What is the common ratio between successive terms in the sequence?

27, 9, 3, 1, one-third, one-ninth, StartFraction 1 over 27 EndFraction, ...–
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The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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Answer:

area of triangle = 1/2×base×height

=1/2×20m×6m

= 20m×6m=120square metre

Answer:

D.

Step-by-step explanation:

it should be the sales tax because you pay a little bit more.

Answer:

After applying the distributive property, Ezra's expression was 8y + 16

After he used the commutative property, his expression was 16 + 8y

Step-by-step explanation:

Distributive property rule: a(x+y) = ax + ay
   Not much to explain here

Commutative property rule: a + b = b + a   or  xy = yx
   We use addition rule in this case, simply place 16 in front of 8y

Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

Answer:

42

Step-by-step explanation:

2+10+3*10 =42 because there are 2 boxes inside each there are 5 then inside each boxes are 3

Answer:

-6x^3 + x^2 - 20

Step-by-step explanation:

First step: write down the problem.

2nd step:

Just lose the first set of parentheses. Write the first four terms exactly the same. Remove also the second set of parentheses but distribute that minus sign to all the last four terms. You get:

-6x^2+4x^3-9x-10-10x^3+7x^2+9x-10

Then combine like terms. Terms with the same exponent can be added or subtracted.

Standard Form means the highest exponent is written first, then the next lower exponent, and then the next lower exponent with a constant (number only) at the end.

So we do the third power first. Then 2nd power. (The x's drop out because -9x and +9x) and constants last.

-6x^3 + x^2 - 20

The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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Answer:

Let's call the number of students at the college "x". Then, the number of faculty/staff is 3 times that number, or 3x. The total number of people at the college is the sum of the students and faculty/staff, which is x + 3x = 4x.

According to the problem, the ratio of faculty/staff to students is 3 to 13, so we can write an equation:

3x / x = 3 / 13

To find the number of students, we can solve for x:

4x = 4000

x = 1000

So, there are 1000 students at the college.

An exponential decay function can be generically written as:

The conditions for this function are:

1) The y-intercept is 4.

2) The values of y decrease by a factor of one half as x increases by 1.

The y-intercept corresponds to the value of y when x = 0, so we can express it as:

This condition let us find the value of a.

The next condition will be used to find the value of b.

As x increases by 1, y decreases by one half.

We can write this as a quotient between consecutive values of y:

Then, we can write the function as:

Answer: y = 4*(1/2)^x

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.

To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.

Given:

Length of the cylindrical steel pipe (hollow part) = 21 cm

Radius of the solid cylinder = 0.4 cm

Radius of the hollow cylinder = 0.1 cm

First, let's calculate the volume of the solid cylinder (hollow part):

V1 = π × \(r1^2\) × h

V1 = π × \((0.4 cm)^2\) × 21 cm

Next, let's calculate the volume of the hollow cylinder:

V2 = π × \(r2^2\) × h

V2 = π × \((0.1 cm)^2\) × 21 cm

Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:

Volume of liquid = V1 - V2

Let's calculate these values:

V1 = π ×\((0.4 cm)^2\) × 21 cm ≈ 10.572 cm³

V2 = π × \((0.1 cm)^2\) × 21 cm ≈ 0.693 cm³

Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³

To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:

Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.

Therefore, none of the options A, B, C, or D provided is the correct answer.

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Answer:

{x,y} = {-4,3}

Answer:

x = 4 and y = 3

Step-by-step explanation:

a) 5x - 2y = 14

b) x + 3y = 13

b) x = -3y + 13

a) 5 (-3y + 13) - 2y = 14

-15y + 65 - 2y = 14

-17y = 14 - 65

y = 51/17

y = 3

b) x + 3(3) = 13

x = 13 - 9

x = 4

Answer42 - 2197

Step-by-step explanation:

Answer:

the answer would be $45.55

<3

Step-by-step explanation:

20$ + $50.00 = $70

$70 - $6.95 = $64.5

$64.5 - $9.95 = $54.55

$54.55 - $20 = $34.55

$34.55 + $15 = $49.55

$49.55 - $4 = $45.55

The rate of interest is given by the equation R = 3.5 %

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the rate of interest be represented as R

Now , the simple interest I = $ 175

The principal amount invested P = $ 2,500

The time period T = 2 years

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Rate of Interest = (Simple Interest x 100 ) / Principal Amount x Time Period )

Substituting the values in the equation , we get

Rate of Interest R = ( 175 x 100 ) / ( 2500 x 2 )

Rate of Interest R = 17500 / 5000

Rate of Interest R = 3.5 %

Hence , the interest rate is 3.5 %

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Answer:

See Explanation

Step-by-step explanation:

\( \overline{CB} ||\overline {ED}... (GIVEN) \\

\& BD\:\&\: CE \: are \: transversals\\

\angle CBF\cong \angle EDF.. (alternate \: \angle 's) \\

\overline{CB} \cong \overline {ED}..... (GIVEN) \\

\angle BCF \cong \angle FED.. (alternate \: \angle 's) \\

\therefore \triangle CBF \cong \triangle EDF.. (By \: ASA\: Postulate) \)

Answer:  see proof below

Step-by-step explanation:

   Statement                     Reason

1. CB || ED                       1. Given

2. ∠E ≅ ∠C                     2. Alternate Interior Angle Postulate

3. ∠D ≅ ∠B                     3. Alternate Interior Angle Postulate

4. CB ≅ ED                     4. Given

5. ΔCBF ≅ ΔEDF            5. ASA Congruency Theorem

a) P(10.99 ≤ X ≤ 11.01) = 0.9544

b) Probability that the sample mean diameter exceeds 11.01 when n = 25 is 0.0062.

We are given the following in the question:

Mean, μ = 11 cm

Standard Deviation, σ = 0.02 cm

We are given that the distribution of diameter is a bell-shaped distribution that is a normal distribution.

Formula: z = (x - μ)/σ

a) P(10.99 ≤ X ≤ 11.01 when n = 16)

Standard error due to sampling = σ/n = 0.02/√16 = 0.005

P(10.99 ≤ X ≤ 11.01) = P((10.99 - 11)/0.005 ≤ z ≤ (11.01 - 11)/0.005)

                              = P(-2 ≤ z ≤ 2) = 0.9772-0.0228

                              = 0.9544 = 95.44%

b) P(sample mean diameter exceeds 11.01 when n = 25)

Standard error due to sampling =  σ/n = 0.02/√25 = 0.004

P(x > 11.01) = P(z > (11.01 - 11)/0.004) = P(z > 2.5)

                 = 1 - P(z ≤ 1) = 1 - 0.9938 = 0.0062 = 0.62%

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Answer:

F and H are both 121 degrees

Step-by-step explanation:

"A kite has 4 interior angles and the sum of these interior angles is 360°. In these angles, it has one pair of opposite angles that are obtuse angles and are equal." - Cue math

Ok, so the two acute angles add up to 118 degrees, and in order to find the remaining angles we need, subtract 118 from 360 to get 242. Because the two obtuse angles are equivalent, divide 242 by 2 to get the measure of each.

Answer:

x = 140°

Step-by-step explanation:

If angle DBC is 35° and angle ABD is 105°, you add them together and you get 140°.

Answer:

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Step-by-step explanation:

hmxkhxkyxhmxykxm

The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65

A = -6 and B = 65

From the question, we are to express the given expression in the form (x + A)^2+B by completing the square

The given expression is

x² -12x + 101

Using the completing the square method

x² -12x + 101

Divide the coefficient of x by 2 and then square it

The coefficient of x is -12

Dividing by 2, we get

-12/2 = -6

Squaring

(-6)²

Now, add and subtract this value from the expression

x² -12x + (-6)² + 101 - (-6)²

Then, we can write that

(x - 6)² + 101 - (-6)²

(x - 6)² + 101 - 36

(x - 6)² + 65

Thus,

The given expression expressed in the form (x+A)^2+B is (x - 6)² + 65

By comparison,

A = -6

and

B = 65

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Answer:

7.5:15

It cannot be simplified further

Step-by-step explanation:

Hope this helps! Have a nice day!

Here we have a dilation of scale factor 2.

We can see that bot figures we have the same slope, so we just have a dilation of scale factor K to go from figure A to figure B.

To find the value of K, notice that for some side length L in figure A, the correspondent length L' in figure B must be:

L' = K*L

Here if we use the left sides, we will get:

for figure A; L= 2

for figure B: L = 4

4 = K*2

4/2 = K

2 = K

So this is a dilation of scale factor k = 2.

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