The required estimation of 11 4/5 divided by 3 1/5 is 4.61.
Given that,
To determine the estimation of 11 4/5 divided by 3 1/5.
<h3>What is arithmetic?</h3>
In mathematics, it deals with numbers of operations according to the statements.
In the given question we have given, 2 mixed fractions we have to determine the simplified fraction by dividing one from the other, as stated in the question.
Simplification,
11 + 4 / 5 = 59 / 4
3 + 1 / 5 = 16 / 5
11 4/5 divided by 3 1/5 estimation,
= ( 59/4 ) / (16 / 5)
= 59 * 5 / 4 * 16
= 4.61
Thus, the required estimation of 11 4/5 divided by 3 1/5 is 4.61.
Learn more about arithmetic here:
brainly.com/question/14753192
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Hello, please consider the following.
When
and
are two roots, we can factorise as
![ax^2+bx+c=a(x-x_1)(x-x_2)=a(x^2-(x_1+x_2)x+x_1x_2)=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3Da%28x-x_1%29%28x-x_2%29%3Da%28x%5E2-%28x_1%2Bx_2%29x%2Bx_1x_2%29%3D0)
So for the first equation, we can say that the sum of the zeros is
![\dfrac{a^2+b^2}{2}=\dfrac{a^2}{2}+\dfrac{b^2}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%5E2%2Bb%5E2%7D%7B2%7D%3D%5Cdfrac%7Ba%5E2%7D%7B2%7D%2B%5Cdfrac%7Bb%5E2%7D%7B2%7D)
and the product is
![\dfrac{a^2b^2}{4}=\dfrac{a^2}{2}\dfrac{b^2}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%5E2b%5E2%7D%7B4%7D%3D%5Cdfrac%7Ba%5E2%7D%7B2%7D%5Cdfrac%7Bb%5E2%7D%7B2%7D)
So we can factorise as below.
![4x^2-2(a^2+b^2)x+a^2b^2=(2x-a^2)(2x-b^2)=0](https://tex.z-dn.net/?f=4x%5E2-2%28a%5E2%2Bb%5E2%29x%2Ba%5E2b%5E2%3D%282x-a%5E2%29%282x-b%5E2%29%3D0)
And the solutions are
![\boxed{\sf \n\bf \ \dfrac{a^2}{2} \ \ and \ \ \dfrac{b^2}{2}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csf%20%5Cn%5Cbf%20%20%5C%20%5Cdfrac%7Ba%5E2%7D%7B2%7D%20%5C%20%5C%20and%20%5C%20%5C%20%5Cdfrac%7Bb%5E2%7D%7B2%7D%7D)
For the second equation, we will complete the square and put the constant on the right side and take the root.
Let's do it!
![9x^2-9(a+b)x+2a^2+5ab+2b^2=0\\\\9(x-\dfrac{a+b}{2})^2-9\dfrac{(a+b)^2}{4}+2a^2+5ab+2b^2=0\\\\9(x-\dfrac{a+b}{2})^2=\dfrac{9(a+b)^2-8a^2-20ab-8b^2}{4}\\\\9(x-\dfrac{a+b}{2})^2=\dfrac{9a^2+18ab+9b^2-8a^2-20ab-8b^2}{4}\\\\9(x-\dfrac{a+b}{2})^2=\dfrac{a^2+b^2-2ab}{4}=\dfrac{(a-b)^2}{4}\\\\(x-\dfrac{a+b}{2})^2=\dfrac{(a-b)^2}{2^2\cdot 3^2}](https://tex.z-dn.net/?f=9x%5E2-9%28a%2Bb%29x%2B2a%5E2%2B5ab%2B2b%5E2%3D0%5C%5C%5C%5C9%28x-%5Cdfrac%7Ba%2Bb%7D%7B2%7D%29%5E2-9%5Cdfrac%7B%28a%2Bb%29%5E2%7D%7B4%7D%2B2a%5E2%2B5ab%2B2b%5E2%3D0%5C%5C%5C%5C9%28x-%5Cdfrac%7Ba%2Bb%7D%7B2%7D%29%5E2%3D%5Cdfrac%7B9%28a%2Bb%29%5E2-8a%5E2-20ab-8b%5E2%7D%7B4%7D%5C%5C%5C%5C9%28x-%5Cdfrac%7Ba%2Bb%7D%7B2%7D%29%5E2%3D%5Cdfrac%7B9a%5E2%2B18ab%2B9b%5E2-8a%5E2-20ab-8b%5E2%7D%7B4%7D%5C%5C%5C%5C9%28x-%5Cdfrac%7Ba%2Bb%7D%7B2%7D%29%5E2%3D%5Cdfrac%7Ba%5E2%2Bb%5E2-2ab%7D%7B4%7D%3D%5Cdfrac%7B%28a-b%29%5E2%7D%7B4%7D%5C%5C%5C%5C%28x-%5Cdfrac%7Ba%2Bb%7D%7B2%7D%29%5E2%3D%5Cdfrac%7B%28a-b%29%5E2%7D%7B2%5E2%5Ccdot%203%5E2%7D)
We take the root, and we find the two solutions
![\begin{aligned}x_1&=\dfrac{a+b}{2}-\dfrac{a-b}{6}\\\\&=\dfrac{3a+3b-a+b}{6}\\\\&=\dfrac{2a+4b}{6}\\\\&\boxed{=\dfrac{a+2b}{3}}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dx_1%26%3D%5Cdfrac%7Ba%2Bb%7D%7B2%7D-%5Cdfrac%7Ba-b%7D%7B6%7D%5C%5C%5C%5C%26%3D%5Cdfrac%7B3a%2B3b-a%2Bb%7D%7B6%7D%5C%5C%5C%5C%26%3D%5Cdfrac%7B2a%2B4b%7D%7B6%7D%5C%5C%5C%5C%26%5Cboxed%7B%3D%5Cdfrac%7Ba%2B2b%7D%7B3%7D%7D%5Cend%7Baligned%7D)
![\begin{aligned}x_1&=\dfrac{a+b}{2}+\dfrac{a-b}{6}\\\\&=\dfrac{3a+3b+a-b}{6}\\\\&=\dfrac{4a+2b}{6}\\\\&\boxed{=\dfrac{2a+b}{3}}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dx_1%26%3D%5Cdfrac%7Ba%2Bb%7D%7B2%7D%2B%5Cdfrac%7Ba-b%7D%7B6%7D%5C%5C%5C%5C%26%3D%5Cdfrac%7B3a%2B3b%2Ba-b%7D%7B6%7D%5C%5C%5C%5C%26%3D%5Cdfrac%7B4a%2B2b%7D%7B6%7D%5C%5C%5C%5C%26%5Cboxed%7B%3D%5Cdfrac%7B2a%2Bb%7D%7B3%7D%7D%5Cend%7Baligned%7D)
Thank you.
Answer:
$6932
Step-by-step explanation:
Let last year's sales = x. Since there was a decrease of 5%, that means this year's sales are 95% of last year's sales.
So, .95x = 6585
x = 6932 to the nearest dollar
when you get this kind of exercise, you find need to find y or x in one of the exactions and fill it in in the other, however in this exercise the two y's are already given so all you need to do is replace the y in one of the exactions with the other exactions like this:
(keep in mind, you need to keep writing both of the exactions over again, otherwise you'll lose an exaction. and we'll need it later on)
y=-2x+6
y=3x-4
y=-2x+6
-2x+6=3x-4
y=-2x+6
-2x-3x=-4-6
y=-2x+6
-5x=-10
y=-2x+6
x= 2
and now replace the x in the first exaction with the x that we found:
y=-2(2)+6
x=2
y=-4+6
x=2
y=2
x=2
Answer:
90 degree
Step-by-step explanation:
Let represent the measure of the third angle. Then, − can represent the measure of the second angle. The
sum of the two angles in the right triangle will be °.
− + =
− =
− + = +
=
=
=
The third angle is and therefore measures °. Replacing with in − gives () − = − = .
Therefore, the measure of the second angle is °. The measure of the third angle is °.