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4 years ago

HELP TRIGONOMETRY !!!!

Mathematics

1 answer:

Lunna [17]4 years ago

4 0

We want x which is known as the hypotenuse in this triangle.

Because of the given side we know that...

sin(70°) × hypotenuse = 12

hypotenuse = 12/sin(70°) = 12.8 cm rounded to the nearest tenth

answer: 12.8 cm

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Diana averages 6 mph walking

Diano4ka-milaya [45]

Answer:

Distance between school and home = 105 miles.

Step-by-step explanation:

Let distance = D miles

Time to take walking/jogging, t1 = D/6 hours

Time by car, t2 = D/35 hours

Average time, t

= (t1+t2)/2

= D(1/6+1/35)

= (D/210)(35+6)

=41D/210 hours

Given t = t1-3 hours

41D/210 - D/6 = 3

Solve for D

41D/210 - 35D/210 = 3

(41-35)D/210 = 3

6D/210 = 3

D = 3*210/6 = 105 miles.

(Appreciate very much Diana's efforts to walk/job 105 miles to school, and we understand how lucky we are in most of Europe and North America)

3 0

3 years ago

Find the vertex of the given quadratic function.

AleksandrR [38]

Answer: Choice B. The vertex is (6,-4)

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

Work Shown:

Step 1 is to expand out (x-8)(x-4) using the FOIL rule or the box method or the distribution rule

(x-8)(x-4) = x(x-4)-8(x-4)

(x-8)(x-4) = x*x+x*(-4)-8*x-8*(-4)

(x-8)(x-4) = x^2-4x-8x+32

(x-8)(x-4) = x^2-12x+32

So (x-8)(x-4) turns into x^2-12x+32

x^2-12x+32 is the same as 1x^2+(-12x)+32 which is in the form ax^2+bx+c. We see that a = 1, b = -12, c = 32

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

Use the values of a & b to find the value of h, which is the x coordinate of the vertex

h = -b/(2*a)

h = -(-12)/(2*1)

h = 12/2

h = 6

Then this is plugged back into the original function to find the y coordinate of the vertex. We can use either (x-8)(x-4) or x^2-12x+32 since they are equivalent expressions

k = y coordinate of vertex

k = f(h) = f(6) since h = 6

f(x) = (x-8)(x-4)

f(6) = (6-8)(6-4)

f(6) = (-2)(2)

f(6) = -4

note that

f(x) = x^2-12x+32

f(6) = (6)^2-12(6)+32

f(6) = 36-72+32

f(6) = -36+32

f(6) = -4

So we get the same result using either expression

So k = f(h) = f(6) = -4

Since h = 6 and k = -4, the vertex is (h,k) = (6,-4). So that's why the answer is choice B.

8 0

3 years ago

Is 4/5 and 5/6 equivalent or not

Cloud [144]

Answer:

For the two fractions 4/5 and 5/6, the least common denominator is 30. The fraction 4/5 is equivalent to 24/30 (To get this I multiplied both the numerator and denominator by 6). The fraction 5/6 is equivalent to 25/30 (To get this I multiplied both the numerator and denominator by 5).

Step-by-step explanation:

They are equivalent (Except for the numerator)

7 0

3 years ago

Hellp me solve this thanks

stellarik [79]

Answer:

c. 10 cm

Step-by-step explanation:

The parallel sides of trapizium are the bases so

base 1(B1) =9cm , base(B2)= 12cm

$area(a) = 105 {cm}^{2}$