(b) is the answer.
Step-by-step explanation:
By the Pythagorean Theorem,
A² + B² = C²
Where:
A = Length of side 1
B = Length of side 2
C = Hypotenuse
This rule applies to all right-angled triangles.
The length of the hypotenuse of a right-angled triangle is always the largest value.
Therefore, we can test the answers with the equation above.
(a)
8² + 18² = 20²
64 + 324 = 400
388 ≠ 400
The rule of Pythagorean theorem doesn't work on a, so (a) is not a right-angled triangle.
(b)
12² + 35² = 37²
144 + 1225 = 1369
1369 = 1369
The rule of Pythagorean theorem works here, so (b) is a right-angled triangle.
Answer:
Each small candleholder holds 3 candles, and each large one holds 5 candles.
Step-by-step explanation:
This question can be solved by a system of equations.
I am going to say that:
x is the number of candles that a small candleholder holds.
y is the number of candles that a large candleholder holds.
24 small candle holders and 3 large candle holders, using a total of 87 candles.
This means that
Simplifying by 3
14 small candle holders and 7 large candle holders, for a total of 77 candles.
This means that 
Simplifying by 7
Since
Each small candleholder holds 3 candles, and each large one holds 5 candles.
Okay, so this is what I came to. I think that you might need to look through the placement of the problem again and your x's, but other than that, here it is!
Step 1: Simplify both sides of the equation.<span>425=<span><span>−<span>250<span>x2</span></span></span>+<span>6250x
</span></span></span>Step 2: Subtract -250x^2+6250x from both sides.<span><span>425−<span>(<span><span>−<span>250<span>x2</span></span></span>+<span>6250x</span></span>)</span></span>=<span><span><span>−<span>250<span>x2</span></span></span>+<span>6250x</span></span>−<span>(<span><span>−<span>250<span>x2</span></span></span>+<span>6250x</span></span>)</span></span></span><span><span><span><span>250<span>x2</span></span>−<span>6250x</span></span>+425</span>=0
</span>
Step 3: Use quadratic formula with a=250, b=-6250, c=425.<span>x=<span><span><span>−b</span>±<span>√<span><span>b2</span>−<span><span>4a</span>c</span></span></span></span><span>2a</span></span></span><span>x=<span><span><span>−<span>(<span>−6250</span>)</span></span>±<span>√<span><span><span>(<span>−6250</span>)</span>2</span>−<span><span>4<span>(250)</span></span><span>(425)</span></span></span></span></span><span>2<span>(250)</span></span></span></span><span>x=<span><span>6250±<span>√38637500</span></span>500</span></span><span><span>x=<span><span>252</span>+<span><span><span><span>110</span><span>√15455</span></span><span> or </span></span>x</span></span></span>=<span><span>252</span>+<span><span><span>−1</span>10</span><span>√15455
</span></span></span></span><u>
Answer:</u><span><span>x=<span><span>252</span>+<span><span><span><span>110</span><span>√15455</span></span><span> or </span></span>x</span></span></span>=<span><span>252</span>+<span><span><span>−1</span>10</span><span>√<span>15455</span></span></span></span></span>
