The garden view hotel is 235 feet tall
Step-by-step explanation:
The given is:
- The garden view hotel is seventeen less than twice the height of the plaza hotel
- Their combined height is 361 feet
We need to find the height of the garden view hotel
Assume that the height of garden view hotel is x feet and the height of the plaza hotel is y feet
∵ The height of the garden view hotel = x feet
∵ The height of the plaza hotel = y feet
∵ The height of the garden view hotel is 17 less than twice the
height of the plaza hotel
- That means x is less than 2 × y by 17, equate x by the difference
of 2 × y and 17
∴ x = 2y - 17 ⇒ (1)
∵ Their combined height = 361 feet
∴ x + y = 361
- Find y in terms of x by subtraction x from both sides
∴ y = 361 - x ⇒ (2)
Substitute y in equation (1) by equation (2)
∵ x = 2(361 - x) - 17
- Simplify the right hand side
∴ x = 722 - 2x - 17
- Add like terms
∴ x = 705 - 2x
- Add 2x to both sides
∴ 3x = 705
- Divide both sides by 3
∴ x = 235
The garden view hotel is 235 feet tall
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You can learn more about the word problems in brainly.com/question/13174281
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Answer:
p(x) = x⁶- 2x⁵- 10x⁴ + 20x² + 9x - 18
d(x) = (x - 2)
r = 0
f(x) = x⁵ - 10x³ + 9
Step-by-step explanation:
From the synthetic division given in the question,
Polynomial p(x) = x⁶- 2x⁵- 10x⁴ + 20x² + 9x - 18
Divisor d(x) = (x - 2)
After synthetic division of this polynomial by 2 we get the remainder,
r = 0
And the new polynomial f(x) that can be used further to find the other factors will be,
f(x) = x⁵ + (0).x⁴ + (-10)x³ + (0).x² + 9
f(x) = x⁵ - 10x³ + 9
The perpendicular slope is expressed as the negative reciprocal of the slope or − 1 m. In this scenario, the slope, or m, is −4 so the slope of the perpendicular line is − 1 −4 which simplifies to 1 4
Answer:
C ≈ 22.1°
Step-by-step explanation:
The law of cosines formula is given. Solving it for C, we find ...
C = arccos((a^2 +b^2 -c^2)/(2ab))
where a and b are the sides adjacent to the angle.
Then we have ...
C = arccos((14^2 +19^2 -8^2)/(2·14·19)) = arccos(493/532)
C ≈ 22.1°
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If you have a fair number of these to do, a spreadsheet is a useful tool. There are also triangle solver apps on the web or your local smart platform that will do this, too.
4/6 = 12/18
8/10 = 16/20
2/5 = 4/10
1/4 = 4/16
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