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2 years ago

What is the measure of each exterior angle of the right triangle?

Mathematics

2 answers:

spayn [35]2 years ago

4 0

I think x=90°, and z=136°

n200080 [17]2 years ago

4 0

X=90 degrees
Y=134 degrees
Z=136 degrees

Angle X and the right angle of the triangle are supplementary angles. Meaning when added together, they equal to 180 degrees.

So 180-90=90

To find y, first you have to find the missing measure of the right triangle. And to do that, you use the triangle angle sum theorem.

44+90+x=180

134+x=180

Subtract 134 from both sides

X=46.

The angle with the measure 46 is supplementary to angle y

180-46=134

Angle Z is supplementary angles with the angle with the measure of 44.

So 180-44=136

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Ples help me find slant assemtotes

FrozenT [24]

A polynomial asymptote is a function $p(x)$ such that

$\displaystyle\lim_{x\to\pm\infty}(f(x)-p(x))=0$

$(y+1)^2=4xy\implies y(x)=2x-1\pm2\sqrt{x^2-x}$

Since this equation defines a hyperbola, we expect the asymptotes to be lines of the form $p(x)=ax+b$ .

Ignore the negative root (we don't need it). If $y=2x-1+2\sqrt{x^2-x}$ , then we want to find constants $a,b$ such that

$\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0$

We have

$\sqrt{x^2-x}=\sqrt{x^2}\sqrt{1-\dfrac1x}$
$\sqrt{x^2-x}=|x|\sqrt{1-\dfrac1x}$
$\sqrt{x^2-x}=x\sqrt{1-\dfrac1x}$

since $x\to\infty$ forces us to have $x>0$ . And as $x\to\infty$ , the $\dfrac1x$ term is "negligible", so really $\sqrt{x^2-x}\approx x$ . We can then treat the limand like

$2x-1+2x-ax-b=(4-a)x-(b+1)$

which tells us that we would choose $a=4$ . You might be tempted to think $b=-1$ , but that won't be right, and that has to do with how we wrote off the "negligible" term. To find the actual value of $b$ , we have to solve for it in the following limit.

$\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-4x-b)=0$

$\displaystyle\lim_{x\to\infty}(\sqrt{x^2-x}-x)=\frac{b+1}2$

We write

$(\sqrt{x^2-x}-x)\cdot\dfrac{\sqrt{x^2-x}+x}{\sqrt{x^2-x}+x}=\dfrac{(x^2-x)-x^2}{\sqrt{x^2-x}+x}=-\dfrac x{x\sqrt{1-\frac1x}+x}=-\dfrac1{\sqrt{1-\frac1x}+1}$

Now as $x\to\infty$ , we see this expression approaching $-\dfrac12$ , so that

$-\dfrac12=\dfrac{b+1}2\implies b=-2$

So one asymptote of the hyperbola is the line $y=4x-2$ .

The other asymptote is obtained similarly by examining the limit as $x\to-\infty$ .

$\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0$

$\displaystyle\lim_{x\to-\infty}(2x-2x\sqrt{1-\frac1x}-ax-(b+1))=0$

Reduce the "negligible" term to get

$\displaystyle\lim_{x\to-\infty}(-ax-(b+1))=0$

Now we take $a=0$ , and again we're careful to not pick $b=-1$ .

$\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-b)=0$

$\displaystyle\lim_{x\to-\infty}(x+\sqrt{x^2-x})=\frac{b+1}2$

$(x+\sqrt{x^2-x})\cdot\dfrac{x-\sqrt{x^2-x}}{x-\sqrt{x^2-x}}=\dfrac{x^2-(x^2-x)}{x-\sqrt{x^2-x}}=\dfrac
 x{x-(-x)\sqrt{1-\frac1x}}=\dfrac1{1+\sqrt{1-\frac1x}}$

This time the limit is $\dfrac12$ , so

$\dfrac12=\dfrac{b+1}2\implies b=0$

which means the other asymptote is the line $y=0$ .

4 0

3 years ago

Hat is he probability of pick 1 green marble from a bag with 7 green and 8 blue marbles

disa [49]

Answer:

7/15

Step-by-step explanation:

No. of green marbles in the bag= 7

No. of blue marbles in the bag= 8

Total no. of marbles in the bag= 7+8=15

As we know that,

Probability( of a random event A)= $\frac{Favourable\ no.\ of\ elementary\ events}{Total\ no.\ of\ elementary\ events}$

Hence in this case,

Favourable np. of elementary events (green marbles)=7

Total no. of elementary events (Total no. of marbles in the bag)= 15

Hence, Probability of picking a green marble from the bag= $\frac{7}{15}$

7 0

2 years ago

A bakery makes 4 dozen raisin muffins and 8 dozen blueberry muffins. A dozen is 12 muffins.

swat32

Answer:

144

Step-by-step explanation:

8x12 = 96 and 4x12= 48 and 96+48= 144

7 0

2 years ago

Jacob received a deck of cards for his birthday. The length, width, and height of the card box are shown below. What is the volu

ollegr [7]

The question is incomplete :

The height, width and Lenght isn't Given. However, we can create an hypothetical scenario, with a height 6, length 8 and width 4

Answer:

192 unit³

Step-by-step explanation:

The volume of the card box :

Recall the volume of box formula :

V = length * width * height

Volume = 8 * 6 * 4

Volume = 192 unit³

This is the procedure for any given dimension of the card deck.

6 0

2 years ago

I need the measure of

WINSTONCH [101]

Answer:

90-55= 35 degrees

Step-by-step explanation:

5 0

2 years ago