or Line p has an equation of y= – 8x+6. Line q, which is perpendicular to line p, includes the point (2, – 2). What is the equation of line q?

The solutions to the given simultaneous equations as required in the task content are; (1.4, 9.2) and (-0.9, 2.3).

It follows from the task content that the solution to the simultaneous equations as given in the task content is to be determined.

Given: y = 3x + 5 and y = 4x² + x.

Therefore, since y = y; it follows that the equation which holds true is;

3x + 5 = 4x² + x

4x² - 2x - 5 = 0.

Therefore, the quadratic equation above can be solved for the values of x so that by approximation, we have;

x = 1.4 OR x = -0.9.

Therefore, the corresponding values of y are;

y = 3(1.4) + 5 = 9.2

OR

y = 3(-0.9) + 5 = 2.3

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Answer: check the image attached

Step-by-step explanation:

Hope this helps

Answer:

Just point the graph on Y=33x+0

Step-by-step explanation:

There's no B or starting point, so you would just plant the point on 0,33

Answer:

y=3+5x

Step-by-step explanation:

Add 5x to both sides.

Dora solved the equation.

She multiplies 4 inside the bracket. But she fails to know that 4× -1 = -4. Instead she multiplied that 4×-1 = -41. This is her first mistake.

In the second step, she shifted -41 to the right side in order to find the value of x. As -41 gets shifted to right side , -41 becomes +41 and added with +11 to get 52. which is totally a wrong method.

Step-by-step explanation:

Here is the exact method of solvation.

[tex]{ \blue{ \bold{4(x - 1) = 11}}}[/tex]

[tex]{ \blue{ \bold{4x - 4 = 11}}}[/tex]

[tex]{ \blue{ \bold{4x = 11 + 4}}}[/tex]

[tex]{ \blue{ \bold{4x = 15}}}[/tex]

[tex]{ \blue{ \boxed{ \red{ \sf{x = \frac{15}{4}}}}}} [/tex]

The overall budget the Mr Hollis has is $12800.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, Mr.Hollis determines that he gives away 800 each month and the fraction is 1/6 of his budget.

The value of the overall budget will be illustrated as x.

Therefore 1/16 × x = 800

x / 16 = 800

x = 16 × 800

x = 12800

Hollis has $12800 as budget.

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Answer:

12=b

Step-by-step explanation:

2b+7=3b-4 is what your gonna do ti solve the problem because both segments have the same length. Then you solve for b by -2b from each side. Then it will become 7=b-4. Add 4 to the seven to get 12=b

Answer:

7 is correct.

There are 4 small triangles, 2 medium-sized triangles, and 1 large triangle.

The statement that best analyzes the role this event plays in The Necklace plot is A. It leads to the resolution where Mathilde learns (a little too late) a lesson about the downfall that can come from vanity and greed.

There are both planned and unplanned events, and the start and end times may be noted. Event types include accidents, celebrations, natural disasters, and rallies. The event is the occurrence of the event.

Loisel is well-liked and adored by all. As she walks away, she searches for the pendant and discovers it has gone missing. After days of searching, she and her husband decide to replace it with something similar. It takes her ten decades to pay for the successor, which costs the same as your salary.

In this case, it best analyzes the role this event plays in leading to the resolution where Mathilde learns a lesson about the downfall that can come from vanity and greed The plot of The Necklace.

Therefore, the correct option is A.

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Complete question

Which statement best analyzes the role this event plays in The Necklace plot?

“Oh, my poor Mathilde! Why, my necklace was paste! It was worth at most only five hundred francs!”

It leads to the resolution where Mathilde learns (a little too late) a lesson about the downfall that can come from vanity and greed.

It is the climax of the story since the reader is most excited at this point.

It serves as a complicating incident because Mathilde will have to suffer the consequences of her actions.

It serves as the falling action because it shows that Mathilde will have to get used to her place in life.

There is no graph in your question

Answer:

Peni will need a total of $17.90

Step-by-step explanation:

$1.20 x 7 = $8.40

$0.50 x 5 = $2.50

$1.00 x 7 = $7.00

$8.40 + $2.50 + $7.00 = $17.90

Answer:

each student get 2.5 of graham crackers

Step-by-step explanation:

[tex]total \: students \: = 12 \\ graham \: crackers \: = 30 \\ 30 \div 12 \\ = 2.5[/tex]

The number of days that it will take to sell his box of 35 is 21 days.

Ratio simply demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this case, Nigel is selling candy bars for his outdoor club and he is averaging 4 bars every 3 days.

Let the number of days be x.

This will be:

3/x = 4/35

Cross multiply

4x = 3 × 35

x = (3 × 35)/4

x = 105 / 4

x = 21

It will take 21 days

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The probability that the next spin will land on red or green or purple is 75%

Given , A spinner is divided into five colored sections that are not of equal size

Color      Frequency

Red            18

Blue            11

Green          8

Yellow         4

Purple          19

Total spin recorded = 18+11+8+4+19

=60

Let "A" be the event when spinner land on Red , "B" be the event when spinner land on Green and "C" be the event when spinner land on Purple

P(A) = 18/60 = 0.3

P(B) = 8/60 = 0.134

P(C) = 19/60 = 0.32

Probability that the next spin will land on red or green or purple will be P(A∪BC) = P(A) + P(B) + P(C)

P(A∪BC)  = 0.3 + 0.134 + 0.32 =0.754

= 0.754 × 100 = 75%

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The number of months till Dan and Sydney would have paid the same amount for the high-speed Internet service is 6.12 months

Assuming the number of months is denoted as x, the total cost equation for Dan's provider would be:

= Installation cost + internet charge per month x number of months

= 60 + 42.95x

The total cost equation for Sydney's provider is:

= Installation cost + internet charge per month x number of months

= 0 + 52.75x

= 52.75x

To find the number of months till Dan and Sydney pay the same amount, equate the equations:
60 + 42.95x = 52.75x

52.75x - 42.95x = 60

9.8x = 60

x = 60 / 9.8

x = 6.12 months

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Step-by-step explanation:

2x - 27 + 3x + 27 = 180

5x = 180

x = 36

When the number of people is multiplied by 4, the number of pizzas is multiplied by 4.

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a proportional relationship can be modeled by the following mathematical expression:

y = kx

Where:

If the x-value is multiplied by 4, we have:

x = 5 × 4

x = 20

From the corresponding y-value for 20 is equal to 8 and as such the number of pizzas needed should be multiplied by 4, in order to produce an equivalent ratio.

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You started with a total of 28 muffins

From the question, the given parameters are:

Proportion carried away = 16 of the total muffins

Proportion carried away = 4/7 of the total muffins

The above parameters implies that

4/7 of the total muffins = 16

Represent the amount you started with x

So, we have the following representation

4/7 of x = 16

Express as products

4/7x = 16

Make x the subject

x = 7 * 16/4

Evaluate

x = 28

Hence, the total number of muffins is 28

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Answer:

1/6

Step-by-step explanation:

y = -6x + 8

Perpendicular line would be the reciprocal of the slope

The length of the shorter piece is 33 inches.

According to the question,

We have the following information:

A 132 ​-inch is cut into two pieces. One piece is three times the length of the other.

Now, let's take the length of the shorter piece to be x inches and the length of another piece will be 3x inches.

Now, we have the following expression:

x+3x = 132

4x = 132

4 is in multiplication on the left hand side. So, it will be in the division on the right hand side.

x = 132/4

x = 33 inches

Hence, the length of the shorter piece is 33 inches.

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(a) The nth term of the sequence is given by A(n)=195 + (n - 1)10.

(b) The 12th term of the sequence is A(12) = 305.

One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...

The term "finite arithmetic progression" or "arithmetic progression" refers to a limited segment of an arithmetic progression.

A mathematical sequence has the following structure: a, a+d, a+2d, a+3d, etc., up to n terms. The initial term is a, the shared distinction is d, and n is the total number of words. Find the AP, the first term, the number of terms, and the common difference for the computation using the arithmetic sequence formulae. To determine the nth term, sum, or common difference of a given arithmetic sequence, many formulae related to arithmetic series are utilized.

A(n)=195+(n-1)10

The given arithmetic sequence is 195, 205, 215, 225,.....

The first term a =195

The common difference d= 205-195

d =215-205

d =225-215

So, d = 10

(a) The nth term is given by

A(n)=a+(n-1)d

A(n)=195+(n-1)10

(b) For n=12, the 12th term is given by

A(12)=195+11(10)

A(12)=305

Therefore, A(n)=195+(n-1)10

And A(12)=305

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for an ordered pair (x comma y )in a relation, the x element represents the horizontal axis.

The cost for 14 boxed lunches is $107.10.

From the information, the company orders 11 boxed lunches from a deli for $84.15. Therefore, we need to calculate the unit price and this will be:

= Total amount / Number of orders

= $84.15 / 11

= $7.65

Therefore, the value for 14 boxes will be:

= Unit price × Number of orders

= $7.65 × 14

= $107.1

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Answer:

[tex]-3[/tex]

Step-by-step:

[tex]8+ (-3) + (-8)[/tex]

1  ) Combine like terms...

[tex]=5 - 8[/tex]

2 ) Solve...

[tex]= - 3[/tex]

Hope this helps! :)

The window width in the blueprint is 1.5 in.

As per the given question-

A window in the room measures 2. 5 feet in width.

The given scale is-

Blue print (inches) : original (feet)

3 in : 5 ft

Divide both side by 2

1.5 in : 2.5 ft

Window's width in Blue print (inches) = 1.5 in.

As a result, the window width in the blueprint is 1.5 in.

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The equation which represents the price of the ticket after the discount is y = 0.25x.

A linear equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given that the movie theatre is giving a discount of 75% the original cost of the ticket is x and discounted cost is represented by the variable y.

The equation for the cost of the ticket will be written as,

y = x - 0.75x

y = 0.25x

The graph of the linear equation is attached with the answer below.

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The equation for the quadratic graphed is [tex]2x^{2}+4x+2[/tex].

Let the quadratic equation be [tex]y =a x^{2}+bx+c[/tex]

Points given in graph,

A(-1,0), B(-2,2), C(0,2)

Put the values in quadratic equation

For C(0,2)

[tex]2 =a(0)^{2}+b(0)+c[/tex]

[tex]2 = 0+0+c[/tex]

c = 2

For A(-1,0)

[tex]0 =a(-1)^{2}+b(-1)+2[/tex]

[tex]a-b+2 = 0[/tex]

a - b = -2              ...........(i)

For B(-2,2)

[tex]2 =a(-2)^{2}+b(-2)+2[/tex]

[tex]4a-2b+2=2[/tex]

2a - b = 0            ............(ii)

Solving eq (i) and (ii)

a = 2

b = 4

Putting the value of a, b and c in quadratic equation,

[tex]y =2x^{2}+4x+2[/tex]

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Main answer:

a) 18 millions of dollars/year

b) 6 millions of dollars/year

Step-by-step explanation:

a) the average rate of change of annual sales between 2001 and 2002 millions of dollars/year

Average rate = (Final year - Initial year) / (Sales on Final year - Sales on Initial year)

                     = (417 - 399) / (2001 - 2002)

                     = 18 / 1

                     = 18 millions of dollars/year

b) the average rate of change of annual sales between 2001 and 2006 millions of dollars/year

Average rate = (Final year - Initial year) / (Sales on Final year - Sales on Initial year)

                      = (369 - 399) / (2006 - 2001)

                      = 30 / 5

                      = 6 millions of dollars/year

The average rate of change of annual sales between 2001 and 2002 is 18 millions of dollars/year ,  between 2001 and 2006 is 6 millions of dollars/year

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Answer:

No

Step-by-step explanation:

The value that corresponds with the other value on a data (34 to 2, 51 to 3, 68 to 5 etc.) needs to have the same quotient (or ratio) when you compare them.

34/2 = 51/3 ? Yes (but you can't stop here because you need to test ALL the values, what I mean is ALL the values UNTIL you found one that is not equal to each other, if all of them are equal, then the data are proportional.

34/2 = 68/5 ? No (Now you can stop here and say it's not proportional because we already found one pair that are not equal).

The graph has no vertex

The transformations from the parent function are

The graph represents the given parameter

As a general rule, the maximum or the minimum of a graph is the vertex

However, the graph has no maximum or minimum

This means that there is absence of a vertex in the graph

Here, we have:

This transformation can be represented as (x - 4, y - 2)

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Answer:

I do not see the original triangle, but you would take the original and move it one unit to the left and 5 units up.

Step-by-step explanation:

For example, if the three vertices (corners) of the triangle were points:

(0,0), (1,5) and (-2,3).

Point (0,0) would move to (-1, 5)  0-1 and 0+5

Point (1,5) would move to (0, 10)

Point (-2,3) would move to (-3, 8)

Answer:

To graph the image of the triangle after the transformation, we first need to have the coordinates of the vertices of the original triangle. Once we have those coordinates, we can apply the transformation to each vertex to obtain the coordinates of the corresponding vertex in the transformed image. Then, we can plot the three transformed vertices to obtain the image of the triangle.

Let's say the original triangle has vertices A, B, and C with coordinates A(x1, y1), B(x2, y2), and C(x3, y3), respectively.

To obtain the transformed coordinates of A, we apply the transformation rule (x, y) → (x - 1, y + 5) to the coordinates of A:

A' = (x1 - 1, y1 + 5)

Similarly, we can obtain the transformed coordinates of B and C:

B' = (x2 - 1, y2 + 5)

C' = (x3 - 1, y3 + 5)

Now that we have the transformed coordinates of the three vertices, we can plot them to obtain the image of the triangle.

Here's an example:

Suppose the original triangle has vertices A(2, 4), B(5, 6), and C(7, 3). Applying the transformation rule (x, y) → (x - 1, y + 5) to each vertex gives us:

A' = (2 - 1, 4 + 5) = (1, 9)

B' = (5 - 1, 6 + 5) = (4, 11)

C' = (7 - 1, 3 + 5) = (6, 8)

Plotting these three points gives us the image of the triangle after the transformation:

Before transformation:

B (5, 6)

/ \

/ \

A (2, 4) C (7, 3)

After transformation:

B' (4, 11)

/ \

/ \

A' (1, 9) C' (6, 8)

Here's what the image of the transformed triangle would look like on a graph:

|

|

C' | B'

|

---------|--------

|

A' |

|