Find the values of x and y in these equations. (x + yi) + (4 + 6i) = 7 − 2i (equation A) (x + yi) − (-8 + 11i) = 5 + 9i (equation B)

Answer:

94 cm

Step-by-step explanation:

The formula for finding the circumference of a circle is;

Circumference = 2πr

where π = [tex]\frac{22}{7}[/tex] or 3.14 and

r = radius

Here radius is 15 cm so;

Circumference = [tex]2 * \frac{22}{7} * 15[/tex]

                         = [tex]\frac{660}{7}[/tex]cm

                         = 94.28cm

                         = 94 cm (  rounded to the nearest centimetre )

Answer:

x = 2, y = 5

Step-by-step explanation:

Hello,

   y=6x-7

   9x-2y=8

can be written as

   (1) 6x - y = 7

   (2) 9x -2y = 8

(2)-2*(1) gives

   9x -2y -12x +2y = 8 - 2*7 = 8 - 14 = -6

   <=> -3x=-6

   <=> x = 6/3=2

and we replace it in (1)

  y = 6*2-7=12-7=5

hope this helps

The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

We have,

To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:

CI = X ± (Z * (σ/√n))

where:

CI is the confidence interval

X is the sample mean

Z is the critical value corresponding to the desired confidence level (90% confidence level corresponds to Z = 1.645 for a large sample size)

σ is the population standard deviation

n is the sample size

Given that the sample mean X of the net change in LDL cholesterol is 2.7, the standard deviation (σ) is 17.8, and the sample size (n) is 47, we can calculate the confidence interval as follows:

CI = 2.7 ± (1.645 * (17.8/√47))

Calculating the standard error (SE):

SE = σ/√n = 17.8/√47 ≈ 2.587

Substituting the values into the confidence interval formula:

CI = 2.7 ± (1.645 * 2.587)

Calculating the upper and lower bounds of the confidence interval:

Upper bound = 2.7 + (1.645 * 2.587) ≈ 7.199

Lower bound = 2.7 - (1.645 * 2.587) ≈ -1.799

Therefore, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199.

Interpreting the confidence interval:

Since the confidence interval contains both positive and negative values, it suggests that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

The interval includes zero, indicating that there is a possibility that the mean net change in LDL cholesterol after the garlic treatment could be zero (no change).

However, it is important to note that further studies or a larger sample size may be needed to draw more definitive conclusions.

Thus,

The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.

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The 90% confidence interval suggests that the true mean net change in LDL cholesterol after the garlic treatment lies between -1.57 and 6.97 mg/dL. Since the interval contains both positive and negative values, it indicates that the garlic treatment may or may not be effective in reducing LDL cholesterol.

To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:

CI = mean ± (Z * (standard deviation / √n))

Here, n represents the sample size (47), Z is the critical value corresponding to a 90% confidence level (Z = 1.645 for a 90% confidence level), and the mean is 2.7 with a standard deviation of 17.8.

Plugging in the values:

CI = 2.7 ± (1.645 * (17.8 / √47))

CI = 2.7 ± (1.645 * (17.8 / 6.856))

CI = 2.7 ± (1.645 * (2.596))

CI = 2.7 ± 4.270

CI = 2.7 + 4.270  ;  CI = 2.7 - 4.270

CI = 6.97             ;  CI = -1.57

Thus, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately (-1.57, 6.97).

The confidence interval suggests that the effectiveness of garlic in reducing LDL cholesterol is inconclusive. The interval spans both positive and negative values, indicating that the true mean change in LDL cholesterol could be anywhere within this range. Further research or a larger sample size might be needed to draw a more definitive conclusion about the effectiveness of garlic in lowering LDL cholesterol.

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Answer:

24 feet.

Step-by-step explanation:

The side  of the square = √36 = 6 feet.

The square has 4 equal sides so the perimeter = 4*6 = 24 feet.

Answer:

Well I took it"s Reflect the intermediate image.  and Multiply the vertices of polygon ABCD by One-half.

Step-by-step explanation:

Answer:

2 and 5 or B and E

Step-by-step explanation:

i did it on edge! ; )

Answer:

1/20

Step-by-step explanation:

5 brown marbles, 3 yellow marbles, 4 red marbles, 6 blue marbles, and 2 orange marbles = 20 marbles

P( brown) = brown / total = 5/20 = 1/4

Replace

5 brown marbles, 3 yellow marbles, 4 red marbles, 6 blue marbles, and 2 orange marbles = 20 marbles

P( red) = red / total = 4/20 = 1/5

P( brown, replace, red) = 1/4 * 1/5 = 1/20

Answer:

19/9 because it equals to 2.111..  Which is greater than 1

Step-by-step explanation:

By the way if it's right can i get brainliest.

Answer:

1 < 19/9

Step-by-step explanation:

1  vs 19/9

Rewriting 19/9 as 9/9 + 9/9+ 1/9

1 vs 1+1 +1/9

1 vs 2 1/9

1 < 19/9

Answer:

4(x + 1) = 16

x + 1 = 4 (Divide equation by 4)

x = 3 (subtract 1)

Answer:

x = 3

Step-by-step explanation:

4(x + 1)=16

Expand the brackets.

4x + 4 = 16

Subtract 4 on both sides.

4x + 4 - 4 = 16 - 4

4x = 12

Divide both sides by 4.

4x/4 = 12/4

x = 3

Answer:

61,925 miles

Step-by-step explanation:

Given :

The p-value of the tires to outlast the were warranty were given in the the question as = 0.96

Checking the normal distribution table, The probability that corresponds to 0.96

from the Normal distribution table is 1.75.

Mean : 'μ'= 60000 miles

Standard deviation : σ=1100

The formula for z-score is given by

: z= (x-μ)/σ

1.75=(x-60000)/1100

1925=x-60000

x=61925

Therefore, the tread life of tire should be 61,925 miles if they want 96% of the tires to outlast the warranty.

Answer:

  2 1/4

Step-by-step explanation:

The volume of soil needed is ...

  (14/3 yd)(26/3 yd)(2/36 yd) = 728/324 yd³ = 2.247 yd³

The nearest higher quarter-yard is 2.250 yd³. That's how much you need to order.

  You need to order 2 1/4 cubic yards.

___

There are 3 ft or 36 inches to a yard.

Answer:

54

give me brainliest please please please and follow my page

Step-by-step explanation:

To find length of KC...we need to find the length of HM and MU first ...

so....HM= 96- 78 = 14

JU = 96 + HM = 96 + 14 = 110

....

KU = 110 - JK = 110 - 82 = 28

....

UN = 105+ 82 -( 96 + 14 )

187 - 110

= 77

UC = 77 - 51 = 26

KC = UC + KU = 26 + 28 = 54

The length of [tex]\overline{KC}[/tex] along line [tex]\overline{JN}[/tex] is given as 54 (Option A) See the computation below.

To determine the length of [tex]\overline{KC}[/tex], the length of [tex]\overline{HM}[/tex] and [tex]\overline{MU}[/tex]must first be derived.

[tex]\overline{HM}[/tex] = 96 - 78

[tex]\overline{HM}[/tex] = 14

[tex]\overline{JU}[/tex] = 96 + [tex]\overline{HM}[/tex]

= 96 + 14

[tex]\overline{JU}[/tex]= 110

[tex]\overline{KU}[/tex] = 110 - [tex]\overline{JK}[/tex]

= 110 - 82

[tex]\overline{KU}[/tex]= 28

[tex]\overline{UN}[/tex] = 105+ 82 -( 96 + 14 )

=187 - 110

[tex]\overline{UN}[/tex]= 77

[tex]\overline{UC}[/tex] = 77 - 51

[tex]\overline{UC}[/tex]= 26

Thus,

[tex]\overline{KC}[/tex] = [tex]\overline{UC}[/tex] + [tex]\overline{KU}[/tex]

[tex]\overline{KC}[/tex]= 26 + 28

[tex]\overline{KC}[/tex]= 54

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Answer:

Y=1/4x-4

Explanation: The y intercept is -4 that is your B. Using the rise over sun method the line rises 1 and goes to the right 4 making the slope 1/4 or .25

Answer:

I didn't know which one you wanted...

Step-by-step explanation:

1. Finding the x an y-intercepts

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (2,0)

y-intercept(s): (0,−24)

2. Finding the slope and y-intercept

Use the slope-intercept form to find the slope and y-intercept.

Slope: 12

y-intercept: −24

Answer: 1x + 2y = 4

Step-by-step explanation:

The equation of the line is y = -1/2x + 2.

First, let's make 4 on one side of the equation.  First, bring x to the left.  y + 1/2x = 2.  Then multiply the whole equation by two.  Thus, 1x + 2y = 4.

Hope it helps <3

Find the intercepts for both planes.

Plane 1, x + y + 2z = 2:

[tex]y=z=0\implies x=2\implies (2,0,0)[/tex]

[tex]x=z=0\implies y=2\implies(0,2,0)[/tex]

[tex]x=y=0\implies 2z=2\implies z=1\implies(0,0,1)[/tex]

Plane 2, 4x + 4y + z = 8:

[tex]y=z=0\implies4x=8\implies x=2\implies(2,0,0)[/tex]

[tex]x=z=0\implies4y=8\impliesy=2\implies(0,2,0)[/tex]

[tex]x=y=0\implies z=8\implies(0,0,8)[/tex]

Both planes share the same x- and y-intercepts, but the second plane's z-intercept is higher, so Plane 2 acts as the roof of the bounded region.

Meanwhile, in the (x, y)-plane where z = 0, we see the bounded region projects down to the triangle in the first quadrant with legs x = 0, y = 0, and x + y = 2, or y = 2 - x.

So the volume of the region is

[tex]\displaystyle\int_0^2\int_0^{2-x}\int_{\frac{2-x-y}2}^{8-4x-4y}\mathrm dz\,\mathrm dy\,\mathrm dx=\displaystyle\int_0^2\int_0^{2-x}\left(8-4x-4y-\frac{2-x-y}2\right)\,\mathrm dy\,\mathrm dx[/tex]

[tex]=\displaystyle\int_0^2\int_0^{2-x}\left(7-\frac72(x+y)\right)\,\mathrm dy\,\mathrm dx=\int_0^2\left(7(2-x)-\frac72x(2-x)-\frac74(2-x)^2\right)\,\mathrm dx[/tex]

[tex]=\displaystyle\int_0^2\left(7-7x+\frac74 x^2\right)\,\mathrm dx=\boxed{\frac{14}3}[/tex]

hello

[tex]A-B=\left[\begin{array}{cc}4-(-2)&7-5\\-3-7&8-(-1)\\-5-(-3)&-2-2\end{array}\right] \\\\=\left[\begin{array}{cc}4+2&2\\-10&8+1\\-5+3&-4\end{array}\right] \\\\=\left[\begin{array}{cc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]

hope this helps

Using matrices A  and B, the result of A-B is

[tex]A-B=\left[\begin{array}{ccc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]

Given :

Two matrices A  and B. We need to subtract both matrix

Lets find out A-B

Given matrices  A  and B  are

[tex]A=\left[\begin{array}{ccc}4&7\\-3&8\\-5&-2\end{array}\right] \\B=\left[\begin{array}{ccc}-2&5\\7&-1\\-3&2\end{array}\right][/tex]

When we subtract A-B  we need to subtract the corresponding elements in that matrix

[tex]A-B=\left[\begin{array}{ccc}4&7\\-3&8\\-5&-2\end{array}\right] -\left[\begin{array}{ccc}-2&5\\7&-1\\-3&2\end{array}\right]=\left[\begin{array}{ccc}4-(-2)&7-5\\-3-7&8-(-1)\\-5-(-3)&-2-2\end{array}\right] \\A-B=\left[\begin{array}{ccc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]

The above is the resultant matrix .

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Answer:

[tex]\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \ }[/tex]

Step-by-step explanation:

Hello,

let's follow the advise and proceed with the substitution

first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t

[tex]x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)<=>y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})[/tex]

Now we can substitute in the equation

[tex]x^2y''(x)+9xy'(x)-20y(x)=0\\<=> e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\<=> \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\<=> \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\[/tex]

so the new equation is

[tex]y''(t)+ 8y'(t)-20y(t)=0[/tex]

the auxiliary equation is

[tex]x^2+8x-20=0\\<=> x^2-2x+10x-20=0\\<=>x(x-2)+10(x-2)=0\\<=>(x+10)(x-2)=0\\<=> x=-10\text{ or }x=2[/tex]

so the solutions of the new equation are

[tex]y(t)=ae^{2t}+be^{-10t}[/tex]

with a and b real

as

[tex]x(t)=e^t\\<=> t(x)=ln(x)[/tex]

[tex]y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}[/tex]

hope this helps

do not hesitate if you have any questions

Answer:

Polly can choose 33264 schedules.

Step-by-step explanation:

None of these sections interfere with each other, so:

For each statistics choice, there are 12 composition choices.

For each composition choice, there are 11 section of Ethics choices.

For each section of Ethics choice, there are 18 Physics choises.

There are 14 statistics choices.

From how many possible schedules can Polly choose?

14*12*11*18 = 33264

Polly can choose 33264 schedules.

Answer:

2x-y=4

Step-by-step explanation:

Standard form of a line: Ax+by=c

Use slope intercept form: y=mx+b

slope= 2

y=2x-4

Add 4 to both sides.

y+4=2x

subtract y from both sides.

4=2x-y

Rotate the equation

2x-y=4

Answer:

2x-y=4

Step-by-step explanation:

y=2x-4 is the slope intercept.

y-2x=-4

-2x+y=-4

2x-y=4

Answer:

At a significance level of 0.05, there is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.

Then, the null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0

The significance level is 0.05.

The sample 1 (Pernod 5), of size n1=400 has a proportion of p1=0.06.

[tex]p_1=X_1/n_1=24/400=0.06[/tex]

The sample 2, of size n2=400 has a proportion of p2=0.1.

[tex]p_2=X_2/n_2=40/400=0.1[/tex]

The difference between proportions is (p1-p2)=-0.04.

[tex]p_d=p_1-p_2=0.06-0.1=-0.04[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{24+40}{400+400}=\dfrac{64}{800}=0.08[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.08*0.92}{400}+\dfrac{0.08*0.92}{400}}\\\\\\s_{p1-p2}=\sqrt{0.000184+0.000184}=\sqrt{0.000368}=0.019[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.04-0}{0.019}=\dfrac{-0.04}{0.019}=-2.085[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]\text{P-value}=2\cdot P(z<-2.085)=0.037[/tex]

As the P-value (0.037) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that there is a significant difference in the proportion of vines infested using Pernod 5 as opposed to Action.

First find the distance it is reflected:

D = 20.0 x 10.0 /(20-10) = 200/10 = 20cm away.

Now calculate the magnification: -20/ 20 = -1

Now calculate the height:

-1 x 2.50 = -2.50

The negative sign means the image is inverted.

The mirrored image would be inverted, 2.50 cm tall and 20 cm in front of the mirror.

Answer:<5 and <4 are exterior angles

Step-by-step explanation:

Because they are the only ones outside it they are the only ones that are exterior angles!

<!> Brainliest is appreciated! <!>

Answer:

for AL Its 3 and 4

Answer:

the probability that 7 out 10 Internet users will order something online is 0.78 or 78%

Step-by-step explanation:

Given that:

Internet users who order something online = 85%

To find:

Probability that 7 out of 10 Internet users will order something online ?

Solution:

This problem is of binomial distribution of probability.

where, p = 0.85

q = 1-p = 0.15

r = 7 and

n = 10

Formula is given as:

[tex]P(x = r) = _nC_r q^{n-r}p^r[/tex]

Putting all the values:

[tex]P(x = 7) = _{10}C_7 0.15^{10-7}\times 0.85^7\\P(x = 7) = _{10}C_3 0.15^{3}\times 0.85^7\\P(x = 7) = 10\times 9 \times 8 \times 0.15^{3}\times0.85^7\\P(x = 7) = 720 \times .0034 \times0.32\\P(x = 7) = 0.78[/tex]

So, the probability that 7 out 10 Internet users will order something online is 0.78 or 78%.

Answer:

Let's list out the points that belong to T. They are T{(-1, -4), (2, 2), (2, -3)}.

The domain is all of the x values. Therefore the domain is {-1, 2}.

The range is all of the y values. Therefore the range is {-4, -3, 2}.

We don't use ( ) or [ ] because T is a discrete relation.

Answer:

A) 360

B) 360

Step-by-step explanation:

Part A)

Given that there are a total of 6 people and 4 person subcommittee is to be selected.

Number of ways to select 1st person = 6

Now, 1 person is selected, total persons left are 5

Number of ways to select 2nd person = 5

Now, 1 person is selected, total persons left are 4

Number of ways to select 3rd person = 4

Now, 1 person is selected, total persons left are 3

Number of ways to select 4th person = 3

So, total number of ways = 6[tex]\times[/tex]5[tex]\times[/tex]4[tex]\times[/tex]3 = 360

Part B)

Given that there are a total of 6 people in the committee

Number of ways to select president  = 6

Now, 1 person is selected, total persons left are 5

Number of ways to select vice president = 5

Now, 1 person is selected, total persons left are 4

Number of ways to select secretary = 4

Now, 1 person is selected, total persons left are 3

Number of ways to select treasurer = 3

So, total number of ways = 6[tex]\times[/tex]5[tex]\times[/tex]4[tex]\times[/tex]3 = 360

Answer:

  x ║ z

Step-by-step explanation:

Lines parallel to the same line are parallel to each other.

x and z are both parallel to y, so are parallel to each other:

  x ║ z

Answer:

  (–ꝏ, 0) U (0, 5)

Step-by-step explanation:

The relation can be written as ...

  x³ < 5x²

  x³ -5x² < 0

  x²(x -5) < 0

This is not true for x = 0. It is true for x < 5, otherwise. Then the solution set is ...

  x ∈ {(–ꝏ, 0) U (0, 5)}

Answer:

C

Step-by-step explanation:

got it right on edge

This is a great question!

When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -

[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]

____

Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,

[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]

Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,

( 1. The new store will have a profit of $3400 after its third month in business.  

( ​​2. The new store will have a profit of $2400 after its third month in business.

( 3. ​The new store will sell 2400 items in its third month in business.

( 4. The new store will sell 3400 items in its third month in business.

The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.

The substitution method is the algebraic method to solve simultaneous linear equations.

Given function is,

[tex]r(x) = x^2+5x+14[/tex]...(1)

And [tex]c(x) = x^2-4x+5[/tex]...(2)

Now, substituting the value into the equation (1) and (2).

[tex]r(5) = (5)^2+5(5)+14=64[/tex]

[tex]c(5) = (5)^2-4(5)+5=10[/tex]

Therefore,

[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]

Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.

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Answer:

  y = √(900 -x²); see below for a graph

Step-by-step explanation:

The high point (30 ft) is the radius of the circle, so the equation is ...

  x² +y² = 30²

Subtract the x-term and take the square root to find y.

  y² = 30² -x²

  y = √(30² -x²) = √(900 -x²)

The graph is shown in the attachment.

_____

Comment on "how that website works"

We don't know what web site you're referring to, but the one I like is Desmos. It only takes a few minutes to learn to graph the equation here.

You don't even need to solve for y to get the desired graph. You can simply specify that y ≥ 0.

Answer:

Its the first answer choice.

Step-by-step explanation:

Its open circle because the sign is just greater than. And since x is an absolute value, the negative sign doesnt matter so, it points to the right of 10 and to the left of -10.