False, No Triangle can be formed with those side lengths. Here's why:
The sum of side a and side a has to be greater than side c.
a+b>c
3+5= 8
8 is not greater than 9
Let:
L = Length
W = Width
The length is 7cm longer than its width, so:
![L=W+7](https://tex.z-dn.net/?f=L%3DW%2B7)
The area is given by:
![A=W\cdot L](https://tex.z-dn.net/?f=A%3DW%5Ccdot%20L)
Therefore:
![\begin{gathered} 240=(W+7)\cdot(W) \\ 240=W^2+7W \\ W^2+7W-240=0 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20240%3D%28W%2B7%29%5Ccdot%28W%29%20%5C%5C%20240%3DW%5E2%2B7W%20%5C%5C%20W%5E2%2B7W-240%3D0%20%5Cend%7Bgathered%7D)
Solve for W using the quadratic formula:
![\begin{gathered} W=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ W=\frac{-7\pm\sqrt[]{7^2-4(1)(-240)}}{2(1)} \\ W=\frac{-7\pm\sqrt[]{1009}}{2} \\ W\approx12.38238 \\ or \\ W\approx-19.38238 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20W%3D%5Cfrac%7B-b%5Cpm%5Csqrt%5B%5D%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5C%5C%20W%3D%5Cfrac%7B-7%5Cpm%5Csqrt%5B%5D%7B7%5E2-4%281%29%28-240%29%7D%7D%7B2%281%29%7D%20%5C%5C%20W%3D%5Cfrac%7B-7%5Cpm%5Csqrt%5B%5D%7B1009%7D%7D%7B2%7D%20%5C%5C%20W%5Capprox12.38238%20%5C%5C%20or%20%5C%5C%20W%5Capprox-19.38238%20%5Cend%7Bgathered%7D)
Therefore:
W = 12.38238 since a negative width wouldn't make any sense
and:
![\begin{gathered} L=W+7 \\ L=19.38238 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20L%3DW%2B7%20%5C%5C%20L%3D19.38238%20%5Cend%7Bgathered%7D)
Answer:
W = 12.38238 m
L = 19.38238 m
You need to use the quadratic formula for this question.
![\frac{-b+- \sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-b%2B-%20%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D%20)
In your equation, a is 1, b is 6, and c is 4. (I couldn't find a plus minus sign, so that's what the +- means, sorry if there's confusion.)
Sub those into the quadratic formula, and
![\frac{-6+- \sqrt{(6)^2-4(1)(4)} }{2(1)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-6%2B-%20%5Csqrt%7B%286%29%5E2-4%281%29%284%29%7D%20%7D%7B2%281%29%7D%20)
For the first answer, we should get
x1=-0.7639, when you add the √6^2-4(1)(4)
For the second answer, we get
x2=-5.2361 when we subtract the √6^2-4(1)(4)
Therefore, the x values that make this equation equal to 0 should be approximately -0.7639 and -5.2361.
The more specific answers are
x1= -3+√5 and x2=-3-√5.
Answer:
18x^2 + 27x - 35
Step-by-step explanation:
f(g(x)) means function f times function g. substitute for f and g, which gets you (3x+7)(6x-5). Now, multiply using the distributive property.
3x * 6x = 18x^2
3x * -5 = -15x
7*6x = 42x
7 * -5 = -35
The equation then becomes 18x^2 - 15x + 42x - 35. Simplify the equation.
18x^2 stays, -15x and 42x combine to make 27x, and the -35 stays too.
Finally, you get the equation, 18x^2 + 27x -35.