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3 years ago

Are these lines parallel, perpendicular, or neither? 3y=x+4 and 3x+y=1

Mathematics

2 answers:

Goryan [66]3 years ago

6 0

Answer:

These lines are perpendicular

Step-by-step explanation:

3y=x+4

$y = \frac{1}{3}x+\frac{4}{3}$

Slope (m1) = 1/3

3x+y=1

y = -3x + 1

Slope (m2) = - 3

m1 * m2 = $\frac{1}{3}* -3$

= -1

So, these lines are perpendicular.

If product of two slopes is (-1), then they are perpendicular lines.

If both lines have same slope, then they are parallel.

REY [17]3 years ago

5 0

Answer:

perpendicular

Step-by-step explanation:

3y = x + 4 in slope intercept form y = 1/3x +4/3

3x + y = 1 in slope intercept form y = -3x +1

the slopes are negative reciprocals of each other so they are perpendicular

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Miss Jones it it it is Southern living home party to purchase a vase which cost $34.99 the shipping charge was three dollars and

creativ13 [48]

Answer:

The amount paid for the vase is $41.12.

Step-by-step explanation:

Given:

A vase which cost $34.99 the shipping charge was $3.00 and 8.25% sales tax was paid on the subtotal which including the shipping charge.

Now, to find the amount paid for the vase.

Cost of vase = $34.99.

Shipping charge = $3.00.

Sales tax = 8.25%.

So, on adding shipping charge on cost of vase:

$34.99+3.00=\$37.99.$

As, given sales tax was paid on the subtotal which including the shipping charge.

Now, to get the amount paid for the vase:

$37.99 + 8.25% of $37.99

$=37.99+\frac{8.25}{100} \times 37.99$

$=37.99+0.0825\times 37.99$

$=37.99+3.13$

$=\$41.12.$

Therefore, the amount paid for the vase is $41.12.

6 0

3 years ago

The local bike shop charges a rental fee of 12$ as was as 4$ per hour to rent a bike if I spent 44$ write an equation to model t

vfiekz [6]

Answer:

8 hours

Step-by-step explanation:

rental fee = 12 + 4/hr

spent = 44

44 = 12+4(hr)

32 = 4(hr)

32/4 = hr

hr = 8

5 0

4 years ago

__________ is a problem solving technique that attempts to come up with as many solutions as possible in a short time without ce

Misha Larkins [42]

Brainstorming is a problem solving technique that attempts to come up with as many solutions as possible in a short time without censoring the ideas.

4 0

3 years ago

Plzz answer all odd questions if not all plzzz do at least 4 and show work. I will give brainliest to the one with the most corr

tatyana61 [14]

1) x^2=36
x=6

3) x^2-8x+13=0 —> x= (8±√64-4(1)(13))/2(1)
x=4±√3

5) x^2-6x+9-k=0 —> x=(6±√36-4(1)(9-k))/2(1) —> (6±√4k)/2 —> (6±2√k)/2
x=3±√k

7) y=x^2-4x+11 —> y-11=x^2-4x —> take the half of the coefficient of the single x term and square it and add it on both sides —> y-11+4=x^2-4x+4 —> y-7=(x-2)^2 —> y=(x-2)^2+7
Minimum: (2,7)
Maximum: n/a
X intercepts: none (never crosses the x-intercept)

9) y=x^2+2x-8 —> y+8+1=x^2+2x+1 —> y=(x+1)^2-9
Minimum: (-1,-9)
Maximum: n/a
x-intercepts: (x+4)(x-2) —> (-4,0),(2,0)

11) c

13) (x+7)(x+3)

15) x=(-6±√36-4(1)(10))/2 —> x=(-6±√-4)/2 —> (-6±2i)/2
x=-3±i OR no real solutions

3 0

3 years ago

A Survey of 85 company employees shows that the mean length of the Christmas vacation was 4.5 days, with a standard deviation of

GenaCL600 [577]

Answer:

The 95% confidence interval for the population's mean length of vacation, in days, is (4.24, 4.76).

The 92% confidence interval for the population's mean length of vacation, in days, is (4.27, 4.73).

Step-by-step explanation:

We have the standard deviations for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 85 - 1 = 84

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 84 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 1.989.

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.989\frac{1.2}{\sqrt{85}} = 0.26$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 4.5 - 0.26 = 4.24 days

The upper end of the interval is the sample mean added to M. So it is 4.5 + 0.26 = 4.76 days

The 95% confidence interval for the population's mean length of vacation, in days, is (4.24, 4.76).

92% confidence interval:

Following the sample logic, the critical value is 1.772. So

$M = T\frac{s}{\sqrt{n}} = 1.772\frac{1.2}{\sqrt{85}} = 0.23$

The lower end of the interval is the sample mean subtracted by M. So it is 4.5 - 0.23 = 4.27 days

The upper end of the interval is the sample mean added to M. So it is 4.5 + 0.23 = 4.73 days

The 92% confidence interval for the population's mean length of vacation, in days, is (4.27, 4.73).

8 0

3 years ago