Passes through (-6,5) and parallel to 2x-3y=12

Answers

Answer 1
Answer: Steps:
1. Do the point slope form
Y-Y1=m(x-x1)
Y-5=2(x + 6)
Y-5=2x +12
2. Now you add 5 to the number 12
3. Your answer is
Y=2x +17

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I need help with this ASAP, please thank you

20 POINTS FOR 3 QUESTIONS!!!!Given: ∆ABC, AB = BC, m∠1<90°


Perimeter of ∆ABC = 25


Difference between the two sides is 4


Find: AB, BC, AC



List the sides of ΔRST in in ascending order (shortest to longest) if:


m∠R = 3x+42°, m∠S = 4x−11°, and m∠T = x+13°



List the sides of ΔRST in in ascending order (shortest to longest) if:


m∠R = 2x+11°, m∠S = 3x+23°, and m∠T = x+42°

Answers

Answer with Step-by-step explanation:

1.In triangle ABC

AB=BC

Let AB=BC=x and AC=y

Perimeter of triangle ABC=25

x+x+y=25

2x+y=25...(1)

x-y=4...(2)

Adding equation (1) and (2)

3x=29

x=(29)/(3)=9.67

Substitute x=9.67 in equation (2)

9.67-y=4

y=9.67-4=5.67

AB=BC=9.67

AC=5.67

2.m\angle R=2x+11

m\angle S=3x+23

m\angle T=x+42

m\angle R+m\angle S+m\angle T=180^(\circ)

By using triangle angle sum property

Substitute the values then we get

3x+42+4x-11+x+13=180

8x+44=180

8x=180-44=136

x=(136)/(8)=17

Substitute the value

m\angle R=3(17)+42=93^(\circ)

m\angle S=4(17)-11=57^(\circ)

m\angle T=17+13=30^(\circ)

m\angle R>m\angle S

m\angle S>m\angle T

ST>RT (Side ST is opposite to angle R, Side RT is opposite to angle S

RT>RS  (side RS is opposite to angle T)

When a>b

Then , opposite side of a> opposite side of b

RS<RT<ST

3.m\angle R=2x+11

m\angle S=3x+23

\angle T=x+42

m\angle R+m\angle S+m\angle T=180^(\circ)

By using triangle angle sum property

Substitute the values then we get

2x+11+3x+23+x+42=180

6x+76=180

6x=180-76

6x=104

x=(104)/(6)=17.3

Substitute the value

m\angle R=2(17.3)+11=45.6

m\angle S=3(17.3)+23=74.9

m\angle T=17.3=42=59.3

m\angle S>m\angle T

m\angle T>m\angle R

RT>RS

RS>ST

ST<RS<RT

Factoring, x squared +x-6?

Answers

x² + x - 6 is the same as (x + 3) times (x - 2) .

Colvert the decimal to percent: 0.272

Answers

Answer:

27.2%

Step-by-step explanation:

multiply 0.272 by 100

Graph y = 5x and y = log5x on a sheet of paper using the same set of axes. Use the graph to describe the domain and range of each function. Then identify the y-intercept of each function and any asymptotes of each function. Explain also.

Answers

Answer:

1) For  y=5x

A)  Domain=(-\infty,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x\varepsilon \mathbb{R}]

B) Range= (-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]

C) y-intercept = 0

D) Asymptote= No asymptote

2) For   y=log_5x

A)  Domain=Domain=  (0,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x>0]

B) Range= (-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]

C) y-intercept =  None

D) Vertical Asymptote:   x=0

Step-by-step explanation:

Given : y=5x and y=log_5x

Refer the graph attached.

1)  In equation (1)  y=5x

The domain is the set of all possible values in which function is defined.  

y=5x is a linear polynomial defined on all real numbers.

Domain=(-\infty,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x\varepsilon \mathbb{R}]

Range is the set of all values that function takes.

It also include all real numbers.

Range= (-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]

→y-intercept- Value of y at the point where the line crosses the y axis.

put x=0 in equation y=5x we get, y=0

Therefore, y-intercept = 0 (We can see in the graph also)

→An asymptote is a line that a curve approaches, but never touches.

Asymptote= No asymptote

2) Now in equation (2) y=log_5x

Domain=  (0,\infty) [ \left.\begin{matrix}x\end{matrix}\right|x>0]

because log function is not defined in negative.

Range=  (-\infty,\infty) [ \left.\begin{matrix}y\end{matrix}\right|y\varepsilon \mathbb{R}]

y-intercept - None

Vertical Asymptote:   x=0

1)

A)  Domain= (-∞, ∞) for all x

B) Range= (-∞, ∞) for all y

C) y-intercept = 0

D) Asymptote= No asymptote

2)

A)  Domain=(0, ∞) for all x > 0

B) Range= (-∞, ∞) for all y

C) y-intercept =  None

D) Vertical Asymptote:   x=0

Here, we have,

Function 1: y = 5x

Domain: The domain of this function is all real numbers because there are no restrictions on the values that x can take.

Range: The range of this function is also all real numbers because for every value of x, we can find a corresponding y value by multiplying it by 5.

Y-intercept: To find the y-intercept, we set x = 0 and solve for y. Substituting x = 0 into the equation, we get y = 5(0) = 0. Therefore, the y-intercept is (0, 0).

Asymptotes: There are no asymptotes in this linear function.

Function 2: y = log₅x

Domain: The domain of this function is all positive real numbers because the logarithm function is only defined for positive values of x.

Range: The range of this function is all real numbers because the logarithm function can produce any real number output.

Y-intercept: To find the y-intercept, we set x = 1 and solve for y. Substituting x = 1 into the equation, we get y = log₅(1) = 0. Therefore, the y-intercept is (0, 0).

Asymptotes: The logarithmic function has a vertical asymptote at x = 0 because the logarithm is undefined for x ≤ 0. Additionally, there is no horizontal asymptote.

When plotting these functions on the same set of axes, we will observe that the graph of y = 5x is a straight line passing through the origin (0, 0) with a slope of 5.

The graph of y = log₅x will appear as a curve that starts at the point (1, 0) and approaches the vertical asymptote x = 0 as x approaches zero.

The two graphs will intersect at the point (1, 0) because log₅1 = 0.

To learn more on function click:

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Suppose A is n x n matrix and the equation Ax = 0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to In. By Theorem 7, this shows that A must be Invertible.)Theorem 7: An n x n matrix A is invertible if and only if A is row equivalent to In, and in this case, any sequence of elementary row operations that reduces A to In also transfrms In into A-1.

Answers

Answer:

Remember, a homogeneous system always is consistent. Then we can reason with the rank of the matrix.

If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.

Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.

Please help me please

Answers

Answer:

11

Step-by-step explanation:

its number 2