Rectangular apartments are 12 ft longer than they are wide. Each apartment has 1,053 ft^2 of floor space. What are the dimension
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The question is incomplete, the complete question is here
Find the measures of the angles of an isosceles triangle whose equal sides measure 8 and whose altitude drawn to the base measures 4
Answer:
The measures of the angles of the isosceles triangle are 30°, 30° and 120°
Step-by-step explanation:
In a triangle whose sides a, b, c and angles A, B and C, where a is opposite to ∠A, b is opposite to ∠B, and c is opposite to ∠C, the given is
- a = c
- m∠A = m∠C
The height from ∠B to side b is 4 units
That means the length of the height is half the length of each equal sides, then there is a right triangle its hypotenuse is 8 and the side opposite to the base angle is 4, so we can find the measure of the base angle by using the rule sin(base angle) =
∵ The base angles are ∠A and ∠C
∵ a = c = 8
∵ The altitude to b is 4
∵
- By using
∴ m∠A =
∴ m∠A = 30°
∵ m∠A = m∠C
∴ m∠C = 30°
Use the rule of the sum of the measures of the interior angle of a Δ is 180° to find m∠B
∵ m∠A + m∠C + m∠B = 180
∵ m∠A = m∠C = 30°
∴ 30° + 30° + m∠B = 180°
∴ 60 + m∠B = 180
- Subtract 60 from both sides
∴ m∠B = 120°
The measures of the angles of the isosceles triangle are 30°, 30° and 120°
Mini inequality crash course:
<em />
<em>Is it greater than or less then?</em>
This can be a bit tricky to remember. How I do this is looking at the shape of the sign?
So the number that is BIGGER is on the side where the mouth opens or the WIDDER side. Biggest number goes on widest side
Bigger number goes here---> __ >
< __ <--- Bigger number goes here
The number that is the SMALLEST goes on the side where the "pointy" part is
Smallest number goes here---> ___<
> ___ <---Smallest number goes here
***There's an image bellow that also explains it. Hopefully it makes sense
(This all applies the same way to ≥ and ≤ )
You read and say inequalities from left to right. For example I will use example 6:
s < -6 ...............….......S is less then -6
-6 > s..........................-6 is greater then s
^^^Notice that these show the exact same thing yet they are said differently
Here is another example, but with some easy numbers I made up:
3 < 6.........Three is less then six
6 > 3.........Six is greater then three
There are two kind of inequalities:
≥ / ≤
Or
> / <
≥ / ≤
^^^ These two are the greater then or equal to / less then or equal to signs
This means that it includes the number.
***How I remember is the little bar underneath the symbol is like half an equal sign, so the numbers can be equal or not***
For example in number 5:
x ≤ 3 ---> x is less than or equal to 3
^^^This means that x can be three OR any number SMALLER then three
Another example:
x ≥ -34 ---> x is any number greater then OR equal to -34
Graphing inequalities on a number line:
The circles will always be placed on the number that the variable is greater then, less the, greater then or equal to, or less then or equal to
<em>How to tell if the circle is colored or not:</em>
If the inequality has either > or < then the circle is hollow/empty/not colored in
If the inequality has either ≥ or ≤ then the circle is shaded/colored in
***How I remember this is that the symbol has the extra bar at the bottom so the circle will have a little extra something in it
Which direction will the arrow go?
If it is x < # or x ≤ # or # > x or # ≥ x then the arrow will go to the left of the circle. It signifies that x is any number less then/ less then or equal to the #
****How I remember it is if the variable is<em> L</em>ess then it goes <em>L</em>eft
If it is x ># or x ≥ # or # < x or # ≤ xthen the arrow will go to the right of the circle. It signifies that x is any number more then/ more then or equal to the #
16. She has 3,187 signatures but she still needs more, so the expression would be 3,187 + x (x being how many more signitures she needs to reach her goal)
She needs at least 5,000. It has to be more or equal to 5,000
So we have the equation:
5,000 ≤ 3,187 + x or 3,187 + x ≥ 5,000
Now solve for x by subtracting 3,187 to both sides
x ≥ 1, 813
To reach her goal she has to still get 1,813 or more signitures
I really hope this helped and that you understand now!
