Find the average rate of change of each function over the interval [0, 2]. Match each representation with its respective average rate of change.

Answer:

Step-by-step explanation:

y = x² + 7x - 5 ............ (1)

2x - y = - 9 ................ (2)

(1) ------> (2)

2x - ( x² + 7x - 5 ) = - 9

- x² - 5x + 14 = 0 ........ (3)

- 1 × (3)

x² + 5x - 14 = 0

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

[tex]x_{1}[/tex] = - 7 and [tex]x_{2}[/tex] = 2

2( - 7) - [tex]y_{1}[/tex] = - 9 ⇒ [tex]y_{1}[/tex] = - 5

2(2) - [tex]y_{2}[/tex] = - 9 ⇒ [tex]y_{2}[/tex] = 13

The solutions of system are

( - 7, - 5 ) and ( 2, 13 )

[tex]4(a + 3) = - 32 \\ 4a + 12 = - 32 \\ 4a = - 32 - 12 \\ 4a = - 44 \\ a = - 11[/tex]

Hope it helps

Please give brainliest

Step-by-step explanation:

4(a+3)=-32

4(a+3)/4=-32/4

(a+3)=-8

a+3-3=-8-3

a=-11

[tex]|\Omega|=6^2=36\\|A|=4\cdot3=12\\\\P(A)=\dfrac{12}{36}=\dfrac{1}{3}\approx33.3\%[/tex]

Answer: 1/5

Step-by-step explanation:

There are three kinds of Marbles. (M) marbles

(G) green: 4m

(R) red: 1m

(B) blue: 1m

Dan pulled a green marble out leaving

(G) green: 3m

So, the probability of picking a green marble is 1/5

sorry if I'm wrong/correct me if I'm wrong.

Triangle ABC is similar to triangle DEC, ∠B ≅ ∠E and 3DE = 2BC

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease in the size of a figure by a scale factor.

Right triangle ABC is reflected over AC, then dilated by a scale factor of 2/3 to form triangle DEC, hence:

Triangle ABC is similar to triangle DEC, corresponding angles are congruent (∠B ≅ ∠E) and DE = (2/3)BC i.e. 3DE = 2BC

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The value of the variables are y = -45/2, r = -9, x = 2/9 and x = 2

(1) y/3 + 6 = -3/2

Multiply through by 3

y + 18 = -9/2

Subtract 18 from both sides

y = -18 - 9/2

Take LCM

y = (-18 * 2 - 9)/2

Evaluate

y = -45/2

(2) -2r/3 - 3 = 3

Multiply through by 3

-2r - 9 = 9

Add 9 to both sides

-2r = 18

Divide by 2

r = -9

(3) 2/3 - 2x = x

Multiply through by 3

2 - 6x = 3x

Add 6x to both sides

2 = 9x

Divide by 9

x = 2/9

(4) 7x/2 + -5/2 = 9/2

Multiply through by 2

7x - 5 = 9

Add 5 to both sides

7x = 14

Divide by 7

x = 2

Hence, the value of the variables are y = -45/2, r = -9, x = 2/9 and x = 2

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Answer:

Step-by-step explanation:

m∠5 + m∠6 = 180° - This is true because the exterior angle and interior angle form a linear pair, and are thus supplementary.

m∠2 + m∠3 = m∠6 - This is true by the exterior angle theorem.

m∠2 + m∠3 + m∠5 = 180° - This is true because the interior angles of a triangle add to 180 degrees.

The three right options are:

m∠5 ₊ m∠6 = 180° which represents a linear pair.

∠2 ₊ ∠3 = ∠6 showing the exterior angle property of triangle.

m∠2  m∠3  m∠5 = 180° as the sum-triangle

sum-triangleproperty.

Given,

the interior angles of the triangle are 2,3,5

the exterior angle at ∠2 is ∠1.

the exterior angle at ∠3 is ∠4.

the exterior angle at ∠5 is ∠6.

Now, take into account a triangle with external angles as ∠1 , ∠4 and ∠6.

Apply the exterior angle property of a triangle.

The sum of the opposing internal angles determines the outer angle of a triangle.

For exterior ∠1 we get

∠1 = ∠5 ₊ ∠3

Similarly, for exterior ∠4 we get

∠4 = ∠5 ₊ ∠2

Then for exterior ∠6 we get

∠6 = ∠2 ₊ ∠3

∴ through the exterior angle property we get the correct option as

m∠6 = m∠2 ₊ m∠3

Now we know the sum-triangle property that sum of the angles in triangle is equal to 180°

∴ m∠2 ₊ m∠3 ₊ m∠5 = 180°

We know the linear pair property i.e, If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.,

∴ m∠5 ₊ m∠6 = 180°

Hence we get the statements which match the diagram are:

m∠5 ₊ m∠6 = 180°

m∠2 ₊ m∠3 ₊ m∠5 = 180°

m∠6 = m∠2 ₊ m∠3

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The box plot that represents the data is the first option.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

Minimum value = 30

Maximum value = 57

1st quartile = 1/4 (n + 1)

1/4 x 10 = 2.5th term = 35

Third quartile = 3/4 x (n + 1 )

3/4 x 10 = 7.5 term = 53

Median = 46

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Answer:

-6

Step-by-step explanation:

Well you just plug in the value 3 for x. This will give you the following equation: [tex]\frac{4(3+3)(3+1)}{(3+5)(3-5)}[/tex] which simplifies to [tex]\frac{4(6)(4)}{(8)(-2)}[/tex] which further simplifies to [tex]-\frac{96}{16}[/tex] which can further be simplified by dividing the two numbers and that results in -6

Answer:

A

Step-by-step explanation:

it really only means to replace every x by 3 and then simply calculate.

4(3+3)(3+1) / ((3+5)(3-5)) =

= 4×6×4 / (8×-2) = 96/-16 = -6

The coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a trapezoid GHJK that was rotated 180° about the origin.

The rule for 180-degree rotation about the origin:

(x, y) → (-x , -y)

From the graph:

Coordinate of H' is (-3, -2)

(-3, -2) → (3, 2)

Thus, the coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.

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Sin3A=Cos3A

Cos(90-3A)=Cos3A

90-3A=3A

90=3A+3A

90=6A

90/6=A

^•^

The answer is A=15

Answer:

[tex]144 cm^{2}[/tex]

Step-by-step explanation:

Step 1: Find the true length of each side

We know that the perimeter is 56cm and the ratio of AD:AB:DC:BC is 5:12:6:5. It is safe to assume that this ratio is the simplified version, which means that if we multiply each of these numbers by a scale factor of [tex]x[/tex], then we get the true length of each side, so we would get [tex]5x, 12x, 6x, 5x[/tex] for the sides. We also know that when we add these numbers, we get the perimeter, which is 56. So, we can create the equation [tex]5x + 12x + 6x + 5x = 56[/tex]. Then, solve the equation for x, which would be 2, and go back and multiply each number with 2 to get the following:

AD = 5*2 = 10cm, AB = 12*2 = 24cm, DC = 6*2 = 12cm, BC = 5*2 = 10cm  

Step 2: Calculate the Height

Now we know the lengths of each side, lets take a look at the formula for the area of a trapezium: [tex]\frac{base_{1} + base_2}{2}*height[/tex]. So, the next step would be to calculate the height. We can draw the height by drawing a line straight down from the vertex D and another straight down from the vertex C. These lines are both the height, and will be the exact same length. We can calculate that the height is 8 because AB is 24 cm, but the length from the height at vertex D to the height at vertex C is 12 cm, so that means that the base of each triangle is 12/2 = 6 cm. Then we can use Pythagorean theorem to figure out that the height is 8cm.

Step 3: Calculate the Area

Lastly, we can calculate the area. The formula is [tex]\frac{base_{1} + base_2}{2}*height[/tex]. In this case, the numbers would be [tex]\frac{12 + 24}{2} * 8 = 144cm^{2}[/tex]

I know this is a lot, so let me know if you have any questions!

Answer:

Show the process

The answers to the question have been written below

1. If the number of sides of the polygon should increase then the measure of the interior angle would increase by 180.

2. A regular polygon has the sum of its external angles as 360. This is solved as 360/n = 0

Hence the value of the exterior would move towards 0 as its sides increases.

4. As the total sum of the of the polygon changes, it would tend towards infinity.

5. The total sum of the exterior angles as the number of sides changes would tends towards 360 degrees.

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Answer:

09 l

Step-by-step explanation:

p0-9

The equivalent exponential expression for the given radical expression √(3 + 7) is √10.

To convert the given radical expression √(3 + 7) into its equivalent exponential expression. This process involves using exponentiation to represent the radical form.

The given radical expression is √(3 + 7). To find its equivalent exponential expression, we need to express the radical in terms of an exponent.

Recall that a radical expression of the form √(a) is equivalent to raising 'a' to the power of 1/2. In this case, 'a' is the quantity inside the radical, which is 3 + 7. So, we can write:

√(3 + 7) = (3 + 7)^(1/2).

Next, we simplify the expression inside the parentheses:

3 + 7 = 10.

Now, the expression becomes:

(10)^(1/2).

To further simplify, we raise 10 to the power of 1/2. Recall that raising a number to the power of 1/2 is the same as finding the square root of that number. So:

(10)^(1/2) = √10.

Therefore, the equivalent exponential expression for the given radical expression √(3 + 7) is √10.

To summarize, we transformed the radical expression √(3 + 7) into its equivalent exponential expression √10 by using the rule that √(a) is equal to a^(1/2). By raising the expression inside the radical to the power of 1/2, we simplified it and found the square root of 10 as the final result.

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Answer:

y = x/2 -3

Step-by-step explanation:

x - 2y = 6

Slope intercept form is y = mx+b  where m is the slope and b is the y intercept

We need to solve for y

Subtract x from each side

x-2y-x = -x+6

-2y = -x+6

Divide each side by -2

-2y/-2 = -x/-2 +6/-2

y = x/2 -3

The slope intercept form is

y = x/2 -3

Answer: slope intercept form is

y = x/2 -3

Step-by-step explanation:

hope this helps ; )

Answer:

center = (-5, -7)

radius = 21

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

Given equation:

[tex](x+5)^2 + (y+7)^2 = 21^2[/tex]

Comparing the given equation with the standard equation of a circle:

Hence, the coordinates of centre is (-5,-2).

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

The given equation  of circle,

(x+5)² + (y+7)² = 21²

We know that,

Equation of a circle is:

(x-a)² + (y-b)² = r²

where:

(a, b) is the center

And r is the radius

Comparing with the given equation we have,

center = (-5,-7)

And radius = 21 units

Thus,

Coordinates =  (-5,-7).

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Factor the rational function,

.

.

.

.

Notice that the denominator and numerator both have x-1. This means that we have a removable discontinuity there so set x-1=0.

.

.

So our domain can be all reals except 1.

Range: First factor out the x-1. We will be left with

.

Since 1 isn't in the domain, plug in 1 to find the what won't be in the range

.

So 7 isn't in the range,

End Behavior:

Since the rational function numerator is a quadratic and the denominator is a linear function, the rational function will approach will not have a horizontal asymptotes.

Cooper left his dinner server a 19% tip.

To find the percent tip, we need to first subtract the cost of the meal from the total amount paid, which will give us the tip amount:

Tip amount = Total amount paid - Cost of the meal

Tip amount = $33.32 - $28

Tip amount = $5.32

Now we can calculate the percentage of the tip by dividing the tip amount by the cost of the meal and multiplying by 100:

Percent tip = (Tip amount / Cost of the meal) x 100

Percent tip = ($5.32 / $28) x 100

Percent tip = 0.19 x 100

Percent tip = 19%

Therefore, Cooper gave a 19% tip on his dinner.

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Median: 6

Range: 9

Mode: 7, appeared 3 times

The common ratio of the given Geometric progression is one-half.

Let a be first term and r common ratio of the Geometric progression.

The Geometric sequence is the form a,ar,ar^2, ...

Given that the sequence begins with 12, i.e a = 12

and also given that the sequence are in Geometric Progression.

By dividing the preceeding number by 2, we get the successive number

Then the Geometric sequence is 12, 12×1/2, 12×1/4, 12×1/8, 12×1/16 ...

= 12, 6, 3, 3/2, 3/4, ...

Common ratio = Second term / First term

= 6/12

=1/2

Therefore, the common ratio of the given geometric progression is one-half.

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Answer:

its a

Step-by-step explanation:

The equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

The given coordinate are (8, -1) and (2, -5).

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

The slope of the equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].

The standard form of an equation is Ax + By = C.

The given the point-slope form is [tex]y+1=\frac{2}{3} (x-8)[/tex].

Multiply each term by 3 of the equation.

[tex](y+1) \times3=\frac{2}{3} (x-8) \times3[/tex]

⇒3y + 3 = 2x - 16

Subtract 2x from both sides of a equation.

That is, -2x + 3y + 3 = - 16

Subtract 3 from both sides of a equation.

That is, -2x + 3y = - 19

Multiply each term by - 1 from both sides of an equation.

That is, 2x - 3y = 19

Therefore, the equation of the line that passes through the points (8,-1) and (2,-5) is 2x - 3y = 19.

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The points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible the answers are D, E, and H.

A graphing calculator is a portable computer that can plot graphs, solve multiple equations at once, and carry out other variable-related activities.

We have points shown in the coordinate plane.

As the window of a graphing utility is set at:

X(min) : -6

X(max): 6

Y(min) : -6

Y(max) : 6

The points out of 6 will not be visible.

We can draw a square as shown in the attached picture.

The points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible.

Thus, the points D(-7, 5), E(-8, -3), and H(10, -5) will not be visible the answers are D, E, and H.

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Answer:

Option B is correct

Answer:

B there is enough raspberries to make 4 pie they can 6 pies if they 2 more of raspberries

Answer:

(0, 4) and (-1, 0)

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=2x^2+6x+4\\y=-4x^2+4\end{cases}[/tex]

Solve by substitution

Substitute the first equation into the second:

[tex]\implies 2x^2+6x+4=-4x^2+4[/tex]

Add 4x² to both sides:

[tex]\implies 2x^2+6x+4+4x^2=-4x^2+4+4x^2[/tex]

[tex]\implies 6x^2+6x+4=4[/tex]

Subtract 4 from both sides:

[tex]\implies 6x^2+6x+4-4=4-4[/tex]

[tex]\implies 6x^2+6x=0[/tex]

Factor out 6x from the left side:

[tex]\implies 6x(x+1)=0[/tex]

Therefore:

[tex]\implies 6x=0 \implies x=0[/tex]

[tex]\implies x+1=0 \implies x=-1[/tex]

To find the y-coordinates of the found x-values, substitute the found values of x into one of the equations:

[tex]x=0 \implies -4(0)^2+4=4 \implies (0,4)[/tex]

[tex]x=-1\implies -4(-1)^2+4=0\implies (-1,0)[/tex]

Therefore, the solutions to the system of equations are:

(0, 4) and (-1, 0)

Answer:

Solutions:

a) x = 0, y = 4 ⇒ (0, 4)

b) x = -1, y = 0 ⇒ (-1, 0)

Step-by-step explanation:

Given system of equations:

a) y = 2x² + 6x + 4

b) y = -4x² + 4

1. Substitute the value of y in the second equation into the first equation:

⇒ -4x² + 4 = 2x² + 6x + 4

2. Solve for x:

⇒ -4x² + 4 = 2x² + 6x + 4 [subtract 4 from both sides]

⇒ -4x² + 4 - 4 = 2x² + 6x + 4 - 4

⇒ -4x² = 2x² + 6x [subtract 2x² from both sides]

⇒ -4x² - 2x² = 2x² - 2x² + 6x

⇒ -6x² = 6x [subtract 6x from both sides]

⇒ -6x² - 6x = 6x - 6x

⇒ -6x² - 6x = 0 [factor out -6x from the equation]

⇒ -6x(x + 1) = 0

Two cases:

a)

⇒ -6x = 0 [divide both sides by -6]        

⇒ -6x ÷ -6 = 0 ÷ -6

⇒ x = 0

b)

⇒ x + 1 = 0 [subtract 1 from both sides]

⇒ x + 1 - 1 = 0 - 1

⇒ x = -1

3. Find the value of y by substituting the found x values into one of the given equations:

a) x = 0:

⇒ y = -4x² + 4

⇒ y = -4(0)² + 4

⇒ y = -4(0) + 4

⇒ y = = 0 + 4

⇒ y = 4

coordinate: (0, 4)

b) x = -1:

⇒ y = -4x² + 4

⇒ y = -4(-1)² + 4

⇒ y = -4(1) + 4

⇒ y = -4 + 4

⇒ y = 0

coordinate: (-1, 0)

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Step-by-step explanation:

Line L → 2x - 3y = 6

Where a = 2 and b = -3

• So, we can use this formula to find the gradient of Line L.

m = -a/b

m = -2/-3

m = 2/3 IS THE ANSWER

Answer:

gradient = 2/3

Step-by-step explanation:

Here is another way....manipulate the equation to y = mx+ b form

  where m = slope ( gradient)

2x - 3y = 6          add 3 y to both sides

6 + 3y = 2x         subtract 6 from both sides

3y = 2x - 6          divide by 3

y = 2/3 x - 2        gradient = 2/3

Answer:

Step-by-step explanation:

Find the volume of the sample container.

Given:

Volume formula:

Substitute to get:

Find the volume of the trace element, using the given proportion: