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miv72 [106K]
2 years ago
9

what key features can be identified from graphs of polynomials with higher degrees and explain how the key features can be used

to sketch the graph of the polynomial function.
Mathematics
1 answer:
Natali [406]2 years ago
3 0
Polynomials are algebraic expressions that contain more than two terms. AN example would be: f(x) = x^3 + x^2 + x +1. This equation contains three terms, with the 3rd degree as its highest term. It also means that the graph passed three x-intercepts. This depends in the highest degree. So, the first thing you do is plot the intercepts because for sure, the graph will pass there.
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The line passes through (-5,6), slope=3. Write the equation in point-slope form​
Nataly_w [17]

Answer:

y = 3x + 21

Step-by-step explanation:

Use the given slope and point to substitute into the point-slope formula  

4 0
3 years ago
A 55m and 35m broad park is surrounded by a 2.5m wide path.
daser333 [38]

Step-by-step explanation:

☄ \underline {\underline{ \text{Given}}} :

  • Length of a park ( l ) = 55 m
  • Breadth of a park ( b ) = 35 m
  • Width running outside the park ( d ) = 2.5 m
  • Rate of paving the path with stones = Rs 120 per sq.metre

☄ \underline{ \underline{ \text{To \: find}}}:

  • Area of the park
  • Cosy of paving the path with stones at Rs 130 per sq.metre

☄ \underline{ \underline{ \text{Solution}}} :

Part 1 : \boxed{\text{Area \:of \:a \:path \: running \:outside = 2d(l + b + 2d)}}

plug the known values and simplify :

⟹ \sf{2 \times 2.5(55 + 35 + 2 \times 2.5)}

⟹ \sf{5  \times 95}

⟹ \sf{475 \:  {m}^{2} }

Part 2 : \boxed{ \sf{Total \: cost = Area \: of \: paths \:  \times  Rate}}

⟹ \sf{475  \times 120}

⟹\sf{Rs \: 57000}

\purple{ \boxed{ \boxed{ \sf{ \tt{⟿ \: Our \: final \: answer : (i) = 475 \:  {m}^{2}   \:  and \: (ii ) = Rs \: 57000}}}}}

Hope I helped ! ♡

Have a wonderful day /night ツ

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7 0
3 years ago
Solve the following linear system by graphing <br> 4x+5y=10<br> 3x-3y=21
Inga [223]

Answer:

y = 2

x = 5

Step-by-step explanation:

4x + 5y = 10 | ×3 |

3x - 3y = 21 | ×4 |

12x + 15y = 30

12x - 12y = 84

____________--

27y = -54

y = -54/27

y = 2

4x + 5y = 10 | ×3 |

3x - 3y = 21 | ×5 |

12x + 15y = 30

15x - 15y = 105

____________+

27x = 135

x = 135/27

x = 5

6 0
3 years ago
Find , , and if and terminates in quadrant .
ioda

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

STEP - BY - STEP EXPLANATION

What to find?

• sin2x

,

• cos2x

,

• tan2x

Given:

tanx = 2/3 = opposite / adjacent

We need to first make a sketch of the given problem.

Let h be the hypotenuse.

We need to find sinx and cos x, but to find sinx and cosx, first determine the value of h.

Using the Pythagoras theorem;

hypotenuse² = opposite² + adjacent²

h² = 2² + 3²

h² = 4 + 9

h² =13

Take the square root of both-side of the equation.

h =√13

This implies that hypotenuse = √13

We can now proceed to find the values of ainx and cosx.

Using the trigonometric ratio;

\sin x=\frac{opposite}{\text{hypotenuse}}=\frac{2}{\sqrt[]{13}}\cos x=\frac{adjacent}{\text{hypotenuse}}=\frac{3}{\sqrt[]{13}}

And we know that tanx =2/3

From the trigonometric identity;

sin 2x = 2sinxcosx

Substitute the value of sinx , cosx and then simplify.

\sin 2x=2(\frac{2}{\sqrt[]{13}})(\frac{3}{\sqrt[]{13}})=\frac{12}{13}

Hence, sin2x = 12/13

cos2x = cos²x - sin²x

Substitute the value of cosx, sinx and simplify.

\begin{gathered} \cos 2x=(\frac{3}{\sqrt[]{13}})^2-(\frac{2}{\sqrt[]{13}})^2 \\  \\ =\frac{9}{13}-\frac{4}{13} \\ =\frac{5}{13} \end{gathered}

Hence, cos2x = 5/13

tan2x = 2tanx / 1- tan²x

\tan 2x=\frac{2\tan x}{1-\tan ^2x}=\frac{2(\frac{2}{3})}{1-(\frac{2}{3})^2}=\frac{\frac{4}{3}}{1-\frac{4}{9}}=\frac{\frac{4}{3}}{\frac{9-4}{9}}=\frac{\frac{4}{3}}{\frac{5}{9}}=\frac{4}{3}\times\frac{9}{5}=\frac{4}{1}\times\frac{3}{5}=\frac{12}{5}

OR

\tan 2x=\frac{\sin 2x}{\cos 2x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}

Hence, tan2x = 12/5

Therefore,

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

3 0
1 year ago
What was the simple interest rate on a $8,000 Investment that was left in an account for 18 months and earned $360 in Interest?
Karolina [17]
I think it would be 8,228 I think if it is 8000 - 18+360 hopefully I am right
3 0
3 years ago
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