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3 years ago

14

At the beginning of the summer, Paul has $76. During the summer, he earns money by mowing lawns. The table shows the total amoun

t of money Paul has after mowing the given number of lawns.
Number of lawns mowed Total amount of money ($)
0 76
2 100
4 124
6 148

Select from the drop-down menus to make an equation in slope-intercept form that gives the total amount of money, y, Paul has after mowing x lawns.

1 answer:

san4es73 [151]3 years ago

3 0

y<span> = 12x+76 is the answer to your question i know it was a little late but at least other people who would like to know can see it.</span>

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A regulation baseball field measures 90 feet between each base. What is the distance around the bases in yards

professor190 [17]

The distance between each base is 30 yards since 90*(1/3) = 90/3 = 30
In other words, 90 feet is equivalent to 30 yards (3 ft per 1 yard)

The total distance around the bases is 30*4 = 120 yards. This is the perimeter.

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3 years ago

Consider the function f(x) =2x-6 find f(2)

tester [92]

Step-by-step explanation:

✧ $\underline{ \underline{ \large{ \tt{G \: I \: V \: E\: N}}} } :$

f ( x ) = 2x - 6

✧ $\underline{ \underline{ \large{ \tt{T\: O \: \: F\: I\: N\: D}}}}:$

value of f ( 2 )

✧ $\underline{ \underline{ \large{ \tt{S \:O \: L \: U \: T \: I \: O \: N}}}} :$

❀ $\large{ \text{When \: x = 2 ,\: f}(2) = 2 \tt{ \times 2 - 6}}$

⟼ $\large{ \text{f(2) = 4 - 6 = \boxed{ \large{ \text{ - 2}}}}}$

♨ $\boxed{ \boxed{ \large{ \text{OUR\: FINAL \: ANSWER : \boxed{ \underline{ \bold{ \text{ - 2}}}}}}}}$

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2 years ago

Use Gaussian elimination to write each system in triangular form

Feliz [49]

Answer:

To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is $x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

Step-by-step explanation:

Gauss elimination method consists in reducing the matrix to a upper triangular one by using three different types of row operations (this is why the method is also called row reduction method). The three elementary row operations are:

Swapping two rows
Multiplying a row by a nonzero number
Adding a multiple of one row to another row

To solve the system using the Gauss elimination method we need to write the augmented matrix of the system. For the given system, this matrix is:

$\left[\begin{array}{cccc|c}1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & -1 & -1 \\-1 & 1 & 1 & 2 & 2 \\1 & 2 & -1 & 1 & 0\end{array}\right]$

For this matrix we need to perform the following row operations:

$R_2 - 1 R_1 \rightarrow R_2$ (multiply 1 row by 1 and subtract it from 2 row)
$R_3 + 1 R_1 \rightarrow R_3$ (multiply 1 row by 1 and add it to 3 row)
$R_4 - 1 R_1 \rightarrow R_4$ (multiply 1 row by 1 and subtract it from 4 row)

$R_2 \leftrightarrow R_3$ (interchange the 2 and 3 rows)

$R_2 / 2 \rightarrow R_2$ (divide the 2 row by 2)
$R_1 - 1 R_2 \rightarrow R_1$ (multiply 2 row by 1 and subtract it from 1 row)
$R_4 - 1 R_2 \rightarrow R_4$ (multiply 2 row by 1 and subtract it from 4 row)
$R_3 \cdot ( -1) \rightarrow R_3$ (multiply the 3 row by -1)
$R_2 - 1 R_3 \rightarrow R_2$ (multiply 3 row by 1 and subtract it from 2 row)
$R_4 + 3 R_3 \rightarrow R_4$ (multiply 3 row by 3 and add it to 4 row)
$R_4 / 4.5 \rightarrow R_4$ (divide the 4 row by 4.5)

After this step, the system has an upper triangular form

The triangular matrix looks like:

$\left[\begin{array}{cccc|c}1 & 0 & 0 & -0.5 & -0.5 \\0 & 1 & 0 & -0.5 & -0.5\\0 & 0 & 1 & 2 & 2 \\0 & 0 & 0 & 1 & \frac{7}{9}\end{array}\right]$

If you later perform the following operations you can find the solution to the system.

$R_1 + 0.5 R_4 \rightarrow R_1$ (multiply 4 row by 0.5 and add it to 1 row)
$R_2 + 0.5 R_4 \rightarrow R_2$ (multiply 4 row by 0.5 and add it to 2 row)
$R_3 - 2 R_4 \rightarrow R_3$ (multiply 4 row by 2 and subtract it from 3 row)

After this operations, the matrix should look like:

$\left[\begin{array}{cccc|c}1 & 0 & 0 & 0 & -\frac{1}{9} \\0 & 1 & 0 & 0 & -\frac{1}{9}\\0 & 0 & 1 & 0 & \frac{4}{9} \\0 & 0 & 0 & 1 & \frac{7}{9}\end{array}\right]$

Thus, the solution is:

$x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

7 0

3 years ago

suppose two different fractions with the same denominators are both less than 1 Can their sum equal 1? can their sum be greater

pochemuha

The sum could be greater than 1 but not equal to 1.

6 0

3 years ago

Determine the zero of F(x)=x^2+3x-5

IgorLugansk [536]

Answer:

The answer to your question is:

Step-by-step explanation:

x² + 3x - 5

x² + 3x + (3/2)² = 5 + (3/2)²

(x + 3/2)² = 5 + 9/4

(x + 3/2)² = (20 + 9) /4

(x + 3/2)² = 29/4

x + 3/2 = ±√29 / 2

x 1 = -3/2 + √29/2 x2 = -3/2 - √29/2

x1 = 1.19 x2 = -4.19

3 0

3 years ago