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3 years ago

5

which qaudratic equation is equivalent to (x+2)^2+5(x+2)-6=0 a. (u+2)^2+5(u+2)-6=0 where u=(x-2) b. u^2+4+5u-6=0 where u= (x-2)

c. u^2+5u-6=0 where u=(x+2) d. u^2+u-6=0 where u=(x+2)

1 answer:

Lisa [10]3 years ago

5 0

Answer:

D

Step-by-step explanation:

Given

(x + 2)² + 5(x + 2) - 6 = 0

Using the substitution u = x + 2 , then the equation can be expressed as

u² + 5u - 6 = 0 → D

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Emma Drew 13 hearts and 20 circles what is the ratio of hearts to all shape

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13 : 33

Step-by-step explanation:

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What two numbers multiplied equal 2048

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There is more than one answer, but one could be:
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Chantal bicycles at a speed of 20 miles per hour and has already riden 45 miles when Trisha begins cycling. Trish bicycles at a

melomori [17]

Answer:

Chantal and Trisha will have both traveled 105 miles in 20 minutes.

Step-by-step explanation:

$y$ is distance in miles, $x$ is time in hours.

The two equations are:

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Set them equal to each other and solve for x:

$\frac{35}{x} = \frac{20}{x} + 45$

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Plug that back into the equations to confirm this $x$ gives the same $y$ :

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3 years ago

The first term of a geometric sequence is 6 and the fourth term is 384. What is the sum of the first 10 terms of the correspondi

aleksandrvk [35]

Answer:

2097150

Step-by-step explanation:

<u>GIVEN :-</u>

First term of G.P. = 6
Forth term of G.P. = 384

<u>TO FIND :-</u>

Sum of first 10 terms of the G.P.

<u>CONCEPT TO BE USED IN THIS QUESTION :-</u>

<em>Geometric Progression :-</em>

It's a sequence in which the successive terms have same ratio.

General form of a G.P. ⇒ a , ar , ar² , ar³ , ....... [where a = first term ; r = common ratio between successive terms]

Sum of 'n' terms of a G.P. ⇒ $\frac{a(r^n - 1)}{r-1}$ .

<em>[NOTE :- </em> $\frac{a(1-r^n)}{1-r}$ can also be the<em> formula for "Sum of n terms of G.P." because if you put 'r' there (assuming r > 0) you'll get negative value in both the numerator & denominator from which the negative sign will get cancelled from the numerator & denominator. </em><em>YOU'LL BE GETTING THE SAME VALUE FROM BOTH THE FORMULAES.</em><em>]</em>

<u>SOLUTION :-</u>

Let the first term of the G.P. given in the question be 'a' and the common ratio between successive terms be 'r'.

⇒ a = 6

It's given that <u>forth term</u> is 384. So from "General form of G.P." , it can be stated that :-

$=> ar^3 = 384$

$=> 6r^3 = 384$

Divide both the sides by 6.

$=> \frac{6r^3}{6} = \frac{384}{6}$

$=> r^3 = 64$

$=> r = \sqrt[3]{64} = 4$

Sum of first 10 terms $= \frac{6(4^{10}-1)}{4 - 1}$

$= \frac{6(1048576 - 1)}{3}$

$= 2 \times 1048575$

$= 2097150$

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3 years ago

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