All categories

3 years ago

If COS(W) = sin(zº), which of the following statements is true?

Mathematics

1 answer:

yawa3891 [41]3 years ago

4 0

Answer:

The third option is the answer.

Step-by-step explanation:

These triangles are clearly not congruent because they have different side length so the first 2 options are wrong.

Since both triangles already share a right angle. The other two angles in both triangles must both add up to 90.

It is given to use that sin z=cos w. That doesn't mean that angle z= angle w.

Consider a two similar two 30-60-90 triangles We are given the 90 degree right angle in both triangles. We are also given one 60 degree angle in one and a 30 degree triangle in one.

$\cos(30) = \sin(60)$

But they have two different angle measures.

However, by triangle interior theorem. The third angle must be

equal to the other corresponding angle of the other triangle. So angle z corresponds with Angle X.

By the AA theorem, The triangles are similar.

The third option is the answer.

You might be interested in

Kate is at a T-shirt sale where she can buy one and get a second one for 30% off. She wants to buy two T-shirts listed at $19 ea

gladu [14]

So in this problem we can state that each T-shirt costs S19 each. And if Kate buys two she gets a 30% off with the second shirt she buys. And how much will she pay?

Solution: 
1. 19 for each t-shirt 
2. Total of $38 if not provided with 30% off
3. 19 x 0.3 = 5.7
4. Hence 30% of $19 is $5.7
5. Next is we deduct $5.7 which is 30% of $19. 
6. 19 – 5.7 = $13.3 
7. Therefore we add one shirt for $19 and the second, less 30% off which now only costs for $13.3. 
8. 19 + 13.3 = 32.3
9. Conclusively, she will pay $32.3 for the shirts.

3 0

4 years ago

Lines m and n are parallel. Which list of angles are all congruent to angle 2?

kramer

C. 4,5, 6

hopes this helps

6 0

3 years ago

Find all pairs of real numbers (a,b) such that (x-a)^2+(2x-b)^2=(x-3)^2+(2x)^2

Mrrafil [7]

Answer:

$(3,0)$

$(\frac{-9}{5},\frac{12}{5})$

Step-by-step explanation:

Let's expand both sides.

I'm going to use the following identity to expand the binomial squared expressions: $(u+v)^2=u^2+2uv+v^2$ or $(u-v)^2=u^2-2uv+v^2$ .

Left-hand side:

$(x-a)^2+(2x-b)^2$

$(x^2-2ax+a^2)+((2x)^2-2b(2x)+b^2)$

$x^2-2ax+a^2+4x^2-4bx+b^2$

Reorder so $x^2$ 's are together and that $x[tex]'s are together.[tex](x^2+4x^2)+(-2ax-4bx)+(a^2+b^2)$

$5x^2+(-2a-4b)x+(a^2+b^2)$

Right-hand side:

$(x-3)^2+(2x)^2$

$x^2-2(3)x+9+4x^2$

$x^2-6x+9+4x^2$

Reorder so $x^2$ 's are together and that $x[tex]'s are together.[tex](x^2+4x^2)+(-6x)+9$

$5x^2-6x+9$

Now let's compare both sides.

If we want both sides to appear exactly the same we need to choose values $a$ and $b$ such the following are true equations:

$-2a-4b=-6$

$a^2+b^2=9$

So if we solve the system we can find the values $a$ and $b$ such that the left=right.

Let's solve the first equation for $a$ in terms of $b$ .

Add $2a$ on both sides:

$-4b=-6+2a$

Divide both sides by -4:

$b=\frac{-6+2a}{-4}$

Reduce (divide top and bottom by -2):

$b=\frac{3-a}{2}$

Now let's plug this into second equation:

$a^2+b^2=9$

$a^2+(\frac{3-a}{2})^2=9$

$a^2+\frac{9-6a+a^2}{4}=9$ (I used the identity $(u-v)^2=u^2-2uv+v^2$ )

Multiply both sides by 4 to clear the fractions from the problem:

$4a^2+(9-6a+a^2)=36$

Combine like terms on left hand side:

$4a^2+a^2-6a+9=36$

$5a^2-6a+9=36$

Subtract 36 on both sides:

$5a^2-6a-27=0$

Now let's try to factor.

We are going to try to find two numbers that multiply to be 5(-27) and add to be -6.

5(-27)=(5*3)(-9)=15(-9)=-15(9) while -15+9=-6.

So let's replace $-6a$ with $-15a+9a$ and factor by grouping.

$5a^2-15a+9a-27=0$

$5a(a-3)+9(a-3)=0$

$(a-3)(5a+9)=0$

This implies $a-3=0$ or $5a+9=0$ .

Solving the first is easy. Just ad 3 on both sides to get: $a=3$ .

The second requires two steps. Subtract 9 and then divide by 5 on both sides.

$5a=-9$

$a=\frac{-9}{5}$ .

So let's go back to finding $b$ now that we know the $a$ values.

If $a=3$ and $b=\frac{3-a}{2}$ ,

then $b=\frac{3-3}{2}=0$ .

So one ordered pair $(a,b)$ that satisfies the equation is:

$(3,0)$ .

If $a=\frac{-9}{5}$ and $b=\frac{3-a}{2}$ ,

then $b=\frac{3-\frac{-9}{5}}{2}$ .

Let's multiply top and bottom by 5 to clear the mini-fraction.

$b=\frac{15-(-9)}{10}$

$b=\frac{24}{10}$

$b=\frac{12}{5}$

So one ordered pair $(a,b)$ that satisfies the equation is:

$(\frac{-9}{5},\frac{12}{5})$ .

5 0

4 years ago

Write 3 ½% as a fraction

jeka57 [31]

Answer:

7/200

Step-by-step explanation:

3.5% = 3.5/100 = (3.5/100)×(2/2) = 7/200

_____

The % symbol is a shorthand way to write "/100", so 3.5% = 3.5/100.

3 0

4 years ago

There are 8 students in a group. There is 3/4 of a cake. How much of the cake will each student get if it is split evenly betwee

andre [41]

You need to split something 8 ways, you need to divide it by 8, or multiply it by 1/8.

If you need to split 3/4 of a cake 8 ways, you can multiply it by 1/8

(3/4)(1/8)
=(3x1)/(4x8)
=3/32

Therefore, every one will get 3/32 of the cake

5 0

4 years ago