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3 years ago

4X + 8 < 1 + ( 2X - 5) PLEASE EXPLAIN

Mathematics

1 answer:

Simora [160]3 years ago

5 0

Answer:

x < - 6

Step-by-step explanation:

Given

4x + 8 < 1 +(2x - 5) ← remove parenthesis

4x + 8 < 1 + 2x - 5, that is

4x + 8 < 2x - 4 ( subtract 2x from both sides )

2x + 8 < - 4 ( subtract 8 from both sides )

2x < - 12 ( divide both sides by 2 )

x < - 6

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Answer:

Isosceles trapezoid

Step-by-step explanation:

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3 years ago

From the set of 5, 6, 38 use substitution to determine which value of x makes the equation true.

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3 years ago

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Step-by-step explanation:

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3 years ago

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If the parent function f(x) = x^2 is fatter translated 11 units to the left, then translated 5 units down, write the resulting f

nikklg [1K]

The quadratic function given by:

$f(x)=a(x-h)^2+k, \ \ \ a\neq 0$

is in vertex form. The graph of $f$ is a parabola whose axis is the vertical line $x=h$ and whose vertex is the point $(h, k)$ . So:

To translate the graph of a function to the right, left, upward or downward we have:

$For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)$

By knowing this things, we can solve our problem as follows:

FIRST.

Translating 11 units to the left:

$g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2$

Then translating 5 units down:

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5$

Since the new function is fatter, the factor we need to multiply the term $(x+11)^2$ must be less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.

Therefore, the right answer is b. f(x) = 1/2(x + 11)^2 - 5

SECOND.

Translating 8 units to the right:

$g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2$

Then translating 1 unit down:

$g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1$

As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.

Therefore, the right answer is a. g(x) = 1/3(x - 8)^2 - 1

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3 years ago

Solve the equation 4(y-3)=13

I am Lyosha [343]

Step-by-step explanation:

$4(y - 3) = 13 \\ \\ \therefore \: 4y - 4 \times 3 = 13 \\ \\ \therefore \: 4y - 12 = 13\\ \\ \therefore \: 4y = 13 + 12 \\ \\ \therefore \: 4y = 25 \\ \\ \therefore \:y = \frac{25}{4} \\ \\ \therefore \:y = 6\frac{1}{4}$

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3 years ago

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