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3 years ago

A line has a slope of 5 and includes the points (1,t) and (3,2). What is the value of t?

Mathematics

1 answer:

bogdanovich [222]3 years ago

5 0

Hello!

$\large\boxed{t = -8}$

We can find the value of t using the slope formula:

$slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Plug in the given slope and coordinates into the appropriate places:

$5 = \frac{2-t}{3-1}$

Simplify:

$5 = \frac{2-t}{2}$

Multiply both sides by 2 to begin isolating for t. Simplify and solve for t:

$5 * 2 = 2 - t\\\\10 = 2 - t\\\\8 = -t\\\\t = 8$

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Write a polynomial function of least degree with the given zero. -1+ √ 2, √ 3

kirill115 [55]

Answer:

f(x) = $x^{4}$ + 2x³ - 4x² - 6x + 3

Step-by-step explanation:

Note that radical zeros occur in conjugate pairs, thus

- 1 + $\sqrt{2}$ is a zero then - 1 - $\sqrt{2}$ is also a zero

$\sqrt{3}$ is a zero then - $\sqrt{3}$ is also a zero

Thus the corresponding factors are

(x - (- 1 + $\sqrt{2}$ ) ), (x - (- 1 - $\sqrt{2}$ ) ), (x - $\sqrt{3}$ ), (x - (- $\sqrt{3}$ )), that is

(x + 1 - $\sqrt{2}$ ), (x + 1 + $\sqrt{2}$ ), (x - $\sqrt{3}$ ), (x + $\sqrt{3}$ )

The polynomial is then the product of the roots

f(x) = (x + 1 - $\sqrt{2}$ )(x + 1 + $\sqrt{2}$ )(x - $\sqrt{3}$ )(x + $\sqrt{3}$ )

= ((x + 1)² - ( $\sqrt{2}$ )²)((x² - ( $\sqrt{3}$ )²)

= (x² + 2x + 1 - 2)(x² - 3)

= (x² + 2x - 1)(x² - 3) ← distribute

= $x^{4}$ - 3x² + 2x³ - 6x - x² + 3

= $x^{4}$ + 2x³ - 4x² - 6x + 3

6 0

3 years ago

HG is the perpendicular bisector of FK. What is the length of GH? 8 9 15 34

igor_vitrenko [27]

Answer:

GH=15

Step-by-step explanation:

HK= FK/2= 16/2= 8

Using pythagoras theorem in triangle GHK,

GH²= GK²-HK²

= 17²-8²

= 225

GH= √225

=15

4 0

3 years ago

How will the area of the circle change if it is dilated by a scale factor of 1/2? The area will be 2 times greater than the orig

coldgirl [10]

We know that

[scale factor]=1/2
[dilated area of circle]=[original area of circle]*[scale factor]²
so
[dilated area of circle]=[original area of circle]*[1/2]²
[dilated area of circle]=[original area of circle]*[1/4]

therefore

the answer is
The area will be 1/4 the original

7 0

3 years ago

Read 2 more answers

I really need help with this Can someone help me thx Plsssssss

omeli [17]

Answer:

10x^2 - 4x

Step-by-step explanation:

5x - 2 times 2x will equal the area of 'Potatoes.'

5x times 2x is 10x^2.

2 times 2x is 4x.

I cannot provide an exact value because x hasn't been identified.