Answer the following
Answers
Answer:
Explanation:
rearrange to
a
x
2
+
b
x
+
c
=
0
−
2
x
2
=
2
x
−
4
⇒
2
x
2
+
2
x
−
4
=
0
divide by 2
x
2
+
x
−
2
=
0
factorise
(
x
+
2
)
(
x
−
1
)
=
0
giving
x
+
2
=
0
⇒
x
=
−
2
x
−
1
=
0
⇒
x
=
1
Answer link
Jacq
Oct 6, 2017
x
=
−
2
or
x
=
1
Explanation:
To solve this, you first need to put everything on one side:
−
2
x
2
=
2
x
−
4
2
x
2
+
2
x
−
4
=
0
From here, we can factor
2
out:
2
(
x
2
+
x
−
2
)
=
0
Dividing by two, we get:
x
2
+
x
−
2
=
0
This can then be factorised by finding two numbers that multiply to get
−
2
and add to get
1
. Looking at the factors of
2
, you can find these numbers are
−
1
and
2
.
(
x
−
1
)
(
x
+
2
)
=
0
Now, you have two things multiplied together that equal
0
. This means that one of them has to equal
0
. To find the values of
x
for this to happen, we split the two parts:
x
−
1
=
0
∴
x
=
1
OR
x
+
2
=
0
∴
x
=
−
2
So, the solution to this equation is
x
=
−
2
or
x
=
1
Answer:
Remember? When you multiply whole numbers by 10, 100, 1000, and so on (powers of ten), you can simply “tag” as many zeros on the product as there are in the factor 10, 100, 1000 etc.
There is a similar shortcut for multiplying decimal numbers by numbers such as 10, 100, and 1000:
Move the decimal point to the right as many places as there are zeros in the factor.
10 × 0 . 4 9 = 04.9 = 4.9
Move the decimal point one step to the right (10 has one zero).
100 × 2 . 6 5 = 265. = 265
Move the decimal point two steps to the right (100 has two zeros). The number 265. is 265 (as shown above).
1000 × 0 . 3 7 0 = 3 7 0 . = 370
1000 means we move the point three steps. Write a zero at the end of 0.37 so that the decimal point can “jump over to” that place.
1. Multiply.
a. 10 × 0.04 = ________
b. 100 × 0.04 = ________
c. 1000 × 0.04 = ________
d. 10 × 0.56 = ________
e. 100 × 0.56 = ________
f. 1000 × 0.56 = ________
g. 10 × 0.048 = ________
h. 100 × 0.048 = ________
i. 1000 × 0.048 = _______
Another helpful shortcut! Since 100 × 2 = 200, obviously the answer to
100 × 2.105 will be a little more than 200. Hence, you can just write the digits
2105 and put the decimal point so that the answer is 200-something: 210.5.
2. Let's practice some more.
a. 100 × 5.439 = ________
b. 100 × 4.03 = ________
c. 1000 × 3.06 = ________
d. 100 × 30.54 = ________
e. 30.73 × 10 = ________
f. 93.103 × 100 = _______
105 × 0 . 1 2 0 0 0 = 12000. = 12,000
105 = 100,000 has five zeros. Again, write additional zeros so that the decimal point can “jump over to” those places.
3. Now let's practice using powers of ten.
a. 102 × 0.007 = _____________
103 × 2.01 = _____________
105 × 4.1 = ______________
b. 105 × 41.59 = _____________
3.06 × 104 = ______________
0.046 × 106 = _____________