BRAINLIEST + POINTS?!<br><br> Can someone help me please explain!

PLS HELP ILL MARK BRAINLIST!!

hammer [34]

Answer:

the range will decrease

5 0

3 years ago

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The perimeter of a triangle is 510 feet and the sides are in the ratio of 11:16:24. Find the area of the triangle

Nutka1998 [239]

If the sides are in the ratio of 11:16:24, it means that they are all multiples of a same number x, according to these factors.

So, the shorter side is 11x feet long, the middle one is 16x feet long, and the longest side is 24x feet long.

This means that the perimeter is

$11x+16x+24x = 51x$ feet long. But we know that this is 510 feet, so we have

$51x = 510 \implies x = \cfrac{510}{51} = 10$ .

So, the three sides are 110, 160 and 240 feet long.

To find the area of a triangle knowing its three sides, you can use Heron's formula, which states that, if $s$ is half the perimeter of the triangle whose sides are $a,b,c$ , the area $A$ is given by

$A = \sqrt{s(s-a)(s-b)(s-c)}$

In our case, $s = 255, a = 110, b = 160, c = 240$ so the formula becomes

$A = \sqrt{255(255-110)(255-160)(255-240)} = \sqrt{255(145)(95)(15)} = \sqrt{52689375} \approx 7258.74$

5 0

3 years ago

Suppose x is a real number and epsilon > 0. Prove that (x - epsilon, x epsilon) is a neighborhood of each of its members; in

kaheart [24]

Answer:

See proof below

Step-by-step explanation:

We will use properties of inequalities during the proof.

Let $y\in (x-\epsilon,x+\epsilon)$ . then we have that $x-\epsilon$ . Hence, it makes sense to define the positive number delta as $\delta=\min\{x+\epsilon-y,y-(x-\epsilon)\}$ (the inequality guarantees that these numbers are positive).

Intuitively, delta is the shortest distance from y to the endpoints of the interval. Now, we claim that $(y-\delta,y+\delta)\subseteq (x-\epsilon,x+\epsilon)$ , and if we prove this, we are done. To prove it, let $z\in (y-\delta,y+\delta)$ , then $y-\delta$ . First, $\delta \leq y-(x-\epsilon)$ then $-\delta \geq -y+x-\epsilon$ hence $z>y-\delta \geq x-\epsilon$

On the other hand, $\delta \leq x+\epsilon-y$ then $z$ hence $z$ . Combining the inequalities, we have that $x-\epsilon$ , therefore $(y-\delta,y+\delta)\subseteq (x-\epsilon,x+\epsilon)$ as required.

3 0

3 years ago

How many ways are there to assign 8 visiting different studetns to one Stony Brook summer course, chossing from Calculus I, Line

Dmitry_Shevchenko [17]

Answer:

56 ways

Step-by-step explanation:

Number of ways is given by n combination r (n!/(n - r)!r!)

n = total number of students = 8, r = the number of summer courses = 3

Number of ways = 8 combination 3 = 8!/(8-3)!3! = 8!/5!3! = 8×7×6×5!/5!×6 = 8×7 = 56 ways

6 0

3 years ago

After spending 30% of her salary Sara was able to deposit $120 in the bank. What is her salary?

Katena32 [7]

Answer: $400

Step-by-step explanation:

So first you set it up in a equation. You put the amount she put in the bank over x (the x represents her full salary) which equals the percent she already spent over her full salary. That would be 120/x=30/100 you would then cross-multiply to get 12,000 = 30x. you then divide 30 from both sides to get x =400.

3 0

3 years ago

BRAINLIEST + POINTS?! Can someone help me please explain!