Find the equation of a line parallel to 2x-3y+6=0, with the same y-intercept as y=7x-1

Find the slope between two points ( -2,4) 3,-6)

Ksivusya [100]

Answer:

-1/2

Step-by-step explanation:

4 0

2 years ago

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Show with work please.

kolbaska11 [484]

Answer:

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

Step-by-step explanation:

The identity you will use is:

$\csc \left(x\right)=\frac{1}{\sin \left(x\right)}$

So,

$\csc \left(\theta-\frac{\pi }{2}\right)$

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{\sin \left(-\frac{\pi }{2}+\theta\right)}$

Now, using the difference of sin

Note: state that $\text{sin}(\alpha\pm \beta)=\text{sin}(\alpha) \text{cos}(\beta) \pm \text{cos}(\alpha) \text{sin}(\beta)$

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)}$

Solving the difference of sin:

$-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)$

$-\cos \left(\theta\right) \cdot 1+0\cdot \sin \left(\theta\right)$

$-\text{cos} \left(\theta\right)$

Then,

$\csc \left(\theta-\frac{\pi }{2}\right)=-\frac{1}{\cos \left(\theta\right)}$

Once

$\text{sec}(-\theta)=\text{sec}(\theta)$

And, $\text{sec}(\theta)=-0.73$

$-\frac{1}{\cos \left(\theta\right)}=-\text{sec}(\theta)$

$-\frac{1}{\cos \left(\theta\right)}=-(-0.73)$

$-\frac{1}{\cos \left(\theta\right)}=0.73$

Therefore,

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

3 0

2 years ago

A pecan pie is being served for dessert. One piece of pie has an arc length of 7.85 in. It has been cut into 8 equal pieces. Wha

grin007 [14]

Answer:

The radius of the pie is 6.17 in.

Step-by-step explanation:

The formula for arc length as a function of radius is

s = r·Ф, where Ф is the central angle in radians.

Here we know that the arc length is 7.85 in. Assuming that the whole pie has been cut into 8 equal pieces, the central angle of one such piece is

2π / 8, or π /4 (radians).

thus, s = r·Ф, solved for r, is r = s/Ф

and in this instance r = (7.85 in)/(π/4). Evaluating this, we get:

r = 6.17 in

The radius of the pie is 6.17 in.

8 0

3 years ago

A random sample of 25 statistics examinations was selected. The average score in the sample was 76 with a variance of 144. Assum

Mazyrski [523]

Answer:

99% confidence interval for the population average examination score is between a lower limit of 69.2872 and an upper limit of 82.7128.

Step-by-step explanation:

Confidence interval = mean +/- margin of error (E)

mean = 76

variance = 144

sd = sqrt(variance) = sqrt(144) = 12

n = 25

degree of freedom (df) = n - 1 = 25 - 1 = 24

confidence level (C) = 99% = 0.99

significance level = 1 - C = 1 - 0.99 = 0.01 = 1%

t-value corresponding to 24 df and 1% significance level is 2.797

E = t×sd/√n = 2.797×12/√25 = 6.7128

Lower limit = mean - E = 76 - 6.7128 = 69.2872

Upper limit = mean + E = 76 + 6.7128 = 82.7128

99% confidence interval is (69.2872, 82.7128)

6 0

2 years ago

Matthew has 219 pens to put in the packages. Each package must hold 8 pens

erica [24]

219 divided by 8=27.35
27x8=216
219-216=3
Matthew can make 27 packages.
3 pens will be left over.
Please mark Brainelist

7 0

2 years ago

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