try these amc 8 algebra questions and check your knowledge! amc 8,2020 problem 1 luka is making lemonade to sell at a school fundraiser. his recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. he uses 3 cups of lemon juice. how many cups of water does he need?

The number of units that he walks will be 18 units.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be,

Perimeter of the rectangle = 2(L + W) units

Sway needs to get a few things done in and out of town. Take a gander at the guide underneath to compute his distance on the off chance that he begins at home, goes to the video store, or the supermarket, snatches a quick tidbit and finishes at home.

The perimeter of the rectangle is given as,

P = 2(6 + 3)

P = 2(9)

P = 18 units

The number of units that he walks will be 18 units.

The graph is given below.

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Answer: 18 units is the answer so B

Step-by-step explanation:

As per the Boolean algebra, the simplification law is M.(~M+N) = M.N

The term Boolean algebra is defined as the  branch of mathematics that deals with operations on logical values with binary variables.

Here we have to find the simplification law from the given set of expression.

While we looking into the given option, we have identified that by Simplification Law we can have X.(~X+Y) = X.Y and X+(~X.Y) = X+Y.

According to De’ Morgan’s law ~(X+Y) = ~X.~Y.

And according to commutative law we can say that A.(B.C) = (A.B).C.

Therefore, option (a) is correct.

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Answer: 27

Step-by-step explanation:

A one-to-one function is a function that assigns a unique output for each input in its domain, and the graph of a one-to-one function will have no vertical asymptotes, cusps, or self-intersections, and will pass the horizontal line test.

A function is said to be one-to-one (or injective) if no two distinct inputs in the domain of the function produce the same output. In other words, a function is one-to-one if it assigns a unique output to each input in its domain.

A graph of a one-to-one function will have the following properties:

The graph will pass the horizontal line test; no horizontal line will intersect the graph more than once.

The graph will have no vertical asymptotes, which would indicate that the function is not defined for certain inputs.

The graph will have no cusps or self-intersections, which would indicate that the function assigns multiple outputs to the same input.

A one-to-one function has a inverse function, which is also a function and satisfies the same properties as the original function.

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Randomization is a crucial step in experimental design that helps to increase the validity and generalizability of the results, by controlling the extraneous variables that might influence the outcome.

Randomization is important in an experimental design because it helps to reduce the effects of confounding variables. Confounding variables are factors that can affect the outcome of an experiment but are not part of the experimental manipulation. By randomly assigning subjects to different groups, the effects of confounding variables will be distributed equally among the groups, making it more likely that any differences observed between the groups are due to the experimental manipulation and not to the confounding variables.

Randomization also helps to ensure that the groups being compared are representative of the population being studied. This is important because if the groups are not representative, the results of the experiment may not be generalizable to the population as a whole.

Additionally, randomization helps to ensure that the groups being compared are not systematically different in ways that could affect the outcome of the experiment. This is important because if the groups are systematically different, it could be difficult to determine whether any differences observed between the groups are due to experimental manipulation or systematic differences.

Therefore, Overall, randomization is a crucial step in experimental design that helps to increase the validity and generalizability of the results, by controlling the extraneous variables that might influence the outcome.

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According to the given information the line integral is [tex]=\frac{8}{15}(1+125.\sqrt{10})[/tex].

Line integrals include several integrals across a curve, but definite integrals only entail a single integral over a specified interval. This is the primary distinction between the two types of integrals.

[tex]\int_C\hairsp xyds,C:x=t^2,y=2t,0\le t\le3\\x^\prime=2t\\y^\prime=2\\ds=\sqrt{\left(x^\prime\right)^2+\left(y^\prime\right)^2}\\\sqrt{{4\left(t\right)}^2+4}\\\int C\ xy\ ds\ =\int_0^3\hairspt^2\cdot2t\cdot2\cdot\sqrt{1+t^2}\mathrm{\ }dt\\t=\ \ tan\ \theta\\dt=(1+{tan}^2\theta)d\theta=({Sec}^2\theta)d\theta\ \\{=\int}_0^3\hairsp4t^3\sqrt{1+t^2}\mathrm{\ }dt\\=\frac{8}{15}(1+125.\sqrt{10})[/tex]

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Answer: 4⋅(2+5) = 4 * (2+5) = 4 * 7 = 28

Step-by-step explanation:

Line 1 shows the original expression and Line 2 shows the expression is simplified by using the distributive property.

4⋅2 + 4⋅5 = 8+20 = 28

So the final result is 28.

The  constant of proportionality 'k' is 247.

Since y = k/x

x= 13 y= 19

19=k/13

k=19*13

k=247

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional. If equivalent elements in two sequences have a constant product, also known as the coefficient of proportionality, then the two sequences are inversely proportional.

This definition is frequently expanded to include connected variable quantities, also known as variables. Variable has a distinct meaning in mathematics than it does in everyday language (see variable (mathematics)); these two ideas use the same name due to a shared etymology.

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Answer:

1.) x=1; y=1

2.) x=1; y=5

3.) No solution

Step-by-step explanation:

1.) To start off with number one, we see that in both equations the x and y are positive, and the sums aren't equal to each other, this means we have to do something to make them equivalent. For example, we can multiply the top equation by 8 and the bottom equation by 7, so we get the equations 32x + 24y = 56 and the bottom equation to be 21x+35y=56. From here we can just make the equations equal each other to get 32x+ 24y = 21x +35y. From here we can just get a certain amount of x to equal certain amount of y by taking away the smaller amount of each and bringing it to the other side by subtracting. From that we get 11x = 11y. We can simplify this to be x=y. Now we can substitute either x or y in either equation to get 4x + 3(x) = 7. Then you solve algebraically and you get x=1. Now since we established that x was already equal to y, both x AND y are equal to 1.

2.) For this problem, we have an x that is negative in one equation and positive in the other. This means we can use the method of multiplying the bottom equation by 3 to get 3x +3y = 18. Now we are able to add both equations to each other crossing out the x's because they cancel out. From this we get 4y=20, Which means y=5. We can now plug this back into the equation to get x+(5) = 6. Which means y=5 and x=1.

3.) For this problem, we have both equations equal to y. However the x's are also equal to each other. Meaning if we were to solve them like in problem one, we would get the issue of cancelling the x's out and just getting 13/2=9/2 which is a problem because they do not equal each other. But, we can notice that both of the given systems are linear lines, meaning we could plot them off a graph. But to save time, we can notice that both equations have the exact same slope but different starting positions. Meaning that both lines would be parallel to each other. Since both lines are parallel to each other, There will never be an intersection, or answer between them. Making x and y null (no answer)

An exponential function can be mixed with other exponential functions via addition, subtraction, multiplication, or division.

An exponential function is a mathematical function that has the following structure: f (x) = an x. where x is a variable and with an is a support to keep as the function's base. The most typical exponential-function base is the transcendent number e, or approximately 2.71828. Exponential functions are often used to model phenomena in the real world, including bacterial growth, population growth, and compound interest. Consider that you are investigating the effects of an antibiotic on a certain bacteria.

Given that (f + g) (x) equals (f (x) + g (x), (f + g) (x) equals (2x + 1) + (x2+ 2x - 1), which translates to 2x + 1 + x2 + 2x - 1 as 2x+ 4x.

(f + g) (2) = 22+ 4(2) = 4 + 8 = 12 since (f + g) (x) = x2 + 4x.

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Answer: 2

Step-by-step explanation:

The factorize expression of 25x²-4x²-9 is 3(7x²-3).

Factorization is a process to simplify the expression by finding the factors of that expression.

And to find the same expression from factors, you have to reverse the process.

We have the quadratic function,

25x²-4x²-9.

To factorize the function:

First, combine similar terms,

25x²-4x²-9,

= 21x²-9.

Now, factor out the common factor.

That means,

3(7x²-3).

Therefore, the required function is 3(7x²-3).

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The amount that Johnny can borrow on a mortgage for a new house, given the Banker's Rule is between $225,000 to $270,000.

The Banker's Rule is a rule of thumb used to determine how much a person can afford to borrow on a mortgage. According to the Banker's Rule, a person should not borrow more than 2.5 to 3 times their annual income for a mortgage.

Using this rule, if Johnny makes $90,000 per year, he can afford to borrow between $225,000 to $270,000 on a mortgage for a new house. However, this is a rough estimate, and other factors such as credit score, debt-to-income ratio, and the lender's requirement also play a role in determining how much Johnny can borrow.

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C. X=6 is a true solution and X=-6 is an extraneous solution

2log6(x) = 2

log6(x2) = 2

x2 = 6^2

x2 = 36

x = 6, -6

Since 6 and -6 are the only real solutions, 6 is a true solution and -6 is an extraneous solution.

2log6(x) = 2

log6(x)2 = 2

By taking the power of both sides with base 6,

x2 = 62

x2 = 36

By taking the square root of both sides,

x = ±6

x = 6, -6

Since 6 and -6 are the only real solutions, 6 is a true solution and -6 is an extraneous solution.

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The total number of boys is 8 and that of girls is 22.

Let x be the number of boy members in the math club. According to the problem, the number of girl members is 2 less than 3 times the number of boy members, so we can write the equation:

G = 3*B - 2

We also know that the total number of club members is 30, so we can write the equation:

B + G = 30

We can substitute the first equation into the second equation to eliminate "G":

B + (3*B - 2) = 30

Combining like terms:

4*B - 2 = 30

⇒ 4*B = 30 + 2

⇒ 4B = 32

Dividing by 4:

∴ B = 34/4

⇒ B = 8

So there are 8 boy members in the math club. To find the number of girl members, we can substitute this value back into the first equation:

G = 3*8 - 2 = 22

So there are 22 girl members in the math club.

Therefore,

The number of boys = B = 8

The number of girls = G = 22

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The midpoint of the given line segment can be determined by using the formula ( x , y ) = [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ] .

As given in the question,

Let the two endpoints of the given line segment be A(x₁ , y₁) and B(x₂ ,y₂).

As per midpoint concept it divides the given line segment in the equal ratio.

let the given line segment AB divided in the equal ratio of n : n

Consider the coordinates of the required mid point be ( x , y ) :

using midpoint formula we have :

( x , y ) =  [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ]

If the point divides the given line segment in the ratio 2 : 2

The required midpoint is given by

(x ,y ) = [ (2x₁ + 2x₂ )/2(2) , (2y₁ + 2y₂ )/2(2)]

        =  [ (x₁ + x₂ )/2 ) , (y₁ + y₂ )/2 ]

Therefore, the required midpoint which divides the given line segment into equal parts is ( x , y ) =  [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ].

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Answer:

Step-by-step explanation:

Rotation, dilation, reflection and translation are all a type of transformation.

The transformation, i.e., f: X X, is a function, f, that maps to itself. Following the transformation, the pre-image X changes into the image X. Any operation, including translation, rotation, reflection, and dilation, may be used to create this transformation.

A rectangular array of numbers is called a matrix, and different operations are provided for it. The components are arranged in vertical columns and horizontal rows.

Rotation, dilation, reflection and translation are all a type of transformation.

A rectangular array of numbers or other objects arranged in a grid position system is called a matrix.

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Answer:

b

Step-by-step explanation:

de=40

Answer:

DE = 58 is the incorrect statement

The function that gives the number of tickets bought by dragons fans after w consecutive wins is: t(w)= 200*(1.11)^w

Tickets bought by Dragon fans in one game = 200

For every consecutive win, the tickets increase by a factor of 1.11

Therefore, for the first win, the number of tickets were 200

For the second consecutive win, the number of tickets increased to 200*1.11= 200*(1.11)^1, since after each consecutive win the number of tickets increases by a factor of 1.11

For the third consecutive win, the number of tickets bought by fans increased to 200*1.11*1.11= 200*(1.11)^2

Hence, for w consecutive wins, the function will turn out to be;

t(w)= 200*(1.11)^w

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Answer:

L^2 = area of square = As

As = 14 L H / 2      where L H /2 = area of triangle

L^2 = 14 L H / 2

H = L / 7    or L = 7 H

Let the length of one side of square = 7 in

As = 7^2 = 49 in^2        area of square

H = 7     height of one side of triangle (other side = 1)

Area of triangle = 7 * 1 / 2 = 7/2 in^2

14 * At = 49

Area of square 7 * 7 = 49 in^2      Seems to checkout

Answer:

Step-by-step explanation:

2 7/9 divided by 2

First, convert the mixed number into a improper fraction:

25/9

Then multiply by the reciprocal of 2, by multiplying it by 1/2,

which turns into 25/8

Turn it into a mixed number: 1 7/18 OR 25/8

Answer:

multiply 16-y this is correct

Step-by-step explanation:

it is a square.

so, all sides are equally long.

that means e.g.

y - 3 = 2y - 11

-3 = y - 11

8 = y

and then

3x - 10 = 3y - 19 = 3×8 - 19 = 24 - 19 = 5

3x = 15

x = 15/3 = 5

so the length of all 4 sides is by using e.g.

y - 3 = 8 - 3 = 5

each side is 5 units long.

The volume of the right circular cone hat has a height of 19 feet and base diameter of 178 is calculated as: 1,575.2 ft³.

To find the volume of a right circular cone, we can use the formula:

V = (1/3) * π * r² * h

Where V is the volume, π is approximately 3.14, r is the radius of the base, and h is the height of the cone.

Given that the diameter of the base is 17.8 feet, we can divide it by 2 to find the radius, which is 8.9 feet.

Substituting these values into the formula:

V = (1/3) * π * (8.9²) * 19

V = (1/3) * 3.14 * 78.41 * 19

V = 1,575.2 ft^3

Rounded to the nearest tenth, the volume of the cone is 1,575.2 ft³

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Answer:

Irrational Numbers: Any real number that cannot be written in fraction form is an irrational number. These numbers include non-terminating, non-repeating decimals, for example , 0.45445544455544445555..., or . Any square root that is not a perfect root is an irrational number.

Answer=

square root of 1000, square root of 64, etc.

These numbers cant be written as a fraction.

Answer: The area of the trapezoid can be found using the formula:

Area = (a + b)h/2

where a and b are the lengths of the parallel sides and h is the height (perpendicular distance between the parallel sides).

In this case, the parallel sides are 13ft and 15ft, and the height is 5ft.

Therefore, the area of the trapezoid is:

(13 + 15) * 5 / 2 = (28) * 5 / 2 = 140 / 2 = 70 ft^2

Step-by-step explanation: The area of the trapezoid is calculated by taking the sum of the parallel sides, multiplying by the height and then dividing by 2. The parallel sides are given as 13ft and 15ft, and the height is given as 5ft.

By substituting the given values in the formula we get (13+15)5/2 = 285/2 = 140/2 = 70 ft^2.

So, the area of the trapezoid is 70 ft^2.

The final value would be 1,534,947.20

Joe Schmo:

Joe Shmoe (also spelled Joe Schmoe and Joe Schmo), meaning "Joe Anybody", or no one in particular, is a commonly used fictional name in American English. Adding an "Shm" to the beginning of a word is meant to diminish, negate, or dismiss an argument (for instance, "Rain, shmain, we've got a game to play"). It can also indicate that the speaker is being ironic or sarcastic. This process was adapted in English from the use of the "schm" prefix in Yiddish to dismiss something; as in, "Fancy, schmancy" (thus denying the claim that something is fancy). While "schmo" ("schmoo", "schmoe") is thought by some linguists to be a clipping of Yiddish.

If the home appreciates 7% per year, it will be worth approximately 1,534,947 dollars in 8 years. This can be calculated by multiplying the initial value of the home (800,000) by (1 + 0.07)^8.

You can also use the following formula:

Final Value = Initial Value x (1 + rate)^Years

The final value would be 1,534,947.20

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Answer:

x=2.5 and y=-1

Step-by-step explanation:

Firstly we have to state the formula to avoid making mistakes when calculating the points.

So we use the midpoint formula to be able to calculate; midpoint=(x1+x2 , y1+y2)

2 2

So when calculating x we are goin to take the coordinates A(-4,5) and C(9,y)

then we substitute into the formula accordingly so since x will be the midpoint calculation we will say, (-4+9) =2.5 meaning x = 2.5

2

Next, inorder to find y we will ...

5+y=2 and then we will have to get rid of the

2

denominator by multiplying the denominator to both sides of the equals sign. The 2 will cancel each other out then 2×2 =4 an equation will be formed ; 5+y=4 work it out then it will bring you to y= -1 as the answer

Answer:

mPR = (-3.5, 0.5)

mQR= (-1,-0.5)

Step-by-step explanation:

Answer: One way to find the total number of handshakes is to use a table of values to track the number of handshakes as the number of people in the meeting increases.

Number of People | Number of Handshakes

1 | 0

2 | 1

3 | 3

4 | 6

5 | 10

6 | 15

7 | 21

8 | 28

9 | 36

10 | 45

11 | 55

12 | 66

13 | 78

14 | 91

We can use the formula for the triangular number (n*(n-1))/2 where n is the number of people in the meeting.

So, total handshakes (14*13)/2 = 91

Step-by-step explanation: