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2 years ago

Can someone give me a step by step explanation because my teacher doesn’t teach us anything? :(

Mathematics

1 answer:

Alex2 years ago

7 0

Answer:

(7x^2 -1)(x - 2).

Step-by-step explanation:

7x^3 - 14x^2 - x + 2

We can factor this by grouping - that is factoring the first 2 terms and the last 2:

= 7x^2(x - 2) - 1(x - 2) <-- the x - 2 is common to both parts so we have:

(7x^2 -1)(x - 2).

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−2(2x+3)≤26 - 2 2 x + 3 ≤ 26 ?

SashulF [63]

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

$- 2 ( 2 x + 3 ) \leq 26.$

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$- 2 ( 2 x + 3 ) \leq 26$

Divide both sides by -2. We know that since 2 is negative, it'll be < (less than) 0. So, the direction of inequality will change.

$2x+3\geq \frac{26}{-2} \\$

Divide 26 by -2..we'll get the answer as -13.

$2x+3\geq -13$

Now, subtract 3 from both the sides.

$2x\geq -13-3$

Subtracting -13 by 3..we'll get the answer as -16.

$2x\geq -16$

Divide both sides by 2. We know that since 2 is positive, the direction of inequality will remain the same.

$x\geq \frac{-16}{2} \\$

Divide -16 by 2..we'll get the answer as -8.

$\huge \boxed{ \boxed{ \bf \: x\geq -8 }}$

The correct answer is ⇨ x greater than or equal to -8.

3 0

2 years ago

What is an algebraic expression

Annette [7]

Math Term Definition. Algebraic Expression. An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide). Here are some algebraic expressions: a + 1.

8 0

2 years ago

What% is 32 divided by 300

cupoosta [38]

Answer:

The answer is 0.106666667

4 0

3 years ago

Read 2 more answers

Number ten please thanks

BlackZzzverrR [31]

-3^2= -(3)^2

The exponent of 2 only applies to the number 3. -(3)^2 should equal -9. This is true because according to the order of operations, exponents should be evaluated before multiplication. The negative sign here represents -1* 3^2.
If you want to find -3 to the power of 2 it must be written (-3)^2.

5 0

2 years ago

Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (naut

frozen [14]

Answer:

a) $\sqrt{144-288t+208t^2}$ b.) -12knots, 8 knots c) No e) $4\sqrt{13}$

Step-by-step explanation:

We know that the initial distance between ships A and B was 12 nautical miles. Ship A moves at 12 knots(nautical miles per hour) south. Ship B moves at 8 knots east.

We know that at time t , the ship A has moved $12\dot t (n.m)$ and ship B has moved $8\dot t (n.m)$ . We also know that the ship A moves closer to the line of the movement of B and that ship B moves further on its line.

Using Pythagorean theorem, we can write the distance s as:

$\sqrt{(12-12\dot t)^2 + (8\dot t)^2}\\s=\sqrt{144-288t+144t^2+64t^2}\\s=\sqrt{144-288t+208t^2}$

We want to find $\frac{ds}{dt}$ for t=0 and t=1

$\sqrt{144-288t+208t^2}|\frac{d}{dt}\\\\\frac{ds}{dt}=\frac{1}{2\sqrt{144-288t+208t^2}}\dot (-288+416t)\\\\\frac{ds}{dt}=\frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\\frac{ds}{dt}(0)=\frac{208\dot 0-144}{\sqrt{144-288\dot 0 + 209\dot 0^2}}=-12knots\\\\\frac{ds}{dt}(1)=\frac{208\dot 1-144}{\sqrt{144-288\dot 1 + 209\dot 1^2}}=8knots$

We know that the visibility was 5n.m. We want to see whether the distance s was under 5 miles at any point.

Ships have seen each other = $s\leq 5\\\\\sqrt{144-288t+208t^2}\leq 5\\\\144-288t+208t^2\leq 25\\\\199-288t+208t^2\leq 0$

Since function $f(x)=199-288x+208x^2$ is quadratic, concave up and has no real roots, we know that $199-288x+208x^2>0$ for every t. So, the ships haven't seen each other.

Attachedis the graph of s(red) and ds/dt(blue). We can see that our results from parts b and c were correct.

Function ds/dt has a horizontal asympote in the first quadrant if

$\lim_{t \to \infty} \frac{ds}{dt}$

So, lets check this limit:

$\lim_{t \to \infty} \frac{ds}{dt}=\lim_{t \to \infty} \frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\=\lim_{t \to \infty} \frac{208-\frac{144}{t}}{\sqrt{\frac{144}{t^2}-\frac{288}{t}+208}}\\\\=\frac{208-0}{\sqrt{0-0+208}}\\\\=\frac{208}{\sqrt{208}}\\\\=4\sqrt{13}$

Notice that:

$4\sqrt{13}=\sqrt{12^2+5^2}$ =√(speed of ship A² + speed of ship B²)

5 0

3 years ago