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3 years ago

Is (1, 6) a solution to this system of equations? 5x + 2y = 17 x + 3y = 19 yes no

2 answers:

5 0

Answer:
Yes

Explanation:
5x + 2y = 17

We are given the values (1, 6)

Substitute then into the equation

(I put a question mark to basically ask the question “is 5(1) + 2(6) equal to 17?”)

5(1) + 2(6) = 17?
5 + 12 = 17?
Yes!

Hope this helped and made sense :)

gladu [14]3 years ago

3 0

Yes because when you plug it in you get the the same Y. Which means yes

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The circle Ci, intersects the y-axis at two points, one of which is (0.4).

Anuta_ua [19.1K]

Answer:

Part 1) r=5 units (see the explanation)

Part 2) $(x-4)^2+(y-7)^2=25$

Part 3) The center of the circle is (-3,4) and the radius is 4 units

Part 4) see the explanation

Step-by-step explanation:

Part 1)

step 1

Find the center of circle C_1

we know that

The distance between the center and point (0,4) is equal to the radius

The distance between the center and point (4,2) is equal to the radius

Let

(x,y) ----> the coordinates of center of the circle

Remember that

The tangent y=2 (horizontal line) to the circle is perpendicular to the radius of the circle at point (4,2)

That means ----> The segment perpendicular to the tangent is a vertical line x=4

The x-coordinate of the center is x=4

The coordinates of center are (4,y)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Remember

The distance between the center (4,y) and point (0,4) is equal to the radius

The distance between the center (4,y) and point (4,2) is equal to the radius

substitute

$\sqrt{(y-4)^{2}+(4-0)^{2}}=\sqrt{(4-4)^{2}+(y-2)^{2}}$

$\sqrt{(y-4)^{2}+16}=\sqrt{(0)^{2}+(y-2)^{2}}$

squared both sides

$(y-4)^{2}+16=(y-2)^{2}$

solve for y

$y^2-8y+16+16=y^2-4y+4$

$y^2-8y+32=y^2-4y+4\\8y-4y=32-4\\4y=28\\y=7$

The coordinates of the center are (4,7)

step 2

Find the radius of circle C_1

$r=\sqrt{(y-4)^{2}+(4-0)^{2}}$

substitute the value of y

$r=\sqrt{(7-4)^{2}+(4-0)^{2}}$

$r=\sqrt{(3)^{2}+(4)^{2}}$

$r=\sqrt{25}$

$r=5\ units$

Part 2)

Find the equation of the circle C, in standard form.

we know that

The equation of a circle in standard form is

$(x-h)^2+(y-k)^2=r^2$

where

(h,k) is the center

r is the radius

substitute the given values

$(x-4)^2+(y-7)^2=5^2$

$(x-4)^2+(y-7)^2=25$

Part 3) Another circle C2 has equation x² + y2 + 6x – 8y +9=0

Find the centre and radius of C2

we have

$x^2+y^2+6x-8y+9=0$

Convert to standard form

$(x-h)^2+(y-k)^2=r^2$

where

(h,k) is the center

r is the radius

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$(x^2+6x)+(y^2-8y)=-9$

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

$(x^2+6x+9)+(y^2-8y+16)=-9+9+16$

$(x^2+6x+9)+(y^2-8y+16)=16$

Rewrite as perfect squares

$(x+3)^2+(y-4)^2=16$

$(x+3)^2+(y-4)^2=4^2$

therefore

The center of the circle is (-3,4) and the radius is 4 units

Part 4) Show that the circle C2 is a tangent to the x-axis

we know that

If the x-axis is tangent to the circle, then the equation of the tangent is y=0

The radius of the circle must be perpendicular to the tangent

That means ----> The segment perpendicular to the tangent is a vertical line The equation of the vertical line is equal to the x-coordinate of the center

x=-3

The circle C_2, intersects the x-axis at point (-3,0)

<em>Verify</em>

The distance between the center (-3,4) and point (-3,0) must be equal to the radius

Calculate the radius

$r=\sqrt{(0-4)^{2}+(-3+3)^{2}}$

$r=\sqrt{16}$

$r=4\ units$ ----> is correct

therefore

The circle C_2 is tangent to the x-axis

7 0

3 years ago

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Of five random selected students how many would you expect to vote for bill

Gennadij [26K]

Answer:

none

Step-by-step explanation:

80% of 5 is 4 meaning that the chances of someone voting for Bill are not likely at all

6 0

1 year ago

Read 2 more answers

Who is good with math like trig.??

Mnenie [13.5K]

I am good with all math from alg-calc

4 0

3 years ago

MP Persevere with Problems Suppose 20

grigory [225]

9514 1404 393

Answer:

8 people

Step-by-step explanation:

If 20 of 140 people play tennis, then in a group of 504 people, we expect ...

(20/140) × 504 = 72 . . . . tennis players

If 1 of 9 tennis players has a coach, then in a group of 72 tennis players, we expect ...

(1/9) × 72 = 8 . . . . have a coach

We expect 8 of the 504 people have a tennis coach. We made this prediction by applying the given rates to the larger group.

7 0

2 years ago

What is the probability of selection for any man in a proportionate random sample, where a sample of 100 will be drawn from a po

kolbaska11 [484]

Working Principle: Stratified Random Sampling

nx = (Nx/N)*n

where:
nx = sample size for stratum x
Nx = population size for stratum x
N = total population size
n = total sample size

Given:

Nx = 100
N = 1000
n = 0.5*(1000) = 500

Required: Probability of Man to be selected

Solution:

nx = (Nx/N)*n
nx = (100/1000)*500 = 50 men

ny = (Nx/N)*n
ny = (100/1000)*500 = 50 women

Probability of Man to be selected = nx/(nx + ny)*100 = 50/(50+50)*100 = 50%

<em>ANSWER: 50%</em>

7 0

3 years ago