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3 years ago

Consider this system of two linear equations.

Mathematics

1 answer:

katen-ka-za [31]3 years ago

4 0

Answer:

Step-by-step explanation:

so these two lines cross at some point.. and they want to know the y point at which they cross... sooo..

solve them as a system to find the points that are common to both

Eq. 1) 5x -2y = 16

Eq. 2) -4x+6y=-15

i'll use the elimination method as these equations "lend" themselves to that way.. they are easy to solve that way .. in other words..

multiply Eq. 1 by 3 the add Eq. 2 .. to it... add the terms as columns....

15x-6y = 48

+ ( -4x+6y=-15)

= 11x+ 0y =33

x=3

nice, now plug 3 in for x in one of the Eq. try Eq. 1

5(3)-2y=16

15-2y=16

-2y =1

y = $-\frac{1}{2}$

since we're looking for the y coordinate... that's your answer $-\frac{1}{2}$

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Caden states that n^2 +3n + 2n is an equivalent expression to 6n. Why is Caden's statement incorrect?

malfutka [58]

$\begin{gathered} \text{The simplification of n}^2+3n+2n\text{ is:} \\ i)n^2+5n \\ By\text{ collecting common term, this can be written in form of:} \\ ii)\text{ n(n+5)} \end{gathered}$

Thus, options A and D hold, from the simplifications above.

Let's consider the validity of the remaining options provided.

$\begin{gathered} \text{For option B)} \\ \text{substitute for n=1 into the expression n}^2+3n+2n,\text{ we have} \\ 1^2+3(1)+2(1)=1+3+2=6 \\ \text{substitute for n=1 into the expression 6n, we have} \\ 6(1)=6 \\ \text{Thus, the expression n}^2+3n+2n\text{ is equivalent to 6n, for n=1} \end{gathered}$ $\begin{gathered} \text{For option C)} \\ \text{The expression n}^2+3n+2n\text{ does not simplify to 7n} \end{gathered}$ $\begin{gathered} \text{For option E)} \\ \text{substitute for n=4 into the expression n}^2+3n+2n,\text{ we have:} \\ 4^2+3(4)+2(4)=16+12+8=36 \\ \text{substitute for n=6 into the expression 6n, we have:} \\ 6(4)=24 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=4} \end{gathered}$ $\begin{gathered} \text{For option F)} \\ \text{substitute for n=3 into the expression n}^2+3n+2n,\text{ we have:} \\ 3^2+3(3)+2(3)=9+9+6=24 \\ \text{substitute for n=3 into the expression 6n, we have:} \\ 6(3)=18 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=3} \end{gathered}$

Hence, the correct options that apply are options A, D, E and F

7 0

1 year ago

Charles can ride his bike 4 miles in 20 minutes. Which of the following ratios show the number of miles to minutes Charles can r

Veronika [31]

Answer:

1:5

Step-by-step explanation:

He rode one mile in 5 minutes because 4/4 is 1 and 20/4 is 5

7 0

4 years ago

During a dig, an archaeological team starts at an elevation of −512 feet. At a rate of 234 feet per hour, the team digs deeper i

creativ13 [48]

Are you referring to this question?
During a dig, an archaeological team starts at an elevation of −5 1/2 feet. At a rate of 2 3/4 feet per hour, the team digs deeper into the surface for 3 1/2 hours. For the next 4 1/2 hours, the team digs at a rate of 1 5/12 feet per hour. Then the team quits for the day.
How many feet did the archaeological team dig after 3 1/2 hours?
What was the team's elevation at the end of the day?

If so, then let us find out the elevation.

The rate of their dig is 2 3/4 ft per hr for 3 1/2 hours, then the total distance dug after 3 1/2 hours should be: 9 5/8 ft

Here’s how we get the total distance:

First, change mixed number into improper fraction and proceed to multiplication

2 3/4--> 11/4 and 3 1/2 becomes 7/2

Multiply.

11/4 x 7/2 = 77/8

Simplify 77/8--> 9 5/8 ft

Let us move on at the rate of 1 5/12 ft per hr for the next 4 1/2 hr,

Following the same procedure as above, the distance would be: 6 9/24 ft

Distance= 1 5/12 x 4 1/2

= 17/12 x 9/2

= 153/24

= 6 9/24 ft

Thus,to sum up everything, they have a total dug of:

9 5/8 + 6 9/24 = 9 15/24 + 6 9/24 = 16 ft

Then, their elevation on that day is -5 1/2 - 16 = -21 1/2 ft

5 0

4 years ago

I really don't get what this means -0.1 = -10c

baherus [9]

Answer:

C is variable. -10 times c is equal to -0.1

Step-by-step explanation:

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3 years ago

Explain how you can find the sign of the product of two or more rational numbers

mr_godi [17]

If the number of positive signs is even and the number of negative signs is odd then it is negative and vice versa. If the number of positive signs is even and the number of negative signs is even then the answer is odd. If the number of positive and negative signs are odd then the answer is always negative.

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3 years ago