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3 years ago

Whith graph shows a system of equations with a solution at (2,-1)?

Mathematics

2 answers:

Olenka [21]3 years ago

8 0

The last graph.

Explanation:
Since you are looking for a solution you need to look at the place where both lines connect, in this case, we are looking for the coordinate ( 2, -1 )
2 being the x-axis and -1 being the y-axis
The last graph is the only one that shows that the two lines touch at the coordinate ( 2, -1 )

aksik [14]3 years ago

6 0

The solution to a system of equations is the point on a graph where the two lines intersect. The graph where the point of intersection is (2, -1) is the last graph. The last graph is the correct answer.

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Daniel traveled to his cabin on the lake and back. On the trip there he traveled 40 km/h and On the return trip he went 60 km/h.

Keith_Richards [23]

Answer:

The trip took total of 5 hrs out of which 3 hrs took for going to the trip and 2 hours for returning from the trip.

Step-by-step explanation:

Given:

Speed to the cabin = 40 km/h

Speed on return trip = 60 km/h

Time for return trip = 2 hrs.

We need to find the time for total trip.

Solution:

First we will find the Distance of the trip.

Now we know that Distance is equal to Speed times Time.

Now we can say that;

$\textrm{Distance of return trip} = \textrm{Speed of the return trip}\times \textrm{Time of return trip}$

Distance of return trip = $60\times 2 =120\ km$

Now we can say that Distance of return trip will equal to Distance to the trip.

Now we will find the time required to travel the trip.

time required to travel the trip can be calculated by dividing distance from the speed.

framing in equation form we get;

time required to travel the trip = $\frac{120}{40} = 3\ hrs$

Total time is equal to time took to travel the trip and Time took for return trip.

framing in equation form we get;

Total time = 3 + 2 = 5 hrs

Hence The trip took total of 5 hrs out of which 3 hrs took for going to the trip and 2 hours for returning from the trip.

5 0

3 years ago

When Gail goes on a hike, she always packs a ratio of 20 protein bars to 15 water bottles in her backpack. Complete the statemen

Oduvanchick [21]

Answer: The ratio of protein bars to water bottles will be 4:3.

Explanation:

Since we have given that

Number of protein bars = 20

Number of water bottles = 15

We need to calculate the ratio of protein bars to water bottles which is given by

$\text{ Number of protein bars}:\text{ Number of water bottles }\\\\=20:15\\\\=4:3$

So, the ratio of protein bars to water bottles will be 4:3.

6 0

3 years ago

Read 2 more answers

Determine whether the series is arithmetic or geometric. Then evaluate the finite series for the specified number of terms. 10 +

Salsk061 [2.6K]

Answer:

10 + 7 + 4 + . . .; n = 5

The series is arithmetic

Common difference between terms = (-3)

10 - 3 = 7

7 - 3 = 4

Or:

10 + (-3) = 7

7 + (-3) = 4

--------------------------------------------------------------------------

Another example:

Arithmetic:

5, 9, 13, 17

common difference = 4

5 + 4 = 9

9 + 4 = 13

Geometric:

4, 8, 16, 32

4 × 2 = 8

8 × 2 = 16

16 × 2 = 32

common ratio = 2

--------------------------------------------------------------------------

10 + 7 + 4 + . . .; n = 5

a₁ = 10

a₂ = 7

a₄ = a₃ + d = 4 + (-3) = 4 - 3 = 1 (d = common difference)

a₅ = a₄ - 3 = 1 - 3 = -2

Or with formula:

$d=a_{n} -a_{n-1}$

d = a₂ - a₁ = 7 - 10 = -3

aₙ = a₁ + (n - 1)d

fourth term = a₄ = 10 + (4 - 1)(-3) = 10 + 3(-3) = 10 + (-9) = 10 - 9 = 1

fifth term = a₅ = 10 + (5 - 1)(-3) = 10 + 4(-3) = 10 + (-12) = 10 - 12 = -2

Sum of the finite series (if n = 5):

$S_{n} =\frac{n(a_{1} +a_{n} )}{2} \\S_{5} =\frac{5(a_{1} +a_{5} )}{2} \\S_{5} =\frac{5(10 +(-2) )}{2} \\S_{5} =\frac{5(8 )}{2} =\frac{40}{2} =20$

Manual count: S₅ = 10 + 7 + 4 + 1 + (-2) = 20

7 0

2 years ago

In Ms. Renault's classroom, 2/5 of the students play sudoku. Of the student who play sudoku, 5/6 also play checkers. If there ar

likoan [24]

Answer:

10 students play sudoku and checkers

Step-by-step explanation:

First find the number of students that play sudoku

2/5 * 30

of those 12 students, 5/6 play checkers

12 * 5/6 = 10

10 students play sudoku and checkers

8 0

3 years ago

Which of the following expressions describes the solution set m ≥ -3?

Mrrafil [7]

"All real numbers that are negative three or greater" because ≥ means 'greater than or equal to' in this case.

4 0

3 years ago

Read 2 more answers