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3 years ago

The measures of two angles of pairs of triangles are given. Which pairs of triangles are similar?

Mathematics

2 answers:

nasty-shy [4]3 years ago

8 0

Answer:

1, 2, and 5 are similar

Step-by-step explanation:

morpeh [17]3 years ago

6 0

If the triangles are similar then the angles in both are equal. Let's look at each set individually:

(1) Triangle 1: 25°, 35°
Triangle 2: 25°, 120°
Now it may be hard to tell if the triangles are similar at the moment so we must calculate the third angle in each triangle (The angles in a triangle add up to 180°, therefor the missing angle = 180 - (given angle 1 + given angle 2)
Triangle 1: 180 - (25 + 35) = 120°
Triangle 2: 180 - (25 + 120) = 35°

Now writing out the set of angles again we have:
Triangle 1: 25°, 35°, 120°
Triangle 2: 25°, 120°, 35°

So in fact Triangle 1 and 2 are similar.

Now we can repeat this process for (2) - (5):

(2) Triangle 1: 100°, 60°, 20°
Triangle 2: 100°, 20°, 60°
This pair is also similar

(3) Triangle 1: 90°, 45°, 45°
Triangle 2: 45°, 40°, 95°
This pair is not similar

(4) Triangle 1: 37°, 63°, 80°
Triangle 2: 63°, 107°, 10°
This pair is not similar

(5) Triangle 1: 90°, 20°, 70°
Triangle 2: 20°, 90°, 70°
This pair is similar

Therefor pairs (1), (2) and (5) are similar

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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

EleoNora [17]

Answer:

The system of equation are $\left \{ {{15+1x} \atop {3+5x}} \right.$ .

In 3 weeks, the friends will each have passed 18 scales.

Step-by-step explanation:

Let number of weeks be 'x'.

Given:

Number of scale Pablo has passed = 15 scales

Number of scale Kayla has passed = 3 scales

Number of scales passing per week by Pablo = 1 scale

Number of scales passing per week by Kayla = 5 scale

We need find the number of weeks when both have same scales.

First we will find the Total number of scales Pablo will passed after 'x' weeks.

Total number of scales Pablo will passed after 'x' weeks is equal to sum of Number of scale Pablo has passed and Number of scales passing per week by Pablo multiplied by number of weeks.

framing in equation form we get;

Total number of scales Pablo will passed after 'x' weeks = $15+1x$

Now we will find Total number of scales Kayla will passed after 'x' weeks.

Total number of scales Kayla will passed after 'x' weeks is equal to sum of Number of scale Kayla has passed and Number of scales passing per week by Kayla multiplied by number of weeks.

framing in equation form we get;

Total number of scales Kayla will passed after 'x' weeks = $3+5x$

Hence the system of equation are $\left \{ {{15+1x} \atop {3+5x}} \right.$ .

Now we need to find the number of weeks when both have passed equal scales.

Hence we can say that;

Total number of scales Pablo will passed after 'x' weeks = Total number of scales Kayla will passed after 'x' weeks

Substituting the value we get;

$15+1x=3+5x$

On Solving the equation we get;

Combining like terms first;

$5x-x=15-3\\\\4x=12$

Now by Division property dividing both side by 4 we get;

$\frac{4x}{4}=\frac{12}{4} \\\\x=3 \ weeks$

Now we will find the total scales passed by each after 3 weeks;

Total number of scales Pablo will passed after 3 weeks = $15+x=15+3 = 18 \ scales$

Total number of scales Kayla will passed after 3 weeks = $3+5x=3+5\times3 = 18 \ scales$

Hence: In 3 weeks, the friends will each have passed 18 scales.

4 0

3 years ago

Find the midpoint of A and B where A has coordinates (-5, 3) and B has coordinates (3,-1).

scoundrel [369]

Answer:

(-1,1)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates and divide by 2

(-5+3)/2 = -2/2 = -1

To find the y coordinate of the midpoint, add the y coordinates and divide by 2

(3+-1)/2 = 2/2 = 1

(-1,1)

6 0

3 years ago

Read 2 more answers

What is the measure of the missing angle?) Please explain how u got the answer so I can learn

anygoal [31]

Step-by-step explanation:

let x be the another angle

x+40=90

x=90-40

x=50

The measure of missing angle is 50

hope it helps

7 0

3 years ago

Read 2 more answers

I know the answers but i need the work. plz help

inysia [295]

For number 3.

You add 8 to both sides as you need to separate the variable

4x-8=32
+8 +8

4x=32

now divide 32 by 4

x=8

for number 4

you use pemdas to multiply the parenthisis

2(x-5)=-20

(2•x)-(2•5)

2x-10=-20

then add 10 to both sides

2x-10=-20
+10 +10

2x=10

divide 10 by two

x=5

5 0

3 years ago

The ice cream shop sells sundaes for $2 each and banana splits for $3 each. One day, the shop sold 8 more sundaes than banana sp

Nataliya [291]

Answer:

$82 sundaes

$74 banana split

Step-by-step explanation:

Step one :

Given data

Cost of sundaes =$2 each

Cost of banana split =$3 each

Let the number of sundaes bought be x

And the number of banana split bought be y

The total is x+y

The shop sold 8 more Sundaes than the Banana split

x=8+y—-------1

Total amount made = $156

Therefore the system of equation for the situation is

x=8+y----—----------1

2x+3y=156---------2

But x=8+y

8+y+y=156

8+2y=156

2y=156-8

2y=148

Divide both sides by 2

y=148/2

y=74

On That day they sold $74 banana split

And also they sold x=8+74=$82 sundaes

4 0

2 years ago