a) 3y = 43 + x

b) 8y + 5x = 61

Using proportions, it is found that the coordinates of point C are given as follows: C(-7, -2).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Point C divides the line segment OP into the ratio 3:5, hence the following equation is used to relate the points:

[tex]C - O = \frac{3}{8}(P - O)[/tex]

Then, for the x-coordinate:

[tex]x + 10 = \frac{3}{8}(-2 + 10)[/tex]

x + 10 = 3

x = -7

For the y-coordinate:

[tex]y + 8 = \frac{3}{8}(8 + 8)[/tex]

y + 8 = 6

y = -2

The coordinates of point C are given as follows: C(-7, -2).

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Answer:

6.4%

Step-by-step explanation:

percentage decrease= decrease/actually amount×100

2.35-2.20/2.35×100

0.15/2.35×100

0.06383×100=6.4%

Percentage decrease=6.4%

Answer:

A.

Step-by-step explanation:

I just typed it in the calculator graph and scrolled down past the errors

Answer:

y = 2x + 5

Step-by-step explanation:

Here we have the two points as (x1=1, y1=7) and (x2 = -3, y2 = -1)

Slope of this line = (y2-y1)/(x2-x1) = (-1 -7)/(-3 - 1)  = 8/4 = 2

Using slope intercept form of y = mx + c

we get y = 2 x + c

Substituing the coordinates (1,7) in this equation gives us

7 = 2.1 + c or c =5

hence y = 2x + 5

Check

if x = -3 then y = (-2)(-3) + 5 = -6 + 5 = -1 which satisfies the coordinates for the second point

Answer:

Step-by-step explanation:

slope is rise over run  2/5,  and it's positive b/c the line goes up hill.

when X =0  then the line is at -6

y = (2/5)X - 6

slope = 2/5

y intercept is -6

Answer:

2.546cm

Step-by-step explanation:

formular for calculating the circumference of a circle is = πd

where π = 3.142

d = diameter

from the question,

C= πd

8=3.142×d

8= 3.142d

dividing bothsides by 3.142

8/3.142= 3.142f/3.142

d = 8/3.142

d = 2.546cm

Answer:

The median of the data set:

6, 15, 30, 45, 47, 49

The middle numbers are 30 and 45 so

You have to do 30 + 45

= 75

Then do 75 ÷ 2

= 37.5

The mean of the data set:

47, 15, 6, 49, 45, 30 (add them all)

= 192

Then divide 192 by 6 (because there are 6 numbers)

192 ÷ 6

= 32

So the median is 37.5 and the mean is 32.

Step-by-step explanation:

Hope this helps!

From your neighborhood softie :)

Answer:

x^2 + y^2 = 9

Step-by-step explanation:

The equation of a circle is (x^2) -a)^2 + (x^2) - b)^2 = r^2, where a and b are the center of the circle. Because the center of the circle is (0,0), it'll just be x^2+y^2 for one half of the equation. If the circle passes through (-3,0), that would mean the radius of the circle is 3. r^2 is 3^2, which is 9, so the equation of the circle is x^2 + y^2=9. Hope this helps!

The equation of the circle is x² + y² = 9

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the point be represented as A ( -3 , 0 )

Now , the center of the circle = O ( 0 , 0 )

And , standard form of a circle is

( x - h )² + ( y - k )² = r²

where In this case, we know that the circle passes through the point (-3, 0) and is centered at the origin (0, 0). Therefore, the radius of the circle is the distance from the origin to (-3, 0), which is:

r = √((-3 - 0)² + (0 - 0)²) = √(9)

r = 3 units

So the equation of the circle in standard form is:

(x - 0)² + (y - 0)² = 3²

On simplifying , we get

x² + y² = 9

Hence , the equation in standard form for the circle passing through (-3,0) centered at the origin is x² + y² = 9

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The coordinates of the point B are given as (2, - 4)

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

Under a reflection in the y- axis

A point (x, y) → (- x, y), hence

A(- 2, - 4) → B(2, - 4)

Therefore the coordinates of the point B are given as (2, - 4)

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Answer:

Therefore the ration 5 : 9 is equal to 10 : 18 , 15.27 and so on

Step-by-step explanation:

Answer:

60 months

Step-by-step explanation:

20 000 =  5000 + 250 m

20 000  -  5000   = 250 m

(15 000) / 250 = m = 60 months

Answer:

It would take roughly four months

Step-by-step explanation:

month one: 5,250

month two: 10,500

month three: 15,750

month four: 21,000

Answer:

[tex]\boxed{\bf \angle B = 58^{o}}[/tex]

Step-by-step explanation:

The cyclic quadrilateral sum of the opposite angle is 180°. From the given figure....

[tex]\bf \angle B + \angle D= {180}^{o} [/tex]

Where....

~[tex]\bf \angle B = 3x+7[/tex]

~[tex]\bf \angle D = 6x+20[/tex]

Now, that we found x, let's find angle B....

[tex]\sf Therefore, \: \boxed{\sf \angle B = 58^{o}}[/tex]

Answer:

5 eggs

Step-by-step explanation:

1x1000=1000g

3eggs : 600g

x eggs : 1000g

1000/600=5/3

5/3 x 3=5

Answer:

52

Step-by-step explanation:

Answer:

52 cubic units

Step-by-step explanation:

so first, you would do the top rectangle

2 x 4 = 8

then the one below

4 x 2 = 8

times the hight now

8 x 3 = 24

now the bottom

4 x 5 = 20

add them all up

8 + 24 + 20 =

32 + 20 =

52

Answer:

5.236 units

Step-by-step explanation:

The relation between r, θ and arc length ( l ) is,

l = rθ

l = 1 * 5π / 3

( The value of π = 3.14 approximately )

5π = 5 x 3.14 = 15.7

l = 1 * 5π / 3

= 5π / 3

= 15.7/3

l = 5.236 units

Note : -

Arc length is denoted by " l ".

Answer:

7/30

Step-by-step explanation:

First we subtract. 3/5-1/4 is 12/20-5/20=7/20. Then we multiply 2/3 with 7/20.

7/20*2/3=14/60 or 7/30

We can evaluate the mean, median, standard deviation and many other statistical measures from the stem-leaf table.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

From the stem leaf table, we can find different statistical measures.

From the picture attached, we can find different data

The minimum value  = 12

The maximum value = 49

Total number of observation = 30

The sum of the all data = 986

Mean of the data = 986/30 = 32.87

Median of the data = 34.5

Standard deviation = 11.24

Variance = 126.4

Thus, we can evaluate the mean, median, standard deviation and many other statistical measures from the stem-leaf table.

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Answer:

B (4-x = x-4)

Step-by-step explanation:

both the x-intercepts are (4,0)

Answer:

x>-1

Step-by-step explanation:

divide 3 on both sides

The length of the fish caught that is equal to the lower quartile in the given box plot is: 10 inches.

The lower quartile (Q1) of a data is indicated on a box plot as the value at the beginning of the edge of the rectangular box.

The value at the beginning of the edge of the rectangular box in the box plot is 10.

Therefore, the length that is equal to the lower quartile is: 10 inches.

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Answer: the answer is D or for some people that have theres fliped its 10 inches

If she paddles directly to Kono's then the minimum time for the lunch will be 3.9 hours.

It is the study of the motion of a body without considering mass. And the reason behind them is neglected.

Brooke is located 5 miles out from the nearest point A along a straight shoreline in her sea kayak.

Hunger strikes and she wants to make it to Kono's for lunch; see picture.

Brooke can paddle at 7 mph and walk at 14 mph.

Distance from Brooke to shore will be

→ √(5² + x²)

Then the time will be

[tex]t_1 = \dfrac{\sqrt{5^2 + x^2}}{2}[/tex]

Then the distance from shore to Kono's will be

→ 6 - x

Then the time will be

t₂ = (6 - x) / 4

Then the total time will be

t  = t₁ + t₂

Then we have

[tex]t = \dfrac{\sqrt{5^2 +X^2}}{2} + \dfrac{6-x}{4}\\[/tex]

t = 1/4[2√(5² + x²) + 6 - x]

If she paddles directly to point A will be

t = 1/4[2√(5² + 0²) + 6 - 0]

t = 1/4 (10 + 6)

t = 16 /4

t = 4 hr

If she paddles directly to Kono's, then we have x = 6. Then the time will be

t = 1/4[2√(5² + 6²) + 6 - 6]

t = 1/4[2√61]

t = 3.9 hr

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Answer:

V≈217.82

Step-by-step explanation:

I'm pretty sure

Answer:

(f - g)(x) = x - 6

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

= [3x - 2] - [2x + 4]

= 3x - 2 - 2x - 4

= x - 6

(f - g)(x) = x - 6

Answer:

the answer to this question is 19

Answer: m=19

Step-by-step explanation:

First you cross multiply the two fractions. So you get 9*m = 57*3.

When you put 57*3 in a calculator you get 171. So the equation is 9m=171 and then to isolate the x you divide by 9. So when you put 171/9 in a calculator you get 19. So the correct answer is C. 19.

Answer:

By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232Step-by-step explanation:The Empirical Rule states that, for a normally distributed random variable:68% of the measures are within 1 standard deviation of the mean.95% of the measures are within 2 standard deviation of the mean.99.7% of the measures are within 3 standard deviations of the mean.In this problem, we have that:Mean = 190Standard deviation = 14Using the empirical rule, what percentage of the games that Aubree bowls does she score between 148 and 232?148 = 190 - 3*14So 148 is 3 standard deviations below the mean.232 = 190 + 3*14So 232 is 3 standard deviations above the meanBy the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232

Answer:

The price of other chair is $3841.25

Step-by-step explanation:

Step 1: Write equations.

First equation: The price of one type of chair is three times the price of the other.

Let x be the price of one type of chair and y the price of the other type of chair.

[tex]x = 3y[/tex]

Second equation: The total price for both is $15365

[tex]x + y = 15365[/tex]

Step 2: Solve the system of equations.

1) [tex]x = 3y[/tex]

2) [tex]x + y = 15365[/tex]

Substitute x in the second equation with x from first.

[tex]x + y = 15365\\(3y) + y = 15365[/tex]

Now solve for y (y is the price of the other chair).

[tex]4y = 15365\\y = \frac{15365}{4}\\y = \$3841.25[/tex]

The potential problems with Antonia's simulation is that she over simulated the situation and her conclusion has the misleading data.

The potential problems is the simulation or method to analysis what is gone wrong in a particular program.

She sets her chess computer program to play 100 first moves in the game of chess. In this simulation, she only focuses on first move and overstimulated the situation.

Antonia concludes that of the 20 possible opening moves in chess, most players will move the pawn piece in front of the queen forward two spaces.

In this conclusion she has misleading data as each player has different strategy.

Thus, the potential problems with Antonia's simulation is that she over simulated the situation and her conclusion has the misleading data.

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Answer:

we know,

Volume of cylinder = Base area × height

1500= 100×h

so, Height h = 15 cm