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3 years ago

The system of equations y = three-fourths x minus 4 and y = –x + 3 is shown on the graph below.

Mathematics

2 answers:

Virty [35]3 years ago

6 0

Step-by-step explanation:

The answer to this question is where both of the lines intersect. For this problem, the answer is (4, -1)

<em>Look at the attachment for clarification:</em>

Sedaia [141]3 years ago

3 0

Answer:

(4, -1)

Step-by-step explanation:

The point of intersection of two lines is also the solution to the system of equations of the two lines

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Sarah read 64 1/2 pages of her book in 6 hours. What is the average number of pages that Sarah reads per hour?

MAVERICK [17]

Answer:

We conclude that the average number of pages that Sarah reads per hour will be: 10.75 page per hour

Step-by-step explanation:

Given

Number of pages Sarah read $=64\frac{1}{2}=\frac{129}{2} = 64.5$

Number of hours Sarah spent = 6 hours

The average number of pages per hour can be calculated by simply dividing the total number of pages i.e. 64.5 pages by the number of hours spent on reading i.e. 6 hours.

Thus,

Average number of pages per hour = 64.5 pages / 6 hours

= 10.75 page per hour

Therefore, we conclude that the average number of pages that Sarah reads per hour will be: 10.75 page per hour

8 0

3 years ago

Oliver works 5 days a week. He drives 53 kilometres each day and walks a total of 25 kilometres over the week: He uses the follo

nikklg [1K]

I think it’s 36 but I’m not good at math so don’t count me on it

7 0

2 years ago

PLEASE HELP!!!!!!!!!!!

garik1379 [7]

First convert the hours to minutes

$1hr = 60mins$

$15hrs = 15 \times 60mins$

$= 900minutes$

now change the 900mins to seconds

$1mins = 60sec$

$900mins = 900 \times 60sec$

4 0

3 years ago

An endpoint of a line segment is (4,5) and the midpoint of the line segment is (3, -2). Find the other endpoint.

Makovka662 [10]

Answer:

(2,-7)

Step-by-step explanation:

$(4 + x) \div 2 = 3 \\ 4 + x = 6 \\ x = 2$

$(5 + y) \div 2 = - 2 \\ 5 + y = - 4 \\ y = - 7$

7 0

4 years ago

Find all values of k, if any, that satisfy the equation.

aleksklad [387]

Answer:

There are two such values of $k$ , $k = 6-4\sqrt{3}$ and $k = 6+4\sqrt{3}.$

Step-by-step explanation:

The question is to find all values of $k$ , if any, that satisfy the following matrix equation.

$\begin{bmatrix}2 & 2 & k\end{bmatrix} \cdot \begin{bmatrix}1 & 1 & 0\\1 & 0 & 3 \\0 & 3 & -1\end{bmatrix} \cdot \begin{bmatrix}2 \\2\\k\\\end{bmatrix} = 0$

Let's multiply the first two matrices. We can do that, since the number of columns in the first matrix equals the number of rows in the second matrix, which means that their product is defined.

$\begin{bmatrix}2 \cdot 1 + 2 \cdot 1 + k \cdot 0 & 2 \cdot 1 + 2 \cdot 0+ k \cdot 3 & 2 \cdot 0 + 2 \cdot 3 + k \cdot (-1)\end{bmatrix} \cdot \begin{bmatrix}2\\2\\k\end{bmatrix}= 0$

Next, we need to solve the matrix equation

$\begin{bmatrix} 4 & 2+3k & 6-k\end{bmatrix} \cdot \begin{bmatrix}2\\2\\k\end{bmatrix}= 0$

Again, the number of columns in the first matrix equals the number of rows in the second matrix, which means that their product is defined and we can multiply them. The result will be $1$ × $1$ matrix, and that will be the dimension of the zero matrix, as well.

$\begin{bmatrix}4 \cdot 2 + (2+3k) \cdot2 + (6+k)\cdot k\end{bmatrix} = 0\\\begin{bmatrix}8 + 4 + 6 \cdotk + 6 \cdot k - k^2 \end{bmatrix} = 0 & \iff 8 + 4 + 6 \cdot k + 6 \cdot k - k^2 = 0$

Now, all we need to do is to solve the quadratic equation

$-k^2 +12k +12 = 0$

By using the well known formula, we obtain

$k_{1/2} = \frac{-12 \pm \sqrt{12^2 - 4 \cdot (-1) \cdot 12}}{-2} = \frac{-12 \pm \sqrt{192}}{-2} = \frac{-12 \pm \sqrt{64 \cdot 3}}{-2} = \frac{-12 \pm 8\sqrt{3}}{-2}$

Therefore, we obtain two values for $\mathbf{k}$ , $k = 6-4\sqrt{3}$ and $k = 6+4\sqrt{3}$ .

6 0

3 years ago