how to determine proofs

Answer:

y = 3x + 7

Step-by-step explanation:

When lines are parallel, the slope is the same but the y-intercept is not

The blue line is the graph for y = 3x + 2

The slope for the line is 3/1

So the slope for the line containing (-2,1) should be 3/1

I plotted (-2,1) and used the Rise/Sun (3/1) to find a point on the y-axis, the teal point.

I graphed the line in yellow

In y=mx + b, b = 7, and mx = 3x

So the equation is y = 3x + 7

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

48

Step-by-step explanation:

The given parameters are;

The activities in which the students of the school participate = 1) Debate, 2) Music, and 3) Community services

The number of students that do all three activities = 3

The number of students that do two or more activities = 21

The number of the students that participate in music = Half of the students

The ratio of the students that take part in debate, music, and community service = 5 : 4 : 3

Let x represent a common number factor of participants in each of the given three activities, we have;

5·x participate in debate, A

4·x participate in music, B

3·x participate in community service, C

We get;

The sum of the students in the school = A∪B∪C = A + B + C - A∩B - A∩C - B∩C + A∩B∩C

Given that the number of students that do two or ore activities = 21, we have;

(A∩B)∪(A∩C)∪(B∩C) = 21

However, we have;

(A∩B)∪(A∩C)∪(B∩C) = (A∩B) + (A∩C) + (B∩C) - A∩B∩C - B∩A∩C - C∩B∩A + A∩B∩C

∴ 21 = (A∩B) + (A∩C) + (B∩C) - 3 - 3 - 3 + 3

(A∩B) + (A∩C) + (B∩C) = 21 + 3 + 3 + 3 - 3 = 21 + 6 = 27

∴ -(A∩B) - (A∩C) - (B∩C) = -27

Therefore;

A + B + C - A∩B - A∩C - B∩C + A∩B∩C = 5·x + 4·x + 3·x - 27 + 3

5·x + 4·x + 3·x - 27 + 3 = 12·x - 24

The total number of students = A∪B∪C = 12·x - 24

The number of students participating in music, B = 4·x = Half the total number of students = (12·x - 24)/2

∴ 4·x = (12·x - 24)/2

8·x = 12·x - 24

12·x - 8·x = 24

4·x = 24

x = 24/4 = 6

The total number of students at the school = 12·x - 24 = 12 × 6 - 24 = 48

Answer:

] 14/3 ; ♾ [

Step-by-step explanation:

3x-5>9

3x>9+5

3x>14

x>14/3

wich make it ] 14/3 ; ♾ [

when three times a certain number is subtracted from 5 the result is more than 9 find the number.

Let us assume :

The number be x

Data :

A number is 3 times = 3x

Subtracted from 5

The result = 9

Henceforth, the equation we got is :

Transposing 9 to the other side

Hence, the value of x is 14/3 respectively

the students took math and physics = 55

Answer:

x = 9.4m

Hope this helps...Have a good day!!

Answer:

x=35

Step-by-step explanation:

For a polygon with n sides, the sum of its interior angles is equal to

(n-2) * 180

Here, there are 6 sides, so the sum of this polygon's interior angles is equal to (6-2)* 180 = 720

Therefore, the sum of the interior angles is 720. We can add them up to get

(4x-5) + 117 + (3x-3) + (3x+6) + 118 + 4x-3

= 14x +230 = 720

subtract 230 from both sides to isolate the x and its coefficint

14x = 490

divide both sides by 14 to get x

x=35

By using the corresponding angles theorem we can see that (6x - 5)° and (x - 25)° are supplementary angles, so they add up to 180°.

This means that:

(6x - 5) + (x - 25) = 180

7x - 30 = 180

7x = 210

x = 30

If you want to find the exact values of the angles, just plug x = 30 into the angle values! :)

Answer:

The length of the school garden is 4  97/132 feet

Step-by-step explanation:

Divide 31  1/4 by 6  3/5.

125/4 divided by 33/5 = 625/132

625/132 = 4  97/132

Hope this helps :)

The length of garden is 625/ 132 ft

The area of any rectangle is calculated, once its length and width are known. By multiplying length and breadth, the rectangle's area will obtain in a square-unit dimension

Given:

area of garden = 31 1/4 ft = 125/4

width = 6 3/5 ft = 33/5 ft

Now, area of garden

=length * width

125/4 = length * 33/5

length= 125/4 * 5/33

length = 625/ 132 ft

Learn more about area of rectangle here:

https://brainly.com/question/8663941

#SPJ2

Answer:

n-35=40

n=75 (the amount she started with)

Step-by-step explanation:

When a line is rotated, it is rotated about a fixed point to its new position. Line AB must turn 180 degrees about point A to coincide with line AE.

The complete question is that we determine the angle which AB will turn to, about point A to align with AE (see attachment for the figure)

Line AB and AE form a straight line. This means that the angle between these two lines on either side of point A is [tex]180^o[/tex]

So for line AB to coincides with line AE, the line AB must turn 180 degrees about point A.

Hence, option (B) is correct.

Read more about rotation of points at:

https://brainly.com/question/22363471

Answer:

yes, it is B

Step-by-step explanation:

every input value of x has an unique result value y.

there are no 2 values for x that produce the same result value y.

and there are no multiple result values possible for a subject x value.

bottom line, yes, it is a function, and a 1:1 function at that.

Answer:

D

Step-by-step explanation:

g(x) = 9x^2 satisfy the point (1,9).

Problem 1

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

Explanation:

The notation A U B means we're applying a union between A and B. This will form a larger set in which items from A or B are thrown into A U B. Think of "union" as in getting married, and person A's stuff is combined with person B's stuff to form a larger set. Any duplicates are tossed. It's often helpful to sort from smallest to largest.

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

Problem 2

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

Explanation:

Set C is defined as the set of prime numbers less than or equal to 20. The roster form is C = {2,3,5,7,11,13,17,19} which basically lists every item that fits the description earlier. Note how the value 1 is not prime, so it's not in the set C.

From here, we simply count out the values in set C to find there are 8 values. Therefore, n(C) = 8.

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

Problem 3

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

Explanation:

Let's consider a real world example of set vs subset. Consider the set of all animals and consider the subset of all dogs. Let's say

A = all animals

B = all dogs

We can see that set A is clearly larger than B. Also, any member of set B is also in set A, but not the other way around. In other words, if something is a dog, then they are also an animal. However, this doesn't work the other way around. For instance, we could have a cat in set A that wouldn't be in set B.

Let's return to the problem at hand. Since B is a subset of A, this must mean everything in B = {2,12,x,9} is found in set A. Sure enough, the 2, 12 and 9 are all in set A. The x must also be a value in set A so we could have

x = 3

x = 4

x = 5

x = 6

x = 7

as our possible answers. I'm not listing x = 2, x = 9 or x = 12 as they have been taken care of. I'm assuming that your teacher wants {2,12,x,9} to list unique items (ie it's after the duplicates are tossed out).

Answer:

14. x=16, 15. x=9

Step-by-step explanation:

14.

4x+4=7x-44 by alternate exterior angles

3x=48

x=16

15.

15x-26=12x+1 by alternate exterior angles

3x=27

x=9

Answer:

6^10

Step-by-step explanation:

We know that a^ -b = 1/ a^b

So 1/ a^-b = a^b

1/6^-10 = 6^10

Answer:

6¹⁰

Step-by-step explanation:

Whenever there is a negative exponent, switch its place between the vinculum (line). In this case, since there is a negative exponent in the denominator, move it up to the numerator and make the exponent positive.

Therefore, the answer is [tex]6^{10}[/tex].

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

⇛ x = 90° + 46°

⇛ x = 136°

Answer:

√13

Step-by-step explanation:

To get the side a, we will use the cosine rule as shown;

a² = b²+c²-2bcCosθ

Substitute the given values

a² = 5²+(3√2)²-2(5)(3√2)Cos45

a² = 25+18-30√2*1/√2

a² = 25+18-30

a² = 13

a = √13

Hence the value of a is √13

Answer: The missing number is 73

Step-by-step explanation:

Given:

4, 6, 9, 14, 23, 40, ?, 138, 266

Solve:

First, we try arithmetic patterns.

6 - 4 = 2

9 - 6 = 3

14 - 9 = 5

23 - 14 = 9

40 - 23 = 17

Clearly, there aren't arithmetic patterns.

Then, try through multiplication, exponents, and combination.

Finally, the pattern is multiplied by 2 on each number, then subtract 2 starting with 4 and add 1 for each increasing number.

4×2-2=6

6×2-3=9

9×2-4=14

As it goes on, the missing number would be:

40×2-7=73

Hope this helps!! :)

Please let me know if you have any questions

Answer:

12/5

Step-by-step explanation:

Tan Z

= opposite/adjacent

= 24/10

= 12/5

Answered by GAUTHMATH

Answer:

The answer is below

Step-by-step explanation:

The general form of a line is given by:

Ax + By + C = 0

The slope intercept form of a line is give by:

y = mx + b;

where m is the slope and b is the y intercept

Given a line with equation Ax + By + C = 0; the slope of the line can be gotten by representing in slope intercept form, hence it becomes:

By = -Ax - C

y = (-A/B)x - C/B

The slope is -A/B

For a line with equation Bx - Ay + C = 0:

Ay = Bx + C

y = (B/A)x + C/A

the slope is B/A

Two lines are said to be perpendicular if the product of the slopes is -1. Hence:

-A/B * B/A = -1; hence the two lines are perpendicular

Answer:

Tony

Step-by-step explanation:

Answer:

2x-24

I think that you changes the problem...

you went from a derivative to an inverse ???

y = 1/2x + 14

x = 1/2 y + 14

2x = y + 24

y = 2x-24

Step-by-step explanation:

Answer:

[tex]f^{-1}[/tex] (x) = 2x - 28

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = [tex]\frac{1}{2}[/tex] x + 14 ( multiply through by 2 to clear the fraction )

2y = x + 28 ( subtract 28 from both sides )

2y - 28 = x

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x)

[tex]f^{-1}[/tex] (x) = 2x - 28

Answer: Distance = 4

Step-by-step explanation:

Concept:

Here, we need to know the concept of the distance formula.  

The distance formula is the formula, which is used to find the distance between any two points.  

If you are still confused, please refer to the attachment below for a clear version of the formula.

Solve:

Find the distance from Layan's house to the store, where:

[tex]Distance = \sqrt{(x_2 - x_1)^2+(y_2-y_1)^2}[/tex]

[tex]Distance = \sqrt{(-1\frac{1}{3} - 2\frac{2}{3} )^2+(7\frac{1}{3} -7\frac{1}{3} )^2}[/tex]

[tex]Distance = \sqrt{(-4)^2+(0)^2}[/tex]

[tex]Distance = \sqrt{16+0}[/tex]

[tex]Distance = \sqrt{16}[/tex]

[tex]Distance = 4[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

A

Step-by-step explanation:

Did the test sorry I'm late

0.453682

= 0.4+0.05+0.003+0.0006+0.00008+0.000002

453682.0

= 400000+50000+3000+600+80+2+0.0

Must click thanks and mark brainliest

Answer:

the ...ha answer is =99 in.^3

(3x/6) + 2 = 8

=> 3x/6 = 8 - 2

=> 3x/6 = 6

=> 3x = 6 × 6

=> 3x = 36

=> x = 36/3

=> x = 12

Answer:

x=12

Step-by-step explanation:

3x/6+2=8

3x/6=8-2

      =6

3x/6(6)=6(6)

3x=36

x=12

Answer:

One of the scenarios:

The transformation that maps the pre-image to the image is given as follows:

Dilation.

The four types of transformation listed in this problem cause these following changes:

From the image, we get that the side lengths were doubled, while the angle measures remained constant, meaning that the transformation is a dilation and the first option is the correct option.

More can be learned about transformations at https://brainly.com/question/28792248

#SPJ1

Answer:

dilation

Step-by-step explanation:

took the test

one pipe 6 hours fill

two pipe 6 ÷2= 3 hours

Answer:

x=9

Step-by-step explanation:

Answer:

[tex]3^{3} + 3 + 3 = 33[/tex]

Step-by-step explanation: