The slope is 0.1
To find a perpendicular slope, find the negative reciprocal.
The reciprocal of 0.1 is 10
The negative of 10 is -10
Final answer:-10
Answer:
(5/12)d - (23/36)g
Step-by-step explanation:
First you can eliminate g and -g to get (1/6)d - (3/4)g + (1/9)g + (1/4)d. Then you need to get common denominators to add like terms together.
1/6 = 4/24 and 1/4 = 6/24. Add them together to get (10/24)d or (5/12)d.
-3/4 = -27/36 and 1/9 = 4/36. Add them together to get (-23/36)g.
So in standard form, (5/12)d - (23/36)g
Add the exponents and keep the same base. Then reciprocal it and change the sign of the exponent. Then the value of the exponent expression is 0.5.
<h3>What is an exponent?</h3>
Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
The exponent expression is 2³ × 2⁻⁴ can be simplified.
Add the exponents and keep the same base. Then we have
2³ × 2⁻⁴ = 2⁽³⁻⁴⁾
2³ × 2⁻⁴ = 2⁻¹
Then find the reciprocal and change the sign of the exponent.
![2^3* 2^{-4} = 2^{-1}\\\\2^3* 2^{-4} = \dfrac{1}{2}\\\\2^3* 2^{-4} = 0.5](https://tex.z-dn.net/?f=2%5E3%2A%202%5E%7B-4%7D%20%3D%202%5E%7B-1%7D%5C%5C%5C%5C2%5E3%2A%202%5E%7B-4%7D%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5C%5C%5C%5C2%5E3%2A%202%5E%7B-4%7D%20%3D%200.5)
The value is 0.5.
More about the exponent link is given below.
brainly.com/question/5497425
In 1 minute, bison runs 3520 feet
In 60 minutes, the bison would run
3520*60 feet
211200 feet per hour.
These are equivalent to;
40 miles per hour since 1 mile is equivalent to 5280 feet.
The bison is faster by 10 miles per hour
Given:
![$\frac{12 x^{2}+31 x+7}{16 x^{2}+8 x+1}](https://tex.z-dn.net/?f=%24%5Cfrac%7B12%20x%5E%7B2%7D%2B31%20x%2B7%7D%7B16%20x%5E%7B2%7D%2B8%20x%2B1%7D)
To find:
The simplified expression by factoring.
Solution:
Let us factor the numerator:
![12 x^{2}+31 x+7](https://tex.z-dn.net/?f=12%20x%5E%7B2%7D%2B31%20x%2B7)
31x can be written as 3x + 28x.
![=\left(12 x^{2}+3 x\right)+(28 x+7)](https://tex.z-dn.net/?f=%3D%5Cleft%2812%20x%5E%7B2%7D%2B3%20x%5Cright%29%2B%2828%20x%2B7%29)
Take 3x common in 1st two terms and 7 common in next two terms.
![=3 x(4 x+1)+7(4 x+1)](https://tex.z-dn.net/?f=%3D3%20x%284%20x%2B1%29%2B7%284%20x%2B1%29)
Make sure the remaining terms in the both brackets must be same.
Now, take out common factor (4x + 1).
![=(4 x+1)(3 x+7)](https://tex.z-dn.net/?f=%3D%284%20x%2B1%29%283%20x%2B7%29)
In the same way, factorize the denominator:
![16 x^{2}+8 x+1](https://tex.z-dn.net/?f=16%20x%5E%7B2%7D%2B8%20x%2B1)
8x can be written as 4x + 4x.
![=(16 x^{2}+4 x)+(4x+1)](https://tex.z-dn.net/?f=%3D%2816%20x%5E%7B2%7D%2B4%20x%29%2B%284x%2B1%29)
Take 4x common in 1st two terms and 1 common in next two terms.
![=4x(4 x+1)+1(4x+1)](https://tex.z-dn.net/?f=%3D4x%284%20x%2B1%29%2B1%284x%2B1%29)
Make sure the remaining terms in the both brackets must be same.
Now, take out common factor (4x + 1).
![=(4x+1)(4x+1)](https://tex.z-dn.net/?f=%3D%284x%2B1%29%284x%2B1%29)
Substitute the terms we found for numerator and denominator:
![$\frac{12 x^{2}+31 x+7}{16 x^{2}+8 x+1}=\frac{(4 x+1)(3 x+7)}{(4 x+1)(4 x+1)}](https://tex.z-dn.net/?f=%24%5Cfrac%7B12%20x%5E%7B2%7D%2B31%20x%2B7%7D%7B16%20x%5E%7B2%7D%2B8%20x%2B1%7D%3D%5Cfrac%7B%284%20x%2B1%29%283%20x%2B7%29%7D%7B%284%20x%2B1%29%284%20x%2B1%29%7D)
Cancel the common factors.
![$=\frac{3 x+7}{4 x+1}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B3%20x%2B7%7D%7B4%20x%2B1%7D)
The simplified expression is
.