PLEASE HELP ME OUT AND PLEASE

What property is used to rewrite (x + 2)(y + z) as y (x + 2) + z (x + 2)

Answer:

Distributive Property

Step-by-step explanation (if you were to show the steps):

(x+2)(y+z) (first expression)

xy + xz + 2y + 2z (Distributive Property of Multiplication)

yx + 2y + zx + 2z (use the Commutative Property of Addition and Commutative Property of Multiplication to group xy (also known as yx) and 2y together, and to group xz (also known as zx) and 2z together)

y(x + 2) + z(x + 2) (use factoring to get the rewritten expression at the end)

5 0

3 years ago

If 2 pounds of meat can serve 5 people how many to serve 13

Svetllana [295]

$\bf \begin{array}{ccll} \stackrel{meat}{lbs}&people\\ \cline{1-2} 2&5\\ x&13 \end{array}\implies \cfrac{2}{x}=\cfrac{5}{13}\implies 26=5x \\\\\\ \cfrac{26}{5}=x\implies 5\frac{1}{5}=x$

7 0

4 years ago

20 POINTS!! ASAP, PLS SHOW WORK TYY

Sergeeva-Olga [200]

Answer:

$\sin(\theta)=-\sqrt5/5\text{ and } \csc(\theta)=-\sqrt5\\\cos(\theta)=2\sqrt5/5\text{ and } \sec(\theta)=\sqrt5/2\\\tan(\theta)=-1/2\text{ and } \cot(\theta)=-2$

Step-by-step explanation:

First, let's determine which quadrant our angle θ lies in.

Remember ASTC, where:

Everything is positive in QI,

Only sine (and cosecant) is positive in QII,

Only tangent (and cotangent) is positive in QIII,

And only cosine (and secant) is positive in QIV.

Since our tangent is negative, and our cosine is positive, this means that our θ must be in QIV.

In QIV, sine is negative, tangent is negative, and cosine is positive.

With that, let's figure out the remaining trig ratios.

We know that:

$\tan(\theta)=-1/2$

Remember that tangent is the ratio of the opposite side to the adjacent side.

Let's figure out our hypotenuse using the Pythagorean Theorem:

$a^2+b^2=c^2$

Substitute 1 for a and 2 for b (we can ignore the negative since we're squaring anyways). This yields:

$(1)^2+(2)^2=c^2$

Square:

$1+4=c^2$

Add:

$c^2=5$

Take the square root:

$c=\sqrt{5}$

So, our square root is √5.

So, our three sides are: Opposite=1, Adjacent=2, and Hypotenuse=√5.

Sine and Cosecant:

Remember that:

$\sin(\theta)=opp/hyp$

Substitute 1 for the opposite and √5 for the hypotenuse. This yields:

$\sin(\theta)=1/\sqrt5$

Rationalize:

$\sin(\theta)=\sqrt5/5$

And since our angle is in QIV, we add a negative:

$\sin(\theta)=-\sqrt5/5$

Cosecant is simply the reciprocal of sine. So:

$\csc(\theta)=-\sqrt5$

Cosine and Secant:

Remember that:

$\cos(\theta)=adj/hyp$

Substitute 2 for the adjacent and √5 for the hypotenuse. This yields:

$\cos(\theta)=2/\sqrt5$

Rationalize:

$\cos(\theta)=2\sqrt5/5$

Since our angle is in QIV, cosine stays positive.

Secant is the reciprocal of cosine. So:

$\sec(\theta)=\sqrt5/2$

Tangent and Cotangent:

We were given that:

$\tan(\theta)=-1/2$

To find cotangent, flip:

$\cot(\theta)=-2$

And we're done!

7 0

3 years ago

Find the length of l on the curve r(t)=5cos(3t)i-5sin(3t)j+3tk over the interval [3,7]

stealth61 [152]

$\mathbf r(t)=5\cos3t\,\mathbf i-5\sin3t\,\mathbf j+3t\,\mathbf k$
$\mathrm d\mathbf r(t)=\mathbf r'(t)\,\mathrm dt=(-15\sin3t\,\mathbf i-15\cos3t\,\mathbf j+3\,\mathbf k)\,\mathrm dt$

$\displaystyle\int_C\mathrm d\mathbf r(t)=\int_{t=3}^{t=7}\|\mathbf r'(t)\,\mathrm dt\|=\int_{t=3}^{t=7}\sqrt{225\sin^23t+225\cos^23t+9}\,\mathrm dt$
$=\displaystyle3\sqrt{26}\int_{t=3}^{t=7}\mathrm dt$
$=12\sqrt{26}$

4 0

4 years ago

What is the value of m in mn= 12? A) m= 12-n B) m = 14 C) m= 12n D) m = 12 + n

Gekata [30.6K]

Answer: There is no choice available for the answer.

Step-by-step explanation:

The question is asking for the value of m in terms of n, so we need to isolate m to one side.

Given

mn=12

Divide n on both sides

mn/n=12/n

m=12/n

Hope this helps!! :)

Please let me know if you have any questions

6 0

3 years ago