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lions [1.4K]
3 years ago
9

Write equivalent expressions for x-7.x-2 and x7\x2

Mathematics
1 answer:
navik [9.2K]3 years ago
7 0
The first one is 
-6x-2

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Maisie bought a house.
sergeinik [125]

Answer:

55.52+10=65.52%

65.52 divide 3=21.84%

Ans:21.84%

7 0
3 years ago
Find the solution set of this inequality|10x+20| ≤10
Pavlova-9 [17]

Answer:

solution is

[-3,-1]

Step-by-step explanation:

we are given

|10x+20|\leq 10

Firstly, we will find critical values

so, let's assume it is equal

|10x+20|= 10

now, we can break absolute sign

For |10x+20|= -(10x+20):

-(10x+20)= 10

we can solve for x

-10x-20= 10

Add both sides by 20

-10x-20+20= 10+20

-10x= 30

Divide both sides by -10

and we get

x=-3

For |10x+20|= (10x+20):

(10x+20)= 10

we can solve for x

10x+20= 10

Subtract both sides by 20

10x+20-20= 10-20

10x= -10

Divide both sides by 10

and we get

x=-1

so, critical values are

x=-3

x=-1

now, we can draw a number line and locate these values

and then we can check inequality on each intervals

For (-\infty,-3):

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-5

|10\times -5+20|\leq 10

|-50+20|\leq 10

30\leq 10

so, this is FALSE

For [-3,-1]:

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=-2

|10\times -2+20|\leq 10

|-20+20|\leq 10

0\leq 10

so, this is TRUE

For (-1,\infty):

We can select any random value from this interval and plug that in inequality

and we get

we can plug x=0

|10\times 0+20|\leq 10

|0+20|\leq 10

20\leq 10

so, this is FALSE

so, solution is

[-3,-1]

7 0
3 years ago
How many terms are there in the sequence 1, 8, 28, 56, ..., 1 ?
BabaBlast [244]

Answer:

9 terms

Step-by-step explanation:

Given:  

1, 8, 28, 56, ..., 1

Required

Determine the number of sequence

To determine the number of sequence, we need to understand how the sequence are generated

The sequence are generated using

\left[\begin{array}{c}n&&r\end{array}\right] = \frac{n!}{(n-r)!r!}

Where n = 8 and r = 0,1....8

When r = 0

\left[\begin{array}{c}8&&0\end{array}\right] = \frac{8!}{(8-0)!0!} = \frac{8!}{8!0!} = 1

When r = 1

\left[\begin{array}{c}8&&1\end{array}\right] = \frac{8!}{(8-1)!1!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8

When r = 2

\left[\begin{array}{c}8&&2\end{array}\right] = \frac{8!}{(8-2)!2!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} =2 8

When r = 3

\left[\begin{array}{c}8&&3\end{array}\right] = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56

When r = 4

\left[\begin{array}{c}8&&4\end{array}\right] = \frac{8!}{(8-4)!4!} = \frac{8!}{4!3!} = \frac{8 * 7 * 6 * 5 * 4!}{4! *4*3* 2 *1} = \frac{8 * 7 * 6*5}{4*3 *2 *1} = 70

When r = 5

\left[\begin{array}{c}8&&5\end{array}\right] = \frac{8!}{(8-5)!5!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56

When r = 6

\left[\begin{array}{c}8&&6\end{array}\right] = \frac{8!}{(8-6)!6!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} = 28

When r = 7

\left[\begin{array}{c}8&&7\end{array}\right] = \frac{8!}{(8-7)!7!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8

When r = 8

\left[\begin{array}{c}8&&8\end{array}\right] = \frac{8!}{(8-8)!8!} = \frac{8!}{8!0!} = 1

The full sequence is: 1,8,28,56,70,56,28,8,1

And the number of terms is 9

3 0
3 years ago
Which system of inequalities does the graph represent? Which test point satisfies both of the inequalities in that system?
AveGali [126]

Answer:

1) The inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

2)  The test point (0,0)  satisfies both of the inequalities in the system represented by the graph.

Step-by-step explanation:

Given : A graph showing  a system of inequalities.

We have to find the system of inequality.

For line 1)

The points that cut the x and y axis are (1,0) and (0,-4)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as m=\frac{y_2-y_1}{x_2-x_1}

Substitute, we get,

m=\frac{-4-0}{0-1}=4

Slope is 4.

Thus, equation becomes y = 4x + c

For c put (0,-4)  in the above equation , we have,

-4 = 4(0) + c ⇒ c = -4

Thus, equation becomes y = 4x - 4

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = 4x - 4 becomes 0 = - 4  is satisfied when 0 > -4

thus, the inequality becomes y ≥ 4x - 4

Since, the line is a solid so it will take up equality sign too.

For line 2)

The points that cut the x and y axis are (1.5,0) and (0,-1.5)

Thus, we can find the equation of line using two given point.

Since the general equation of line is y = mx + c

Where m is slope and c is y intercept

Slope is find as m=\frac{y_2-y_1}{x_2-x_1}

Substitute, we get,

m=\frac{-1.5-0}{0-1.5}=1

Slope is 1.

Thus, equation becomes y = x + c

For c put (0,-1.5)  in the above equation , we have,

-1.5 = (0) + c ⇒ c = - 1.5

Thus, equation becomes y = x - 1.5

For inequality take a test point (0,0) and we check for which inequality it satisfies the graph region

For (0,0)

y = x - 1.5 becomes 0 = -1.5  is satisfied when 0 > - 1.5

thus, the inequality becomes y ≥ x - 1.5

Since, the line is a solid so it will take up equality sign too.

Thus, the inequality for the given system are

y ≥ 4x - 4

y ≥ x - 1.5

Also,  The test point (0,0)  satisfies both of the inequalities in the system represented by the graph.

6 0
3 years ago
2y = x + 3 5y = x - 7 What is the solution set of the given system?
olga_2 [115]
-3=2x+10=  -13=2x = -0.153
5 0
3 years ago
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