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3 years ago

What is x and measure b? please help:)

Mathematics

2 answers:

jonny [76]3 years ago

8 0

Answer:

x = 22.5° B = 67.5

Step-by-step explanation:

90° + 3x° + x° = 180°

4x = 90°

x = 22.5°

BARSIC [14]3 years ago

5 0

Answer: x= 22.5, angle B = 67.5

Step-by-step explanation:

90+3x+x= 180

4x = 90

x=22.5

3(22.5)= 67.5

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brilliants [131]

Answer:

(a) x=2, y=-1

(b) x=2, y=2

(c) $\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) x=-2, y=-7

Step-by-step explanation:

Cramer's Rule

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

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

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

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3 years ago

What is the slope of a line that is parallel to the line y = 3/4 + 2?

Elodia [21]

3/4 because it’s parallel so it has the same slope. It just doesn’t pass through the same line.

7 0

3 years ago

Arvin has $10000 to invest. He invests part in a term deposit paying 5%/year, and the remainder in Canada savings bonds paying 3

Delicious77 [7]

Answer:

$4,562.5

Step-by-step explanation:

The amount Arvin has to invest, P = $10,000

The interest paid on the investment in the term deposit = 5%/year

The interest paid om the investment in Canada savings bonds = 3.4%/year

The amount Arvin earned at the of the year as simple interest, A = $413

Let, x, represent the amount Arvin invested in the term deposit and let, y, represent the amount he invested in Canada savings bonds, we can get the following system of equations

x + y = 10,000...(1)

0.05·x + 0.034·y = 413...(2)

Making y the subject of equation (1) and substituting the value in equation (2), we get;

From equation (1), we get, y = 10,000 - x

Plugging the above value of y in equation (2) gives;

0.05·x + 0.034 × (10,000 - x) = 413

∴ 0.05·x - 0.034·x + 340 = 413

x = (413 - 340)/(0.05 - 0.034) = 4,562.5

Therefore, the amount Arvin invested in the term deposit at 5%, x = $4,562.5

(y = 10,000 - x

∴ y = 10,000 - 4,562.5 = 5,437.5

The amount Arvin invested in Canada savings bonds, y = $5,437.5.)

8 0

3 years ago