a) Complete the table of values for y = x² - 2x - 3
-2 -1 0 1
2
3
4
0
X
y
-3
5

The slope of the line between the two points defined in the graph is 1/2.

Slope of the line:

The slope of a line is the change in y coordinate with respect to the change in x coordinate.

m = Δy/Δx

Where the net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx. Where “m” is the slope of a line

Given,

There is a graph presented here.

Through the graph we have identified two points,

They are (3,0) and (-3, -3).

Now we need to find the slope of the line between these points.

Here we consider the values of (x1,y1) as (3,0) and the value of (x2,y2) as (-3,-3).

Through the values we have to identify the slope of the line.

For that, we have to apply the values on the formula,

Then we get,

m = (-3 - 0)/(-3-3)

m = -3/-6

m = 1/2

Therefore, the slope of the line is 1/2.

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The value of the given function, [tex] \displaystyle{\lim_{n \to \\ \frac{\pi}{4} } \frac{ {sec}^{4} x - 4}{x - \frac{\pi}{4} } }[/tex], found using L'Hospital's rule is; [tex] \displaystyle{\lim_{n \to \\ \frac{\pi}{4} } \frac{ {sec}^{4} x - 4}{x - \frac{\pi}{4} } = 16}[/tex]

L'Hospital's rule states that if the limits [tex]\displaystyle{ \lim \limits_ {x \rightarrow c}f(x)} [/tex] = [tex]\displaystyle{ \lim \limits_{x \rightarrow c}g(x)} [/tex]= 0 or [tex]\pm \infty[/tex], g'(x) ≠ 0 for all x in I and x ≠ c, also, [tex]\displaystyle{ \lim \limits _ {x \rightarrow c}\frac{f ' (x)}{ g ' (x)} } \: exists, \: then;[/tex]

[tex]\displaystyle{ \lim \limits _ {x \rightarrow c}\frac{f (x)}{ g (x)} =\lim \limits _ {x \rightarrow c}\frac{f ' (x)}{ g ' (x)} } [/tex]

The given function is [tex] \displaystyle{\lim_{n \to \\ \frac{\pi}{4} } \frac{ {sec}^{4} x - 4}{x - \frac{\pi}{4} } }[/tex]

According to L'Hospital's rule, we have;

Where;

f(x) = sec⁴x - 4

[tex] \displaystyle g(x) = x - \frac{\pi}{4} [/tex]

[tex] \displaystyle f'(x) = \frac{4\cdot sin(x)}{cos^5(x)} [/tex]

g'(x) = 1

Therefore;

[tex] \displaystyle{\lim_{n \to \\ \frac{\pi}{4} } \frac{ {sec}^{4} x - 4}{x - \frac{\pi}{4} }= \frac{ \frac{4\cdot sin(x)}{cos^5(x)}}{1}=\frac{4\cdot sin(\frac{\pi}{4})}{cos^5(\frac{\pi}{4})} = 16}[/tex]

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Your friend claims that the graph of f(x) = x - 2 can be produced by two distinct translations of the graph of the parent linear function. The graph moves down by 2 units.

Given that,

Your friend claims that the graph of f(x) = x - 2 can be produced by two distinct translations of the graph of the parent linear function.

We have to find how much units the graph moves.

This linear equation's parent function is y=x.

The way your friend described this function wasn't exactly accurate.

If the function's transformation takes the form y=f(x)+c, the graph will move vertically up or down along the y-axis depending on the value of c.

The graph moves up if c>0.

The graph drops down if c>0.

When y=x-2 and y=f(x)+c are compared, we see that c = -2, which is smaller than 0, in the equation y=x-2.

Therefore, the graph moves down by 2 units.

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4 tickets----------------------------->$40

8 tickts------------------------------->$x

Using cross multiplication:

8 tickets cost $80

Answer:

  z = 134°

Step-by-step explanation:

You want to know the measure of exterior angle z given remote interior angles of the triangle are 77° and 57°.

The exterior angle of a triangle is equal to the sum of the remote interior angles of the triangle. (It is useful to remember this.)

  z = 77° +57°

  z = 134°

__

Additional comment

As you know the value of the interior angle at C will be the supplement of the value of z: (180° -z). Then the sum of the interior angles is ...

  77° +57° +(180°-z) = 180°

Add (z -180°) to both sides of this equation and you get ...

  77° +57° +(180°-z) +(z -180°) = 180° +(z -180°)

  77° +57° = z . . . . simplified

Answer:

Grade A: 0.2

Grade B: 0.3

Grade C: 0.2

Grade D: 0.15

Grade F: 0.15

Step-by-step explanation:

You take the number of the grade and divide that by the total.  The total is 20.  A 4/20 = 0.2

Grade B 6/20 = 0.3 and so on

Answer:

For part b. its grade D so it says how much right so I think u need to times it or divide it or so sorry if this doesn't help u

Answer: 87

Step-by-step explanation:
You would do 26/30 which gives 86.6666666 but we round up to 87

Answer:

0.86666...

Step-by-step explanation:

26/30=0.86666...

rounded  to the nearest tenth is

0.9

Answer:

25%

Step-by-step explanation:

5/20 = 1/4

1/4 x 100 = 100/4 = 25

(1 x 25)/(4x100) = 25/100

25%

Answer:

25%

Step-by-step explanation

5/20 = 1/4

1/4 x 100 = 100/4 = 25

(1 x 25)/(4x100) = 25/100

25%                                   Therefore They have lost 25% of there games

Given the expression:

The first step to solve it using the square root property, is moving the coefficient on the right side of the equation to the left side, changing it's sign:

Now, remember the rule for conjugates:

in this case we have the following:

therefore, we can factor the expression like this:

Finally, we have that the only values that make true the expression are:

The association between two numerical variables measured for the same individuals is displayed in a scatterplot. One variable's values are displayed on the horizontal axis, and the other variable's values are displayed on the vertical axis. On the graph, each individual in the data is represented by a point.

The relationship between two economic phenomena, such as employment and output, inflation and retail sales, and taxes and economic growth, can be visually illustrated using scatter plots.

Spread Plots. Points on a scatter (XY) plot depict how two sets of data relate to one another. Each dot in this illustration represents a person's weight in relation to their height. (The information is displayed as "Cartesian (x, y) Coordinates")

Display a connection between the data and a trend. Display all data points, including outliers, minimum, and maximum values. can draw attention to relationships. the sample size and exact data values are retained.

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He got a 61.5% Discount

The required equation is g(x)=x+6

What is an equation?

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. A polynomial equation is the most common sort of equation. A mathematical equation is akin to a weighted scale. When equal weights of material (for example, grain) are placed in the two pans, the scale is balanced and the weights are said to be equal. To keep the scale in balance, if grain is withdrawn from one pan of the balance, an equal amount of grain must be removed from the other pan. In general, if the identical operation is done on both sides of an equation, it stays balanced.

The required equation is g(x)=x+6, when the parent function is 6 units up

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solution

For this case we can use the following proportion rule:

Then we can solve for f on this way and we got:

Answer:

-6.3 is your slope.

Step-by-step explanation:

Hello, there! Nice to meet you.

This is a pretty easy question, as it's written in y = mx + b form.

When it's written like this, the m in replacement is your slope value.

So, in this case, -6.3 is your slope.

If I had y = 3x + 6, then 3 would be the slope, but that's just an example.

Once more, the m value is your slope.

Hope this helped, and best of luck with the rest of your assignment! (:

The coordinates of the point M' is (-6,2) when the point M was reflected across x =-2.

Here, assume that there is a point A(a, b). This point is reflected across the line x = -2. When reflected across this line, the value of the y coordinate of this point A will not change, only the value of the x coordinates of the point A will change.

Here, the point M(1,2) is reflected across the line x = -2.

The coordinates of the reflected point M' are (a, b).

The value of will b will remains same as that of the point M.

Now, the location of a,

the distance between the line x = -2 and a will be same as that of the distance between 2 and x =-2 which is 4 units,

So, the location of a will be fours units away from x =-2 and in the opposite direction so, a = -6

So, the Point M' is (-6,2)

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Answer:

a = 3 ; b = 1 ;  c = -5

Step-by-step explanation:

     a +b - 2c = 14 -----------------------------(I)

         4b + c = -1  -----------------------------(II)

                 c  = -5 ------------------(III)

Substitute c = -5 in equation (II) and find the value of 'b',

        4b + (-5) = -1

             4b     = -1 + 5

                4b  = 4

                  b = 4 ÷ 4

                 [tex]\sf \boxed{b = 1}[/tex]

Substitute c = -5 and b = 1 in equation (I)

        a + 1 - 2*(-5) = 14

          a + 1 + 10    = 14

                     a +11 = 14

                           a = 14 - 11

                           [tex]\sf \boxed{a = 3 }[/tex]

 a + b - 2c = 14

LHS = a + b - 2c

       = 3 + 1 - 2*(-5)

       = 3 + 1 + 10

       = 14 = RHS

Hence verified.

Answer:

(3, 1, - 5 )

Step-by-step explanation:

a + b - 2c = 14 → (1)

4b + c = - 1 → (2)

c = - 5 → (3)

substitute c = - 5 into (2)

4b - 5 = - 1 ( add 5 to both sides )

4b = 4 ( divide both sides by 4 )

b = 1

substitute b = 1 and c = - 5 into (1)

a + 1 - 2(- 5) = 14

a + 1 + 10 = 14

a + 11 = 14 ( subtract 11 from both sides )

a = 3

solution is (3, 1, - 5 )

as a check substitute values into (1) and (2)

a + b + c = 3 + 1 - 2(- 5) = 4 + 10 = 14 ← correct

4b + c = 4(1) - 5 = 4 - 5 = - 1 ← correct

In February, Robbins and Myers, Inc. executed a 2-for-1 split, then the

(a) . The shares did she hold after the split is 940 shares.

(b) . The post-split price per share is $34.74

(c) . Janine didn't gain or lose any money during the event.

Based on the given conditions,

In February, Robbins and Myers, Inc. executed a 2-for-1 split.

That means,

2 - for - 1 stock split.

= 2 / 1

= 2

(a) . How many shares did she hold after the split?

Then,

Janine had 470 shares before the split.

Each share was worth $69.48.

= 470 shares * 2

= 940 shares

Hence,

The shares did she hold after the split is 940 shares.

(b) . What was the post-split price per share?

Each share was worth $69.48.

Then,

= $69.48/2

= $34.74

Hence,

The post-split price per share is $34.74

(c) . Show that the split was a monetary non-event for Janine

We can write,

After the split, Janine had 940 share worth $34.74.

Since they doubled the amount of share, but decrease the amount of each share.

So,

Janine didn't gain or lose any money during the event.

Therefore,

Robbins and Myers, Inc. executed a 2-for-1 split,

(a) . The shares did she hold after the split is 940 shares.

(b) . The post-split price per share is $34.74

(c) . Janine didn't gain or lose any money during the event.

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Answer:

The place value of 5 is HUNDREDTH

Explanation:

From the right-hand side, the place value of:

8 is Hundred

2 is Ten

6 is Unit

1 is Tenth

and finally, what we are required to tell,

5 is Hundredth.

Answer: C. Both are correct. Gregory's definition can be simplified to get Felipe's definition.

Step-by-step explanation:

-1, 6, 13

[tex]a_n=a_1+(n-1)d\\\\d=a_2-a_1\\\\d=6-(-1)\\\\d=6+1\\\\d=7[/tex]

Hence,

[tex]a_n=-1+7(n-1)\\\\a_n=-1+7(n)-7(-1)\\\\a_n=-1+7n-7\\\\a_n=7n-8[/tex]

Answer:

Step-by-step explanation:

the first one

Answer:

20 pencils for $2.50 has the lesser price per pencil.

Step-by-step explanation:

$0.13 compared to $2.50 ÷ 20 = $0.125

$0.13 > $0.125

Best fit quadratic equation is: y = 77x + 140

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. An example of a quadratic equation is x² + 2x + 1. Here, an is greater than zero because if it equals zero, the equation will cease to be quadratic and change to a linear equation, such as bx+c=0. As a result, we cannot refer to this equation as a quadratic equation.

Given,

A shot-putter throws a shot and its height is noted every 20 feet

Best fit quadratic equation is:

y = 77x + 140

As after this equation, feet above ground is decreasing.

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Answer: 5:12

Step-by-step explanation:

[tex]\displaystyle\\30:72=\\\\\frac{30}{72}=\\\\ \frac{6(5)}{6(12)}=\\\\ \frac{5}{12}=\\\\ 5:12[/tex]

Solution

Where

Now,

Therefore, V = 150

Answer: y = -3x + 1

Step-by-step explanation:

Find the slope, rise/run:

-5 - (-17) / 2 - 6

-12/4 or -3

Find the y-intercept by substitution:

y = mx + b

-5 = -3(2) + b (Using the first coordinate)

1 = b

Solution:

Given the data below:

A) Mean monthly flow:

The mean monthly flow is evaluated as

Thus, the mean monthly flow is 338.5 KAF

B) Median monthly flow:

The median is evaluated as

Answer:

32 feet

Step-by-step explanation:

See attached worksheet

If He rides back home, taking the same route, on a bus that travels at a rate of 40mi/hr. The entire trip takes 3.5 hrs. How far along this route is Terrence’s house from the theater is : 50 mile.

Movie time = 2hrs and 15mins

Let convert the movie time

2hrs and 15mins = 2 15/60 h = 2 1/4 h = 2.25 h

Now let calculate the bus time and the distance

Bus time = Entire time - Walking time

Bus time = 3.5 h - 2. 25 h

Bus time =  1.25 h

Now let calculate the distance

Distance = Speed × Time

Distance =  40mi/hr ×  1.25 h

Distance = 50 mile

Therefore the distance is 50 mile.

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