Given the following geometric sequence, find the 12th term: {2, -4, 8, ...}.

-4096
2048
4096
-2048

Answer:

1. a) SR = 23

b) QV = 25

c) QT = 20

d) PQ = 40

e) VS = 4·√6

2. a) LH = 16

b) EL = 2·√185

c) JG = 30

d) EK = 22

e) KG = 30

3. a) XT = 37

b) TZ = 34

c) ZW = 17

d) XZ = 21

e) SY = 69

Step-by-step explanation:

The circumcenter ΔPQR is the center of the circle that circumscribes ΔPQR

The length of the radius of the circle ≡ VR = VP = QV = 25

a) Given that VR ≅ VP - Radius of circumcircle

VS ≅ VS Reflective property

∠VPS ≅ ∠VRS - Base angles of an isosceles triangle

Right triangle VPS ≅ Right triangle VRS -Hypotenuse and one Leg HL congruency

Therefore, SR ≅ PS -Corresponding parts of congruent triangles are congruent CPCTC

SR + PS = PR = 46

SR + PS = SR + SR = 2·SR = 46

∴ SR = 46/2 = 23

b) QV = VR = 25 = Radius of circumcircle of ΔPQR -Given V = center and Q = vertices of the triangle circumscribed by the circle referred to in the question

c) QT = √(QV² - TV²) = √(25² - 15²) = √400 = 20

d) TV ≅ TV - Reflexive property of congruency

ΔTQV ≅ ΔTVP - Hypotenuse and one Leg (HL) congruency

QT ≅ TP -Corresponding parts of congruent triangles are congruent CPCTC

PQ = QT + TP Given

∴ PQ = QT + QT since QT = TP

PQ = 2·QT = 2 × 20 = 40

e) VS = √(VR² - SR²) = √(25² - 23²) = √96 = 4·√6

2.  The incenter is the center of the incircle of ΔEFG

 a) LH = LK = JL = 16 -Radius of incircle of ΔEFG

b) EL = Hypotenuse of right triangle LHE = √(LH² + EH²) = √(16² + 22²) = √740 = 2·√185

c) JG = Leg length of right triangle JGL = √(LG² - JL²) = √(34² - 16²) = √900 = 30

d) EK = Leg length of right triangle LKE = √(EL² - LK²) = √(740 - 256) = 22

e) KG = Leg length of right triangle LKG = √(LG² - LK²) = √(34²- 16²) = √900 = 30

3. Point Z id the centroid of ΔRST

a) XT = XS - point X on ST bisected by median line RX

ST = XT + XS = XT + XT = 2.XT = 74

XT = 74/2 = 37

b) TZ = 2/3×TW  - Length from a vertex to the centroid on a median line is equal to two third the length of the median line

TZ = 2/3×51 = 34

c) TZ + ZW = TW

∴ ZW = TW - TZ = 51 - 34 = 17

d) RZ = 42 = 2/3×RX - Length from a vertex to the centroid on a median line is equal to two third the length of the median line

∴ RX = 3/2×42 = 63

RZ + XZ = RX - Given

XZ = RX - RZ = 63 - 42 = 21

e) SZ = 2/3×SY - Length from a vertex to the centroid on a median line is equal to two third the length of the median line

SZ + ZY = SY

∴ ZY = SY - SZ = SY - 2/3×SY = 1/3×SY = 23

Which gives;

SY = 3 × 23 = 69.

Answer:

x=3

y=3

Step-by-step explanation

Here we have been given with two equations and we will solve them by substitution by elimination method.

Transposing y in 1st equation from L.H.S. to R.H.S. it would be negative,

[tex] \implies \: \displaystyle\sf{x \: = \: 6 - y}[/tex]

Now, we would substitute this value of x in Equation No 1.

[tex] \implies \: \displaystyle\sf{2 \: (6 - y) \: = \:15 }[/tex]

[tex] \implies \: \displaystyle\sf{2 \: \times (6 - y) \: = \:15 }[/tex]

[tex]\implies \: \displaystyle\sf{12 - 2y \: = \:15 }[/tex]

Transposing 12 to R.H.S.,

[tex] \implies \: \displaystyle\sf{ - 2y \: = \:15 - 12 }[/tex]

[tex]\implies \: \displaystyle\sf{ - 2y \: = \:3}[/tex]

[tex]\implies \: \displaystyle\bf{ y \: = \: - \dfrac{3}{2} }[/tex]

Therefore, value of y is - 3/2.

★ Finding out value of x:-

[tex] \implies \: \displaystyle\sf{x \: = \: 6 - y }[/tex]

[tex]\implies \: \displaystyle\sf{x \: = \: 6 - ( \dfrac{ - 3}{ 2} )}[/tex]

[tex]\implies \: \displaystyle\sf{x \: = \: \frac{12 + 3}{2} }[/tex]

[tex]\implies \: \displaystyle\bf{x \: = \: \frac{15}{2} }[/tex]

Henceforth,

Answer:

d 2.5 line is 6.9 which is 9.4

Step-by-step explanation:

because

Answer: the answer is “B”

Step-by-step explanation: answer is LETTER B

Answer:

[tex]\mathsf{y < \dfrac47x-4}[/tex]

Step-by-step explanation:

First, find the equation of the line.

Slope-intercept form of a linear equation:  [tex]\mathsf{y=mx+b}[/tex]

(where m is the slope and b is the y-intercept)

From inspection of the graph, the y-intercept is at (0, -4)

Therefore, b = -4

Choose another point on the line, e.g. (7, 0)

Now use the slope formula to find the slope:

[tex]\mathsf{slope=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

where:

[tex]\implies \mathsf{slope=\dfrac{0-(-4)}{7-0}=\dfrac47}[/tex]

Therefore, the equation of the line is:

[tex]\mathsf{y=\dfrac47x-4}[/tex]

For an inequality, the dashed line means < or >  (whereas a solid line means ≤ or ≥)

As the shading is below the line, we need to use <

Therefore, the final inequality is:

[tex]\mathsf{y < \dfrac47x-4}[/tex]

Answer:

C

Step-by-step explanation:

Answer:

hello

f (2 ) = 6 et  f ( 0 ) = 3

( 3 - 6 ) / ( 0 - 2 ) = - 3/- 2 = 3/2

ax =  3 x /2

f (0) = 3  ⇔ b =  3

f (x) =  3 x /2 + 3

also  f ( 0) = 0 + 3 = 3  

sorry

y = ax + b

b = 3

since the line cuts the y-axis in 3

then for a ? which is the slope..

we take 2 points on the line (0 ; 3) and (2 ; 6)

we move 2 units to the left to go up 3 units

so a = 3/2

=> y = 3/2x + 3

or

f(x) = 3/2x + 3

Answer:

18.84 square centimeters

Step-by-step explanation:

[tex]C =[/tex] [tex]\pi[/tex][tex]d[/tex]

[tex]C = (3.14)(6)[/tex]

[tex]C = 18.84[/tex] [tex]cm^{2}[/tex]

P.S: Diameter is radius + radius so that means that diameter is 3 + 3 for this problem.

x + 10 = - 6x - 18

7x = - 28

x = - 4

and y = - 4 + 10 = - 6

Answer: 5√(50) = 35.36 m^2

Step-by-step explanation:

The cross section is a rectangle, so its area formula is: Area = length * width.

If you look, the width is the diagonal of the side of the cube; thus, you can use Pythagorean theorem to find its measurement: a^2 + b^2 = c^2 → 5^2 + 5^2 = c^2 →

50 = c^2 → c = √(50)

Now, use the area formula and get: Area = 5 * √(50) = 5√(50) = 35.36 m^2 :)

Answer:

Step-by-step explanation:

Given is the quadratic function

In order to have two real roots the discriminant should be posivive

We need D > 0

There is no solution as b² is never negative

Step-by-step explanation:

1a) =>3(3x+1)/4(3x+1)=3/4

b) => 2x(x+5)/(x+5)²=2x/x+5

2) a raph restriction means that the graph stops where the restriction says. But because the y's are the output of the x's, they only give u the x restriction and then you can calculate the point by finding the y coordinate. This may sound weird but here is an example:

[1,3] => this means the graph will only show between the points 1 and 3 (on the x-as). Both points are included in the graph.

[1,3[ => this means the raph will only show between the points 1 and 3 but 1 is still a part of the graph but not 3 so up till every little number but just not 3.

hope u get it lol

Answer:

4200

Step-by-step explanation:

I got that answer because your problem asked for the hundredth. Pretend the first 4 isn't there for a moment and round 184 to the nearest hundredth. Then place the 4 in front of what you got.

Answer: 48

Step-by-step explanation:

3x16=48

3 gallons=48 cups

There are 48 cups in 3 gallons.

To start your conversion, you need to know how many cups are in one gallon.

There are 2 cups in 1 pint, and 2 pints in 1 cup.

Answer:

I believe it is 106 Square meters

Step-by-step explanation:

Easiest way to find area for these kind of shapes is to break them into smaller rectangles, this specific one can be broken 3 ways...

Right: 4m long, 7m tall

Top: 10 long, 5 tall *(12-7)*

Left: 4m long, 7m tall

*To find incomplete ones, you find clues in other sides, for instance the whole side was 12, the broken part was 7, therefor you just subtract 7 from 12, giving you 5 for the top.*

Then you just multiply...

4x7=28
4x7=28
10x5= 50

Now, you have the area for three individual smaller rectangles. So you simply add them together to get the whole shapes area...

28+28+50=106

Therefor, your answer should be 106 square meters- if I'm not mistaken.

Hope this helps, brainliest is appreciated if its right, trying to rank up :)

Have a great day! cx

~Mitsuna

Answer:

106

Step-by-step explanation:

Here's one way of finding the area:

Find the area of the entire outer rectangle. Then subtract the area of the samlle rectangle in the bottom middle.

A = LW - lw

A = (10 m)(12 m) - (2 m)(7 m)

A = 120 m² - 14 m²

A = 106 m²

Answer:

I think it would be 10

Step-by-step explanation:

Hope this helps:)...if not then sorry for wasting your time and may God bless you:)

Answer: The mode is 12 because it is repetitive among the numbers in the set of numbers.

Answer:

f(x) = 3^x+3

f(x) = 9.3^x+1

Step-by-step explanation:

Hope it helps you in your learning process.

The mean of the data set, 6, 11, 5, 2, 7, is: 6.2.

The mean of a data set is the average of the data points or the sum of all the data points divided by the total number of data points in the data set.

Given the data set, 6, 11, 5, 2, 7:

Mean = (6 + 11 + 5 + 2 + 7)/5

Mean = 31/5

Mean = 6.2

Therefore, the mean of the data set, 6, 11, 5, 2, 7, is: 6.2.

Learn more about the mean on:

https://brainly.com/question/19243813

Answer:

6.2

Step-by-step explanation:

Answer:

3.6.

Step-by-step explanation:

15% = 15/100 = 0.15

so the answer is 0.15 * 24

= 3.6

Answer:

3.60

Step-by-step explanation:

Note:

Of = Multiply

15% can also be written as .15 as decimal

Solve:

.15 × 24 = 3.60

 Or we can solve like this:

[tex]\frac{24}{x}=\frac{100\%}{15\%}[/tex]

[tex]\frac{x}{24}=\frac{15}{100}[/tex]

[tex]\Rightarrow x=3.6[/tex]

Therefore, 15% of  £24 is 3.60

~Lenvy~

There is no solution for the given function [tex]\rm f(x) = -0.5|2x+2|+1[/tex] when f(x) = 6 option fourth is correct.

It is given that the function  [tex]\rm f(x) = -0.5|2x+2|+1[/tex]

It is required to find the values of x when f(x) = 6

It is defined as a special type of relationship and they have a predefined domain and range according to the function.

We have a function:

[tex]\rm f(x) = -0.5|2x+2|+1[/tex]

And f(x) = 6

Putting the value of f(x) in the above equation, we get:

[tex]\rm 6 = -0.5|2x+2|+1[/tex]   or

[tex]\rm -0.5|2x+2|+1= 6\\\\\rm -0.5|2x+2|= 6-1\\\\\rm -0.5|2x+2|+5\\\\\rm |2x+2|= \frac{5}{-0.5} \\\\\rm |2x+2|= -10[/tex]

Here we can see the mod function values is negative which is not possible, hence there is no solution for the above equation for any 'x'

Thus, there is no solution for the given function [tex]\rm f(x) = -0.5|2x+2|+1[/tex] when f(x) = 6.

Learn more about the function here:

brainly.com/question/5245372

Answer:

a. False : because 10^-5= 1/10^5 where as -10^5=-1 × 10^5

therefore 1/10^5 not equal to -1×10^5

b. False : because (10^2)^-3 = 100^-3=1/100^3 where as (10^2)^3 = 100^3=1000000 there fore 1/100^3 not equal to 1000000

c. True : because 10^3/10^14=10^(3-14)=10^-11 therefore both left side and right side of the equation are equal

Answer: Look at the screenshot

Step-by-step explanation:

Ive added a screenshot of what this graph should look like

Answer:

*View attached graph*

Step-by-step explanation:

I graphed 6 points, so you are able to choose the ones you want :)

*View attached graph*

Hope this helps!

Answer:

139.0932

Step-by-step explanation:

729×18%×(1+6%)

729x0.18x(1+0.06)

729x0.18x1.06

139.0932

Answer:

I'll assume the equation is h(d) = -(1/1125)d^2 + d  

Please check, the (1/1125) term is disturbing.

Step-by-step explanation:

When the ball hits the ground, the height, h(d) is 0.  We want the value of d, the distance the ball has travelled horizontally, that would give the function a value of 0.

h(d) = -(1/1125)d^2 + d

0 = -(1/1125)d^2 + d

(1/1125)d^2 - d = 0

Solve using the quadratic equation:  I get 0 and - 1125 seconds.  I conclude that the factor (1/1125) is incorrect, or some other error in the equation.

The horizontal distance from the point where the ball is hit to the point at which the ball lands on the ground is 1125.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

When the ball hits the ground, the height, h(d) is 0.  We need to find the value of d, the distance the ball has traveled horizontally, which would give the function a value of 0.

Solve using the quadratic equation

h(d) = -(1/1125)d^2 + d

0 = -(1/1125)d^2 + d

(1/1125)d^2 - d = 0

(1/1125)d^2 = d

d = 1125

Thus,  the horizontal distance from the point where the ball is hit to the point at which the ball lands on the ground is 1125.

Learn more about quadratic equations;

brainly.com/question/13197897

Answer:

34.54

Step-by-step explanation:

you do 2 * 3.14 * 5.

to find the area 2pie r the 3.14 comes from the directions, the 2 comes from the circle because the full length of the circle is 10 but you divide by 2 to get 5 and the 5 also comes from the circle and that is the radius.

Hey there!

x(-2x + 3)

= 1x(-2x + 3)

DISTRIBUTE 1x WITHIN the PARENTHESES

= 1x(-2x) + 1x(3)

= -2x(1x) + 3(1x)

= -2x^2 + 3x

Therefore, your answer is: -2x^2 + 3x

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

Answer:

Rs. 22,080.

Step-by-step explanation:

Let the height be x m then the breadth is 3x and the length 5x m.

x * 3x * 5x = 960

15x^3 = 960

x^3 = 64

x = ∛ 64 = 4m.

Therefore the height is 4m, the breadth = 12 m and the length = 20m.

So the area of all the surfaces

= 2 * short wall + 2 * long wall + floor + ceiling

= 2 *4*12 + 2*4*20 + 12*20 + 12*20

=  96 + 160 + 240 + 240

= 736 m^2.

Cost plastering  = 736 * 30 = Rs. 22,080

Answer:

240 ft^2

Step-by-step explanation:

10*18=180

20*6=120

120/2 = 60

180+60=240