Assignment: ![\bold{Solve \ Equation: \ x^2-4x-5=0}](https://tex.z-dn.net/?f=%5Cbold%7BSolve%20%5C%20Equation%3A%20%5C%20x%5E2-4x-5%3D0%7D)
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Answer: ![\boxed{\bold{x=5,\:x=-1}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cbold%7Bx%3D5%2C%5C%3Ax%3D-1%7D%7D)
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Explanation: ![\downarrow\downarrow\downarrow](https://tex.z-dn.net/?f=%5Cdownarrow%5Cdownarrow%5Cdownarrow)
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[ Step One ] Solve With Quadric Formula
Note: ![\bold{For\:a\:quadratic\:equation\:of\:the\:form\ ax^2+bx+c=0}](https://tex.z-dn.net/?f=%5Cbold%7BFor%5C%3Aa%5C%3Aquadratic%5C%3Aequation%5C%3Aof%5C%3Athe%5C%3Aform%5C%20ax%5E2%2Bbx%2Bc%3D0%7D)
![\bold{the \ solutions \ are \ x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}](https://tex.z-dn.net/?f=%5Cbold%7Bthe%20%5C%20solutions%20%5C%20are%20%5C%20x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%7D)
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![\bold{a=1,\:b=-4,\:c=-5:\quad x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\left(-5\right)}}{2\cdot \:1}}](https://tex.z-dn.net/?f=%5Cbold%7Ba%3D1%2C%5C%3Ab%3D-4%2C%5C%3Ac%3D-5%3A%5Cquad%20x_%7B1%2C%5C%3A2%7D%3D%5Cfrac%7B-%5Cleft%28-4%5Cright%29%5Cpm%20%5Csqrt%7B%5Cleft%28-4%5Cright%29%5E2-4%5Ccdot%20%5C%3A1%5Cleft%28-5%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A1%7D%7D)
[ Step Two ] Simplify Expressions
![\bold{\frac{-\left(-4\right)+\sqrt{\left(-4\right)^2-4\cdot \:1\cdot \left(-5\right)}}{2\cdot \:1}: \ 5}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cfrac%7B-%5Cleft%28-4%5Cright%29%2B%5Csqrt%7B%5Cleft%28-4%5Cright%29%5E2-4%5Ccdot%20%5C%3A1%5Ccdot%20%5Cleft%28-5%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A1%7D%3A%20%5C%205%7D)
![\bold{\frac{-\left(-4\right)-\sqrt{\left(-4\right)^2-4\cdot \:1\cdot \left(-5\right)}}{2\cdot \:1}: \ -1}](https://tex.z-dn.net/?f=%5Cbold%7B%5Cfrac%7B-%5Cleft%28-4%5Cright%29-%5Csqrt%7B%5Cleft%28-4%5Cright%29%5E2-4%5Ccdot%20%5C%3A1%5Ccdot%20%5Cleft%28-5%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A1%7D%3A%20%5C%20-1%7D)
[ Step Three ] Combine Solutions
![\bold{x=5,\:x=-1}](https://tex.z-dn.net/?f=%5Cbold%7Bx%3D5%2C%5C%3Ax%3D-1%7D)
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Answer:
75.36mm
Step-by-step explanation:
In order to be a function, every value of the independent variable must be associated to only one value of the dependent variable.
If A is a function of G, that means G is the independent variable.
Looking at the table, the value G = 3 has two different values of A (A = 7 and A = 8), therefore A can't be a function of G (answer = NO).
If G is a function of A, that means A is the independent variable.
Looking at the table, the value A = 7 has two different values of G (G = 2 and G = 3), therefore G can't be a function of A (answer = NO).
Let d = number of dimes, q = number of quarters
<span>Sally has 20 coins in her piggy bank, so </span>
<span>d + q = 20 </span>
<span>The total amount of money is $3.05. </span>
<span>Use the value of each coin multiplied by its number to get total value </span>
<span>.10d + .25q = 3.05 </span>
<span>multiply everything by 100 to clear the decimal places </span>
<span>10d + 25q = 305 and </span>
<span>d + q = 20 </span>
<span>solve the second equation above in terms of either d or q - lets do d </span>
<span>d = 20 - q </span>
<span>sub that into the first equation </span>
<span>10d + 25q = 305 </span>
<span>10(20 - q) + 25q = 305 </span>
<span>200 - 10q + 25q = 305 </span>
<span>15q = 105 </span>
<span>q = 105/15 = 7 </span>
<span>and from above </span>
<span>d = 20 - q = 20 - 7 = 13 </span>
<span>so, there are 13 dimes and 7 quarters </span>
<span>verify with orig problem </span>
<span>13 + 7 = 20, OK, and $1.30 + $1.75 = $3.05
</span>
Answer:
x-10
Step-by-step explanation:
you have to do what is in the parenthesis first. Do distributive property to
-(x-8)
-(x)-(-8)= -x+8
now you have 5-(3-x+8)
Do distributive property again
5-3+x-8
x-8+2
x-10
hope this helps ~D~