Answer:
Nina has $10.47 left.
Step-by-step explanation:
$20.14 minus $9.67 is $10.47
Answer:
−135z
2
−2z
The 2 is representing Square
Step-by-step explanation:
(3z)
2
−4z+11−(12z)
2
+2z−11
Expand (3z)
2
.
3
2
z
2
−4z+11−(12z)
2
+2z−11
Calculate 3 to the power of 2 and get 9.
9z
2
−4z+11−(12z)
2
+2z−11
Expand (12z)
2
.
9z
2
−4z+11−12
2
z
2
+2z−11
Calculate 12 to the power of 2 and get 144.
9z
2
−4z+11−144z
2
+2z−11
Combine 9z
2
and −144z
2
to get −135z
2
.
−135z
2
−4z+11+2z−11
Combine −4z and 2z to get −2z.
−135z
2
−2z+11−11
Subtract 11 from 11 to get 0.
−135z
2
−2z
The equation of second graph is ![d = 2.5 t + 1](https://tex.z-dn.net/?f=d%20%3D%202.5%20t%20%2B%201)
We have given the linear equation is
![d = 2.5 t +2.2,](https://tex.z-dn.net/?f=d%20%3D%202.5%20t%20%2B2.2%2C)
If the graph of the position of the second object is parallel to
![d = 2.5 t +2.2,](https://tex.z-dn.net/?f=d%20%3D%202.5%20t%20%2B2.2%2C)
<h3>What is the form of linear equation?</h3>
The equation of slope intercept form is
![d=mt+b](https://tex.z-dn.net/?f=d%3Dmt%2Bb)
compare the given equation with the slope intercept form
we get m = 2.5
t = 0, d = 1
1 = 2.5 · 0 + b
b = 1
Therefore,the equation of second graph is ![d = 2.5 t + 1](https://tex.z-dn.net/?f=d%20%3D%202.5%20t%20%2B%201)
To learn more about the linear equation visit:
brainly.com/question/14323743
Look at the picture.
![\csc\theta=\dfrac{1}{\sin\theta}=\dfrac{1}{\frac{y}{r}}=\dfrac{r}{y}](https://tex.z-dn.net/?f=%5Ccsc%5Ctheta%3D%5Cdfrac%7B1%7D%7B%5Csin%5Ctheta%7D%3D%5Cdfrac%7B1%7D%7B%5Cfrac%7By%7D%7Br%7D%7D%3D%5Cdfrac%7Br%7D%7By%7D)
We have the right triangle x, y and r. From the Pythagorean theorem we have:
![r^2=x^2+y^2\to r=\sqrt{x^2+y^2}](https://tex.z-dn.net/?f=r%5E2%3Dx%5E2%2By%5E2%5Cto%20r%3D%5Csqrt%7Bx%5E2%2By%5E2%7D)
We have the point
![\left(-\dfrac{2}{3};\ \dfrac{\sqrt5}{3}\right)](https://tex.z-dn.net/?f=%5Cleft%28-%5Cdfrac%7B2%7D%7B3%7D%3B%5C%20%5Cdfrac%7B%5Csqrt5%7D%7B3%7D%5Cright%29)
Substitute:
![r=\sqrt{\left(-\dfrac{2}{3}\right)^2+\left(\dfrac{\sqrt5}{3}\right)^2}\\\\r=\sqrt{\dfrac{4}{9}+\dfrac{5}{9}}\\\\r=\sqrt{\dfrac{9}{9}}\\\\r=1](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%5Cleft%28-%5Cdfrac%7B2%7D%7B3%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B%5Csqrt5%7D%7B3%7D%5Cright%29%5E2%7D%5C%5C%5C%5Cr%3D%5Csqrt%7B%5Cdfrac%7B4%7D%7B9%7D%2B%5Cdfrac%7B5%7D%7B9%7D%7D%5C%5C%5C%5Cr%3D%5Csqrt%7B%5Cdfrac%7B9%7D%7B9%7D%7D%5C%5C%5C%5Cr%3D1)
![\csc\theta=\dfrac{1}{\frac{\sqrt5}{3}}=\dfrac{3}{\sqrt5}=\dfrac{3\cdot\sqrt5}{\sqrt5\cdot\sqrt5}=\boxed{\dfrac{3\sqrt5}{5}}](https://tex.z-dn.net/?f=%5Ccsc%5Ctheta%3D%5Cdfrac%7B1%7D%7B%5Cfrac%7B%5Csqrt5%7D%7B3%7D%7D%3D%5Cdfrac%7B3%7D%7B%5Csqrt5%7D%3D%5Cdfrac%7B3%5Ccdot%5Csqrt5%7D%7B%5Csqrt5%5Ccdot%5Csqrt5%7D%3D%5Cboxed%7B%5Cdfrac%7B3%5Csqrt5%7D%7B5%7D%7D)