What is the range of the following relation?
{(5,0), (6, -1), (1, 4), (0,5), (2,3)}
​

The resulting equation after substituting [tex]\( y = 4x \)[/tex] into [tex]\( x^2 + y^2 = 81 \)[/tex] is [tex]\( x^2 = \frac{81}{17} \)[/tex]

Let's isolate the variable [tex]\( y \)[/tex] in the first equation [tex]\( 3y = 12x \)[/tex]:

Divide both sides by 3 to solve for [tex]\( y \)[/tex]:

[tex]\[ y = 4x \][/tex]

Now that we have an expression for [tex]\( y \)[/tex], substitute it into the second equation [tex]\( x^2 + y^2 = 81 \)[/tex]:

[tex]\[ x^2 + (4x)^2 = 81 \][/tex]

Now simplify the equation:

[tex]\[ x^2 + 16x^2 = 81 \][/tex]

Combine like terms:

[tex]\[ 17x^2 = 81 \][/tex]

Divide both sides by 17 to solve for [tex]\( x^2 \)[/tex]:

[tex]\[ x^2 = \frac{81}{17} \][/tex]

So, the resulting equation after substituting [tex]\( y = 4x \)[/tex] into [tex]\( x^2 + y^2 = 81 \)[/tex] is [tex]\( x^2 = \frac{81}{17} \)[/tex].

The official formula is 2B+ Ph

where B is the area of a base of the prism, P is the perimeter of a base, and h is the height of the prism (distance between the two bases)

However, length x width x height can also be used

Answer:

D. 11/20

Step-by-step explanation:

7, 8, and 9 represent late flights.  We want to count how many of the 20 trials have at least two of these digits.  Counting, we find that 11 of the 20 have at least two of these digits.

D. 11/20

Answer:

y=5/7   x=31/7

Step-by-step explanation:

Make the x values the opposite of each other:

-2(x+5y=8)

-2x-10y=-16

2x+3y=9

Combine like terms and solve for y:

-7y=-5

y=5/7

Plug y in to find x.

x+5(5/7)=8

x+25/7=8

56/7-25/7=x

x=31/7

Answer:

[tex]\large\boxed{\left(3x^2y\right)^3=27x^6y^3}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\\left(3x^2y\right)^3=3^3(x^2)^3y^3=27x^6y^3[/tex]

For this case we must find the inverse of the following function:[tex]f (x) = 4x[/tex]

We follow the steps below:

We change f(x) to y:

[tex]y = 4x[/tex]

We exchange the variables:

[tex]x = 4y[/tex]

We solve for and:

[tex]4y = x[/tex]

We divide between 4 on both sides of the equation:

[tex]y = \frac {x} {4}[/tex]

then y  by [tex]f ^ {-1} (x):[/tex]

[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]

ANswer:

[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]

Answer:

c

Step-by-step explanation:

There are 6 red and 2 black balls.

The total number of balls = 2 + 6 = 8

The probability of drawing a black ball first is 2/8 = 1/4

The probability of drawing a red ball second is 6/7

P(black, red)=1/4 * 6/7 = 6/28 = 3/14

C

Answer:

It could be anywhere from eight to 15 members.

Step-by-step explanation:

Answer:

A. Count the members on each team

   Hurdles  = ⅜ × 40 = 3 × 5 = 15

Long jump = ⅘ × 40 = 4 × 8  = 32

Let's look at the two extremes.

B. Most people will compete in only one event

Then the teams will overlap by seven members (Figure 1).

C. All those in Hurdles compete in the Long Jump

Then 15 members will compete in both Hurdles and Long Jump (Figure 2).

Answer:

12 do both hurdles and long jump

Step-by-step explanation:

3/8 of the team does hurdles, so that number is 3/8·40 = 15.

Of those 15, 4/5 do long jump, so there are ...

4/5·15 = 12 . . . hurdlers who do long jump

Answer:

Step-by-step explanation:

10^9 x 0.007

e 95,970 l dont know any work just looked it up sorry

[tex]\bf y=2x+b~~\hspace{8em} (\stackrel{x}{-1},\stackrel{y}{0})~\hspace{8em} 0=2(-1)+b \\\\\\ 0=-2+b\implies 2=b[/tex]

To find the value of b plug in the point (-1,0) into the known part of the equation ( y = 2x + b ) and solve for b

0 = 2(-1) + b

0 = -2 + b

To isolate b add 2 to both sides (addition of 2 will make -2 zero and cancel it from the right side and bring it to the left)

0 + 2 = (-2 + 2) + b

2 = 0 + b

2 = b <------------------------B. 2

Hope this helped!

3.14 • 3 I think I hope this is right and helps

The area of circle in inches be: 3.14* [tex](3)^{2}[/tex]

The area of a circle is pi times the radius squared (A = π r²).

As it is known that the triangle in inscribed under the circle.

The diameter of the circle will be = 6 inches (hypotenuse of triangle)

                                             radius = 3 inches

So, Area of circle= π[tex]r^{2}[/tex]

                            = 3.14* 3 * 3

                            = 3.14* [tex](3)^{2}[/tex]

So, the area of circle is : 3.14* [tex](3)^{2}[/tex]

Learn more about area of circle here:

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Answer:

The answer is C

Explanation:

8x + 4 = 8x + 4

x = x

Answer:

A. DE

Step-by-step explanation:

The side opposite the angle with the largest measure is the longest

<F has a measure of 72, so it is the largest angle and DE is opposite <F

Side DE is the longest

Answer:

kilograms

Step-by-step explanation:

Answer: 1

Step-by-step explanation: the cosine function oscillates between the values -1 to 1

The amplitude of this particular function is understood to be 1

The maximum value that a graph of y = cos(x) assumes is y = 1.

In a triangle, the cos function (or cosine function) is the ratio of the base side to the hypotenuse.

cos(0°) = 1

cos(30°) = √3/2

cos(45°) = 1/√2

cos(60°) =  1/2

cos(90°) = 0

Cosine function is a periodic function and the value repeat themselves at an interval of 2π. The maximum value the cosine function achieves is y=1. The graph of the function is shown below:

Learn more about trigonometry on:

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Answer:

There are 5 1/2 oranges altogether.

Step-by-step explanation:

The 2 and 3 in front of each fraction indicate that there are a total of 5 whole oranges altogether. Now we have to settle these fractions. the 1/4 and the 1/4 both have a common denominator so there is no need to find one. When the common denominator is found, we simply have to add the numberators on the top of the fraction. 1+1 is 2, and, since the denominator stays the same, we should get a total of 2/4. I am unsure as to whether you were asked to simplify your answer (if you weren't you could keep your answer like this), but if you were to simplify the answer, both the numerator and denominator of our total can be divided by 2, so when that is done, we have a simplified total of 1/2. Take that 1/2 of an orange and add it to our 5 whole oranges, and we should get our answer of 5 1/2 oranges in total.

27\1000 is your rational form.

To simplify (9/100)^3/2, cube 9/100 to get 729/1000000 and then take the square root, which simplifies to 3/100 in rational form.

To simplify (9/100)^3/2 in rational form, we first understand that the exponent 3/2 can be broken down into two steps: first cubing the number, then taking the square root. Cubing 9/100 gives us (9^3)/(100^3), or 729/1000000. Then, taking the square root of this result and multiplying by the convenient factor of 1 in the form of 100/100, we simplify to 3/100, which is the result in rational form.

Answer:

Step-by-step explanation:

Given is table as follows

1500 75

2800 73

3500 72

4500 70

5000 66

6000 63

8000 60

8500 60

9000 57

9500 55

r -0.98649651

We get correlation coefficient is negative and near -1

Hence there is a strong negative correlation.

Whenever x increases y decreases with almost constant slope.

Answer:

correlation coefficient of the data ---->strong negative linear correlation

interpretation of the correlation coefficient ----> -0.986

Step-by-step explanation:

Answer: ($2.50k) + $5

The distance you can ride is 6 kilometers.

($2.50 x 6) + $5 = $20

Answer:

[tex]2.50d+5\leq 20[/tex]

Step-by-step explanation:

Let d represent distance in kilometers.

We have been given that a taxi ride costs $2.50 per kilometer, so the cost of d kilometers would be [tex]2.50d[/tex] dollars.

We are also told that ride costs a fixed charge of $5, so total cost of d kilometers would be [tex]2.50d+5[/tex] dollars.

You have $20 to spend on taxi fare, so the total cost of riding d kilometers should be less than or equal to 20.

We can represent this information in an inequality as:

[tex]2.50d+5\leq 20[/tex]

Therefore, our required inequality would be [tex]2.50d+5\leq 20[/tex].

Answer:

Answer in attachment

Step-by-step explanation:

Answer:

Boys = 150

Girls = 315

Total Boys and Girls 465

Step-by-step explanation:

We call x the number of boys and we call y the number of girls.

So we have to find the total number of children

We know that

[tex]\frac{2}{7}y = \frac{3}{5}x[/tex]

[tex]x =y-165[/tex]

Now we substitute the second equation in the first and solve for y.

[tex]\frac{2}{7}y = \frac{3}{5}(y-165)[/tex]

[tex]\frac{2}{7}y = \frac{3}{5}y-99\\\\99 = \frac{3}{5}y-\frac{2}{7}y\\\\\frac{11}{35}y=99\\\\y = 315\\[/tex]

Now we find x.

[tex]x = 315-165 = 150\\\\x = 150[/tex]

Finally we have that:

Boys = 150

Girls = 315

Total Boys and Girls 465

The equation [tex]\(525=25(x-2)\)[/tex] helps answer option (C): How many members are in the band when no one is absent?

let's break it down step by step:

1. Define variables: Let [tex]\(x\)[/tex] represent the total number of members in the band.

2. Calculate members present: Since 2 members were absent, the number of members present is [tex]\(x - 2\).[/tex]

3. Programs folded by each member: We know that each present member folded 25 programs.

4. Total programs folded: To find the total number of programs folded, we multiply the number of present members by the number of programs each member folded. So, the total programs folded is \(25(x-2)\).

5. Set up equation: We are given that the total number of programs folded is 525. So, we set up the equation:

[tex]\[ 25(x-2) = 525 \][/tex]

6. Solve for [tex]\(x\):[/tex] By solving this equation, we can find the value of [tex]\(x\),[/tex]which represents the total number of members in the band when no one is absent.

So, the equation [tex]\(525=25(x-2)\)[/tex] helps us determine how many members are in the band when no one is absent. This aligns with option (C).

Complete Question:

Answer:

135

Step-by-step explanation:

[tex]\frac{5}{9}\times243=\frac{5\times243}{9}=

\frac{1250}{9}=\boxed{135}

[/tex]

Answer:

Step-by-step Answer:

This question expects a choice out of the four answers.

We can reason it as follows:

If the angles had been 90-45-45, then the triangle would be isosceles with each leg equal to 14, and the area would be 14*14/2 =  192/2 = 96.

Now one of the base angles has been reduced from 45 to 35 (still assuming a right triangle), the other leg can only diminish, and therefore the area is LESS than 96.

We also realize that changing from 90 to 95 degrees will not change the area by a whole lot, so we are looking for a number LESS than 96, the only of which is 72.8.

The exact value, by solving the triangle,

the opposite side of 35 degrees is 10.483 (using sine rule), and

the area is 73.378 (using A=(1/2)a*b*sin(C), not far from 72.8, if we are looking for the exact value.

Answer:

9/24 or 3/8

Step-by-step explanation:

Spinner gives a 4.

Suppose the 4 shows up on the spinner.

There is a 1/4 chance of that happening.

Suppose the cube does not have a 4 on the top face. There is a 5/6 chance of that happening

Together the probability is 1/4 * 5/6 = 5/24

The cube gives a 4

The cube gives a four 1/6 of the time.

The spinner cannot give a 4, which happens 3/4 of the time.

Together the probability is 1/6 * 3/4 = 3/24

Both Cube and Spinner give a 4

The cube will give a four 1/6 of the time

The spinner gives a four 1/4 of the time.

1/6*1/4 = 1/24

Total

1/24 + 3/24 + 5/24 = 9/24 = 3/8

What happens to the rest?

The answer is neither gives a four.

Spinner 3/4

Die: 5/6

Combined amount = 3/4 * 5/6 = 15/24

There is a quick way to do this.

1 - no fours =

1 - 15/24 = 9/24

It’s -125 and you welcome

I think the answer is b) C=.10x+25

Answer: B. C = .10x + 25

Step-by-step explanation: If the original equation uses .05, and that equation is .05x + 25 = C, then increasing it to .10 would mean that the new equation is .10x + 25.

Answer:

B. No solution

Step-by-step explanation:

y = 3x+9

y = 3x-7

Set the two equations equal since they are both equal to y

3x+9 = 3x-7

Subtract 3x from each side

3x+9-3x = 3x-7-3x

9 = -7

This is never true, so there are no solutions

Answer: on edge its one and then after that 0,-3

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

x – 2 = 7

Isolate the variable, x.

x-2+2=7+2

x=9

x=9

Answer: [tex]x=9[/tex]

Step-by-step explanation:

Given the equation [tex]x-2=7[/tex], you need solve for the variable "x", to do this, you need to remember the Addition property of equality, which states that:

[tex]If\ a=b,\ then\ a+c=b+c[/tex]

Therefore, add 2 to both sides of the equation to calculate the value of the variable "x", then you get the following result:

[tex]x-2+(2)=7+(2)[/tex]

[tex]x=9[/tex]