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3 years ago

Help two helpless triangles?

Mathematics

2 answers:

mezya [45]3 years ago

5 0

Answer:

1) they are similar by AAA postulate

2) 9.6 cm

Explanation:

Triangles CAB and CED are similar

because:

1) both have the same angle C

(vertically opposite angles)

2) Angle A = Angle E

(alternate angles)

3) Angle B = Angle D

(alternate angles)

CA/CE = AB/ED

10/8 = 12/DE

DE = 12 × 8/10

DE = 9.6 cm

Illusion [34]3 years ago

3 0

Answer:

see below

Step-by-step explanation:

Angle ACE = DCE since they are vertical angles

Angle A = Angle E parallel lines cut by a transversal form congruent alternate interior angles

Angle B = Angle D parallel lines cut by a transversal form congruent alternate interior angles

When all three angles are equal, the triangles are similar.

We can use ratios to find DE

DE CE

------- = ----------

AB AC

DE 8

------- = ----------

12 10

Using cross products

10 DE = 8*12

10 DE = 96

Divide by 10

DE = 9.6

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Find the coordinates of the point

alina1380 [7]

Answer:

$(x,y) = (\frac{-10}{13},3)$

Step-by-step explanation:

<em>Question is not well formatted; However, the given parameters are</em>

Given

Point = 3/10

A = (-4,-6)

B = (10,7)

Required

Determine the coordinates of the point

Represent the point as ratio

$Point = 3:10$

The coordinates can be solved using

$(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

Where

$m:n = 3:10$

$(x_1,y_1) = (-4,-6)$

$(x_2,y_2) = (10,7)$

Substitute these values in the above formula:

$(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})$

$(x,y) = (\frac{3 * 10 + 10 * -4}{3+10},\frac{3 * 7 + 10 * -6}{10+3})$

$(x,y) = (\frac{30 -40}{13},\frac{21 -60}{13})$

$(x,y) = (\frac{-10}{13},\frac{-39}{13})$

$(x,y) = (\frac{-10}{13},3)$

Hence;

The coordinates of the point is $(x,y) = (\frac{-10}{13},3)$

4 0

4 years ago

(x + y = 17<br> (y = x+7<br> Solve using substitution

Cloud [144]

X+y=17
Y=x+7
X+x+7=17
2x+7=17
-7. -7
2x. =10
—- —
2. 2
X. = 5

Check:
Y=5+7
Y=12

Answer
X=5
Y=12

7 0

4 years ago

Keith is saving money for a car. He has saved the same amount each year for the past three years, and records how much he has at

noname [10]

Answer:

Keith's unit rate of change of dollars with respect to time is $1500.

Step-by-step explanation:

It is given that Keith is saving money for a car.

Year 1: 1500

year 2: 3000

year 3: 4500

Let y be the saved amount after x year.

The coordinate pairs according to the given table are (1,1500), (2,3000) and (3,4500).

The formula for rate of change is

Consider any two coordinate pairs.

Let as consider (1,1500) and (2,3000). So, Keith's unit rate of change of dollars with respect to time is

Therefore, Keith's unit rate of change of dollars with respect to time is $1500.

8 0

3 years ago

If x = 9 and y = -3, evaluate the following expression: = 6x - 8y

masha68 [24]

Answer: 78

Step-by-step explanation:

Step 1:

Substitute the variables in:

6(9) - 8(-3)

Step 2:

Multiply to get rid of the parentheses:

54 - -24 = 54 + 24 (the two negatives cancel out)

Step 3:

Add, and then you're done:

54 + 24 = 78

hope this helps :)

8 0

2 years ago

The value of a car over a period of 8 years is linear.

STALIN [3.7K]

I guess A i don't know hope the answer is correct

7 0

3 years ago