a car starts off 186 miles directly south from the city of hartville. it travels due east at a speed of 48 miles per hour. after travelling 111 miles, how fast is the distance between the car and hartville changing?

3cm is the length of the third side.

Given that an obtuse triangle with area 12 has two sides of lengths 4 and 10.

To find the length of the third side, we can use the formula for the area of a triangle; Area of a triangle = 1/2 × base × height, where base and height are perpendicular to each other.

Considering 4 and 10 as the base and height of the triangle respectively, the area of the triangle will be;

Area of the triangle = 1/2 × 4 × 10Area of the triangle

= 20 cm²

But given that the area of the triangle is 12 cm².

Thus, 20 cm² = 1/2 × 4 × 10 ⇒ length of the third side = 3 cm

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The simplified algebraic expression for the perimeter of the yard is 28m+10x, and if x=3m, then the perimeter is 58m.

The simplified algebraic expression for the perimeter of the yard is 28m+10x, and if x=3m, then the perimeter is 58m.

In the given figure, the yard is in the shape of a rectangle with dimensions (4x - 6) m and (2x + 3) m. The perimeter of a rectangle is the sum of the lengths of all four sides, which can be expressed as:

Perimeter = 2(Length + Width)

Perimeter = 2(4x - 6 + 2x + 3) m

Perimeter = 2(6x - 3) m

Perimeter = 12x - 6 m

So, a simplified algebraic expression for the perimeter of the yard is 12x - 6 m.

To find the perimeter in meters when x = 3 m, substitute x = 3 into the algebraic expression for perimeter:

Perimeter = 12(3) - 6 m

Perimeter = 30 m

Therefore, the perimeter of the yard when x = 3 m is 30 meters.

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Answer:

x ≤ 55/7

Step-by-step explanation:

7x - 5 ≤ 50

7x ≤ 55

x ≤ 55/7

fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1 , ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05 are the required functional estimations of a given representations.

However, we can estimate the partial derivatives with respect to x (fv) and y (ft) at the point (40,20) using the definition of partial derivatives:

fv = ∂f/∂x ≈ (f(40+h,20) - f(40,20))/h

where h is a small increment in the x direction. Similarly,

ft = ∂f/∂y ≈ (f(40,20+k) - f(40,20))/k

where k is a small increment in the y direction.

To estimate fv(40,20) and ft(40,20), we need to choose small values of h and k and evaluate the function at the corresponding points. Let's say h = 0.1 and k = 0.05:

fv(40,20) ≈ (f(40.1,20) - f(40,20))/0.1

ft(40,20) ≈ (f(40,20.05) - f(40,20))/0.05

We can then use these estimates to approximate the value of f(40.1,20.05) using the first-order Taylor approximation:

f(40.1,20.05) ≈ f(40,20) + fv(40,20)0.1 + ft(40,20)0.05

Note that this is an approximation and may not be very accurate if the function is highly nonlinear or has discontinuities. However, it can give us a rough idea of the value of f(40,20) and how it changes with small variations in x and y.

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Answer:

x = 65° , y = 115° , z = 65°

Step-by-step explanation:

consecutive angles in a parallelogram are supplementary , then

x + 115° = 180° ( subtract 115° from both sides )

x = 65°

opposite angles in a parallelogram are congruent , then

y = 115° and z = x = 65°

Answer:

See below!

Step-by-step explanation:

So,

So,

y + x = 180°

115 + x = 180

x = 180 - 115

Again,

z = x (Opposite angles)

So,

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

Without seeing the graph, it's difficult to determine the exact solution to the system of equations. However, the point of intersection between the two lines represents a solution that satisfies both equations. To find the x-coordinate of this point, you can use algebraic methods, such as substitution or elimination, to solve for the value of x.

Answer:

[tex]744x100=7,440[/tex]

Step-by-step example

all to do this is to 744x10

and it would help if you got this simple answer I hope this helps:D

Answer:

To find the volume of a prism, you need to multiply the area of the base by the height of the prism. Here are the steps:

Identify the shape of the base of the prism. It could be a rectangle, square, triangle, hexagon, or any other polygon.

Find the area of the base of the prism. The formula for finding the area of different shapes are:

Rectangle: A = length x width

Square: A = side x side

Triangle: A = (base x height) / 2

Hexagon: A = (3 x √3 x side²) / 2 (where side is the length of one of the sides of the hexagon)

Determine the height of the prism. This is the perpendicular distance between the two parallel bases.

Multiply the area of the base by the height of the prism. The formula is:

Volume = Area of Base x Height

For example, if the base of the prism is a rectangle with length 4 cm and width 5 cm, and the height of the prism is 10 cm, the volume of the prism would be:

Volume = 4 cm x 5 cm x 10 cm

= 200 cubic cm

Therefore, the volume of the prism is 200 cubic cm.

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

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hope it helps⸙

Answer:

Step-by-step explanation:

E(lh girls) [tex]=0.2\times 320=64[/tex]

E(lh boys) [tex]=0.1 \times 250 =25[/tex]

Estimated total left handed students [tex]=64+25=89[/tex]

Answer:

x = 8

y = 12

Step-by-step explanation:

m∠A = sin⁻¹(9/15) = 36.87⁰

cos36.87 = y/15

y = 15(cos36.87) = 12

sin36.87 = 12/(12+x)

12 + x = 12/(sin36.87)

x = 12/(sin36.87) - 12 = 8

Answer: A - (-5, 43)

Step-by-step explanation:

Answer:

Range = Highest number -Lowest number

= 13-2=11

Answer:

11

Step-by-step explanation:

Highest number = 13

Lowest number = 2

Range = highest number - lowest number

Range = 13 - 2 = 11

Alien is an extraterrestrial species or a hypothetical species that lives beyond the planet Earth. They are beings from other planets that can travel in spacecraft. They are often depicted as having unique or supernatural powers that are beyond those of humans. The question given is about an alien species that leaves its planet to explore other planets. We are given the information that 120 aliens have left planet zenith over the past 3 years. We need to write an expression to model the change in aliens per year on planet zenith. We can write the following expression:Change in aliens per year = Total number of aliens left / Number of yearsThe total number of aliens left in the past 3 years is 120. Therefore,Total number of aliens left = 120Number of years = 3Substituting the values in the above expression, we get:Change in aliens per year = 120 / 3Change in aliens per year = 40 aliens per yearThe expression to model the change in aliens per year on planet zenith is 40 aliens per year. This means that 40 aliens are leaving planet zenith each year to explore other planets in the universe.

The average change in aliens per year can be calculated using the above expression. The change in aliens per year is 40 aliens. Hence, every year 40 aliens are leaving planet Zenith to explore other planets in the universe.

To model the change in aliens per year on planet Zenith, an expression can be formed from the given data. Let's look into the steps to model the change in aliens per year on planet zenith.

Step 1: We are given that 120 aliens have left planet zenith over the past 3 years.

Step 2: To find the change in aliens per year, we can divide the total number of aliens who left the planet over the past 3 years by the number of years.

Change in aliens per year = (120 aliens) / (3 years)

Step 3: Simplifying the above expression we get,Change in aliens per year = 40 aliens per year

Therefore, the expression to model the change in aliens per year on planet Zenith is 40 aliens per year. This implies that every year 40 aliens are leaving planet Zenith to explore other planets in the universe.

Evaluation: As per the given problem, 120 aliens have left planet Zenith over the past 3 years.

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The correct option is (c). A graphical method of representing the sample points of an experiment is a dot plot.

Dot plot is a graphical method of representing the sample points of an experiment. In a dot plot, each point represents an observation in the sample, and the points are placed on a number line.

A stem-and-leaf display is another graphical method of representing the sample points of an experiment. In a stem-and-leaf display, the digits in the observation are separated into two parts, with one part representing the "stem" and the other representing the "leaf."

A bar chart is a graphical method of representing data that uses bars to represent different categories or values.

A tree diagram is a graphical method of representing a series of events or outcomes.

Therefore, option (c) dot plot is the graphical method of representing the sample points of an experiment.

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Using trigonometry, we can determine that the length of the support wire is approximately 91.7 meters, by using the tangent function of the angle and solving for the hypotenuse of the right triangle formed by the tower, the support wire, and the ground.

Lori will receive a semiannual interest of $950 from the bond with a face value of $20,000 and a coupon rate of 9.5%, which will mature in 20 years.

To calculate the semiannual interest that Lori will receive from the bond, we need to use the following formula:

Semiannual interest = (Coupon rate x Face value) / 2

Substituting the given values, we get:

Semiannual interest = (9.5% x $20,000) / 2

Semiannual interest = ($1,900) / 2

Semiannual interest = $950

Therefore, Lori will receive a semiannual interest of $950 from the bond. This means that she will receive a total of $1,900 in interest every year until the bond matures in 20 years.

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Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. -1/4 can be expressed as a ratio of -1 and 4, so it is a rational number.

An irrational number cannot be stated using fractions, whereas a rational number can be expressed as the ratio of two integers with the denominator not equal to zero. Irrational numbers are non-terminating and non-recurring, whereas rational numbers have terminating digits.

Rational numbers contain the integer 0. It is not illogical to think that 0 is a number.

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So, the correct option is: The median is the best measure of center because there are outliers present.

A line plot is a type of graph that is used to display data along a number line. In a line plot, each data point is represented by a dot or mark placed above the corresponding value on the number line. Line plots are commonly used to represent small to moderate-sized data sets, especially those with discrete values or categories. The line plot typically consists of a horizontal line, called the axis, representing the numerical values of the data, with marks or dots above the line indicating the frequency or count of each value in the data set. Each mark or dot is placed directly above the value on the number line that it represents.

Here,

Since the data in the graph is skewed to the right, there are outliers present. Outliers are data points that are significantly different from the other values in the data set. Therefore, the median is the most appropriate measure of center to represent the data in the graph because it is less affected by outliers compared to the mean.

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Answer: the train got a head start

Step-by-step explanation:

the train got a head start