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2 years ago

Given f(x)=x-7 and g(x)=x^2 Find g(f(-1)) Find f(g(-1)) With explanation

Mathematics

1 answer:

Arlecino [84]2 years ago

4 0

Step-by-step explanation:

f (x)= x-7

= -1-7

= -6

g (x)= x^2

= (-1)^2

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Recall that in a 30 – 60 – 90 triangle, if the shortest leg measures x units, then the longer leg measures xStartRoot 3 EndRoot

Brums [2.3K]

The area of the shaded region is $\rm (150\sqrt{3} \ - 75\pi ) \ feet^2$ option first is correct.

It is given that a circle is inscribed in a regular hexagon with sides of 10 feet.

It is required to find the shaded area (missing data is attached shown in the picture).

<h3>What is a circle?</h3>

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

We have a hexagon with a side length of 10 feet.

We know the area of the hexagon is given by:

$\rm A = \frac{3\sqrt{3} }{2} a^2$ where a is the side length.

$\rm A = \frac{3\sqrt{3} }{2} 10^2$ ⇒ $150\sqrt{3}$ $\rm feet^2$

We have the shortest length = x feet and from the figure:

2x = 10

x = 5 feet

The radius of the circle r = longer leg

$\rm r = x\sqrt{3} \Rightarrow 5\sqrt{3}$ feet

The area of the circle a = $\pi r^2$ ⇒ $\pi (5\sqrt{3} )^2 \Rightarrow 75\pi \ \rm feet^2$

The area of the shaded region = A - a

$\rm =(150\sqrt{3} \ - 75\pi ) \ feet^2$

Thus, the area of the shaded region is $\rm (150\sqrt{3} \ - 75\pi ) \ feet^2$

Learn more about circle here:

brainly.com/question/11833983

7 0

2 years ago

Rewrite in Polar Form....<br> x^(2)+y^(2)-6y-8=0

skad [1K]

$\bf x^2+y^2-6y-8=0\qquad 
\begin{cases}
x^2+y^2=r^2\\\\
y=rsin(\theta)
\end{cases}\implies r^2-6rsin(\theta)=8
\\\\\\
\textit{now, we do some grouping}\implies [r^2-6rsin(\theta)]=8
\\\\\\\
[r^2-6rsin(\theta)+\boxed{?}^2]=8\impliedby 
\begin{array}{llll}
\textit{so we need a value there to make}\\
\textit{a perfect square trinomial}
\end{array}$

$\bf 6rsin(\theta)\iff 2\cdot r\cdot \boxed{3\cdot sin(\theta)}\impliedby \textit{so there}
\\\\\\
\textit{now, bear in mind we're just borrowing from zero, 0}
\\\\
\textit{so if we add, \underline{whatever}, we also have to subtract \underline{whatever}}$

$\bf [r^2-6rsin(\theta)\underline{+[3sin(\theta)]^2}]\quad \underline{-[3sin(\theta)]^2}=8\\\\
\left. \qquad \right.\uparrow \\
\textit{so-called "completing the square"}
\\\\\\\
[r-3sin(\theta)]^2=8+[3sin(\theta)]^2\implies [r-3sin(\theta)]^2=8+9sin^2(\theta)
\\\\\\
r-3sin(\theta)=\sqrt{8+9sin^2(\theta)}\implies r=\sqrt{8+9sin^2(\theta)}+3sin(\theta)$

3 0

3 years ago

3. If a ladder is x feet long, how high up a wall can it safely reach?

sineoko [7]

Answer:

xsin∅

Step-by-step explanation:

If the ladder is <em>x foot long</em>, and it can safely make a <em>maximum angle ∅</em> with the floor, then, the maximum height it can reach will be xsin∅

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3 years ago

Ariana owns a food truck that sells tacos and burritos. She sells each taco for $4 and each burrito for $8.25. Ariana must sell

Serjik [45]

Answer:

Step-by-step explanation:

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2 years ago

I need to find the product of f and g. what is the domain and range of the product

velikii [3]

Step-by-step explanation:

Putting both functions into a graphing calculator, we can easily find the domain and range. (attatched)

By looking at the graph, we can tell that f(x) is a quadratic function because of the symmetry. We can also tell that it never goes below 4. Knowing this, we can determine the domain and range.

Domain: {x | all real numbers}

Range: {y | y > 4}

By looking at the graph, we can tell that g(x) is an exponential function because it has a curve, and never goes below the x. Knowing this, we can determine the domain and range.

Domain: {x | all real numbers}

Range: {y | y > 0}

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3 years ago