The two shapes on the grid below are similar.
What is the ratio of side x to side y?

Should this not have measurements?

Answer:

3rd option: 32/24

Step-by-step explanation:

8/6 = 4/3

1st option: Now let's change the denominator to 24:

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

2nd option: Now let's change the numerator to 24:

4/3 ==> 24/?

4/3 =

4*6 / 3*6 = 24/18, not 24/32

24/32 = 3/4, not 4/3 ==> don't get confused by this

3rd option: 32/24 is correct [Look at the explanation for 1st option]

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

Hence, the 3rd option is correct.

The indicated operation 1/3 x 6/7 can be performed as 2/7.

The concept that will be used in this operation is the multiplication operation.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream. By multiplying their outputs, you can multiply one function by another.

Given operation is  1/3 x 6/7

1/3 x 6/7

=[ (1 x 6)/(3 x 7) ]

= (6/21)

= 2/7

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check the correct question:

Perform the indicated operation. 1/3 x 6/7

The opportunity cost of a concert is 2 movies.

Opportunity cost is the cost of the next best option a decision maker forgoes when he chooses one option over other options.

If Anna decides to go to the concert, she forgoes the opportunity  of going to the movies. On the other hand, if Anna decides to go to the movies, she forgoes the opportunity of going to the cinema.

Opportunity cost of a concert = number of movies she can go to / number of concerts she can go to

Opportunity cost of a concert = 70 / 35 = 2

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The cultivation of maize affected the settlement patterns in the American Southwest and present-day Mexico as B. It caused Native Americans in the area to develop permanent settlements supported by farming and irrigation system

The cultivation of maize had a significant impact on settlement patterns in the American Southwest and present-day Mexico. In the American Southwest, the cultivation of maize, along with other crops such as beans and squash, allowed for the development of more permanent settlements as people were able to rely on a stable food supply. This, in turn, led to the growth of larger, more complex societies and the development of elaborate systems of trade and exchange.

In present-day Mexico, the cultivation of maize played a central role in the development of complex societies such as the Olmec, Maya, and Aztec. These societies built sophisticated systems of agriculture, including terracing, irrigation, and crop rotation, which allowed them to support large populations and build elaborate cities. The cultivation of maize was also closely tied to the religious and cultural practices of these societies, and it played a central role in their economies and social systems.

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The solution to the equation 9(6^3x) - 13(6^3x) + 4(6^3x) = 0 is x = 0.

Generally, To solve the equation we try to get the values to be coherent by writing as

9(6^3x)-13*(6^3x)+4*(6^3x)=0

Therefore we solve the coefficients of the solution

To solve this equation, we can first distribute the constants in front of the parentheses:

9(6^3x) - 13(6^3x) + 4(6^3x) = 0

This simplifies to:

(9 - 13 + 4)(6^3x) = 0

Then, we can simplify the expression in the parentheses:

(0)(6^3x) = 0

This means that either (0) = 0 or (6^3x) = 0.

The second case is not possible, because the base of an exponent can't be zero. So, the only solution to this equation is x = 0.

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The Boolean expression A >= B is equivalent to  !(A < B) (option A)

To simplify a Boolean expression, use De Morgan's Law.

De Morgan's Law is used to simplify or find the equivalent of a negation of compound expressions.

The principle is:

NOT (A AND B) is equivalent to (NOT A) OR (NOT B)

NOT (A OR B) is equivalent to (NOT A) AND (NOT B)

When the expression involves >, <, = signs, then to simplify the expression, move the not and flip the sign.

! is the symbol of negation or NOT.

Hence,

! (>) becomes <=

! (<) becomes >=

Here are some examples:

!(A > B) is equivalent to (A <= B)

!(A <= B) is equivalent to (A > B)

!(A >= B) is equivalent to (A < B)

!(A == B) is equivalent to (A != B)

!(A != B) is equivalent to (A == B)

!(A < B) is equivalent to (A >= B)

From the above list we can conclude that A >= B is equivalent to !(A < B) (option A)

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Answer:

C (2)

Step-by-step explanation:

• √32 = 4√2 ( bc √32 = √16×2 = √16×√2 = 4×√2 )

• √8 = 2√2 ( bc √8 = √4×2 = √4×√2 = 2×√2 )

So √32 ÷ √8 is equal to 4√2 ÷ 2√2

And there √2 cancels for both

So what you're left with is 4 ÷ 2

And 4÷2 = 2

We have prepared the table and drawn the graph.

What is a graph of a function?

A graph of a function is a visual representation of the relationship between the inputs (x-coordinates) and the outputs (y-coordinates) of a function. The inputs are typically represented on the x-axis and the outputs are represented on the y-axis.

Table:

x (days) y (number of cells)

0        1000

1        2000

2       4000

Graph:

The graph would be a line graph with x-axis showing the day passed and y-axis showing the number of bacteria cells,

The point (0,1000) would be plotted on the graph, representing the initial number of bacteria cells on the first day.

The point (1,2000) would be plotted on the graph, representing the second day and the number of bacteria cells.

The point (2,4000) would be plotted on the graph, representing the third day and the number of bacteria cells.

The graph would be a upward sloping line, representing the growth of bacteria cells.

Hence we have prepared the table and drawn the graph.

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Answer:

105

Step-by-step explanation:

y=kx where k is a constant

When y=15 and x=3

15=k3

k=15/3

k=5

Therefore y=5x

So, when x=21

y=21x5

=105

Please mark me brainliest

==============================================

Work Shown:

C = 2pi*r

9pi = 2pi*r

r = (9pi)/(2pi)

r = 4.5

A = pi*r^2

A = pi*(4.5)^2

A = 20.25pi  square cm

------------------

Explanation:

The first portion involves using the circumference C = 9pi to determine the radius r. The circumference is the perimeter around the circle.

Once we know that r = 4.5 cm, we then plug that into the area of a circle formula A = pi*r^2

Side notes:

Answer:

30%

Step-by-step explanation:

(13-10) / 10  * 100% = 30 %

Answer:

Step-by-step explanation:

pass it then

Answer:

13. x=4

14. x=8

Step-by-step explanation:

We know that these are both isosceles triangle because the two base angles are the same on #13, and the two sides are the congruent on #14. So all we need to do is make equations of equivalence. So #13 9x-8=28 and #14 11x-18=70. Look at the work shown in the image and follow those steps.

-Hope this helped & Happy New Year!

The only expression that can be solved using product rule of exponents is; (11²a⁻⁵)(11a⁹b⁷) / 5²

The Product Rule for Exponents states that to find the product of two numbers with the same base, add the exponents.

For example : a² * a³ = a²⁺³

1) We are given the exponential expression as; (4⁵ a⁰)(7²b⁻⁶)

From this expression, the numerator and denominator don't have any same base and as such we can say we cannot use product rule for it.

2) We are given the exponential expression as; (8⁵a⁻⁴)(b⁷c⁻⁵)

From this expression, the numerator and denominator don't have any same base and as such we can say we cannot use product rule for it.

3) We are given the exponential expression as; a⁻⁷b¹⁰ / c⁷ d¹⁴ . 15

From this expression, the numerator and denominator don't have any same base and as such we can say we cannot use product rule for it.

4) We are given the exponential expression as; (11²a⁻⁵)(11a⁹b⁷) / 5²

Using product rule of exponents, we have;

(111/25) * (a⁻⁵⁺⁹) * b⁷

= (111/25)a⁴b⁷

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If each term in the sum a1+a2+a3...+an is  7 and the sum equals 350, C: 40 would be equal to n.

In equation form, it is:  

                  7s +  77t = 350

In this equation,

          s represents the number of 7's

          t represents the number of 77's

          thus, the number of terms i.e n = s + t =?

now solving the equation,

        7 (s + 11t) = 350

        7 (s + 11t) = 350

            s + 11t = 50

            s + 11t = 50

now, if  

       s=39     &      t =1  

then

         s + 11t = 50 -> 39 + 11 (1)  = 50

Since the number of terms n = s + t

        n = s + t

        n = 39 + 1

        n = 40

Hence, the if each term in the given sum is 7 which gives a total sum as 350, then number of terms in the given series is 40.

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Answer:

A

Step-by-step explanation:

For an ideal gas : PV=RT

And the internal energy of an ideal gas:

E

in

​

=

2

3

​

RT

E

in

​

=

2

3

​

PV

V

E

in

​

​

=

2

3

​

P

Energy density (E)=

2

3

​

P

P=2/3E

The Equations  is b/4 + 2= 8 and b = 24.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of expressions.

Mathematical statements called expressions must contain at least two phrases including numbers, variables, or both, and they must be joined by an operator.

Given Two more than the quotient of a number and 4 is 8,

Let number be b

b/4 + 2= 8

b/4 = 8 -2

b/4 = 6

b = 24

Hence, two more than the quotient of a number is 24.

Hence the equation for phrase is b/4 + 2= 8 and b = 24.

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If mr alvarez tells his students that next math test has 50 questions. he also says 20% will be word problems. The number of word problems that will be in the test is 10.

Using this formula to find the number of word problem

Number of word problem =Next math test problems × Percentage of word problem

Where:

Next math test problems = 50 problem

Percentage of word problem = 20% or .20

Let plug in the formula

Number of word problem  = 50 × .20

Number of word problem = 10 problem

Therefore we can conclude that the  number of word problem is 10 problem.

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The complete question is;

mr alvarez tells his students that next math test has 50 questions. he also says 20% will be word problems. the students want to know how may word problems will be in the test

Check the picture below.

The mean is 2, the missing data point must be 2 - 6 = -4. Therefore, the missing number of chicken nuggets is -4.

To find the mean of the data set, we need to add up all of the data points and divide by the number of data points. In this case, the sum of the data points is 1 + 3 + 0 + 6 = 10. Since there are 5 data points in total, the mean is 10 / 5 = 2.

Since the mean is 2, the missing data point must be 2 - 6 = -4. Therefore, the missing number of chicken nuggets is -4.

Mean is a type of average, which is a measure of central tendency. It is calculated by adding up a group of numbers and then dividing the sum by the number of numbers in the group. Mean is often referred to as the "arithmetic average".

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As per the given mean, the missing number of chicken nuggets is 5

The term mean in math is defined as the process of adding all numbers in the data set and then dividing by the number of values in the set.

Here we have given that the question assumes there are 5 people at the table.

And the number of nuggets are written as,

=> 1,3,0,6,and x.

Here x refers the missing number of chicken nuggets.

Then the equation is written as

=> 1 + 3 + 0 + 6 + x = 10 + x

Here we can multiply both sides by 5 to clear the denominator:

Then we have to isolate the x by subtracting 10 from both sides.

=> 10 + x - 10 = 15 - 10

Then the value of x is written as

=> x = 5

Therefore, the missing number of nuggets is 5.

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A child's ticket would cost $10 while and adult's ticket would cost $18.

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

5 is an example of a constant.

The expressions are;

3a + 4c = 94 ---- 1

2a + 3c = 66 ---- 2

Multiplying equation 1 by 2 and equation 2 by 3

6a + 8c = 188 ---- 3

6a + 9c = 198 ---- 4

--------------------------

     - c = - 10

therefore;

c = 10

Substituting c in equation 3

6a + 8(10) = 188

6a + 80 = 188

6a = 188 - 80

6a = 108

a = 18

Therefore, child's ticket costs $10 while and adult's ticket cost $18.

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a. The sum of 1/3+1/5= 8/15

b. The sum of 1/8+2/6 = 3/8

c. the sum of 8/9+11/12= 1 87/108

d. the sum of 1/7+5/8= 1 7/36

e. the sum of 1/4+2/4= 3/4

f. the sum of 1/2+3/9= 5/6

g. the sum of 1/10+1/4= 7/20

h. the sum of 3/11+11/12 = 1 25/132

Sum of fractions is the addition of fractions. This is obtained by by using the L.C.M of the denominator method.

a. 1/3 + 1/5 = (5+3)/15 = 8/15

b. 1/8+2/6 = (3+6)/24 = 9/24 = 3/8

c. 8/9 + 11/12 = (96+99)/108 = 195/108 = 1 87/108

d. 1/7+ 5/8 = (8+35)/56 = 43/36 = 1 7/36

e. 1/4+ 2/4 = (2+1)/4 = 3/4

f. 1/2 + 3/9 = (9+6)/18 = 15/18 = 5/6

g. 1/10+1/4 = (2+5)/20 = 7/20

h. 3/11+ 11/12 = (36+121)/132 = 157/132 = 1 25/132

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Completing the table with the appropriate percentage and decimals will be:

Fraction Decimal Percentage

1/4. 0.25. 25% of 1

1/10. 0.1. 10% of 1

3/4. 0.75. 75% of 1

1/5. 0.2. 20% of 1

3/2. 1.5. 150% of 1

7/5. 1.4. 140% of 1

It should be noted that based on the information, 0.1 will be 1/10. The percentage will be:

= 1/10 × 100

= 10%

0.1 to fraction will be:

= 1/10

The percentage for 1/5 will be:

= 1/5 × 100

= 20%

1/5 to decimal will be:

= 1/5

= 0.2

The decimal 1.5 will give 150%

The fraction for 1.5 will be:

= 1.5 / 1

= 15 / 10

= 3/2

Also 3/4 as percentage will be:

= 3/4 × 100

= 75%

75% to decimal will be:

= 75 / 100

= 0.75

140% to fraction will be:

= 140 / 100

= 7 / 5.

The decimal for 140% will be:

= 140 / 100

= 1.4

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the answer is D : 4

According to the problem statement, one side of the rectangle is of length 5 cm. The other side can have any length greater than 4 cm (since the area of the rectangle should be greater than 4 cm^2).

Let's call this other side "x".

We know that the area of a rectangle is given by the formula A = l*w, where l is the length and w is the width.

Therefore, we can write the equation: 5*x = A, where A is the area of the rectangle.

We can also say that the area of the square and the rectangle is equal to 4 cm^2.

If we call the side of the square "y", then we can write the equation: y^2 = 4 cm^2.

Solving for y, we get: y = 2 cm.

Therefore, the length of the rectangle that can be cut into a square and a rectangle of area 4 cm^2 is 5 cm - y = 5 cm - 2 cm = 3 cm.

So, there are 4 possible rectangles that can be cut into a square and a rectangle of area 4 cm^2: (5,3), (3,5), (6,4), and (4,6).

So the answer is D : 4

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In the replacement set, 9 is the solution to this equation 3 (n+7) = 48.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 3 (n + 7) = 48

And, Replacement set: {8, 9, 10}

Now, We can solve the expression as;

⇒ 3 (n + 7) = 48

Divide by 3,

⇒ n + 7 = 48/3

⇒ n + 7 = 16

Subtract 7, we get;

⇒ n = 16 - 7

⇒ n = 9

Thus, The solution of the equation is, 9.

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Answer: its 2

Step-by-step explanation:

the solutions to the system of inequalities are (1,1) and (-2,3).

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

2х + 3у > 2

3x + 5y > 1

for (1,1):

2+3 > 2 (true)

3+5 > 1 (true)

for (-2,-1)

-4-3 > 2 (false)

for (-2,3):

-4+9 >2 (true)

-6+15>1 (true)

for (7,-4):

14-12>2(false)

Hence, the solutions to the system of inequalities are (1,1) and (-2,3).

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The equation of a circle with a center at (4,−9) and a radius of 5 is

(x−4)^2+(y+9)^2=25. The correct Option C.

A circle is a set of all points which are equally spaced from a fixed point in a plane. The fixed point is called the center of the circle. The distance between the center and any point on the circumference is called the radius of the circle.

The equation of a circle with center (h, k) and radius r units is

(x−h)^2+(y−k)^2=r^2 .

where h = 4

k = -9

r = 5

The equation of the circle

(x−4)^2+(y−(-9))^2 = 5^2

The equation of the circle

(x−4)^2+(y+9)^2 = 25

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