Step-by-step explanation:
x=−y−2z+3
x=y+32z+1
x=13y+23z+13
Answer:
It didn't saying anything about rounding but the the dimensions in there exact form are:
![L=\frac{-5+\sqrt{249}}{2} \text{ cm}](https://tex.z-dn.net/?f=L%3D%5Cfrac%7B-5%2B%5Csqrt%7B249%7D%7D%7B2%7D%20%5Ctext%7B%20cm%7D)
and
.
Now if they said to round to the nearest hundredths the dimensions in this rounded form would be:
L=5.39 cm and W=5.19 cm
(Check your question again and see if you meant what you have)
Step-by-step explanation:
L is 5 less than twice W
L = 2W-5
Area of rectangle=L*W
Area is 28 means L*W=28.
I'm going to insert L=2W-5 into L*W=28 giving me
(2W-5)*W=28
Distribute
2W^2-5W=28
Subtract 28 on both sides
2W^2-5W-28=0
a=2
b=-5
c=-28
We are going to use the quadratic formula.
Plug in...
![W=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\W=\frac{5 \pm \sqrt{(-5)^2-4(2)(-28)}}{2(2)}\\\\W=\frac{5 \pm \sqrt{25+224}}{4}\\\\W=\frac{5 \pm \sqrt{249}}{4}](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5CW%3D%5Cfrac%7B5%20%5Cpm%20%5Csqrt%7B%28-5%29%5E2-4%282%29%28-28%29%7D%7D%7B2%282%29%7D%5C%5C%5C%5CW%3D%5Cfrac%7B5%20%5Cpm%20%5Csqrt%7B25%2B224%7D%7D%7B4%7D%5C%5C%5C%5CW%3D%5Cfrac%7B5%20%5Cpm%20%5Csqrt%7B249%7D%7D%7B4%7D)
W needs to be positive so ![W=\frac{5 + \sqrt{249}}{4}](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B5%20%2B%20%5Csqrt%7B249%7D%7D%7B4%7D)
And ![L=2W-5=2(\frac{5 + \sqrt{249}}{4})-5](https://tex.z-dn.net/?f=L%3D2W-5%3D2%28%5Cfrac%7B5%20%2B%20%5Csqrt%7B249%7D%7D%7B4%7D%29-5)
![L=\frac{5+\sqrt{249}}{2}-5](https://tex.z-dn.net/?f=L%3D%5Cfrac%7B5%2B%5Csqrt%7B249%7D%7D%7B2%7D-5)
![L=\frac{5+\sqrt{249}}{2}-\frac{10}{2}](https://tex.z-dn.net/?f=L%3D%5Cfrac%7B5%2B%5Csqrt%7B249%7D%7D%7B2%7D-%5Cfrac%7B10%7D%7B2%7D)
![L=\frac{-5+\sqrt{249}}{2}](https://tex.z-dn.net/?f=L%3D%5Cfrac%7B-5%2B%5Csqrt%7B249%7D%7D%7B2%7D)
Does L*W=28?
Let's check.
![L \cdot W=\frac{-5+\sqrt{249}}{2} \cdot \frac{5 + \sqrt{249}}{4}](https://tex.z-dn.net/?f=L%20%5Ccdot%20W%3D%5Cfrac%7B-5%2B%5Csqrt%7B249%7D%7D%7B2%7D%20%5Ccdot%20%5Cfrac%7B5%20%2B%20%5Csqrt%7B249%7D%7D%7B4%7D)
![L \cdot W=\frac{249-25}{8}](https://tex.z-dn.net/?f=L%20%5Ccdot%20W%3D%5Cfrac%7B249-25%7D%7B8%7D)
In the last step, I was able to do a quick multiplication because I was multiplying conjugates. (a+b)(a-b)=a^2-b^2.
![L \cdot W=\frac{ 224}{8}](https://tex.z-dn.net/?f=L%20%5Ccdot%20W%3D%5Cfrac%7B%20224%7D%7B8%7D)
![L \cdot W=28](https://tex.z-dn.net/?f=L%20%5Ccdot%20W%3D28)
Answer:
a. sine
Step-by-step explanation:
As it can be seen from the figure, triangle ABC is the right-angled triangle with Angle C is equal to 90 degree.
In a right-angled triangle, there is a formula as following:
<em>+) sine (an acute angle) = (length of its opposite side)/ hypotenuse</em>
In the figure, angle B and length of the hypotenuse are given.
As x is the length of AC and AC is the opposite side to angle B
=> So that we can use sine to find x
Answer: The answer is 2.5
Step-by-step explanation:
I just took the quiz and it was the correct answer.