Find the slope of the line containing the points (2,7) and (-5, -4).

Answer:

x= √10 and x= -√10

Step-by-step explanation:

first look to isolate the term with the variable on one side

-5 +5 -2x² = -5 -15; subtract 5 from both sides(inverse of addition)

-2x² = -20; divide both sides by -2 (inverse of multiplication)

x² = 10; square root both sides (the inverse of raising to power of 2)

√x² =√10

x =±√10

Given:

The system of equations is:

Line A: [tex]y=x-4[/tex]

Line B: [tex]y=3x+4[/tex]

To find:

The solution of given system of equations.

Solution:

We have,

[tex]y=x-4[/tex]              ...(i)

[tex]y=3x+4[/tex]           ...(ii)

Equating (i) and (ii), we get

[tex]x-4=3x+4[/tex]

[tex]-4-4=3x-x[/tex]

[tex]-8=2x[/tex]

Divide both sides by 2.

[tex]-4=x[/tex]

Substituting [tex]x=-4[/tex] in (i), we get

[tex]y=-4-4[/tex]

[tex]y=-8[/tex]

The solution of system of equations is (-4,-8).

Now verify the solution by substituting [tex]x=-4, y=-8[/tex] in the given equations.

[tex]-8=-4-4[/tex]

[tex]-8=-8[/tex]

This statement is true.

Similarly,

[tex]-8=3(-4)+4[/tex]

[tex]-8=-12+4[/tex]

[tex]-8=-8[/tex]

This statement is also true.

Therefore, (-4,-8) is a solution of the given system of equations, because the point satisfies both equations. Hence, the correct option is C.

Answer:

y 4       4x + 2

y< 6     x+3

Step-by-step explanation:

...........................

Answer:

LM = 24.3

Step-by-step explanation:

In terms of similar shapes, we know that the ratio of the value of one side to its corresponding side value is equal to another. In other words, we know that LK and HG are corresponding sides by looking at the quadrilaterals. The ratio of LK to HG is equal to the ratio of another pair of corresponding sides, such as LM and IH.

Therefore, the ratio of LK and HG (LK/HG) is equal to the ratio of LM and IH (LM/IH) . Make sure to keep the same quadrilateral's sides on top/bottom. In this example, LM and LK are on the same quadrilateral, and are therefore both on top. Similarly, IH and HG are of the same quadrilateral and are both on bottom. We can write this as

LK / HG = LM / IH

34/7 = LM / 5

Multiply both sides by 5

34*5/7 = LM

LM ≈ 24.2857

Rounding to the nearest tenth, LM = 24.3

Answer:

24.3

Step-by-step explanation:

Answer:

930=9 hundreds 3 tens

93times10

80=8 tens

320= 3 hundreds 2 tens

8000=8 thousands

Answer:

=60

Step-by-step explanation:

18 + 12

=30

18/30 × 100%

=60

Answer:

It is 2 million

Answer:

Million

Step-by-step explanation:

Answer:

9 dots

Step-by-step explanation:

each step adds 2 dots every time

Answer:

10

Step-by-step explanation:

Do HCF of 40,50,60 and the answer is 10

Answer:

ans: -4( x-3 )( x-4 ) I.e -4( x² + x - 12 )

Step-by-step explanation:

as per question

1- (2x-7)²

= (1 + 2x - 7)(1- 2x + 7)

= ( 2x - 6)(-2x +8)

= -4(x-3)(x+4)

The simplified form of [tex](2x-7)^{2}[/tex] is [tex]4x^{2} +49-28x[/tex].

And we get, [tex]-4x^{2} -48+28x[/tex] when we subtract [tex](2x-7)^{2}[/tex] from 1.

Polynomials are algebraic expressions that consist of variables and coefficients.

[tex](a-b)^{2} =a^{2} +b^{2} -2ab[/tex]

According to the given question

We have a polynomial [tex](2x -7)^{2}[/tex].

Therefore, the simplified form of [tex](2x-7)^{2}[/tex] is given by

[tex](2x-7)^{2} =(2x)^{2} +(7)^{2} -2(2x)(7)[/tex]

⇒[tex](2x-7)^{2} =4x^{2} +49-28x[/tex]

Therefore, the simplified form of [tex](2x-7)^{2}[/tex] is [tex]4x^{2} +49-28x[/tex].

Now,

[tex]1-(4x^{2} +49-28x)= 1-4x^{2} -49+28x[/tex]

⇒[tex]1-(4x^{2} +49-28x)=-4x^{2} -48+28x[/tex]

Hence, we get [tex]-4x^{2} -48+28x[/tex] when we subtract [tex](2x-7)^{2}[/tex] from 1.

Learn more about polynomials here:

https://brainly.com/question/11536910

#SPJ2

Answer:

6

Step-by-step explanation:

2x+2y=2*(-2)+2*5=6

Answer:

6

Step-by-step explanation:

Substitute x = - 2, y = 5 into the expression

2x + 2y

= 2(- 2) + 2(5)

= - 4 + 10

= 6

Answer:

gracias por los puntos xd

Answer:

47 ft

Step-by-step explanation:

3.14 x 15

Answer:

the think the answer is €170

because 15000+20/100

Answer: Martina's margin of error is 1.5.

Step-by-step explanation:

Given: Average graduate student (upper limit) = 33

Random sample graduate student (lower limit) = 30

Formula to calculate margin of error is as follows.

Margin of error = [tex]\frac{upper limit - lower limit}{2}[/tex]

Substitute the values into above formula as follows.

[tex]Margin of error = \frac{upper limit - lower limit}{2}\\= \frac{33 - 30}{2}\\= \frac{3}{2}\\= 1.5[/tex]

Thus, we can conclude that Martina's margin of error is 1.5.

Answer:

x > 5.5

Step-by-step explanation:

4(x - 3) - (2x - 1) > 0

4x - 12 - 2x + 1 > 0

4x - 2x - 11 > 0

2x - 11 > 0

2x - 11 + 11 > 0 + 11

2x > 11

2x ÷ 2 > 11 ÷ 2

x > 5.5

Answer:

x>13/2

Step-by-step explanation:

4x-12-2x-1>0

2x-13>0

2x>13

X>13/2

Answer:

Option (1)

Step-by-step explanation:

From the graph of the piecewise function,

There are two pieces of the function,

1). Segment (1) having x < 0

2). Segment (2) having x ≥ 0

Segment (1),

Segment starts with a hollow circle at x = 0 and passes through two points (0, 1) and (-2, 2)

Slope of the segment = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                                     = [tex]\frac{2-1}{-2-0}[/tex]

                                     = [tex]-\frac{1}{2}[/tex]

Equation of the segment passing through (-2, 2) with slope = [tex]-\frac{1}{2}[/tex],

[tex]y-y'=m(x-x')[/tex]

[tex]y-2=-\frac{1}{2}(x+2)[/tex]

[tex]y=-\frac{1}{2}x-1+2[/tex]

[tex]y=-\frac{1}{2}x+1[/tex]

[tex]y=-0.5x+1[/tex] For x < 0

Segment (2),

Segment starts with a solid circle at x = 0 and passes through (0, -2) and (2,2)

Slope of the segment = [tex]\frac{2+2}{2-0}[/tex]

                                    = 2

Equation of the segment passing through (0, -2) and slope = 2,

y - y' = m(x - x')

y + 2 = 2(x - 0)

y = 2x - 2 For x ≥ 0

Therefore, Option (1) will be the correct option.

Answer:

42 units²

Step-by-step explanation:

the area = (11-4) × (9-3)

=7×6 = 42 units²

Answer:

450in^2

Step-by-step explanation:

square root of 900 is 30.

Each side of square is 30.

Each side of a triangle formed by drawing a radi in the square is 15 in.

The hypotenuse is 15[tex]\sqrt{2}[/tex] that is also the radius of the circle.

A= (15[tex]\sqrt{2}[/tex])^2 times pi = 450 in^2

Answer:

Step-by-step explanation:

Correct choice is D

Answer:

D. 270°

Step-by-step explanation:

the reciprocal of 9 is 1 divided by 9, i.e. 1/9

The none of no irrational number in the given option.

Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number.

In another word, irrational numbers are those numbers that can not terminate.

For example, √2, and √3 are irrational numbers because they cannot be written as p/q where p and q both should be integers.

Among the given option

A) √100 = 10 which is integer.

B) 1/8 were 1 and 8 both integer.

C)  -2.2675 here also it is an integer.

D)  [tex]0^{12}[/tex] which is 0 so it is also a rational number.

Hence none of the irrational numbers. It might be possible that there is a typing mistake in the question or in option D there is something else.

For more about the irrational number

https://brainly.com/question/4031928

#SPJ2

Answer:

c = -10

Step-by-step explanation:

For this we can use basic algebra. Add 15 on both sides. This gives us 3c = -30. Divide by 3 on both sides. The final answer is c = -10.

The value of c is -10 in the equation 3c - 15 = -45.

Two or more expressions with an Equal sign is called as Equation.

The given equation is 3c-15=-45

Three times of c minus fifteen equal to minus forty five.

In the given equation minus is the operator and c is the variable.

We need to solve for variable c

3c-15=-45

Add 15 on both sides

3c-15+15=-45+15

3c=-30

Divide both sides by 3

c=-10

Hence, the value of c is -10 in the equation 3c - 15 = -45.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

Answer:

45

Step-by-step explanation:

8-12(-3.5)-5

8+42-5

=45

Step-by-step explanation:

∆ABC =>by reflection over x-axis and then dilation with scale factor 2, the point of center (5, -1) ==> ∆ XYZ