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2 years ago

0.3(8-2x) - 1.2(2-3x) < -21

Mathematics

1 answer:

Semmy [17]2 years ago

8 0

Answer:

x=-7

Step-by-step explanation:

0.3(8-2x) - 1.2(2-3x) < -21

2.4 - 0.6x - 2.4 + 3.6x < -21

3x < -21

x < -7

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In the following exercises, multiply the binomials. Use any method.<br> 248. (m + 11)(m − 4)

romanna [79]

Answer:

Hence the expression $(m+11)(m-4)=m^2+7m-44$

Step-by-step explanation:

Explanation

The given expression is (m+11)(m-4).
We have to multiply the given expression.
Multiply the (m+11) by -4, multiply the (m+11) by m then add like terms.

$$$\frac{\begin{matrix}{} & {} & m & + & 11 \\ \times & {} & m & - & 4 \\ \end{matrix}}$

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${\frac{\begin{matrix}{} & - & 4m & - & 44 \\ {{m}^2} & + & 11m & {} & {} \\ \end{matrix}}{\begin{matrix}{{m}^2} & + & 7m & - & 44 \\ \end{matrix}}}$$$

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1 year ago

Solve 4x+ 1 = 1 and show steps as well

Mice21 [21]

4x+1=1
-1=-1
4x=0
4x/4=4/0
x=4

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8 0

3 years ago

Read 2 more answers

Explain why sin^-1(sin(3pi/4))does not equal 3pi/4 when y=sin x and y=sin^-1 x are inverses.

Fofino [41]

Because they're not inverses, not exactly. $\sin x$ is not invertible on its entire domain because it's not one-to-one. There are infinitely many values of $x$ such that $\sin x=0$ , for example.

The standard function $\sin^{-1}x$ has a domain of $-1\le x\le1$ and outputs values between $-\dfrac\pi2$ and $\dfrac\pi2$ . This means that its inverse, $\sin x$ , is indeed its inverse as long as $-\dfrac\pi2\le x\le\dfrac\pi2$ .

$\dfrac{3\pi}4$ is larger than $\dfrac\pi2$ and thus does not fall in the "invertible part" of the domain of $\sin x$ . We have

$\sin\dfrac{3\pi}4=\dfrac1{\sqrt2}$

which is a value between -1 and 1, so that

$\sin^{-1}\left(\sin\dfrac{3\pi}4\right)=\sin^{-1}\left(\dfrac1{\sqrt2}\right)=\dfrac\pi4$

If we wanted to recover $\dfrac{3\pi}4$ , we'd have to redefine $\sin^{-1}x$ or define a new inverse function that works on a different branch of the domain of $\sin x$ .

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3 years ago

You are in charge of purchases at the student-run used-book supply program at your college, and you must decide how many introdu

Aleonysh [2.5K]

Answer:

Step-by-step explanation:

Maximum textbook to purchase is 750books

Calculus texts occupy 2 units of shelf space each,

history books 1 unit each,

marketing texts 3 units each.

Profit on calculus is $10

Profit on history $4

Profit on Marketing $8

Let calculus be x

Let marketing be y

History be z

Maximum textbooks is 750

x+y+z = 750. Equation 1

Total units =1200.

2unit calculus + 3unit marketing and 1 unit History =1200

2x + 3y +z = 1200. Equation 2

Calculus has the highest value, so to maximize profit, all the calculus books must be bought.

So since their are 1200 units of self space and calculus uses 2units

Then total unit ratio is 2+3+1=6

Then, available space for calculus is

Calculus = 2/6×1200 =400books

So all the calculus book must be bought

So, x=400

To maximum profit again we must buy again more of Marketing

Then, marketing occupy 3units

Then, available space for marketing is

Marketing. =3/6 ×1200 = 600books

So since the maximum book to buy for a semester is 750 books

Then, since we must buy only 750books and 400books already calculus, so we still have ability to buy 600books from marketing to maximize profit, but we only have 350books left to buy, then the 350books of marketing will be bought

So, no book from history will be bought to maximize profit

Calculus is 400books

Marketing is 350books

History is 0 books

2. Maximum profit is given by the amount of book bought multiply by it's selling price.

Maximum profit =400×10 + 350×8 +0×4

Maximum Profit = 4000+2800+0

Maximum profit = $6800

The maximum profit the program can make in a semester is $6800

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3 years ago

Find the quotient. Simplify if possible

Ksenya-84 [330]

$\frac{ \frac{x}{3} }{ \frac{x}{9} } = \frac{x}{3} \frac{9}{x} = \frac{9x}{3x} =3$

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3 years ago