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4 years ago

If U = {all positive integers} and A = {x|x ∈ U and x is an odd positive integer}, which describes Ac?

Mathematics

2 answers:

Viefleur [7K]4 years ago

8 0

Im pretty sure its D i might be wrong i havent finished the test yet

tekilochka [14]4 years ago

6 0

The answer is:

D. Ac = {xΙx ∈ U and is an even positive integer}

:)

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A road perpendicular to a highway leads to a farmhouse located d miles away. An automobile traveling on this highway passes thro

pshichka [43]

Answer:

$\frac{dh}{dt}=\frac{30r}{\sqrt{d^{2}+900}}$

Step-by-step explanation:

A road is perpendicular to a highway leading to a farmhouse d miles away.

An automobile passes through the point of intersection with a constant speed $\frac{dx}{dt}$ = r mph

Let x be the distance of automobile from the point of intersection and distance between the automobile and farmhouse is 'h' miles.

Then by Pythagoras theorem,

h² = d² + x²

By taking derivative on both the sides of the equation,

$(2h)\frac{dh}{dt}=(2x)\frac{dx}{dt}$

$(h)\frac{dh}{dt}=(x)\frac{dx}{dt}$

$(h)\frac{dh}{dt}=rx$

$\frac{dh}{dt}=\frac{rx}{h}$

When automobile is 30 miles past the intersection,

For x = 30

$\frac{dh}{dt}=\frac{30r}{h}$

Since $h=\sqrt{d^{2}+(30)^{2}}$

Therefore,

$\frac{dh}{dt}=\frac{30r}{\sqrt{d^{2}+(30)^{2}}}$

$\frac{dh}{dt}=\frac{30r}{\sqrt{d^{2}+900}}$

3 0

3 years ago

What is the LCD of 2/5 and 4/11

scoundrel [369]

To find the lowest common denominator you need to know the factors of 5 and 11.
So make two lists:
5, 10, 15, 20, 25, 30, and so on.
11, 22, 33, 44, 55, 66, and so on.
Keep doing that until you find the lowest common number in the lists. The LCD will be 55.

3 0

3 years ago

Simplify without the absolute value |x+3| ; if x>2

inna [77]

Answer:

$x+3$ if $x>2$

Step-by-step explanation:

Recall some following basic ideas about absolute value:

$|0|=0$ or I guess $-(0)=0$

$|3|=3$

$|-3|=-(-3)$ or just $3$ but there is a reason why I wrote it the way I did.

You see that the absolute value returned the same value if the value was positive.

You see that the absolute value returned the opposite value if the value was negative.

You can include 0 in either.

Let's look at $|x+3|$ alone for a second.

* $|x+3|=x+3$ if $x+3$ is positive or zero.

When is $x+3$ positive or zero? [greater than or equal to 0]

$x+3\ge 0$

Subtract 3 on both sides

$x\ge -3$

* $|x+3|=-(x+3)$ if $x+3$ is negative or zero.

When is $x+3$ negative or zero? [less or equal to 0]

$x+3\le 0$

Subtract 3 on both sides

$x\le -3$

So looking at the bullet points (the *), $x>2$ fits into the first inequality.

Therefore, $|x+3|=x+3$ .

8 0

3 years ago

10 = 3c − 2<br><br> c = what

creativ13 [48]

Answer:

Step-by-step explanation:

Here you go mate

Step 1

10=3c-2 Equation/Question

Step 2

10=3c-2 Simplify

10=3c-2

Step 3

10=3c-2 Add +2

3c=12

Step 4

3c=12 Then you divide the exponents by 3

answer

c=4

Hope this helps

4 0

3 years ago

Sterre charges $35 to file tax returns, but files for free if she only needs the easiest form. Then she donates $2 to clean wate

borishaifa [10]

We have been given that Sterre charges $35 to file tax returns, but files for free if she only needs the easiest form. Also, she donates $2 to clean water projects per tax return she files.

Further we know that Sterre charged $7,245 and made a donation of $1,242 this year for the tax returns she filed.

Let x be the number of free income tax returns and y be the number of $35 income tax returns.

Therefore, we can set up:

$0\times x+35\times y=7245\Rightarrow 35y=7245\Rightarrow y=\frac{7245}{35}=207$

Since she donates $2 for each return that she files, therefore, we can set up:

$2(x+y)=1242\Rightarrow x+y=621\Rightarrow x+207=621\Rightarrow x=414$

Therefore,

Sterre filed 414 tax returns for free and filed 207 tax returns for $35.

7 0

3 years ago