1.
(03.01 LC)

The leg of a right triangle is 2 units and the hypotenuse is 4 units. What is the length, in units, of the other leg of the triangle? (5 points)

2 units
6 units
Square root of 12 units
Square root of 20 units

Given:

Polynomial = P(x) = 3x² + kx + 6

Factor of the ablove polynomial = (x+3)

To Find:

Value of K, for which (x+3) become the factor of P(x) = 3x² + kx + 6

Solution :

Now,

x + 3 = 0

⇒x = (-3)

So,

As (x+3) is a factor so x = (-3) is one root of the polynomial.

Therefore,

P(-3) = 0

→ P(-3) = 3(-3)² + k(-3) + 6 = 0

→ 3(9) - 3k + 6 = 0

→ 27 - 3k + 6 = 0

→ 27 + 6 - 3k = 0

→ 33 - 3k = 0

→ - 3k = -33

→ k = -33 ÷ -3

→ k = 11

3x²+ kx + 6, by putting the value of k = 11 and taking -3 as root the remainder should be zero

→ 3x²+ 11x + 6

→ 3(-3)² + 11(-3) + 6

→ 3(9) - 33 + 6

→ 27 - 33 + 6

→ 27 + 6 - 33

→ 33 - 33

→ 0

Hence verified !

Answer:

I think the answer is 35x⁴-10

Step-by-step explanation:

3x × 4x=12x²

3x × 5=15x

2 × 4x=8x

2 × -5=-10

15x+8x=23x²

12x²+23x²=35x⁴

35x⁴-10

Answer:

If the left column is the width then the length is 45

If the right column is width then the length is 7.2

Step-by-step explanation:

ratios

Answer:

D. 43

Step-by-step explanation:

45 + (-5) = 40

40 - 4 = 36

36 + 7 = 43

Answer:

The question makes no sense in my opinion

By undestanding the theory behind rational functions and functional theory, we conclude that the function have:

Domain: (- ∞, - 3) ∪ (- 3, + ∞)

Range: (- ∞, 0) ∪ (0, + ∞)

In this question we have a rational function and we must determine its domain and range, whose elements exist if and only if the denominator evaluated at respective point is distinct of zero. Graphically speaking, the domain of the function represents the set of x-values, whereas the range represents the set of y-values.

By a graphing tool (i.e. Desmos) we construct the rational function and derive the following conclusions:

Domain: (- ∞, - 3) ∪ (- 3, + ∞)

Range: (- ∞, 0) ∪ (0, + ∞)

By undestanding the theory behind rational functions and functional theory, we conclude that the function have:

Domain: (- ∞, - 3) ∪ (- 3, + ∞)

Range: (- ∞, 0) ∪ (0, + ∞)

To learn more on rational functions: https://brainly.com/question/27914791

#SPJ1

Answer:

Range: (negative infinity, 0) U (0, 1/9) U (1/9, infinity)

Domain: (negative infinity, -3) U (-3, 6) U (6, infinity)

Step-by-step explanation:

100% on the test

Given:

Original price of a TV = $499

Price increased by 15%.

To find:

The new price of the TV.

Solution:

According to the question,

New price of the TV = Original price + 15% of its original price.

[tex]\text{New price of the TV}=499+\dfrac{15}{100}(499)[/tex]

[tex]\text{New price of the TV}=499+74.85[/tex]

[tex]\text{New price of the TV}=573.85[/tex]

Therefore, the new price of the TV is $573.85.

whats the question?????

Answer:the question is chemistry and the sander is math

Step-by-step explanation:

Answer:

bro just look on a caculater

Step-by-step explanation:

1087658.22

Answer:

4/3 or 1.3

Step-by-step explanation:

y= 3x-4

To find x- intercept/zero, Substuite y=0.

0= 3 x -4

Move the variable to the left-hand side and change its sign

-3x= -4

Divide both sides of the equation by -3

x= 4/3

(1.3 as a decimal)

Answer:

this is not a function because y-values repeat

Step-by-step explanation:

Answer:

simple

Step-by-step explanation:

-12r+8-2r+2

-14r-10

Answer:To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y. ...

To find the x-intercept, set y = 0 \displaystyle y=0 y=0.

To find the y-intercept, set x = 0 \displaystyle x=0 x=0.

answer is in there at the bottem

Step-by-step explanation:

Answer:

bsgdhv is the ghj is the most

Answer:

4 more hours.

Step-by-step explanation:

So, to calculate the remaining time Jill has to drive, we have to first find out how much distance Jill has left to cover:

[tex](450 - 250)[/tex] miles

= [tex]200[/tex] miles

So, at a rate of 50 miles per hour, Jill has to drive:

[tex]\frac{200}{50}[/tex] more hours

= [tex]4[/tex] more hours

Hope this helped!

Answer:

b

Step-by-step explanation:

3(2x+1)-(x-1)

\ / / /

5x+2

Answer:

fgcgfcgchgcchcgccghccghcgcghgghcgchchchgcgcghchgchg

Step-by-step explanation:

Answer:

9016 litres left

Step-by-step explanation:

The fish were not sick.

You would multiply 20.5 by 48 which is the amount of hours in 2 days then subtract that amount from 10000 to see how much is left

Answer:

(-2, 15), (-1, 11), (0, 7), (1, 3), (2, -1)

Step-by-step explanation:

so i just took possible x values and plugged them into the equation, and from there you can solve for y.

from Keith as Joaquin.

solve.

Answer:

y=1/2x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=k or kx

The value of the constant k is equal to the value of the slope m

In this problem we have the point (8,4)

Find the value of k

y/x=k------> substitute the value of x and y

4/8=k

k=1/2

The equation is equal to

y=1/2x

Answer:

no

Step-by-step explanation:

it does not fall on the line

Step-by-step explanation:

First let's simplify the upper part which is without x/8a

3a/x multiply xa/x

3a xa

__ x __

x x

x the denominator of 3a is cancelled with the x from xa the numerator.

that leaves us with

3a × a

__

x

we get 3a squared divided by x =

3a^2

____

x

now since we're dividing it with x/8a

3a^2 x

____ ÷ _____

x 8a

we change the sign ÷ to x so we flip the x/8a

3a^2 8a

_____ x ____

x x

8x3 = 24

a^2 x a = a^3

x multiply x = x^2

the final answer

24a^3

_____

x^2

========================================================

Explanation:

The old dimensions of the rectangle were 30 by 15.

The new dimensions are 30+x by 15+x, where x is some positive number.

The new rectangle dimensions multiply to 1000

(30+x)(15+x) = 1000

Use the FOIL rule to expand out the left side like so

(30+x)(15+x) = 1000

450+30x+15x+x^2 = 1000

450+45x+x^2 = 1000

x^2+45x+450

Then lets get everything to one side

x^2+45x+450 = 1000

x^2+45x+450-1000 = 0

x^2+45x-550 = 0

---------------------

From here we use the quadratic formula

Plug in a = 1, b = 45, and c = -550.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(45)\pm\sqrt{(45)^2-4(1)(-550)}}{2(1)}\\\\x = \frac{-45\pm\sqrt{4225}}{2}\\\\[/tex]

[tex]x = \frac{-45\pm65}{2}\\\\x = \frac{-45+65}{2} \ \text{ or } \ x = \frac{-45-65}{2}\\\\x = \frac{20}{2} \ \text{ or } \ x = \frac{-110}{2}\\\\x = 10 \ \text{ or } \ x = -55\\\\[/tex]

Earlier we defined x to be a positive number. This means we ignore x = -55. It makes no sense to add on a negative amount to each dimension.

The only practical answer is x = 10.

So each dimension is increased by 10 feet.

--------------------------

If x = 10, then the old dimensions of 30 by 15 bump up to 30+10 = 40 by 15+10 = 25

Then note how 40*25 = 1000, which helps confirm we have the correct dimensions.

--------------------------

Now go back to the question at hand: we want to find the new width. The old width was 30 feet. The new width is 30+x = 30+10 = 40 feet

Answer:

See drawing below.

Step-by-step explanation:

use the equation y=3x+2 to determine points needed, by substituting in the x values of -1, 0, 1, etc.

plot points

(-1, -1)

(0, 2)

(1, 5)

Please give thanks :)

Answer and Step-by-step explanation:

The word, "Consecutive" means, "Back-to-back" or "One after the other." Therefore, consider these integers:

1, 2, 3, 4, 5, 6, 7, 8, . . .

If we write down these integers in such a way that only even integers follow back-to-back, we have:

2, 4, 6, 8, . . .

If we write down these integers in such a way that only odd integers follow back-to-back, we have:

1, 3, 5, 7, . . .

Since 2, 4, 6, 8, . . . Are all even integers that follow back-to-back, then this is known of consecutive even integers.

Since 1, 3, 5, 7, . . . Are all odd integers that follow back-to-back, then this is known of consecutive odd integers.

Answer:

true :)

Step-by-step explanation:

hope this helps <3