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zmey [24]
3 years ago
12

Draw the triangle with vertices a(1, 1), b(5, 3), c(1, 7). find the parametrization, including endpoints, and sketch to check. (

enter your answers as a comma-separated list of equations. let x and y be in terms of t.)
Mathematics
1 answer:
Firlakuza [10]3 years ago
8 0
Part A:

The parametric equations x=x_1+(x_2-x_1)t and y=y_1+(y_2-y_1)t where 0\leq t\leq1 describes the line segment that joins the points (x_1,\ y_1) and (x_2,\ y_2).

The parameterization of the line joining points A(1, 1) and B(5, 3) are given by substituting x_1=1,\ \ y_1=1,\ \ x_2=5,\ \ y_2=3.

Thus, we have

x = 1 + (5 - 1)t = 1 + 4t
y = 1 + (3 - 1)t = 1 + 2t

Therefore, the parameterization of line joining points A(1, 1) and B(5, 3) are x = 1 + 4t and y = 1 + 2t.



Part B:

The parametric equations x=x_1+(x_2-x_1)t and y=y_1+(y_2-y_1)t where 0\leq t\leq1 describes the line segment that joins the points (x_1,\ y_1) and (x_2,\ y_2).

The parameterization of the line joining points B(5, 3) and C(1, 7) are given by substituting x_1=5,\ \ 
y_1=3,\ \ x_2=1,\ \ y_2=7.

Thus, we have

x = 5 + (1 - 5)t = 5 - 4t
y = 3 + (7 - 3)t = 3 + 4t

Therefore, the parameterization of line joining points B(5, 3) and C(1, 7) are x = 5 - 4t and y = 3 + 4t.



Part C:

The parametric equations x=x_1+(x_2-x_1)t and y=y_1+(y_2-y_1)t where 0\leq t\leq1 describes the line segment that joins the points (x_1,\ y_1) and (x_2,\ y_2).

The parameterization of the line joining points C(1, 7) and A(1, 1) are given by substituting x_1=1,\ \ 
y_1=7,\ \ x_2=1,\ \ y_2=1.

Thus, we have

x = 1 + (1 - 1)t = 1
y = 7 + (1 - 7)t = 7 - 6t

Therefore, the parameterization of line joining points A(1, 1) and B(5, 3) are x = 1 and y = 7 - 6t.
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\frac{f(b)-f(a)}{b-a}.


For the left function, from x = 4 to x = 5, the rate of change is


\frac{100-64}{5-4} = \frac{36}{1} = 36.


For the right function, the rate of change is


\frac{1024-256}{5-4} = \frac{768}{1} = 768


Using a ratio to compare the right function's growth rate with that of the left function, you get 768 \div 36 \approx 21.3.


The right function is growing approximately 21 times faster than the left function (over the interval from 4 to 5).

3 0
3 years ago
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Which expressions are equivalent to the given sort 40 (there is more than one and the one selected is correct)
Basile [38]

Answer:

40 {}^{ \frac{1}{2} }

Step-by-step explanation:

The last one is also the answer

Using the rational exponet rule,

\sqrt[n]{ {x}^{m} }  = x {}^{ \frac{m}{n} }

Using this number,

\sqrt{40}

40 is the base so it will stay same. Remember this is a square root sign so our nth root is 2 so our denominator if the rational exponet is 2.

40 {}^{1}  = 40

so our numerator is 1 so

40 {}^{ \frac{1}{2} }

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3 years ago
Solve the system using elimination.
Molodets [167]

Answer:

(-1, 3)

Step-by-step explanation:

x - 5y = -16  [Equation 1]

-x + 3y = 10 [Equation 2]

<u>Adding both equations</u>

  • x - x - 5y + 3y = -16 + 10
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<u>Solution</u> : (-1, 3)

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Y + 12 = -26 thank you if you answer me ​
tia_tia [17]

Answer:

-38

Step-by-step explanation:

1. Isolate y to one side.

y+12=-26

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3 years ago
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blagie [28]

Answer:

36

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(20:100)* 180 =

(20* 180):100 =

3600:100 = 36

Now we have: 20 percent of 180 = 36

Question: What is 20 percent of 180?

Percentage solution with steps:

Step 1: Our output value is 180.

Step 2: We represent the unknown value with $x$.

Step 3: From step 1 above,$180=100\%$.

Step 4: Similarly, $x=20\%$.

Step 5: This results in a pair of simple equations:

$180=100\%(1)$.

$x=20\%(2)$.

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

$\frac{180}{x}=\frac{100\%}{20\%}$

Step 7: Again, the reciprocal of both sides gives

Step-by-step explanation:

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