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3 years ago

Find the rational solution of x3 – 3x2 + x + 5 = 0. Show your use of the Rational Zero Theorem to receive credit!

1 answer:

5 0

A zero of a function is a number that, when plugged in for the variable, makes the function equal to zero.
P ( x ) = 0
As P ( - 1 ) = 0:
( x³ - 3 x² + x + 5 ) : ( x + 1 ) = x² - 4 x + 5
-x³ - x²
--------------
- 4 x² + x
4 x²+ 4 x
--------------
5 x + 5
-5 x - 5
------------
0
The remaining trinomial: x² - 4 x + 5 doesn´t have rational roots.
Answer: x = -1

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What is the distributive property of 14+63?

ycow [4]

Ok so
a(b+c)=ab+ac or
ab+ac=a(b+c)
find the 'a' of 14 and 63
it is 7
14+63=7(2)+7(9)=7(2+9)=7(11)=77

8 0

3 years ago

2- If A=(3, 4) and B = (7,8), find AB.

Mice21 [21]

Use distance formula and take this question down, <em><u>easily</u></em>.

Step-by-step explanation:

Distance xy =

$\sqrt{ {(x_2 - x_1) }^{2} + {(y_2 - y_1)}^{2} }$

Therefore AB

= $\sqrt{(7-3)^2 +(8-4)^2}$

= $\sqrt{(4)^2 +(4)^2}$

= $\sqrt{32}$

= $\boxed{4 \sqrt{2}-units}$

4 0

2 years ago

Read 2 more answers

Fathers age is twice his daughter age but 16 years ago fathers age was 4 times his daughters age . Calculate their ages

zvonat [6]

Answer:

Father's age = 48

Daughter's age = 24

Step-by-step explanation:

Let x be father's age and y be daughter's age.

1st equation:

x = 2y

2nd equation:

(x - 16) = 4(y - 16)

Replacing value of x from 1st equation,

(2y - 16) = 4(y - 16)

2y - 16 = 4y - 64

4y - 2y = 64 - 16

2y = 48

y = 48/2

y = 24

And,

x = 2y

x = 2 x 24

x = 48

8x - x = 64 - 16

7x = 48

4 0

3 years ago

In ΔEFG, the measure of ∠G=90°, the measure of ∠E=40°, and EF = 75 feet. Find the length of GE to the nearest tenth of a foot

juin [17]

Answer:

19.4 feet

Step-by-step explanation:

Since the triangle has a right angle( as one of the angles in it is equal to 90°), we may find the length of the unknown side using the trigonometric notations SOH CAH TOA where

SOA stands for

Sin Ф = opposite side/hypotenuses side

Cosine Ф = adjacent side/hypotenuses side

Tangent Ф = opposite side/adjacent side

Given that the measure of ∠G=90° and ∠E=40°

EF is the hypotenuse side

FG is the opposite side and

GE is the adjacent side. As such if EF = 75 feet

Cos 75 = GE/75

GE = 75 Cos 75°

= 19.41 feet

≈ 19.4 feet in the nearest tenth of a foot

5 0

3 years ago

Read 2 more answers

I know you’re supposed to change the bounds and break up the integral, but for some reason, I can’t get the 44/3. Can someone ex

tatyana61 [14]

First, look for the zeroes of the integrand in the interval [0, 6] :

x² - 6x + 8 = (x - 4) (x - 2) = 0 ⇒ x = 2 and x = 4

Next, split up [0, 6] into sub-intervals starting at the zeroes we found. Then check the sign of x² - 6x + 8 for some test points in each sub-interval.

• For x in (0, 2), take x = 1. Then

x² - 6x + 8 = 1² - 6•1 + 8 = 3 > 0

so x² - 6x + 8 > 0 over this sub-interval.

• For x in (2, 4), take x = 3. Then

x² - 6x + 8 = 3² - 6•3 + 8 = -1 < 0

so x² - 6x + 8 < 0 over this sub-interval.

• For x in (4, 6), take x = 5. Then

x² - 6x + 8 = 5² - 6•5 + 8 = 3 > 0

so x² - 6x + 8 > 0 over this sub-interval.

Next, recall the definition of absolute value:

$|x| = \begin{cases}x & \text{for }x \ge0 \\ -x & \text{for }x < 0\end{cases}$