the following group of equations represents which type of system {x^2 + y^2 = 9 x^2/16 + y^2/9 =1

Given data:

The given figure is shown.

For figure A, the expression for sin(A) is,

Thus, the value of angle A is 23 degrees.

(b)

The vaue of tan(A) is,

Thus, the value of A is 49 degrees.

(c)

The value of cos(A) is,

Thus, the value of A is 53 degrees.

(d)

The value of tan(A) is,

Thus, the measurement of angle A is 35 degrees.

Question 16

[tex](f(x), g(x))=x^2, (x-9)[/tex]

Question 17

[tex](f(x), g(x))=\sqrt{x}, 9+\sqrt{x}[/tex]

The values for first question are f(x) = x², g(x) = (x - 9) and for second question f(x) = √x, g(x) = 9 + √x.

A function may be defined as an expression in which for one value of input variable x there is only one value of output variable y. The input variable is called independent variable and output variable is called dependent variable. A composite function is the one which is written as a combination of two function. For two given functions f(x) and g(x) the composite functions are f(g(x)) and g(f(x)). In the first question the composite function is F(x) = (x - 9)². the parent functions will be f(x) = x² and g(x) = (x - 9).

in the second question the composite function is H(x) = √(9 + √x). The parent functions will be f(x) = √x and g(x) = 9 + √x.

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The bananas will last 2 days at the zoo (found by division).

According to the question,

We have the following information:

The elephants at the zoo eat [tex]3\frac{1}{6}[/tex] buckets of bananas each day. The zookeeper bought [tex]6\frac{1}{3}[/tex] buckets of bananas.

Now, first we will find the number of days taken in eating 1 bucket of bananas.

[tex]3\frac{1}{6}[/tex] buckets = 1 day

Now, we will convert this mixed fraction into simple fraction.

19/6 buckets = 1 day

1 bucket = 1/(19/6) days

1 bucket = 6/19 days

Now, we have the total number of buckets as [tex]6\frac{1}{3}[/tex].

Now, after converting this mixed fraction, we have:

19/3 buckets

1 bucket =  6/19 days

19/3 buckets = (6/19)*(19/3)

19/3 buckets = 2 days

2 is a whole number.

Hence, the given buckets of bananas will last 2 days.

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Answer:

it would be 600

Answer:

72.7% to nearest 10th percent would be 73%!

Step-by-step explanation:

Hope it helps! =D

We know that the mean is 80, the median is 90, and the mode is 70. This means that the majority of students got an 80 on the test.

However, the median is 90, which means half of the class is below 90 where Tom's grade is placed.

(120 + 10x) sq. feet or 10(12+x) sq. feet will be the combined area of the two rooms.

the given dimensions of the living room are given as follows,

length =12

width/breadth =10

thus the area of the living room will be,

length x breadth, i.e.

=12 x 10

=120 sq. feet

the given dimensions of the dining room are given as follows,

length= x

width/breadth=10

thus the area of the dining room can be calculated as

length x breadth

=10x sq. feet

Now, to calculate the combined area of both the rooms, we have to add the area of the dining room and the area of the living room,

that is,

(120 + 10x) sq. feet

What is area?

The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

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The equation of the line that passes through the point (8, 0) is parallel to the line x - 4y = 20 is 1/4x - y = 2

Given,

The equation of the line: x - 4y = 20

The points which the line passes through, (x₁, y₁) = (8, 0)

We have to find the equation of the line parallel to the given line.

The formula for the slope intercept form:

(y - y₁) = m(x - x₁)

m is the slope of the line.

Lets find the slope of the line given.

x - 4y = 20

x = 20 + 4y

x - 20 = 4y

y = (x - 20) / 4

y = 1/4x - 5

Here, slope of the line is 1/4

Now, substitute the slope of the line and (x₁, y₁) in the slope intercept formula to get the equation of line parallel to the given line

(y - y₁) = m(x - x₁)

(y - 0) = 1/4(x - 8)

y = 1/4x - 8/4

y = 1/4x - 2

1/4x - y = 2

Therefore,

The equation of the line that passes through the point (8, 0) is parallel to the line x - 4y = 20 is 1/4x - y = 2

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The slope of g(x) is -3 and the g(x) is reflected across the x-axis

The table of values is

x    f(x) = x   g(x) = -3x

0        0              0

1          1              -3

2         2             -6

From the question, we have the definition of the functions to be

f(x) = x and g(x) = -3x

Also, we have the following x values from the blank table of values

x = 0, 1 and 2

Next, we calculate f(x) and g(x) at these x values

For the function f(x), the values are

f(0) = 0, f(1) = 1 and f(2) = 2

For the function g(x), the values are

g(0) = 0, g(1) = -3 and g(2) = -6

The next step is to calculate the slope and the transformation

Recall that

f(x) = x and g(x) = -3x

Generally, the form of a linear equation is

y = mx

Where m is the slope

This means that the slope of g(x) is -3

Lastly, the negative sign in g(x) = -3x implies that the graph is reflected across the x-axis or the y-axis

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A mixed fraction exists one that is represented by both its quotient and remainder.

Product of -2 1/2 and -3 1/3 is  [tex]8\frac{1}{3}[/tex].

Product of 1 1/3 and -3 1/2  is [tex]-5\frac{5}{6}[/tex] .

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction exists, for example, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

Product of -2 1/2 and -3 1/3 is  [tex]8\frac{1}{3}[/tex].

Product of 1 1/3 and -3 1/2  is [tex]-5\frac{5}{6}[/tex] .

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The point-slope form of the equation of a line is given to be:

where

The equation of the line is given to be:

This means that the slope is 5/2.

We know that

• Anne could run a mile in ,m, minutes.

• Now, time has decreased by 16%.

The following expressions represent the number of minutes She uses to run a mile now.

This expression represents 16% of m in fraction form.

This expressed represents 16% of m in decimal form.

Both expressions are equivalent because they refer to the same percentage 16%. That is 0.16 and 16/100 are equivalent to 16%

Answer:

54 inches

Step-by-step explanation:

There are 12 inches in 1 foot

12in = 1ft

There are 4 feet and 6 inches

If you break it down its 4×12

4 × 12 = 48

Add 6 inches

48 + 6 = 54

Therefore the answer would be 54 inches

Your welcome <3

Answer:
The sum of a sequence is known as a series. Thus means a harmonic series is infinite with no limit

We need to count the number of zeros in a number multiplied by a power of 10. Which is shown below:

The power of 10 will add a certain number of zeros, which is equal to the expoent of the power, in this case it's 7, but there is one more zero which is present in the "40", therefore the total number of zeros will be 8.

Using the conversion factors, 454 grams of butter is used by the chef each day.

So, grams of butter used each day:

Then,

Therefore, using the conversion factors, 454 grams of butter is used by the chef each day.

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The correct question is given below:

A chef at a restaurant uses 19 pounds of butter each day. About how many grams of butter does the chef use each day? Use the conversion factors

Answer:

(3 1/3)·(y + (1 1/8)) = 6 11/12

(9/3 + 1/3)·(y + (8/8 + 1/8)) = 72/12 + 11/12

10/3·(y + 9/8) = 83/12

y + 9/8 = 83/12·3/10

y + 9/8 = 83/4·1/10

y + 9/8 = 83/40

y = 83/40 - 9/8

y = 83/40 - 45/40

y = 38/40

y = 19/20

The solution is written down, and the graph is drawb below

The simplified form of the expression is a³ which is calculated by using the properties of exponents.

Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as bⁿ. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to repeated base multiplication where n is a positive integer; so, bⁿ is the result of multiplying n bases.

Typically, a superscript to the right of the base indicates the exponent. Then, bⁿ is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, most succinctly, "b to the nth."

The given expression is a³(2a² + 4bc⁴)⁰.

From the properties of exponents we know that:

a⁰ = 1

Therefore the value of the part of the expression (2a² + 4bc⁴)⁰ is 1

Therefore the total value of the exponential expression is a³

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The most appropriate choice for equation of line in slope intercept form x intercept = 90

y intercept = 60

Domain = {0, 3, 6, 9, ....., 90}

Range = {0 , 2, 4,...., 88}

What is equation of line in slope intercept form?

Equation of line in slope intercept form is written as y = mx + c, where m is the slope of the line and c is the y intercept of the line.

The distance from origin to the point where the line cuts the x axis is the x intercept and the distance of origin to the point where the line cuts the y axis is the y intercept.

Here,

Selling price of one painting = $30

Selling price of x paintings = $30x

Selling price of y sculptures = $45

Selling price of y sculptures = $45y

Total revenue = $(30x + 45y)

By the problem,

                         30x + 45y = 2700

a)

For x intercept, y = 0

30x = 2700

x = [tex]\frac{2700}{30}[/tex]

x = 90

x intercept is $90

For y intercept, x = 0

45 y = 2700

y = [tex]\frac{2700}{45}[/tex]

y = 60

y intercept is 60

b)

In 30x + 45y = 2700

Since x represents the number of paintings sold and y represents the number of sculptures sold, then x and y has to be integers.

If x = 0 , y = [tex]\frac{2700}{45}[/tex] = 60

If x = 3, y = [tex]\frac{2700 -90}{45} = 58[/tex]

If x = 6, y =  [tex]\frac{2700 -180}{45} = 56[/tex]

If x = 9, y =  [tex]\frac{2700 -270}{45} = 54[/tex]

_______________________________

If x = 90 , y =  [tex]\frac{2700 -2700}{45} = 0[/tex]

Domain is the values of x

Domain = {0, 3, 6, 9, ....., 90}

Range is the values of y

Range = {0 , 2, 4,...., 88}

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Complete Question

The diagram with the questions have been attached below

We have to write 8.94 in fractional notation without simplification.

For decimal values, we can convert them to fractions taking into account the number of decimals they have.

In this case, 8.94 has two decimals. Then, we can multiply it by a fraction 100/100, as 100 has two zeros.

Then, we will get:

This works beacuse we multiply the number 8.94 by a number that will make it become an integer (without decimals). To keep the value of the fraction equal to the decimal number, we have to divide by the same factor (in this case, 100).

This fraction can be simplified.

Answer: the fractional notation, without simplification, of 8.94 is 894/100.

[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]

To answer this question, we will use the next table (obtained from the Question Tab):

City -------- Number of restaurants

Carlsbad 489

Potter Valley 261

Little Heath 282

Edgbaston 216

Barrow 317

If we want to know how many more restaurants there are in Carlsbad than in Barrow, we need to subtract the number of restaurants in Barrow from Carlsbad as follows:

From the table, we have that in Carlsbad there are 489 restaurants, while there are 317 in Barrow.

We can check this as follows:

In summary, we can say that there are 172 more restaurants in Carlsbad than in Barrow.

When we have a function and want to evalueate it for some "x", we just substitute every "x" with the value in parenthesis. So, to evaluate f(a + 2), we have x = a + 2, so we need to substitute every "x" in the function with a + 2:

Now, to simplify, we first need to use the distributive property on the second parenthesis and evaluate the binomial in the first:

Now, we group the like-terms and add them:

For yhe other one, Let's do each term and then make the substraction:

So:

Let's begin by identifying key information given to us:

The population is represented by the equation:

We will compare the equation for the population with the general exponential growth equation, we have:

Comparing, we have:

Therefore, the rate of change is 7%. Hence, C is the answer

Step-by-step explanation:

to find 24 times 17 i multiply 20 times 17 and add it to 4 times 17?

Yes, that is one way of doing it:

Your method:

20 × 17 = 340

4 × 17 = 68

340 + 68 = 408

The typical way of solving is:

24 × 17 = 408

Both return the correct answer.

Answer:

24 times 17 = 408

But if you multiply:

20 times 17 = 340 Then add that to:

4 times 17 = 68

340 + 68 = 408

You would get the same answer so this is correct!

Step-by-step explanation:

Hope it helps! =D

The product of  (7) (-16)(-7) (-1) is - 784 by using simple multiplication.

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. The symbols for multiplication are a cross (x), an asterisk (*), and dot (.). You seem to utilize the cross a lot when you write in your notebooks. In both algebra and computer languages, the asterisk and dot are symbols (higher mathematics).

7 × -16 = -112

-112 × -7 = 784

784 × -1 = -784

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Hi i hope this helps you out