The angle measurements in the diagram are represented by the following expressions;

We are given the Geometric Series:

[tex]2 + \frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81} + \frac{2}{243} + \frac{2}{729}[/tex]

which can be rewritten as:

[tex]2 + \frac{2}{3} + \frac{2}{3^{2} } + \frac{2}{3^{3}} + \frac{2}{3^{4}} + \frac{2}{3^{5}} + \frac{2}{3^{6}}[/tex]

here, we can see that every term is (1/3) times the last term

Hence, we can say that the common ratio of this Geometric Series is 1/3

Finding the Sum:

We know that the sum of a Geometric Series is:

[tex]S_{n} = \frac{a(r^{n}-1)}{r-1}[/tex]

(where r is the common ratio, a is the first term, and n is the number of terms)

another look at the given Geometric Series tells us that the first term is 2 and the number of terms is 7

plugging these values in the formula, we get:

[tex]S_{n} = \frac{2((1/3)^{7}-1)}{(1/3)-1}[/tex]

[tex]S_{n} = \frac{-1.99}{-0.67}[/tex]

Sₙ = 2.97

Step-by-step explanation:

[tex] \tt2 + \frac{2}{3} + \frac{2}{ {3}^{2} } + \frac{2}{ {3}^{3} } + \frac{2}{ {3}^{4} } + \frac{2}{ {3}^{5} } + \frac{2}{ {3}^{6} } [/tex]

r = [tex]\tt{a_2 \div a_1}[/tex]

r = [tex]\tt{\frac{2}{3} \div 2}[/tex]

r = [tex]\tt{\bold{\frac{1}{3}}}[/tex]

Soo :

[tex] \sf s_n = \frac{a( {r}^{n} - 1) }{r - 1} [/tex]

[tex] \sf s_7 = \frac{2(( \frac{1}{3} ) {}^{7 - 1} - 1) }{( \frac{1}{3} - 1) } [/tex]

[tex] \sf s_7 \approx \bold{ \underline{2.97}}[/tex]

Answer:

The initial value is the value of the y-coordinate when the x-coordinate is equal to 0. That is the same to say the value at which the graph intercepts the y-axis. So, you just have to pick the graph whose line intercepts the y-axis at 1/2.

Answer:

12.7

Step-by-step explanation:

Remember this rule when rounding 5 and below let it go (ex. 12.32 = 12.3) 6 and above give it a shove (ex. 12.47 = 12.5).

Answer:

g = 10

f = 21

Step-by-step explanation:

Given equations:

24 = g + 14

f - 9 = 12​

24 = g + 14

Subtract 14 from both sides

24 - 14 = g + 14 - 14

10 = g

g = 10

Check:

24 = g + 14

24 = 10 + 14

24 = 24

f - 9 = 12​

Add 9 to both sides

f - 9 + 9 = 12​ + 9

f = 21

Check:

f - 9 = 12​

21 - 9 = 12

Answer:

You have to do 7x+2+6x+9 Which is 13x+11.

Step-by-step explanation:

Answer:

A) 2x+4y=2 and -2x+2y=10

Step-by-step explanation:

2(-3)+4(2)=2

-6+8=2

-2(-3)+2(2)=10

6+4=10

Answer:

He is 62.72 inches tall now

Step-by-step explanation:

the twelve over 100 is the percentage, he increased by 12 percent. and the x over 56 is the new value (x) over the old value. We get 6.72 so we add that to 56 to get 62.72.

Answer:

d.

Step-by-step explanation:

Let's examine each statement:

Option A: m<CUD = m<VUM (CORRECT)

Rationale: vertical angles are congruent to each other.

Option B: m<AUV + m<DUA = 180 (CORRECT)

Rationale: angles on a straight line

Option C: m<MUC - m<MUD = m<CUD (CORRECT)

Rationale:

m<MUC = m<MUD + m<CUD

Subtract m<MUD from each side

m<MUC - m<MUD = m<CUD

Option D is FALSE

Rationale:

m<PUD + m <VUP = 180° (angles on a straight line)

m<PUM + m<CUA ≠ 180°

Therefore,

m<PUD + m<VUP = m<PUM + m<CUA IS FALSE.

Answer:

B

Step-by-step explanation:

Jrkrkr

Answer:

Step-by-step explanation:

p(A) = a^3 + 3a^2 + 9a + 27

put brackets around the 1st and second terms and another set around the 3rd and 4th

P(a)= (a^3 + 3a^2) + (9a + 27)

Using the distributive property, pull out the common factor for each of the 2 terms that contain the brackets.

P(a) = a^2 ( a + 3) + 9(a + 3)

Let a + 3 = x

P(a) = a^2x + 9x

Put brackets around these 2 terms

P(a)= x(a^2 + 9)

Substitute a + 3 for x

P(a) = (a + 3) ( a^2 + 9)

Answer:

Step-by-step explanation:

First, we can eliminate answer A. As you should know, answer A is a pie chart as it is a circle and cut into many slices.

Now both answer B and C look similar. They are both a bar graph. So we will come back and look at these later.

Answer D is about math test scores. I have forgotten the name of this graph but I can assure you this is incorrect.

So we are left with B and C. They both are bar graphs, right? Well sort of. Although they look identical, answer B is a histogram. If you look at graph B, you will notice it says age. This shows that there is time between each subject or event. Graph C is a personal question. What kind of pet you have is not directly related to something over time

Therefor the answer has to be B.

Answer: 4) 49 1/2  

5) 15

Step-by-step explanation:

To find volume you must use L x W x H.

4) 3 x 3 x 5.5= V

3 x 3 = 9

9 x 5. 5=  49.5

5) 2 x 2 x 3.75= V

2 x 2= 4

4 x 3. 75 = 15

Answer:

A. 57.8°

Step-by-step explanation:

Reference angle = θ

Length of hypotenuse = 15

Length of adjacent side = 8

Recall, SOHCAHTOA.

Thus, apply CAH to find θ.

Cos θ = Adj/Hyp

Cos θ = 8/15

θ = Cos^{-1}(8/15)

θ = 57.7690474° = 57.8°

Answer:

Step-by-step explanation:

Use slope formula:

Answer:

The answer is  h = -3

Step-by-step explanation:

(1 - h)/(10 - 3) = 4/7

(1 - h) / 7 = 4/7

1 - h = 4

h = 1 - 4

h = -3

Answer:

10

Step-by-step explanation:

Answer: 13

Step-by-step explanation: subtract 22 from 9

Answer:1 yard = 36 inches

48 X 36 = 1728 inches

So far, we have found area for rectangles, triangles, trapezoids, and circles. An irregular figure is a figure that is not a standard geometric shape. Its area cannot be calculated using any of the standard area formulas. But some irregular figures are made up of two or more standard geometric shapes. To find the area of one of these irregular figures, we can split it into figures whose formulas we know and then add the areas of the figures.

Answer:

408.2sq inches

Step-by-step explanation:

Area of the cylindrical box = 2πr(r+h)

r is the radius  = diameter/2

r = 10/2 = 5in

h is the height = 8in

Substitute

Area of the cylindrical box  = 2(3.14)(5)(5+8)

Area of the cylindrical box = 2 * 3.14 * 5 * 13

Area of the cylindrical box  = 408.2sq inches

9514 1404 393

Answer:

  (C)  angles A and B and those corresponding

Step-by-step explanation:

If sides are used to show similarity, at least two sides from each triangle are required. If only two sides are used, then the angle between them must also be shown to be congruent.

A -- has 2 sides, but no angles; (SS) not sufficient

B -- has 2 sides but not the angle between; (SSA) not sufficient

C -- has 2 angles; (AA) sufficient

D -- effectively, one angle; (A) not sufficient

Answer:

od I'd the correct answer

Answer:

It represents the 270 miles that Roy and Travis must travel in 4 hours in order to meet somewhere along the highway.

Step-by-step explanation:

From the information given, the point of interception (4, 270) represent the number of distance, 270 miles, that both Roy and Travis must travel in 4 hours in order to meet along the highway where Roy will give Travis the key to a treasure chest to Roy.

The point intersection (4, 270) represents the time and distance Roy and Travis met

The graph above are linear graph.

Linear graph are straight line graph.

Therefore,

d represents a distance in miles from Dallas

h represents the hours travelled

Roy is leaving for Pecos while Travis is in Pecos ready to leave for Dallas.

Therefore, the point intersection (4, 270) represents the time and distance Roy and Travis met.

learn more on linear graph here:https://brainly.com/question/1328896

Answer:

12x-20

Step-by-step explanation:

f(x)=6x-8

3f(x)=3(6x-8)

3f(x)=18x-24

g(x)=-3x+2

2g(x)= -6x+4

3f(x)+3g(x)=(18x-24)+(-6x+4)

=18x-24-6x+4

=12x-20

Answer:

He should have to spell at least 36 of these words correctly.

Step-by-step explanation:

40 words.

He must spell at least 90% of those words correctly.

At least how many words should he have to spell correctly to get the prize?

90% of 40. So

0.9*40 = 4*9 = 36

He should have to spell at least 36 of these words correctly.

Answer:

sin ( 330 ) − 4 cot( − 45 ) csc ( 60 )

Step-by-step explanation:

Answer:

The most common rock-forming minerals are quartz, feldspar, mica, pyroxene, amphibole, and olivine. The most reliable way to identify a mineral is by using a combination of several tests. A crystal is a solid in which the atoms are arranged in repeating patterns.

Answer:

[tex]A = \frac{r}{2}C[/tex]

Step-by-step explanation:

Given

Shape: Circle

Required

The area and the circumference (relationship)

This implies that, we write an expression that relates the area and the circumference.

Circumference is calculated as:

[tex]C = 2\pi r[/tex]

Area is calculated as:

[tex]A = \pi r^2[/tex]

The area can be rewritten as:

[tex]A = \frac{2\pi r^2}{2}[/tex]

Further rewrite as:

[tex]A = \frac{r}{2}*2\pi r[/tex]

Recall that:[tex]C = 2\pi r[/tex]

So, the expression becomes

[tex]A = \frac{r}{2}*C[/tex]

[tex]A = \frac{r}{2}C[/tex]

Answer:

48

Step-by-step explanation:

One nice, reliable thing about triangles is that their interior angles will ALWAYS add up to 180 degrees.  So, if one angle is 43 degrees and the other angle is 48 degrees, we can see that

180 - 43 - 48 = 89

Now, the tricky part: how to determine which type of triangle this is.

An acute triangle is one in which all interior angles are less than 90 degrees.  An isoceles triangle is one in which two of the interior angles are the same, while the third is different.  An obtuse triangle is one in which one of the interior angles is greater than 90 degrees.  A right triangle is one in which one of the interior angles is equal to 90 degrees.

We distinguish between these different types because they each have useful, but different, properties.

By these definitions, it is clear that the triangle in question is acute.