Parallel lines, slope is the same so
1) 3x+8y = 12
8y = -3x + 12
y = -3/8(x) + 3/2, slope = -3/8

slope of a line that is parallel = -3/8

2)5x+4y = 5
4y = -5x + 5
y = -5/4(x) + 5/4; slope is -5/4

slope of a line that is parallel = -5/4
--------------------
perpendicular, slope is opposite and reciprocal

3)
3x+8y = 11
8y = -3x + 11
y = -3/8(x) + 11/8. slope = -3/8
slope of perpendicular line = 8/3

4)
x = -7, slope is undefined
so slope of perpendicular line is 0

5)
3x+2y = 12
2y = -3x + 12
y = -3/2(x) + 6 ; slope = -3/2

5x - 6y = 8
6y = 4x - 8
y = 2/3(x) - 4/3; slope is 2/3

slope is opposite and reciprocal, so the equals are perpendicular

6)
3x + y = 5
y = -3x + 5; slope = -3

6x + 2y = -15
2y = -6x - 15
y = -3x - 7.5; slope = -3

both have slope = -3 so equations are parallel

3 0

3 years ago

Ramon makes nectar for a hummingbird feeder by mixing 8 cups of water with 2 cups of sugar. Tiffany makes nectar by mixing 9 cup

cluponka [151]

Answer:

Tiffany

Step-by-step explanation:

Ramon is 4 to 1 water to sugar

Tiffany is 3 to 1 water to sugar

4 0

3 years ago

Explain the error a student is asked to find when the value of an investment of $5200 is an account that earns 4.2% annual inter

zloy xaker [14]

We are given the following information

Investment = $5200

Annual interest rate = 4.2% = 0.042

Final amount = $16,500

Number of years = 27.7 years

Number of compoudings = quartely = 4

The student uses the following model

$V(t)=5200(1.014)^{3t}$

The general formula for compound interest is given by

$V(t)=P(1+\frac{r}{n})^{nt}$

As you can see, the number of compoundings is incorrect (3 vs 4)

The interest rate is also incorrect.

Let us substitute the given values into the above formula

$\begin{gathered} V(t)=P(1+\frac{r}{n})^{nt} \\ V(t)=5200(1+\frac{0.042}{4})^{4\cdot27.7} \\ V(t)=5200(1+0.0105)^{110.8} \\ V(t)=5200(1.0105)^{110.8} \\ V(t)=\$16543.5^{} \end{gathered}$

Therefore, the final amount is approximately $16,543.5

5 0

1 year ago