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2 years ago

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Decide whether the statement is true or false. If it is false, explain why. The union of the solution sets of 4xplus5equals13,

4xplus5greater than13, and 4xplus5less than13 is empty set

1 answer:

postnew [5]2 years ago

4 0

The given statement is false because it isn't an empty set!

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

We have following sets of inequalities:

$4x+5=13\\4x+5>13\\4x+5$

From $4x+5=13$ we get ,

$4x = 8 \\x=2$

Therefore solution set is x=2.

Now, for $4x+5>13$ we get ,

$4x+5>13 \\4x>8\\x>2$

Therefore solution set is x>2.

For $4x+5$ we get ,

$4x+5$

Therefore solution set is x<2.

Now, the union of x=2, x<2 & x>2 is -∞<x<∞. i.e. all possible values of x. And so above statement is false because it isn't an empty set!

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Marley had $495.66 in her bank account after she paid her monthly bills. She took her sister out to lunch, and paid $38.90. How

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Answer: the answer is $456.76

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2 years ago

If the ratio of the length of segment AC to the length of segment CB is 3:1, what is the y-coordinate of point C?

Yuki888 [10]

Answer:

The coordinates of point C are (8,8.5)

Step-by-step explanation:

The picture of the question in the attached figure

Let

$(C_x,C_y)$ ----> coordinates of point C

we have that

The horizontal distance AB is equal to

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The vertical distance AB is equal to

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we know that

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so

$\frac{AC_x}{CB_x}=\frac{3}{1}$

$AC_x=3CB_x$ ----> equation A

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substitute equation A in equation B

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so

The x-coordinate of point C is equal to the x-coordinate of point A plus the horizontal distance between the point A and point C

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Find the vertical coordinate of point C

we know that

$\frac{AC}{CB}=\frac{3}{1}$

so

$\frac{AC_y}{CB_y}=\frac{3}{1}$

$AC_y=3CB_y$ ----> equation A

$AC_y+CB_y=6$ ----> equation B

substitute equation A in equation B

$3CB_y+CB_y=6$

$4CB_y=6\\CB_y=1.5$

$AC_y=3(1.5)=4.5$

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$C_y=A_y+AC_y=4+4.5=8.5$

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Step-by-step explanation:

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2 years ago

Read 2 more answers

How does f(x) = 3* change over the interval x = 4 to x = 57

Vilka [71]

f(x) increase by a factor of 3

Explanation:

Given that f(x)= 3* and the interval is x=4 to x=57

Now we put the value for x is 4 to 57 then value of f(x) increase with the multiply of 3.

Because the x is multiplied with 3 i.e., 3*

So f(x) increase by a factor of 3.

If we put x=4, then f(x)= 12 (∵ 3×4=12)

If we put x=5, the f(x)= 15 (∵ 3×5=15)

If we put x=6,the f(x)= 18 (∵ 3×6=18)

similarly., values of x= 7,8,9,...155.

Then,

If we put x=56, the f(x)=168

This process will continue until f(x)=171 for x=57.

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