Answer:
The ladder is not safe at this height. The height from ground to top of the ladder is < 11.6 ft for safety reasons and this can be determined by using trigonometry functions.
Step-by-step explanation:
The ladder is not safe at this height. The height from ground to top of the ladder is < 11.6 ft for safety reasons and this can be determined by using trigonometry functions.
Given :
Joshua has a ladder that is 12 ft long.
He wants to lean the ladder against a vertical wall so that the top of the ladder is 11.8 ft above the ground.
For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°.
Check the angle that the ladder makes with the ground:
The ladder is safe when the angle the ladder makes with the ground to be no greater than 75° but is so, the ladder won't be safe.
To make the ladder safe, the height should not be 11.8ft.
The height from ground to top of the ladder is < 11.6 ft for safety reasons.
Answer:
5 9/14
Step-by-step explanation:
keeping in mind that anything raised at the 0 power, is 1, with the sole exception of 0 itself.
![\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{(r^{-7}b^{-8})^0}{t^{-4}w}\implies \cfrac{1}{t^{-4}w}\implies \cfrac{1}{t^{-4}}\cdot \cfrac{1}{w}\implies t^4\cdot \cfrac{1}{w}\implies \cfrac{t^4}{w}](https://tex.z-dn.net/?f=%20%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bnegative%20exponents%7D%0A%5C%5C%5C%5C%0Aa%5E%7B-n%7D%20%5Cimplies%20%5Ccfrac%7B1%7D%7Ba%5En%7D%0A%5Cqquad%20%5Cqquad%0A%5Ccfrac%7B1%7D%7Ba%5En%7D%5Cimplies%20a%5E%7B-n%7D%0A%5Cqquad%20%5Cqquad%20a%5En%5Cimplies%20%5Ccfrac%7B1%7D%7Ba%5E%7B-n%7D%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A%5Ccfrac%7B%28r%5E%7B-7%7Db%5E%7B-8%7D%29%5E0%7D%7Bt%5E%7B-4%7Dw%7D%5Cimplies%20%5Ccfrac%7B1%7D%7Bt%5E%7B-4%7Dw%7D%5Cimplies%20%5Ccfrac%7B1%7D%7Bt%5E%7B-4%7D%7D%5Ccdot%20%5Ccfrac%7B1%7D%7Bw%7D%5Cimplies%20t%5E4%5Ccdot%20%5Ccfrac%7B1%7D%7Bw%7D%5Cimplies%20%5Ccfrac%7Bt%5E4%7D%7Bw%7D%20)
Answer:
10
Step-by-step explanation:
(x + 2) + (-2 + x) = 20
2x + 0 = 20
2x = 20
x = 20/2
x = 10
Answer:
6
Step-by-step explanation:
Cost per item is found by dividing the cost by the number of items. If the woman bought n items for $120, the cost of each item is $120/n. If the woman bought 24 more items, n+24, at the same price, then the cost per item is $120/(n+24). The problem statement tells us this last cost is $16 less than the first cost:
120/(n+24) = (120/n) -16
Multiplying by n(n+24) gives ...
120n = 120(n+24) -16(n)(n+24)
0 = 120·24 -16n^2 -16·24n . . . . . . subtract 120n and collect terms
n^2 +24n -180 = 0 . . . . . . . . . . . . . divide by -16 to make the numbers smaller
(n +30)(n -6) = 0 . . . . . . . . . . . . . . factor the quadratic
The solutions to this are the values of n that make the factors zero: n = -30, n = 6. The negative value of n has no meaning in this context, so n=6 is the solution to the equation.
The woman bought 6 items.
_____
Check
When the woman bought 6 items for $120, she paid $120/6 = $20 for each of them. If she bought 6+24 = 30 items for the same money, she would pay $120/30 = $4 for each item. That amount, $4, is $16 less than the $20 she paid for each item.
