A triangle with vertices at A(0, 0), B(0, 4), and C(6, 0) is dilated to yield a triangle with vertices at A′(0, 0), B′(0, 10), and C′(15, 0)-. The origin is the center of dilation. What is the scale factor of the dilation?

Answers

Answer 1

Answer: A triangle ABC is similar to a triangle A´B´C´ The scale factor of the dilatation : s.
0 * s =0
4 * s = 10
6 * s = 15
s= 10/4=15/6=2.5
The scale factor of the dilatation is 2.5. It is shown in the attachment.

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The first one to answer gets ( a best answer )

Answers

Step-by-step explanation:

1- 9.34

2- 5.85

3- 40.14

Hope this can help you

Answer: 1) 9.34, 2) 5.85,

Step-by-step explanation:

Bruce has a bottle that contains 60% of lemon juice and the rest water. The bottle has 1 liter of water. PARTA: Write an equation in one variable that can be used to find the total number of liters of lemon juice and water in the bottle. Define the variable used in the equation. (5 points) Part B: How many liters of lemon juice are present in the bottle? Show your work. (5 points)

Answers

Let x= the total volume of liquid the bottle can hold.
Since 40% of the liquid is water, then .4x = 1L

Then you solve for x.

0.4x=1L
0.4x/0.4 = 1L/0.4
x = 2.5 L

So we have the total volume of the bottle which is 2.5 L.

Now, let the number of liters of lemon juice be y.
y=0.6x
So the equation would be x = 0.4x + y
or simply, x = .4x + .6x

Solve for y.
y= 0.6(2.5L)
y= 1.5L

So the amount of lemon juice in the bottle is 1.5 L.

The correct answers are:

2.5 L of liquid total and 1.5 L of lemon juice.

Explanation:

Since the bottle contains 60% lemon juice, this means that 100-60 = 40% of the bottle is water. We know that there is 1 liter of water; this means we have the equation

0.4x = 1, where x is the total amount of liquid in the bottle.

Divide both sides by 0.4:

0.4x/0.4 = 1/0.4

x = 2.5

There are 2.5 L of liquid.

60% of the liquid is lemon juice; this gives us

0.6(2.5) = 1.5

There are 1.5 L of lemon juice.

Under what circumstances are two nonright triangles congruent?

Answers

If these are the given choices of the above problem,

a. one side and one angle are equal.
b.three sides are equal
c.two angles are equal
d. three angles are equal

Two non-right triangles are congruent when B. THREE SIDES ARE EQUAL.

Two triangles are congruent if:
1) All corresponding sides are equal (SSS)
2) A pair of corresponding sides and the included angle are equal (SAS)
3) A pair of corresponding angles and the included side are equal (ASA)
4) A pair of corresponding angles and a non-included side are equal (AAS)

3х – 13 = 23
Please give an explanation to the answer

Answers

Answer:

x = 12

Step-by-step explanation:

This equation is very easy to solve.

3x - 13 = 23 Add 13 to both sides of the equation.

3x = 36 Divide by 3 on both sides of the equation.

x = 12

Then, check your answer by substituting the solved value.

3(12) - 13 = 23

36 - 13 = 23

23 = 23

Therefore, x = 12 is the solution to the equation.

Answer:

x = 12

Step-by-step explanation:

3x - 13 = 23

Bring non-variable numbers to other side:

3x = 36

Divide both sides by 3:

x = 12

The center of a circle is located at (3, 8), and the circle has a radius that is 5 units long. What is the general form of the equation for the circle? A. x2 + y2 − 6x − 16y + 48 = 0 B. x2 + y2 − 6x − 16y − 25 = 0 C. x2 + y2 + 6x + 16y + 48 = 0 D. x2 + y2 + 6x + 16y − 25 = 0

Answers

Answer:

A. x² +y² -6x -16y +48 = 0

Step-by-step explanation:

The standard-form equation for a circle centered at (h, k) with radius r is ...

(x -h)² +(y -k)² = r²

For your circle, this is ...

(x -3)² +(y -8)² = 5²

To put this in general form, you subtract the constant on the right, and eliminate parentheses:

x² -6x +9 +y² -16x +64 -25 = 0

x² +y² -6x -16y +48 = 0 . . . . . rearrange to descending powers of x, y

(will give brainliest)a hiker, whose eye is 1.6 meters above ground, stands 50 meters from the base of connecting her eye and the top of the cliff and a horizontal line is 58°. draw a diagram representing the situation and find the height of the cliff