How many solutions does the following system of equations have?

2x - Y=3
-4x + 2y=5

The radius of the full-size pool is 2 times greater than the radius of kiddie pool

The formula for determining the area of a circle is expressed mathematically as;

Area = πr²

Where;

From the information given, we have that;

Radius = √A/3

Where;

A is the radius of the circle

For the circular kiddie, we have;

Radius = √28/3

Find the ratio

Radius = √9. 3

Find the square root

Radius = 3 feet

For the circular pool

Radius = √ 113/3

Find the ratio

Radius = √37. 66

Find the square root

Radius = 6 feet

We then have;

Radius of the pool/radius of the kiddie pool

6/3

Find the quotient

2

Hence, the value is 2

Learn more about radius here:

https://brainly.com/question/20489969

#SPJ1

Reflection across the y axis the y coordinate values remains the same but the x coordinates value changes sign. For example

Therefore,

Set D has an error.

If the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6

The equation is

y = -x

The slope intercept form

y = mx+b

Where m is the slope of the line

Comparing the slope intercept form and the given equation

Slope of the line m = -1

The line is passing through the points (-8,2)

The point slope form of the line

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute the values in the equation

y-2 = -1(x-(-8))

y-2 = -1(x+8)

y-2 = -x-8

y = -x-8+2

y = -x-6

Hence, if the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6

Learn more about slope intercept form here

brainly.com/question/9682526

#SPJ1

Answer:

y = -x + 1

Step-by-step explanation:

y =mx + b

It is crossing the y axis at 1 that is the b

The slope (m) is -1.  From one point on the line to another you go down 1 and left 1.  That represents a negative slope of 1

The values of the angle x in the line segments is 40 degrees.

When parallel lines are are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.

Therefore, the line FG is parallel to line HI. The line segment BC and AD are the transversal lines that cut across the parallel lines FG and HI.

Therefore,

3x + 20 + x = 180 (Same interior angles)

Same interior angles are supplementary.  That is the angles sum up to 180 degrees.

Therefore,

3x + 20 + x = 180

4x + 20 = 180

4x = 160

divide both sides by 4

x = 160 / 4

x = 40 degrees

learn more on angles here: https://brainly.com/question/13873168

#SPJ1

Answer:

154 feet squared

Step-by-step explanation:

1. Divide 14 by 2

2. Use the equation pie times radius squared

3. Answer is 153 foot squared

The solution set of real numbers that are 3 units from -2 is :

|x +2| = 3

Here

Function : |x +2| = 3

since ,

|x +2| = 3 => x + 2 = 3 ∨ x + 2 = -3

x = 3 - 2 ∨ x = -3 - 2

x = 1 ∨ x = -5

| - 2 - 1 | = | -3| = 3

| -2 -(-5) | = | -2 + 5 | = 3.

To learn more about solution set refer to :

https://brainly.com/question/10588366

#SPJ13

Answer:

I think the answer is 0.

Step-by-step explanation:

-0.6,-0.5,-0.4,-0.3,-0.2,-0.1,0,0.1,0.2,0.3,0.4

ANSWER

EXPLANATION

We want to find the expression that best represents the measure of the interior angle of a regular polygon with n sides.

The general formula for finding the total angle in a regular n sided polygon is given as:

Therefore, to find the measure of each interior angle of the polygon, we have to divide the total angle by the number of sides.

That is:

Hence, that is the expression that best represents the measure in degrees of the interior angle of a regular polygon having n sides.

Answer:

[tex]6x - \frac{3}{X^2} + 2[/tex]

Step-by-step explanation:

Hope this is correct and helps you! :))

Answer:

I got you, the answer is c+32.

Step-by-step explanation:

Hope this helps. Please mark branliest if right.

Answer:

Step-by-step explanation:

The time interval of interest is 6 hours

There is an average of 18 trains per 24 hours or 18/(24/6)=49/12 trains per 6 hours.

The probability can be found using the Poisson distribution with parameter

λ=49/12

Using the law of cosines, the length of BC in the given quadrilateral is: 8.1 cm.

The law of cosines that can be used to find the length of a side of a triangle with a known included angle and two sides is:

c² = a² + b² - 2 × a × b × Cos C.

Considering right triangle ABD,

BD = a

DC = b

BC = c

Use the Pythagorean theorem to find the length of BD in the quadrilateral as shown in the diagram:

BD = √(7.5² + 5²)

BD = √(7.5² + 5²)

BD = 9.0 cm

Use the law of cosines to find the length of BC:

BC² = BD² + DC² - 2 × BD × DC × Cos <BDC.

Substitute

BC² = 9.0² + 13² - 2 × 9.0 × 13 × Cos 38

BC² = 250 - 184.4

BC² = 65.6

BC = √65.6

BC = 8.1 cm

Learn more about the law of cosines on:

https://brainly.com/question/4372174

#SPJ1

Answer: g/15 = 3 ; g = 45 gifts.

Step-by-step explanation: You would basically have to multiply 15 by 3, and it equal 45. This answer choice shows an equation that will make the answer 45, so it is right.

g/15 will equal 3.

Then, you would break them apart and do the denominator (15) multiplied by the numerator (3).

This will get you the answer 45.

So, you will get the answer choice A.

The Sarah's path and Marcus path will intersect at the point  (5,4) .

In the question ,

it is given that

the park is modeled by the equation y = x − 1  .

On comparing with the slope intercept form ,

we get

the slope as 1 .

Since both the paths are perpendicular ,

the slope for Marcus path is -1 .

hence the equation of line with slope -1 and passing through the point (0,9) is y = (-1)x + c

9 = (-1)0 + c

9 = c

so equation is y = (-1)x + 9

So to find the point of intersection , we solve both the equations .

Substituting y = x − 1 in y = (-1)x + 9 ,

we get

x − 1 = (-1)x + 9

x - 1 = -x + 9

x + x = 9 + 1

2x = 10

x = 5

So, y = 5 - 1 = 4

the point of intersection is (5,4) .

Therefore , The Sarah's path and Marcus path will intersect at the point  (5,4) .

Learn more about Equations here

https://brainly.com/question/19700463

#SPJ1

Answer:x=    1/4=0.250

Step-by-step explanation:

Answer:

[tex]y=-\dfrac{2}{3}x+490[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]2x + 3y = 1470[/tex]

To change the equation to slope-intercept form, isolate y:

[tex]\implies 2x + 3y -2x=1470 -2x[/tex]

[tex]\implies 3y=-2x+1470[/tex]

[tex]\implies \dfrac{3y}{3}=\dfrac{-2x+1470}{3}[/tex]

[tex]\implies y=-\dfrac{2}{3}x+\dfrac{1470}{3}[/tex]

[tex]\implies y=-\dfrac{2}{3}x+490[/tex]

Therefore:

To graph this line with the slope-intercept method:

To write the equation in function notation, replace the y-variable for f(x).

[tex]\implies f(x)=-\dfrac{2}{3}x+490[/tex]

The graph of the function represents:

The y-intercept of the graph is (0, 490).

To find the x-intercept, set the function to zero and solve for x:

[tex]\implies -\dfrac{2}{3}x+490=0[/tex]

[tex]\implies -\dfrac{2}{3}x=-490[/tex]

[tex]\implies -2x=-1470[/tex]

[tex]\implies x=735[/tex]

Therefore, the x-intercept is (735, 0).

The graph of the function is attached.

If Sal's total profit on lunch specials for the next month is $1,593 (where the profit amounts are the same) the equation would be 2x + 3y = 1593 and the function would be:

[tex]g(x)= -\dfrac{2}{3}x+531[/tex]

As the coefficient of the x-variable has not changed, the slopes of the two functions are the same.

As the total profit has changed, the intercepts are different.

The y-intercept of the first function is (0, 490) and its x-intercept is (735, 0).  Whereas the y-intercept of the second function is (0, 531) and its x-intercept is (796.5, 0).

Answer:

x = 7

Step-by-step explanation:

If the two equations are x - y = 11 and -x + y = -11 then the system has  infinitely many solutions.

Let the two equations be

x - y = 11 ..................(1)

-x + y = -11  ..................(2)

Express the first equation in the term of x and substitute it into the second equation:

From (1) and (2), we get

-(y + 11) + y = -11

simplifying the above equation, we get

-y - 11 + y = -11

-y + y = 11 - 11

0 = 0

So, the system has infinitely many solutions.

Therefore, the correct answer is option c. infinitely many solutions.

To learn more about infinite solutions refer to:

https://brainly.com/question/27927692

#SPJ13

Using trigonometry, it is found that:

1. Graph 2 shows an angle in which cos(θ) = -8/17 and sin (θ) is negative.

2. The angles are θ = 157.38º and θ = 202.62º, as shown in Graph 1.

3. Graph 3 shows an angle of θ = 315º.

In item 1, it asks for an angle in which both the sine and the cosine of the angle are negative. This happens in the third quadrant, hence Graph 2 shows an angle in which cos(θ) = -8/17 and sin (θ) is negative.

The secant of an angle is given by one divided by the cosine of the angle, that is:

sec(θ) = 1/cos(θ)

Considering the numeric value of the secant in this problem, we have that:

-13/12 = 1/cos(θ)

-13cos(θ) = 12

cos(θ) = -12/13

The cosine is negative in the second and the third quadrant, hence graph 1 shows these equivalent angles.

Applying the inverse cosine, the angles are given as follows:

θ = arccos(-12/13)

θ = 157.38º and θ = 202.62º. (two equivalent angles).

An angle of 315º is on the fourth quadrant of the unit circle, hence Graph 3 shows this angle.

More can be learned about trigonometry at https://brainly.com/question/24349828

#SPJ1

The amount that must be deposited to get a final amount of
$ 125,000 is $ 26.34 .

What is compound interest and how is it calculated?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Mathematically, A = P (1 + (R/n))^t

Given, the amount that will be developed after interest is laid
= A = $125,00
Also, number of years for which amount is loaned = n = 16 years
Annual Percentage Rate of the loan availed = R = 7.3
Frequency with which interest is paid out per year = 1
Following the formula established in the literature, we have:
125000 = P(1 + 7.3)⁴ ⇒ P = 125000/(1 + 7.3)⁴ ⇒ P = 125000/8.3⁴ = 26.34
Therefore, the amount that must be deposited to get a final amount of
$ 125,000 is $ 26.34 .

To learn more about this, tap on the link below:
https://brainly.com/question/24924853

#SPJ13

Answer:  The correct answer is x=18 and y=59

Step-by-step explanation:

Opposite angles are congruent:

(6x+13) = (7x-5)

Solve for x:

6x+13−7x=7x−5−7x

−x+13−13=−5−13

−x=−18

x=18

Plug x value in for y:

Y=180-(7x-5)

Y=180-(126-5)

Y=180-121

Y=59

The measure of the numbered angles formed by the common transversal to the two parallel lines are;

[tex] \angle 1 = 113^{ \circ} [/tex]

[tex] \angle 2 = 67^{ \circ} [/tex]

[tex] \angle 3 = 67^{ \circ}[/tex]

[tex]\angle 4 = 113^{ \circ} [/tex]

The relationships between the angles are;

The given angle is 113°

According to corresponding angles theorem, we have;

[tex] \angle 1 = 113^{ \circ} [/tex]

[tex]\angle 1 \: and \: \angle 4 [/tex] are vertical angles

According to vertical angles theorem, we have;

[tex]\angle 1 = \angle 4 = 113^{ \circ} [/tex]

[tex] \angle 3 \: and \: 113^{ \circ} [/tex] are same side exterior angles.

According to same side exterior angles theorem, we have;

[tex] \angle 3 \: and \: 113^{ \circ} [/tex] are supplementary angles. Which gives;

[tex] \angle 3 + 113^{ \circ} = 180^{ \circ} [/tex]

[tex] \angle 3 = 180^{ \circ} - 113^{ \circ} = 67^{ \circ}[/tex]

[tex] \angle 2 \: and \: \angle 3 [/tex] are vertical angles, which gives;

[tex] \angle 2 = \angle 3 [/tex] = 67°

Learn more about the angles formed by two parallel lines that have a common transversal here:

https://brainly.com/question/1751268

#SPJ1

A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

Bean advertised footwear on 29 of its 192 catalog pages.

we randomly survey 20 pages

the random variable X is

X = The number of pages that advertise footwear

It is given that 20 pages have been surveyed

so, X = 1, 2, 3.....20

The average value for binomial distribution can be calculated as follows

μ = np

= 20 (29/192)

= 580/192

=3.02

On average 3.02 pages expect to advertise footwear on them

Therefore, A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

To learn more about probability refer here

https://brainly.com/question/251701

#SPJ1

4x^4-10x^3-15x^2+27x

(use foiling)

<EOG =90° AS INDICATED IN THE DIAGRAM

<EOF+<FOG=<EOG(THEY MAKE THE ANGLE)

[tex]27 + 3y = 90 \\ 3y = 90 - 27 \\ 3y = 63 \\ \frac{3y}{3} = \frac{63}{3} \\ y= 21[/tex]

<AOB =180°( STRAIGHT LINE )

<AOE+EOF+<FOG+<GOB=<AOB(THWY MAKE THE ANGLE)

[tex]x + 27 + 3(21) + 8x + 18 = 180[/tex]

[tex]x + 27 + 63 + 8x + 18 = 180 \\ x + 8x + 27 + 63 + 18 = 180 \\ 9x - + 108 = 180 \\ 9x = 180 - 108 \\ 9x =72 \\ \frac{9x}{9} = \frac{72}{8} \\ x = 9[/tex]

ATTACHED IS THE SOLUTION

The beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.

Given that, a lighthouse is located on a small island 4 km away from the nearest point P.

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

[tex]\frac{d\theta}{dt}[/tex] = 6 rev/min

= 6π rad/min

tan θ = x/6

[tex]\frac{d}{dt}tan\theta=\frac{d}{dt}(\frac{x}{6} )[/tex]

[tex]sec^2\frac{d\theta}{dt} = \frac{1}{6}(\frac{dx}{dt} )[/tex]

[tex]\frac{dx}{dt}=6sec^2\theta\frac{d\theta}{dt}[/tex]

At x=1 km; tan θ= x/6 = 1/6

[tex]sec^2 \theta= 1+tan^2 \theta= 1 + (\frac{1}{6})^2[/tex]

[tex]sec^2 \theta = \frac{10}{9}[/tex]

[tex]\frac{dx}{dt} = 6 sec^2\theta \frac{d\theta}{dt}[/tex]

dx/dt = 6 × 10/9 × 6π

dx/dt = 125.66 km/min

Therefore, the beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.

To learn more about the differentiation of an equations visit:

https://brainly.com/question/25731911.

#SPJ1