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Alinara [238K]
2 years ago
5

Do the equations y = -6x +4 and y = 4x + 6 have one solution, no solution, or infinitely many solutions

Mathematics
2 answers:
Black_prince [1.1K]2 years ago
6 0

Answer:

One solution

Step-by-step explanation:

We know there is only one solution because the lines do not have the same slope, nor are they the exact same line.

So we know they must have just one solution.

Best of luck

Sindrei [870]2 years ago
5 0

Answer:

One solution

Step-by-step explanation:

This is because they are not the same line and do not have an equal m value with different y-intercepts

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What is the height of an airplane as it descends to an airport runway
stepladder [879]
The set of Real numbers consists of following sets:
- Rational numbers,
- Integers,
- Whole numbers.
And : R > I > W
The height of an airplane as it descends to an airport runway is in the whole numbers, rounded to the nearest 100 feet.
Answer: Whole number.

3 0
3 years ago
Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)
ELEN [110]

Question:

Find the point (,) on the curve y = \sqrt x that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})

Step-by-step explanation:

y = \sqrt x can be represented as: (x,y)

Substitute \sqrt x for y

(x,y) = (x,\sqrt x)

So, next:

Calculate the distance between (x,\sqrt x) and (3,0)

Distance is calculated as:

d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}

So:

d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}

d = \sqrt{(x-3)^2 + (\sqrt x)^2}

Evaluate all exponents

d = \sqrt{x^2 - 6x +9 + x}

Rewrite as:

d = \sqrt{x^2 + x- 6x +9 }

d = \sqrt{x^2 - 5x +9 }

Differentiate using chain rule:

Let

u = x^2 - 5x +9

\frac{du}{dx} = 2x - 5

So:

d = \sqrt u

d = u^\frac{1}{2}

\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}

Chain Rule:

d' = \frac{du}{dx} * \frac{dd}{du}

d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}

d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}

d' = \frac{2x - 5}{2\sqrt u}

Substitute: u = x^2 - 5x +9

d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}

Next, is to minimize (by equating d' to 0)

\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0

Cross Multiply

2x - 5 = 0

Solve for x

2x  =5

x = \frac{5}{2}

Substitute x = \frac{5}{2} in y = \sqrt x

y = \sqrt{\frac{5}{2}}

Split

y = \frac{\sqrt 5}{\sqrt 2}

Rationalize

y = \frac{\sqrt 5}{\sqrt 2} *  \frac{\sqrt 2}{\sqrt 2}

y = \frac{\sqrt {10}}{\sqrt 4}

y = \frac{\sqrt {10}}{2}

Hence:

(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})

3 0
3 years ago
Fill in the blank for Remainder Therom<br><br><br> x 3 + x 2 - 21x - 45 = (x + 3)(x - 5)(x+?)
icang [17]
Not sure about remainder theorem but I'm sure that the last terms should all multiply tho the last term


see the expanded form is -45

so the last terms of each binomial should multiply to -45

3 times -5 times ?=-45
-15 times ?=-45
divide by -15
?=3

the question mark is 3
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3 years ago
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Gloria biked the farthest.
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The utility bill shows that a household used 2,001 gallons of water in a 5day period what was the average amount of water used b
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The average water used per day is 400.2
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