A recursive rule for an arithmetic sequence is a1=4;an=an−1−3.

What is the explicit rule for this sequence?



Enter the simplified answer in the box.

an=

I NEED HELP ASAP

The sequence of angles from smallest to largest is m∠T,m∠S,m∠R.

Given three angles be m∠T=4x-52°,m∠S=x+38°,m∠R=2x+47°.

We are required to arrange the angles in ascending order.

Ascending order means values that are written in a way that smallest values come first and larger values comes last.

First we have to find the angles at one value of x.

The values will differ as the values of x differ so we have to choose point or value of x.

Suppose x=20.

Then the angles are:

m∠T=4x-52°

=4*20-52

=80-52

=28°

m∠S=x+38°

=20+38

=58°

m∠R=2x+47°

=2*20+47

=40+47

=87°

Hence the sequence of angles from smallest to largest is m∠T,m∠S,m∠R.

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The plot of [tex]\sqrt{25-x^2}[/tex] is that of the top half of a circle with radius 5. The interval [-5, 0] captures the left half of this semicircle.

Adding 5 to this shifts the plot up by 5 units. The area under this curve is then the combined area of a square with side length 5 and the area of a quarter circle with radius 5.

So we have

[tex]\displaystyle \int_{-5}^0 5 + \sqrt{25-x^2} \, dx = 5^2 + \frac\pi4\cdot5^2 = \boxed{25 + \frac{25\pi}4}[/tex]

Answer:

40°

Step-by-step explanation:

Using external angle intercepted arcs calculation:

    50° = 1/2 (210-x)    shows x = 110°

then z = 360 - 210 -110 = 40°

Answer:

second option

Step-by-step explanation:

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Since the two triangles ABE and ADE are congruent, their corresponding sides and angles are equal.

After observing all the options, we can conclude that :

Only angle AED and angle AEB are angles of given triangles and are actually equal.

[tex] \qquad \large \sf {Conclusion} : [/tex]

The marked price of the ring given the cost as 8740 inclusive of 15% tax and discount of 5% is $7,283.3.

8740 = x + (15% of x) + (5% of x)

8740 = x + (0.15x) + (0.05x)

8740 = x + 0.15x + 0.05x

8740 = 1.20x

x = 8740 / 1.20

x = 7283.33333333333

Approximately,

x = $7,283.3

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Answer:

1 (3.66)

2(3.5)

3(5.25)

By solving the equations x+2y=5, 4x-12y=-20 through elimination or substitution method we will get the value of x=1 and y=2.

Given two equations x+2y=5 and 4x-12y=-20.

We are required to solve the equations through elimination and substitution method.

Firstly we will solve the equations through elimination method.

x+2y=5-------------1

4x-12y=-20--------2

Multiply the equation 1 by 4 and then subtract the equation 2 from equation 1.

4x+8y-4x+12y=20+20

20y=40

y=2

Use the value of y in 1

x=5-2*2

x=5-4

x=1

From substitution method.

First find the value of x from first equation in terms of y.

x=5-2y-----4

Now put this value in second equation to get the value of y.

4(5-2y)-12y=-20

20-8y-12y=-20

20-20y=-20

-20y=-40

y=2

Put the value of y in equation 4.

x=5-2y

x=5-2*2

x=5-4

x=1

Hence by solving the equations x+2y=5, 4x-12y=-20 through elimination or substitution method we will get the value of x=1 and y=2.

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The domain of the function is [-4, 4) and the range of the function is [-5, 2)

The domain

As a general rule, it should be noted that the domain of a function is the set of input values or independent values the function can take.

This means that the domain is the set of x values

From the graph, we have the following intervals on the x-axis

x = -4 (closed circle)

x =4 (open circle)

This means that the domain of the function is [-4, 4)

The range

As a general rule, it should be noted that the range of a function is the set of output values or dependent values the function can produce.

This means that the range is the set of y values

From the graph, we have the following intervals on the y-axis

y = -5 (closed circle)

y = 2 (open circle)

This means that the range of the function is [-5, 2)

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Check the picture below.

now hmmm let's observe, hmmmm 11 has two digits, and low and behold, the 2 is right in the middle, then 1 and 1 on flanking it.

let's check 111 hmmmm has three digits and has a 3 right in the middle as well, and low and behold, is flanked by a regressing count, namely an "outwards" count.

let's check 1111 and 11111, same happens, one has a digit of 4 in the middle and the other 5, and yes, the "outwards" count on each, outwards count towards 1 each time btw.

so, if we were to take that pattern, we can say that eight 1's, namely 11111111 x 11111111, will have an 8 in the middle, and will look like 1234567   8   7654321.

Answer:

9

Step-by-step explanation:

To find the rate of change we use the formula

f(x2) - f(x1)

------------------

x2 -x1

f(x) = 9x

x2 = 9  and x1 = 0

f(x2) = 9( 8) = 72

f(x1) = 9(0) =0

The rate of change is

72 - 0

------------

8-0

72

----

8

9

The rate of change is 9

Answer:

9

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given:

Therefore:

Substitute the given values into the average rate of change formula:

[tex]\begin{aligned}\implies \dfrac{f(8)-f(0)}{8-0} & = \dfrac{9(8)-9(0)}{8-0}\\\\& = \dfrac{72-0}{8-0}\\\\& = \dfrac{72}{8}\\\\& = 9\end{aligned}[/tex]

Therefore, the average rate of change of the function f(x) over the interval 0 ≤ x ≤ 8 is 9.

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Answer:

45°

Step-by-step explanation:

it is an inverted angle within a circle

==========================================================

Explanation:

Minor arc AD is the shortest path from A to D along the circle's edge. This is 90 degrees. Minor arc AD combines with DC  to get arc ADC

Arc ADC is a semicircle because of the diameter AC. Any semicircle has a measure of 180 degrees.

So,

(minor arc AD) + (minor arc DC) = arc ADC

(minor arc AD) + (minor arc DC) = 180

(90) + (minor arc DC) = 180

minor arc DC = 180 - 90

minor arc DC = 90

AD and DC are 90 degrees each.

Then notice that inscribed angle DAC subtends minor arc DC. Use the inscribed angle theorem to determine angle DAC is 90/2 = 45 degrees

Answer:

B

Step-by-step explanation:

Comment

√15 = 3.87

√12 = 3.46              Subtract these 2

Difference = 0.41

Answer:

Slope: [tex]-\frac{1}{5}[/tex]   Y-intercept: (0,0)

Step-by-step explanation:

By putting this into a graph you can see that the y-intercept is (0,0). Also, by looking at the chart and using the walk, rise rule you can see that the slope is [tex]-\frac{1}{5}[/tex].

Answer:

8v-28/v^2-2v-24

Step-by-step explanation:

1. Find common denominator

2. Combine fractions with common denominator

3. Re-order terms so constants are on the left

Answer:

42 - 24 = 18

18/24 = 3/4

the answer would be 1 and 3/4 days

Answer:

1 and 3 over 4 days

Step-by-step explanation:

Since 24 hours is 1 day  all we have to do is divide 42 into 24 and see what the resulting fraction is

42/24 = 7/4  (reducing to lowest fraction)

7/4 = 1 3/4 days (7 ÷ 4 gives quotient 1 and remainder is 3)

Answer:
1 and 3 over 4 days

Answer:

no solutions

Step-by-step explanation:

We can actually deduce here that when the tournament ended, team Olympus have tied for 13, 10, 7, 4, 1 times.

In Mathematics, inequality is used to express or show quantities that are less than, greater than, greater than or equal to,  less than or equal to.

The following can be seen in inequality expressions:

Looking at the question, we can see that each team plays exactly 19 games.

Every win (w) = 3

Every tie (t)= 1

Every loose = 0

But Olympus got a total of 28 points

Thus: 3w + t = 28 ---------(1)

Note that each team plays  19 games

Thus, T + W  ≤  19 --------------(2)

and T , W ≥ 0

Looking at equation (1) and (2)

=> 2W  ≥  9

=> W ≥ 4.5  

( match can be won in integers only )

=> W  ≥  5  

W - 5, 6, 7, 8, 9    

T - 13, 10, 7, 4, 1  

Loose - 1, 3, 5, 7, 9

Thus, team Olympus have tied for 13, 10, 7, 4, 1 times.

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The  equation of the circle whose center and radius are given as center ( 5, 6), radius = 3 is; x² + y² - 10x - 12y + 52 = 0

We know that the general form of equation of a circle whose center is (h, k) and radius is r is expressed as;

(x - h)² + (y - k)² = r²     --- (1)

We are given;

Center coordinate; (h, k) = (5, 6)

radius; r = 3

Plug in the values of h = 5 , k = 6 and r = 3 into the equation to get;

(x - 5)² + (y - 6)² = 3²

Expanding the equation gives;

x² - 10x + 25 + y² - 12y + 36 = 9

x² + y2 - 10x - 12y + 52 = 0

Thus the  equation of the circle whose center and radius are given as center ( 5, 6), radius = 3 is; x² + y² - 10x - 12y + 52 = 0

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Answer:

Step-by-step explanation:

If two triangles are similar, their corresponding sides will be k times greater or smaller, where k is the scale factor.

We have two corresponding sides given, 6 and 24 or 6k. Using this info, find the value of k:

The other sides of the larger triangle are:

The perimeter is the sum of sides:

Answer:

10, -7, -35, 5

Step-by-step explanation:

f(9) = -5(-9 + 7) = 10

0 = -5(x + 7)

0 = x + 7

x = -7

f(0) = -5(0 + 7) = -35

-60 = -5(x + 7)

12 = x + 7

x = 5

Answer: 55

Step-by-step explanation:

Congruent angles intercept congruent chords, so since the circumference of a circle is 360 degrees, the arc angle 1 is inscribed in measures 110 degrees.

So, by the inscribed angle theorem, angle 1 measures 55 degrees.

Congruent angles intercept congruent chords, so since the circumference of a circle exists 360 degrees, arc angle 1 exists inscribed in measures 110 degrees.

So, by the inscribed angle theorem, angle 1 measures 55 degrees.

Congruent angles exist as two or more angles that exist identical to each other. Therefore, the measure of these angles exists equivalent to each other. The kind of angles does not create any distinction in the congruence of angles, which implies they can be acute, obtuse, exterior, or interior angles.

The Inscribed Angle Theorem states that the measure of an inscribed angle exists half the measure of its intercepted arc. Inscribed angles that intercept the exact arc exist congruent. This exists named the Congruent Inscribed Angles Theorem and exists shown below.

∠ A D B and ∠ A C B intercept, so m ∠ A D B = m ∠ A C B.

Congruent angles intercept congruent chords, so since the circumference of a circle exists 360 degrees, arc angle 1 exists inscribed in measures 110 degrees.

So, by the inscribed angle theorem, angle 1 measures 55 degrees.

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1. By de Moivre's theorem,

[tex]\left(4\left(\cos\left(\dfrac{7\pi}9\right) + i \sin\left(\dfrac{7\pi}9\right)\right)\right)^3 = 4^3 \left(\cos\left(\dfrac{21\pi}9\right) + i \sin\left(\dfrac{21\pi}9\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac{7\pi}3\right) + i \sin\left(\dfrac{7\pi}3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac\pi3\right) + i \sin\left(\dfrac\pi3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\dfrac12 + i\dfrac{\sqrt3}2\right) \\\\ ~~~~~~~~ = \boxed{32 + 32\sqrt3\,i}[/tex]

2. First write the given number in exponential/trigonometric form.

[tex]z = 5-5\sqrt3\,i[/tex]

has modulus

[tex]|z| = \sqrt{5^2 + \left(-5\sqrt3\right)^2} = \sqrt{100} = 10[/tex]

and since it lies in the second quadrant of the complex plane, its argument is

[tex]\arg(z) = \pi + \tan^{-1}\left(-\dfrac{5\sqrt3}5\right) = \pi + \tan^{-1}\left(-\sqrt3\right) = \pi - \dfrac\pi3 = \dfrac{2\pi}3[/tex]

So, we have

[tex]z = 5 - 5\sqrt3\,i = 10 e^{i2\pi/3} = 10 \left(\cos\left(\dfrac{2\pi}3\right) + i \sin\left(\dfrac{2\pi}3\right)\right)[/tex]

Now we apply de Moivre's theorem again, and make sure to account for the multivalued-ness of the exponential function. For [tex]k\in\{0,1,2,3,4\}[/tex], the fifth roots of [tex]z[/tex] are

[tex]z^{1/5} = 10^{1/5} e^{i(2\pi/3 + 2\pi k)/5}[/tex]

[tex]k=0 \implies z^{1/5} = 10^{1/5} e^{i2\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{2\pi}{15}\right) + i \sin\left(\dfrac{2\pi}{15}\right)\right)}[/tex]

[tex]k=1 \implies z^{1/5} = 10^{1/5} e^{i8\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{8\pi}{15}\right) + i \sin\left(\dfrac{8\pi}{15}\right)\right)}[/tex]

[tex]k=2 \implies z^{1/5} = 10^{1/5} e^{i14\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{14\pi}{15}\right) + i \sin\left(\dfrac{14\pi}{15}\right)\right)}[/tex]

[tex]k=3 \implies z^{1/5} = 10^{1/5} e^{i20\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{4\pi}3\right) + i \sin\left(\dfrac{4\pi}3\right)\right)}[/tex] [tex]k=4 \implies z^{1/5} = 10^{1/5} e^{i26\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{26\pi}{15}\right) + i \sin\left(\dfrac{26\pi}{15}\right)\right)}[/tex]

Answer: No

Step-by-step explanation:

The sum of exterior angles in a polygon is always equal to 360 degrees.

Answer:

Step-by-step explanation: -3/2 divided by 9/6

= -3/2 multiply (to divide fractions we multiply by their recipical) 6/9
Then, simplify
= -3/3 = 1
Answer: -1

Hope this helps lol

The simplified result is -1. The correct option is b.

Given that:

Expression, -3/2 ÷ 9/6

To solve the given expression, follow as:

Rewrite the division as multiplication by the reciprocal of the second fraction.

-3/2 ÷ 9/6 = -3/2 × (6/9)

Now, simplify the fractions:

-3/2 × (6/9) = -3/2 × (2/3)

-3/2 × (6/9) = - (3 × 2)/(2 × 3)

-3/2 × (6/9) = -6/6

Finally, the simplified expression is -6/6. However, further simplify it by dividing the numerator and denominator by their greatest common divisor, which is 6:

-6/6 = -1

So, the simplified result is -1. The correct option is b.

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Complete question:

Simplify Negative 3 over 2 divided by 9 over 6.

a. −4

b. −1

c. 4

d. 1

Answer:

none

Step-by-step explanation:

A. -7 <= x < 0

B. x <= -7 or x > 0

C. -7 < x <= 0

D. x < -7 or x >= 0

To create a graph to represent -7 < x < 0, draw empty circles at -7 and 0, then connect the two with a line.

The two different ways of finding the area are,
Case 1 = assume horizontal rectangles,
Case 2 = assume vertical rectangles.

the rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.

Here,

case 1,
As shown in the image
Area = sum of horizontal rectangles
Area = 10 * 3 + 2 * 5 + 2 * 1
Area  = 30 + 10 + 2
Area = 42    

Case II,
As shown in right figure,
Area of the vertical rectangles
Area = 3 * 5 + 5 * 3 + 2 * 6
Area = 15 + 15 + 12
Area = 42
Here, the area in case 1 is equal to case 2.

Thus, the two different ways of finding the area have shown above.

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By the definition and properties of absolute value, there are two possible resulting functions: (i) g(x) = 5 · |x|, (ii) g(x) = |5 · x|. (Correct choices: B, D)

Herein we must modify a parent function to get a resulting function by the use of rigid transformations, defined as those transformations applied on geometric loci, including functions, such that Euclidean distance is conserved.

Based on the statement seen in the picture, the enlargement of the parent function can be done by a rigid transformation known as dilation, whose definition is shown below:

g(x) = k · f(x), where k is the stretch factor and is greater than 1.     (1)

If we know that f(x) = |x| and k = 5, then the resulting function is:

g(x) = 5 · |x|     (1)

This expression is also equivalent to the expression g(x) = |5 · x| by definition of absolute value.

By the definition and properties of absolute value, there are two possible resulting functions: (i) g(x) = 5 · |x|, (ii) g(x) = |5 · x|. (Correct choices: B, D)

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