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Law Incorporation [45]
3 years ago
15

3. What are the intersection points of the line whose equation is y=3x +3 and the

Mathematics
1 answer:
densk [106]3 years ago
6 0

Answer:

Points of intersection of these graphs are (-2, -3) and (0.6, 4.8).

Step-by-step explanation:

Equation of the circle → (x - 2)² + y² = 25 ---------(1)

                                   → (x - 2)² + (y - 0)² = 5²

By comparing this equation with the standard equation of the circle,

(x - a)² + (y - b)²= r²

Here (a, b) is the center and r is the radius of the circle.

Therefore, center of the circle is (2, 0) and radius = 5 units

Second equation is a linear equation → y = 3x + 3 -------(2)

x-intercept of the equation → x = -1

y-intercept of the equation → y = 3

By graphing these equations we can get the point of intersections.

Solving these equations algebraically,

Substitute the value of y from equation (2) in the equation (1),

(x - 2)² + (3x + 3)² = 25

x² - 4x + 4 + 9x² + 18x + 9 = 25

10x² + 14x - 12 = 0

5x² + 7x - 6 = 0

x = \frac{-7\pm \sqrt{7^2-4(5)(-6)}}{2(5)}

x = \frac{-7\pm \sqrt{169}}{10}

x = \frac{-7\pm13}{10}

x = -2, 0.6

From equation (2),

y = -3, 4.8

Therefore, points of intersection of these graphs are (-2, -3) and (0.6, 4.8).

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A solid shape is made by joining two cones.
dlinn [17]

The surface area of the solid shape is the amount of space on it

The radius of the two cones is 2.93 cm

<h3>How to determine the radius?</h3>

The given parameters are:

  • Cone 1: slant height, l = 2r
  • Cone 2: slant height, L = 3r
  • Surface area = 135. 21 cm²

The surface area of the shape is calculated using:

T = πr(L + l)

So, we have:

135.21 = πr(2r + 3r)

Evaluate

135.21 = 5πr²

Divide both sides by 5π

r² = 135.21/5π

Evaluate the quotient

r² = 8.61

Take the square root of both sides

r = 2.93

Hence, the radius of the cones is 2.93 cm

Read more about surface area at:

brainly.com/question/6613758

3 0
2 years ago
What is the greatest common factor of 24 30 and 42
Helen [10]
List the factors of 24,30, and 24. Factors of 24: 1,2,3,4,6,8,12,24. Factors of 30: 1,2,3,5,6,10,15,30. Factors of 42: 1,2,3,6,7,14,21,42. The highest number that all of these numbers is 6. Therefore, the greatest common factor of GCF of 24,30, and 42 is 6.
6 0
3 years ago
Read 2 more answers
Type the correct answer in the box. Write the standard form of the quadratic equation modeled by the points shown in the table b
White raven [17]
Y =ax² + bx +c

1) Point (0,7)

7 = a*0² +b*0 +c
c = 7
y=ax² + bx + 7

2) Point (1,4)
4=a*1² + b*1 + 7, ----> 4 = a +b + 7, ------> a+b= - 3
3) Point (2, 5)
5=a*2² + b*2 + 7, ----> 5=4a+2b +7,---> -2=4a+2b, ----> -1=2a + b

4)  a+b= - 3, ----> b= -3 - a (substitute in the second equation)
    2a+b= -1
2a - 3 - a = -1, ----> a - 3 = -1, a =2

5) a+b= - 3
    2 + b = -3
b = -5

y=2x² - 5x + 7

8 0
3 years ago
Do you agree? Explain why or why not.
Lelu [443]

Answer:

if x = 4

\sqrt{8 + 1} + 3 = 0

\sqrt{9} + 3 = 0

3 + 3 = 0

6 = 0

wrong.

6 0
2 years ago
Read 2 more answers
PLEASE HELP ME BAD AT GEOMETRY PLEASE THANKS A WHOLE BUNCH
Setler [38]
V = π r² h

V = π (4)² 8
 
V = 402.12

Hope this helps :)
5 0
3 years ago
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