*The side with the middle length is 12cm, therefore BC must be 12 cm
------------------------------------------------------------<span>
Ratio
------------------------</span>---------------------------------<span>--
BC:AC:AB
4 : 3 : 5
</span>-----------------------------------------------------------
<span>Find 1 share
</span>-----------------------------------------------------------<span>
Given that BC = 12 cm
4 shares = 12 cm
1 share = 12 ÷ 4 = 3cm
</span>-----------------------------------------------------------
Find AC (4 shares)
-----------------------------------------------------------<span>
3 shares = 3 x 3 = 9 cm
BC = 9cm
</span>-----------------------------------------------------------
<span>Find AB (5 shares)
</span>-----------------------------------------------------------<span>
5 shares = 5 x 3 = 15cm
AB = 15cm
</span>------------------------------------------------------------
Length
-----------------------------------------------------------
BC : AC : AB
12cm : 9cm : 15cm<span>
---------------------------------</span>---------------------------------<span>
Perimeter
</span>------------------------------------------------------------------
<span>12 + 9 + 15 = 36cm
</span>------------------------------------------------------------------
<span>Answer: The perimeter is 36cm
</span>------------------------------------------------------------------<span>
</span>------------------------------------------------------------------
<span>Area
</span>------------------------------------------------------------------
1/2 x 9 x 12 = 54cm²<span>
</span>------------------------------------------------------------------
Answer: Area = 54cm²
------------------------------------------------------------------<span>
Given that the biggest ratio is AB
</span>⇒AB is the hypotenuse
AB = 15 cm
------------------------------------------------------------------
Answer: Hypotenuse = AB = 15cm
------------------------------------------------------------------
Answer:
Please read the answers below that solve the crossword puzzle about linear equations. Tested and proved offline!
Step-by-step explanation:
Across:
2. V a r i a b l e
9. S o l v e
10. S u b t r a c t i o n p r o p e r t y (Two words)
Down:
1. M u l t i p l i c a t i o n p r o p e r t y (Two words)
3. A d d i t i o n p r o p e r t y (Two words)
4. L i n e a r
5. D i v i s i o n p r o p e r t y (Two words)
6. L i n e a r i n e q u a l i t y (Two words)
7. C o n s t a n t t e r m (Two words)
8. C o e f f i c i e n t
Answer:
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
n=60 represent the sample size
X=12 represent the number of masks that had lenses pop out at 250°
represent the estimated proportion of masks that had lenses pop out at 250°
p represent the population proportion of masks that had lenses pop out at 250°
Confidence =0.9 or 90%
represent the significance level
Confidence interval
On this case we want a interval on this form : 
So the critical value would be on this case 
and we can use the following excel code to find it: "=NORM.INV(1-0.1,0,1)"
We found the lower limit like this:
And the interval would be: 
Answer:
Step-by-step explanation:
Whether we divide using long division or using synthetic division, the rule is the same: If, after division, there is no remainder (i. e., the remainder is zero), the divisor binomial is a factor or the associated root is indeed a root/zero/solution.
Divide 5x³+8x²-7x-6 by (x+2) using synthetic division. Use the divisor -2 (which comes from letting x+2 = 0):
--------------------------
-2 / 5 8 -7 -6
-10 4 6
------------------------------
5 -2 -3 0 Since the remainder here is 0, we know that
-2 is a root of 5x³+8x²-7x-6 and that (x+2) is
a factor of 5x³+8x²-7x-6.
Now check out the possibility that (x+1) is a factor of 5x^3 + 8x^2 - 7x - 6:
Use -1 as the divisor in synthetic division:
--------------------------
-1 / 5 8 -7 -6
-5 -3 10
------------------------------
5 3 -10 4
Since there is a non-zero remainder (4), we can conclude that (x + 1) is NOT a factor of the given polynomial expression.
Answer:
x = 1 or -3/4
factoring is easier for me
Step-by-step explanation:
<u>Factoring</u>
We rewrite to ...
4x^2 -x -3 = 0
We want factors of (4)(-3) = -12 that have a sum of -1. They are -4 and 3. Then the factorization is ...
(4x -4)(4x +3)/4 = (x -1)(4x +3)
Solutions are values of x that make the factors zero: x = 1, x = -3/4.
__
<u>Completing the square</u>
We start by factoring the leading coefficient from the left side:
4(x^2 -x/4) = 3
Now, we add the square of half the x-coefficient (inside parentheses):
4(x^2 -x/4 +1/64) = 3 + 4/64
4(x -1/8)^2 = 49/16 . . . . . . . . . write as squares
x -1/8 = ±√(49/64) = ±7/8
x = 1/8 ± 7/8
x = -3/4 or +1
__
<u>Preference</u>
In this instance <em>I prefer factoring</em>, because it deals with whole numbers up until the end. It does not involve adding and subtracting fractions. On this page, it takes fewer steps.
If you're unfamiliar with math facts, such as the factors of 12, then the purely mechanical "completing the square" method may be preferable. It does not require anything other than finding half of a number and then squaring that.
