Answer :
inequality form: k ≥ -4
OR
interval form: [-4, ∞)
<span><span>2<span>(<span>1+<span>5x</span></span>)</span></span>=<span>5<span>(<span><span>2x</span>−1</span>)</span></span></span>
Step 1: Simplify both sides of the equation.<span><span>2<span>(<span>1+<span>5x</span></span>)</span></span>=<span>5<span>(<span><span>2x</span>−1</span>)</span></span></span><span><span><span><span>(2)</span><span>(1)</span></span>+<span><span>(2)</span><span>(<span>5x</span>)</span></span></span>=<span><span><span>(5)</span><span>(<span>2x</span>)</span></span>+<span><span>(5)</span><span>(<span>−1</span>)</span></span></span></span>(Distribute)<span><span>2+<span>10x</span></span>=<span><span><span>10x</span>+</span>−5</span></span><span><span><span>10x</span>+2</span>=<span><span>10x</span>−5</span></span>
Step 2: Subtract 10x from both sides.<span><span><span><span>10x</span>+2</span>−<span>10x</span></span>=<span><span><span>10x</span>−5</span>−<span>10x</span></span></span><span>2=<span>−5</span></span>
Step 3: Subtract 2 from both sides.<span><span>2−2</span>=<span><span>−5</span>−2</span></span><span>0=<span>−7</span></span><span>
</span>
Answer:
The quadratic function representing the total area of the park and the path is
Step-by-step explanation:
The width of the rectangle is x----------(1)
Then the length = twice it's width
Length =
Length = 2x------------------(2)
Now the width along with the foot path = x +3+3 = x+9
the length along with the foot path = 2x + 3+3 = 2x +9
The total area of the park and the path =
that is
=> (2x + 9)(x+9)
=>
=>
Answer: they can rent the room for less than 6 hours.
Step-by-step explanation:
Let x represent the possible amounts of time in which they can rent the room.
There is a reservation fee of $47 and an additional hourly fee of $7.40. This means that the total cost of renting the room for x hours would be
47 + 7.4x
The math club wants to spend less than $91.40 on renting the room. This would be expressed as
47 + 7.4x < 91.4
7.4x < 91.4 - 47
7.4x < 44.4
x < 44.4/7.4
x < 6
Answer:
Length of the side opposite to angle is 31.49
Step-by-step explanation:
Included angle can be defined as the angle in between two sides of the triangle.
So angle is in between sides 16 and 21.
Refer to the attachment for triangle diagram.
To find the length of opposite side, use cosine rule as follows
From the diagram,
Substituting the values in the formula,
Simplifying,
Taking square root on both sides,
Therefore length of third side is 31.49