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2 years ago

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Which graph shows the solution to the system of linear inequalities? x – 4y < 4 y < x + 1 Image for option 1 Image for opt

ion 2 Image for option 3 Image for option 4

1 answer:

slava [35]2 years ago

7 0

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$x-4y$ ----> inequality A

solve for y

$-4y$

$4y>x-4$

$y> (x/4)-1$

The solution of the inequality A is the shaded area above the dashed line

The slope of the dashed line is positive

The y-intercept is the point $(0,-1)$

The x-intercept is the point $(4,0)$

$y< x+1$ ----> inequality B

The solution of the inequality B is the shaded area below the dashed line

The slope of the dashed line is positive

The y-intercept is the point $(0,1)$

The x-intercept is the point $(-1,0)$

Using a graphing tool

The solution of the system of inequalities in the attached figure

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If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ?

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Answer:

The answer is

$sin(\theta)=-\frac{\sqrt{2}}{2}$

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Step-by-step explanation:

we know that

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In this problem we have

$cos(\theta)=\frac{\sqrt{2}}{2}$

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so

The angle $\theta$ belong to the third or fourth quadrant

The value of $sin(\theta)$ is negative

Step 1

Find the value of $sin(\theta)$

Remember

$sin^{2}(\theta)+cos^{2}(\theta)=1$

we have

$cos(\theta)=\frac{\sqrt{2}}{2}$

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$sin^{2}(\theta)+(\frac{\sqrt{2}}{2})^{2}=1$

$sin^{2}(\theta)=1-\frac{1}{2}$

$sin^{2}(\theta)=\frac{1}{2}$

$sin(\theta)=-\frac{\sqrt{2}}{2}$ ------> remember that the value is negative

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$sin(\theta)=-\frac{\sqrt{2}}{2}$

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Answer: Daniel bought 3 apples and 7 bananas.

Step-by-step explanation:

Let x represent the number of apples that Daniel bought.

Let y represent the number of bananas that Daniel bought.

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x + y = 10

Daniel and his children went into a grocery store and he bought $10.15 worth of apples and bananas. Each apple costs $1.75 and each banana costs $0.70. This means that

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Substituting x = 10 - y into equation 1, it becomes

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Given that:

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Therefore, the probability that the selected fish is a male, is $\dfrac{3}{7}.$

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Therefore, probability that the selected fish is a male green swordtail is $\dfrac{9}{35}.$

D.

We have to find the probability that the selected fish is either a male or a green swordtail.

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