I think she can make 15 different ones but not 100%sure
Answer:
40m below sea level
Step-by-step explanation:
25m+15=40
Answer:
lcm (14,15)=210 and lcm (98,8)=392
Step-by-step explanation:
You must get the like terms on the correct sides, so here is how to solve it:
First subtract 5x from both sides: 3x+4=-11
Then subtract 4 from both sides: 3x=-15
Finally divide by 3: x=-5
Answer:
Part 5) Option b ![2x\sqrt{3}\ ft](https://tex.z-dn.net/?f=2x%5Csqrt%7B3%7D%5C%20ft)
Part 6) Option d. ![4y\sqrt[3]{2}\ mm](https://tex.z-dn.net/?f=4y%5Csqrt%5B3%5D%7B2%7D%5C%20mm)
Step-by-step explanation:
Part 5) we know that
The area of a square is equal to
![A=b^2](https://tex.z-dn.net/?f=A%3Db%5E2)
where
b is the length side of the square
we have
![A=12x^2\ ft^2](https://tex.z-dn.net/?f=A%3D12x%5E2%5C%20ft%5E2)
substitute
![12x^2=b^2](https://tex.z-dn.net/?f=12x%5E2%3Db%5E2)
Solve for b
take square root both sides
![b=\sqrt{12x^{2}}](https://tex.z-dn.net/?f=b%3D%5Csqrt%7B12x%5E%7B2%7D%7D)
Remember that
![12=(2^2)(3)](https://tex.z-dn.net/?f=12%3D%282%5E2%29%283%29)
substitute
![b=\sqrt{(2^2)(3)x^{2}}](https://tex.z-dn.net/?f=b%3D%5Csqrt%7B%282%5E2%29%283%29x%5E%7B2%7D%7D)
Applying property of exponents
![b=\sqrt{(2^2)(3)x^{2}}=[(2^2)(3)x^{2}]^{\frac{1}{2}}=[2^2x^2]^{\frac{1}{2}}3^{\frac{1}{2}}=2x\sqrt{3}\ ft](https://tex.z-dn.net/?f=b%3D%5Csqrt%7B%282%5E2%29%283%29x%5E%7B2%7D%7D%3D%5B%282%5E2%29%283%29x%5E%7B2%7D%5D%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5B2%5E2x%5E2%5D%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D3%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D2x%5Csqrt%7B3%7D%5C%20ft)
Part 6) we know that
The volume of a cube is equal to
![V=b^3](https://tex.z-dn.net/?f=V%3Db%5E3)
where
b is the length side of the cube
we have
![V=128y^3\ mm^3](https://tex.z-dn.net/?f=V%3D128y%5E3%5C%20mm%5E3)
substitute
![128y^3=b^3](https://tex.z-dn.net/?f=128y%5E3%3Db%5E3)
Solve for b
take cubic root both sides
![b=\sqrt[3]{128y^3}](https://tex.z-dn.net/?f=b%3D%5Csqrt%5B3%5D%7B128y%5E3%7D)
Remember that
![128=(2^7)=(2^6)(2)=(2^2)^3(2)](https://tex.z-dn.net/?f=128%3D%282%5E7%29%3D%282%5E6%29%282%29%3D%282%5E2%29%5E3%282%29)
substitute
![b=\sqrt[3]{(2^2)^3(2)y^3}](https://tex.z-dn.net/?f=b%3D%5Csqrt%5B3%5D%7B%282%5E2%29%5E3%282%29y%5E3%7D)
Applying property of exponents
![b=\sqrt[3]{(2^2)^3(2)y^3}=[(2^2)^3(2)y^3]^{\frac{1}{3}}=[(2^2)^3y^3]^{\frac{1}{3}}2^{\frac{1}{3}}=2^2y\sqrt[3]{2}=4y\sqrt[3]{2}\ mm](https://tex.z-dn.net/?f=b%3D%5Csqrt%5B3%5D%7B%282%5E2%29%5E3%282%29y%5E3%7D%3D%5B%282%5E2%29%5E3%282%29y%5E3%5D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%5B%282%5E2%29%5E3y%5E3%5D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D2%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D2%5E2y%5Csqrt%5B3%5D%7B2%7D%3D4y%5Csqrt%5B3%5D%7B2%7D%5C%20mm)