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3 years ago

Find the value of a°

Mathematics

2 answers:

Misha Larkins [42]3 years ago

7 0

Answer:

If two vectors are parallel, applying the same side interior angles theorem:

=> 80 + a + 59 = 180

=> a = 180 - 80 - 59 = 41 deg

Hope this helps!

Goshia [24]3 years ago

4 0

Or you could apply alternate angle theorem

Alternate angles make a "z" shape. Alternate angles are equal

So now that we know the third side of the triangle is equal to 59, we do 180=a+59+80

Move fifty nine and eighty to the other side as negative numbers

a=180-59-80

So, a is equal, to 41 :))

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What is the order of these numbers from least to greatest?<br><br> 4.03 4.3 4.003

Gekata [30.6K]

The order is 4.003 then 4.03 then 4.3

8 0

2 years ago

Find the locus of a point such that the sum of its distance from the point ( 0 , 2 ) and ( 0 , -2 ) is 6.

jok3333 [9.3K]

Answer:

$\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1$

Step-by-step explanation:

We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.

First, we will need the distance formula, given by:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Let the point on the locus be P(x, y).

So, the distance from P to (0, 2) will be:

$\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}$

And, the distance from P to (0, -2) will be:

$\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}$

So sum of the two distances must be 6. Therefore:

$d_1+d_2=6$

Now, by substitution:

$(\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6$

Simplify. We can subtract the second term from the left:

$\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}$

Square both sides:

$(x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)$

We can cancel the x² terms and continue squaring:

$y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4$

We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:

$-8y=36-12\sqrt{x^2+(y+2)^2}$

We can divide both sides by -4:

$2y=-9+3\sqrt{x^2+(y+2)^2}$

Adding 9 to both sides yields:

$2y+9=3\sqrt{x^2+(y+2)^2}$

And, we will square both sides one final time.

$4y^2+36y+81=9(x^2+(y^2+4y+4))$

Distribute:

$4y^2+36y+81=9x^2+9y^2+36y+36$

The 36y will cancel. So:

$4y^2+81=9x^2+9y^2+36$

Subtracting 4y² and 36 from both sides yields:

$9x^2+5y^2=45$

And dividing both sides by 45 produces:

$\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1$

Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.

5 0

3 years ago

Read 2 more answers

A salsa recipe uses 14 ounces of peppers and 7 ounces of onions

mixer [17]

Answer:

$s = salsa$

$p = peppers$

$o = onions$

$s = 14p + 7o$

Step-by-step explanation:

Hope this helps!

14 + 7 = 21 ounces.

8 0

3 years ago

Right isosceles triangles are constructed on the sides of a 3−4−5 right triangle, as shown. A capital letter represents the area

Ivenika [448]

Answer:

Step-by-step explanation:

because the triangles are isosceles, that means that the area of Z is 5x5x1/2, which equals 12.5

the area of X is 4.5

the area of y is 8

(8+4.5)/(12.5) = 1

5 0

3 years ago

Consider the example of finding the probability of selecting a black card or a 6 from a deck of 52 cards.

Marina86 [1]

Answer:

The probability of selecting a black card or a 6 = 7/13

Step-by-step explanation:

In this question we have given two events. When two events can not occur at the same time,it is known as mutually exclusive event.

According to the question we need to find out the probability of black card or 6. So we can write it as:

P(black card or 6):

The probability of selecting a black card = 26/52

The probability of selecting a 6 = 4/52

And the probability of selecting both = 2/52.

So we will apply the formula of compound probability:

P(black card or 6)=P(black card)+P(6)-P(black card and 6)

Now substitute the values:

P(black card or 6)= 26/52+4/52-2/52

P(black card or 6)=26+4-2/52

P(black card or 6)=30-2/52

P(black card or 6)=28/52

P(black card or 6)=7/13.

Hence the probability of selecting a black card or a 6 = 7/13 ....

7 0

3 years ago