Which statements are true? * 1:2 = 50:100 2:1 = 50:100 1:2 = 2:1 3:4 = 9:12

This is how a triangle is equal to one another, SAS is side angle side, AA is angle angle, ASA is angle side angle, and SSS is side side side, yours looks like AA but I might be wrong. I believe it is AA, so if you have no clue just go with AA

5 0

3 years ago

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A car is moving 70 miles per hour. how far does it travel in 16 seconds

Serjik [45]

Answer:

0.311 miles

Step-by-step explanation:

Convert 16 seconds to hours :

16 /60×60

= 16÷3600

= .004444hrs

Distance = Speed × time

= 70 × 0.00444444

= 0.311 miles

4 0

3 years ago

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For how many real values of x is <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B120-%5Csqrt%7Bx%7D%7D%20" id="TexFormula1" title

leva [86]

A good place to start is to set $\sqrt{x}$ to y. That would mean we are looking for $\sqrt{120-y}$ to be an integer. Clearly, $y\leq 120$ , because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since $\sqrt{x}$ is a radical, it only outputs values from $[0,\infty]$ , which means y is on the closed interval: $[0,120]$ .

With that, we don't really have to consider y anymore, since we know the interval that $\sqrt{x}$ is on.

Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval $[0,120]$ , which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:

$\sqrt{120-\sqrt{x}}=k \implies \\ \sqrt{x}=k^2-120 \implies\\ x=(k^2-120)^2$

Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.

5 0

3 years ago