Find the average rate of change of the function f(x) - 2x² + 6x + 6, from x=-3 to x=-1. Note, the directions are equivalent to "Find the average rate of change over the interval [-3,-1]".​

Answer: [tex]\sum^{7}_{n=1} (-2+9n)[/tex]

Step-by-step explanation:

This is an arithmetic series with first term 7 and common difference 9, so the general formula for the nth term of the sequence is [tex]7+9(n-1)=7+9n-9=-2+9n[/tex].

The sequence has 7 terms, so the sigma notation is:

[tex]\sum^{7}_{n=1} (-2+9n)[/tex]

Answer:

[tex] \frac{1}{4} [/tex]

Step-by-step explanation:

To find the gradient of the graph, we use the formula,

[tex]gradient \: (m) = \frac{(y2 - y1)}{(x2 - x1)} [/tex]

From the graph, we obtain values for x and y

x1 = 4, x2 = 8

y1 = 2, y2 = 3

Substitute the values into our formula.

[tex]m \: = \frac{(3 - 2)}{(8 - 4)} \\ = \frac{1}{4} [/tex]

Therefore, the gradient, m, =

[tex] \frac{1}{4} [/tex]

Note:-

Hey there!

10/4

≈ 10 ÷ 2 / 4 ÷ 2

≈ 5/2

≈ 2 1/2

Therefore, your answer should be:

2 1/2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

2025 $

Step-by-step explanation:

275 multiply 3 +1200

Answer:

A.$2,025

Step-by-step explanation:

$275 x 3 years + $1,200

= $2,025

Answer:

By using opposite angles of two intersecting straight lines are congruent we proved that x = 28°

Step-by-step explanation:

Opposite angles of two intersecting straight lines are congruent

Therefore ∠DLE = ∠GLH

Here ∠DLE = 2x = ∠GLH

Sum of all angles on a straight line is 180°

Therefore ∠ELG + ∠GLH = 180°

Given that ∠ELG = 124°

124° + ∠GLH = 180°

124° + 2x  = 180°

2x = 180° -  124°

2x = 56°

x = 28°

hence proved that x = 28°

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The equation of the red graph is g(x)=^x+2-3.

Since the upscaling in the y-axis is not the main focus of this equation (being g(x) and not g(y)), the change is not applied to the x-axis.

The y-intercept and the slope in order to write the equation in y-intercept (y=mx+b) form. The slope is the change in y over the change in x.

Hence, we can rule out (-3)^2 and (x+3)^2 since they apply changes to the x-axis.

Finally, since this is an upscaling of the y-value on the y-axis, the answer is x^2 + 3 and not x^2 - 3.

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The equation is [tex]\boxed{y-2=6(x+9)}[/tex].

The half life of the radioactive substance is 10.22 years.

Half Life is the amount of time needed by the radioactive substance to reduce to its half concentration (as compared to the initial concentration).

It is given that

y = ae⁻ᵇˣ

here a is the initial amount , y is the amount remaining after x years

a = 90mg at x =0

Value of y = 12.6 mg at x = 29 years

On substitution of value

12.6 = 90 e⁻²⁹ᵇ

0.14 = e⁻²⁹ᵇ

b = 0.0678

The equation is

[tex]\rm y = 90 e^{-0.0678 * x}\\[/tex]

Half life is when the concentration is reduced to half

On 1st half life , the concentration = 90/2 = 45 mg

[tex]\rm 45 = 90 e^{-0.0678 * x}\\[/tex]

x = 10.22 years

Therefore the half life of the radioactive substance is 10.22 years.

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The statements can be completed by using the following :

1) -2 is multiplied with (5x+8)

2)  transposing of numeral values and variable values

3) The numerical values are taken one side and added to each other

4) 30 is divided by -16

5) The numerator and denominator are cancelled to the lowest possible value

x= -15/8

Given:  -2(5x+8)=14+6x  

and steps for solving them have also been given

In the first step, -2 is multiplied with (5x+8) and we get

-10x -16 = 14 +6x

In step 2, transposing of numeral values and variable values is done and we get -16x - 16 = 14

In step 3,

The numerical values are taken one side and added to each other and we get -16x=30

In step 4, 30 is divided by -16

In step 5, they are cancelled to the lowest possible value and we get

x= -15/8

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An equivalent ratio to the tape diagram shown is 1 to 2

From the tape diagram, we have:

Red = 2

Blue = 4

Express as a ratio

Red : Blue = 2 : 4

Divide by 2

Red : Blue = 1 : 2

Hence, an equivalent ratio to the tape diagram shown is 1 to 2

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Answer:

< $0 --------------$35------ $50>

Step-by-step explanation:

I see it's still the same, the maximum discount can be put off is still $50

and you can find that out by discount 30% off 50 to get $35 :)

< $0 --------------$35------ $50>

Answer:

1 HR ---> 42 km

? .----> 119 km

119 * 1/42

2.833

Answer:

[tex]\boxed {2 \frac{5}{6}}[/tex]

Step-by-step explanation:

Formula used :

[tex]\boxed {Time = \frac{Distance}{Speed}}[/tex]

Solving :

Time = 119/42

Time = 17/6

Time = 2 5/6 hours

Answer:

Step-by-step explanation:

1) Cancel [tex]x^5[/tex].

[tex]\frac{9y^{16} }{45y^4}[/tex]

2) Take out the constants.

[tex]\frac{9}{45} \times\frac{y^{16} }{y^4}[/tex]

3) Simplify [tex]\frac{9}{45}[/tex] to [tex]\frac{1}{5}[/tex].

[tex]\frac{1}{5} \times\frac{y^{16} }{y^4}[/tex]

4) Simplify.

[tex]\frac{y^{16} }{5y^4}[/tex]

5) Use Quotient Rule: Use Quotient Rule: [tex]\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}[/tex].

[tex]\frac{{y}^{16-4}}{5}[/tex]

6)  Simplify [tex]16-4[/tex] to [tex]12[/tex].

[tex]\frac{y^{12} }{5}[/tex]

[tex]y=200(0.5)^2^t[/tex] is Decay

[tex]y=\frac{1}{2}(2.5)^\frac{t}{6}[/tex] is Growth

[tex]y=(0.65)^\frac{t}{4}[/tex] is Decay

Answer:

Step-by-step explanation:

regular decagon = all side equal and all angles congruent, so your answer is 144°

Answer:

x = 3

Step-by-step explanation:

8/2 = 4

6/2 = 3

x = 3

Answer: 180 degrees

Step-by-step explanation:

Angles on a line add to 180 degrees since they form a straight angle.

Answer:

Step-by-step explanation:

hello :

y=x²-10x+16  in the form y=(x-h)²+k

y= x²-2(5)(x)+16  

y = x²-2(5)(x)+5²-9

y= (x-5)²-9    when h=5 and k = -9

Answer:

20

Step-by-step explanation:

To calculate f(2), just replace x in the equation of f(x) with 2:

[tex]f(x) = 5(x + 2)\\\\f(2) = 5(2+2)\\\\f(2) = 5(4)\\\\f(2) = 20[/tex]

1)  The volume of the quarter sphere shaped tank is; V =  20510 ft³

2) The volume of the smaller mock-up tank is; 230790 ft³

1)  The volume of the quarter sphere shaped tank is;

V = ⁴/₃πr²

V = ⁴/₃π * 70 * 70

V =  20510 ft³

2) We multiply dimensions by 2 not radius to make 1 whole cylinder. Thus

r = 35 feet remains the same as radius can only be half of a joined circle,

Since vertically cut, we have;

h = 125 * 2 = 250ft

Let's find the Area;

A = πr²

A = π * 35 *  35

A = Surface Area = 3846.5 ft²

Volume = Surface area * h

V = 3846.5 * 120 = 461580 combined.

For each; V = 461580/2 = 230790 ft³

3) Volume of smaller mock-up tank is;

V = (1/6) * 20510

V = 3418.33 ft³

4) 5/6 * 20510 = 17091.66 ft³

For the larger tank the increase is 17092 ft rounded up (0.165 value) of that of the smaller mock up tank. Therefore percentage is 1/6 = 16.67% and 5/6 = 83.33%

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Option A. is correct for the given condition.

Lets solve it through steps of range and functions,

First of all, Solve the equation:
[tex]f(x) = |x|+5[/tex]
[tex]= > x = -5[/tex] (1)

[tex]= > x = 5[/tex] (2)

So these would be the ranges of X in between 5 and -5.

Hence option A. [tex]R{f(x)eR [f(x) < 5}[/tex] is correct.

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Answer: D

Step-by-step explanation:

[tex]\left(\frac{f(x)}{g(x)} \right)=\frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{4x+1}[/tex].

This eliminates A and B.

Also, the domain excludes when the denominator equals 0, which in this case, makes the answer D

A mean is an arithmetic average of a set of observations. The correct option is A.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

Since the median is the middle value of the given data set, therefore, the median will not be changed for the given data set. But since the mean is the arithmetic average, therefore, the $100 gift will increase the mean value of the prizes.

Hence, the correct option is A.

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Answer:

this is the anwser

this

Answer:

x = 5 (If solved algebraically)

No Solution (If the parentheses are absolute value lines)

Step-by-step explanation:

Result when solving this way: 3|-3x + 9| = -18

1) Divide both sides by 3
|-3x + 9| = -18/3

2) Simplify 18/3 to 6

|-3x + 9| = -6

3)  Break down the problem into these 2 equations.

-3x + 9 = -6

- (-3x + 9) = -6

4) Solve the 1st equation: -3x + 9 = -6

- Subtract 1 from both sides.

-3x = -6 - 9

-Simplify -6 - 9 to -15.

-3x = -15

-Divide both sides by -3.

x = -15/-3

- Two negatives make a positive.

x = 15/3

- Simplify 15/3 to 5.

x = 5

6)  Solve the 2nd equation:  - (-3x+ 9) = -6

1 - Remove parentheses

3x - 9 = -6

2 - Add 9 to both sides

3x = -6 + 9

3 - Simplify -6 + 9 to 3.

3x = 3

- Divide both sides by 3.

x = 1

6) Collect all solutions.

x = 1,5

7) Check solution.

When x = 1, the original equation 3|-3x + 9| = -18 does not hold true.

We will drop x = 1 from the solution set.

8) Check solution.

When x = 5, the original equation 3|-3x + 9| = -18  does not hold true.

We will drop x = 5 from the solution set.

9) Therefore,

No solution exists.

Result when solving algebraically:

Simplifying

3(-3x + 9) = -18

Reorder the terms:

3(9 + -3x) = -18

(9 * 3 + -3x * 3) = -18

(27 + -9x) = -18

Solving

27 + -9x = -18

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-27' to each side of the equation.

27 + -27 + -9x = -18 + -27

Combine like terms: 27 + -27 = 0

0 + -9x = -18 + -27

-9x = -18 + -27

Combine like terms: -18 + -27 = -45

-9x = -45

Divide each side by '-9'.

x = 5

Simplifying

x = 5

Answer:

14m

Step-by-step explanation:

Area = πr²

A = 153.86m²

153.86 = 3.14 *r²

r² = 153.86/3.14

r = √49

r = 7

d = 2r

d = 2*7

d = 14

Answer:

x>-60

Step-by-step explanation:

Combine multiplied terms into a single fraction

2/5x - 9 < 3/5x + 3

2x/5 - 9 < 3/5x + 3

Find common denominator

2x/5 - 9 < 3/5x + 3

2x/5 + 5(-9)/5 < 3/5x + 3

Combine fractions with the common denominator

2x + 5(-9)/5 < 3/5 + 3

I HOPE YOU GOT THE ANSWER JUST SIMPLIFY IT (2x + 5(-9)/5 < 3/5 + 3) AND YOU WILL GET THE ANSWER YOURSELF AS I HAVE GIVEN ABOVE PLS MARK ME AS THE BRAINLILEST IF YOU LIKE TO AND MY ANSWER HELPED YOU:)

Answer:

[tex]\boxed {x > -60}[/tex]

Step-by-step explanation:

2/5x - 9 < 3/5x + 3

-1/5x < 12

x > -12 x 5

x > -60

Answer:

1764

Step-by-step explanation:

[tex]from \: the \: question \: rt {}^{2} \\ were \: r =9 \\ and \: t = 14 \\ rt {}^{2} = 9 \times (14) {}^{2} = 9 \times 196 = 1764[/tex]

Hii!

__________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer.}\circ \leftharpoonup[/tex]

1764

[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]

Stick in the values: 9 for r and 14 for t, and simplify.

[tex]\twoheadrightarrow\sf 9\cdot14^2}[/tex]

[tex]\bullet[/tex] Square 14 first

[tex]\twoheadrightarrow\sf 9\cdot196}[/tex]

[tex]\bullet[/tex] Multiply the numbers

[tex]\twoheadrightarrow\sf 1764}[/tex]

[tex]\bullet[/tex] Great job! We found the answer

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Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

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