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2 years ago

Solving special systems.

Mathematics

1 answer:

irinina [24]2 years ago

3 0

Given:

The equations of system of equations are

$y=-4x-6$

$-4x-y-6=0$

To find:

The solution of given system of equations.

Solution:

We have,

$y=-4x-6$ ...(i)

$-4x-y-6=0$ ...(ii)

Adding y on both sides in (ii), we get

$-4x-6=y$

$y=-4x-6$

It is same as equation (i). So, we can say that equation (i) and (ii) represent the same line or they are coincident.

Thus, the system of equations has infinitely many solutions.

Therefore, the correct option is C.

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Divide 72 ft in the ratio 9:4:5

Anton [14]

9:4:5.....added together = 18

9/18 (72) = 648/18 = 36
4/18 (72) = 288/18 = 16
5/18 (72) = 360/18 = 20

so we have 36:16:20

5 0

3 years ago

Express 20minutes as ratio of 2hours

Flauer [41]

Answer:

1hr : 10min

Step-by-step explanation:

2 hrs = 120 min

1 hr : 60 min

1hr : 10min

3 0

2 years ago

M is the midpoint of line segment AB

SVEN [57.7K]

Answer:

The coordinates of A would be (-1, 2)

Step-by-step explanation:

In order to find this, use the mid-point formula.

(xA + xB)/2 = xM

In this, the xA is the x value of point A, xB is the x value of point B, and xM is the x value of M. Now we plug in the known information and solve for xA.

(xA + 5)/2 = 2

xA + 5 = 4

xA = -1

Now we can do the same using the midpoint formula and the y values.

(yA + yB)/2 = yM

(yA + 10)/2 = 6

yA + 10 = 12

yA = 2

This gives us the midpoint of (-1, 2)

6 0

2 years ago

From a random sample of 58 businesses, it is found that the mean time the owner spends on administrative issues each week is 21.

zzz [600]

Answer: (20.86, 22.52)

Step-by-step explanation:

Formula to find the confidence interval for population mean :-

$\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}$

, where $\overline{x}$ = sample mean.

z*= critical z-value

n= sample size.

$\sigma$ = Population standard deviation.

By considering the given question , we have

$\overline{x}= 21.69$

$\sigma=3.23$

n= 58

Using z-table, the critical z-value for 95% confidence = z* = 1.96

Then, 95% confidence interval for the amount of time spent on administrative issues will be :

$21.69\pm (1.96)\dfrac{3.23}{\sqrt{58}}$

$=21.69\pm (1.96)\dfrac{1.7}{7.61577}$

$=21.69\pm (1.96)(0.223221)$

$\approx21.69\pm0.83$

$=(21.69-0.83,\ 21.69+0.83)=(20.86,\ 22.52)$

Hence, the 95% confidence interval for the amount of time spent on administrative issues = (20.86, 22.52)

7 0

3 years ago

A path 2.5m wide is running outside a square field whose side is 45m. Determine the area of the path.

aliya0001 [1]

Answer:

The area of the path would be 231.25 squared meters.

Step-by-step explanation:

Consider the path as 45m (the field's area), then add 2.5m to all of the sides. You'll get 47.5m on all sides. Then you do 47.5² to get 2256.25 squared meters. After that, you'll remove the area of the squared field. To do this, do 45m². By doing this, you'll get 2025 squared meters. Lastly, to finish up the question, do 2256.25 - 2025. This would get you 31.25 squared meters, the answer.

4 0

2 years ago