The scale of a map is 1 inch : 10 miles. On the map, Main Street is 0.6 inch long. What is the actual length of Main Street?

The surface area of a piece of paper is 137 cm2. Use the fact that 10 mm = 1 cm to convert this area to mm2. Give your answer as

irakobra [83]

<h3>The surface area of a piece of paper is $13700\ mm^2$ </h3>

Solution:

surface area of a piece of paper = 137 sq cm

Use the fact that 10 mm = 1 cm to convert this area to mm^2

$1\ cm = 10\ mm$

Then,

$1\ cm^2 = 100\ mm^2$

Convert 137 sq cm to sq mm

$137\ cm^2 = 137 \times 100\ mm^2\\\\137\ cm^2 = 13700\ mm^2$

Thus, surface area of a piece of paper is $13700\ mm^2$

7 0

3 years ago

How do I find the horizontal asymptote of h(x)=x+6/x^2-64 ?

SashulF [63]

I assume the equation described is:

( x + 6 ) / ( x^2 - 64 )

You can compare the degree of the numerator and denominator in a function that takes the form of this type of rational equation.

Here are the three rules

#1 (Correct Answer): When the degree of the numerator is smaller then the denominator the horizontal asymptote is y = 0

#2 If the degree of the numerator and denominator is the same, then you take the leading coefficient of the numerator (n) and denominator (d) to create the answer y = n / d in this equations case it would be 1 / 1 since variables technically have an invisible 1 in front of them since anything multiplied by 1 is its self, 1x = x

#3 When the degree of the numerator is greater then the degree of the denominator then this means that it does not have a horizontal asymptote.

Again the final answer is that the horizontal asymptote is y = 0

5 0

3 years ago

Is 16g + 10 - 4g and 20g + 10 equivalent

-Dominant- [34]

No 16g-4g+10 = 12g+ 10

6 0

3 years ago

In RST, RS = 7, RT = 10, and ST = 8. Which angle of RST has the smallest measure? A T BCANNT BE DETERMINDED C R D S

Scrat [10]

Answer:

Correct answer is option A. T

Step-by-step explanation:

Given that

In a $\triangle RST$ , RS = 7, RT = 10, and ST = 8.

To find:

Smallest angle = ?

Solution:

We can use cosine rule here to find the angle.

Formula for cosine rule:

$cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

Using the cosine rule:

$cos T = \dfrac{ST^{2}+RT^{2}-RS^{2}}{2\times ST \times RT}\\\Rightarrow cos T = \dfrac{8^{2}+10^{2}-7^{2}}{2\times 8 \times 10}\\\Rightarrow cos T = \dfrac{64+100-49}{160}\\\Rightarrow cos T = \dfrac{115}{160}\\\Rightarrow \angle T = cos^{-1}(0.71875)\\\Rightarrow \angle T = 44.05^\circ$

Now, let us use Sine rule to find other angles:

$\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}$

$\dfrac{RS}{sinT} = \dfrac{ST}{sinR} = \dfrac{RT}{sinS}\\\Rightarrow \dfrac{7}{sin44.05} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow \dfrac{7}{0.695} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow sin R = \dfrac{8 \times 0.695}{7}\\\Rightarrow R = 52.58^\circ$