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product: 3x 4 = 12
sum: 3+4 = 7
Related Questions
The lines y = 2x + 1 and y = -5x - 6 intersect at?
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so intersect at (-1,-2)
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
x/9=4/y=y/36 solve for x
Answers
How do you tell if the shape on a data distribution is symmetric or not symmetric?
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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]
Which statement is true about the solutions for the equation 3y + 4 = −2?
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
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Answer:
B, One solution
Step-by-step explanation:
a polynomial of degree zero is constant term. true or false
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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;
https://brainly.com/question/4061870
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
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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]
If 3a+4b = 4a-4b = 21 find the value of a
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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
is √2/3 a rational or irrational
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sqrt(2/3) = 0.816496
since it is a decimal with no repeating numbers it would be irrational
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 value of x?
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=>5x-20=180
=>5x=200
=>x=40
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
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What is 2.33 written as a mixed number in simplest form?
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ur mixed number is 2 33/100...and this does not reduce
What does interior angle A of the polygon in the figure equal? A. 110 B. 150 C. 230 D. 100
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(n-2) × 180° = 4 x 180 = 720
A = 720 - (50+100-120-110 - 230)
A = 110
answer is A. 110
Is 7/2 the same thing as 3.5
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3.5 as a fraction is 7/2 but in mixed numbers it's 3 1/2
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
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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.
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%
give and example of a repeating decimal where two digits repeat
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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)
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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
answer both questions to get brain ( if u cant see all the answers its fine all u need is the question)
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Answer:
a and c
Step-by-step explanation:
The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 2 units, the value of k is ________. Numerical Answers Expected!
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Answer: The value of k is 2.
Step-by-step explanation:
Given : The graph of [tex]f(x)=(0.5)x[/tex] is replaced by the graph of [tex]g(x)=0.5)x-k.[/tex]
If g(x) is obtained by shifting f(x) down by 2 units, then [tex]g(x)=(0.5)-2[/tex]
[since f(x)shifted down down by 2 , so only the value of dependent variable effect]
When we compare both functions of g(x), we found that k=2.
Hence, the value of k is 2.
The value of [tex]k[/tex] is 2.
The following information should be considered:
when [tex]g(x)[/tex] is obtained by shifting f(x) fall by 2 units so [tex]g(x) = (0.5) - 2.[/tex]Since [tex]f(x)[/tex] shifted down by 2 so there is the effect on the dependent variable. Now at the time of comparing both functions of g(x) the k should be 2.Learn more: brainly.com/question/17429689
What is the least common denominator of the equation ? 2/9x+2/3x=7
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Solve the inequality.
15 + 12c ≥ 9(c + 15)
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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
Dominic buys a 64-ounce container of salad mix. About how many ounces of romaine lettuce does the container have?
6 ounces
12 ounces
18 ounces
27 ounces
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Answer:
The answer is C. 18 ounces
Step-by-step explanation:
Answer:
c on egde
Step-by-step explanation:
express this sentence as a formula: z varies directly with the square of s.
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How many times does 6 go into 22
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3.
Why?
6 X 3 = 18.
Glad I Could Help, And Good Luck!
My Brainly Name: AnonymousGiantsFan
We can use long division to solve this,
Let's write it.
[tex]6\overline{|\smallspace22}\space\space\space\space[/tex]
Then, divide [tex]22[/tex] by [tex]6[/tex] to get [tex]3[/tex].
[tex]\begin{matrix}\space\space\space\space\space\space\emptyspace3\space\space\space\space\space\space\space\space\space\space\space\space\\ 6\overline{|\smallspace22}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
Multiply the quotient by the divisor...
[tex]\begin{matrix}\space\space\space\space\space\space\emptyspace3\space\space\space\space\space\space\space\space\space\space\space\space\\ 6\overline{|\smallspace22}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace1\emptyspace8}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
Subtract [tex]18[/tex] from [tex]22[/tex].
[tex]\begin{matrix}\space\space\space\space\space\space\emptyspace3\space\space\space\space\space\space\space\space\space\space\space\space\\ 6\overline{|\smallspace22}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace1\emptyspace8}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\space\space\emptyspace4\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}[/tex]
As you can see, our answer using long division would be 3 with a remainder of 4.
Thanks!
-TetraFish
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
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 <==