Find the measure of the angle marked with a question mark using inverse trig
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The [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex] .

Quadratic sequences are sequences that include  [tex]nth[/tex]  term. They can be identified by the fact that the differences between the terms are not equal, but the second differences between terms are equal.

Quadratic sequence [tex]=an^2+bn+c[/tex]

Here [tex]a,b,c[/tex] are constant and [tex]n[/tex] is the position of term.

First difference [tex]= 3a+b[/tex]

Second difference [tex]=2a[/tex]

We have,

Quadratic sequence [tex]8,16,26,38,52,68,86,....[/tex]

Quadratic sequence [tex]=an^2+bn+c[/tex]

so,

For [tex]n=1[/tex];

[tex]8=an^2+bn+c[/tex]

[tex]8=a+b+c[/tex]   [tex]........(i)[/tex]

For [tex]n=2[/tex];

[tex]16=4a+2b+c[/tex]    [tex]........(ii)[/tex]

For [tex]n=3[/tex];

[tex]26=9a+3b+c[/tex]    [tex]........(iii)[/tex]

Now,

Subtract equation [tex](i)[/tex] from [tex](ii)[/tex]

we get,

[tex]8=3a+b[/tex]    [tex]........(iv)[/tex]

Subtract equation [tex](ii)[/tex] from [tex](iii)[/tex] we get,

[tex]10=5a+b[/tex]    [tex]........(v)[/tex]

Subtract equation [tex](iv)[/tex] from [tex](v)[/tex] we get,

[tex]2=2a[/tex]  (This is second difference mentioned above)

[tex]a=1[/tex]

Putting [tex]a=1[/tex]  in [tex](iv)[/tex]

⇒[tex]b=5[/tex]

Now putting values of [tex]a[/tex] and [tex]b[/tex] in equation [tex](i)[/tex]

[tex]8=1+5+c[/tex]

[tex]c=2[/tex]

Now, putting values of [tex]a[/tex] , [tex]b[/tex] and [tex]c[/tex] in,

Quadratic sequence [tex]=an^2+bn+c[/tex]

we get,

[tex]nth[/tex] term rule [tex]=n^2+5n+2[/tex]

Hence, we can say that the [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex].

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Answer:

x=7.5y

Step-by-step explanation:

I took the test

Answer:

$14.80

Step-by-step explanation:

You just have to 0.8 * 18.50 becuase the new price is 80% of the old price. That would result in 14.80.

Answer:

1*4 = 4 in^2

Step-by-step explanation:

The area for this shape is calculated by multiplying width and length:

1*4 = 4 in^2

Answer:

C

Step-by-step explanation:

C

Answer:

c

Step-by-step explanation:

c is the answer to this problem

Answer:

$3.75 every 8 oz bags.

Step-by-step explanation:

7.5 divided by 2 to get 3.75. 1 LB is equal to 16 oz so 8 is half of 16.

Answer:

Yes

Step-by-step explanation:

It is a function because the x value doesnt repeat itself. The x value is the input

Answer:

1 juice boxes = 153 millimeters

459 ?

3 juice boxes = 459 millimeters

Step-by-step explanation:

Answer:

yes, the question is proportional. if you multiply 9.50 by 2 you get 19 and so on and so forth. the constant rate is 9.50

Answer:

35°

Step-by-step explanation:

As we know vertically opposite angles are equal . So ,

x + 90= 125

x = 125-90 = 35°

Answer:

35

Step-by-step explanation:

125 + 90(APC) + DPA + EPB + x = 360

215 + DPA + EPB + x = 360

DPA = 180 - 125 = 55

EPB = DPA

EPB = 55

X = 90(EPC) - EPB

X = 90 - 55

X = 35

OR easy way

DB is a straight line so angels on it add up to 180

EPB = 180 - 125

EPB = 55

X = 90(EPC) - EPB

X = 90 - 55

X = 35

(BC + AD) / 2 = 17

(2x + 1 + 3x + 8) / 2 = 17

5x + 9 = 34

5x = 25

x = 5

Answer:

The number of hours Jenny babysits

Step-by-step explanation:

Since we know that the 10 is the fixed fee for the babysitting services and 5 represents the amount charged per hour, it is safe to say x represents the number of hours Jenny babysits.

Ex.: Let us say she baby sits for 3 hours. 3 would take the place of the x

   5(3)+10. This means Jenny will charge the person she babysat for a total of  

   $15 just for the hours alone.

Hope this helps! :)

Answer:

x represent the number of hours Jenny Babysits

Step-by-step explanation:

since she charges $5 per hour, then X is always how many hours

the answer is 1/6 bbbbbbbbb

Step-by-step explanation:

bring both fractions to the same denominator (bottom number). then we can readily compare our add or subtract them.

what is the snaked common multiple of 2 and 3 (the smallest number that can be divided without remainder by both numbers)?

it is 6 (in case of doubt simply multiply both numbers and use the result as common denominator).

so, we need to bring both to fractions in the form .../6.

2/3 = 4/6

1/2 = 3/6

so,

4/6 - 3/6 = 1/6

and that is the answer to the original question.

Answer:

Step-by-step explanation:

The surface area of a sphere is given by

A=4πr^2

The volume is

V = (4/3)πr^3

At r = 4":

A = 64π in^2

V = 85.3π in^3

At r = 5" (a 25% increase in r)

A = 100π in^2  (a 156.25% increase)

V = 167π in^3  ( a 195.8% increase)

We can show the ratio of these two measures by dividing the Volume by the Area:

V/A = ((4/3)πr^3/(4πr^2))

V/A = (1/3)r

For the 2 examples (4" and 5"), V/A is:

4":  (85.3π in^3)/(64π in^2) = 1.33   [(1/3)r = 4/3 = 1.33]

5":  (167π in^3)/(100π in^2) = 1.67   [(1/3)r = 5/3 = 1.67]

V/A = (1/3)r

Since Volume is a function of r^3 and Area is related to r^2, Volume will always increase faster, by a ratio of 1/3 r.

Answer:

To get the slope, we can first mark out any 2 points of the line.

In this case, I will use the point (-2, 0) which will be (x1, y1) and (0, -2) which I will call (x2, y2).

To get the slope, you need to do [tex]\frac{y2-y1}{x2-x1}[/tex]

Substitute these values in:

[tex]\frac{-2-0}{0-(-2)} =\frac{-2}{2} =-1[/tex]

The slope is -1.

Answer:

x2 - x - a2 - 3a - 2

Step-by-step explanation:

STEP 1

 ((x2) -  x) -  (a + 1) • (a + 2)

STEP 2

Final result :

 x2 - x - a2 - 3a - 2

Answer:

14.28

Step-by-step explanation:

9514 1404 393

Answer:

  D.  -17%

Step-by-step explanation:

The change from March to April is (April - March) = (100 -120) = -20. As a fraction of the March bill, that is ...

  -20/120 = -1/6

As a percentage, that change is ...

  -1/6 × 100% ≈ -16.667% ≈ -17%

The electric bill changed by about -17% from March to April.

_____

Additional comment

Water went up 4%; groceries went up about 14%, and restaurant changed by -15%.

The percentage change is found by ...

  % change = ((new amount)/(original amount) -1) × 100%

Above, we have rearranged this to ...

  % change = ((new amount) -(original amount))/(original amount) × 100%

Answer:

-3 > P

Step-by-step explanation:

1 > 3P + 10​

Subtract 10 from each side

1-10 > 3P + 10-10​

-9 > 3P

Divide each side by 3

-9/3 > 3P/3

-3 > P

Answer:

for which one all ?

Step-by-step explanation:

because if so lemme know

Answer:

B is the answer I'm pretty sure

Answer:

Step-by-step explanation:

26. -14

27. -4.732050808

Answer:

26.  (-14)

27.  −4.732050808

Step-by-step explanation:

26.  [tex](\sqrt{2}+4)(\sqrt{2}-4)[/tex]

Multiplication can be transformed into difference of squares using the rule:

(a − b) (a + b) = a² - b²

[tex](\sqrt{2} ^{2} ) - 4^{2}[/tex]

The square of √2 is 2.

[tex]2 - 4^{2}[/tex]

Calculate 4 to the power of 2 and get 16.

2 - 16

Subtract 16 from 2 to get −14.

27.  [tex](\sqrt{3} +2)(\sqrt{3} -3)[/tex]

Apply the distributive property by multiplying each term of √3 + 2 by each term of √3 - 3.

[tex]\sqrt{3} ^{2}-3\sqrt{3} +2\sqrt{3} -6[/tex]

The square of √3 is 3.

[tex]3-3\sqrt{3} +2\sqrt{3} -6[/tex]

Combine -3√3 and 2√3 to get -√3.

[tex]3-\sqrt{3} -6[/tex]

Subtract 6 from 3 to get −3.

-3 - √3

Answer:

A shortened version of a text that includes the most important events, ideas, and details without a reader’s opinion

Step-by-step explanation:

Summaries are used to quickly explains what the text is about. They include key details that express important facts, not opinions.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{3}[/tex] x + 3 ← is in slope- intercept form

with slope m = [tex]\frac{1}{3}[/tex]

and y- intercept c = 3