4. You would need to set up equations. Two per problem. So 5x+2s=98. And 9x+2s=154. Then you would multiply one of them by a negative one to make the 2 student tickets cancel out. I would use the top one. So it turns to -5c-2s=-98. The -2c and 2c cancel out. You put the rest together to get 4X=56. And 56/4 is 14. So the senior tickets (X) are 14$. You would then replace X with fourteen one of the original equations. Again I'm going to use the first one. So 5(14)+2c=98. 5x14 is 70. Subtract 70 from both sides to get 2c=28. Divide both sides by 2 to get C=14. So the student tickets are 14$ and the seniors are also 14$.
5. Same thing on this one. Two equations. 8h+7i=84 and 3h+1i=25. Like going to multiply the second equation by -7 so the i's will cancel out to get -21h-7i=-175. So you will end up with -13h=-91. Divide both sides by -13 to get H=7. Replace H in one of the equations. I'll use second one. So 3(7)+1i=25. 3x7=21 so subtract 21 from both sides to get i=4. So the ivy is 4$ and the hostas are 7$.
Hope that helped a little bit!
Answer:
2,058
Step-by-step explanation:
first term : a_1 = 6
common ratio r = 7
a_n = (a_1) * r ^(n-1)
a_4 = 6 * 7^(4-1)
a_4 = 6 *7^3
a_4 = 6 * 343 = 2,058
Answer:
Lets start with d, since its all alone, take 180 - 58 = d, which is 122 = d, next c, 180 - 48 - 58 = c, which is 74 = c, next a, since d is 122, 180 - 122 = a because d + a = 180, a = 58, a + b + c = 180 so, 180 - 58 - 74 = b, b = 48
A=58
B=48
C=74
D=122
If f(x) = 2x -6+4
Then
f(-2) = 2(-2) -2
f(-2) = -6
Answer:
Step-by-step explanation:
The domain of that function is all real numbers. The x values will drop into negative infinity and will grow to positive infinity.
The range is found from the vertex form of a parabola, which is
![y=(x-h)^2+k](https://tex.z-dn.net/?f=y%3D%28x-h%29%5E2%2Bk)
where h indicates side to side movement of the vertex and k indicates up or down. Our function has a +3 at the end of it and is positive (so it opens upwards), so the range is y ≥ 3.
To find the inverse of that function, switch the x and y coordinates and solve for the new y. Let f(x) be y, then switch the x and y:
![x=y^2+3](https://tex.z-dn.net/?f=x%3Dy%5E2%2B3)
Now solve for the new y:
y = ±![\sqrt{x-3}](https://tex.z-dn.net/?f=%5Csqrt%7Bx-3%7D)
To find the domain of a radical, set the radicand greater than or equal to 0 and solve for x (this is because the radicand cannot be a negative number or we are dealing with imaginary numbers and that's not what you want. BTW, a radicand is the term under the radical sign).
x - 3 ≥ 0 so x ≥ 3. The domain of the inverse is all real numbers greater than or equal to 3.
This is a sideways parabola (the inverse is), and it opens to the right starting at the x value of 3. It will grow into positive values of y to infinity and will drop into negative values of y into negative infinity.
Just a little trick here to remember, and it ALWAYS holds true: the domain of a function is the range of its inverse, and the range of a function is the domain of its inverse. Look to our solution for your problem here and you'll see that it is true.