Change to standard form 3.42x10^-5

Draw an angle in standard position whose terminal side contains the point

kvasek [131]

Answer:

The distance of the point from the origin = 9.29 units.

Step-by-step explanation:

Given point:

(7,-6)

The angle lies such that the terminal side of the angle contains the given point.

To draw the angle and find the distance from the origin to the given point.

Solution:

The terminal side of the angle is where the angle ends with the initial side being the positive side of the x-axis.

So, we can plot the point (7,-6) by moving 7 units on the x-axis horizontally and -6 units on the y-axis vertically.

We can find the distance of the point from the origin by find the hypotenuse of the triangle formed.

Applying Pythagorean theorem.

$Hypotenuse^2=Shorter\ Leg^2+Shortest\ Leg^2$

$Hypotenuse^2 = (7)^2+(-6)^2$

$Hypotenuse^2=49+36\\Hypotenuse^2=85$

Taking square root both sides :

$\sqrt{Hypotenuse^2}=\sqrt{85}$

$Hypotenuse = 9.29\ units$

Thus, the distance of the point from the origin = 9.29 units.

The figure is shown below.

5 0

3 years ago

HELPPPPPP PLEASE

avanturin [10]

C. The functions fans g have different axes of symmetry and different minimum values

7 0

3 years ago

Complete the point-slope equation of the line through (-8,-8) and (-7,9)

denis23 [38]

Step-by-step explanation:

point slope formula: y-y1=m(x-x1)

m= y2-y1/x2-x1

input numbers

so slope:

m=(9--8)/(-7--8)

(-)×(-)=+

(+)×(-)=(-)

so m=17/1

m=17

now point slope

y--8=17(x--8)

y+8=17x+136

to get y alone we have to use opposite operations

y and 8 are adding so we need to subtract on both sides

y+8-8=17x+136-8

y=17x+128

5 0

2 years ago

A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. U

balu736 [363]

Answer:

Step-by-step explanation:

number of samples, n = 10

Mean = (48 + 51 + 46 + 52 + 47 + 48 + 47 + 50 + 51 + 59)/10 = 49.9

Standard deviation = √(summation(x - mean)/n

Summation(x - mean) = (48 - 49.9)^2 + (51 - 49.9)^2 + (46 - 49.9)^2+ (52 - 49.9)^2 + (47 - 49.9)^2 + (48 - 49.9)^2 + (47 - 49.9)^2 + (50 - 49.9)^2 + (51 - 49.9)^2 + (59- 49.9)^2 = 128.9

Standard deviation = √128.9/10 = 3.59

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 10 - 1 = 9

Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 2.262

Margin of error = 2.262 × 3.59/√10

= 2.57

the lower limit of this confidence interval is

49.9 - 2.57 = 47.33

the lower limit of this confidence interval is

49.9 + 2.57 = 52.47

So it is false

6 0

3 years ago

The apother is 4 m and a side is 5.8 m. What is the area

jekas [21]

Answer:

58 m^2.

Step-by-step explanation:

The area of one of the 5 triangles is:

1/2 * 5.8 * 4 = 11.6 m^2

So the area of the pentagon

= 5 + 11.6

= 58 m^2

4 0

3 years ago

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