The range of the following relation R:

The equation representing a proportional relationship, which is defined by a constant ratio and passes through the origin, is option A) y = 3x.

The question which equation represents a proportional relationship refers to a type of linear equation in which the ratio of one variable to another is constant. The form of a proportional relationship is y = kx, where k is the constant of proportionality. Looking at the options provided:

Therefore, the equation representing a proportional relationship is option A) y = 3x.

Answer: Choice A -- f(x) = (1/3)*|x|

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

The input of a function is x and the output is y = f(x)

To vertically compress a function, we will multiply the y value by some fraction smaller than 1. This is so that the y coordinates are a fraction of what they once were.

In this case, we multiply y by 1/3 so that something that has a y coordinate of y = 81 becomes y = 27 (divide by 3)

So we have y = f(x) become (1/3)*y = (1/3)*f(x) = (1/3)*|x|

Answer:

find below

Step-by-step explanation:

it would either be -1 1/3 or -3/4 since that is the reciprocal of -1 1/3

Answer:

The sum of x and y is a rational number

Step-by-step explanation:

X+Y or 5+7=12

A rational number is any number that can be divided without going on and on forever.

Answer:

The correct answer is A) The sum of the two is a rational number.

Step-by-step explanation:

Since both 5 and 7 are rational numbers, we know that their sum is also a rational number. This is true for any value of rational numbers.

Answer:

44   You will get the 2x and 88 and divide 88 by 2x

Step-by-step explanation:

Answer:  The required value of x is 22.

Step-by-step explanation:  Given that B and F are the midpoints of the sides AC and AE of triangle ACE.

Also, BF = 2x  and  CE = 88.

We are to find the value of x.

Midpoint theorem :  If a line segment joins the midpoints of any two sides of a triangle, then it is parallel to the third side and its length is equal to half of the length of the third side.

From triangle ACE, we have

B and F are the midpoints of the sides Ac and AE respectively, so BF will be parallel to CE and its length will ne half of the length of side CE.

Therefore,

[tex]BF=\dfrac{1}{2}\times CE\\\\\Rightarrow 2x=\dfrac{1}{2}\times88\\\\\Rightarrow 2x=44\\\\\Rightarrow x=\dfrac{44}{2}\\\\\Rightarrow x=22.[/tex]

Thus, the required value of x is 22.

Answer:

Yes, they are.

Step-by-step explanation:

Lets simplify both rates to the rate typer per minute.

(m is minutes)

3m = 96

Divide both sides by 3:

[tex]\frac{3m}{3} = \frac{96}{3}[/tex]

m = 32

So the rate is 32 words per minute.

5m = 160

Divide both sides by 5:

[tex]\frac{5m}{5} = \frac{160}{5}[/tex]

m = 32

Answer:

x = 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = - [tex]\frac{7}{2}[/tex] and c = 12

y = - [tex]\frac{7}{2}[/tex] x + 12 ← equation in slope-intercept form

given (x, 5) lies on the line, solve for x by letting y = 5

- [tex]\frac{7}{2}[/tex] x +12 = 5

multiply all terms  by 2 to eliminate the fraction

- 7x + 24 = 10 ( subtract 24 from both sides )

- 7x = - 14 ( divide both sides by - 7 )

x = 2

Answer:

Set the two equations equal to each other if you want me to solve tell me.

So.... 15x+10=16x+3

-15                  -15

10=1x+3

-3

7=x

Answer:

Step-by-step explanation:

Set them equal bc they are vertical angles

15x+10=6x+3

-6x. -6x

9x=

I don't know the rest

Answer:

3 3/5

Step-by-step explanation:

3 fives go into 18 with a remainder of 3.

Answer:

3 3/5

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x-y=8&(**)\\y=x-3&(*)\end{array}\right\\\\\text{Substitute }\ (*)\ \text{to}\ (**):\\\\2x-(x-3)=8\\2x-x-(-3)=8\\x+3=8\qquad\text{subtract 3 from both sides}\\\boxed{x=5}\\\\\text{Put the value of x to}\ (*):\\\\y=5-3\\\boxed{y=2}\\\\Answer:\ \boxed{a.\ (5,\ 2)}[/tex]

Answer:

Solution for the given system of equations is (5,2)

Step-by-step explanation:

We have been given the system of equations

[tex]2x-y=8....(1)\\y=x-3...(2)[/tex]

On substituting the value of y from equation (2) in equation (1)

[tex]2x-(x-3)=8[/tex]

Now, we solve the equation for x

[tex]2x-x+3=8\\x+3=8\\x=5[/tex]

Substituting the value of x in equation (2)

[tex]y=5-3\\y=2[/tex]

Therefore, the solution for the given system of equations is (5,2)

a is the correct option.

Answer:

x=34

Step-by-step explanation:

Please, see the attached file.

Thanks.

Answer:

Hence final answer is x=34

Step-by-step explanation:

∠ADC= ∠EDF {Vertically opposite angles are always equal}

∠ADC= 36°  {Given }

∠ADB= 36°...(i)  {Same angles}

∠ABI + ∠ABC = 180° {supplementry angles }

113° + ∠ABC = 180°  {Given }

∠ABC = 180° - 113°

∠ABC = 67°

∠ABD = 67° ...(ii)  {same angle}

We know that sum of all three angles of triangle is 180 degree so we can write:

∠ABD + ∠ADB + ∠BAD =  180°

67° + 36° + ∠BAD =  180°  {using (i) and (ii) }

67° + 36° + x°+43° =  180°  {from diagram }

146° + x° =  180°

x° =  180° - 146°

x° =  34°

Hence final answer is x=34

Question 1. 2P + 14 = 0

Step 1. You need to subtract 14 from both sides.

2p+14−14=0−14

2p=−14

Step 2. Then divide both sides by 2.

2p /2 = −14 /2

Answer:  p=−7

Question 2.  - 2/3 w + 5 = 4

Step 1. Subtract 5 from both sides.

−2 /3 w+5−5=4−5

Step 2. Then multiply both sides by 3/(-2).

( 3 /−2 )*( −2 /3 w)=( 3 /−2 )*(−1)

Answer: w=  3 /2

Question 3. 5d - 1 = - 11

Step 1. First add 1 to both sides.

5d−1+1=−11+1

5d=−10

Step 2. Divide both sides by 5.

5d /5 = −10 /5

Answer: d=−2

Hope this helps! :)

The numbers that make the statement true are:

( -14, -∞ ) or [-15, -∞).

i.e -15, -16, -17, - 18, -19, ,,,,,,,,,-∞

Given,

Nine more than twice a number is less than negative nineteen.

We need to find all numbers that make this statement true.

More than - addition.

Twice - multiplication of 2.

Less than - <

-∞.......-5 < -4 < -3 < -2 < -1 < 0 < 1 < 2 < < 3 ...........∞

Find the expression.

Let the number be M.

"Nine more than twice a number is less than negative nineteen".

We can write this statement as:

2M + 9 < -19

Find the number M.

2M + 9 < -19

2M < -19 - 9

2M < -28

M < -28/2

M < -14

Let us check the statement is true with M < -14.

2M + 9 < -19

2 x -15 + 9 = -19

-30 + 9 = -19

-21 < -19

This is true.

We see that all numbers below -14 will make the statement true.

So,

The numbers are -15, -16, -17, -18,..........-∞

Thus the numbers that make the statement true are ( -14, -∞ ) or [-15, -∞).

i.e -15, -16, -17, - 18, -19, ,,,,,,,,,-∞

Learn more about finding numbers that satisfy an inequality here:

https://brainly.com/question/17646627

#SPJ2

To solve the inequality, we need to translate the given statement into an algebraic expression and then solve for 'x' using subtraction and division.

To solve the inequality, we will translate the given statement into an algebraic expression. Let's say the number is represented by 'x'. 'Twice a number' can be written as 2x. 'Nine more than twice a number' can be written as 2x + 9.

So, the inequality becomes 2x + 9 < -19.

To solve for 'x', we subtract 9 from both sides of the inequality, giving us 2x < -28. Then, we divide both sides by 2, resulting in x < -14.

Therefore, any number less than -14 will make the statement true.

To find the percent of change from 500,000 to 10,000, subtract 10,000 from 500,000 to get 490,000, then divide that difference by the original number and multiply by 100 to get the percentage.

To find the percent of change from 500,000 to 10,000, we need to calculate the difference between the two numbers and then find the percentage of that difference relative to the original number.

Step 1: Find the difference: 500,000 - 10,000 = 490,000.

Step 2: Find the percent: (490,000/500,000) × 100 = 98%.

The percent of change from 500,000 to 10,000 is 98%.

Answer:

40 books

Step-by-step explanation:

36-16=20

20 is half her original collection

20*2=40

Answer: He began with 40 Comic Books.

Step-by-step explanation: First exclude the 16 he bought from the 36. This leaves 20. Then dubble it because he sold half so it brings it up to 40! Hope this helps! ;)

36 - 16 = 20

20 * 2 = 40

The answer is 40!

Answer:

We can translate Circle C (x+6, y-2) to have the same center as D. The ratio of radius to radius is 10/5=2. Scale factor 2 from C to D.

Step-by-step explanation:

Similar objects are objects which are the same shape but not the same size. This means they have the same angle measures and a scale factor between the side lengths. To show similarity, we can use transformations and proportions. We can translate to shift the object, dilation to increase or decrease size and so forth. We use proportions to find scsale factor or missing length.

We have a circle. Circles do not have a specific angles and all circles have 360 degrees. They do not have sides but do have radius. All circles are similar because all are the same shape - a fixed center with points equidistant from the center (the radius). To show similar we can translate the circle so the centers are the same and create a ratio between the radius.

We can translate Circle C (x+6, y-2) to have the same center as D. The ratio of radius to radius is 10/5=2. Scale factor 2 from C to D.

Answer:

 = 420 in^2

Step-by-step explanation:

The area of a triangle is one half the base times the height

A = 1/2 bh

In this figure the base is equal to 24 inches and the height is  35 inches

Substituting what we know.

A =1/2 (24) * 35

A= 12*35

  = 420 in^2

Answer: The answer is 420

Step-by-step explanation:

24 x 35 equals 840. Then you divide by 20 and you get 420. I also took the test on iready.

Have a great day!

b + a = 14

b = 14 - a

14 - a + a = 14

14 = 14

Since we can't gain any further information after solving for b the first time, we know b = 14 - a to be the simplest form of b.

Answer:

y=2x-11

Step-by-step explanation:

Answer:

The student should have simplified the equation to have y + 8 on the left. Then, the student should have subtracted 8 from both sides of the equation. The value of b should be 4, not 20.

Step-by-step explanation:

edge 2021.

Answer:

The equation you should solve to find b is:

Option D. sin 35° / 9 = sin 40° / b

Step-by-step explanation:

m<A=35°

m<B=40°

a=9

b=?

We can use the Law of sines:

sin A / a = sin B / b

Replacing the given values:

sin 35° / 9 = sin 40° / b

This is option D.

Answer: 0

Step-by-step explanation:

2^3+16/4-3*4

2*2*2=8

8+16/4-3*4

16/4=4

8+4-3*4

12-3*4

3*4=12

12-12=0

Answer:

The 3rd equation on the left column  and second one on the right column.

Step-by-step explanation:

These 2 equations have same  coefficients of x and y if we divide the first one by 4 and the second by 2.

This gives the 2 equations

x^2 + y^2 - 4x + 6y - 7 = 0

x^2 + y^2 - 4x + 6y - 20 = 0

If we compete the square on these we get

(x - 2)^2 + (y + 3)^2 =  20

(x - 2(^2 + (y + 3)^2 =  33

These are in standard form . The center is the same (2, -3) but the radii are different so they are concentric.

In mathematics, concentric circles have the same center but different radii. Their general equation is (x-h)²+ (y-k)² = r², sharing the same (h, k) coordinates. Examples include equations like (x - 2)² + (y - 3)² = 4 and (x - 2)² + (y - 3)² = 9.

In mathematics, concentric circles are circles that share the same center but have different radii. The general equation of a circle is given by (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. Two such equations will represent concentric circles if and only if their center coordinates (h, k) are the same.

For example, consider the equations:

(x - 2)² + (y - 3)² = 4

(x - 2)² + (y - 3)² = 9

Both these circles have the center at (2, 3) but different radii (2 and 3 respectively), making them concentric circles.

Answer: 5-6i

The rule is that if f(x) has real number coefficients, then a root of x = a+bi pairs up with its conjugate pair of x = a - bi. In this case, a = 5 and b = 6.

Answer:

5 -6i is also the root of  f(x).

Step-by-step explanation:

Given : If 5 + 6i is a root of the polynomial function f(x),

To find  : which of the following must also be a root of f(x).

Solution : We have given that 5+6i is the on of the root of polynomial function f(x).

It has two parts real and imaginary  part so , it is a complex number .

Real part  = 5  and 6i is imaginary part.

Complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. For example, the complex conjugate of a + bi is a − bi.

a = 5 , b = 6.

Then by the complex conjugate defination , Another root would be 5 - 6i

Therefore, 5 -6i is also the root of  f(x).

Answer:

(4,1)

Step-by-step explanation:

3x+4y=16

-4x-3y=-19

I will solve this system by elimination.  I will eliminate x

Multiply the first equation by 4 and the second equation by 3

4 (3x+4y)=4*16

12x + 16y = 64

3 (-4x-3y)=3*-19

-12x -9y = -57

Add the two modified equations together to eliminate x

12x + 16y = 64

-12x -9y = -57

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

7y = 7

y=1

We still need to find x

3x+4y = 16

Substitute y=1

3x+4(1) = 16

3x+4=16

Subtract 4 from each side

3x = 16-4

3x =12

Divide each side by 3

3x/3 = 12/3

x=4

Answer:  The required solution is (x, y) = (4, 1).

Step-by-step explanation:  We are given to solve the following system of linear equations :

[tex]3x+4y=16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-4x-3y=-19~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

We will be using the method of Elimination to solve the given system as follows :

Multiplying equation (i) by 4 and equation (ii) by 3, we have

[tex]4(3x+4y)=4\times16\\\\\Rightarrow 12x+16y=64~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]

and

[tex]3(-4x-3y)=-19\times3\\\\\Rightarrow -12x-9y=-57~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)[/tex]

Adding equations (iii) and (iv), we get

[tex](12x+16y)+(-12x-9y)=64+(-57)\\\\\Rightarrow 7y=7\\\\\Rightarrow y=\dfrac{7}{7}\\\\\Rightarrow y=1.[/tex]

Substituting the value of y in equation (i), we get

[tex]3x+4\times1=16\\\\\Rightarrow 3x+4=16\\\\\Rightarrow 3x=16-4\\\\\Rightarrow 3x=12\\\\\Rightarrow x=\dfrac{12}{3}\\\\\Rightarrow x=4.[/tex]

Thus, the required solution is (x, y) = (4, 1).

Answer:

D. The two triangles are congruent because a translation does not change size and shape.

Step-by-step explanation:

I'm pretty sure that D is the answer. It jut basically moved , didn't change anything.

Answer:

1. The equation of line is [tex]y=-\frac{1}{2}(x)+1[/tex].

2. The correct option is D.

Step-by-step explanation:

1.

The slope intercept form of a line is

[tex]y=mx+b[/tex]

Where, m is slope and b is y-intercept.

The given equation of a line is

[tex]y=2x+8[/tex]

The slope of line is 2 and y-intercept is 8.

The product of slopes of two perpendicular lines is -1.

[tex]m_1\times m_2=-1[/tex]

[tex]2\times m_2=-1[/tex]

[tex]m_2=-\frac{1}{2}[/tex]

The slope of required line is [tex]-\frac{1}{2}[/tex] and it passes through the point (6,-2).

The equation of required line is

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y+2=-\frac{1}{2}(x-6)[/tex]

[tex]y+2=-\frac{1}{2}(x)+3[/tex]

[tex]y=-\frac{1}{2}(x)+3-2[/tex]

[tex]y=-\frac{1}{2}(x)+1[/tex]

Therefore the equation of line is [tex]y=-\frac{1}{2}(x)+1[/tex].

2.

Translation is a rigid transformation. It means if a figure translated then the image and preimage are congruent

It the given figure two triangles are congruent because a translation does not change size and shape.

Therefore the correct option is D.

Answer:

It is given that,  

there are 8 balls in the bag numbered 1 to 8

5 balls are  color is gray and all others are white

The gray color balls are 2,3,4,5 and 7

The white color balls are 1,6 and 8

P(X) = probability of getting white ball

P(not X) = Probability of getting gray ball

a) To find Probabilities P(X) and P(not X)

For event X, 1,,6,8 are checked and P(X) = 3/8

for event 'not X' 2,3,4,5 and 7 are checked and P(not X ) = 5/8

b) To find 1 - P(X)

1 - P(X) = 1 - 3/8 = (8 - 5)/8 = 5/8  

c)1 - P(X) is same as P(not X)