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3 years ago

Determine if the lines are parallel, perpendicular, or neither 4x+5y=10 and 5x -4y= 28

1 answer:

6 0

To do this, we will need to compare the slopes and the y int. So we will put each equation in y = mx + b form, where m will be the slope and b will be the y int..

4x + 5y = 10
5y = -4x + 10
y = -4/5x + 2.....the slope here is -4/5...the y int is 2

5x - 4y = 28
-4y = -5x + 28
y = 5/4x - 7...the slope here is 5/4...and the y int is -7

for the lines to be parallel, they would need the same slope and different y intercepts. So, as u can see, they are not parallel because they do not have the same slope.

for the lines to be perpendicular, the lines would have to have negative reciprocal slopes. They do....u have perpendicular lines. To find the negative reciprocal of a number, u flip the number and change the sign. One line had a slope of -4/5....the negative reciprocal is : flip the number making it -5/4....change the sign, making it 5/4...which is the slope of the other line...so these slopes are negative reciprocals.

so u have perpendicular lines

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What is the area of triangle DEF

kolezko [41]

Answer:

76.5 cm²

Step-by-step explanation:

Given the triangles are similar , then

ratio of sides = a : b , so

ratio of areas = a² : b²

Here ratio of sides = 9 : 13.5 = 2 : 3

ratio of areas = 2² : 3² = 4 : 9

let x be the area of Δ DEF and using proportion

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3 years ago

A restaurant has a main location and a traveling food truck. The first matrix A shows the number of managers and associates empl

denis-greek [22]

Answer:

A*B= $\left[\begin{array}{cc}705&80\\121&14 \end{array}\right]$

Step-by-step explanation:

Given A= $\left[\begin{array}{cc}5&25\\1&4\end{array}\right] \left[\begin{array}{cc}41&6\\20&2\end{array}\right]$ = B

Finding A*B means multiplying the first row with the first column and first row with the second column would give the first row elements. The second ro0w elements are obtained by multiplying the second row with the 1st column and second row with the second column.

so A*B= $\left[\begin{array}{cc}5*41+ 25*20&5*6 + 25*2\\ 1*41+4*20 & 1*6+ 4*2\end{array}\right]$

Now multiply and add the separate elements of the matrix A*B=

$\left[\begin{array}{cc}205+500&30+50\\41+80&6+8\end{array}\right]$

A*B= $\left[\begin{array}{cc}705&80\\121&14 \end{array}\right]$

b. The 1st element of the 1st row shows the salaries of the managers and 2nd element of the 1st row the salaries of associates at the restaurant . The second row 1 st element shows the benefits of the managers and 2nd element the benefits of the associates at the food truck.

c. The total cost of salaries for all employees (managers and associates) at the restaurant = 705 + 80 = 785

Total cost of benefits for all employees at the food truck= 121 + 14= 135

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3 years ago

9. Which is the graph of the function y = 3x?

Fudgin [204]

Answer: 4th graph

Step-by-step explanation:

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3 years ago

What is 13+21? A). 53 B).-34 C).27 D).34

olga nikolaevna [1]

The answer for 13+21 =34

8 0

3 years ago

Read 2 more answers

X=y 1.25x = 1.25y no soulation exactly 1 soulation infintely many soulations

Cerrena [4.2K]

For any equation with more than one variable, there is either no solution or infinitely many solutions.

If we can find just one solution that works, that would eliminate the possibility of there being no solution, and so we could prove it to have infinitely many solutions.

Can we come up with at least one solution to these equations? Of course!

For x=y
Thinking of two equal numbers is extremely easy. For instance, if we chose x to be 2 and y to be 2, that's a solution right there! Thus x=y has infinitely many solutions.
It's just as easy picking two numbers that are equal when you multiply them by 1.25. Think back to the multiplication property of equality. If two things are equal, and you multiply them by a number, they will still be equal. So all we need is, once again, two equal numbers. 2 and 2, boom and boom. 1.25x=1.25y has infinitely many solutions as well.

4 0

3 years ago