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4 years ago

Question 21

Mathematics

1 answer:

RUDIKE [14]4 years ago

6 0

Answer:

y=-2x+1

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals of one another. slope 1/2 perpendicular will be -2/1=-2

y-5=-2(x-(-2))

y-5=-2(x+2)

y-5=-2x-4

y=-2x-4+5

y=-2x+1

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Terms and coefficients of 7p - 3r + 6 - 5s

Sophie [7]

Term=7p
coefficient=7

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3 years ago

Find all values of c such that 3^2c+1=28*3^c-9. If you find more than one value of c, then list your values in increasing order

avanturin [10]

$3^{2c} + 1 = 28\times3^c - 9 \implies 3^{2c} - 28\times3^c = -10$

Complete the square on the left side:

$3^{2c} - 28\times3^c = \left(3^{2c}-28\times3^c+14^2\right)-14^2 = \left(3^c-14\right)^2 - 196$

Then the equation becomes

$\left(3^c-14\right)^2 - 196 = -10 \\\\ \left(3^c-14\right)^2 = 186 \\\\ 3^c - 14 = \pm\sqrt{186} \\\\ 3^c = 14\pm\sqrt{186}$

Both 14 + √186 and 14 - √186 are positive numbers, so we can take the logarithm (base 3) of both sides without issue:

$\log_3\left(3^c) = c = \log_3\left(14\pm\sqrt{186}\right)$

Then in increasing order, the solutions are

c = log₃(14 - √186), c = log₃(14 + √186)

3 0

3 years ago

How many solutions does x^2-6x=-14 have

valina [46]

Answer:

it has 0 solution

Step-by-step explanation:

b^2-4ac<0=0 real # solution

brainliest please

4 0

3 years ago

Read 2 more answers

A random sample of 500 registered voters in Phoenix is asked if they favor the use of oxygenated fuels year-round to reduce air

Stells [14]

Answer:

a) 0.0853

b) 0.0000

Step-by-step explanation:

Parameters given stated that;

H₀ : p = 0.6

H₁ : p = 0.6, this explains the acceptance region as;

p° ≤ $\frac{315}{500}$ =0.63 and the region region as p°>0.63 (where p° is known as the sample proportion)

a).

the probability of type I error if exactly 60% is calculated as :

∝ = P (Reject H₀ | H₀ is true)

= P (p°>0.63 | p=0.6)

where p° is represented as pI in the subsequent calculated steps below

= P $[\frac{p°-p}{\sqrt{\frac{p(1-p)}{n}}} >\frac{0.63-p}{\sqrt{\frac{p(1-p)}{n}}} |p=0.6]$

= P $[\frac{p°-0.6}{\sqrt{\frac{0.6(1-0.6)}{500}}} >\frac{0.63-0.6}{\sqrt{\frac{0.6(1-0.6)}{500}}} ]$

= P $[Z>\frac{0.63-0.6}{\sqrt{\frac{0.6(1-0.6)}{500} } } ]$

= P [Z > 1.37]

= 1 - P [Z ≤ 1.37]

= 1 - Ф (1.37)

= 1 - 0.914657 ( from Cumulative Standard Normal Distribution Table)

≅ 0.0853

The probability of Type II error β is stated as:

β = P (Accept H₀ | H₁ is true)

= P [p° ≤ 0.63 | p = 0.75]

where p° is represented as pI in the subsequent calculated steps below

= P $[\frac{p°-p} \sqrt{\frac{p(1-p)}{n} } }\leq \frac{0.63-p}{\sqrt{\frac{p(1-p)}{n} } } | p=0.75]$

= P $[\frac{p°-0.6} \sqrt{\frac{0.75(1-0.75)}{500} } }\leq \frac{0.63-0.75}{\sqrt{\frac{0.75(1-0.75)}{500} } } ]$

= P $[Z\leq\frac{0.63-0.75}{\sqrt{\frac{0.75(1-0.75)}{500} } } ]$

= P [Z ≤ -6.20]

= Ф (-6.20)

≅ 0.0000 (from Cumulative Standard Normal Distribution Table).

6 0

3 years ago

How to solve this please help!!

Angelina_Jolie [31]

Mary is incorrect. Perimeter is not proportional to area. An example which you can use is garden A is an 8 by 1 rectangle. The perimeter is 18 while the area is 8. Graden B is a 4 by 4 square. The perimeter is 16 (less than garden A) while the area is 16 (two times more than garden B).

8 0

3 years ago