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3 years ago

Solve this Inequality 1 > -1 - w

Mathematics

1 answer:

Rom4ik [11]3 years ago

8 0

Answer:

$\displaystyle -2 < w$

Step-by-step explanation:

1 > −1 - w

+ 1 + 1

________

$\displaystyle \frac{2}{-1} > \frac{-w}{-1} \\ \\ -2 < w$

Whenever you divide\multiply by a <em>negative</em>, you reverse the inequality symbol.

I am joyous to assist you anytime.

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Solve each system of inequalities by graphing. x>2 y<4

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Step-by-step explanation:

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3 years ago

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Which statement is true about the extreme value of the given quadratic equation? y = -3x2 + 12x − 33

Zina [86]

Answer:

The equation has a maximum value with a y-coordinate of -21.

Step-by-step explanation:

Given

$y =-3x^2 + 12x - 33$

Required

The true statement about the extreme value

First, write out the leading coefficient

$Leading = -3$

$-3 < 0$ means that the function would be a downward parabola;

Downward parabola always have their vertex on top of the parabola and as such, the function has a maximum value.

The maximum value is:

$x = -\frac{b}{2a}$

Where:

$a= -3; b =12; c =-33$

So, we have:

$x = -\frac{12}{2 * -3}$

$x = -\frac{12}{-6}$

$x =2$

Substitute $x =2$ in $y =-3x^2 + 12x - 33$

$y = -3*2^2 + 12 * 2 - 33$

$y = -21$

<em>Hence, the maximum is -21.</em>

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3 years ago

Find the measure of each arc.

Gemiola [76]

9514 1404 393

Answer:

GX = 122°
XU = 148°
UG = 90°

Step-by-step explanation:

Each arc has the same measure as its central angle. The sum of all of them is 360°.

angle UOG is marked as a 90° angle, so arc UG is 90°.

angle GOX is marked as 122°, so arc GX is 122°.

angle XOU fills out the rest of 360°, so its measure is 360° -90° -122° = 148°. That means are XU is 148°.

The arc measures are ...

GX = 122°
XU = 148°
UG = 90°

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3 years ago

Find the value of yy in each equation. Explain how you determined the value of y.

Hitman42 [59]

Answer:

a) 3

b) 9

c) 81

d) x

Step-by-step explanation:

We know the properties of log function as:

1) log(AB) = log(A) + log(B)

2) $\log(\frac{A}{B}) = \log(A)+\log(B)$

3) log(aᵇ) = b × log(a)

also,

4) $\log_b(a)=\frac{\log(a)}{\log(b)}$

Given:

a. y = $3^{\log_3(3)}$

Now,

taking log both sides, we get

log(y) = $\log(3^{\log_3(3)})$

using 3, we get

log(y) = log₃(3) × log(3)

using 4, we get

log(y) = $\frac{\log(3)}{\log(3)}$ × log(3)

log(y) = 1 × log(3)

taking anti-log both sides

y = 3

b. y = $3^{log_3(9)}$

Now,

taking log both sides, we get

log(y) = $\log(3^{\log_3(9)})$

using 3, we get

log(y) = log₃(9) × log(3)

using 4, we get

log(y) = $\frac{\log(9)}{\log(3)}$ × log(3)

log(y) = log(9)

taking anti-log both sides

y = 9

c. y = $3^{\log_3(81)}$

Now,

taking log both sides, we get

log(y) = $\log(3^{\log_3(81)})$

using 3, we get

log(y) = log₃(81) × log(3)

using 4, we get

log(y) = $\frac{\log(81)}{\log(3)}$ × log(3)

log(y) = log(81)

taking anti-log both sides

y = 81

d. y = $3^{\log_3(x)}$

Now,

taking log both sides, we get

log(y) = $\log(3^{\log_3(x)})$

using 3, we get

log(y) = log₃(x) × log(3)

using 4, we get

log(y) = $\frac{\log(x)}{\log(3)}$ × log(3)

log(y) = log(x)

taking anti-log both sides

y = x

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3 years ago

A suit was marked with a 20% discount.

Debora [2.8K]

Answer:

130

Step-by-step explanation:

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3 years ago

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