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2 years ago

Determine the range of the function graphed above

Mathematics

1 answer:

STALIN [3.7K]2 years ago

8 0

Answer: A

Step-by-step explanation:

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values.

The possible values of y are [-infinity,4], so the answer is A

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1. What is the volume of the prism that can be constructed from this net?

Irina-Kira [14]

1. V = lwh
V = (8)(4)(5)
V = (32)(5)
V = 160 units³

2. V = lwh + lwh
V = (4)(2)(1) + (3)(1)(1)
V = (8)(1) + (3)(1)
V = 8 + 3
V = 11 units³

3. V = leh + s³
V = (9)(3)(4) + (3)³
V = (27)(4) + 27
V = 108 + 27
V = 135 units³

4. V = lwh
V = (3)(7)(2)
V = (21)(2)
V = 42 units³

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3 years ago

A railroad track rises 30 feet for every 400 feet of track. What is the measure of the angle of elevation of the track?

gtnhenbr [62]

Answer:

Step-by-step explanation:

Rising 30 feet for every 400 feet of track is not a very large angle of elevation. We set this up as a right triangle to use right triangle trig to solve for the missing angle. The height is 30 and the hypotenuse is 400. The height is the side opposite the angle in question, and the hypotenuse is the hypotenuse! This is the sin ratio. Setting up the ratio using our info:

$sin\theta=\frac{30}{400}$

When you are looking for a missing angle measure, as we are here, use the 2nd-->sin buttons to find the inverse of sin, which looks like this:

$sin^{-1}($

Enter in the fraction 30/400 after the parenthesis and then hit enter to get the angle measure of 4.3 degrees.

3 0

3 years ago

Identify the polygon with vertices A(5,0), B(2,4), C(−2,1), and D(1,−3), and then find the perimeter and area of the polygon. HE

inn [45]

Answer:

Part 1) The polygon is a square

Part 2) The perimeter is equal to $20\ units$

Part 3) The area is equal to $25\ units^{2}$

Step-by-step explanation:

we have

$A(5,0), B(2,4), C(-2,1),D(1,-3)$

Plot the points

see the attached figure

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance AB

$A(5,0),B(2,4)$

substitute in the formula

$d=\sqrt{(4-0)^{2}+(2-5)^{2}}$

$d=\sqrt{(4)^{2}+(-3)^{2}}$

$d=\sqrt{25}$

$AB=5\ units$

Find the distance BC

$B(2,4), C(-2,1)$

substitute in the formula

$d=\sqrt{(1-4)^{2}+(-2-2)^{2}}$

$d=\sqrt{(-3)^{2}+(-4)^{2}}$

$d=\sqrt{25}$

$BC=5\ units$

Find the distance CD

$C(-2,1),D(1,-3)$

substitute in the formula

$d=\sqrt{(-3-1)^{2}+(1+2)^{2}}$

$d=\sqrt{(-4)^{2}+(3)^{2}}$

$d=\sqrt{25}$

$CD=5\ units$

Find the distance AD

$A(5,0),D(1,-3)$

substitute in the formula

$d=\sqrt{(-3-0)^{2}+(1-5)^{2}}$

$d=\sqrt{(-3)^{2}+(-4)^{2}}$

$d=\sqrt{25}$

$AD=5\ units$

we have that

AB=BC=CD=AD

Find the distance BD (diagonal)

$B(2,4),D(1,-3)$

substitute in the formula

$d=\sqrt{(-3-4)^{2}+(1-2)^{2}}$

$d=\sqrt{(-7)^{2}+(-1)^{2}}$

$BD=\sqrt{50}\ units$

Verify if the polygon is a square

If the triangle BDA is a right triangle, then the polygon is a square

Applying the Pythagoras theorem

$BD^{2}=AD^{2}+AB^{2}$

substitute

$(\sqrt{50})^{2}=5^{2}+5^{2}$

$50=50$ -----> is true

The triangle BDA is a right triangle

therefore

The polygon is a square

Find the Area of the polygon

The area of a square is equal to

$A=b^{2}$

we have

$b=5\ units$

$A=5^{2}=25\ units^{2}$

Find the perimeter of the polygon

The perimeter of a square is equal to

$P=4b$

we have

$b=5\ units$

$P=4(5)=20\ units$

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3 years ago

A company hires five people for the same job for one week. The amount that each person is paid

dangina [55]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Two triangles are similar with a scale factor of 3. The preimage triangle has a base of 7 inches and a height of 10 inches. What

vaieri [72.5K]

Answer:

The area of the larger triangle is 315 inches²

Step-by-step explanation:

1. Let's review all the information provided for answering the questions properly:

Pre-image triangle has a base of 7 inches and a height of 10 inches

Scale used : Factor of 3

2. What is the area of the larger triangle??

For calculating the area of the larger triangle, we use the scale this way:

Base = 7 inches * 3

21 inches

Height = 10 inches * 3

30 inches

Area of the larger triangle = 1/2 (Base * Height)

Area of the larger triangle = 1/2 (21 * 30)

Area of the larger triangle = 630/2 = 315 inches²

6 0

3 years ago