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Directions: Graph these in one cartesian plane(clue: it would form a triangle)​

The population of the small city in the year 2020 using the given growth rate is; 51600 people

We are given that;

Population of the small city in the year 2010 = 36000

Population in the year 2015 = 43800

Now, we are told that the growth rate occurs at the same rate per year. Thus;

Population change from 2010 to 2015 = 43800 - 36000 = 7800

Thus, the population increases by 7800/5 = 1560 people each year.

General form of exponential function is; y = bˣ

where b is rate of growth while x is number of years

But here we will use sequence to get;

y(10) = 1560 * 10 = 15600

Thus;

Population in 2020 = 36000 + 15600 = 51600 people

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Answer the answer is 12 units:

Step-by-step explanation:

Since it is a right triangle, we can use the Pythagorean Theorem. This one states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse. In algebraic notation:

So, in this case, we have:

Therefore, the measure of the other leg rounded to the nearest hundredth is 11.49 centimeters.

Answer: 2.5, 5.4

Step-by-step explanation:

[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]

A system of linear equations that has the ordered pair of (-2,8) as it's solution is Oy - 2x = 12 and x - 2y.

calculation:-

x = -2

for 2y - 4x = 24 plug in x = -2

2y + 8 = 24

Subtract 8 from both sides

2y + 8 - 8 = 24 - 8

2y = 16

divide both sides by 2

2y/2 = 16/2

y = 8

Therefore, the solution to the system of linear equations is:

(x, y) = (-2, 8).

A non-linear equation is such that it does not form a straight line. It looks like a curve in a graph and has a variable slope value. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y. The graph of a linear equation always forms a straight line. The definition of a linear equation is an algebraic equation in which each term has an exponent of 1.

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Answer:

The answer is B.

Step-by-step explanation:

The circle is filled in so we know the answer cannot be A. All the numbers after 4 are greater than or equal to 4. The arrowing is pointing toward the numbers after 4.

Statement Reason

WXYZ is a parallelogram Given

WX || ZY and WZ || XY Definition of a parallelogram

∠ZYW ≅ ∠XWY Alternate interior angles

WX ≅ YZ Definition of a parallelogram

WY ≅ WY Reflexive property of congruence

ΔWXY ≅ ΔZYW SAS

∠X ≅ ∠Z CPCTC

Considering the linear equation in slope-intercept form:

The y-intercept of the line is the constant of the equation, in this case, the y-intercept is -1.

The slope of the line corresponds to the coefficient of the x-term, i.e. the value that multiplies x. For this line, the slope is equal to 11.2

Answer:

so? what is your question here?

Step-by-step explanation:

To find the equation of the line, we will use the formula:

y=mx + b

The formula for calculating the slope is given as :

Given:

The total = 846.

The number of hot dogs sold at Tuesday night = 150.

Required:

We need to find the approximate probability of a person buying a hot dog and going to a Tuesday night game.

Explanation:

The total possible outcomes = 846.

Let A be the given event.

The favourable outcomes = The number of hot dogs sold at Tuesday night = 150.

The approximate probability of a person buying a hot dog and going to a Tuesday night game.

Final answer:

Explanation

Step 1

to find the answer just replace the values for x and y

for x=3 and y =4

I hope this helps you

well, we know it's a rectangle with two removed semicircle's, hmmm hold on!! two semicircles make together a whole circle, well, let's remake that circle and put it inside the rectangle, then, let's subtract that area from that of the rectangle's, Check the picture below.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(16)(4)}~~ - ~~\stackrel{circle}{\pi (2)^2} }\implies 64~~ - ~~4\pi ~~ \approx ~~ \text{\LARGE 51.4}[/tex]

The smallest value of x is 2 for which these three numbers 2, 60, and 240 have an LCM of 240.

LCM of two or more than two given numbers is the smallest common multiple that is divisible by two or more than two given numbers.

Given, Are three numbers x, 60, and 240 of which x is unknown.

The lowest common multiple of these three numbers will be when x is the smallest.

Let x be 2 therefore the numbers are now, 2, 60, and 240.

And LCM of 2, 60, and 240 is 240 as it is the smallest number that is divisible by all these three numbers.

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A system of equations is simply a collection of equations that can be dependent, independent, consistent, or inconsistent.

2x + y = 8x - 2y = -6 is x,y = 2,4

Given equation,

2x + y = 8x - 2y = -6

x,y = 2,4

[1]    2x + y = 8

[2]    x - 2y = -6

Solve [2] for the variable  x

[2]    x = 2y - 6

Plug this in for variable  x  in [1]

[1]    2•(2y-6) + y = 8

[1]    5y = 20

Solve [1] for the variable  y

[1]    5y = 20

[1]    y = 4

By now we know this much

x = 2y-6

y = 4

Use the  y  value to solve for  x

x = 2(4) -6 = 2

Hence, {x,y} = {2,4}

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The number of wild bears the naturalist can relocate per month is 2 wild bears.

Number of wild bears relocated by the naturalist = 12 wild bears

Time taken by the naturalist to relocate these wild bears = 6 months

Thus the number of bears the naturalist can relocate in 1 month can be found out by using unitary method

This implies that the number of bears relocated by the naturalist in 1 month or per month = 12 / 6 = 2 wild bears

Thus the number of wild bears the naturalist can relocate per month is 2 wild bears .

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By the concept of unitary method, she will take 20 hours to complete a video as definition of unitary method says "The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value".

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel. The unitary method refers to the process of determining the value of a single unit from the values of several other units and using that value to determine the value of the necessary number of units.

Here,

As she takes 4 hours to edit a 3 minute video,

by unitary method,

so she take 4/3 hour to edit a 1 minute video.

To edit a 15 minute video,

she will take 15*4/3 hours.

=20 hours

As stated in the definition of the unitary method, "the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value," it will take her 20 hours to complete a video using this method.

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Answer: -42g-29

Step-by-step explanation:

-6(8g+4)    -5+6g

-48g-24 -5+6g

-48g+6g=-42g

-24-5=-29

The slope of the line that passes through the points (10,6) and (6,6) is 0.

The Slope of a line can be described as a change in the y coordinate with respect to the x coordinate.

Formula to find the slope of the line that passes through the points [tex](x1,y1)[/tex] and [tex](x2,y2)[/tex] is

                             [tex]m= (y2-y1)/(x2-x1)[/tex]

                          where, m=slope

As per the given problem, let us consider

                                [tex](x1,y1)=(10,6)[/tex]

                                [tex](x2,y2)=(6,6)[/tex]

Substitute the given values such as [tex]x1=10,x2=6,y1=6,y2=6[/tex] in the formula,

                             [tex]m=(6-6)/(6-10)\\m=0/(-4)\\m=0[/tex]

Therefore, the slope of the line that passes through the points (10,6) and (6,6) is o.

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A polygon is a plane figure characterized by a finite number of straight-line segments joined to form a closed polygonal chain in geometry.

A polygon is a plane figure characterized by a finite number of straight-line segments joined to form a closed polygonal chain in geometry. A polygon is defined as a bounded plane region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.

Given coordinates are,

J(-3, 1), K(0, 3), L(4, -1), M(1, -3); y = -2

Plot all the points on a coordinate geometry in a sequence we will get the polygon of four sides.

The image of the constructed polygon with all its coordinates is attached with the answer below.

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Hello

To solve this question, i will use quadratic formula; however, there are other methods we can use to solve this question.

Step 1

Collect like terms

A standard quadratic equation can be represented as

The quadratic equation is given as

Therefore,

From the calculations above, the value of x is either 3.3 or -0.3

Answer:

135 feet

Step-by-step explanation:

you divide 540÷4 to get the answer

In order to determine the initial investment, use the following formula for the composed interest:

where:

P: initial investment = ?

r: interest rate = 6% = 0.06

n: number of times per time period = 6

t: time period = 5 x 2 = 10

I: final account = 35,000

replace the previous values of the parameters and solve for P, as follow:

Hence, the initial investment was 19,273.13

The numbers are 82 and 48

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Let x represent the first number and y represent the second number.

Equation 1, sum of the numbers:

x + y = 130

Equation 2, difference of the numbers:

x - y = 34

Using the elimination method system of equations to solve:

 x  +  y  =  130

 x  -   y  =  34

-------------------

Add the two equations to eliminate the y term leaving:

2x = 164

Divide both sides by 2:

x = 82

Find y from first equation: x  +  y  =  130

substituting 82 for x in the equation

82 + y = 130

Subtract 82 from both sides:

y = 48

The two numbers in the system of equation are 82 and 48.

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ANSWER

Options: II and IV

EXPLANATION

Mean: Is the sum of data values divided by the total number of data values

Deviation: Is the difference between an individual data item and the set's mean.

Absolute value: Is the distance (a positive quantity) between any two points on a number line.

Variability: This relates to how dispersed (or clustered) the values in a data set are. High variability indicates that the data is dispersed. Low variability indicates that the data is grouped together (close together).

MAD: Is the average distance between each data value and the mean is the Mean Absolute Deviation (MAD) of a set of data. The higher the MAD, the more data variability there is (the data is more spread out).

Hence, II and IV are most likely to have the greatest number of values in common because they both have higher MAD (8) meaning that they have more data variability (their data is more spread out) compared to I and III which have MADs equal 4 and 2 respectively.

The given information is:

Andrea is 108 miles away from Destiny.

Destiny travels 9 mph faster than Andrea.

They meet after 4 hours.

Let's convert that information into equations:

Let's call x the distance that Destiny travels to find Andrea and y the distance Andrea travels to find Destiny, then:

If they meet after 4 hours, the equation for the distance Destiny traveled is:

But the problem also says that Destiny travels 9 mph faster than Andrea, then let's call z the mph that Andrea is traveling, thus:

And the equation for the distance Andrea traveled is:

Then you have a system of 3 equations and 3 variables.

Let's solve it to find how fast each was traveling.

From equation 3 you know that y=4z. You can replace the y-value into equation 1, you will obtain:

Next, you can solve for x in terms of z, from equation 4:

Replace the x-value into equation 2 and solve for z:

Then if z=18 mph, this is how fast Andrea is traveling.

And Destiny travels 9 mph faster than Andrea, then Destiny travels at (z+9)=18+9=27 mph

Given the function:

The graph is attached below:

• The period of the function, T = π-(-2π)=3π.

Thus, the function has been graphed to show at least one full period, the x and y-axes are also clearly labeled above.

Answer: smallest area- 56.25cm2      largest area- 70.56cm2

Given that:

and we are given that:

we can say that:

adjacent = 7, hypothenus = 8

And we can apply the Pythagorean theorem which is:

Thus, we have that: