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Zinaida [17]
3 years ago
5

Find an equation of the tangent line to the graph of

Mathematics
2 answers:
lakkis [162]3 years ago
6 0

Answer:

y + 4 = -3 (x - 5)

In other words,

y = -3 x + 11

Step-by-step explanation:

The slope of the tangent line to y = g(x) at x = 5 is the same as the value of g'(x). g'(5) = 3. Therefore, 3 will be the slope of the tangent line.

The tangent line goes through the point of tangency (5, g(5)). g(5) = -4. Therefore, the tangent line passes through the point (5, -4).

Apply the slope-point form of the line. The equation for a line with slope <em>m</em> that goes through point (a, b) will be y - b = m(x - a). For the tangent line in this question,

  • m = 3,
  • a = 5, and
  • b = -4.

What will be the equation of this line?

Darina [25.2K]3 years ago
5 0

Answer:   y = 3x - 19

<u>Step-by-step explanation:</u>

            y = g(x)

                 g(5) = -4  

⇒        y =           -4       <em>when x = 5</em>     ⇒    (5, -4)  


g'(5) = 3     means that when x = 5, the tangent slope (m) = 3

  • <em>because the first derivative gives the tangent slope</em>

Use the Point-Slope formula to find the equation of the line that passes through the point (5, -4) with slope (m) of 3:

y - y₁ = m(x - x₁)

y -(-4) = 3(x - 5)

y + 4 = 3x - 15

y       = 3x - 19

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Evaluate 0.67y + 4 when y = 2 and when y = -2
jarptica [38.1K]

Answer:

2.66 and 4.34

Step-by-step explanation:

To evaluate, substitute the values of y and solve.

So, when y =-2

0.67y + 4 = -1.34 + 4 = 2.66

And when y = 2

0.67y + 4 = 1.34 + 4 = 4.34

Hope this helps.

5 0
3 years ago
Read 2 more answers
The ratio of red counters to blue counters is 1 : 3
jolli1 [7]

Answer:

Nov 20, 2016 · If we assume that initially Number of red counter is 1 Number of blue counter is 3 Now to make ratio reverse you need to add 8 more red counters so that ratio becomes 9:3=3:1

Step-by-step explanation:

6 0
3 years ago
Question Navigator<br> Enter the answer.cubed roots What is
Helen [10]
The answer is 11..and there's a pic for u too...my pleasure helping you

5 0
3 years ago
Please help me its about solving system by substitution
Andrew [12]

Answer:

(-3, 4)

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
  • Subtract Property of Equality

<u>Algebra I</u>

  • Terms/Coefficients
  • Solving systems of equations using substitution/elimination

Step-by-step explanation:

<u>Step 1: Define Systems</u>

y = -x + 1

2x + 3y = 6

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

<em>Substitution</em>

  1. Substitute in <em>y</em>:                    2x + 3(-x + 1) = 6
  2. Distribute 3:                         2x - 3x + 3 = 6
  3. Combine like terms:           -x + 3 = 6
  4. Isolate <em>x</em> terms:                   -x = 3
  5. Isolate <em>x</em>:                              x = -3

<u>Step 3: Solve for </u><em><u>y</u></em>

  1. Define equation:                     y = -x + 1
  2. Substitute in <em>x</em>:                        y = -(-3) + 1
  3. Simplify:                                   y = 3 + 1
  4. Add:                                         y = 4
6 0
3 years ago
Need an explanation on number 44 to why E is correct
aliina [53]

Before we can make sure that E is correct, we need to make the denominator is equal with questions and the choices or convert into decimal.

2/3 = 0.66

1/3=0.33

1/5=0.2

2/6=1/3 = 0.33

1/2 = 0.5

7/10 = 0.7

7/9 = 0.77

The question is :

2/3 < x < 7/9

0.66 < x < 0.77

We need to divide into 2 parts :

0.66 < x

x < 0.77

So we need to find the answer that x is greater that 0.66 and we got 7/10. And 7/10 is less than 7/9.

Hope this helps. Please ask if you don't understand.

6 0
3 years ago
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