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3 years ago

Please Help!!!!

Mathematics

1 answer:

Iteru [2.4K]3 years ago

5 0

Step-by-step explanation:

Given : m∥n , ∠1= 50° , ∠2= 48° , and line s bisects ∠ABC

To prove = ∠3= 49°

Solution:

In figure, m∥n cut by traversal t.

So, ∠DEF = ∠ABC(alternative exterior angles)

∠1 + ∠2 = ∠4 + ∠5

∠ABC = ∠1 + ∠2 = 50° + 48° = 98°

Also given that s bisect angles ∠ABC.

∠4 = ∠5

∠ABC = ∠4 + ∠5 = 98°

∠4 + ∠4 = 98°

2∠4 = 98°

∠4 = 49°

∠4= ∠3 = 49° (vertically opposite angles)

∠3 = 49° ,hence proved

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Francine ran 3 1/2 laps around the circular track in the school gym. The track has a diameter of 1/2 miles. About how far does F

Juliette [100K]

Answer:

Francine run 5.495 miles

Step-by-step explanation:

Given :

Francine ran $3\frac{1}{2}$ laps around the circular track in the school gym.

The track has a diameter of 1/2 miles.

To Find : About how far does Francine run?

Solution :

First we need to calculate the perimeter of circular track :

Perimeter of circle : $2\pi r$

Since we are given the diameter = 1/2 miles = 0.5 miles

So, Radius will be (Diameter/2) = 0.5/2 = 0.25 miles

So, The perimeter will be:

$2\pi *0.25$

$0.5\pi$

Since $\pi =3.14$

⇒ $0.5*3.14$

⇒ $1.57$

Thus the circular track is of 1.57 miles .

Since she ran $3\frac{1}{2}$ = 7/2=3.5 laps

1 lap = 1.57 miles

So, 3.5 laps = 1.57*3.5 =5.495 miles .

Hence , Francine run 5.495 miles

6 0

3 years ago

Circle L is shown. Line segments K L and M L are radii. The length of K L is 12. Angle M L K is 60 degrees. Sector M L K with a

sergejj [24]

Answer:

$120\pi$ square units

Step-by-step explanation:

We are given that

Radius of circle=12 units

Angle MLK=60 degree

We have to find the area of sector that is not shaded.

Area of shaded sector MLK= $\frac{\theta}{360}\times \pi r^2$

Area of shaded sector MLK= $\frac{60}{360}\times \pi(12)^2=$ 24 square units

Area of whole circle= $\pi r^2=\pi (12)^2=144\pi$ square units

Area of sector that is not shaded =Area of whole circle-Area of shaded sector MLK= $144\pi-24\pi$

Area of sector that is not shaded= $120\pi$ square units

4 0

3 years ago

Read 2 more answers

Elena walked 20 minutes more than Lin. Jada walked twice as long as Elena. Jada walked for 90 minutes. The equation 2(x +20) = 9

KonstantinChe [14]

Answer:

(x+20) explains the elena walked 20 minutes more than Lin

Step-by-step explanation:

(x+20) explains the elena walked 20 minutes more than Lin

As given in the question that elena walked 20minutes more than lin means if elena walked x then lin walked (x+20) and also jada walked twice as long as elena means 2(x+20) and according to question jada walked 90 minutes means 2(x +20) = 90

7 0

3 years ago

Read 2 more answers

1. A hammock is suspended between two trees. The curve the hammock makes can be modelled by the equation, y = 0.2x2 – 0.4x – 0.6

Rina8888 [55]

Answer:

Step-by-step explanation:

Given that:

The modeled equation y = 0.2x² - 0.4x - 0.6

To find x- intercepts

y = 0.2x² - 0.4x - 0.6

y = 0.2(x² - 2x - 3)

y = 0.2(x - 3)(x + 1)

Suppose the upward parabola cuts x axis at x = 3 and x = - 1

Then, the length of the intercepts will be = 3 -(-1)

We can say that the trees will be 4 unit apart.

To find y-intercepts;

y = 0.2(0)² - 0.4(0) -0.6

y = -0.6 meters

8 0

3 years ago

Unit 1 geometry basics quiz 1-3 angle measures and relationships

ASHA 777 [7]

Answer/Step-by-step explanation:

1. Side CD and side DG meet at endpoint D to form <4. Therefore, the sides of <4 are:

Side CD and side DG.

2. Vertex of <2 is the endpoint at which two sides meet to form <2.

Vertex of <2 is D.

3. Another name for <3 is <EDG

4. <5 is less than 90°. Therefore, <5 can be classified as an acute angle.

5. <CDE is less than 180° but greater than 90°. Therefore, <CDE is classified as an obtuse angle.

6. m<5 = 42°

m<1 = 117°

m<CDF = ?

m<5 + m<1 = m<CDF (angle addition postulate)

42° + 117° = m<CDF (Substitution)

159° = m<CDF

m<CDF = 159°

7. m<3 = 73°

m<FDE = ?

m<FDG = right angle = 90°

m<3 + m<FDE = m<FDG (Angle addition postulate)

73° + m<FDE = 90° (Substitution)

73° + m<FDE - 73° = 90° - 73°

m<FDE = 17°

3 0

3 years ago