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The floor of the entryway to an office building will be triangular. Two angles of the triangle will measure 40º, and the side be

ruslelena [56]

Answer:

The drawing in the attached figure

Step-by-step explanation:

we know that

An isosceles triangle, has two equal sides and two equal interior angles

In this problem, the floor of the entryway to an office building is in the shape of an isosceles triangle

step 1

Find the measure of the vertex angle

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

Let

x ---> the measure of the vertex angle of triangle

$x=180^o-2(40^o)=100^o$

step 2

Find the length of the congruent sides of triangle

Applying the law of sines

Let

c ----> the length of one congruent side

$\frac{a}{Sin(A)}=\frac{b}{Sin(B)}$

we have

$a=8\ m\\A=100^o\\B=40^o$

substitute

$\frac{8}{Sin(100^o)}=\frac{b}{Sin(40^o)}$

solve for b

$b=\frac{8}{Sin(100^o)}(Sin(40^o))$

$b=5.22\ m$

step 2

Make a scale drawing of the entryway

The scale drawing is 1 cm : 2 cm

That means

1 cm in the drawing represent 2 cm in the actual

or

1 cm in the drawing represent 0.02 m in the actual

Find the dimensions in the drawing

For a=8 m

$8\ m=8/0.02=400\ cm$

For b=5.22 m

$5.22\ m=5.22/0.02=261\ cm$

step 3

Draw the triangle

see the attached figure

3 0

3 years ago

Suppose you sequentially add 10 drops of water to a graduated cylinder and read the volume add 10 more drops read and so on. how

aleksandr82 [10.1K]

It depends on what is being referred to by "this."

The description of the activity is that 10 drops are added twice and two readings are taken. If you do *that* 4 times, then a total of 20*4 = 80 drops will have been added.

If the activity referred to by "this" is the pair of acts {add 10 drops, read the volume}, then four repetitions will have added 10*4 = 40 drops.

Probably the expected interpretation is that "this" is {add 10 drops, read}, so 40 drops is likely the expected answer.

3 0

3 years ago

5. The shaded area is 327, find r.

vfiekz [6]

Answer: 10.2

Step-by-step explanation:

Area of a circle is

A= pixr^2

327= 3.14r^2

Divide by 3.14

= 104.14

Get the sq rat of 104.14

= 10.2

3 0

4 years ago

I need help with pre calculus.

otez555 [7]

Question 1

<h3>Answer: Choice A) -7</h3>

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

Explanation:

To compute f(g(2)), we'll first need to find g(2).

Locate 2 in the x row. Then read straight down until you get to the g(x) row. You should find that g(2) = 4

This means f(g(2)) becomes f(4). We then repeat the same process as before. Locate 4 in the x row, read straight down til you get to the f(x) row to find that f(4) = -9

Overall, we can say f(g(2)) = -9

We do the same set of steps to compute g(f(-1)). You should find that f(-1) = -1 and g(f(-1)) = g(-1) = -2

Lastly, we subtract the results we got:

f(g(2)) - g(f(-1)) = -9 - (-2) = -9+2 = -7

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

Question 2

<h3>Answer: Choice B) 0</h3>

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

Explanation:

If you were to graph each equation, you should get what you see below.

The red and blue curves do not intersect in any way. We need an intersection point to have a solution. Because there are no intersections, we don't have any solutions. The system is considered inconsistent.

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

Question 3

<h3>Answer: Choice B</h3><h3> $-2x^2+250x-2000$ </h3>

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

Explanation:

x = number of scooters made and sold

Each scooter costs $150 to make. If you made x of them, then it costs 150x dollars. Then tack on the fixed cost of $2000 to get the expression $150x+2000$

The cost function is $C(x) = 150x+2000$ . We'll subtract this from the revenue function R(x) to get the profit P(x)

$\text{Profit} = \text{Revenue} - \text{Cost}\\\\P(x) = R(x) - C(x)\\\\P(x) = (400x-2x^2) - (150x+2000)\\\\P(x) = 400x-2x^2-150x-2000\\\\P(x) = -2x^2+250x-2000\\\\$

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

Question 4

<h3>Answer: Choice B</h3>

$\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}$

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

Explanation:

$g(x) = \frac{1}{x+1}\\\\g(f(x)) = \frac{1}{f(x)+1}\\\\g(f(x)) = \frac{1}{x^2+x-3+1}\\\\g(f(x)) = \frac{1}{x^2+x-2}\\\\g(f(x)) = \frac{1}{(x+2)(x-1)}\\\\(g\circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\$

I started with the outer function g(x) and replaced each x with f(x) in the second step. Then I plugged in f(x) = x^2+x-3 and simplified. Factoring the denominator is helpful to determine where the denominator becomes zero. Specifically, it happens when x = -2 and x = 1. These x values must be kicked out of the domain to avoid a division by zero error.

So we start off with the real number line, and poke holes at x = -2 and x = 1.

The notation $x \in \mathbb{R}$ means x is a real number. Then we tack on $x \ne -2, x \ne 1$

Overall, the domain is $\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}$

Let's see what happens if we tried plugging x = -1 into this composite function:

$(g \circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\(g \circ f)(-1) = \frac{1}{(-1+2)(-1-1)}\\\\(g \circ f)(-1) = \frac{1}{(1)(-2)}\\\\(g \circ f)(-1) = \frac{1}{-2}\\\\(g \circ f)(-1) = -0.5\\\\$

We don't get a division by zero error, so x = -1 is allowed. The same can be said about any other x value as long as it's not -2 and not 1 either.

4 0

2 years ago

How do u solve 2x - 30000y???????????

Fed [463]

Answer:

2(x-15000y)

Step-by-step explanation:

2x-30000y

2(x-15000y)

4 0

3 years ago