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raketka [301]
3 years ago
12

A rectangular flower garden in Samantha's backyard has 220 feet around its edge. The width of the garden is 50 feet. What is the

length of the garden? The length of the garden is feet.
Mathematics
1 answer:
Ede4ka [16]3 years ago
4 0

Answer: 60 ft

Step-by-step explanation:

Given

The perimeter of the garden is 220\ ft

The width of the garden is 50\ ft

Suppose the length of the garden is x

Perimeter is the sum of the lengths of the sides

\Rightarrow 220=2(x+50)\\\Rightarrow 110=x+50\\\Rightarrow x=60\ ft

So, the length of the garden is 60\ ft

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One fifth of one number and one fourth of a number are added, the result is 29. What is the original number?
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Answer:

\dfrac{580}{9}

Step-by-step explanation:

\dfrac{1}{5}x + \dfrac{1}{4}x = 29

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What is the solution to the equation
Dafna11 [192]
\sqrt{4t+5}=3-\sqrt{t+5}\\\\D:4t+5\geq0\ \wedge\ t+5\geq0\ \wedge\ \sqrt{t+5}\leq3\\\\t\geq-\dfrac{5}{4}\ \wedge\ t\geq-5\ \wedge\ t\leq6

therefore
D:x\in\left< -\dfrac{5}{4};\ 6\right>

\sqrt{4t+5}=3-\sqrt{t+5}\ \ \ |^2\\\\(\sqrt{4t+5})^2=(3-\sqrt{t+5})^2\ \ \ |use:(a-b)^2=a^2-2ab+b^2\\\\4t+5=3^2-2\cdot3\cdot\sqrt{t+5}+(\sqrt{t+5})^2\\\\4t+5=9-6\sqrt{t+5}+t+5\ \ \ \ |-t\\\\3t+5=14-6\sqrt{t+5}\ \ \ \ |-14\\\\3t-9=-6\sqrt{t+5}\ \ \ \ |change\ signs
9-3t=6\sqrt{t+5}\ \ \ \ |:3\\\\3-t=2\sqrt{t+5}\ \ \ \ |^2\\\\(3-t)^2=(2\sqrt{t+5})^2\\\\3^2-2\cdot3\cdot t+t^2=4(t+5)\\\\9-6t+t^2=4t+20\ \ \ |-4t-20\\\\t^2-10t-11=0\\\\t^2+t-11t-11=0\\\\t(t+1)-11(t+1)=0\\\\(t+1)(t-11)=0\iff t+1=0\ \vee\ t-11=0\\\\t=-1\in D\ \vee\ t=11\notin D
Answer: t = -1.


7 0
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Answer:

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