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Ierofanga [76]
3 years ago
14

The given line passes through the points (0, -3) and (2, 3).

Mathematics
1 answer:
puteri [66]3 years ago
6 0

The equation, in point-slope form of the line that is  parallel to the given line and passes through the point  (-1, -1) is y + 1 = 3(x + 1).

<u>Solution:</u>

Given that, a line passes through (0, -3) and (2, 3).

We have to find the line equation which is parallel to above line and  passes through (-1, -1).

Now, let us find the slope of the given line.

\text { slope } m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}, \text { where }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right) \text { are points on that line }

\text { Then, } m=\frac{3-(-3)}{2-0}=\frac{3+3}{2}=\frac{6}{2}=3

So, slope of given line is 3,  

Then, slope of required line is also 3, as slopes of parallel lines are equal.

Then, required line equation in point – slope form is given as:

\begin{array}{l}{y-y_{1}=m\left(x-x_{1}\right)} \\\\ {y-(-1)=3(x-(-1))} \\\\ {\rightarrow y+1=3(x+1)}\end{array}

Hence, the line equation is y + 1 = 3(x + 1).

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Complete the square:<br> x2 - 6x + 9=-13+ blank
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Answer:

to complete the square, you add (b/2)^2  on both side. in this case, b is -6, half of -6 is -3, -3 squared is 9, so:

x^2-6x+9=-13+9

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Step-by-step explanation:

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Read 2 more answers
If triangle CAT is similar to triangle DOG, which of the following statements is incorrect?
jeyben [28]

Answer:

1. triangle TCA ~ triangle GOD

4. If TC/GD=3/2, then m<T/m<G=3/2.

Step-by-step explanation:

<u><em>The statements of the question are</em></u>

1. triangle TCA ~ triangle GOD

2. AT: OG= AC:OD

3. If TC/GD=3/2, then AC/OD=3/2.

4. If TC/GD=3/2, then m<T/m<G=3/2.

5. If the scale factor of triangle CAT to triangle DOG is 3 to 2, then the scale factor of triangle DOG to triangle CAT is 2 to 3.

6. If AC is twice as long as AT, then OD is twice as long as OG

<u><em>Verify each statement</em></u>

1) triangle TCA ~ triangle GOD

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

triangle CAT ~ triangle DOG -----> is given

so

Reorder

Corresponding sides are named using pairs of letters in the same position on either side of the congruence statement

triangle TCA ~ triangle GDO

therefore

The statement is not correct

2). AT: OG= AC:OD

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

triangle CAT ~ triangle DOG -----> is given

so

Applying proportion

\frac{AT}{OG}=\frac{AC}{OD}=\frac{TC}{GD}

The statement is true

3). If TC/GD=3/2, then AC/OD=3/2.

we have that

\frac{AT}{OG}=\frac{AC}{OD}=\frac{TC}{GD} ---> see part 2)

so

\frac{TC}{GD}=\frac{AC}{OD}

therefore

The statement is true

4). If TC/GD=3/2, then m<T/m<G=3/2

Remember that

In two similar triangles, corresponding angles are congruent

so

m\angle T=m\angle G

m\angle T/m\angle G=1

therefore

The statement is false

5). If the scale factor of triangle CAT to triangle DOG is 3 to 2, then the scale factor of triangle DOG to triangle CAT is 2 to 3

we know that

If the scale factor of triangle CAT to triangle DOG is a/b. then  the scale factor of triangle DOG to triangle CAT is b/a

The scale factor will be the reciprocal

therefore

The statement is true  

6). If AC is twice as long as AT, then OD is twice as long as OG

we know that

\frac{AT}{OG}=\frac{AC}{OD}

Reorder

\frac{AT}{AC}=\frac{OG}{OD}

If AC is twice as long as AT ----> AC=2AT

If OD is twice as long as OG ----> OD=2OG

substitute

\frac{AT}{2AT}=\frac{OG}{2OG}

simplify

\frac{1}{2}=\frac{1}{2} ----> is true

therefore

The statement is true

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A case from all the courts in the options can be reversed by a higher court if the courts judgement lacks merit by the higher court, at any given times, irrespective of the court.

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Solve for x + 24 = -12<br><br> answer in the box <br><br>x equals_______​
Mandarinka [93]

Answer:

x = -36

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality<u> </u>

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

x + 24 = -12

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. [Subtraction Property of Equality] Subtract 24 on both sides:                       x + 24 - 24 = -12 - 24
  2. [Subtraction] Simplify:                                                                                        x = -36
5 0
3 years ago
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