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1 year ago

Find the set of values of k for which the equation 3x² - 12x + k >. 0 has no real roots.

Mathematics

1 answer:

anzhelika [568]1 year ago

3 0

Answer:

k > 12

Step-by-step explanation:

If a quadratic equation has no real roots the values of b^2 - 4ac

( for the general form ax^2 + bx + c = 0) is negative,

So we have the inequality:

(-12)^2 - 4*3* k < 0

144 - 12k < 0

12k > 144

k > 12

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The correct answer is D the very last one.

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2 years ago

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Which word phrase represents the variable expression? 5n + 8 A. eight more than the sum of a number and five B. eight more than

balu736 [363]

B, eight more than five times a number because you would multiply 5 times n first due to the rule of pemdas

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2 years ago

Can someone please explain how to do this!!!

DedPeter [7]

Hi there!

So we are given that:-

tan theta = 7/24 and is on the third Quadrant.

In the third Quadrant or Quadrant III, sine and cosine both are negative, which makes tangent positive.

Since we want to find the value of cos theta. cos must be less than 0 or in negative.

To find cos theta, we can either use the trigonometric identity or Pythagorean Theorem. Here, I will demonstrate two ways to find cos.

Using the Identity

$\large \displaystyle{ {tan}^{2} \theta + 1 = {sec}^{2} \theta}$

Substitute tan theta = 7/24 in.

$\large \displaystyle{ {( \frac{7}{24}) }^{2} + 1 = {sec}^{2} \theta }$

Evaluate.

$\large \displaystyle{ \frac{49}{576} + 1 = {sec}^{2} \theta} \\ \large \displaystyle{ \frac{625}{576} = {sec}^{2} \theta}$

Reminder -:

$\large \displaystyle{ sec \theta = \frac{1}{cos \theta} }$

Hence,

$\large \displaystyle{ \frac{576}{625} = {cos}^{2} \theta} \\ \large \displaystyle{ \sqrt{ \frac{576}{625} } = cos \theta} \\ \large \displaystyle{ \frac{24}{25} = cos \theta}$

Because in QIII, cos<0. Hence,

$\large \displaystyle \boxed{ \blue{cos \theta = - \frac{24}{25} }}$

Using the Pythagorean Theorem

$\large \displaystyle{ {a}^{2} + {b}^{2} = {c}^{2} }$

Define c as our hypotenuse while a or b can be adjacent or opposite.

Because tan theta = opposite/adjacent. Therefore:-

$\large \displaystyle{ {7}^{2} + {24}^{2} = {c}^{2} } \\ \large \displaystyle{49 + 576 = {c}^{2} } \\ \large \displaystyle{625 = {c}^{2} } \\ \large \displaystyle{25 = c}$

Thus, the hypotenuse side is 25. Using the cosine ratio:-

$\large \displaystyle{cos \theta = \frac{adjacent}{hypotenuse}}$

Therefore:-

$\large \displaystyle{cos \theta = \frac{24}{25} }$

Because cos<0 in Q3.

$\large \displaystyle \boxed{ \red{cos \theta = - \frac{24}{25} }}$

Hence, the value of cos theta is -24/25.

Let me know if you have any questions!

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2 years ago

When this polynomial is divided by (x+3) , the remainder is 0. What is the value of the polynomial’s constant term.

saveliy_v [14]

Answer:

- 15

Step-by-step explanation:

Given f(x) divided by (x + h) then the remainder is the value of f(- h)

Here

f(x) = 3x³ - 5x² - 47x + k ← k is the constant term , then

f(- 3) = 3(- 3)³ - 5(- 3)² - 47(- 3) + k = 0 , that is

3(- 27) - 5(9) + 141 + k = 0

- 81 - 45 + 141 + k = 0

15 + k = 0 ( subtract 15 from both sides )

k = - 15

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galina1969 [7]

Based on the image, FJH is perpendicular to JI as these two lines form a right angle.

<h3>What is a perpendicular line?</h3>

This name is given to a line that creates a right angle when it intersects or meets with another line.

This concept opposes the concept of parallel line, which is used to describe lines that never intersect and are always the same distance apart.

<h3>How do you identify a perpendicular line?</h3>

Look for a right angle or a a 90° angles.
Identify the lines that intersect to create this angle.
Write down the two lines or line sections.

Based on the above, in the image given two lines that can be classified as perpendicular are the lines FJH (horizontal lines) and JI (vertical line) as their intersection creates a right angle.

Learn more about coordinate planes in: brainly.com/question/14462788

#SPJ1

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1 year ago

Find the set of values of k for which the equation 3x² - 12x + k >. 0 has no real roots.​

Find the set of values of k for which the equation 3x² - 12x + k >. 0 has no real roots.