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4 years ago

0.02x - 4 - 0.01x - 2 = - 6.3

1 answer:

7 0

X = -30

First combine like terms (0.02x - 0.01x = 0.01x) (-4 - 2 = -6)
0.01x - 6 = -6.3
Then add 6 (-6 + 6 = 0) (-6.3 + 6 = -0.3)

0.01x = -0.3
Then divide by 0.01 to find what x is alone (0.01x ÷ 0.01 = x) (-0.3 ÷ 0.01 = -30)

x=-30

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Seven times the first (smaller) of two consecutive odd integers is equal to five times the second (larger) integer. Find each in

lbvjy [14]

<h2>Answer:</h2>

The smaller consecutive odd integer is: 5

and the larger consecutive odd integer is: 7

<h2>Step-by-step explanation:</h2>

Let the smaller odd integer be: a

then the larger odd integer which is consecutive to a will be: a+2

It is given that:

Seven times the first (smaller) of two consecutive odd integers is equal to five times the second (larger) integer.

This means that:

7 times of a is equal to 5 times of (a+2)

i.e.

$7a=5(a+2)\\\\i.e.\\\\7a=5\times a+5\times 2$

( Since, by using the distributive property of multiplication)

i.e.

$7a=5a+10\\\\i.e.\\\\7a-5a=10\\\\i.e.\\\\2a=10\\\\i.e.\\\\a=5$

Hence, the smaller number is: 5

and the larger number is: 7

( Since a+2=5+2=7 )

8 0

4 years ago

HELP with these questions

zlopas [31]

<u>Step-by-step explanation:</u>

transform the parent graph of f(x) = ln x into f(x) = - ln (x - 4) by shifting the parent graph 4 units to the right and reflecting over the x-axis

(???, 0): 0 = - ln (x - 4)

$\frac{0}{-1} = \frac{-ln (x - 4)}{-1}$

0 = ln (x - 4)

$e^{0} = e^{ln (x - 4)}$

1 = x - 4

5 = x

(5, 0)

(???, 1): 1 = - ln (x - 4)

$\frac{0}{-1} = \frac{-ln (x - 4)}{-1}$

1 = ln (x - 4)

$e^{1} = e^{ln (x - 4)}$

e = x - 4

e + 4 = x

6.72 = x

(6.72, 1)

Domain: x - 4 > 0

x > 4

(4, ∞)

Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that

No vertical asymptotes

*************************************************************************

transform the parent graph of f(x) = 3ˣ into f(x) = - 3ˣ⁺⁵ by shifting the parent graph 5 units to the left and reflecting over the x-axis

Domain: there is no restriction on x so domain is all real number

(-∞, ∞)

Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0. the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.

(-∞, 0)

Y-intercept is when x = 0:

f(x) = - 3ˣ⁺⁵

= - 3⁰⁺⁵

= - 3⁵

= -243

Horizontal Asymptote: y = 0 <em>(explanation above)</em>