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1 month ago

Which set of ordered pairs represents a function?

Mathematics

2 answers:

PIT_PIT [12.4K]1 month ago

5 0

Answer:

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}

Step-by-step explanation:

For the given collection to be classified as a function, each x-coordinate must correspond to just a single y-coordinate, meaning each x-value must have a distinct y-value.

In this instance, the image illustrates the graphical depiction of each set, distinguished by color.

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)} -> Green points

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)} -> Blue points

{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)} -> Black points

{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)} -> Red points

The graph reveals that the only set possessing a single y-value for each x-value is the second one (Blue points).

lawyer [12.5K]1 month ago

5 0

A function is defined as a relationship where every element from the set of first components in ordered pairs correlates to exactly one element from the set of second components.

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)} - this is a function

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)} - this is also a function

{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)} - this represents a function

{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)} - this does not qualify as a function

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PIT_PIT [12445]

B. The correct ratio is sen α = BC/b. Step-by-step explanation: Trigonometric identities are utilized for resolving problems involving right angles. In any right-angled triangle, the side opposite to the angle is known as the opposite side, while the adjacent side runs parallel to the angle, ultimately leading to the longest side, called the hypotenuse.

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21 day ago

2. Santiago wants the lateral surfaces of the

Inessa [12570]

Answer:

Red paint will cover 262 square feet

of the ramp.

Step-by-step explanation:

The lateral surface area represents the surface area of the sides of the ramp without including the top and bottom surfaces

This ramp has three surfaces

The two sides are triangular with dimensions of length 20 and height 8.5

The back consists of a rectangular shape with length 12 and height 8.5

Step 1: Calculating the Area of Triangle

The area of the triangular side = $\frac{1}{2} length \times height$

The area of the triangle = $\frac{1}{2} (20 \times 8.5)$

The area of the triangle = $\frac{170}{2}$

Thus, the area of the triangle = 85 square feet

Area of both triangles = $85 \times 2$ = 170

Step 2: Finding the Area of Rectangle

Area of rectangle = $length \times height$

therefore,

Area of the rectangular back = $12 \times 8.5$ = 102 square feet

Step 3: Calculating the total lateral surface area

Overall Lateral Surface Area

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8 0

1 month ago

Students have organized

tester [12383]

Answer:

Part A. At least 6 hours

Part B. In less than 2.5 hours, Elijah will fall behind Mercedes

Part C. In over 2.5 hours, Elijah will lead Aubrey

Step-by-step explanation:

D = distance

v = speed

t = time

Formula connecting D, v, and t:

$D=v\cdot t$

Part A.

Steve's speed: $v=3.5\ mph$

Distance: a minimum of 21 miles

Time: unknown, so

$3.5\cdot t\ge 21\\ \\35t\ge 210\ [\text{Multiplied by 10}]\\ \\t\ge \dfrac{210}{35}\\ \\t\ge \dfrac{30}{5}\\ \\t\ge 6$

It would require Steve a minimum of 6 hours to traverse at least 21 miles on Day 1.

Part B.

Mercedes's speed: $v_M=2.4\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Mercedes's Distance walked: $D_M$ miles

Time: x hours

Mercedes is 2 miles ahead, therefore

$D_E=3.2x\\ \\D_M=2.4x+2$

Elijah will trail behind until

$D_E$

In 2.5 hours, Elijah will close the gap on Mercedes, and in less than 2.5 hours, Elijah will trail behind her.

Part C.

Aubrey's speed: $v_M=3\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Aubrey's Distance walked: $D_A$ miles

Time: x hours

At the beginning of Day 3, Elijah starts from Mile 42, while Aubrey begins at Mile 42.5.

$D_E=42+3.2x\\ \\D_A=42.5+3x$

Elijah will be ahead of Aubrey when

$D_E>D_A\\ \\42+3.2x> 42.5+3x\\ \\3.2x-3x>42.5-42\\ \\0.2x>0.5\\ \\2x>5\ [\text{Multiplied by 10}]\\ \\x>\dfrac{5}{2}\\ \\x>2.5\ hours$

In 2.5 hours, Elijah will surpass Aubrey, and after more than 2.5 hours, Elijah will outpace Aubrey.

4 0

1 month ago

The expression 17n+11 represents the perimeter of a triangle. The other two sides measure 4n+5 and 5n+6. A simplified expression

Zina [12379]

Response: 8n

==========================================================

Clarification:

The two sides, 4n+5 and 5n+6, comprise terms 4n and 5n which total to 9n. We require 8n to add to this to achieve 17n. In simpler terms, 4n + 5n + 8n = 9n + 8n = 17n

That is the reason why the outcome is 8n. There are no additional terms because the "+5" and "+6" in the two given expressions (4n+5 and 5n+6) sum to 5+6 = 11, matching what we aim for in the perimeter expression 17n + 11

Side 1 = 4n + 5

Side 2 = 5n + 6

Side 3 = 8n

Perimeter = (side1) + (side2) + (side3)

Perimeter = (4n + 5) + (5n + 6) + (8n)

Perimeter = 4n + 5 + 5n + 6 + 8n

Perimeter = (4n + 5n + 8n) + (5 + 6)

Perimeter = 17n + 11

So this confirms we possess the correct expression for the third side that is missing.

3 0

13 days ago

Read 2 more answers

You are in an airplane 5.7 miles above the ground. What is the measure of BD⌢

AnnZ [12381]

Result:

6.1°; 425.86 m.

Step-by-step breakdown:

The information provided states that the airplane is at an altitude of 5.7 miles above ground level, while the "radius of Earth is about 4000 miles." Thus,

θ = 2 × cos^-1 (a/ (a + b)), where a = 4000 miles, and b = 5.7 miles.

θ = 2 × cos^-1 (4000/ (4000 + 5.7)) = 6.1°.

To calculate the distance in meters:

Change in distance = 6.1° /360° × 2π × 4000 miles = 425.86 meters.

Consequently, BD⌢ measures at 6.1° and the distance corresponding to this section of Earth is 425.86 meters.

6 0

1 month ago