Answer: g=2
Step-by-step explanation:5.5g+3=2.5g+9
We move all terms to the left:
5.5g+3-(2.5g+9)=0
We get rid of parentheses
5.5g-2.5g-9+3=0
We add all the numbers together, and all the variables
3g-6=0
We move all terms containing g to the left, all other terms to the right
3g=6
g=6/3
g=2
Answer:
One triangle
Step-by-step explanation:
The angles being fixed at 30° and 60° cause the legs to be fixed.
For the 30° angle, one side is the given side of 12, the other side is at a fixed position.
The same goes for the 60° angle.
So both missing legs of the triangle are at fixed angles. The missing angle is 90° (if one is 30° and the other is 60°, then the last angle must add up to 180°, so it is 90°)
Since the last angle is also fixed, it means that there is only one way for the legs to intersect to cause a 90° angle, so there is only one triangle that can be formed
<span><span>3.(4p−2)</span>(p−4)</span><span>
=<span><span>(<span>4p+−2</span>)</span><span>(<span>p+−4</span>)
</span></span></span><span>=<span><span><span><span><span>(4p)</span>(p)</span>+<span><span>(4p)</span><span>(−4)</span></span></span>+<span><span>(−2)</span>(p)</span></span>+<span><span>(−2)</span><span>(−4)
</span></span></span></span><span>=<span><span><span><span>4p2</span>−16p</span>−2p</span>+8
</span></span><span>=<span><span><span>4p2</span>−18p</span>+<span>8
Simplified form - </span></span></span>4p2−18p+<span>8
4.</span><span>(<span><span><span>2x2</span>+4x</span>−3</span>)</span><span>(<span>3x+1</span>)
</span><span>=<span><span>(<span><span><span>2x2</span>+4x</span>+−3</span>)</span><span>(<span>3x+1</span>)
</span></span></span><span>=<span><span><span><span><span><span><span>(<span>2x2</span>)</span><span>(3x)</span></span>+<span><span>(<span>2x2</span>)</span>(1)</span></span>+<span><span>(4x)</span><span>(3x)</span></span></span>+<span><span>(4x)</span>(1)</span></span>+<span><span>(−3)</span><span>(3x)</span></span></span>+<span><span>(−3)</span>(1)</span></span></span><span>
=<span><span><span><span><span><span>6x3</span>+<span>2x2</span></span>+<span>12x2</span></span>+4x</span>−9x</span>−3
</span></span><span>=<span><span><span><span>6x3</span>+<span>14x2</span></span>−5x</span>−<span>3
Simplified form - </span></span></span><span>6x3+14x2−5x</span>−<span>3</span>
