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AlladinOne [14]
3 years ago
12

What is the range of the data set 22 30 49 71 85 88 92 97 99

Mathematics
1 answer:
Genrish500 [490]3 years ago
5 0
The range is 77. you calculate range by subtracting the smallest number from the biggest number.
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M(-5,9) and N(-2,7)<br> P(-3,-7) and Q(3,-5
jek_recluse [69]

Answer:

M=(4,112)=(4,5.5) A

Step-by-step explanation:

The midpoint for two points P=(px,py) and Q=(qx,qy) is M=(px+qx2,py+qy2).

We have that px=3, py=2, qx=5, qy=9.

Thus, M=(3+52,2+92)=(4,112).

7 0
2 years ago
Find the missing measures of the following rectangle
Allushta [10]

Answer:

see explanation

Step-by-step explanation:

In a rectangle

• All angles are right angles

• the diagonals are congruent

In Δ WXV the sum of the 3 angles = 180°

∠ WXZ = ∠ XWY = \frac{180-64}{2} = \frac{116}{2} = 58°

∠ YXZ = 90° - 58° = 32°

∠ WVZ = 180° - 64° = 116° ( adjacent angles are supplementary )

∠ XWZ = 90° ( by definition of rectangle )

∠ XZY = ∠ WXZ = 58° ( corresponding angles )

7 0
3 years ago
Simplify 2x + 1 - x +2.​
Pavlova-9 [17]

Answer:

the answer is x + 3

Step-by-step explanation:

7 0
3 years ago
<img src="https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx%2By%3D1%7D%20%5Catop%20%7Bx-2y%3D4%7D%7D%20%5Cright.%20%5C%5C%5Clef
brilliants [131]

Answer:

<em>(a) x=2, y=-1</em>

<em>(b)  x=2, y=2</em>

<em>(c)</em> \displaystyle x=\frac{5}{2}, y=\frac{5}{4}

<em>(d) x=-2, y=-7</em>

Step-by-step explanation:

<u>Cramer's Rule</u>

It's a predetermined sequence of steps to solve a system of equations. It's a preferred technique to be implemented in automatic digital solutions because it's easy to structure and generalize.

It uses the concept of determinants, as explained below. Suppose we have a 2x2 system of equations like:

\displaystyle \left \{ {{ax+by=p} \atop {cx+dy=q}} \right.

We call the determinant of the system

\Delta=\begin{vmatrix}a &b \\c  &d \end{vmatrix}

We also define:

\Delta_x=\begin{vmatrix}p &b \\q  &d \end{vmatrix}

And

\Delta_y=\begin{vmatrix}a &p \\c  &q \end{vmatrix}

The solution for x and y is

\displaystyle x=\frac{\Delta_x}{\Delta}

\displaystyle y=\frac{\Delta_y}{\Delta}

(a) The system to solve is

\displaystyle \left \{ {{x+y=1} \atop {x-2y=4}} \right.

Calculating:

\Delta=\begin{vmatrix}1 &1 \\1  &-2 \end{vmatrix}=-2-1=-3

\Delta_x=\begin{vmatrix}1 &1 \\4  &-2 \end{vmatrix}=-2-4=-6

\Delta_y=\begin{vmatrix}1 &1 \\1  &4 \end{vmatrix}=4-3=3

\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2

\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{3}{-3}=-1

The solution is x=2, y=-1

(b) The system to solve is

\displaystyle \left \{ {{4x-y=6} \atop {x-y=0}} \right.

Calculating:

\Delta=\begin{vmatrix}4 &-1 \\1  &-1 \end{vmatrix}=-4+1=-3

\Delta_x=\begin{vmatrix}6 &-1 \\0  &-1 \end{vmatrix}=-6-0=-6

\Delta_y=\begin{vmatrix}4 &6 \\1  &0 \end{vmatrix}=0-6=-6

\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2

\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-6}{-3}=2

The solution is x=2, y=2

(c) The system to solve is

\displaystyle \left \{ {{-x+2y=0} \atop {x+2y=5}} \right.

Calculating:

\Delta=\begin{vmatrix}-1 &2 \\1  &2 \end{vmatrix}=-2-2=-4

\Delta_x=\begin{vmatrix}0 &2 \\5  &2 \end{vmatrix}=0-10=-10

\Delta_y=\begin{vmatrix}-1 &0 \\1  &5 \end{vmatrix}=-5-0=-5

\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-10}{-4}=\frac{5}{2}

\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-5}{-4}=\frac{5}{4}

The solution is

\displaystyle x=\frac{5}{2}, y=\frac{5}{4}

(d) The system to solve is

\displaystyle \left \{ {{6x-y=-5} \atop {4x-2y=6}} \right.

Calculating:

\Delta=\begin{vmatrix}6 &-1 \\4  &-2 \end{vmatrix}=-12+4=-8

\Delta_x=\begin{vmatrix}-5 &-1 \\6  &-2 \end{vmatrix}=10+6=16

\Delta_y=\begin{vmatrix}6 &-5 \\4  &6 \end{vmatrix}=36+20=56

\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{16}{-8}=-2

\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{56}{-8}=-7

The solution is x=-2, y=-7

4 0
3 years ago
What is the equation for 5 units left and 3 units up from f(x)=x
erastovalidia [21]

The new equation after shifting will be:

g(x) = (x+5)+3\\g(x) = x + 8

Step-by-step explanation:

Function trnafomations upward and left are defined as:

Upward:

f(x) => f(x)+b where b is an integer

Left:

f(x) => f(x+b) where b is an integers

Given function is:

f(x) = x

Shifting the function 5 units left

g(x) = f(x+5) => x+5\\g(x) = x+5

Shifting the function upward 2 units

So,

g(x) = (x+5)+3\\g(x) = x + 8

The new equation after shifting will be:

g(x) = (x+5)+3\\g(x) = x + 8

Keywords: Functions, shifting

Learn more about functions at:

  • brainly.com/question/4054269
  • brainly.com/question/4163549

#LearnwithBrainly

3 0
3 years ago
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