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2 years ago

Solve for x and y

Mathematics

1 answer:

bekas [8.4K]2 years ago

7 0

Answer:

x = 2√2

y = 2√6

Step-by-step explanation:

Consider the ratio of the two legs of the two smaller interior right triangles. (refer to attached diagrams for the triangles - I have outlined one in blue and the other in red)

These will be equal since the triangles are similar

shorter leg : longer leg

(blue triangle = red triangle)

⇒ x : 4 = 2 : x

⇒ x/4 = 2/x

⇒ x² = 8

⇒ x = √8

⇒ x = 2√2

Now we have x, we have the two legs of the right triangle with hypotenuse labelled y.

Using Pythagoras' Theorem a² + b² = c² (where a and b are the legs and c is the hypotenuse)

⇒ 4² + (2√2)² = y²

⇒ y² = 24

⇒ y = √24

⇒ y = 2√6

You might be interested in

Which statement best describes parallel lines?

Margaret [11]

Answer:

Step-by-step explanation:

Parallel lines have identical slopes and different y intercepts.

y = 3x + 2

y = 3x + 9

These lines are parallel with the same slopes (3) and different y intercepts (2 and 9)

7 0

2 years ago

Assume all variables represent non negative numbers . Help please!!

Dafna1 [17]

Answer:

A). $2p^{8}$

B). $3m^{7}$

Step-by-step explanation:

A). $\sqrt{4p^{16}}$

To get the square root of the given expression we will convert it into the square form.

$4p^{16}=(2)^2(p^{8})^2$ [Since 2×2 = 4 and $p^{8}\times p^{8}=p^{16}$ ]

Therefore, $\sqrt{4p^{16}}=\sqrt{2^{2}\times (p^{8})^2 }$

$=2p^{8}$

B). $\sqrt{9m^{44}}$

Since, $9m^{14}=(3)^2\times (m^7)^2$

Therefore, $\sqrt{9m^{44}}=\sqrt{(3)^2\times (m^7)^2}$ [Since 3² = 9 and (m⁷)² = m¹⁴]

$=3m^{7}$

7 0

3 years ago

A private school opened in 2005 with an initial enrollment of 85 students. The enrollment has increased by an average of 18 stud

mafiozo [28]

1. Let t = time in years, with t = 0 representing the year 2005. Let f(t) = the number of students enrolled at the private school and g(t) = the number of students enrolled at the public school. Create the two functions to represent the situation.

f(t) = 85 + 18t ⇒ y = 85 + 18x
g(t) = 95 + 15t ⇒ y = 95 + 15x

y = y
85 + 18x = 95 + 15x
18x - 15x = 95 - 85
3x = 10
x = 10/3
x = 3 1/3

y = 85 +18(10/3) = 85 + 180/3 = 85 + 60 = 145
y = 95 + 15(10/3) = 95 + 150/3 = 95 + 50 = 145

x = 10/3 or 3 1/3
y = 145

4 0

3 years ago

A standard number cube is tossed. Find the following probability. P(greater than 4 or odd)

lorasvet [3.4K]

A standard cube has 6 possible outcomes. But since we want to find P(4+ or odd), the outcomes become more narrow.
So:
6 outcomes -> 1, 2, 3, 4, 5, 6

But we want to find 4+
So:
4+ = 4, 5, 6

We also want to find all odd possibilities.
So:
odd = 1, 3, 5

As you can see, there is a 5 in both the 4+ and the odd numbers so 5 will only be counted once.
P(4+ or odd) = 1, 3, 4, 5, 6

So the probability of having an outcome that is P(4+ or odd) is:
5/6 or 0.8333 or 83.33%

Hope I helped!

8 0

3 years ago

Read 2 more answers

Twenty percent of the ice melted. If 680 grams remained, how many grams melted?

musickatia [10]

Answer:

−33999/50

Step-by-step explanation:

2/100−680

1/50−680

−33999/50

5 0

3 years ago