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disa [49]
2 years ago
7

Write the equation in graphing form and the graph the shape. NO LINKS/ASSESSMENT!!

Mathematics
1 answer:
charle [14.2K]2 years ago
4 0

Answer:

see explanation

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Given

16 + x² + y² - 8x - 6y = 0 ( subtract 16 from both sides )

x² + y² - 8x - 6y = - 16 ( collect x and y terms together )

x² - 8x + y² - 6y = - 16

Use the method of completing the square

add ( half the coefficient of the x/y terms)² to both sides

x² + 2(- 4)x + 16 + y² + 2(- 3)y + 9 = - 16 + 16 + 9

(x - 4)² + (y - 3)² = 9 ← in standard form

with centre (4, 3 ) and r = \sqrt{9} = 3

This is a circle with centre (4, 3 ) and radius 3

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What is the measure of x to the nearest degree?<br> 8
faust18 [17]

We know that :

\sf{\bigstar \ \ Cos\theta = \dfrac{Adjacent \ Side}{Hypotenuse}}

From the figure, We can notice that :

Ф   Adjacent side length = 8

Ф  Hypotenuse length = 11

\sf{\implies Cosx^{\circ} = \dfrac{8}{11}}

\sf{\implies x^{\circ} = Cos^{-1}\bigg(\dfrac{8}{11}\bigg)}

\sf{\implies x^{\circ} = 43.34}

7 0
3 years ago
Solve the system of equations by substitution 3x+y=9z
poizon [28]

Answer:

x = 1.27

y = 5.18

Step-by-step explanation:

to solve this system of  equation by simultaneous equation we say that let

3x+y=9.............................. equation 1

-5x+2y=4 .......................... equation 2

from equation 1

3x+y=9.............................. equation 1

y = 9 -3x.............................. equation 3

substitute the value of y = 9 -3x into equation 2

-5x+2y=4 .......................... equation 2

-5x + 2( 9 -3x) = 4

-5x + 18 - 6x = 4

collect the like terms

18 - 4 = 6x + 5x

14 = 11x

divide both side by 11

14/11 = 11x/11

x = 14/11

x = 1.27

put the value of x = 1.27 into  equation 3

y = 9 -3x.............................. equation 3

y = 9 - 3( 1.27)

y = 9 - 3.82

y = 5.18

<em>to check if you are correct put the value of x and y into either equation 1 or equation 2.</em>

<em>3x+y=9.............................. equation 1</em>

<em>3( 1.27) + 5.18 = 9</em>

<em>3.81 + 5.18 = 9</em>

<em>9 = 9</em>

3 0
3 years ago
3. The picture below shows a relationship between the number of circles and triangles.
dimaraw [331]

Answer:

D or A

Step-by-step explanation:

(D) One circle : four triangles  

  Example:

One triangle is 1/4 of a circle

(A) One circle : four triangles

    Example:

If there is two circles, the triangles will double like it shows [evidences]

6 0
3 years ago
If y=e5t is a solution to the differential equation
a_sh-v [17]

Answer:

k = 30, y(t) = C_1e^{5t}+C_2e^{6t}

Step-by-step explanation:

Since y=e^{5t} is a solution, then it must satisfy the differential equation. So, we calculate the derivatives and replace the value in the equation. We have that

\frac{d^2y}{dt^2} = 25 e^{5t},\frac{dy}{dt} = 5e^{5t}

Then, replacing the derivatives in the equation we have:

25e^{5t}-11(5)e^{5t}+ke^{5t}=0 e^{5t}(25-55+k) =0

Since e^{5t} is a positive function, we have that

25-55+k = 0 \rightarrow k = 30.

Now, consider a general solution y(t) = Ae^{rt}, A \in \mathbb{R}, then, by calculating the derivatives and replacing them in the equation, we get

Ae^{rt}(r^2-11r+30)=0

We already know that r=5 is a solution of the equation, then we can divide the polynomial by the factor (r-5) to the get the other solution. If we do so, we get that (r-6)=0. So the other solution is r=6.

Therefore, the general solution is

y(t) = C_1e^{5t}+C_2e^{6t}

8 0
3 years ago
Which is greater 5,280 yards or 1 mile
KengaRu [80]
5,280 is greater because there is 1,760 yards in a mile.
3 0
3 years ago
Read 2 more answers
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