find the distance between each pair of points (-1 4) (1 -1)​

Answer:

[tex]-3\cdot x + 5\cdot y = 6[/tex], [tex]6\cdot x -10\cdot y = 14[/tex] is inconsistent.

Step-by-step explanation:

Two linear equations are inconsistent when each group of coefficients associated with each variable have the same multiple and independent coefficients are different and have the same multiple. Since, the set of variables is [tex](x,y)[/tex], then the following condition must be observed:

[tex]k_{x} = k_{y} \ne k_{c}[/tex] (1)

[tex]k_{x} = \frac{a_{x}}{b_{x}}[/tex] (2)

[tex]k_{y} = \frac{a_{y}}{b_{y}}[/tex] (3)

[tex]k_{c} = \frac{a_{c}}{b_{c}}[/tex] (4)

Now we proceed to check each option:

Option 1: [tex]x + 4\cdot y = 20[/tex], [tex]2\cdot x - y = 7[/tex]

([tex]a_{x} = 1[/tex], [tex]a_{y} = 4[/tex], [tex]b_{x} = 2[/tex], [tex]b_{y} = -1[/tex])

[tex]k_{x} = \frac{1}{2}[/tex], [tex]k_{y} = -4[/tex] (This system is not inconsistent)

Option 2: [tex]3\cdot x + 2\cdot y = -2[/tex], [tex]4\cdot x -y = -2[/tex]

([tex]a_{x} = 3[/tex], [tex]a_{y} = 2[/tex], [tex]b_{x} = 4[/tex], [tex]b_{y} = -1[/tex])

[tex]k_{x} = \frac{3}{4}[/tex], [tex]k_{y} = -2[/tex] (This system is not inconsistent)

Option 3: [tex]8\cdot x + 4\cdot y = 16[/tex], [tex]4\cdot x - 2\cdot y = 6[/tex]

([tex]a_{x} = 8[/tex], [tex]a_{y} = 4[/tex], [tex]b_{x} = 4[/tex], [tex]b_{y} = -2[/tex])

[tex]k_{x} = 2[/tex], [tex]k_{y} = -2[/tex] (This system is not inconsistent)

Option 4: [tex]-3\cdot x + 5\cdot y = 6[/tex], [tex]6\cdot x -10\cdot y = 14[/tex]

([tex]a_{x} = -3[/tex], [tex]a_{y} = 5[/tex], [tex]b_{x} = 6[/tex], [tex]b_{y} = -10[/tex])

[tex]k_{x} =-\frac{3}{5}[/tex], [tex]k_{y} = -\frac{3}{5}[/tex] (This system may be inconsistent)

([tex]a_{c} = 6[/tex], [tex]b_{c} = 14[/tex])

[tex]k_{c} = \frac{3}{7}[/tex] (This system is inconsistent)

Answer:

P(X ≥ 2) = 0.5967

Step-by-step explanation:

Using binomial probability distribution formula;

P(X = k) = C(n, k) × p^(k) × (1 - p)^(n - k)

two percent of a product are defective. Thus; p = 0.02

a lot of 100 items are ordered. Thus, n = 100

Probability that there are no defective items is;

P(X = 0) = C(100, 0) × 0.02^(0) × (1 - 0.02)^(100 - 0)

P(X = 0) = 0.98^(100) = 0.1326

the probability that there are at least two defective items will be;

P(X ≥ 2) = 1 - P(X < 2)

Now,

P(X < 2) = P(X = 0) + P(X = 1)

P(X = 1) = C(100, 1) × 0.02^(1) × (1 - 0.02)^(100 - 1)

P(X = 1) = 100 × 0.02 × 0.98^(99) = 0.2707

Thus;

P(X < 2) = 0.1326 + 0.2707

P(X < 2) = 0.4033

P(X ≥ 2) = 1 - 0.4033

P(X ≥ 2) = 0.5967

Answer:

Step-by-step explanation:

two-dimension

Answer:

I believe two dimensional and a intersection of two angles, not for sure tho

Step-by-step explanation:

9514 1404 393

Answer:

  (x, y) = (2.5, 6.5)

Step-by-step explanation:

I find it easier just to solve the system of equations:

  x + 4 = 3x - 1

  5 = 2x

  x = 5/2 = 2.5

  y = x+4 = 6.5

  (x, y) = (2.5, 6.5)

__

Additional comments

The first equation has a positive y-intercept and a positive slope, so makes a triangle with the axes in the 2nd quadrant.

The second equation has a negative y-intercept and a (more) positive slope, so makes a triangle with the axes in the 4th quadrant. The slope is greater for this line, so the lines will intersect in the 1st quadrant. Without more effort, the best estimate at this point is that x and y are both positive and y > 4.

Answer:

The constant of proportionality(Unit rate) is 0.23

Step-by-step explanation:

Given equation is:

[tex]P = 0.23n[/tex]

Here

P is the price and n is the number of apples

The price is usually directly proportional to quantity so the relationship can be written as:

P ∝ n

Removing the proportionality symbol, we get

P = kn

Comparing the given equation with this equation we get

k = 0.23

Hence,

The constant of proportionality(Unit rate) is 0.23

Answer:

Rewrite the problem vertically, align the decimals, and add a zero. Add the numbers. Jessica ran 26.95 miles.

Step-by-step explanation:

Edge 2021

Thank youuu

Answer:

15

Step-by-step explanation:

$17.7 rounded to $18

$3.25 rounded to $3

$18 - $3 = $15

Answer:

(b) and (c).

Step-by-step explanation:

The given expression is : 5y+9

In this equation, y is only variable. 5 times of y is added to 9.

Option (a) is incorrect as 9 is constant instead of 5.

Option (b) is correct.

Option (c) is correct as y is only variable here.

Option (d) is incorrect as 5 is coefficient of y only not of whole expression.

Option (d) is incorrect as there are 2 terms i.e 5y and 9.

Hence, correct options are : (b) and (c).

Answer:

you turn a fraction into a percentage by dividing the numerator by the denominator. then multiply the decimal by 100.

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

Given that,

The slope of the line, m = 3/4

First point = (x,2)

Another point = (3,-4)

We need to find the value of x.

The slope of a line is given by the formula as follows :

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Put x₁ = x, y₁ = 2, x₂ = 3, y₂ =-4 and m = 3/4

Put all the values,

[tex]\dfrac{3}{4}=\dfrac{-4-2}{3-x}\\\\3(3-x)=4(-6)\\\\9-3x=-24\\\\9+24=3x\\\\33=3x\\\\x=11[/tex]

So, the value of x is 11.

Answer:

It repeats over and over..

Step-by-step explanation:

Answer:

As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design.

Step-by-step explanation:

Answer:basically a small percentage of product you can buy from any company that increases in value over the years

Step-by-step explanation:

Answer:

Roxana's normal pay is $12.00

Step-by-step explanation:

1.5 times normal hourly rate.

72 in 4 hours,

18 in 1 hour.

18/1.5=12.

Her pay is 12.

Hope this helps plz hit the crown :D

Answer:

The answer is 52$

Step-by-step explanation:

the ratio converted in fraction is 1/5 by doing 4+1,

now you do 1/5 of 65 total dollars,

so you do 1/5 of 65,

=65/5

=13

jill will get 13$. but the question is asking for how much money did stephanie get. So now we do 13*4 which is 52$.

So stephanie gets 52$

Hope this helps,

Have a great day,

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Answer:

Graph C

Step-by-step explanation:

Graph C shows a linear relationship

Answer:

For that one is C

Step-by-step explanation:

sqrt(x + 2) - 15 = -3

sqrt(x + 2) = 12 (add 15 to both sides)

x + 2 = 12² = 144 (square both sides)

x = 142.

Answer:

x = 142

Step-by-step explanation:

√x+2 - 15 = -3 (Given)

√x+2 = 12 (Add 15 on both sides)

x + 2 = 144 (Square both sides to get rid of the radical)

x = 142 (Subtract 2 on both sides)

Answer:

Step-by-step explanation:

As per diagram we have:

As per 30° right triangle property:

Area of triangle:

Answer:

54.6 or 1 4/10

Step-by-step explanation:

If you find the 40 percent and add that to 39 (which is 100) you get 54.6.

Answer: 127,500

Step-by-step explanation: I just used a calculator

Answer:

the answer is 127,500

Step-by-step explanation:

Answer:

4/6 of a pizza.

Step-by-step explanation:

We know that:

Both pizzas are of the same size.

Jasmine cut her's into 12 slices.

Kelly cut her's into 6 slices, and ate 2 slices, then Kelly ate 2/6 of a pizza.

Jasmine ate X of a pizza, and we know that between them ate a total of 1 pizza.

This means that:

X of a pizza + 2/6 of a pizza = 1 pizza

X + 2/6 = 1

X = 1 - 2/6

X = 6/6 - 2/6 = 4/6

Jasmine ate 4/6 of a pizza, knowing that she cut her's into 12 slices, this would mean that she ate 8/12 of a pizza, or 8 slices.

Answer:

7.5 mins

Step-by-step explanation:

60 ÷ 8 = 7.5

hope it's right

Answer:

im pretty sure 36

Step-by-step explanation:

if you do 120 devided by 30 you get 4, then u just multipy by 9 which is 36.

Answer: b

i got it right and the answer was b for me

Answer:

[tex] x = \frac{3}{2} + \frac{ \sqrt{5} }{2} ; \: \: x = \frac{3}{2} - \frac{ \sqrt{5} }{2} [/tex]

Step-by-step explanation:

[tex]1 + \frac{1}{ {x}^{2} } = \frac{3}{x} \\ \\ \frac{ {x}^{2} + 1 }{ {x}^{2} } = \frac{3}{x} \\ \\ {x}^{2} + 1 = \frac{3 {x}^{2} }{x} \\ \\ {x}^{2} + 1 = 3x \\ \\ {x}^{2} - 3x + 1 = 0 \\ equating \: it \: with \\ a {x}^{2} + bx + c = 0 \\ a = 1 \\ b = - 3 \\ c = 1 \\ \\ x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x = \frac{ - ( - 3) \pm \sqrt{ {( - 3)}^{2} - 4 \times 1 \times 1} }{2 \times 1} \\ \\ x = \frac{ 3 \pm \sqrt{ {9 - 4}} }{2} \\ \\ x = \frac{ 3 \pm \sqrt{ {5}} }{2} \\ \\ x = \frac{3}{2} + \frac{ \sqrt{5} }{2} ; \: \: x = \frac{3}{2} - \frac{ \sqrt{5} }{2} [/tex]