12 * 34 + 13(50/10)
<em><u>We can simplify 50/10 to just 5.</u></em>
12 * 34 + 13(5)
<em><u>Multiplication first, left to right.</u></em>
408 + 65
<em><u>Simplify.</u></em>
473. (This is your answer.)
Answer:
Step-by-step explanation:
We'll call height h.
The equations of a cone and sphere are:
Cones: 1/3 * base area * h
Spheres: 4/3 π * r³
The base area of a cone would be the area of a circle equation:
π * r² = π * 2² = 4π.
Because you're converting from sphere to cone, you would set their equations equal to each other.
1/3 * 4π * h = 4/3 π * 5³
Next, isolate h.
h = (4/3 π * 5³)/(1/3 * 4π)
h = 125
Hope this helps!
Answer:
![\large \boxed{\sf \ \ 6 \ and \ 11 \ \ }](https://tex.z-dn.net/?f=%5Clarge%20%5Cboxed%7B%5Csf%20%5C%20%5C%206%20%5C%20and%20%5C%2011%20%5C%20%5C%20%20%7D)
Step-by-step explanation:
Hello,
Let's note a and b the two numbers.
a = b - 5
![a^2+b^2=157](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3D157)
We replace a in the second equation and we solve it
![(b-5)^2+b^2=157 \\ \\ \text{*** develop the expression ***} \\ \\b^2-10b+25+b^2=157 \\ \\ \text{*** subtract 157 from both sides ***} \\ \\2b^2-10b+25-157=2b^2-10b-132=0 \\ \\ \text{*** divide by 2 both sides ***} \\ \\b^2-5b-66=0](https://tex.z-dn.net/?f=%28b-5%29%5E2%2Bb%5E2%3D157%20%5C%5C%20%5C%5C%20%5Ctext%7B%2A%2A%2A%20develop%20the%20expression%20%2A%2A%2A%7D%20%5C%5C%20%5C%5Cb%5E2-10b%2B25%2Bb%5E2%3D157%20%5C%5C%20%5C%5C%20%5Ctext%7B%2A%2A%2A%20subtract%20157%20from%20both%20sides%20%2A%2A%2A%7D%20%5C%5C%20%5C%5C2b%5E2-10b%2B25-157%3D2b%5E2-10b-132%3D0%20%5C%5C%20%5C%5C%20%5Ctext%7B%2A%2A%2A%20divide%20by%202%20both%20sides%20%2A%2A%2A%7D%20%5C%5C%20%5C%5Cb%5E2-5b-66%3D0)
It means that the sum of the two roots is 5 and the product is -66.
because
![(x-\alpha )(x-\beta )=x^2-(\alpha +\beta )x+\alpha \beta \\ \\ \text{ where } \alpha \text{ and } \beta \text{ are the roots }](https://tex.z-dn.net/?f=%28x-%5Calpha%20%29%28x-%5Cbeta%20%29%3Dx%5E2-%28%5Calpha%20%2B%5Cbeta%20%29x%2B%5Calpha%20%5Cbeta%20%5C%5C%20%5C%5C%20%5Ctext%7B%20where%20%7D%20%5Calpha%20%5Ctext%7B%20and%20%7D%20%5Cbeta%20%5Ctext%7B%20are%20the%20roots%20%7D)
And we can notice that 66 = 6 * 11 and 11 - 6 = 5
So let's factorise it !
![b^2-5b-66=0 \\ \\b^2+6b-11b-66=0 \\ \\b(b+6)-11(b+6)=0 \\ \\(b-11)(b+6) =0 \\ \\ b=11 \ or \ b=-6](https://tex.z-dn.net/?f=b%5E2-5b-66%3D0%20%5C%5C%20%5C%5Cb%5E2%2B6b-11b-66%3D0%20%5C%5C%20%5C%5Cb%28b%2B6%29-11%28b%2B6%29%3D0%20%5C%5C%20%5C%5C%28b-11%29%28b%2B6%29%20%3D0%20%5C%5C%20%5C%5C%20b%3D11%20%5C%20or%20%5C%20b%3D-6)
It means that the solutions are
(6,11) and (-6,-11)
I guess we are after positive numbers though.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
To find the original price, you could use a variable to represent the original price in this equation;
Let p represent the original price
.70 × p=11.20
to solve this, we'd isolate the variable (p)
p=11.20 ÷.70
p=16
The original price was $16