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Naily [24]
3 years ago
14

Triangle ABC has coordinates A(-2, -3), B(1, 1), and C(2, -1). If the triangle is translated 4 units up, what are the coordinate

s of A'?
Mathematics
1 answer:
DochEvi [55]3 years ago
8 0

Answer:

The coordinates of point A' will be: A'(-2, 0)

Step-by-step explanation:

We know that a translation is basically a transformation that occurs when an object is moved from one place to another place.

Translation does not change the size, orientation, or shape of the original object.

Translating a point P(x, y) 4 units up means we need to add to use P'(x, y+4), that is adding 4 units to the y-coordinate of the point P'(x, y).

Now we have to translate the triangle 4 units up. So, use the formula

P(x, y) → P'(x, y + 3)

Thus, the coordinates of point A' will be:

A(-2, -3) → A'(-2, -3+3) → A'(-2, 0)

Therefore, the coordinates of point A' will be: A'(-2, 0)

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The t value for a 95% confidence interval estimation with 24 degrees of freedom is
Alborosie

Answer: the value us 2.064

Step-by-step explanation:

To determine the t value, we would need the t distribution table. Since degree of freedom is known as 24, we would determine alpha/2

A 95% confidence level is 95/100 = 0.95

1 - alpha = 0.95

alpha = 1 - 0.95

alpha = 0.05

alpha/2 = 0.05/2 = 0.025

this is the area to the left. The area to the right 1 - 0.025 = 0.975

alpha/2 = 0.975

Looking at the t distribution table, the t value is

2.064

4 0
3 years ago
Isosceles Right Triangle Reflection to prove ASA Congruence
adell [148]

Answer:

Yes they went through rigid motion

Step-by-step explanation:

The original triangle is the same as the one on the left but the only thing that changed was its place(translation) making it a RIGID MOTION

7 0
3 years ago
Jerome is making prizes for a game at the school fair. He has two bags of different pins, One with 15 pins and one with 20 pins.
DanielleElmas [232]
You are looking for the GCF or greatest common factor of 15 and 20 a way to do the is the upside down cake method.

6 0
3 years ago
Consider the shape below. (1) determine the value of x so that the volume of the shape is 165cm cube, and (2) once you have foun
Reika [66]

Answer:

  • x = 5 cm
  • 248 cm²

Step-by-step explanation:

The volume of the solid with x=0 is the product of its length, width, and height:

  V0 = (10 cm)(3 cm)(8 cm) = 240 cm³

The volume of the cutout is the same:

  Vc = (x cm)(3 cm)(x cm) = 3x² cm³

Then the volume of the solid with the cutout is ...

  V1 = V0 -Vc = 240 cm³ - 3x² cm³

This is 165 cm³, so we have ...

  165 = 240 -3x²

  55 = 80 -x² . . . . . divide by 3

  x² = 80 -55 = 25 . . . . add x²-55

  x = √25 = 5 . . . . . take the square root

___

The surface area is the total of the front and back faces and the lateral area of all the faces between them. That lateral area is the product of the perimeter of the front (or back) face and the width (3 cm). The perimeter (p) is the total of all edge lengths around the front face:

  p = 10 + 8 + (10-x)/2 + x + x + x + (10-x)/2 + 8 = 36 +2x

For x=5, the perimeter is ...

  p = 36 +2·5 = 46

so the lateral area is ...

... la = (46 cm)(3 cm) = 138 cm².

The area of each of the front and back faces is the area of the overal rectangular shape (10 cm by 8 cm) less the area of the cutout (x² cm²). So, that face area is ...

  fa = 2×((10 cm)(8 cm) -(5 cm)²) = 2×(55 cm²) = 110 cm²

Then the total surface area is the sum of lateral area and face area:

  S = la + fa = 138 cm² + 110 cm² = 248 cm²

7 0
3 years ago
The water level of a river is 170 feet. The river recedes 4 feet each year. Ingrid claims that the equation that represents this
Irina-Kira [14]
1. y=f(x)=170x-4 is a function with variable x representing a year.

2. Let's consider the difference between 2 consecutive years, say year 3 and year 4

f(3)=170*3-4
f(4)=170*4-4

we expect f(3)-f(4) to be 4 since after 4 years, the water will be 4 feet less than after 3 years.

check: f(3)-f(4)=(170*3-4)-(170*4-4)=170*3-4-170*4+4=170*3-170*4=170*(3-4)=170*(-1)=-170
3 0
3 years ago
Read 2 more answers
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