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madam [21]
3 years ago
11

If a pair of linear equations is consistent, then the lines will be

Mathematics
1 answer:
Lesechka [4]3 years ago
8 0
C
Intersecting or coincident
If a pair of linear equation is consistent, then it has unique solutions and infinity solutions.
For unique solution-
⇒
a
2
​

a
1
​

​


=
b
2
​

b
1
​

​

∴ the lines will be intersecting.
For infinity solution-
⇒
b
1
​

a
1
​

​
=
b
2
​

b
1
​

​
=
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stiv31 [10]
The answer will be as shown in the pic 15x^(2) +35x

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3 years ago
Jim is enclosing a rectangular garden with 170 feet of fencing. The length of the garden is 10 feet more than twice it’s width,
Darina [25.2K]

Answer:

1,500\ ft^2

Step-by-step explanation:

Let

L ----> the length of the rectangular garden in feet

w ---> the width of  the rectangular garden in feet

step 1

Find the width

we know that

The perimeter of the rectangular garden is

P=2(L+W)

P=170\ ft

so

170=2(L+W)

Simplify

85=(L+W) ----> equation A

L=2W+10 ----> equation B

substitute equation B in equation A and solve for W

85=(2W+10+W)

85-10=3W

3W=75

W=25\ ft

Find the value of L

L=2(25)+10=60\ ft

step 2

Find the area

we know that

The area of the rectangular garden is

A=(LW)

substitute the values

A=(60)(25)=1,500\ ft^2

6 0
3 years ago
What is the percentage 33% of $145.00
yan [13]

Answer:

47.85

Step-by-step explanation:

33% of 145

of means multiply

Changing to decimal form

.33* 145

47.85

5 0
3 years ago
Read 2 more answers
Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3
nlexa [21]

Answer:

(x,y) = (5,-6)

Step-by-step explanation:

\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\

                     ~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)

\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\

\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5

y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6

\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)

7 0
1 year ago
The table represents a function.
yan [13]

Answer:

The table represents a function.

What is the value of f(-1)?

f(-1) = - 3

f(-1) = -1

f(-1) = 0

f(-1) = 6

Step-by-step explanation:

7 0
3 years ago
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