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3 years ago

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

1 answer:

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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Distribute5x (3x + 7)

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

$P=2(L+W)$

$P=170\ ft$

$170=2(L+W)$

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