Can the range of a function be written like this {6,7,8,10} instead of like this $6\leq x\leq 10$ ?

Answers

Answer 1

Answer:

No unless x is being used to define only elements of an integer set.

Step-by-step explanation:

No, not in general unless x is defined as a integer or a subset of the integers like the naturals, whole numbers....

Usually 6<=x<=10 means all real numbers between 6 and 10, inclusive. This means example that 6.6 or 2pi are in this set with infinitely other numbers that I can't name.

{6,7,8,9,10} just means the set containing the numbers 6,7,8,9,10 and that's only those 5 numbers.

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You have been saving dimes for long time and take all of them to the bank to exchange for dollar bills. the teller weighs the dimes and records a total mass of 3358 g. of a dime has an average mass of 2:30g. how much money are you owed? chemistry

Answers

Since 2:30 gm so 1 dime is 15 grams . So if we divide the total mass/ individual mass = 3358/15 =223.866 approx 224 dimes.

Which polygons have at least one pair of parallel sides but are not parallelograms? Choose all that apply.

Answers

The correct option is polygon E.

What are polygons?

A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

Given that, Which polygons have at least one pair of parallel sides but are not parallelograms,

Such polygons are called trapezoid.

A trapezoid, also known as a trapezium, is a flat-closed shape having 4 straight sides, with one pair of parallel sides.

Hence, the correct polygon is E.

Learn more about polygons, click;

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C, E, F, D I’m pretty sure

I need help with this review

Answers

Answer:

What do you need help with?

Step-by-step explanation:

Help!!!

prove triangle PAB is an equilateral triangle

HELP PLEASEE

Answers

Answer:

If three sides of a triangle are equal and the measure of all three angles is equal to 60 degrees then the triangle is an equilateral triangle. Therefore it is an equilateral triangle.

In ∆PAM and ∆PBM

$\because\pink{\sf\begin{cases} \sf AM=BM(Bisected\:by\:PM)\n \sf PA=PB(Given)\n \sf PM(Common\:side)\end{cases}}$

$\n \sf\longmapsto ∆PAM\cong ∆PBM(SSS)$

$\n \sf\longmapsto PA+AM=PB+BM$

Put AM =BM

$\n \sf\longmapsto PA+AM+AM=PB+BM+BM$

Put PA=PB

$\n \sf\longmapsto PA+AB=PB+AB$

Hence

∆APB is a equilateral triangle

Vanessa is skiing along a circular ski trail that has a radius of 2.5 km. She starts at the 3-o'clock position and travels in the CCW direction. Vanessa stops skiing when she is 1.244 km to the right and 2.169 km above the center of the ski trail. Imagine an angle with its vertex at the center of the circular ski trail that subtends Vanessa's path.How many radians has the angle swept out since Vanessa started skiing?

Answers

Answer:

1.05 radians

Step-by-step explanation:

Given that Vanessa is skiing along a circular ski trail that has a radius of 2.5 km. She starts at the 3-o'clock position and travels in the Counter Clockwise direction.

She stops skiing when she is 1.244 km to the right and 2.169 km above the center of the ski trail.

This can be represented as (1.244, 2.169) on a circle of radius 2.5 km.

From the coordinate point (1.244, 2.169) derived, x=1.244 and y=2.169.

By the definition of tangent,

$\tan \theta =(y)/(x) \n\n\tan \theta =(2.169)/(1.244)\n\n \theta=\arctan (2.169)/(1.244)\n\n\n \theta=1.05006$

Vanessa swept out approximately 1.05 radians since she started skiing.

Final answer:

Vanessa's path on the circular ski trail has swept out an angle of 1.076 radians since she started skiing.

Explanation:

First, let's find the position vector of Vanessa's stop point. The position vector is given by the coordinates (x, y), where x is the horizontal distance and y is the vertical distance from the center of the ski trail. In this case, x = 1.244 km to the right and y = 2.169 km above the center. Therefore, the position vector is (1.244 km, 2.169 km).

Next, we need to find the angle swept out by Vanessa's path. To do this, we can use trigonometry. The radius of the ski trail is 2.5 km, and the position vector is (1.244 km, 2.169 km). We can use the inverse tangent function to find the angle:

angle = tan^(-1)(y/x) = tan^(-1)(2.169/1.244) = 61.63 degrees

Finally, we need to convert the angle from degrees to radians. To convert degrees to radians, we use the conversion factor π/180. So, the angle in radians is:

angle_radians = 61.63 degrees * (π/180) = 1.076 radians