Step-by-step explanation:
Ok. First of all, we need to follow the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. We don't have any parentheses, exponents, or division to resolve, so you can skip those. So now you have: Multiplication, Addition, and Subtraction. We have multiplication in each term, but each term is fully simplified, so we have Addition and Subtraction left.
With that out of the way, let's go ahead and rearrange this equation so it is easier to solve. (<em>Note: we can only rearrange terms that are positive because subtraction is not commutative. But we can turn negative terms into "positive" terms by the method shown below.</em>)
4a - 7b + 2ab - a + b
4a + (-7b) + 2ab + (-a) + b (<em>Now the terms are all positive, so we can rearrange them, but they still have the same value.</em>)
4a + (-a) + 2ab + (-7b) + b
3a + 2ab + 7b
And there we go. Our answer is fully simplified. If you can understand this, you'll be able to simplify without isolating and rearranging the terms each time.
Hopefully this was helpful and not confusing.
If triangle RST and triangle XYZ are similar, the statement that must be true is :
Angle R equals angle X
Triangle R S T
Triangle X Y Z
those three angles will be similar in this case
hope this helps
Answer:
Q1
cos 59° = x/16
x = 16 cos 59°
x = 8.24
Q2
BC is given 23 mi
Maybe AB is needed
AB = √34² + 23² = 41 (rounded)
Q3
BC² = AB² - AC²
BC = √(37² - 12²) = 35
Q4
Let the angle is x
cos x = 19/20
x = arccos (19/20)
x = 18.2° (rounded)
Q5
See attached
Added point D and segments AD and DC to help with calculation
BC² = BD² + DC² = (AB + AD)² + DC²
Find the length of added red segments
AD = AC cos 65° = 14 cos 65° = 5.9
DC = AC sin 65° = 14 sin 65° = 12.7
Now we can find the value of BC
BC² = (19 + 5.9)² + 12.7²
BC = √781.3
BC = 28.0 yd
All calculations are rounded
Let us start with the unknown. Let us give one of the base angles the
value of x. The other base angle is also x since both the base angles in
an isosceles triangle will be equal. The remaining angle is 40 more
than three times one of the base angles.It is 3x + 40. Here we get the
equation
x+x+3x+40=180
5x + 40 = 180
5x = 180 - 40 = 140
Therefore x = 140/5 = 28
So the angles are 28, 28 and 124.
The third angle is 3 times 28 + 40 = 84 + 40 = 124.
From the information given, the original price per pound was increased by $ 0.75
Let the original price be x, so the new price is x + 0.75
Sam bought 3 pounds of apples at new price and it cost him 5.88
so we form an equation:
3 (x + 0.75) = 5.88
3x + 2.25 = 5.88
3x = 5.88 - 2.25
3x = 3.63
x = 3.63 / 3
x = 1.21
Therefore the original price per pound is 1.21 dollars
