Are the lines x− 2y= 4 and y= 2x − 2 parallel, perpendicular, or neither? Explain your answer. [ Select ] ; their [ Select ] [ Select ] the same and [ Select ] receiprocals.

Answer:

See convergence analysis below

Step-by-step explanation:

For the expansion of 1/(1-t) in powers of t, we can recall that an infinite  Geometric series with first term "1" and common ratio "t", in the case that the absolute value of "t" is smaller than 1, can be represented by:

[tex]\Sigma\limits^\infty_0\, t^n=\frac{1}{1-t} \\[/tex]

The condition for such, is that the absolute value of "t" is smaller than "1", which gives us the radius of convergence for this series "1" and the interval of convergence:  - 1 < t < 1

Recall as well that using the geometric sequence  [tex]1 + t + t^2 + t^3 +...[/tex]

The ratio test becomes [tex]\frac{a_{n+1}}{a_n} = t[/tex]

which is the SAME as the common ratio for the geometric sequence, and which in order to converge to the value [tex]\frac{1}{1-t}[/tex]   requires that the absolute valu of the common ration be smaller than "1" rendering the same radius of convergence as discussed above.

Answer:

A = 192 cm²

Step-by-step explanation:

Given that,

The length of the diagonal of a rectangle is 20 cm.

The difference between its length and its width is 4 cm.

Let the length is l and width is b.

ATQ,

l-b = 4 ...(1)

Let x is the diagonal of the rectangle such that,

[tex]x^2=l^2+b^2[/tex]

or

[tex]20^2=l^2+b^2\\\\l^2+b^2=400[/tex] ....(2)

Now we need to solve equation (1) and (2).

Squaring equation (1) : [tex]l^2+b^2-2lb=16[/tex]

Put equation (2) in above equation.

[tex]400-2lb=16\\\\400-16=2lb\\\\2lb=384\\\\lb=192[/tex]

Since, the area of the rectangle, A = lb

A = 192 cm²

Answer:

x=6

Step-by-step explanation:

-5(x - 2) = -20

first multiple 5 by x and -2

-5x 10 = -20

subtract 10 from 10 and -20

-5x=-30

then divide 5

x=6

Answer:

<1=55°

Step-by-step explanation:

180-125=55

Answer:

Step-by-step explanation:

2 and 2/3 i believe

Answer:8/3

Step-by-step explanation:i don't know if you wanted improper or not

plz leave a like

Answer:

Step-by-step explanation:

Each hour, Jim does 1/3 of the job if working alone.

Each hour, John does 1/5 of the job if working alone.

Let x = number of hours to do the job if they work together.  So, each hour, they do 1/x of the job when they work together.

We get the equation:  1/3 + 1/5 = 1/x

Multiply the equation by the LCD, 15x:   5x + 3x = 15

                                                                             8x = 15

                                                                               x = 15/8 = 1 7/8 hrs

ANSWER:  (C).  

Answer:

Y:4     X:540

Step-by-step explanation:

Answer: first divide so you make it one and then you multiply hope that helps

Step-by-step explanation: then you can add them to get by one then multiply

Answer:

Option B is correct .

Step-by-step explanation:

According to Question , both the graph have same shape . If we look at the the first graph it cuts x - axis at (0 , 2) and ( 0 , -2) . Hence x = 2 and -2 are the zeroes of the equation .

And ,the given function is ,

[tex]\implies f(x) = 4 - x^2 \\\\\implies f(x) = 4-x^2=0 \\\\\implies 2^2-x^2=0\\\\\implies (2-x)(2+x) = 0 \\\\\boxed{\red{\bf \implies x = 2 , (-2) }}[/tex]

• Hence ,we can can see that x = 2 and (-2) are the zeroes of graph.

This implies that if we know the zeroes , we can frame the Equation.

On looking at second parabola , it's clear that cuts x - axis at ( 1, 0 ) and (-1,0). So , 1 and -1 are the zeroes of the quadratic equation . Let the function be g(x) . Here , a and ß are the zeroes.

[tex] \begin{lgathered}\implies g(x) = (x-\alpha)(x-\beta) \\\\\implies g(x) = (1+x)(1-x) \\\\\boxed{\pink{\bf \implies g(x) = 1 - x^2}}\end{lgathered} [/tex]

Hence option B is correct .

Answer:

3.2

Step-by-step explanation:

12.8/4 which makes the answer 3.2

Answer:

2 solutions

Step-by-step explanation:

Given the expression

2m/2m+3 - 2m/2m-3 = 1

Find the LCM of the expression at the left hand side:

2m(2m-3)-2m(2m+3)/(2m+3)(2m-3) = 1

open the bracket

4m²-6m-4m²-6m/(4m²-9) = 1

Cross multiply

4m²-6m-4m²-6m = 4m²  - 9

-12m = 4m²  - 9

4m²  - 9+12m = 0

4m² +12m-9 = 0

Since the resulting equation is a quadratic equation, it will have 2 solutions since the degree of the equation is 2

Answer:

t = 17

s = 46

Step-by-step explanation:

Congruent Triangles

If two triangles are determined to be congruent, their side lengths and angles have the same measure.

We are given the condition that triangles HIJ and DCB are congruent. This implies that sides JH and DB have the same measure, thus:

s = 46

We can also say that sides IJ and CB have the same measure, thus:

t = 17

Answer:

n^2 +24n +144

Step-by-step explanation:

(-12-n)^2

(-12-n)(-12-n)

144+12n+12n+n^2

n^2 +24n +144

i think... :)

Answer:

triangle formula  1/2* base * height

Step-by-step explanation:

1/2*9*7 = 31.5 sq units

Answer:

[tex]y +9 = -4(x - 4)[/tex]

Step-by-step explanation:

Given

[tex]m = -4[/tex] --- slope

[tex](x_1,y_1) = (4,-9)[/tex] --- point

See attachment for complete question

Required

Determine the line equation

This is calculated as follows:

[tex]y - y_1 = m(x - x_1)[/tex]

Substitute values for m, x1 and y1

[tex]y - (-9) = -4(x - 4)[/tex]

Simplify the expression on the left-hand side:

[tex]y +9 = -4(x - 4)[/tex]

303.02

Three hundred three=303

Two hundredths= .02

= 303.02

Answer:

120

Step-by-step explanation:

5!

=5×4!

=5×4×3×2×1

=120

Step-by-step explanation:

5!

= 5×4×3×2×1

=20×6

=120 is the correct answer

Answer:

y = 60*

x = 30*

Step-by-step explanation:

the bottom angle is the same angle as y and it says 2x meaning that x is 1/2 of y. the full angle across the line is 180* so divide that by 3.

180 / 3 = 60

Answer:

-7/40

Step-by-step explanation:

5/8 - 4/5

~Find common denominators

25/40 - 32/40

~Subtract

-7/40

Best of Luck!

Answer:

5(44 x 10^x)^

Step-by-step explanation:

Multiply 88 x 5 = 44

5(44 x 10^x)^

Answer:

2

Step-by-step explanation:

32 divided by 16 is 2

Answer:

54 students.

Step-by-step explanation:

If you have 600 and 9% the nearest rounding point is %10. %10 of 600 is 60, and 1% of 60 is 6, so 60-6=54.

Step-by-step explanation:

xy = k, where k is a real constant.

When x = 2, y = 60.

=> (2)(60) = k, k = 120.

Hence when y = 24, x(24) = (120), x = 5.

Given:

Length of a cube is 2 cm

To Find:

Surface area of the cube

Solution:

A cube consists of 6 faces.

The area of each face = side x side

So, the total surface area of a cube = 6 x

side x side

Let a be the length of the given cube

: Surface area of a cube = 6a square

a = 2 cm (Given)

Surface area of cube = 6 x 22 =(6 x 4) = 24 cm square.

Hence, the surface area of the given

cube is 24cm square.

Hope it helps!

Answer:

D

it is D D D D D D D D D D D D D D D D D D D

Answer:

15 X w(how many weeks) + 30 = 90 or 15 X 4 + 30 = 90

Step-by-step explanation:

so he needs $90 he has $30 and he gets 15 a week so we are going to say a week will be w so however many weeks (4) so you will need to multiply it by 15 and it will be 60 then you add 30 and you get 90.

Answer:

59.47

Step-by-step explanation:

a calculator might help