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KonstantinChe [14]
3 years ago
15

Which represents a function?

Mathematics
1 answer:
VLD [36.1K]3 years ago
4 0

Answer:

\boxed{  \text{Option \: D}}

Step-by-step explanation:

All the relations are not functions. We can determine ( identify ) whether a relation is function or not by drawing a vertical line intersecting the graph of the relation. This is called vertical line test.

  • If the vertical line intersects the graph of a relation at one point , the relation is a function .
  • If it cuts at more than one point , it is not a function. It means that if there are more points of the graph of a relation of a vertical line , same first component ( pre - image ) has more images ( second component ) which is not the function by definition.

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

Let's check all of the options :

☐ Option A :

  • The vertical line cuts the graph at two points. So , the graph does not represent a function.

☐ Option B

  • No! This is also not a function as the vertical line cuts the graph at two points.

☐ Option C

  • Nah! This too can't be called a function as the vertical line cuts the graph at two points.

☑ Option D

  • Yep! The vertical line cuts the graph at one point. Thus , the graph represents a function.

Yayy!! We found our answer. It's ' Option D '.

Hope I helped ! ツ

Have a wonderful day / night ! ♡

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

You might be interested in
A circle is inscribed in a square is 10 inch sides what is the circumference of the circle use 3.14 as an approximation for pie
MissTica

Answer:

31.4 inches

Step-by-step explanation:

If a circle is inscribed in a square then diameter of circle inscribed is same as  side as of square.

In the given problem it is given that side of square is 10 inches.

So diameter of  circle inscribed is 10 inches

we know radius of circle is half of  diameter of  circle

Thus, radius of circle inscribed = diameter of  circle/2 = 10/2 = 5inches.

Expression to calculate circumference of circle is given by 2\pi r

where r is the radius of circle.

Thus circumference of  circle inscribed is

2*\pi *5\\=> 10*3.14 \\=> 31.4

Thus, circumference of  circle inscribed is  31.4 inches

6 0
3 years ago
You work at a pioneer historical site. On this site you have handcarts. One cart has a handle that connects to the center of the
Gelneren [198K]

Answer:

a)  see below

b)  radius = 16.4 in (1 d.p.)

c)  18°. Yes contents will remain. No, handle will not rest on the ground.

d)  Yes contents would spill.  Max height of handle = 32.8 in (1 d.p.)

Step-by-step explanation:

<u>Part a</u>

A chord is a <u>line segment</u> with endpoints on the <u>circumference</u> of the circle.  

The diameter is a <u>chord</u> that passes through the center of a circle.

Therefore, the spokes passing through the center of the wheel are congruent chords.

The spokes on the wheel represent the radii of the circle.  Spokes on a wheel are usually evenly spaced, therefore the congruent central angles are the angles formed when two spokes meet at the center of the wheel.

<u>Part b</u>

The <u>tangent</u> of a circle is always <u>perpendicular</u> to the <u>radius</u>.

The tangent to the wheel touches the wheel at point B on the diagram.  The radius is at a right angle to this tangent.  Therefore, we can model this as a right triangle and use the <u>tan trigonometric ratio</u> to calculate the radius of the wheel (see attached diagram 1).

\sf \tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle

Given:

  • \theta = 20°
  • O = radius (r)
  • A = 45 in

Substituting the given values into the tan trig ratio:

\implies \sf \tan(20^{\circ})=\dfrac{r}{45}

\implies \sf r=45\tan(20^{\circ})

\implies \sf r=16.37866054...

Therefore, the radius is 16.4 in (1 d.p.).

<u>Part c</u>

The measure of an angle formed by a secant and a tangent from a point outside the circle is <u>half the difference</u> of the measures of the <u>intercepted arcs</u>.

If the measure of the arc AB was changed to 72°, then the other intercepted arc would be 180° - 72° = 108° (since AC is the diameter).

\implies \sf new\: angle=\dfrac{108^{\circ}-72^{\circ}}{2}=18^{\circ}

As the handle of the cart needs to be no more than 20° with the ground for the contents not to spill out, the contents will remain in the handcart at an angle of 18°.

The handle will not rest of the ground (see attached diagram 2).

<u>Part d</u>

This can be modeled as a right triangle (see diagram 3), with:

  • height = (48 - r) in
  • hypotenuse ≈ 48 in

Use the sin trig ratio to find the angle the handle makes with the horizontal:

\implies \sf \sin (\theta)=\dfrac{O}{H}

\implies \sf \sin (\theta)=\dfrac{48-r}{48}

\implies \sf \sin (\theta)=\dfrac{48-45\tan(20^{\circ})}{48}

\implies \theta = 41.2^{\circ}\:\sf(1\:d.p.)

As 41.2° > 20° the contents will spill out the back.

To find the <u>maximum height</u> of the handle from the ground before the contents start spilling out, find the <u>height from center of the wheel</u> (setting the angle to its maximum of 20°):

\implies \sin(20^{\circ})=\dfrac{h}{48}

\implies h=48\sin(20^{\circ})

Then add it to the radius:

\implies \sf max\:height=48\sin(20^{\circ})+45\tan(20^{\circ})=32.8\:in\:(1\:d.p.)

(see diagram 4)

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

<u>Circle Theorem vocabulary</u>

<u>Secant</u>: a straight line that intersects a circle at two points.

<u>Arc</u>: the curve between two points on the circumference of a circle

<u>Intercepted arc</u>: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.

<u>Tangent</u>: a straight line that touches a circle at only one point.

7 0
2 years ago
In a fruit punch drink, the 3 ingredients are apple juice, orange juice and cranberry juice. If 2/7 of
Sladkaya [172]

Answer:

3 : 4 : 7

Step-by-step explanation:

apple juice - 2/7 = 4/14

orange juice - 1/2 = 7/14

AJ + OJ = 11/14

this means that 3/14 of the punch is cranberry juice.

cranberry : apple : orange

3 : 4 : 7

8 0
2 years ago
D=ABC for A solve for A
Dafna1 [17]
A = D/BC. In order to isolate A, all you do is divide by BC
7 0
3 years ago
Which expression is the factorization of x2 + 10x + 21?
LiRa [457]
<h2><u>Sol</u><u>ution</u><u>:</u></h2>

Equation: x² + 10x + 21

<u>Step</u><u> </u><u>1</u><u>:</u> Find two numbers that can add up to 10 and be multiplied to 21. We have: 7 & 3, in the sense that 7+3=10, and 7×3=21. Replacing 10 with 7+3, the equation is now → x² + 7x + 3x + 21

<u>Step</u><u> </u><u>2</u><u>:</u> Get the new equation bracketed → (x² + 7x) (+3x + 21)

<u>Step</u><u> </u><u>3</u><u>:</u> Use 'x' in the equation. For the first part, we have 'x'. x² = x × x so, bring out one x out side the bracket, divide 7x by = 7 → x (x +7). Do the same for the second part by dividing 21 by 3 = 7, and then bringing out 3 from the bracket → 3 (x + 7).

Bringing everything together, we have: x(x+7) +3(x+7) → (x+3) (x+7)

<h3><u>Final</u><u> </u><u>ans</u><u>wer</u><u>:</u></h3>

(x+3) (x+7)

<h3 />

4 0
2 years ago
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