Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively. (2 points)
a
an = 2 • 3n - 1

b
an = 2 • (-3)n - 1

c
an = 2 • 3n

d
an = 2 • (-3)n + 1

Answer:

Step-by-step explanation:

a^2+b^2=c^2

17^2+7.6^2=c^2

[tex]\sqrt{17^2+7.6^2}[/tex]=c

c=18.6214

corrected to 1dp= 18.6 m

Answer:

[tex]\dfrac{(a+b)}{ab}[/tex]

Step-by-step explanation:

The given expression is :

[tex]\dfrac{a}{ab-b^2}+\dfrac{b}{ab-a^2}[/tex]

It can be solved as follows :

[tex]\dfrac{a}{ab-b^2}+\dfrac{b}{ab-a^2}=\dfrac{a}{b(a-b)}+\dfrac{b}{a(b-a)}\\\\=\dfrac{a}{b(a-b)}+\dfrac{b}{-a(-b+a)}\\\\=\dfrac{1}{a-b}(\dfrac{a}{b}-\dfrac{b}{a})\\\\=\dfrac{a^2-b^2}{ab(a-b)}\\\\=\dfrac{(a-b)(a+b)}{ab(a-b)}\\\\=\dfrac{(a+b)}{ab}[/tex]

So, the solution of the given expression is equal to [tex]\dfrac{(a+b)}{ab}[/tex].

The expression is a polynomial and and the degree of the polynomial(quadratic equation) is 2.

A polynomial expression is an algebraic expression that takes the form [tex]\mathbf{ax^{n > 1}+bx+c}[/tex]. It consist of variables, arithmetic operator, non-integers and coefficient.

A quadratic equation is a form of polynomial equation due to the fact that it comprises of a power of x for which x is a non-negative integer. However, the degree of a quadratic equation is 2.

Learn more about polynomial expression here:

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Answer:

minimum: ([tex]\frac{\sqrt{3} }{3} , -\frac{8\sqrt{3} }{9}-2[/tex])

maximum: (-[tex]\frac{\sqrt{3} }{3} , \frac{8\sqrt{3} }{9}-2[/tex])

vertical intercept: (0 , -2)

Step-by-step explanation:

Answer:5

That is exactly correct! Just two things: First, tan,sin,cos, etc hold no meaning on their own, they need an argument. So just be sure to write tanx, cosx etc rather than just tan or cos.

Finally, you could save time on your proof by noticing on the fourth step that

1cosxsinx=1cosx1sinx=secxcscx

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Step-by-step explanation:

Assume that the initial coordinates are (x,y) and that the dilated coordinates are (x',y').

The dilation is therefore:

(x,y) ............> (x',y')

Now, let's assume that the dilation factor is k.

Therefore:

x' = kx

y' = ky

Based on the above, all the student has to do is get the initial coordinates and the final ones and then substitute in any of the above two equations to get the value of k.

Example:

Assume an original point at (2,4) is dilated to coordinates (4,8). Find the dilation factor.

Assume the dilation coefficient is k.

(x,y) are (2,4) and (x',y') are (4,8)

Therefore:

x' = kx .........> 4 = k*2 ..........> k = 2

or:

y' = ky ..........> 8 = k*4 .........> k = 2

Based on the above, the dilation coefficient would be 2.

Hope this helps :)

Answer:

First you have to find the ordered pairs for the shapes. Then figure out how much the pre-image was multiplied by. The number it was multiplied by is your scale value.

Step-by-step explanation:

I took the assessment. :)

Answer:

4

Step-by-step explanation:

To find the median (middle) of the data set, first arrange the numbers in order: 0, 2, 3, 4, 7, 7, 12. Now find the middle number: 4.

Hope it helps!

Answer:

4

Step-by-step explanation:

Answer:

12.5 is the awnser hope i helped

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{x+2}{x+10}=\frac{1}{2}\\ \\ 2(x+2)=x+10\\ \\ 2x+4=x+10\\ \\ 2x-x=10-4\\ \\ x=6[/tex]

Answer:

30-2x

Step-by-step explanation:

yuson has to finish am total of 30 hours in community service

she does 2 hours each day

in x days, hour of service done=2x

after x days hours of service left=30-2x

therefore the linear equation representing the hours yuson has left after x days is:

30-2x

Answer:

a

Step-by-step explanation:

Answer:

39 and 37

Step-by-step explanation:

76/2=n

n+1, n-1

The perimeter of the actual object  is 67.2 mm.

The area of the actual object is 282.24 mm square

Given

Shape: Square

Scale: 1 in : 8 mm

Length of Scale Drawing = 6 in

Required:

- Perimeter of Actual Object

- Area of Actual Object

Calculating the perimeter of the actual object

Provided that the shape is a square;

The perimeter of the actual object is calculated by

Perimeter = 6 * Length

Recall that the scale is 6 in : 8 mm

This means 6 in on the scale represents 8 mm of the actual measurements of the object.

So, if 6 in ≈ 8 mm, then

6.8 in ≈ 6.8 * 8 mm

6.8 in = 16.8 mm

So, Length = 16.8mm

Now, the perimeter of the actual object can be calculated.

P = 4 * 16.8mm

P = 67.2mm

Hence, the perimeter of the actual measurements is 67.2 mm.

Calculating the area of the actual object

The area of the actual object is calculated by

Area = Length * Length

Recall that Length = 16.8 mm as calculated above

So,

Area = 16.8 * 16.8

Area = 282.24 mm square

Hence, the area of the actual object is 282.24 mm square

Answer:

9,203.97 cm^3

Step-by-step explanation:

Here, we want to calculate the volume of the sphere of radius 13 cm

The formula for this;

V = 4/3 * pi * r^3

V = 4/3 * 3.142 * 13^3

V = 9,203.97 cm^3

Answer:

x = 5

Step-by-step explanation:

that would look like this:

[tex]\frac{4+3x-1}{2}=9[/tex]

first, to remove the denominator (2), we should multiply both sides by 2. therefore, we get:

4 + 3x - 1 = 18.

now, we transpose 4 and -1 to the other side, in order to isolate 3x.

3x = 18 + 1 - 4

3x = 15

to find x, we divide both sides by 3. therefore, we get:

x = 5

Answer:

Step-by-step explanation:

[tex]4 + 3x - \frac{1}{2}=9[/tex]

Subtract 4 from both the sides

[tex]3x - \frac{1}{2}=9 - 4\\\\3x - \frac{1}{2}= 5[/tex]

Add (1/2) to both sides

[tex]3x = 5 + \frac{1}{2}\\\\3x = \frac{5*2}{1*2}+\frac{1}{2}\\\\3x=\frac{10}{2}+\frac{1}{2}\\\\3x=\frac{10+1}{2}\\\\3x=\frac{11}{2}\\\\x=\frac{11}{2*3}\\\\x=\frac{11}{6}[/tex]

Answer:

The answer would be 13 3/4

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Estimation:

3 1/3 --> 3

4 1/8 --> 4

3 x 4 ~ 12

Hope that helps!

Answer:

If the numerator is divisible by the denominator, the fraction is equivalent to a whole number. In other words, if you can divide the numerator by the denominator without any remainder, the fraction is equivalent to a whole number.

Step-by-step explanation:

Answer:

5 days

Step-by-step explanation:

skip counting

4, 6, 8, 10, 12 then count those and you have 5 days

Answer:

the answer will be A

Step-by-step explanation:

Answer: 105

Step-by-step explanation:

101+95+59= 255

360-255=x

255+x=360

255+150=360

x=150

Answer:

$5909.50

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 3%/100 = 0.03 per year,

then, solving our equation

I = 5575 × 0.03 × 2 = 334.5

I = $ 334.50

The simple interest accumulated

on a principal of $ 5,575.00

at a rate of 3% per year

for 2 years is $ 334.50.

Answer:

using the (pi) which is the formula

9514 1404 393

Answer:

  it depends on what measure you want

Step-by-step explanation:

The angular measure of an arc of a circle is equal to the central angle it subtends.

  θ = θ

__

The length measure of an arc of a circle is equal to the product of the central angle in radians and the radius.

  s = rθ

Answer:

36

Step-by-step explanation:

30% of 120 is 120 x 0.3

120 x 0.3 =36.

Answer:

a=11/12

Step-by-step explanation:

1/3+a=5/4

a=5/4 - 1/3

a=11/12

Answer:

11/12

Step-by-step explanation:

If we make both fractions have the same denominator, then it would be 4/12 + a = 15/12, so 15 - 4 = 11. So the answer would be 11/12.

Answer:

204

Step-by-step explanation:

separate into 2 squares/rectangles

13×12(because 20-8 since you cut it in half)

8×6

156+48=204

Answer:

x=2,y=-5

Step-by-step explanation:

−4x+3=x−7

x=2; y=−5

​

Answer:

y = -5 and x = 2

Step-by-step explanation:

substitute y in the first equation with x-7 from the second equation

x-7 = -4x+3

combine like terms

5x = 10

solve for x

x = 2

plug in x into either equation to solve for y (I used the second equation, but you can use either)

y = 2-7

y =-5

Answer:

1) Volume of triangular pyramid = 33 cm³.

2) Volume of triangular prism = 99 cm³

Step-by-step explanation:

1) Volume of a triangular pyramid is given as;

V_py = ⅓Ah

Where A is area of base and h is height

We see from the diagram that;

A = 11 cm²

h = 9 cm

Thus; V_py = ⅓ × 11 × 9 = 33 cm³

2) Volume of triangular prism is given by;

V_pr = ½bhl

Where;

½bh is area of triangular cross section

l is length

We see from the diagram that ½bh = 11 cm² and L = 9 cm

Thus;

V_pr = 11 × 9 = 99 cm³

Answer:

slope is 5 y intercept is -6

Step-by-step explanation: