<span>x = 18 and the length of each side of the triangle is 29.
This is a matter of reading the descriptions and converting to mathematical notation.
"QRS is an equilateral triangle"
We now know that all three sides of the triangle have the same length.
"If QR is seven less than twice x". So we can write
QR = 2x - 7
"RS is 61 less than 5 times x". So we can write
RS = 5x - 61
"QS is 11 more than x". And we can write
QS = x + 11
And because we already know that they all have the same length, then we can set those equations equal to each other. Let's just pick 2 of them. Will use the length of QR and QS because they look the simplest and then will solve for x.
QR = 2x - 7
RS = 5x - 61
QS = x + 11
2x - 7 = x + 11
x - 7 = 11
x = 18
So we now know that x = 18. Let's check to make sure all three equations have the same value.
QR = 2x - 7 = 2*18 - 7 = 36 - 7 = 29
RS = 5x - 61 = 5*18 - 61 = 90 - 61 = 29
QS = x + 11 = 18 + 11 = 29
And they all are equal, so 18 is the correct value for x.</span>
Answer:
106°
Step-by-step explanation:
ΔDCB is equilateral which means it must also be equiangular; each angle is 60°
ΔABD is isosceles because AB=BD so ∡ADB=∡BDA
∡ABD = 180-(67 + 67) = 46
∡ABC = ∡ABD + ∡DBC
∡ABC = 46 + 60
You would draw 48 counters and 18 counters which would be 66 counters in total. The picture is 1 of the sixteens and 1 of the nines. Sorry, if I misunderstood or got it wrong, I tried. If you don't understand something or I left out something, tell me in the comments.
When multiply terms with exponents, simply add the exponents.
Hope this helps!
Answer:
Step-by-step explanation:
Given
Required
The complete factored form
We have:
Factor out x + 3
<em>The above represents the completely factored form</em>