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3 years ago

In the figure, AB || CD. If m<1=70° and m<2 = 45°, find the m<3

Mathematics

1 answer:

docker41 [41]3 years ago

8 0

Answer:65 degrees

Step-by-step explanation: a triangle has 180 degrees.

one angle is 45 degrees and the other is 70

if we add them together we get 115

180-115 is 65

m3 is 65 degrees

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A North American river otter wants to cross the North Saskatchewan river. It can swim at a speed of 2.75 m/s. In that location,

insens350 [35]

Answer:

Step-by-step explanation:

time to cross will be the distance divided by the velocity in that direction.

a) t = d/v = 45/2.75 = 16.363636... 16.4 s

In the same time that the otter is swimming cross stream, the stream is also moving perpendicularly at its own pace.

b) d = vt = 2.5(16.36) = 40.9090... 40.9 m

As velocity is a vector, An observer on the bank would see the velocity as the vector addition of the cross stream and down stream velocities

c) v = √(2.75² + 2.5²) = 3.716517... 3.72 m/s magnitude

θ = arctan2.5/2.75 = 42.2736... 42.3° downstream of a line straight across

7 0

3 years ago

the plans for your 13th birthday party are well under way. your parents agree to your guest list of 400 people. you decided it w

diamong [38]

Answer:

11 people will get both the prizes.

Step-by-step explanation:

In this question we need to find common integral multiples of 5 and 7 under 400. As you can see in the figure 35th person is the first one to get both ipod and psp. The LCM (least common multiple) of 5 and 7 which is 35 (!!! I hope you know how to LCM of two integers ).

Therefore the integral multiples of 35 will be same as the common multiples of 5 and 7. So, figuring out the number of integral multiples of 35 under 400 will give the answer.

To do that divide the number 400 with 35. On performing the division the quotient will be 11 and the remainder will be 15.

Therefore 11 persons out of 400 will get both the prizes.

Similarly if you want to find the number of person getting ipod then divide 400 with 5. The quotient will be 80. ∴ 80 people will get ipod.

And for psp, divide 400 with 7. The quotient will be 57. ∴ 57 people will get psp.

In these divisions, consider just the quotient, here remainder is of no use.

5 0

3 years ago

A rhombus has four 6-inch sides and two 120-degree angles. From one of the vertices of the obtuse angles, the two latitudes are

nikitadnepr [17]

Answer:

Area(A)=Area(C)= $9 in^{2}$

Area(B)= $13.2 in^{2}$

Step-by-step explanation:

We begin with finding the angles a and b that from the drawing attached you can see that a=b.

Now, the sum of the internal angles of a rhomboid is equal to 360 degrees, with that we have:

120+120+a+b=360

240+2a=360

2a=120

a=60=b

Next, in the image you can see that the lines coming from the angle at the top 120 degrees vertex, divide the opposite sides by half, thus making two triangles with one side of 6 in and another of 3 in.

We can say from the drawing as well:

Area(A)+Area(B)+Area(C)=Area(rhomboid)

But, we can also say that Area(A)=Area(C)

So, starting with Area(A)

Area(A)=Area(triangle)= $\frac{b*h}{2}$ = $\frac{6*3}{2}$ = $9 in^{2}$

We can then calculate the area B, a rhomboid, or better, take the Total area of the figure and subtract the area of the two triangles.

Area(B)=Area(rhomboid)-Area(A)-Area(C)

Area(rhomboid)=b*h where b=6in and h is the perpendicular distance from the base to the top.

$h=[tex]6*cos(30)=5.20in$ The 30 degrees come from: 120-30-60=30, since the latitudes split the 120 angle in two equal parts and one that is the half of the obtuse angle.

Area(rhomboid)=5.20*6= $31.2 in^{2}$

Area(B)=Area(rhomboid)-Area(A)-Area(C)= $31.2 in^{2}$ - $9 in^{2}$ - $9 in^{2}$ = $13.2 in^{2}$

3 0

3 years ago

Whats is the answer to this question below?

uysha [10]

Hey there. So first we need to know what the point slope form looks like.

It is Y-Y1=M (X-X1)

Knowing this you just plug in the given information.

M is equal to 1/6. So in this case all of the options have the correct m. Next we look at the Year value. We know Y is a positive 4. So the beginning of the equation is going to look like

Y+4=1/6 ( X-X1).

Nown plug in x. It would be a negative 5. Now your final answer would be option A. Hope the explanation helped.. :)

4 0

3 years ago

A container has 12 and 3/4 cups of lemonade .asher gives each of his classmates 7/8 of a cup of lemonade . He gives away all of

Agata [3.3K]

Asher gave lemonade to 14 students

Solution:

Given that, A container has 12 and $\frac{3}{4}$ cups of lemonade