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3 years ago

In circle P, EG and FH are diameters. What is m EH?

Mathematics

1 answer:

zvonat [6]3 years ago

3 0

Answer:

$m(\widehat{EH})$ = 130°

Step-by-step explanation:

Angles subtended at the center by the arcs $(\widehat{HG})$ and $(\widehat{EF})$ are ∠HPG and ∠EPF.

Since these angles are the vertical angles both will be equal.

m∠HPG ≅ m∠EPF

3x - 10 = 2x + 10

3x - 2x = 10 + 10

x = 20

Therefore, $m(\widehat{HG})=(3\times 20) - 10$

= 50°

Similarly $m(\widehat{EF})$ = 50°

In the same way angles subtended at the center will be equal.

m∠EPH ≅ m∠FPG

and $m(\widehat{EH})=m(\widehat{FG})$

Since $m(\widehat{EH})+m(\widehat{FG})+m(\widehat{EF})+m(\widehat{HG})=360$ °

$m(\widehat{EH})+m(\widehat{EH})+50+50=360$

$2m(\widehat{EH})=360-100$

$m(\widehat{EH})=130$

Therefore, measure of arc EH = 130°

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2 years ago

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kondor19780726 [428]

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2 years ago

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garri49 [273]

Answer:

$b = 17$

Step-by-step explanation:

For this triangle we have to

$a=18.2\\B=62\°\\C=48\°$

We want to find the length of b

We know that the sum of the internal angles of a triangle is 180 °

$A + 62 +48=180\\\\A=180-62-48\\\\A=70\°$

Now we use the sine theorem to find the length of b:

$\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$

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$\frac{sin(A)}{a}=\frac{sin(B)}{b}\\\\b=\frac{sin(B)}{\frac{sin(A)}{a}}\\\\b=a*\frac{sin(B)}{sin(A)}\\\\b=(18.2)\frac{sin(62)}{sin(70)}\\\\b=17$

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2 years ago

Every round in a competition costs 30 diamonds and you get 10 shards. How many diamonds will it cost you to reach 1,024 shards?

Firdavs [7]

Answer:

3,090 diamonds

Step-by-step explanation:

To get 10 shards, you need to spend 30 diamonds.

First thing we need to find, how many rounds you need to play to get 1,024 shards if in each round you win 10 shards?

1,024/10 = 102,4

But you can not play 102.4 rounds, you only can play whole numbers, so we need to round it to the next whole number (not the previous one, because in that case, we would get less than 1,024 shards)

Then you need to play 103 rounds.

And each round costs 30 diamonds, then the total number of diamonds that you need is:

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2 years ago

write a polynomial function of least degree with integral coefficients that has the given zeros. -(1/3), -i

inessss [21]

Answer:

$f(x)=3x^3+x^2+3x+1$

Step-by-step explanation:

If a real number $-\frac{1}{3}$ is a zero of polynomial function, then

$x-\left(-\dfrac{1}{3}\right)=x+\dfrac{1}{3}$

is the factor of this function.

If a complex number $-i$ is a xero of the polynomial function, then the complex number $i$ is also a zero of this function and

$x-(-i)=x+i\ \text{ and }\ x-i$

are two factors of this function.

So, the function of least degree is

$f(x)=\left(x+\dfrac{1}{3}\right)(x+i)(x-i)=\left(x+\dfrac{1}{3}\right)(x^2-i^2)=\\ \\ =\left(x+\dfrac{1}{3}\right)(x^2+1)=\dfrac{1}{3}(3x+1)(x^2+1)=\dfrac{1}{3}(3x^3+x^2+3x+1)$

If the polynomial function must be with integer coefficients, then it has a form

$f(x)=3x^3+x^2+3x+1$

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3 years ago