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tia_tia [17]
3 years ago
7

What is the slope of a line that is parallel to to the one shown? (-3, 2) (0, -2)

Mathematics
1 answer:
Slav-nsk [51]3 years ago
8 0
<span>(-3, 2) (0, -2)
slope = (2 + 2)/(-3 - 0) = -4/3
parallel lines have same slope

so answer is -4/3</span>
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How do you solve x^4 - 3x^3 - 3x^2 - 75x - 700
madam [21]

Answer:

  = (x +4)(x -7)(x^2 +25)

  roots are -4, 7, ±5i

Step-by-step explanation:

You have not said what "solve" means in this context. An expression by itself doesn't have a solution. We have assumed you want to find the factoring and/or roots of it.

I like to use a graphing calculator to find the real roots. For this expression, there are two of them, one positive and one negative. (You know there will be one positive real root, and at least one negative real root, from Descartes's rule of signs.)

Then those roots can be factored out and the solution to the remaining quadratic determined. That factoring can occur by polynomial long division, synthetic division, or other means.

I like to see what happens when I plot the graph of the function divided by the known factors. (We expect a parabola that doesn't cross the x-axis.) The vertex of that parabola can be used to find the remaining roots.

The x-intercepts of the given expression are -4 and +7, so two of the factors are (x+4) and (x-7). Dividing these from the given expression (by synthetic division or other means) gives (x^2 +25). This only has imaginary roots (±5i).

____

If you're constrained to doing this "by hand" with only a scientific calculator, Descartes's rule of signs tells you there is one positive real root. (Only one sign change in the sequence of coefficient signs: +----.)

The rational root theorem tells you it will be a divisor of 700. Various estimates of the maximum magnitude of it will tell you it is probably less than 14 (easily checked). So, the numbers you can test as roots would be 1, 2, 4, 5, 7, 10, 14. You will find that 7 is a root, and then you can reduce the problem to the cubic x^3 +4x^2 +25x +100.

When odd-degree term signs are changed, there will be 3 sign changes (-+-+), hence at least one negative real root. The rational root theorem tells you it is a divisor of 100, so possible choices are -1, -2, -4, -5. By trial and error or other means, you can find the root to be -4. Then the problem reduces to the quadratic x^2 +25.

Roots of that are ±√(-25) = ±5i.

This process generally entails a fair amount of trial-and-error work, which is why I prefer one that makes some use of technology.

_____

We have presumed you have some familiarity with ...

  • Descartes's rule of signs
  • Rational Root Theorem
  • synthetic division

This will usually be the case when you're presented with problems like this. If you need additional information on any of these, it is readily available on the internet (and probably also in your reference material).

4 0
3 years ago
what are the steps required to determine the equation of a quadratic function given its zeros and a point?​
mezya [45]

Answer:

Below

Step-by-step explanation:

The quadratic equations form is:

● ax^2+bx+c

Using the zeroes, we can write a factored form.

● a (x-x') (x-x")

x and x' are the zeroes

■■■■■■■■■■■■■■■■■■■■■■■■■■

●y = a (x-x') (x-x")

x' and x" are khown but a is not.

We are given a point so replace x and y with its coordinates to find a.

So the steps are:

● 1) Write the factored form of the quadratic equation

● 2) replace x' and x" with their values.

● 3) replace x and y with the coordinates of a khwon point.

● 4) solve the equation for a.

8 0
3 years ago
3.If ABCD is a parallelogram with AB = 2x + 1, AD = x + 13, and DC = 3x -11. Determine if ABCD is
madam [21]

Answer:

  ABCD is a rhombus

Step-by-step explanation:

Sides AB and DC are opposite and equal in parallelogram ABCD. This means ...

  AB = CD

  2x +1 = 3x -11

  12 = x . . . . . . . . add 11-2x to both sides

Sides AB and CD have length ...

  2x +1 = 2(12) +1 = 24 +1 = 25

Then the length of side AD is ...

  AD = x +13 = 12 +13 = 25

Adjacent sides AB and AD of the parallelogram have the same length, The figure is a rhombus.

3 0
2 years ago
Mother put 22 apples in each basket. How many baskets did she use for 390 apples?
KATRIN_1 [288]

Answer:

To find the no. of baskets used to put 390 apples we have to divide 390/22  which is 17.7272727273,

so to put 390 apples we need approximately 18 baskets.

hope this answer helps you...

8 0
3 years ago
Read 2 more answers
What is the value of x in the equation 3x -1/9<br> y = 18, when y = 27?<br> 5<br> 7<br> 45 63
almond37 [142]

Answer:

x=7

Step-by-step explanation:

we have

3x-\frac{1}{9}y=18

Substitute the value of y=27 in the equation and find the value of x

so

3x-\frac{1}{9}(27)=18

3x-3=18

3x=18+3

3x=21

x=7

4 0
3 years ago
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