circle?
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Thus when the radius is doubled, or in other words if radius mad 2 time the original radius, the area of circle will become 2^2 = 4 time the original area. The circumference will become 2 times the original circumference.
We can calculate exact area and circumference of a circle from its radius using the following equations:
Area of circle = (pi/4)*r^2
Circumference of circle = 2*pi*r
Where r is the radius of the circle.
I know this is a lot, sorry.
what is the inverse of the function f(x) = 2x + 1
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the inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex] is [tex]\( f^{-1}(x) = \frac{x - 1}{2} \).[/tex]
To find the inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex], we'll switch the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] and solve for [tex]\( y \)[/tex].
1. Start with the original function:
[tex]\[ f(x) = 2x + 1 \][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ x = 2y + 1 \][/tex]
3. Solve for [tex]\( y \)[/tex]:
[tex]\[ x - 1 = 2y \][/tex]
[tex]\[ \frac{x - 1}{2} = y \][/tex]
So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[ f^{-1}(x) = \frac{x - 1}{2} \][/tex]
Therefore, the inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex] is [tex]\( f^{-1}(x) = \frac{x - 1}{2} \).[/tex]
Solve the inequality.
15 + 12c ≥ 9(c + 15)
Answers
15 + 12c [tex] \geq [/tex] 9c + 135
12c [tex] \geq [/tex] 9c + 120
3c [tex] \geq [/tex] 120
c [tex] \geq [/tex] 40
3c >= 120
c >= 40
One integer is 7 times another. If the product of the two integers is 28, then find the integers
Answers
xy = 28 so x = 28/y
7y = 28/y
7y^2 = 28
y^2 = 4
y = 2
x = 7y = 7*2 = 14
answer
integers are 2 and 14
double check
14 * 2 = 28
14 = 7(2) = 14
Which best describes the range of the function f(x) = 2(1/4) after it has been reflected over the y-axis? all real numbers all real numbers less than 0 all real numbers greater than 0 all real numbers less than or equal to 0
Answers
all numbers greater than 0
Answer:
All real numbers greater than 0.
Step-by-step explanation:
We have the function, [tex]f(x) = 2(\frac{1}{4})^{x}[/tex].
'Reflection over y-axis means to flip the graph over y-axis', which changes the function by f(x) becomes f(-x).
So, after reflection, the given function transforms into,
[tex]g(x)=f(-x)[/tex]
i.e. [tex]g(x)=2(\frac{1}{4})^{-x}[/tex]
According to the graph of the function g(x), we see that,
Range of [tex]g(x)=2(\frac{1}{4})^{-x}[/tex] is the 'Set of all real non-negative numbers' i.e. {x | x > 0} i.e. [tex](0,\infty)[/tex]
Lauren describes a parabola where the focus has a positive, nonzero x coordinate. Which parabola(s) could Lauren be describing? Check all that apply.
x2 = 4y
x2 = –6y
y2 = x
y2 = 10x
y2 = –3x
y2 = 5x
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it answer is c ,d and f
The correct equations are [tex]y^2 = x[/tex], [tex]y^2 = 10x[/tex] and [tex]y^2 = 5x[/tex] respectively
What is a Parabola?A parabola is symmetrical open plane curve that is created by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.
In the given question, Lauren describes a parabola that has positive non zero coordinate value on
focusThe equation of focus of a parabola is given as
[tex]y = a(x - h)^2 + k[/tex]
In the options given,
[tex]y^2 = x[/tex] is correct
[tex]y^2 = 10x[/tex] is also correct and
[tex]y^2 = 5x[/tex] is correct
This shows that only option c, d and f are the right answers.
The correct equations are [tex]y^2 = x[/tex], [tex]y^2 = 10x[/tex] and [tex]y^2 = 5x[/tex] respectively
Learn more on focus of a parabola here;
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Billy has 1 gallon of paint. He is going to pour it into a paint tray that measures 10 inches wide, 14 inches long, and 4 cm deep.
(1 gallon = 231 in3, 1 inch = 2.54 cm)
hich of the following scenarios will happen?
The paint will not fill the tray by 441 cm3.
The paint will not fill the tray by 10.53 in3.
The paint will fill the tray exactly.
The paint will overfill the tray by 10.53 in3.
Answers
find volume of tray:
convert 4cm to inches 4/2.54 = 1.575 inches
volume = 10*14*1.575 = 220.47 cubic inches
1 gallon = 231 cubic inches
231-220.47 = 10.53 more paint in a gallon
so the paint will over fill the tray by 10.53 in3
Answer:
The answer is:
The paint will overfill the tray by 10.53 in3 (cubic inches).
Step-by-step explanation:
In order to determine the correct option, first we have to get the volume of the tray.
The volume of the tray is a solid prism, where its formula is:
width=10 in
length=14 in
deep=4 cm=[tex]\frac{4}{2.54} =1.575[/tex] in
Volume=[tex]10*14*1.57=220.5[/tex] cubic inches
The value of the deep measure was changed from cm to inches units.
We subtract the allowed volume of the gallon with the volume tray:
231-220.5=10.5 cubic inches
It means that 1 gallon of paint is enough to paint the tray, where the remaining paint is 10.5 cubic inches.
Finally, the correct option is:
The paint will overfill the tray by 10.53 in3 (cubic inches).
What is the least common denominator of the equation ? 2/9x+2/3x=7
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express this sentence as a formula: z varies directly with the square of s.
Answers
Answer the question if you cant see all the answers it don't matter all u need is the question
Answers
area for triangle = 1/2 x h x b
so 1 triangle = 1/2 x 5.12 x 3.23 = 8.2688 since the triangles are congruent they are equal so 8.2688 x 2 = 16.5376
round that up to 17
Answer is C 17 square inches
If the population of Town B is 50% greater than the population of Town A and the populations of Town C is 20% greater than the population of Town A, then what percent greater is the population of Town B tan the population of Town C
Answers
A = population of town A,
B = population of town B,
C = population of town C.
Because the population of town B is 50% greater than that of town A,
B = 1.5A (1)
Because the population of town C is 20% greater than that of town A,
C = 1.2A (2)
From (1), obtain
A = B/1.5 = (2/3)B (3)
Substitute (3) into (2).
C = 1.2*(2/3)*B = 0.8B
Divide each side by 0.8.
1.25C = B
This result means that B is 25% greater than C.
Answer: 25%
Please help!!
Which of the following is a true statement? (round to the nearest tenth as needed)
A If 12n = -6, then n = -6
B If 12n = -6, then n = 0.5
C If 12n = -6, then n = -2
D If 12n = -6, then n = -0.5
Answers
you buy a box of sugar-free gum that has 12 packs each pack has five pieces which expression represents the total number of pieces of gum
Answers
What is the rate of change of the linear relationship modeled in the table?
x y
1 2
3 5
5 8
7 11
(4 points)
a) negative three over two
b) two over three
c) 1
d) three over two
Answers
In this case it is (11-8)/(7-5)=(8-5)/(5-3)=etc=3/2
So the slope is 3/2.
slope(rate of change) = (y2 - y1) / (x2 - x1)
(1,2)...x1 = 1 and y1 = 2
(3,5)...x2 = 3 and y2 = 5
now sub into the formula
slope(rate of change) = (5 - 2) / (3 - 1) = 3/2 <==
Correct answer gets brainliest
Answers
give and example of a repeating decimal where two digits repeat
Answers
A quadratic equation is shown below:
16x2 − 8x + 1 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 − 8x − 45 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Answers
We want to solve 16x² - 8x + 1 = 0
Notice that the quadratic expression is a perfect square because
(4x - 1)² = (4x)² + 2(4x)(-1) + (-1)² = 16x² - 8x + 1
Therefore
(4x - 1)² = 0
4x - 1 = 0 => x = 1/4 (multiplicity of 2)
Answer: x = 1/4 (multiplicity of 2)
Second problem
We want to solve 4x² - 8x - 45 = 0
The discriminant is
D = √[(-8)² - 4(4)(-45)]
= √784
= 28
Because D>0, there will be two real roots.
Use the quadratic formula.
x = (1/8)[8 +/- 28]
= (1/8)(36) = 4.5
or
x = (1/8)(-20)
= -2.5
Answer: x = 4.5 or x = -2.5
If 3a+4b = 4a-4b = 21 find the value of a
Answers
a=8b
Plug it in:
24b+4b=21
28b=21
b=21/28
a=8b=6.
4a-4b=21
4a=21+4b
a=(21+4b)/4
now using 1st and 2nd
3(21+4b)/4+4b=4(21+4b)/4-4b
(63+12b+16b)/4=(84+16b-16b)/4
63+28b=84
28b=21
b=21/28
b=3/4
.... now using 4a-4b=21 we have
4a-4(3/4)=21
4a=3=21
4a=24
a=6
A quadratic equation is shown below: 2x2 − 10x − 8 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points) Part B: Solve 4x2 − 12x + 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Answers
The given quadratic equation is 2x²-10x-8=0
The radicand is given by b²-4ac where a, b, and c are the constants in a quadratic form ax²+bx+c
From the given equation, we have
a = 2
b = -10
c = -8
Radicand b²-4ac = (-10)² - 4(2)(-8) = 100 + 64 = 164
The radicand is >0 hence the quadratic equation has two distinct roots
PART B:
4x²-12x+5 = 0
We can use the factorization method to solve the equation
Firstly, we multiply 4 by 5 to get 20
Then we find the pair of numbers that multiply gives 20 and sum gives -12
The pair of number is -2 and -10
Rewriting the equation
4x²-2x-10x+5 = 0
2x(2x-1)-5(2x-1) = 0
(2x-1)(2x-5) = 0
2x-1 = 0 and 2x-5 = 0
x = 1/2 and x = 5/2
The variable Z is directly proportional to X. When X is 3, Z has the value 57. What is the value of Z when X = 8
Answers
19*8 = 152
So when X is equal to 8, Z is equal to 152.