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ELEN [110]
3 years ago
6

6. Which pair of points has a positive slope?

Mathematics
1 answer:
kondor19780726 [428]3 years ago
4 0
Picture? I can’t answer, I need more info?
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Evaluate each trigonometric equation for θ.
liberstina [14]

Answer:

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

Step-by-step explanation:

Let us revise the trigonometry functions

  • Sin(x) = opposite/hypotenuse
  • Cos(x) = adjacent/hypoteouse
  • Tan(x) = opposite/adjacent
  • Csc(x) = hypotenuse/opposit
  • Sec(x) = hypotenues/adjacent
  • Cot(x) = adjacent/opposite

In the given figure

The opposite side to angle Ф = 8

The adjacent side to angle Ф = 15

Find the hypotenuse using Pythagoras' theorem

Hypotenuse = \sqrt{8^{2}+15^{2}  }

Hypotenuse = \sqrt{64+225}

Hypotenuse = \sqrt{289}

Hypotenuse = 17

Let us use the rules above to find the trigonometry functions

sinФ = 8/17

cosФ = 15/17

tan Ф = 8/15

csc Ф = 17/8

sec Ф = 17/15

cot Ф = 15/8

4 0
3 years ago
On a map the scale is 1 inch = 125 miles. What is the actual distance between two cities of the map distance is 4 inches. ( PLS
kogti [31]

Answer:

500 miles

Step-by-step explanation:

Please mark as brainliest.

8 0
3 years ago
sakyyah picked 12 apples. she gave 1/6 to each of her 5 friends. how many apples did each friends get?
Sergeu [11.5K]
Each of her 5 friends received 2 apples.
3 0
3 years ago
Read 2 more answers
If the parent function f(x) = x^2 is fatter translated 11 units to the left, then translated 5 units down, write the resulting f
nikklg [1K]

The quadratic function given by:


f(x)=a(x-h)^2+k, \ \ \ a\neq 0


is in vertex form. The graph of f is a parabola whose axis is the vertical line x=h and whose vertex is the point (h, k). So:


To translate the graph of a function to the right, left, upward or downward we have:

For \ a \ positive \ real \ number \ c. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:\\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ g(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ g(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{right}: \\ g(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ \mathbf{left}: \\ g(x)=f(x+c)


By knowing this things, we can solve our problem as follows:


FIRST.

  • Translating <em>11 units to the left:</em>

g(x)=f(x+11) \\ \\ \therefore g(x)=(x+11)^2


  • Then translating<em> 5 units down:</em>

g(x)=f(x)-c \\ \\ \therefore g(x)=(x+11)^2-5


Since the new function is fatter, the factor we need to multiply the term (x+11)^2 <em>must be</em> less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.


<em>Therefore, the right answer is </em><em>b. f(x) = 1/2(x + 11)^2 - 5</em>


SECOND.

  • Translating <em>8 units to the right:</em>

g(x)=f(x-8) \\ \\ \therefore g(x)=(x-8)^2


  • Then translating<em> 1 unit down:</em>

g(x)=f(x)-c \\ \\ \therefore g(x)=(x-8)^2-1


As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.


<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>

7 0
3 years ago
Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4.
CaHeK987 [17]

<u>Answer:</u>

y=-\frac{1}{16} x^2

<u>Step-by-step explanation:</u>

Equation of parabola with focus at (0,-4) and directrix is y=4.

We know that parabola is the locus of all the points such that the distance from fixed point on the parabola to fixed line directrix is the same.

The parabola is opening downwards.

Let any point on parabola is (x,y).

Distance from focus(0,-4) to (x,y) = \sqrt{(x-0)^2+(y-(-4))^2}=|y-4|

\sqrt{(x-0)^2+(y-+4)^2}=|y-4|

(x-0)^2+(y+4)^2=(y-4)^2

(x)^2+(y+4)^2=(y-4)^2

x^2+(y^2+4y+4y+16)=y^2-4y-4y+16

x^2+y^2+8y+16=y^2-8y+16

x^2+16y^2=0

16y=-x^2

y=-\frac{1}{16} x^2

6 0
2 years ago
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