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3 years ago

The measure of EFH is twice the measure of GFH. What is the

Mathematics

1 answer:

Vladimir [108]3 years ago

8 0

Answer:

30° = m∠GFH

Step-by-step explanation:

Since ∠EFH and ∠GFH are complementary, the sum of their measures i 90.

Let x = m∠GFH

2x = m∠EFH

m∠GFH + m∠EFH = 90

x + 2x = 90

3x = 90

x = 30° = m∠GFH

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Write an equation for a circle with a diameter that has endpoints at (–4, –7) and (–2, –5). Round to the nearest tenth if necess

Zinaida [17]

since we know the endpoints of the circle, we know then that distance from one to another is really the diameter, and half of that is its radius.

we can also find the midpoint of those two endpoints and we'll be landing right on the center of the circle.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{[-2-(-4)]^2+[-5-(-7)]^2}\implies d=\sqrt{(-2+4)^2+(-5+7)^2} \\\\\\ d=\sqrt{2^2+2^2}\implies d=\sqrt{2\cdot 2^2}\implies d=2\sqrt{2}~\hfill \stackrel{~\hfill radius}{\cfrac{2\sqrt{2}}{2}\implies\boxed{ \sqrt{2}}} \\\\[-0.35em] ~\dotfill$

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-5})\qquad \qquad \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-2-4}{2}~~,~~\cfrac{-5-7}{2} \right)\implies \left( \cfrac{-6}{2}~,~\cfrac{-12}{2} \right)\implies \stackrel{center}{\boxed{(-3,-6)}} \\\\[-0.35em] ~\dotfill$

$\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-3}{ h},\stackrel{-6}{ k})\qquad \qquad radius=\stackrel{\sqrt{2}}{ r} \\[2em] [x-(-3)]^2+[y-(-6)]^2=(\sqrt{2})^2\implies (x+3)^2+(y+6)^2=2$

4 0

3 years ago

Read 2 more answers

A total of 697 tickets were sold for the school play. They were either adult tickets or student tickets. There were 53 fewer stu

Burka [1]

Let x = number of adult tickets sold
Let x-53 = number of student tickets sold

x + x -53 = 697
2x - 53 = 697.

Add 53 to both sides to get:

2x = 750

Divide both sides by 2 to get:

x = 375

375 adult tickets were sold.

5 0

3 years ago

Foe the AP given by a1,a2,......,an,...with non zero common difference, the equation satisfied are

user100 [1]

The given sequence is
a₁, a₂, ..., $a_{n}$

Because the given sequence is an arithmetic progression (AP), the equation satisfied is
$a_{n}=a_{1}+(n-1)d$
where
d = the common difference.

The common difference may be determined as
d = a₂ - a₁

The common difference is the difference between successive terms, therefore
d = a₃ - a₂ = a₄ - a₃, and so on..

The sum of the first n terms is
$S_{n}= \frac{n}{2} (a_{1}+a_{n})$

Example:
For the arithmetic sequence
1,3,5, ...,
the common difference is d= 3 - 1 = 2.
The n-th term is
$a_{n}=1+2(n-1)$

For example, the 10-term is
a₁₀ = 1 + (10-1)*2 = 19
Th sum of th first 10 terms is
S₁₀ = (10/2)*(1 + 19) = 100

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3 years ago

Determine whether the relationship between the circumfrance of a circle and its diameter is a direct variation. If so, identify

kipiarov [429]

Answer:

The relationship between the circumference of a circle and its diameter represent a direct variation and the constant of proportionality is equal to the constant $\pi$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y=kx$

where K is the constant of proportionality

In this problem we know that

The circumference of a circle is equal to

$C=\pi D$

therefore

the relationship between the circumference of a circle and its diameter is a direct variation and the constant of proportionality is equal to the constant $\pi$

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3 years ago

Somebody please help me answer this

Inga [223]

-2x+4 I am pretty sure

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3 years ago