50 POINTS FOR CORRECT ANSWER!

we can always get the common ratio of a geometric sequence by simply dividing the current term by the previous term, in this case for the sake of simplicity let's divide 2/3 by 2, so  

[tex]\cfrac{2}{3}\div 2\implies \cfrac{2}{3}\div \cfrac{2}{1}\implies \cfrac{2}{3}\cdot \cfrac{1}{2}\implies \cfrac{1}{3}\impliedby \textit{common ratio}[/tex]

so the sequence more or less looks like   [tex]2~~,~~\cfrac{2}{3}~~,~~\cfrac{2}{9}~~,~~\cfrac{2}{81}~~,~~\cfrac{2}{243}[/tex]

so we'd want the sum of the first 5 terms

[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio} \end{cases} \\\\\\ S_5=2\left( \cfrac{1~~ - ~~(\frac{1}{3})^5}{1~~ - ~~\frac{1}{3}} \right)\implies S_5=2\left( \cfrac{~~\frac{242}{243}~~}{\frac{2}{3}} \right)\implies S_5=\cfrac{242}{81}\implies S_5=2\frac{80}{81}[/tex]

Answer:

Given equation: x + 2y = 7

Rearrange the given equation to make y the subject:

      [tex]\sf x + 2y = 7[/tex]

[tex]\sf \implies 2y=7-x[/tex]

[tex]\sf \implies y = \dfrac12(7-x)[/tex]

Now input the given x-values into the equation to determine the y-values:

[tex]\sf x=-2\implies y = \dfrac12(7-(-2))=4.5[/tex]

[tex]\sf x=-1\implies y = \dfrac12(7-(-1))=4[/tex]

[tex]\sf x=0\implies y = \dfrac12(7-0)=3.5[/tex]

[tex]\sf x=1\implies y = \dfrac12(7-1)=3[/tex]

[tex]\sf x=2\implies y = \dfrac12(7-2)=2.5[/tex]

[tex]\sf x=3\implies y = \dfrac12(7-3)=2[/tex]

As ordered pairs: (-2, 4.5)  (-1, 4)  (0, 3.5)  (1, 3)  (2, 2.5)  (3, 2)

Plot the endpoints on the graph (-2, 4.5) and (3,2), then connect with a line segment.

Answer:

yes(only if the x is being multiplied to 5/2 and 1/2 respectively. If its a part of the denominator, then no)

Step-by-step explanation:

Answer:

B.75

Step-by-step explanation:

Answer:

h   ≥  -432

Step-by-step explanation:

h/-24<=18

Multiply though by -24:

h  ≥  -24*18

h   ≥  -432  

Note: the inequality signs flips as we are multiplying both sides by a negative value.

[tex] \qquad \qquad \qquad\large\overbrace{\underbrace{\underline{ \boxed{ \sf \:Answer }}}}[/tex]

Let's use distance formula :

[tex]\qquad \sf  \dashrightarrow \: \sqrt{(3 - ( - 3)) {}^{2} + (2 - ( - 4) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{(3 - ( - 3)) {}^{2} + (2 - ( - 4)) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {6}^{2} + {6}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {6}^{2}(1 + 1) } [/tex]

[tex]\qquad \sf  \dashrightarrow \: 6\sqrt{ 2 } \: \: units[/tex]

1 1⁄3

Step-by-step explanation:

In order to find how far was she from her destination

We substract 4 2⁄3 from 3 1⁄3

=> 4 2⁄3 - 3 1⁄3

=> 1 1⁄3 (Decimal: 1.333333)

Answer:

1 1/3 miles

Step-by-step explanation:

2-1

4 2/3-3 1/3= 1-----------

3

=1 1/3miles

Answer:

The slope is -1

Step-by-step explanation:

Formula for finding slope: [tex]\frac{rise}{run} = \frac{y2 - y1}{x2-x1}[/tex]

we got the points:

(−2,−4) and)(3,−9)

let's plug them in.

[-9-(-4)] / [3-(-2)] =

-5 / 5 = -1

[tex]\bf \colorbox{black} {\bf {\textcolor{blue}{ }{ \bf { \textcolor{orange}{ }{ \bf{ \textcolor{cyan}{mathematics = }}}}}}}[/tex]

(3×2-2)+(5×2+5×-1)=

(6-2)+(10-5)=

4+5=

[tex] \bf \textcolor{green}{ \underbrace{9}}[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's simplify ~

[tex]\qquad \sf  \dashrightarrow \:(3 \times 2 - 2) + (5 \times 2 + 5 \times ( - 1))[/tex]

Use BODMAS/PEDMAS rule here :

[tex]\qquad \sf  \dashrightarrow \:(6- 2) + (10 + ( - 5))[/tex]

[tex]\qquad \sf  \dashrightarrow \:4 + (10 - 5)[/tex]

[tex]\qquad \sf  \dashrightarrow \:4 + 5[/tex]

[tex]\qquad \sf  \dashrightarrow \:9[/tex]

Hope it helps you ~

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

Answer:

See below ↓

Step-by-step explanation:

We need to prove :

⇒ cos⁻¹ [tex]\frac{12}{13}[/tex] + sin⁻¹ [tex]\frac{3}{5}[/tex] = tan⁻¹ [tex]\frac{56}{65}[/tex]

Let's simplify the LHS.

Convert the inverse cos and sin functions into inverse tan functions

Identity

Using this identity, we can simplify our earlier equation!

⇒ tan⁻¹ [(5/12 + 3/4)/(1 - (5/12 x 3/4))]

⇒ tan⁻¹ [(20 + 36) / (48 - 15)

⇒ tan⁻¹ (56/65)

⇒ RHS

⇒ Proved ∴√

[tex]\text{L.H.S}\\\\=\cos^{-1} \dfrac{12}{13} + \sin^{-1} \dfrac 35\\\\=\sin^{-1} \dfrac 5{13} + \sin^{-1} \dfrac 35\\\\[/tex]

[tex]=\sin^{-1}\left[\dfrac 5{13}\sqrt{1- \left(\dfrac 35 \right)^2} + \dfrac 35\sqrt{1-\left(\dfrac 5{13} \right)^2} \right]\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{1-\dfrac 9{25} }+\dfrac 35 \sqrt{1-\dfrac{25}{169}} \right)\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{\dfrac{16}{25}}+\dfrac 35 \sqrt{\dfrac{144}{169}} \right)\\\\=\sin^{-1} \left(\dfrac{5}{13} \cdot \dfrac 45 + \dfrac 35 \cdot \dfrac{12}{13} \right)\\[/tex]

[tex]=\sin^{-1} \left(\dfrac 4{13} +\dfrac{36}{65}\right)\\\\=\sin^{-1} \left(\dfrac{20}{65} + \dfrac{36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{20+36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{56}{65} \right)\\\\=\text{R.H.S}[/tex]

Answer:

VOL_cone is 70.7

which is LESS THAN

the vol of cylinder. VOL_cyl is 71.6

Step-by-step explanation:

Volume of a cone:

V= (1/3)pi•r^2 • h

=(1/3)pi•3^2 • 7.5

= 70.7 cubic inches

(rounded to tenths this is the same if you use a pi key on the calculator or if you use 3.14)

The Volume of a cylinder:

V = pi•r^2 • h

= pi• 2.25^2 • 4.5

= 71.6 cubic inches

(more accurate with pi key, using 3.14 it rounds to 71.5)

The last blank could be the words "less than" but if they are asking for a fraction or percent, calculate by putting the big number on the bottom and the smaller number on top.

Answer:

100.

Step-by-step explanation:

The 2 smaller triangles are similar, so:

48 / (x - 64) = 64 / 48

64(x - 64) = 48^2

x - 64 = 48^2/64

x = 48^2/64 + 64

= 100.

Check the picture below.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{19.5^2-18^2}=r\implies \sqrt{56.25}=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\ \stackrel{slant~height}{\sqrt{r^2+h^2}}\\[-0.5em] \hrulefill\\ r=\sqrt{56.25} \end{cases}\implies \begin{array}{llll} LA=\pi \sqrt{56.25}\stackrel{slant~height}{(19.5)} \\\\\\ LA\approx 459.46~cm^2 \end{array}[/tex]

Answer:

yes

Step-by-step explanation:

75/100×75/100=49/100

49/100×20=8.58.5 % Is more than 20%

Answer:

11

Step-by-step explanation:

If you count the total values

it equals 11

Answer:

since it goes down a certain way and it goes down then B will go the same way as a evil ghost literally down to the phone the top right to the left like see if I just a little bit shorter Jay will go all the way up to age and we will go to k

Answer:

Step-by-step explanation:

take figure a and dilate it bigger by 3 that will mean it is bigger and the shapes will be the same.

Answer:

  8

Step-by-step explanation:

One way to solve problems involving the mean of a data set is to consider the way the numbers relate to the mean.

When we subtract the mean from the given numbers, we find the differences are ...

  -1, 1, 3, -3

The sum of these differences is 0. The missing number will make the toal of all differences from the mean be zero. Since it is already zero, the missing number is the mean. The missing number is 8.

Answer:

55 sq meters

Step-by-step explanation:

Area of big triangle 7x5=35/2

but there's two big triangle so 35/2 x 2 =35

area of small triangle 5x4=20/2 10

10 x 2 =20. And then combine 20+35=55

So the area is 55 sq meters.

Answer: 7.5 or 7 1/2

Step-by-step explanation:

Divide 45 divided by 7

Answer:

1289.8089172

Step-by-step explanation:

if you do 90 x 2 = 180 you get the circumference of what would be the complete circle, the formula for area with circumference is A = (C^2/4x3.14) so inserting 180, the answer is 2579.61783439, and half of that is a semi circle so 2579.61783439/2 = 1289.8089172

Answer:

1/8

Step-by-step explanation:

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Answer:

10. s = 1.50x

11. s = 28x + 5

Step-by-step explanation:

10. s (money); so multiply x (the amount of pencils) by the price which is 1.50. Which is equal to 112.50.

11. s (money); multiple x (the amount of shoes) by the price, 28, which equals 84. Then add 5 for the shipping. This equals 89.

Answer:

1. 200

2. 50

Step-by-step explanation:

1. you put 10 over 5 as a proportion with x over 100 on the other side

2. you put 5 over 10 as a proportion with x over 100 on the other side

The solution of the linear system is given by using an arithmetic operation. Then the value of b is 2.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The linear equation is given below.

–12 + 3b – 1 = –5 – b

The value of b will be given as

Add b both sides, we have

–12 + b + 3b – 1 = –5 – b + b

           –13 + 4b = –5

Add 13 on both sides, we have

13 – 13 + 4b = – 5 + 13

              4b = 8

Divide both sides by 4, we have

b = 2

More about the linear system link is given below.

https://brainly.com/question/20379472

Answer:

The fourth option, 2

Answer:

7[tex]\sqrt{5}[/tex]

Step-by-step explanation:

the legs of a 45°- 45°- 90° triangle are congruent , then

one leg = 7[tex]\sqrt{5}[/tex]

the other leg = 7[tex]\sqrt{5}[/tex]

Answer:

  (e)  0.75

Step-by-step explanation:

The correlation coefficient is not affected by translation or scaling of scores. Converting them from "raw scores" to z-scores does not affect their correlation.

The correlation coefficient of the z-scores is 0.75.