Mathematics High School

3. What are the intersection points of the line whose equation is y=3x +3 and the
circle whose equation is (x - 2)² + y2 = 25?

Answers

Answer 1

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 = [tex]\frac{-7\pm \sqrt{7^2-4(5)(-6)}}{2(5)}[/tex]

x = [tex]\frac{-7\pm \sqrt{169}}{10}[/tex]

x = [tex]\frac{-7\pm13}{10}[/tex]

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).

Related Questions

Solve
5x+3y=32
2x+4y=10

Answers

i send u a picture of how i solve it. i hope this can help u

José paid $47.00 for 4 movie tickets. Each ticket cost the same amount. What was the cost of sch movie tidet a dollars and cents?

Answers

Answer: 11.75

Step-by-step explanation:

47 / 4= 11.75

Answer: each ticket cost $11.75

Step-by-step explanation:

47.00/4=11.75

Hope this helps!

HELPP ILL GIVE BRAINLIEST

Answers

When we divide exponents with the same base, we will subtract them
2-8 is -6 so we have 5^-6
We can rewrite exponents with a negative sign over 1 so we get
1/5^6 (A)

It’s choice A........

in this diagram below the angle of depression of the boat is 29° .if the lighthouse is 32 M tall how far is the boat from the base of the lighthouse round your answer to the nearest whole number

Answers

Answer:

Step-by-step explanation:

tan29=32/x

x=32/(tan29)

x=58m

So the boat is 58 meters from the base of the lighthouse.

What is the distance between (4, 7) and (-8, 3)? Round to the nearest tenth.

Answers

Answer:

The distance is approximately 12.6.

Step-by-step explanation:

Moving from (-8, 3) to (4, 7), we see x (the horizontal dimension) increasing by 12 and y (the vertical dimension) increasing by 4. Think of 12 and 4 as the legs of a right triangle whose hypotenuse represents the distance between these two given points.

This distance, from the Pythagorean Theorem, is

d = √(12^2 + 4^2) = √(144 + 16) = √160 = √16√10.

The desired distance is approximately 12.6.

हल गर्नुहोस् (Solve):
3X+1 + 3x = 108
सरल गर्नुहोस् (Simplify):
1
1
+
(a - b) (a-st 16-allo

Answers

107/6

Step-by-step explanation:

3x+1+3x=108

6x=108-1

6x=107

x=107/6

$5,200 at 4% for 3 years. Answers

Answers

answer $5,824

if u need to show work:

5,200(.04)=208
208(3)=624
5,200+624=5,824

hope this helps! can u please give me brainliest

Answer 5,824

Step by step explanation:

I NEED HELPPPPPP PLSSS !!!!

Answers

Answer:

If they scored 8 touch downs then the answer would be 48 points.

Explanation: 8x6=48

For positive acute angles A and B, it is know that tan A= 8/15 and sin B= 11/61. Find the value of cos (a+b) in simplest form

Answers

Answer:

812/1037

Step-by-step explanation:

To solve this, we have to use trigonometric identities.

Cos (A + B) is given as Cos A Cos B - Sin A Sin B. And from the question, we have that

Tan A = 8/15.

We know that in a triangle, the Tan angle is represented Opp/Adj and thus the Opp is 8, and the Adj is 15. Using Pythagoras, we have

hyp² = opp² + adj²

hyp² = 8² + 15²

hyp² = 64 + 225

hyp² = 289

hyp = √289 = 17

The identity of Cos is Adj/Hyp and that of Sin is Opp/Hyp.

Cos A = 15/17

Sin A = 8/17

Repeating the same process for B, we have

Sin B = 11/61

adj² = hyp² - opp²

adj² = 61² - 11²

adj² = 3721 - 121

adj² = 3600

adj = √3600 = 60

Cos B = 60/61

Now, using the earlier stated trigonometric identity, we have

cos (a + b) = CosA CosB - SinA SinB

cos (a + b) = 15/17 * 60/61 - 8/17 * 11/61

cos (a + b) = 900/1037 - 88/1037

cos (a + b) = 812/1037

Pleaseeeeee can anyone help me????

Answers

Answer:

27.63

Step-by-step explanation:

r = 4.4

Circumference of a Circle formula:

C = 2πr

C = 2(3.14)(4.4)

C = 6.28(4.4)

C = 27.632

Rounded to the nearest hundredth:

27.63

Answer:

C= 27.63 inches

Step-by-step explanation:

Use the circumference formula C = 2πr.

Subsitute what you are given into the equation and solve.

C = 2πr

C= 2*(3.14)*(4.4inches)

C= 27.63 inches

Find the surface area. Answer without units.
18 cm
11 cm
9cm
Please help hurry

Answers

Answer:

306

Step-by-step explanation:

v = 1/3bh

2×(18×11 + 18×9 + 11×9) / 3 = 918/3

= 306

hope this helps, mark brainliest if it did luv gl !

8 x (5 + 2) = (8 x h (8 x j)

Answers

Answer:

64hjx^2

Step-by-step explanation:

I hope this helps :)

Let me know if you need an explanation or the steps

1. Find the mean, median, and mode of each set of numbers.
33,000 34,700 35,000 36,500 37,000 34,700

Answers

Answer:

mode is 0 shshshshsbsbsbbsnsnsnsjsnsns

Answer:

Mode 34,700

Median 35,750

Mean 35,150

Leanna opens a savings account with an initial balance of $100. She then deposits $50 each month. Write an equation to explain the relationship between the amount of money in the account, a, and the number of months since Leanna opened the account, m.

HELP ME

Answers

Answer:

Step-by-step explanation:

450-100=350

350/50=7

7 months

Find the missing side length of a right triangle with a leg measure of 3 inches and a hypotenuse measure of 5
inches.

Answers

a=3 in
c=5 in
c^2=a^2+b^2
5^2=3^2+b^2
25=9+b^2
b^2=25-9
b^2=16
b= √16
b=4

the relationship between a and b if a + b = 0

Answers

Answer:

a=-b

Step-by-step explanation:

a+b=0a=-b

Or,

b=-a

Help please
Brainiest answer to whoever is first

Answers

Answer:

Step-by-step explanation:

The answer is 66 because you add every side.

She sold 54 of thin mints, which was 60 percent of the total number she sold. how many total boxes did she sell?

Answers

set up a proportion

54 60
— = —
x 100

(100)(54)= 60(x)

5400=60x

x= 5400/60

x=90

pls help! whats the area of the sector!

Answers

Answer:

Step-by-step explanation:

[tex]\frac{a}{\pi r^2}=\frac{\theta }{360^o}\\ \\ a=\frac{\pi r^2 \theta }{360^o}\\ \\ r=36^o,\ \theta =80^o\\ \\ a=288\pi cm^2[/tex]

AB
Round your answer to the nearest hundredth.
С
4
A
25°
?
B

Answers

Answer:

AB ≈ 4.41

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos25° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{4}{AB}[/tex] ( multiply both sides by AB )

AB × cos25° = 4 ( divide both sides by cos25° )

AB = [tex]\frac{4}{cos25}[/tex] ≈ 4.41 ( to the nearest hundredth )

PLEASE ANSWER FAST!

A water tank contains exactly 1,000 gallons. A pump fills the remainder of the tank using
a logistic function. If the volume of the tank is 15,000 gallons and the pump fills the tank at a rate of 10.4% per minute, explain how to find the value of a for the logistic function that describes this scenario.

Answers

Answer: V ( t ) = 1 + 1 4 e − 0 . 1 0 4 t 1 5 , 0 0 0 

The required value for the logistic function describing the scenario of the water tank being filled at a rate of 10.4% per minute.

What is the logistic function?

The logistic function has the form:

[tex]f(x) = L / (1 + a \times e^{(-kx)})[/tex]

Where:

f(x) is the volume of the tank at time x

L is the maximum volume the tank can hold

a is a constant that determines the growth rate of the function

k is a constant that determines the rate at which the growth slows down as the tank approaches the maximum volume

In this case, the maximum volume of the tank is 15,000 gallons, so L = 15,000.

The pump fills the tank at a rate of 10.4% per minute, so k = 0.104.

To find the value of a, we need to solve the logistic equation for a given the values of f(x), L, and k.

We can rearrange the logistic equation to solve for a:

[tex]a = (1 / f(x)) - (1 / L) \times e^{(kx)}[/tex]

Substituting the known values into this equation, we get:

[tex]a = (1 / 1,000) - (1 / 15,000) \times e^{(0.104x)}[/tex]

This equation can be used to solve for the value of a for any given value of x (time). For example, if we want to know the value of an after 10 minutes, we can substitute x = 10 into the equation to get:

[tex]a = (1 / 1,000) - (1 / 15,000) \times e^{(1.04)}[/tex]

This gives us the value of a for the logistic function that describes the scenario of the water tank being filled at a rate of 10.4% per minute.

To learn more about logistic function click here:

https://brainly.com/question/18686811

#SPJ5

Please help!! I will give brainliest

Answers

The answer is A
I did this class last year

can someone please help me asap

Answers

Answer:

I cant see it....

Step-by-step explanation:

I cant see it....

Showplace Lanes charges
$4.50 per game as well as
$3 for shoe rental
.
Westgate Bowling charges
$4 per game and $4 for
shoe rental. How many
games must be bowled
before the price is the
same at both bowling lanes?
What is the cost?

Answers

Answer:

2 game, $12

Step-by-step explanation:

Given data

Showplace Lanes charges

$4.50 per game as well as

$3 for shoe rental

Let the number of games be x

let the total charge for x games be y

y= 4.5x+3-----------1

Westgate Bowling charges

$4 per game and $4 for

shoe rental

Let the number of games be x

let the total charge for x games be y

y= 4x+4-----------2

Equate 1 and 2

4.5x+3= 4x+4

collect like terms

4.5x-4x= 4-3

0.5x= 1

divide both sides by 0.5

x= 1/0.5

x= 2 games

put x= 2 in equation 1 or 2

y= 4x+4-----------2

y= 4*2+4

y= 8+4

y= $12

Find the volume of a square pyramid with base edge = 9 cm
and height = 7 cm.

PLZ HELP FAST

Answers

right square pyramid V=189cm³

Which operation will isolate the variable?

17b = 54 :

addition

subtraction

multiplication

division

Answers

Answer:

Division

Step-by-step explanation:

here's your process

=>. it is your equation 17b = 54

=> now divide 17 on both side

=> then we get 17b/17 = 54/17

=> hence , we get b = 54/17

=>now b is isolated by the method of division

hope it helps

its coordinate planes

Answers

Answer:

Step-by-step explanation:

If the cos of angle A = 1/2, then find the measure of angle A.

Answers

Answer:

<A= 60 degrees

Step-by-step explanation:

Since cosA=0.5, we can take the inverse cos of 0.5 to get 60 degrees.

Hope this helped!

Which statement describes the graph of y = -2?*

Answers

Answer:

It is parallel to x axis

Step-by-step explanation:

Find the mode using the above data dot plot.

Answers

mode is the most reoccurring number

therefore the mode is 48

Answer:

Step-by-step explanation:

Mode- the most frequently occuring observation ... here in this case it will be 48

I hope im right!!

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3. What are the intersection points of the line whose equation is y=3x +3 and the circle whose equation is (x - 2)² + y2 = 25?

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3. What are the intersection points of the line whose equation is y=3x +3 and the
circle whose equation is (x - 2)² + y2 = 25?