Which of the following is equivalent to 5x − 6y  =  8?

A. y = -5/6x
B. y = 6/5x + 2
C. y = 5/6x - 4/3
D. y = 8/11x​

Answer:

9.55 hope this helps :)

Step-by-step explanation:

  1

  2.30

  2.50

+ 2.75

  2.00

-----------

  9.55

Answer:

Recursive:

[tex]f(1)=4, f(n)=f(n-1)-4[/tex]

Explicit:

[tex]f(n)=4-4(n-1)[/tex]

And the 20th term f(20) is -72.

Step-by-step explanation:

We have the sequence:

4, 0, -4, -8...

Let’s find the recursive and explicit rule for the sequence.

Recursive Rule:

Let’s determine the factor by which the sequence is decreasing by. We see that each subsequent term is 4 less than the previous term. In other words, our common difference is -4.

So, this is a arithmetic sequence.

The standard format for an recursive rule for an arithmetic sequence is:

[tex]f(1)=a , f(n)=f(n-1)+(d)[/tex]

Where a is the initial term and d is our common difference.

From our sequence, we know that our initial term a is 4.

We also determined that our common difference is -4.

Substitute. Hence, our recursive rule is:

[tex]f(1)=4, f(n)=f(n-1)-4[/tex]

Explicit Rule:

The standard format for an explicit rule for an arithmetic sequence is:

[tex]f(n)=a+d(n-1)[/tex]

Where a is the initial term and d is the common difference. So, again, let’s substitute 4 for a and -4 for d. Hence, our explicit formula is:

[tex]f(n)=4-4(n-1)[/tex]

To find f(20), we can use the explicit formula. It is possible to use the recursive formula, but it gets tedious. Therefore, we will substitute 20 for n for our explicit formula:

[tex]f(20)=4-4(20-1)[/tex]

Evaluate:

[tex]\begin{aligned} f(20)&=4-4(19) \\ f(20)&=4-76 \\ f(20)&=-72 \end{aligned}[/tex]

Hence, our 20th term is -72.

Answer:

10

Step-by-step explanation:

If ABCD is a rectangle, then AB=CD and AC=BD.

Check work:

Answer:

{-6}

Step-by-step explanation:

Step 1 Raise both sides of the equation to the index of the radical in the case 2

[tex](\sqrt{2x+13} )^{2} =(x+7)^{2}[/tex]

[tex]2x + 13 = (x+7)(x+7)[/tex]

[tex]2x +13 = x^{2} + 14x + 49\\0=x^{2} +12x+36[/tex]

Step 2 Factor

(x + 6)(x + 6) = 0

x + 6 = 0

x = - 6

Step 3 Check -6

[tex]\sqrt{2(-6)+13} = -6 + 7\\\sqrt{-12+13} = 1\\\sqrt{1} = 1\\1 = 1[/tex]

Answer:

-96 :)

Step-by-step explanation:

12 x (-8) = -96

if there is one negative in the problem the answer will be negative.

Answer:

$1,605

Step-by-step explanation:

As, 7% of $1,500 is = $105

So, the investment is = Principcal + Interest.

= $1,500 + $105 = $1,605

The value of investment after one year will be $1,605.

Given that,

Principal[P] = $1,500.

Rate[R] = 7%.

Time[T] = 1 year.

Formula of simple interest[S.I] :

[tex]\text{ S.I.} = \dfrac{P\times R\times\ T}{100} .\\\\ \text{S.I.} = \dfrac{\$1,500\times7}{100}\\\\ \text{S.I. }=\$105.[/tex]

Investment after one year will be :

[tex]\text {Investment}= \text{Principal} +\text{Interest}.\\\text{Investment}=\$1,500+\$105\\\text{Investment} =\$1,605[/tex]

Hence, the worth of investment after one year will be $ 1,605.

Learn more about Simple Interest, refer:

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Answer:

1/4 is the simplest form

Step-by-step explanation:

Answer:

MARK ME BRAINLIEST MARK ME BRAINLIEST

MARK ME BRAINLIESTMARK ME BRAINLIEST

Answer:

D

Step-by-step explanation:

The value of z^3 is option (D) [tex]z^{3}=64 (cos(\frac{3\pi }{2} ) + isin (\frac{3\pi }{2} ) )[/tex] is the correct answer.

A complex number is characterized by an ordered pair of numbers, the real and imaginary parts. It can be represented in multiple ways such as Standard form(rectangular form), Polar form, Exponential form.

For the given situation,

The complex number, z = 4 (cos (pi/ 2) + i sin (pi/2 ) )

[tex]z=4(cos(\frac{\pi }{2} ) + isin (\frac{\pi }{2} ) )[/tex]

⇒ [tex]z^{3}=4^{3} (cos(\frac{\pi }{2} ) + isin (\frac{\pi }{2} ) )^{3}[/tex]

By De Moivre's theorem,

[tex]{\displaystyle {\big (}\cos x+i\sin x{\big )}^{n}=\cos nx+i\sin nx}[/tex]

Thus, [tex]z^{3}=64 (cos(\frac{3\pi }{2} ) + isin (\frac{3\pi }{2} ) )[/tex]

Hence we can conclude that the value of z^3 is option (D) [tex]z^{3}=64 (cos(\frac{3\pi }{2} ) + isin (\frac{3\pi }{2} ) )[/tex] is the correct answer.

Learn more about complex numbers here  

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Answer:

No for both

Step-by-step explanation:

If 2 x values that are the same but different y values for them then its not a function

Answer:

2,752

Step-by-step explanation:

86x32 = 2752

Product: It means to multiply.

Answer:

I believe the estimated product is 2749

Answer: [tex]\frac{19}{39}[/tex]

Step-by-step explanation:

1. S(a+b) = 15/13

2. I tells us that sina = 2/3

3. 2/3 + sinb = 15/13

4. Solve for sinb which will be 19/39

I hope this is right.

Answer:

A.

Step-by-step explanation:

Answer:

1h 18min

Step-by-step explanation:

Not sure if that is what the problem is asking you.

Answer:

An 1 hour and 18 minutes

Step-by-step explanation:

Yes uhmmm hope this helps I guess

9514 1404 393

Explanation:

∠MRQ ≅ ∠NQR . . . . given

QR ≅ RQ . . . . reflexive property

∠PQR ≅ ∠PRQ . . . . property of isosceles triangle PQR

ΔQNR ≅ Δ RMQ . . . . ASA postulate

Answer:

Part A

Step-by-step explanation:

Use both!

You want to minimize P, so differentiate P with respect to x and set the derivative equal to 0 and solve for any critical points.

P = 8/x + 2x

dP/dx = -8/x² + 2 = 0

8/x² = 2

x² = 8/2 = 4

x = ± √4 = ± 2

You can then use the second derivative to determine the concavity of P, and its sign at a given critical point decides whether it is a minimum or a maximum.

We have

d²P/dx² = 16/x³

When x = -2, the second derivative is negative, which means there's a relative maximum here.

When x = 2, the second derivative is positive, which means there's a relative minimum here.

So, P has a relative maximum value of 8/(-2) + 2(-2) = -8 when x = -2.

Answer:

(8-3x)/4

Step-by-step explanation:

3x+4y=8

4y=8-3x

y=(8-3x)/4

So the answer is (8-3x)/4

Answer:

the first option has a sum of 20

Step-by-step explanation:

Answer:

the first one has a sum of 20

Step-by-step explanation:

Answer:

Enter a problem...

Algebra Examples

Popular Problems Algebra Find the Asymptotes f(x)=10/(x^2-1)

f

(

x

)

=

10

x

2

−

1

Find where the expression

10

x

2

−

1

is undefined.

x

=

−

1

,

x

=

1

Since

10

x

2

−

1

→

∞

as

x

→

−

1

from the left and

10

x

2

−

1

→

−

∞

as

x

→

−

1

from the right, then

x

=

−

1

is a vertical asymptote.

x

=

−

1

Since

10

x

2

−

1

→

−

∞

as

x

→

1

from the left and

10

x

2

−

1

→

∞

as

x

→

1

from the right, then

x

=

1

is a vertical asymptote.

x

=

1

List all of the vertical asymptotes:

x

=

−

1

,

1

Consider the rational function

R

(

x

)

=

a

x

n

b

x

m

where

n

is the degree of the numerator and

m

is the degree of the denominator.

1. If

n

<

m

, then the x-axis,

y

=

0

, is the horizontal asymptote.

2. If

n

=

m

, then the horizontal asymptote is the line

y

=

a

b

.

3. If

n

>

m

, then there is no horizontal asymptote (there is an oblique asymptote).

Find

n

and

m

.

n

=

0

m

=

2

Since

n

<

m

, the x-axis,

y

=

0

, is the horizontal asymptote.

y

=

0

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes:

x

=

−

1

,

1

Horizontal Asymptotes:

y

=

0

No Oblique Asymptotes

image of graph

The vertical asymptotes of the given function are x = 1 and x = -1,

We have given the rational function is 10/(x²-1​).

We need to find the vertical asymptotes of this function.

Since Vertical asymptotes occur when the denominator of the function becomes zero and the numerator is not zero.

To determine the vertical asymptotes of the function, we need to solve the denominator for x²-1=0.

x²-1=0

x²=1

x=±√1

x=±1

Therefore, the vertical asymptotes of the given function are x = 1 and x = -1, since the denominator becomes zero at x=1 and x=-1.

To learn more about vertical asymptotes visit:

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Answer:

ddddddddddxdddxsddddddddD

Step-by-step explanation:

i hope it helps you

Answer:

[tex]288 {x}^{2} + x + 18[/tex]

Step-by-step explanation:

Ayan po ang answer sana po makatulong

Paki heart nalang po kung nakatulong

#carrying learning

Answer:

2/3

Step-by-step explanation:

Answer:

G is the smallest

H is the largest

Step-by-step explanation:

Given

[tex]GH = 21[/tex]

[tex]HJ = 24[/tex]

[tex]GJ = 9[/tex]

Required

Which of the statements is true

First, we need to solve for G, H and J as follows:

[tex]G + H = 21[/tex] --- (1)

[tex]H + J = 24[/tex] --- (2)

[tex]G + J = 9[/tex] --- (3)

Make G the subject in (1)

[tex]G = 21 - H[/tex]

Substitute 21 - H for G in (3)

[tex]21 - H + J = 9[/tex]

Collect Like Terms

[tex]-H + J = 9 - 21[/tex]

[tex]-H + J = -12[/tex]

Make J the subject

[tex]J = H - 12[/tex]

Substitute H - 12 for J in (2)

[tex]H + H - 12 = 24[/tex]

[tex]2H - 12 = 24[/tex]

Collect Like Terms

[tex]2H = 24 + 12[/tex]

[tex]2H = 36[/tex]

Solve for H

[tex]H = 18[/tex]

Substitute 18 for H in [tex]J = H - 12[/tex]

[tex]J = 18 - 12[/tex]

[tex]J = 6[/tex]

Substitute 18 for H in [tex]G = 21 - H[/tex]

[tex]G = 21 - 18[/tex]

[tex]G = 3[/tex]

So, we have that:

[tex]G = 3[/tex]     [tex]J = 6[/tex]     [tex]H = 18[/tex]

Hence, we can conclude that:

G is the smallest

H is the largest

9514 1404 393

Answer:

  k = -50

Step-by-step explanation:

The fraction denominators are 5 and 10. The least common multiple of those values is 10. This means we can eliminate fractions by multiplying both sides of the equation by 10:

  6k -50 = 7k

Subtracting 6k from both sides of the equation leaves you with the solution:

  -50 = k

Answer:

y = 1

hope that helps you