Given the graph below: What is the slope? ___________
What is the y intercept? _____________
What is the equation of the line in slope-intercept form? ____________________
What is the equation of the line in standard form? ____________

It's not possible to determine if Grafton's data collection was fair or not based on the provided information, as the question lacks details like the size of the sample used and where the sample was taken from. Accurate and representative data collection is a critical part of conducting a study.

Based on the data provided in the question, it's not possible to say whether Grafton picked the data fairly or not. The principles of statistics tell us that for data to be considered fair, it must be representative of the population being studied. In the context of the question, this means that for the data to be considered fair, it must accurately represent the car owning population. The question, however, does not provide enough information for us to make this determination.

For example, we don't know the sample size that Grafton used, where the sample was taken from, or any information about the population the data is supposed to represent. Without this additional data, we cannot determine if the data collection was biased or not. Remember, data collection is a crucial part of conducting a valid study and it's important to ensure that the sample used is unbiased and representative of the whole population.

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[tex]H-F=\left[\begin{array}{ccc}198&201\\176&172\\256&267\end{array}\right]-\left[\begin{array}{ccc}234&245\\198&187\\312&345\end{array}\right]\\\\=\left[\begin{array}{ccc}198-234&201-245\\176-198&172-187\\256-312&267-345\end{array}\right]\\\\=\left[\begin{array}{ccc}-36&-44\\-22&-15\\-56&-78\end{array}\right]\\\\Answer:\ \boxed{A}[/tex]

y = x^2 to  Green

y = –2(x – 2)^2 + 2  Blue

The correct answer is D.

Answer:

The correct option is D.

Step-by-step explanation:

The parent function is

[tex]y=x^2[/tex]

The transformed function is

[tex]y=-2(x-2)^2+2[/tex]              .... (1)

The translation is defined as

[tex]f(x)=k(x+a)^2+b[/tex]                .... (2)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (1) and (2) it is clear that

[tex]a=-2,b=2,k=-2[/tex]

It means,

a=-2<0 the graph shifts 2 units right.

b=2>0 the graph shifts 2 units up.

k=-2, the graph reflect across the x-axis and stretch by the factor 2.

The graph reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2. Therefore the correct option is D.

Every year there are 14 more ducks. The starting point would be 50 and the equation is:

d = 14*year+50

Answer: Ruhana and her team should refurbish 15 tv sets and 20 dvd players each week to minimize the cost.

Step-by-step explanation:

For the given situation let the number of tv sets be x and number of dvd players be y.

Now we have to minimize the cost as it costs $75 to refurbish a tv set and $40 to refurbish a dvd player.

i.e. Minimize z=75x+40y

it gives subject to the constraints

4x+2y≥100......(1)(100 hours each week. It takes 4 hours to refurbish a tv set and 2 hours to refurbish a dvd player.)

x+y≥35.......(2)(weekly sales target is to refurbish at least 35 tv sets or dvd players.)

To plot equation (1) we need to find coordinates of points lying on line (1)

put x=0 gives 2y=100⇒y=50

put y=0 gives 4x=100⇒x=25

So we got points (0,50) and(25,0) for (1)..............(3)

Similarly for equation (2)

put x=0 gives y=35

put y=0 gives x=35

So we got points (0,35) and(35,0) for (2).................(4)

with the help of (3) and (4) we plot the following graph (assume x≥0 and y≥0)

The unbounded feasible region determined by constraints gives the corner points as A(0,50),B(15,20)and C(35,0).

from  we get the value of z is minimum at point B (15,20) .

hence we got our optimal solution at B (15,20), where x is the number of tv sets and y is the number of dvd players  .

therefore Ruhana and her team should refurbish 15 tv sets and 20 dvd players each week to minimize the cost.

Answer: Look at photo

Step-by-step explanation:

Step 1. Subtract 3 from both sides

2|7x - 4| = 51 - 3

Step 2. Simplify 51 - 3 to 48

2|7x - 4| = 48

Step 3. Divide both sides by 2

|7x - 4| = 48/2

Step 4. Simplify 48/2 to 24

|7x - 4| = 24

Step 5 Break down the problem into these 2 equations

7x - 4 = 24

-(7x - 4) = 24

Step 6. Solve the 1st equation: 7x - 4 = 24

x = 4

Step 7. Solve the 2nd equation: -(7x - 4) = 24

x = -20/7

Step 8. Collect all solutions

x = -20/7,4

The answer is C.

$6 dollars because 11-8 = 3, 3x2 =6

He starts with $6.00

It says he spends 1/2 of his allowance on the movies. 6/2=3

He has $3. Then it says He gained $8.00 for washing the "family" car.

$6.00+$8.00

=$11

Answer=$6.00

The price of the stock of PEV Corporation varies as shown. we have to determine the net charge. Net change is just how much it changed overall, so we will look for all the ups minus all the downs.  

Here, "went up" goes with a + sign, and "went down" goes with a - sign.

So, Net charge = [tex]\frac{1}{4} - \frac{1}{3}-\frac{3}{4} + \frac{7}{10}[/tex]

= [tex]\frac{1}{4}-\frac{3}{4}- \frac{1}{3} + \frac{7}{10}[/tex]

= [tex]-\frac{2}{4}- \frac{1}{3} + \frac{7}{10}[/tex]

= [tex]-\frac{1}{2}- \frac{1}{3} + \frac{7}{10}[/tex]

LCM of 2,3 and 10 is 30

= [tex]\frac{-15-10+21}{30}[/tex]

= [tex]\frac{-4}{30}[/tex]

= [tex]\frac{-2}{15}[/tex]

So, the net charge is [tex]\frac{-2}{15}[/tex]

The slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (4, 9) and (6, 1).

Substitute

[tex]m=\dfrac{1-9}{6-4}=\dfrac{-8}{2}=-4[/tex]

Answer:

so what’s the answer

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Therefore a geometric figure labeled CD would be a segment and the correct answer is B)

​(x²-y²)² + (2xy)² = (x²+y²)²

Find the missing x- and y-values and Pythagorean triples using the identity given

A Pythagorean triple consists of three positive integers a, b, and c, that satisfy the equation from the Pythagorean theorem, thus, a² + b² = c², such triple is commonly written (a,b,c).​

​We are given the equation : (x²-y²)² + (2xy)² = (x²+y²)² since this, we have :

​a = (x²-y²)

​b = (2xy)

​c = (x²+y²)

​Question 1)

X Value = 4​

​Y Value = 3

​Pythagorean triples: ?

We can replace the values of x and y, to determine a, b and c.​

​a = (x²-y²) = (4²-3²) = 16-9 = 7

​b = (2xy) = (2*4*3) = 24

c = (x²+y²) = (4²+3²) = 16+9 = 25​

​Answer 1 : Pythagorean triples : (7,24,25)

Question 2) ​

​X Value = 5

Y Value = ?​

Pythagorean Triples: (9,40,41)​

​Now we have a, b, and c, to determine Y

​b = (2xy) = 40

Y = 40/2x = 40/2*5 = 40/10 = 4​

Answer 2 : Y = 4​

​Question 3)

X Value = ?​

Y Value = 3​

Pythagorean Triples: (27,36,45)​

Now we have a, b, and c, to determine X​

b = (2xy) = 36​

​X = 36/2y = 36/2*3 = 36/6 = 6

​Answer 3 : X = 6

Question 4)​

​X Value = 7

Y Value = 5​

​Pythagorean Triples: ?

We can replace the values of x and y, to determine a, b and c.​

a = (x²-y²) = (7²-5²) = 49-25 = 24​

b = (2xy) = (2*7*5) = 70​

c = (x²+y²) = (7²+5²) = 49+25 = 74​

Answer 4 : Pythagorean triples : (24,70,74)​

Hope this helps!​​​​​

​[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​​

By using the given identity and substituting known values of x and y, we can find missing x or y values and compute the Pythagorean triples. For instance, when x=4 and y=3, the Pythagorean triple is (7,24,25). Similarly, we can find missing triples or variables for other sets.

This question pertains to the topic of Pythagorean triples and their relationship with a given identity. A Pythagorean triple consists of three positive integers (a, b, c), such that a2 + b2 = c2. Inserting known values of x and y into the identity provided can help us find the Pythagorean triples.

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[tex]x^4-625=(x^2-25)(x^2+25)=(x-5)(x+5)(x-5i)(x+5i)\\\\x^4+10x^2+25=(x^2+5)^2=((x-\sqrt5i)(x+\sqrt5i))^2=(x-\sqrt5i)^2(x+\sqrt5i)^2[/tex]

Answer:

1) [tex]x^4-625=(x+5i)(x-5i)(x+5)(x-5)[/tex]

2) [tex]x^4+10x^2+25=(x+\sqrt{5}i)^2(x-\sqrt5 i)^2[/tex]

Step-by-step explanation:

1) Given : Expression [tex]x^4-625[/tex]

To find : Factor the expression completely over the complex numbers ?

Solution :

We can re-write the expression as,

[tex]x^4-625=(x^2)^2-(25)^2[/tex]

Applying identity, [tex]a^2-b^2 = (a+b)(a-b)[/tex]

[tex]x^4-625=(x^2+25)(x^2-25)[/tex]

[tex]x^4-625=(x^2+25)(x^2-5^2)[/tex]

Again apply same identity,

[tex]x^4-625=(x^2+25)(x+5)(x-5) [/tex]

The factor of [tex]x^2+25=(x+5i)(x-5i)[/tex]

Factor form is [tex]x^4-625=(x+5i)(x-5i)(x+5)(x-5)[/tex]

2) Given : Expression [tex]x^4+10x^2+25[/tex]

To find : Factor the expression completely over the complex numbers ?

Solution :

Expression [tex]x^4+10x^2+25[/tex]

Let [tex]x^2=y[/tex]

[tex]y^2+10y+25[/tex]

To factor we equate it to zero.

[tex]y^2+10y+25=0[/tex]

Apply middle term split,

[tex]y^2+5y+5y+25=0[/tex]

[tex]y(y+5)+5(y+5)=0[/tex]

[tex](y+5)(y+5)=0[/tex]

Substitute back,

[tex](x^2+5)(x^2+5)=0[/tex]

[tex](x^2+5)^2=0[/tex]

[tex]x^2+5=0[/tex]

[tex]x^2=-5[/tex]

Taking root both side,

[tex]x=\sqrt{-5}[/tex]

[tex]x=\pm \sqrt{5}i[/tex]

So, The factors are [tex](x+\sqrt{5}i)(x-\sqrt5 i)[/tex]

Factor form is [tex]x^4+10x^2+25=(x+\sqrt{5}i)^2(x-\sqrt5 i)^2[/tex]

Answer:

B because eaxh section either repeats itself or is close to repeating its previous part

Step-by-step explanation:

Answer:

It is given that Graph the image of the given triangle after the transformation that has the rule (x, y)→(−x, −y) .

From the given figure it is noticed that the vertices of the triangle are (6,7), (7,4), (-2,5).

From the given rule (x, y)→(−x, −y)  the vertices of the image are (-6,-7), (-7,-4) and (2,-5).

Plot these points on the coordinate plane.

In the below graph, the image of the given triangle is represented by green lines.

Area = Base x height:

area =  3 1/2 x 3/4 = 2 5/8 sq. ft.

The answer is the 2nd one.

The answer would be the second one or 2 5/8 sq ft hope that helps

Hey there!!

Given equation :

d(e-f) = g

Solve for d :

Dividing by ( e - f ) on both sides :

d = g / e - f which is [tex]d=\frac{g}{e-f}[/tex]

Hope my answer helps!

$90/10 = 9

$160/20 = 8

$80/10 = 10

$120/20 = 6

The package that has the lowest ratio cost to number of lessons is $120 for 20 lessons.

Hope this Helps!!

The package with the lowest ratio of cost to number of lessons is the $120 for 20 lessons option, calculating to a cost of $6 per lesson, which is the most cost-effective option.

To find this, we calculate the cost per lesson for each package by dividing the total cost by the number of lessons.

Therefore, the package with the lowest ratio of cost to number of lessons is $120 for 20 lessons, with a cost of $6 per lesson.

Answer:

1668

Step-by-step explanation:

8(8)= 64

64+4=68

1,600+68= 1,668

Hello,

To solve we need to factor y^2-2y-35:

(y-7)(y+5)=0

Now solve for :

(When will (y-7)(y+5)equal zero?)

When y-7=0 or y+5=0

Solve for the 2 equations above and;

y= 7,-5

Hope this helps, have a great day!

Answer: Part A = (100% - 80%)P = 35, Part B = 140

Step-by-step explanation:

Percentage:  Like + Don't like = 100%

                     80%  + Don't like = 100%

                   -80%                         -80%

                                  Don't like = 20%

People: 20% of Patrons = Don't Like

             0.20  x Patrons = 35

          ÷ 0.20                   ÷ 0.20    

                           Patrons = 175

Now, let's write the equation we used to get that answer:

Let P represent the total number of patrons, then the equation is:

 (100% - 80%)P = 35

= (1.00 - 0.80)P = 35

=       0.20P     = 35

 =             P      = 175

Part B:  

80% of Patrons = Like

0.80  x    175      = Like

         140            = Like

729 = s^3

9^3 = s^3

s = 9 in.

Answer: D) 40%

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

Work Shown:

Area of purple rectangle (ignore circular cutout for now) = base*height = 6*12 = 72

I'm assuming the center of the circle is located on the right edge of the purple rectangle. If so, then we can subtract off half the circle's area from the purple rectangle area

Semicircle Area = (pi*r^2)/2 = (pi*3^2)/2 = 14.1371669

Area of purple region = (Rectangle Area) - (Semicircle Area)

Area of purple region = 72-14.1371669

Area of purple region = 57.8628331

-------

Now divide this area by 144 as this is the total area of the entire largest square (12 by 12 square) to get 57.8628331/144 = 0.401825 which is approximate. This rounds to 0.40 and converts to 40% which explains how I got choice D as the answer

Answer:

That probability is approx. 40%.  See below.

Step-by-step explanation:

That probability is the area of the purple section divided by the total area of the square before coloring purple.

This area of the square is (12 cm)^2, or 144 cm^2.  

Half the area of the circle is pi*(3 cm)^2, or 9*pi cm^2.

Thus, the purple area is (144 cm^2) / 2  - (9/2)*pi cm^2, or (72 - 9*pi/2) cm^2.  This is approx. 57.86.

The ratio of this purple area to the full area of the square is:

57.86 cm^2

--------------------------------- = 0.4 (approximately)

144 cm^2

Hello,

Please, see the attached files.

Thanks.

The values of x and y is 2 and 17 respectively.

We need to find the value of x and y.

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Now, x+2=4

⇒x=2

y-5=12

⇒y=17

Therefore, the values of x and y is 2 and 17 respectively.

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Answer: Answer would be 23

Step-by-step explanation:

There was no change in Samuel's savings account balance. He made a deposit of $160 but after two weeks, he withdrew the same sum. He still had $20 in his account as a result.

This math query relates to fundamental financial operations. Samuel has $20 in his savings account at the start of the story. His total now stands at $180 after his subsequent $160 deposit. He withdraws $160, though, after two weeks. He now has $20 in his account after that. Finally, there was no change in Samuel's savings account balance. His account was $20 from beginning to end.

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Answer:

The Coordinate of the vertices of Parallelogram RSTU are R(0,0), S(2,3),T(6,3) and U (4,0).

we have to find the vertices of a point which cuts the side of parallelogram ST  .It is given that line y = x passes through R.

Suppose that it cuts the side ST at M (p,q).

Equation of line passing through T(6,3)and S (2,3) is

[tex]\frac{y-3}{x-2}= \frac{3-3}{6-3}\\\frac{y-3}{x-2} = 0\\y- 3=0[/tex]

it passes through (p,q)∴

∴ q -3 =0     ...........(1)

Line y=x passes through (p,q).

p -q=0

p=q

Equation (1) becomes

p= q=3

So the line y =x cuts TU at M (3,3).