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2 years ago

6

The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at (0, 7). Whic

h statement must be true?

1 answer:

denis23 [38]2 years ago

3 0

The true statement is the circle has the radius equal to 7.

<h3>What is Equation of circle?</h3>

The general equation for a circle is (x-h)² + (y-k)² = r², where ( h, k ) is the center and r is the radius.

As, standard form of equation of circle is

(x-h)² + (y-k)² = r²

At origin, equation of circle will be

(0-h)² + (0-k)² = r²

r² = x² + y²

Now, The line intersects the circle at (0,7)

r² = 0² + 7²

r² =49

r=7.

Hence, the circle has the radius equal to 7.

Learn more about this concept here:

brainly.com/question/11702700

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Factor completely 3x2 + x + 7.

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Answer:

-1

Step-by-step explanation:

3 • 7 = 21

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To divide 572 by 4 Stanley estimated to place the first digit of the quotient. In which place is the first digit of the quotient

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The answer should be Hundreds Place

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Korvikt [17]

Question 9:

Given the equations

$5x+2y=6;$

$4x-8y=0$

solving the system of the equations

$\begin{bmatrix}5x+2y=6\\ 4x-8y=0\end{bmatrix}$

$\mathrm{Multiply\:}5x+2y=6\mathrm{\:by\:}4\:\mathrm{:}\:\quad \:20x+8y=24$

$\mathrm{Multiply\:}4x-8y=0\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:20x-40y=0$

$\begin{bmatrix}20x+8y=24\\ 20x-40y=0\end{bmatrix}$

$20x-40y=0$

$-$

$\underline{20x+8y=24}$

$-48y=-24$

$\begin{bmatrix}20x+8y=24\\ -48y=-24\end{bmatrix}$

$-48y=-24$

$\frac{-48y}{-48}=\frac{-24}{-48}$

$y=\frac{1}{2}$

$y = 0.5$ ( 0.5 is the result of rounding 0.5 to the nearest 0.01)

$\mathrm{For\:}20x+8y=24\mathrm{\:plug\:in\:}y=\frac{1}{2}$

$20x+8\cdot \frac{1}{2}=24$

$20x+4=24$

$\frac{20x}{20}=\frac{20}{20}$

$x=1.00$ ( 1.00 is the result of rounding 1 to the nearest 0.01 )

So, the solution is:

(x, y) → (1.00, 0.5)

Question 10)

Similarly the question 10 can be solved.

Given the equations

$5x+2y=9;\:4x-3y=44$

solving

$\begin{bmatrix}5x+2y=9\\ 4x-3y=44\end{bmatrix}$

$\mathrm{Multiply\:}5x+2y=9\mathrm{\:by\:}4\:\mathrm{:}\:\quad \:20x+8y=36$

$\mathrm{Multiply\:}4x-3y=44\mathrm{\:by\:}5\:\mathrm{:}\:\quad \:20x-15y=220$

$\begin{bmatrix}20x+8y=36\\ 20x-15y=220\end{bmatrix}$

$20x-15y=220$

$-$

$\underline{20x+8y=36}$

$-23y=184$

$\begin{bmatrix}20x+8y=36\\ -23y=184\end{bmatrix}$

$-23y=184$

$y=-8.00$ ( -8.00 Rounded to the nearest 0.01 or the Hundredths Place )

$\mathrm{For\:}20x+8y=36\mathrm{\:plug\:in\:}y=-8$

$20x+8\left(-8\right)=36$

$20x=100$

$x=5.00$ ( 5.00 Rounded to the nearest 0.01 or the Hundredths Place )

So, the solution is:

(x, y) → (5.00, -8.00)

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andrey2020 [161]

Step-by-step explanation:

Circumference =

$2\pi \: r$

Area =

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Using r = 8 cm and

$\pi \: = 3.14$

Circumference = 50.24 cm

Area = 200.96 sq cm

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