What is 122/11 equivalent to as a decimal??

Triangle ABC has vertices A(4, 5), B(0, 5), and C(3, –1). The triangle is translated 3 units to the left and 1 unit up. What are

Galina-37 [17]

Answer:

$B' = (-3,6)$

Step-by-step explanation:

Given

$A(4,5)$

$B(0,5)$

$C(3,-1)$

Translation: 3 units left and 1 unit right

Required

Determine the new coordinates of B

Write out the coordinates of B

$x = 0$

$y = 5$

When a function is shifted to the left, we have to subtract the unit from the x value of the function;

Shifting by 3 units left, the new x becomes

$New\ x = 0 - 3$

$New\ x = -3$

When a function is shifted upward, we have to add the unit to the y value of the function;

Shifting by 1 unit up, the new y becomes

$New\ y = 5 + 1$

$New\ y = 6$

Hence, the new coordinates of B is

$B' = (-3,6)$

5 0

3 years ago

Consider the sequence 130, 143, 156, 169, ... Write an explicit formula to represent the arithmetic sequence and use it to fi

Hunter-Best [27]

Answer:

A(n)=130+13(n-1) ; 86

Step-by-step explanation:

Here is the sequence

130,143,156,169.......

the first term denoted by a is 130 and the common difference denoted by d is second term minus first term

143 - 130 = 13

Hence a=130 and d = 13

Now we have to evaluate to 13th term.

The formula for nth term of any Arithmetic Sequence is

A(n) = a+(n-1)d

Hence substituting the values of a ,and d get

A(n)=130+13(n-1)

To find the 13th term , put n = 13

A(13)=130+13*(13-1)

= 130+13*12

= 130+156

A(13) = 286

3 0

4 years ago

What is the area of the triangle? PLSSS help me

AveGali [126]

Answer:

The area of the triangle is $A=6 \:units^2$ .

Step-by-step explanation:

The area A of a triangle is given by the formula $A=\frac{1}{2} bh$ where b is the base and h is the height of the triangle.

From the graph, we can see that the base is 3 units and the height is 4 units. Therefore, the area of the triangle is

$A=\frac{1}{2} \cdot3\cdot 4=\frac{12}{2}=6 \:units^2$

8 0

3 years ago

Emily had $56 in her account. She deposited a $265 check, and bought three equally priced backpacks for her children. The next d

Slav-nsk [51]

56+265= 321
321-243= 78
78/3= 26
Each backpack cost $26

6 0

3 years ago

Read 2 more answers

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27 pi feet cubed.

LenaWriter [7]

Answer:

C. V = two-thirds (27)

Step-by-step explanation:

Given

Solid Shapes: Cylinder and Sphere

Volume of Cylinder = 27π ft³

Required

Volume of the sphere.

From the question,

We have that

1. The volume of the sphere is the same as the volume of the cylinder

2. The height of the sphere is the same as the height of the cylinder.

From (2) above;

This means that the height of the cylinder equals the diameter of the sphere.

Let h represent the height of the sphere and d represent the diameter of sphere.

Mathematical, d = h

Recall that radius, r = $r = \frac{d}{2}$

Substitute h for d in the above expression

$r = \frac{h}{2}$ . ----- (take note of this)

Calculating the volume of a cylinder.

V = πr²h

Recall that V = 27; This gives us

27 = πr²h

Divide both sides by h

$\pi r^2 = \frac{27}{h}$

-------------------

Calculating the volume of a sphere

$V = \frac{4}{3}\pi r^3$

Expand the above expression

$V = \frac{4}{3}\pi r^2 * r$

Substitute $\pi r^2 = \frac{27}{h}$

$V = \frac{4}{3} * \frac{27}{h} * r$

Recall that $r = \frac{h}{2}$

So,

$V = \frac{4}{3} * \frac{27}{h} * \frac{h}{2}$

$V = \frac{4}{3} * \frac{27}{2}$

$V = \frac{2}{3} * 27$

$V = \frac{2}{3} (27)$

V = two-third (27)

4 0

3 years ago