1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Whitepunk [10]
2 years ago
10

Please don't answer wrong.​

Mathematics
1 answer:
Tamiku [17]2 years ago
6 0

Answer:

<h3><u>Part (a)</u></h3>

<u />

<u>Equation of a circle</u>

(x-a)^2+(y-b)^2=r^2

where:

  • (a, b) is the center
  • r is the radius

Given equation:  x^2+y^2=6.25

Comparing the given equation with the general equation of a circle, the given equation is a <u>circle</u> with:

  • center = (0, 0)
  • radius = \sqrt{6.25}=2.5

To draw the circle, place the point of a compass on the origin. Make the width of the compass 2.5 units, then draw a circle about the origin.

<h3><u>Part (b)</u></h3>

Given equation:  x+y=1.5

Rearrange the given equation to make y the subject:  y=-x+1.5

Find two points on the line:

x=-2 \implies -(-2)+1.5=3.5\implies (-2,3.5)

x=2 \implies -(2)+1.5\implies-0.5\implies (2,-0.5)

Plot the found points and draw a straight line through them.

The <u>points of intersection</u> of the circle and the straight line are the solutions to the equation.

To solve this algebraically, substitute  y=-x+1.5  into the equation of the circle to create a quadratic:

\implies x^2+(-x+1.5)^2=6.25

\implies x^2+x^2-3x+2.25=6.25

\implies 2x^2-3x-4=0

Now use the quadratic formula to solve for x:

x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0

\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(2)(-4)}}{2(2)}

\implies x=\dfrac{3 \pm \sqrt{41}}{4}

To find the coordinates of the points of intersection, substitute the found values of x into y=-x+1.5

\implies y=-\left(\dfrac{3 + \sqrt{41}}{4}\right)+1.5=\dfrac{3-\sqrt{41}}{4}

\implies y=-\left(\dfrac{3 - \sqrt{41}}{4}\right)+1.5=\dfrac{3+\sqrt{41}}{4}

Therefore, the two points of intersection are:

\left(\dfrac{3 + \sqrt{41}}{4},\dfrac{3-\sqrt{41}}{4}\right) \textsf{ and }\left(\dfrac{3 - \sqrt{41}}{4},\dfrac{3+\sqrt{41}}{4}\right)

Or as decimals to 2 d.p.:

(2.35, -0.85) and (-0.85, 2.35)

You might be interested in
Bob harvested flour from 4 of his fields. From the first field, he harvested 13 ton of flour. The second field yielded 24 ton of
DIA [1.3K]
Bob harvested 65 tons total (13 + 24 + 14 + 14)
and as far as drawing a diagram I don't know what to tell you 

hope this helps
6 0
3 years ago
Americans who are 65 years of age or older make up 12.2% of the total population. if there are 30.2 million Americans in this ag
tensa zangetsu [6.8K]

Divide the population of 65 or older by the percentage:

30.2 million / 0.122 = 247.54 million total population. (Round answer as needed)

8 0
3 years ago
Which of the following statements about JK and JL is true?
bulgar [2K]

Answer:

14

Step-by-step explanation:

5 0
3 years ago
Jaden is flying a kite with an angle of elevation of 33 degrees. If Jaden lets out 275 feet of string, how high above the ground
pshichka [43]

Answer:

149.8 feet

Step-by-step explanation:

θ = Angle of elevation = 33°

The length of string Jaden lets out = Hypotenuse = 275 feet.

How high above the ground that the kite is flying = Opposite Side.

We are solving this question using the Trigonometric function of Sine

Sin θ = Opposite Side/Hypotenuse

Sin 33 = Opposite/275 feet

Cross Multiply

Sin 33 × 275 feet = Opposite

Opposite side(Height ) = 149.77573463 feet

Approximately to the nearest tenth = 149.8 feet

8 0
2 years ago
PLEASE HELP ME WITH THIS QUESTION what is -48-(-12)
olga_2 [115]

Answer:

-36

Step-by-step explanation:

-48+12=-36

6 0
3 years ago
Read 2 more answers
Other questions:
  • Which equations are equivalent to ? 3^3√x+4 =12 Check all that apply.
    10·2 answers
  • H(n)=−10+12nh, left parenthesis, n, right parenthesis, equals, minus, 10, plus, 12, n
    5·1 answer
  • The square of 9 less than a number is 3 less than the number. What is the number?
    10·2 answers
  • Find the GCF for 11 and 44
    14·2 answers
  • What is the input value other than 7 for which g(x)=4? WILL GIVE BRAINLIEST ANSWER!
    15·1 answer
  • Please help thank you
    9·1 answer
  • If the length of line AC equals 24 what is the length of the mid segment lineDE
    5·2 answers
  • For the polynomial x^3-7x^2+12x-6, 1 is a zero. Express g(x) as a product of linear factors.
    7·1 answer
  • What is the volume of a cube with surface area A m2?
    13·1 answer
  • Pleas help me, i'm not sure which one it is and i think it is 10 students got off the bus every minute, please let me know if i'
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!