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Ad libitum [116K]
3 years ago
7

Which is the equation of a line that has a slope of 1 and passes through point (5, 3)?

Mathematics
2 answers:
max2010maxim [7]3 years ago
8 0

Answer:

y = x - 2

Step-by-step explanation:

y = x + b

3 = 5 + b

y = x - 2

viktelen [127]3 years ago
4 0

We can use the slope intercept form of a line.

y = mx+b where m is the slope and b is the y intercept

y = 1x +b

Substitute the point into the equation

3 = 1*5+b

3 = 5+b

Subtract 5 from each side

3-5 = 5+b-5

-2 =b

y = x-2

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In a triangle ABC, if <B = 60° and the ratio of two sides is a: c= 2: square root 3+1, then <A=
slavikrds [6]

Your answer is 75°.

To answer this question you need to use both the cosine rule and the sine rule. First, we need to find the length of side b by using the cosine rule, where a = 2 and c = √3 + 1. Then you substitute these into the equation:

b² = a² + c² - 2×a×c×cos(B)

b² = (2)² + (√3 + 1)² - 2×2×(√3 + 1)×cos(60)

b² = 4 + 4 + 2√3 - (4 - 4√3)×0.5

b² = 8 - 2 = 6

b = √6

Then you use this length in the sine rule, and find the angle:

\frac{sin(A)}{\sqrt{3}+1 } =\frac{sin(60)}{\sqrt{6} }

sin(A) = (√6 + √2)/4

A = 75

I hope this helps! Let me know if you have any questions

7 0
3 years ago
Which linear inequality is represented by the graph? (A)y ≤1/3 x − 1 (B)y ≥ x − 1 (C)y < 3x − 1 (D)y > 3x − 1
lubasha [3.4K]

The equation of the line is \boxed{y \geqslant \frac{1}{3}x - 1}.

Further explanation:

The linear equation with slope m and intercept c is given as follows.

\boxed{y = mx + c}

The formula for slope of line with points \left( {{x_1},{y_1}} \right) and \left( {{x_2},{y_2}} \right) can be expressed as,

\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}

Given:

Explanation:

The line intersects y-axis at \left( {0, - 1} \right). Therefore, the y-intercept is -1.

The line passes through the points \left( {0, - 1} \right) and \left( {3,0} \right).

The slope can be obtained as follows,

\begin{aligned}m&= \frac{{0- \left( {- 1} \right)}}{{3 - 0}}\\&= \frac{1}{3}\\\end{aligned}

Substitute \dfrac{1}{3} for m, 3 for x and 0 for y in equation y = mx + c to obtain the value of c.

\begin{aligned}0& \frac{1}{3} \cdot 3 + c\\- 1&=c\\\end{aligned}

To check whether the equation includes origin substitute 0 for x and 0 for y in equation y \geqslant \dfrac{1}{3}x - 1.

\begin{aligned}0&\geqslant \frac{1}{3} \times 0 - 1 \\0&\geqslant - 1\\\end{gathered}

The statement is true. The equation contains origin.

The equation of the line is \boxed{y \geqslant \frac{1}{3}x - 1}.

Learn more:

  1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
  2. Learn more about equation of circle brainly.com/question/1506955.
  3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: numbers,slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.

7 0
3 years ago
Read 2 more answers
Please help me understand and answer this !!!!!!!!!!!!!!!!!
-Dominant- [34]

Answer:

5 + 8 = 13

-6 + -4 = -10

No explaination needed This answer is 1000% correct. Trust me i woould never mess someone up for no reason, not even for my own benefit.

4 0
3 years ago
Ada is showing her work in simplifying (5.9 - 1.8) - 6.2 + 4.1. In which step did Ada make an error? (5 points)
soldier1979 [14.2K]

Answer:

Step 4 is where she made the error.

Step-by-step explanation:

This step is actually known as the commutative property. That property states that we can change the order of numbers as long as we keep the signs and it maintains it's validity.

5 0
3 years ago
What is the of cube of 13824​
labwork [276]

Answer:

Step-by-step explanation:

7 0
3 years ago
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