Answer:
x² + 6ax + 4bx + 5a² - 5b²
Step-by-step explanation:
(x+5a+5b )(x+a-b)
x² +a x -bx +5ax + 5a² -5ab + 5bx + 5ab -5b²
x² + 6ax + 4bx + 5a² - 5b²
Answer:
21cm; 28cm; 14cm
Step-by-step explanation:
There is no info in the problem/s text which one of the triangle's side is 21 cm. That is why we have to try all possible variants.
Let the triangle is ABC . Let the AK is the angle A bisector and BM is median.
Let O is AK and BM cross point.
Have a look to triangle ABM. AO is the bisector and AOB=AOM=90 degrees (means that AO is as bisector as altitude)
=> triangle ABM is isosceles => AB=AM (1)
1. Let AC=21 So AM=21/2=10.5 cm
So AB=10.5 cm as well. So BC= P-AB-AC=63-21-10.5=31.5 cm
Such triangle doesn' t exist ( is impossible), because the triangle's inequality doesn't fulfill. AB+AC>BC ( We have 21+10.5=31.5 => AB+AC=BC)
2. Let AB=21 So AM=21 and AC=42 .So BC= P-AB-AC=63-21-42=0 cm- such triangle doesn't exist.
3. Finally let BC=21 cm. So AB+AC= 63-21=42 cm
We know (1) that AB=AM so AC=2*AB. So AB+AC=AB+2*AB=3*AB
=>3*AB=42=> AB=14 cm => AC=2*14=28 cm.
Let check if this triangle exists ( if the triangle's inequality fulfills).
BC+AB>AC 21+14>28 - correct=> the triangle with the sides' length 21cm,14 cm, 28cm exists.
This variant is the only possible solution of the given problem.
Answer:2y + 2z
Step-by-step explanation: you need to multiply the number outside of the parenthesis with the one inside like.
Answer:
1 1/3
Step-by-step explanation:
Step 1: Find the whole number
We first want to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.
8/6= 1.3333333333333 = 1
Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.
Step 2: Get the new numerator
To work this out we'll use the whole number we calculated in step one (1) and multiply it by the original denominator (6). The result of that multiplication is then subtracted from the original numerator:
8 - (6 x 1) = 2
Step 3: Our mixed fraction
We've now simplified 8/6 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:
1 2/6
Step 4: Simplifying our fraction
In this case, our fraction (2/6) can be simplified down further. In order to do that, we need to calculate the GCF (greatest common factor) of those two numbers. You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 2 and 6 is 2.
We can now divide both the new numerator and the denominator by 2 to simplify this fraction down to its lowest terms.
2/2 = 1
6/2 = 3
When we put that together, we can see that our complete answer is,
1 1/3
The greatest common factor of 56, 98, 168 is 14
