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Pavel [41]
3 years ago
14

Is a graph of a slanted line a one-to-one function? Justify your answer.

Mathematics
1 answer:
kkurt [141]3 years ago
7 0

Answer:

Yes

Step-by-step explanation:

A slanted straight line is one-to-one:  It passes the "horizontal ilne test."  This means that any line drawn horizontally through the given line intersects that line only once.  The significance of this is that the given line/function has an inverse.  y = x is one-to-one and has the inverse y = x.  y = 2x is one-to-one and has the inverse y = (1/2)x.

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Describe a method you can use to find the area of the following shape. Provide specific details in your answer, including coordi
insens350 [35]
The area of figure ABCDEF can be computed as the sum of the areas of trapezoid ACDF and triangle ABC, less the area of trangle DEF.
  trapezoid ACDF area = (1/2)(AC +DF)·(CD) = (1/2)(8+5)(6) = 39
  triangle ABC area = (1/2)(AC)(2) = 8
  triangle DEF area = (1/2)(DF)(2) = 5

Area of ABCDEF = (ACDF area) + (ABC area) - (DEF area) = 39 +8 -5 = 42

The actual area of ABCDEF is 42 square units.

7 0
3 years ago
Find the equation for the parabola that has its vertex at the origin and has directrix at x=1/48
Oksana_A [137]

Answer:

The equation for a parabola with vertex at the origin and a directrix at x = 1/48 is x= \frac{1}{12}\cdot y^{2}.

Step-by-step explanation:

As directrix is a vertical line, the parabola must "horizontal" and increasing in the -x direction. Then, the standard equation for such geometric construction centered at (h, k) is:

x - h = 4\cdot p \cdot (y-k)^{2}

Where:

h, k - Horizontal and vertical components of the location of vertex with respect to origin, dimensionless.

p - Least distance of directrix with respect to vertex, dimensionless.

Since vertex is located at the origin and horizontal coordinate of the directrix, least distance of directrix is positive. That is:

p = x_{D} - x_{V}

p = \frac{1}{48}-0

p = \frac{1}{48}

Now, the equation for a parabola with vertex at the origin and a directrix at x = 1/48 is x= \frac{1}{12}\cdot y^{2}.

6 0
3 years ago
PLEASE HELP !!<br><br> Which graph shows a constant of proportionality of 2?
kherson [118]

Answer:

B

Step-by-step explanation:

it rises 2 and goes to the right once; 2/1 = 2

3 0
3 years ago
Read 2 more answers
A child walks 3/10 of a mile in 1\5 hour. At this rate, how far will the child walk in 1 hour
defon

Answer:

1½ mile

Step-by-step explanation:

Given

3/10 mile = ⅕ hour

Required

Determine the distance in 1 hour

Since rate is constant, we have:

3/10 mile = ⅕ hour

Multiply both sides by 5

5 * 3/10 mile = ⅕ hour * 5

15/10 mile = 5/5 hour

3/2 mile = 1 hour

1½ mile = 1 hour

Hence,the child will walk 1½ mile in 1 hour

8 0
4 years ago
Find the value of x
Hunter-Best [27]

Answer:

35.8 deg

Step-by-step explanation:

a/sin A = b/sin B

24/sin x = 39/sin 71.8

sin x = (24 * sin 71.8)/39

sin x = 0.584598

x = sin^-1 0.584598

x = 35.8 deg

6 0
3 years ago
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