Answer:1 pretzel is 0.75$
1 soda is 0.55$
Step-by-step explanation
suppose
soda=x
pretzel=y
according to Juan
x+2y=2.05.....................(1)
according to Keisha
2x+y=1.85........................(2)
multiply 2 to the 1 no. and do subtraction from 1 no. to 2 no.
2x+4y=4.1
2x+y =1.85
<u>(-)(-) (-) </u>
3y=2.25
y=2.25/3
y=0.75
place y=0.75 to 1 no
x+2×0.75=2.05
x=2.05-1.5
x=0.55
Answer:
x < 15
Step-by-step explanation:
Let's first expand the parentheses on both sides. Remember that when expanding parentheses, the result will be the sum of the products of the "outside number" with each of the "inside number".
On the left, the parenthetical expression is: -6(x + 4). Here, the outside term is -6 and the inside terms are x and 4. So:
-6(x + 4) = -6 * x + (-6) * 4 = -6x - 24
On the right, the parenthetical expression is: -5(x + 6). Here, the outside term is -5 and the inside terms are x and 6. So:
-5(x + 6) = -5 * x + (-5) * 6 = -5x - 30
Now put these back in:
-6(x + 4) + 9 > -5(x + 6)
-6x - 24 + 9 > -5x - 30
-6x - 15 > -5x - 30
x < 15
Thus the answer is x < 15.
Hope this helps!
In standard normal distribution, the cutoff for the 95th percentile is about
. So the cutoff height would be
such that
![\dfrac{x-180}7=1.64\implies x\approx191.48](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-180%7D7%3D1.64%5Cimplies%20x%5Capprox191.48)
cm.
The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse
If
![sin \theta= \frac{a^2-b^2}{a^2+b^2}](https://tex.z-dn.net/?f=sin%20%5Ctheta%3D%20%5Cfrac%7Ba%5E2-b%5E2%7D%7Ba%5E2%2Bb%5E2%7D%20)
<span>, then:
</span>opposite = a² - b²
hypotenuse = a² + b²
<span>By the Pythagorean theorem:
</span>
![adjacent = \sqrt{(a^2+b^2)^2-(a^2-b^2)^2} \\= \sqrt{(a^2+b^2+a^2-b^2)(a^2+b^2-(a^2-b^2))} \\= \sqrt{(2a^2)(a^2+b^2-a^2+b^2)} \\= \sqrt{2a^2*2b^2}\\= \sqrt{4a^2b^2} \\ =2ab](https://tex.z-dn.net/?f=adjacent%20%3D%20%20%5Csqrt%7B%28a%5E2%2Bb%5E2%29%5E2-%28a%5E2-b%5E2%29%5E2%7D%20%5C%5C%3D%20%5Csqrt%7B%28a%5E2%2Bb%5E2%2Ba%5E2-b%5E2%29%28a%5E2%2Bb%5E2-%28a%5E2-b%5E2%29%29%7D%20%5C%5C%3D%20%5Csqrt%7B%282a%5E2%29%28a%5E2%2Bb%5E2-a%5E2%2Bb%5E2%29%7D%20%5C%5C%3D%20%5Csqrt%7B2a%5E2%2A2b%5E2%7D%5C%5C%3D%20%5Csqrt%7B4a%5E2b%5E2%7D%20%5C%5C%20%3D2ab%20%20)
<span>So, the other trigonometric ratios:
</span>
![cos \theta= \frac{adjacent }{hypotenuse }= \frac{2ab}{a^2+b^2} \\ \\ \\ tan \theta= \frac{opposite}{adjacent }= \frac{a^2-b^2}{2ab}](https://tex.z-dn.net/?f=cos%20%5Ctheta%3D%20%5Cfrac%7Badjacent%20%7D%7Bhypotenuse%20%7D%3D%20%5Cfrac%7B2ab%7D%7Ba%5E2%2Bb%5E2%7D%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%20tan%20%5Ctheta%3D%20%5Cfrac%7Bopposite%7D%7Badjacent%20%7D%3D%20%5Cfrac%7Ba%5E2-b%5E2%7D%7B2ab%7D%20)
<span>
</span>
The answer would be 35 hope it helps.