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3 years ago

Find the midpoint of the line segment joining the points. (6, -5), (6, 3)

Mathematics

2 answers:

Sphinxa [80]3 years ago

6 0

Answer:

Step-by-step explanation:

3-5/2

6-6/2

-2/2=-1

0/2= 0

(-1,0)

adoni [48]3 years ago

3 0

Answer:

The mid point is (6,-1)

Step-by-step explanation:

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Write an equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the l

mamaluj [8]

The equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5 is $y = \frac{3}{4}x - \frac{5}{4}$

Solution:

The slope intercept form is given as:

y = mx + c ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Given that the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5

Given line is perpendicular to − 4 x − 3 y = − 5

− 4 x − 3 y = − 5

-3y = 4x - 5

3y = -4x + 5

$y = \frac{-4x}{3} + \frac{5}{3}$

On comparing the above equation with eqn 1, we get,

$m = \frac{-4}{3}$

We know that product of slope of a line and slope of line perpendicular to it is -1

$\frac{-4}{3} \times \text{ slope of line perpendicular to it}= -1\\\\\text{ slope of line perpendicular to it} = \frac{3}{4}$

Given point is (-1, -2)

Now we have to find the equation of line passing through (-1, -2) with slope $m = \frac{3}{4}$

Substitute (x, y) = (-1, -2) and m = 3/4 in eqn 1

$-2 = \frac{3}{4}(-1) + c\\\\-2 = \frac{-3}{4} + c\\\\c = - 2 + \frac{3}{4}\\\\c = \frac{-5}{4}$

$\text{ substitute } c = \frac{-5}{4} \text{ and } m = \frac{3}{4} \text{ in eqn 1}$

$y = \frac{3}{4} \times x + \frac{-5}{4}\\\\y = \frac{3}{4}x - \frac{5}{4}$

Thus the required equation of line is found

8 0

2 years ago

11. In AWTY, if mZW is five less than twice mZY and mZX is 21 more than m_Y find the measure

wolverine [178]

9514 1404 393

Answer:

angles (W, X, Y) = (77°, 62°, 41°)

Step-by-step explanation:

Given:

ΔWZY

∠W = 2(∠Y) -5°

∠X = ∠Y +21°

Find:

∠X, ∠Y, ∠W

Solution:

Using angle measures in degrees, we have ...

∠X + ∠Y + ∠Z = 180

(∠Y +21) +∠Y + (2(∠Y) -5) = 180

4(∠Y) +16 = 180 . . . . . simplify

∠Y +4 = 45 . . . . . . . . . divide by 4

∠Y = 41 . . . . . . . . . . . . subtract 4

∠W = 2(41) -5 = 77

∠X = 41 +21 = 62

The angle measures of angles (W, X, Y) are (77°, 62°, 41°), respectively.

7 0

2 years ago

The larger of two numbers is 15 more than three times the smaller number. If the sum of the two numbers is 63, find the numbers.

tangare [24]

The larger number is 51 and the smaller number is 12. ( hope I helped) have a good day

3 0

2 years ago

The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. based on a large number of obser

Liono4ka [1.6K]

The normal distribution curve for the problem is shown below

We need to standardise the value X=405.5 by using the formula

$z-score= \frac{X-Mean}{Standard Deviation}$
$z-score= \frac{405.5-402.7}{8.8} =0.32$

We now need to find the probability of z=0.32 by reading the z-table

Note that z-table would give the reading to the left of z-score, so if your aim is to work out the area to the right of a z-score, then you'd need to do:

$P(Z\ \textgreater \ z)=1 - P(Z\ \textless \ z)$

from the z-table, the reading $P(Z\ \textless \ 0.32)$ gives 0.6255

hence,
$P(Z\ \textgreater \ 0.32)=1-0.6255=0.3475$

The probability that the mean weight for a sample of 40 trout exceeds 405.5 gram is 0.3475 = 34.75%

7 0

2 years ago

Please help with this question!!

barxatty [35]

Answer:

-29/20

Step-by-step explanation:

The cosecant function is the inverse of the sine function. Both sine and cosecant are odd functions, meaning csc(-x) = -csc(x) = -1/sin(x).

csc(-θ) = -1/sin(θ) = -1/(20/29) = -29/20

6 0

2 years ago