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bearhunter [10]
3 years ago
13

What is the length of MN¯¯¯¯¯¯¯, to the nearest tenth of a foot? 10.6 ft 14.7 ft 15.6 ft 18.0 ft A horizontally-aligned scalene

triangle M N P. Side M P is labeled as 10 feet. Side N P is labeled as 13 feet. Angle P is labeled as 78 degrees.
Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
7 0
Using the Law of Cosine formula, you can find the measurement of the third side of a scalene or isosceles triangle. 

C^2 = A^2 + B^2  -  2AB(cosC)

C^2 = 10^2 + 13^2  -  2(10)(13)(cos78degrees)
C^2 = 100 + 169  -  2(10)(13)(cos78degrees)
C^2 = 100 + 169  -  2(10)(13)(0.21)
C^2 = 100 + 169  -  54.06
C^2 = 269  -  54.06
C^2 = 214.94
C^2 = square root of 214.94
C = 14.66

The answer for this question would be 14.7 ft. :D 
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Three vertices of parallelogram ABCD are A(2,-6),B(-1,2),C(5,3).find the coordinates of vertex D
salantis [7]

Check the first picture below.


for a parallelogram, it has to have two pairs of parallel sides, so BC || AD and AB || CD.

if two lines are parallel, they have the same slope, namely the <u>same rise and run</u>.

notice, the line BC has a run of 6 and a rise of 1, <u>arrows in red</u>, therefore, AD must also have a run of 6 and a rise of 1, so if we move from A 6 units over and 1 up, we'd end up at point D.


now, for part atop

Check the 2nd picture, in a parallelogram, opposite sides are parallel and opposite angles are equal, so if WLP is 144°, then PNW is also 144°.

in a parallelogram, diagonals bisect each other, so each cut the other in halves, so if PM is 9 then MW is also 9 and thus PW is just 9+9=18.


now, about QRST.

notice what we said about a parallelogram above, thus


\bf 8x+13=11x-23\implies 8x+36=11x\implies 36=3x \\\\\\ \cfrac{36}{3}=x\implies \boxed{12=x} \\\\[-0.35em] ~\dotfill\\\\ 2y+12=4y-4\implies 2y+16=4y\implies 16=2y \\\\\\ \cfrac{16}{2}=y\implies \boxed{8=y}


so then TQ ==> 2(8) + 12 ==> 16 + 12 ==> 28.

∡Q ==> 8(12) + 13 ==> 96 + 13 ==> 109°.

and since in a parallelogram, adjacent interior angles add up to 180°, then ∡Q + ∡T = 180°.

∡T ==> 180 - 109 ==> 71°.

3 0
3 years ago
In ΔHIJ, the measure of ∠J=90°, HI = 88 feet, and IJ = 62 feet. Find the measure of ∠I to the nearest tenth of a degree.
devlian [24]

Answer:

Step-by-step explanation:

8 0
3 years ago
Amanda spent a total of 70 minutes competing her chores this week. Write and solve an equation to represent the number of minute
gtnhenbr [62]

Answer:

28 minutes spent in washing the dishes.

Step-by-step explanation:

Given the table

Chore             time in minutes

Sweeping           42

Dishes                  ?

Amanda spent a total of 70 minutes competing her chores this week

Total of 70 minutes spent

42 minutes spent in sweeping . to find the number of minutes Amanda spent in washing the dishes , subtract 42 minutes from the total time spent

let x be the number of minutes spent washing the dishes

42+x=70

To solve for x , subtract 42 from both sides

42+x=70\\x= 70-42\\x=28

28 minutes spent in washing the dishes.

4 0
3 years ago
Find the coordinates of the midpoint of the segment whose endpoint are H(8,13) K(2,1)​
sesenic [268]

Answer:(

7

,

6

)

Explanation:

We can find the coordinates of the midpoint of a line segment, by finding the mean of the sum of the  

x

coordinates and the mean of the sum of the  

y

coordinates.

x

=

8

+

6

2

=

7

y

=

2

+

10

2

=

6

Coordinate of midpoint:

(

7

,

6

)

7 0
3 years ago
If the domain of the function <br>f (x)=2x^2-8 is (-2,3,5) then the range is​
sertanlavr [38]

Answer:

<h2>The range: {0, 10, 42}</h2>

Step-by-step explanation:

Put the values of x from the domain to the equation of the function

f(x) = 2x² - 8

for x = -2

f(-2) = 2(-2)² - 8 = 2(4) - 8 = 8 - 8 = 0

for x = 3

f(3) = 2(3)² - 8 = 2(9) - 8 = 18 - 8 = 10

for x = 5

f(5) = 2(5)² - 8 = 2(25) - 8 = 50 - 8 = 42

7 0
3 years ago
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