the third term and the fifth term of a geometric progression are 2 and 1/8 respectively. If all terms are positive, find the sum to the infinity of the progression​

Answer:

C. TRANSLATE 2 UNITS UP AND 4 UNITS DOWN

Step-by-step explanation:

The transformation that takes place with the following rule (x - 2, y + 4) is translates 2 units left AND 4 units up, the correct option is A.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = [tex]k \times f(x)[/tex]

Horizontal stretch by a factor k: y =[tex]f\left(\dfrac{x}{k}\right)[/tex]

We are given that;

The points (x - 2, y + 4)

Now,

The rule (x - 2, y + 4) means that every point (x,y) of the original figure is moved to a new point (x - 2, y + 4) by subtracting 2 from the x-coordinate and adding 4 to the y-coordinate.

The x-axis is horizontal and positive to the right. Subtracting from the x-coordinate means moving left and adding to the x-coordinate means moving right.

The y-axis is vertical and positive upwards. Subtracting from the y-coordinate means moving down and adding to the y-coordinate means moving up.

Subtracting 2 from the x-coordinate means moving 2 units left and adding 4 to the y-coordinate means moving 4 units up.

Therefore, by transforming functions the answer will be translates 2 units left AND 4 units up.

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Answer:

r=-11

Step-by-step explanation:

7r+2=5(r-4)

7r+2=5r-20

2r=-22

r=-11

Answer:

8(3+8)

Step-by-step explanation:

The distributive property of multiplication states that

A(B+C) = A* B + A* C

Here, we can say that

8(3+8) = 8*3 + 8* 8 = 24 + 64. This seems correc,t but we can check the other options to make sure

6(4 + 8) = 6 * 4 + 6*8 = 24 + 48. This is incorrect

24 + (8)(8) . The 24 and 8 are not in the same parenthesis, so we cannot multiply them. Using PEMDAS, we multiply first, so 24+(8)(8) = 24 + 8*8 = 24 + 64. If there are multiple solutions, this can work. If not, this does not use the distributive property as we are not adding anything in the parenthesis.

Similarly, for (2)(12) + (8)(8), we are not adding anything in the parenthesis, but we can use PEMDAS to get 2*12 + 8*8 = 24 + 64, so this would also work but does not use the distributive property.

Answer:

first we have to solve for x in order to find the value of y

2x+8=5x+14

5x-2x=14-8

3x=6

x=2

placing the x value in these two equation to find the value of y

y=2(2)+8

y=12

y=5(2)+14

y=24

now those are the two values of y

hope it's helpful

thank you !

Answer:

let,

√x-5=ky

x=30 when y=2

√30-5=2k

or, k=(√30-5)/2

now, when y=8

√x-5=8×(√30-5)/2

or, √x-5=4√30-20

or, √x=4√30-15

or, x=(4√30-15)²

or, x=47.73..

Answer:

1000000000026

Step-by-step explanation:

i hope this helps!!!!!

Answer:

Square both sides

√(2x+1)=2+√(x-3)

or, 2x+1=(2+√(x-3))²

solving it you'll get two values of x, which are,

x = 4 and x = 12

Answer:

Hello,

x=4 or x=12

Step-by-step explanation:

[tex]\sqrt{2x+1} =2+\sqrt{x-3} \\\\2x+1=4+4\sqrt{x-3} +(x-3)\\\\2x+1-x+3-4=4\sqrt{x-3} \\\\x=4\sqrt{x-3} \\\\ x^2-16x+48=0\\\\\Delta=16^2-4*48=64=8^2\\\\x=\dfrac{16-8}{2} \ or x=\dfrac{16+8}{2}\\\\x=4 \ or\ x=12\\\\Since \ we\ have \ squared \ we\ must\ verify\ the \ solutions\ found:\\\\x=4 \Longrightarrow \sqrt{2*4+1} =? 2+\sqrt{4-3} \Longrightarrow 3 =? 2+1 \\\\x=12 \Longrightarrow \sqrt{2*12+1} =? 2+\sqrt{12-3} \Longrightarrow 5 =? 2+3 \\\\[/tex]

Answer:

B

Step-by-step explanation:

The correct equation will be 4N-3N

It's very blurry can u retake it?

Answer:20-33x

Step-by-step explanation:

Answer:

hope it help ..........you

Answer:

6:150

Step-by-step explanation:

If you like my answer mark me brainliest

Answer:

1:25

Step-by-step explanation:

1.5m=150cm

6:150

1:25

========================================================

Explanation:

We'll need the slope first

m = slope

m = (y2-y1)/(x2-x1)

m = (0-(-4))/(-3-(-5))

m = (0+4)/(-3+5)

m = 4/2

m = 2

The slope is 2.

Next, pick either of the two given points to play the role of [tex](x_1,y_1)[/tex]

Let's say we picked on (-5,-4). The order doesn't matter so you could easily pick the other point as well.

We'll plug these items into the point slope equation below to solve for y.

[tex]y - y_1 = m(x - x_1)\\\\y - (-4) = 2(x - (-5))\\\\y + 4 = 2(x +5)\\\\y + 4 = 2x +10\\\\y = 2x +10-4\\\\y = 2x +6\\\\[/tex]

Or we could have picked on (-3,0). The m value stays the same (at m = 2)

[tex]y - y_1 = m(x - x_1)\\\\y - 0 = 2(x - (-3))\\\\y = 2(x +3)\\\\y = 2x+6\\\\[/tex]

This one takes a few less steps. Either way, we get to the same answer.

You only need to pick one of the points, but doing both of them helps show that the two points are on the same line. It helps confirm the answer.

-----------------------

Another way to check the answer is to plug the (x,y) coordinates into y = 2x+6 for each point.

So let's say we check (x,y) = (-5,-4)

y = 2x+6

-4 = 2(-5)+6 ... replace x with -5, replace y with -4

-4 = -10+6

-4 = -4

This confirms the first point. I'll let you check the second point.

Answer:

y = 2x+6

Step-by-step explanation:

Attached below is my graph

I graphed the two points, and formed a line

From the point (0,0), i counted the units till the first point the line touches on the y axis (6)

This is the y intercept

The slope-intercept form is written as y = mx+b

m = slope

b = y intercept

So so far we have y = mx + 6

The slope is the rise to the next point the line touches, over the run

You can see that as it rises 2, it runs 1

Rise / Run = 2/1 = 2

Slope = 2

Equation: y = 2x + 6

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

Below

Step-by-step explanation:

Volume = area of the circular side * length

Radius of circle = 10

V  = pi r^2 l = pi *10^2 * 6

= 100 pi

= 1884 in^2

Answer:

96 in^2

Step-by-step explanation:

area of rectangle: 24*8=192

Area of triangle: (1/2)*base*height

= .5 * 8 * 24

=192/2

=96

area of shaded=rectangle - triangle

= 192-96

which is also just 192/2

so it is 96

Answer:

angleCFE=21 because inscribed angle is half the central angle standing on same same arc.

Answer:  (4y-9z)( 16y^2 + 36yz + 81z^2 )

=======================================================

Explanation:

We'll use the difference of cubes factoring rule

a^3 - b^3 = (a-b)(a^2+ab+b^2)

In this case,

So,

a^3 - b^3 = (a-b)(a^2+ab+b^2)

64y^3 - 729z^3 = (4y-9z)( (4y)^2 + (4y)(9z) + (9z)^2 )

64y^3 - 729z^3 = (4y-9z)( 16y^2 + 36yz + 81z^2 )

Answer:

[tex]\|a\| = 5\sqrt{13}[/tex].

[tex]\|b\| = 3\sqrt{29}[/tex].

Step-by-step explanation:

Let [tex]m[/tex],[tex]n[/tex], and [tex]k[/tex] be scalars such that:

[tex]\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}[/tex].

[tex]\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}[/tex].

[tex]\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}[/tex].

The question states that [tex]\| a + b \| = 34[/tex]. In other words:

[tex]k\, \sqrt{8^{2} + 15^{2}} = 34[/tex].

[tex]k^{2} \, (8^{2} + 15^{2}) = 34^{2}[/tex].

[tex]289\, k^{2} = 34^{2}[/tex].

Make use of the fact that [tex]289 = 17^{2}[/tex] whereas [tex]34 = 2 \times 17[/tex].

[tex]\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}[/tex].

[tex]k^{2} = 2^{2}[/tex].

The question also states that the scalar multiple here is positive. Hence, [tex]k = 2[/tex].

Therefore:

[tex]\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}[/tex].

[tex](a + b)[/tex] could also be expressed in terms of [tex]m[/tex] and [tex]n[/tex]:

[tex]\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}[/tex].

[tex]\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}[/tex].

Equate the two expressions and solve for [tex]m[/tex] and [tex]n[/tex]:

[tex]\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}[/tex].

[tex]\begin{cases}m = 5 \\ n = 3\end{cases}[/tex].

Hence:

[tex]\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}[/tex].

[tex]\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}[/tex].

Answer:

5/7

Step-by-step explanation:

5x-7y=14

-7y=14-5x

y=-2+5/7x

y=5/7x-2

This slope is 5/7. This is because in the standard form of a line (y=mx + b), m represents the slope. In the equation above, 5/7 is the slope.

Answer:

11.8

Step-by-step explanation:

Refer to the image attached.

Answer:

V = 40 in^3

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h  where r is the radius and h is the height

The diameter is 4 so the radius is 1/2 the diameter or 1/2(4) =2

The height is 10 and we are using 3 for pi

V = 1/3 (3)(2)^2 (10)

V = 40 in^3

Answer:

good question

but I don't know

please I am so sorry

Answer:

Behold.

Step-by-step explanation

The answer to the statement is 1)false 2) false 3) true 4) true and 5) false.

Given functions,f

1) For x ≤ -2: f(x) = -12 + 6x

2) For -2 < x < 1: f(x) = 41 - 15x

3) For x ≥ 1: f(x) = 31 - 4x

1) The graph crosses the y-axis at (0, -15).

This is false because if x = 0, the function value would be -12 + 6 * 0 = -12, not -15.

2) The graph has a point of discontinuity at x = 1.

This is false because the function is defined at x = 1 there is no space, so there is no point of discontinuity at x = 1.

3) The graph is increasing over the interval (4, ∞).

This is true because the coefficient of x in the function's expression is negative, showing that it is decreasing. Therefore, as x increases, the function values decrease.

4) The graph is decreasing over the interval (-12, -2).

This is true because the coefficient of x in the first piece of the function (-12 + 6x) is positive, showing an increasing trend. Therefore, as x decreases from -12 to -2, the function values increase.

Statement 5: The domain of the function is all real numbers.

This is false because the domain of the function is limited by the intervals in its definition. The function is defined differently for different intervals of x.

So, the answer to the statement is

1) false

2) false

3) true

4) true

5) false

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Answer:

45

Step-by-step explanation:

so there is 90 degress and you want to find 6x (5x + x) so just subtract 360-90 = 270 then divide by 6 = 45

Answer:

C

No, because x=−5 corresponds to both y=1 and y=−3.

Step-by-step explanation:

This is not a function.  The graph has values of x that correspond to multiple values of t

Answer:

Less than 360 degree

Step-by-step explanation:

I think so

Answer:

W

Step-by-step explanation:

I done it before

Answer:

C

Step-by-step explanation:

Well, a y-intercept is a the point on a graph where the x value equals 0, because the point sits exactly on the y-axis. In this case, the y-intercept would be (0, -9).

Answer:

(0,-9)

Step-by-step explanation:

The y intercept is where the graph crosses the y axis ( where x =0)

The y intercept is

-9

(0,-9)