Identify the transformation that appears to be a reflection. HELP ASAP!!

1. For the system of linear equations to have an infinite number of solutions, the two lines must cross over an infinite number of times, ie. they would be the same line.

Now, if they are the same line and we were to write out both equations in the form y = mx + c, this would mean that the m value (the gradient) and the c value (the y-intercept) would be the same. Thus, the first step is to write out both equations in the form y = mx + c.

a) Equation 1:

3x - 9y = -6

3x = -6 + 9y (Add 9y to both sides)

3x + 6 = 9y (Add 6 to both sides)

(1/3)x + 2/3 = y (Divide both sides by 9)

Thus, the first equation may be written as y = (1/3)x + 2/3

b) Equation 2:

(1/2)x - (3/2)y = c

(1/2)x = c + (3/2)y (Add (3/2)y to both sides)

(1/2)x - c = (3/2)y (Subtract c from both sides)

(1/3)x - (2/3)c = y (Multiply both sides by 2/3)

Thus, the second equation may be written as y = (1/3)x - (2/3)c.

2. Now that we have both equations in the form y = mx + c, we can look at their gradients and y-intercepts:

Equation 1: gradient = 1/3, y-intercept = 2/3

Equation 2: gradient = 1/3, y-intercept = -(2/3)c

As we can see above, the gradients of the two lines are the same, however for them to be the same line their y-intercepts must also be equal. Thus, we must equate the two y-intercepts to find c:

2/3 = -(2/3)c

1 = -c (Multiply both sides by 3/2)

-1 = c (Multiply both sides by -1)

Thus, if the system of linear equations has infinitely many solutions, and c is a constant, the value of c is -1 (answer D).

The value of 'c' for the given system of the linear equations with infinitely many solutions is - 1.

"A linear equation is an equation in which the highest power of the variable is always 1."

Given system of linear equations are

1. [tex]3x - 9y=-6[/tex]

⇒ [tex]x - 3y = - 2[/tex]

Therefore, [tex]a_{1} = 1, b_{1} = -3, c_{1} = -2[/tex]

2. [tex]\frac{x}{2}-\frac{3y}{2} =c[/tex]

⇒ [tex]x - 3y = 2c[/tex]

Therefore,    [tex]a_{2} = 1, b_{2} = -3, c_{2} = 2c[/tex]

For the system of the linear equations with infinitely many solutions,

[tex]2c = -2[/tex]

⇒ [tex]c = -1[/tex]

Learn more about linear equation here: https://brainly.com/question/2263981

#SPJ2

Answer:

  not really

Step-by-step explanation:

The number of friends (x) is expected to be an integer. 6.5 friends does not really make sense.

_____

There are all kinds of ways this might make sense, but none of them are supported by the information given in the problem statement.

No, the solution (6.5,$ 95.25) do not make a sense.

Since, the number of people going for a movie can't be in decimals.

The function h(x) represents the amount of money spent where x is the number of friends at the movies.

The domain of such a function has to be whole numbers.

Because the number of people that go for a movie must exist as a whole they can't exist in decimals.

( i.e. either no one will go.

1 will go.

2 friends will go and so  on)

i.e. the domain is the set of all non-negative integers.

Answer:

The correct option is:

a) seasons; "This is the

A semicolon is most commonly used to link (in a single sentence) two independent clauses that are closely related in thought.When a semicolon is used to join two or more ideas (parts) in a sentence, those ideas are then given equal position or rank.

Step-by-step explanation:

Answer:

A.  seasons: "This is the

Step-by-step explanation:

Answer:

  (x, y) = (2, 10)

Step-by-step explanation:

Adding the two equations will eliminate the y-variable:

  (-4x -y) +(-7x +y) = (-18) +(-4)

  -11x = -22 . . . . . simplify

  x = 2 . . . . . . . . . divide by -11

__

Put this into the first equation to find y:

  -4·2 -y = -18

  -8 +18 = y = 10 . . . . . add 18+y

The solution is (x, y) = (2, 10).

Answer:

x = 2 and y = 10

Step-by-step explanation:

It is given that,

-4x - y = -18 ---(1)

-7x + y= -4   ---(2)

To find the solution of equations

Step 1:  Add eq(1) + eq(2)

-4x - y = -18 ---(1)

-7x + y=  -4   ---(2)

-11x + 0 = -22

11x = 22

x = 22/11 = 2

Step 2: Substitute the value of x in eq (2)

-7x + y= -4   ---(2)

-7*2 + y = -4

-14 + y = -4

y = -4 + 14 = 10

Therefore x = 2 and y = 10

Answer: First option.

Step-by-step explanation:

Knowing that the transformation T maps triangle XYZ onto triangle X'Y'Z', you can identifyfrom the figure that the triangle XYZ is the preimage, because it is the original shape and the triangle X'Y'Z' is the image, because is the shape obtained after the transformation.

You can observe in the figure that the image of the vertex X is the vertex X', the image of the vertex Y is the vertex Y' and the image of the vertex Z is the vertex Z'.

Therefore, the conclusion is: The image of Y is Y'.

Answer:

A

Step-by-step explanation:

Write each parabola in standard form.

f(x) = x²

f(x) = (x − 0)² + 0

For p(x), complete the square.

p(x) = -50 + 14x − x²

p(x) = -(x² − 14x + 50)

p(x) = -(x² − 14x + 49 + 1)

p(x) = -(x² − 14x + 49) − 1

p(x) = -(x − 7)² − 1

The transformation from f(x) to p(x) includes a reflection about the x-axis, a shift right 7 units, and a shift down 1 unit.

The answer is A.

Answer:

D

Step-by-step explanation:

you need to get the x alone so to do that, you need to add 7y so you do it on both sides and it gives you x=7y+8

The value of the expression  x − 7y = 8 will be x = 7y + 8. The correct option is D.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given expression is  x − 7y = 8. The value of x will be calculated as below:-

x − 7y = 8

x = 7y +  8

Therefore, the value of the expression  x − 7y = 8 will be x = 7y + 8. The correct option is D.

To know more about an expression follow

https://brainly.com/question/723406

#SPJ2

Answer:

(x-y)(y-x)

Step-by-step explanation:

because x-y=y-x

Answer:

The correct answer is option B.  65

Step-by-step explanation:

To find the measure of <VYX

Central angle of arc VW = 44°

Therefore m<VXY = 44/2 = 22°

And central angle of arc XZ = 86° therefore <XVY = 86/2 = 43

To find the mesure of <XYZ

m<XYZ = m<VXY + m<XVY

  = 22 + 43

 = 65°

Therefore the correct answer is option B. 65°

Answer:

  1/8 ft³

Step-by-step explanation:

Apparently cubic blocks that are 1/5 of 2 1/2 ft on a side are used to fill the cube that is 2 1/2 ft on a side. Then each edge of the block is ...

  (1/5) × (5/2 ft) = 1/2 ft

The volume of the block is the cube of that:

  (1/2 ft)³ = 1/8 ft³

Answer:

50m.

Step-by-step explanation:

When 2 chords  of a circle intersect the following products are equal:

15 * 15 = 5 * (TW - 5)

5TW = 225 + 25 = 250

TW = 250/5 = 50 m

Option c 50m

When a line passes through the center of the circle to the chord then the line is perpendicular bisector of the same chord which means it divide the chord in equal parts and makes an angle of 90 degrees with the chord.

Pythagoras theorem is the theorem used to calculate the hypotenuse in a right-angled triangle from the two legs of the triangle.

hypotenuse² = base²+height².

Let the center (the point in bold be C) and the point of intersection between QE and TW be R, So CQ is the radius, CR = radius-5.

Let the radius be 'r' so In Triangle CQR using the Pythagoras theorem

r² = (r-5)²+15²

r²-(r-5)²=225

(r-(r-5))(r+r-5) = 225

5.(2r-5)=225

(2r-5)=45

2r - 5 =45

2r=50

r = 25 and diameter is equal to 2*r and hence the diamter is 50.

The diameter in the figure is 50m

Learn more about Properties of Circle here

https://brainly.com/question/2845884

#SPJ2

answer is B)

x= 85, y = 100

Answer:

D, x=100 and y=85

Step-by-step explanation:

Hello

In every convex polygon, the sum of the measure of the interior angles is given by the expression SUM = 180 ° (n - 2) where n is the number of sides

the polygon has our sides MN, NO,OP  and PM, the sum of the interior angles is

[tex]sum=180(4-2)\\sum=360 degrees[/tex]

[tex]360= x +y +80+95\\360-80-95= x+y\\x+y=185[/tex]

looking at the graph it is observed that angle  x° is obtuse (more than 90° but less than 180°.) and the angle y is acute (The acute angle is the small angle which is less than 90°)

so

[tex]x>y[/tex]

[tex]x+y=185[/tex]

the response option that meets these two conditions is D, x=100 and y=85

Answer:

  width = 13 ft; area = 169 ft^2

Step-by-step explanation:

The equation for the area can be factored as ...

  A = x(26 -x)

This has zeros at x=0 and x=26. The vertex of this downward-opening parabola will be halfway between those, at x=13. Then the area for a width of 13 feet is ...

  A = 13(26 -13) = 13^2 = 169 . . . . ft^2

The maximum area is 169 ft^2, when the width is 13 ft.

_____

You will note that these dimensions make the pen be a square. It can be useful to remember that a square is the rectangle with the largest area for a given perimeter length.

The width that gives the maximum area for the given fencing is 13 feet, and the maximum area is 169 square feet (option B).

The formula given is a quadratic function where x is the width and A is the area. In a quadratic function, the maximum or minimum value occurs at the vertex. The x-coordinate of the vertex can be found using the formula -b/2a where a and b are the coefficients of the quadratic function. Here, a is -1 and b is 26, therefore the x-coordinate of the vertex is -26/-2*-1 = 13. This means that a width of 13 ft will give the maximum area. To find the maximum area, we substitute x = 13 into the function: A = 26*13 - 13^2 = 169 ft2. So, the width that will give the maximum area is 13 feet and the maximum area is 169 square feet.

https://brainly.com/question/16213025

#SPJ3

Answer:

Total = 14,000 * 1 + (.06 / 365) ^365*5

Total = 14,000 * 1.0.000164383561643836^1,825

Total = 14,000 * 1.3498255274

Total = 18,897.56

Step-by-step explanation:

Answer:

1.25(w)-12.50=C

Answer:

13.75

Step-by-step explanation:

3b + d = 8.75

2b + 2d = 7.50

(3b + d = 8.75) times 2

(2b + 2d = 7.50) times -3

6b + 2d = 17.5

-6b + (-6d) = -22.5

the b's cancel out, 2d - 6d = -4d and 17.5 - 22.5 = -5

-4d = -5 Divide it and d = 1.25

then plug in 1.25 for d.

2b + 2(1.25) = 7.50

2b + 2.5 = 7.50

2b = 5

b= 2.5

3(2.5) + 1.25 = 8.75 ? Yes.

2(2.5) + 2(1.25) = 7.50 ? Yes.

4(2.5) + 3(1.25) = 13.75.

Answer:

HL

Step-by-step explanation:

HL (Hypotension-Leg) postulate of congruence : In two right triangles if the hypotenuses are equal and any two corresponding legs are equal in both triangles then the triangles are congruent.

In the given right triangles MAE and TON,

AM = OT,

EM = NT,

Thus, by the HL postulate,

Δ MAE ≅ Δ TON

First option is correct.

Verbal expression of w^2 = 32w is:

W to the second power equals 32 with a variable of w.

To the second power means exponent of 2.

Variable is an unknown number represented by a letter. In this case, the variable is "w".

Hope this helps!

- Melanie

Answer:

Step-by-step explanation:

The square of variable w is equal to 32 times that variable.

The lower end of the digestive tract that gathers and expels solid waste from the body is called the rectum. The process involves the colon, where digestion occurs, water is reabsorbed, and waste is turned into feces, which is then eliminated through the anus.

The thick, lower end of the digestive tract where solid waste is gathered and leaves the body is called the rectum. After digested food passes through the small intestine, it enters the large intestine, or colon, where it undergoes further digestion and water reabsorption. The colon is home to a diverse microbiota that aids in digestion. The waste material, now known as feces, is then moved to the rectum. The rectum stores the feces until it triggers neural signals that lead to the urge to eliminate this waste through the anus.

Answer: B. 548

Step-by-step explanation:

You know that the exponential regression equation [tex]y = 14.08* 2.08^x[/tex] models the number of fish in a lake.

You know that the variable "x" represents the year. Therefore, ir order to predict the number of fish in year 5, you need to substitute [tex]x=5[/tex] into the given exponential regression equation.

Then, you get:

[tex]y = 14.08* 2.08^x\\\\y = 14.08* 2.08^5\\\\y=548.17[/tex]

Rounded to the nearest whole number:

[tex]y=548[/tex]

Answer:

The correct answer option is C. 548.

Step-by-step explanation:

We are given that the number of fish in a lake can be modeled by the following exponential regression equation:

[tex] y = 1 4 . 0 8 \times 2 . 0 8 ^ x [/tex]

where [tex]x[/tex] represents the number of year.

We are to determine whether which of the given answer options best predict the number of fish in year 5.

[tex] y = 1 4 . 0 8 \times 2.08^5[/tex]

[tex]y = 548.17[/tex] ≈ 548

For this case we must find the zeros of the following function:

[tex]f (x) = (x-7) (x-3) (x-2)[/tex]

If we equate each term to 0 and we clear the variable "x", we will find the values that make the function equal to zero. So:

Thus, the zeros of the function are:

7,3,2

Answer:

Option C

The zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2

From the question,

We are to determine the zeros of the given function

The given function is

f(x) = (x - 7)(x - 3)(x - 2)

To determine the zeros of this function, we will set f(x) = 0

That is ,

f(x) = (x - 7)(x - 3)(x - 2)  becomes

0 = (x - 7)(x - 3)(x - 2)

∴ (x - 7)(x - 3)(x - 2) = 0

Then,

We can write that

x -7 = 0 OR x - 3 = 0 OR x - 2 = 0

∴ x = 7    OR    x = 3    OR   x = 2

Hence, the zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2

Learn more here: https://brainly.com/question/12488960

Answer:

  A.  y + 1 = -2(x – 5)

Step-by-step explanation:

For a line with slope m through point (h, k), the equation is ...

  y -k = m(x -h)

Fill in your values of m=-2, h=5, k=-1 and you have ...

  y -(-1) = -2(x -5)

  y +1 = -2(x -5) . . . . . . simplify. Matches selection A.

Answer:172

Step-by-step explanation:

24.5 times 6 is 157

Plus 15 for the paint is 172 for the TOTAL for ALL she spent

Answer:

Step-by-step explanation

Answer:

No, he did not score 3,

Because, 2 times of 5 is 10 and the sum of 10 and 5 is 15.

Step-by-step explanation:

Let x be the score of Skylar,

Since, Wyatt scored 2 times as many goals as Skylar.

So, Wyatt's score = 2x

Thus, total scores = x + 2x = 3x

According to the question,

3x = 15

x = 5

Hence, Skyler have scored 5 goals.

Because, 2 times of 5 is 10 and the sum of 10 and 5 is 15.

Final answer:

Skylar could have scored 3 goals because, based on the information provided, they scored 5 goals after solving the equation that evaluates the total goals scored by both Skylar and Wyatt.

Explanation:

To determine if Skylar could have scored 3 goals, given that Wyatt scored 2 times as many goals as Skylar and together they scored 15 goals, we can set up a simple algebraic equation. Let's denote the number of goals Skylar scored as S, which means that Wyatt scored 2S goals.

The total number of goals is the sum of the goals scored by both Skylar and Wyatt, which is S + 2S = 15. This simplifies to 3S = 15. By dividing both sides of the equation by 3, we get S = 5.

Therefore, Skylar could have scored 3 goals because the calculations show that Skylar scored 5 goals.

Answer:

y = 1.383x - 1.526

Step-by-step explanation:

Intercept-    -1.526

Slope-  1.383

Line of best fit- y = 1.383x - 1.526

Answer:

[tex]y=1.383x-1.526[/tex]

Step-by-step explanation:

The given data table is

x :        4       7       10       12       13

y :        5       7       12       14       18

We need to find the equation of the best fit line.

The general form of a best fit line is

[tex]y=mx+b[/tex]         .... (1)

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

[tex]m=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}[/tex]

[tex]b=\overline{y}-b\overline{x}[/tex]

Using the graphing calculator we get

[tex]m=1.38321\approx 1.383[/tex]

[tex]b=-1.52555\approx -1.526[/tex]

Substitute m=1.383 and b=-1.526 in equation (1).

[tex]y=1.383x-1.526[/tex]

Therefore, the equation of best fit line is [tex]y=1.383x-1.526[/tex].

Answer:

6 movies

Step-by-step explanation:  

:Service A

1. $37.92 +&2.18=$40.1

2. $41.1+$2.18=$42.28

3....

4....

5....

6. $48.82+$2.18=$51

Service B

1. $33.25+free movie=$33.25

2. $33.25+$3.55=$36.8

3....

4....

5....

6. $47.45+$3.55=$51

ANSWER

[tex]S.A = 125 {in}^{2} [/tex]

EXPLANATION

The total surface area of a square pyramid is the area of the 4 triangular faces plus the area of the square base.

This is given by the formula!

[tex]S.A = 4 \times \frac{1}{2} bh + {l}^{2} [/tex]

From the diagram, the base is 5 inches and the height is 10 inches.

We substitute the values to get:

[tex]S.A = 4 \times \frac{1}{2} \times 5 \times 10 + {5}^{2} [/tex]

This simplifies to;

[tex]S.A = 100 + 25[/tex]

[tex]S.A = 125 {in}^{2} [/tex]

Answer:

The best function represented by the scatter plot is f(x) = -5 + 0.5 x ⇒ 1st answer

Step-by-step explanation:

* Lets talk about the scatter plot

- Scatter plots are similar to line graphs in that they use horizontal and

 vertical axes to plot data points

- Scatter plots show how much one variable is affected by another.

- The relationship between two variables is called their correlation

- There are three types of correlation:

  positive: one variable increases so the other increase

  negative: as one variable increases, the other decreases

  no correlation:  there is no clear relationship between the variables

* Lets solve the problem

- The scatter plot shows the relationship between the leaf length (x)

  and leaf width f(x)

- Some leaves of a tree are ordered pairs:

# (11 , 0.5) , (12 , 1) , (13 , 1.5) , (14 , 2) , (15 , 2.5) , (16 , 3) , (17 , 3.5) ,

  (18 , 4) , (19 , 4.5) , (20 , 5) , (21 , 5.5) , (22 , 6)

∵ The scatter plot is similar to the line graph

- Lets find the equation which represents the relation between

 x and f(x)

∵ The form of the linear equation is y = mx + c, where m is the slope

  of the line and c is the y-intercept

- The rule of the slope of the line which passes through points (x1 , y1)

 and (x2 , y2) is: [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

- Chose any two points to find the slope of the line

∵ (12 , 1) and (14 , 2) are two points on the line

∴ [tex]m=\frac{2-1}{14-12}=\frac{1}{2}=0.5[/tex]

- Substitute the value of m in the equation

∴ y = 0.5 x + c

- To find c use any point from above and substitute x and y by its

  coordinates

∵ Point (16 , 3) lies on the line

∴ 3 = 0.5(16) + c ⇒ simplify

∴ 3 = 8 + c ⇒ subtract 8 from both sides

∴ 3 - 8 = c

∴ c = -5  

- Substitute the value of c in the equation

∴ y = 0.5 x - 5

* The best function represented by the scatter plot is f(x) = -5 + 0.5 x

Answer: x=243

Step-by-step explanation:

Answer:$2,000

Step-by-step explanation: