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3 years ago

Find the slope of a line that is PRRPENDICULAR to the line that goes between (3,-8) and (5,2).

Mathematics

1 answer:

LiRa [457]3 years ago

7 0

Answer:

-1/5

Step-by-step explanation:

Slope of the line = (y2-y1)/(x2-x1)

(2-(-8)/(5-3)

10/2 = 5

Perpendicular line = the slope is opposite of the reciprocal

-1/5

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What are the real and complex solutions of the polynomial equation? x^4-41x^2=-400. *work needed*

pickupchik [31]

<h3>Answer: x = -5, -4, 4 and 5.</h3><h3>All four zeros are real solutions.</h3>

Step-by-step explanation:

Given the polynomial equation $x^4-41x^2=-400$ .

Adding 400 on both sides to get rid 400 from right side and set 0 on right side, we get

$x^4-41x^2+400=-400+400$ .

$x^4-41x^2+400=0$ .

Factoring by product sum rule.

We need product of 400 and sum upto -41.

We can see that 400 = -25 × -16 = 400 and -25-16 = -41.

Therefore,

$x^4-25x^2-16x^2+400=0$

Making it into two groups, we get

$(x^4-25x^2)+(-16x^2+400)=0$

Factoring out GCF of each group, we get

$x^2(x^2-25)-16(x^2-25)=0$

$(x^2-25)(x^2-16) =0$

Factoring out $(x^2-25)$ and $(x^2-16)$ separately by difference of the squares identity $a^2-b^2=(a-b)(a+b)$ , we get

$(x^2-25) = x^2-5^2= (x-5)(x+5)$ and

$x^2-16 = x^2-4^2 =(x-4)(x+4)$ .

Therefore,

$(x-5)(x+5)(x-4)(x+4) =0$

Applying zero product rule,

x-5=0

x+5=0

x-4=0 and

x+4=0.

Therefore,

<h3>x = -5, -4, 4 and 5.</h3><h3>All four zeros are real solutions.</h3>

6 0

3 years ago

Will give brainliest

CaHeK987 [17]

Answer:

The vertex is (1,-2)

Step-by-step explanation:

On your page it would be C :)

4 0

2 years ago

The production rate of a steel factory is declining due to old machinery. Over the last eight days production has dropped by 1.2

Marysya12 [62]

Find the unit rate:

-1.2 tons
------------- = -0.15 ton/day, or -3/20 ton/day
8 days

6 0

2 years ago

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Figure ABCD is a rhombus. Find the value of x. <br><br> 58° <br><br> x = [ ? ]°

melisa1 [442]

The diagonals of the rhombus intersect at right angle. Then the value of x will be 32°.

<h3>What is a rectangle?</h3>

It is a polygon with four sides. The total interior angle is 360 degrees. In a rhombus, opposite sides are parallel and equal.

Figure ABCD is a rhombus.

Its diagonals intersect at right angle.

Let the another angle be x. Then we have

x + 58° + 90° = 180°

x + 148° = 180°

x = 32°

More about the rhombus link is given below.

brainly.com/question/27870968

#SPJ1

8 0

1 year ago

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Papa Elf’s size is 75% of the real Bob Newhart. If the real Bob Newhart is 68 inches tall, how tall is Papa Elf?

galina1969 [7]

Answer:

51 inches

Step-by-step explanation:

68÷100 would be 1% then to find 75% you would multiply by 75

8 0

3 years ago

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