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Gala2k [10]
3 years ago
11

Ms. Martinez drove 20 miles in March. She drove 5 times as many miles in March as she did in January. She drove 4 times as many

miles in February as she did in January. How many miles did Ms. Martinez drive in February?
Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
3 0

Answer:

825/3 = 275 which is how many miles she drove in January.

275*4= 1100 which is how many miles she drove in February.

Ms. Turner drove 1100 miles in February.

Step-by-step explanation:

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Answer:

segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX

Step-by-step explanation:

see the attached figure to better understand the problem  

we know that  

If m∠E = m∠Y and m∠F = m∠X  

then  

Triangles EFG and YXZ are similar by AA Similarity Theorem  

Remember that  

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent  

In this problem  

The corresponding sides are  

FE and XY  

EG and YZ  

GF and ZX  

so therefore  

segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX Firstly , let us learn about trigonometry in mathematics.  

Suppose the ΔABC is a right triangle and ∠A is 90°.  

sin ∠A = opposite / hypotenuse

cos ∠A = adjacent / hypotenuse

tan ∠A = opposite / adjacent

Let us now tackle the problem!  

A similar triangle has the same angle, in other words the triangle has the same shape but different sizes.  

From the figure in the attachment , we can conclude that:  

m∠E = m∠Y  

m∠F= m∠X  

m∠G = m∠Z  

∴ ΔEFG ~ ΔYXZ  ( ΔEFG is similar to ΔYXZ )    

Because of the similarity , then:  

FE : XY = EG : YZ = GF : ZX  

Conclusion:

ΔFG is similar to ΔYXZ.  

Segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX , i.e:    

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle

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