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2 years ago

Use Synthetic Division to divide (3x3 + x2 – 4) by (x + 2).

Mathematics

1 answer:

Kitty [74]2 years ago

4 0

X - 2 + 9 OVER x + 2.
in other words x - 2 + 9 /x + 2

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2. What is the measure of angle AOE and angle EOD?<br><br> X+138<br><br> x + 48

horrorfan [7]

Answer:

AOE = 138, EOD = 48

Step-by-step explanation:

Since AD is the diameter of the circle and goes through the middle

angle AOE + angle EOD = 180

Solving the equation (x + 138) + ( x+ 48) = 180

We get x = 0.

8 0

2 years ago

In a G.P the difference between the 1st and 5th term is 150, and the difference between the

liubo4ka [24]

Answer:

Either $\displaystyle \frac{-1522}{\sqrt{41}}$ (approximately $-238$ ) or $\displaystyle \frac{1522}{\sqrt{41}}$ (approximately $238$ .)

Step-by-step explanation:

Let $a$ denote the first term of this geometric series, and let $r$ denote the common ratio of this geometric series.

The first five terms of this series would be:

$a$ ,
$a\cdot r$ ,
$a \cdot r^2$ ,
$a \cdot r^3$ ,
$a \cdot r^4$ .

First equation:

$a\, r^4 - a = 150$ .

Second equation:

$a\, r^3 - a\, r = 48$ .

Rewrite and simplify the first equation.

$\begin{aligned}& a\, r^4 - a \\ &= a\, \left(r^4 - 1\right)\\ &= a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) \end{aligned}$ .

Therefore, the first equation becomes:

$a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) = 150$ ..

Similarly, rewrite and simplify the second equation:

$\begin{aligned}&a\, r^3 - a\, r\\ &= a\, \left( r^3 - r\right) \\ &= a\, r\, \left(r^2 - 1\right) \end{aligned}$ .

Therefore, the second equation becomes:

$a\, r\, \left(r^2 - 1\right) = 48$ .

Take the quotient between these two equations:

$\begin{aligned}\frac{a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right)}{a\cdot r\, \left(r^2 - 1\right)} = \frac{150}{48}\end{aligned}$ .

Simplify and solve for $r$ :

$\displaystyle \frac{r^2+ 1}{r} = \frac{25}{8}$ .

$8\, r^2 - 25\, r + 8 = 0$ .

Either $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ or $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ .

Assume that $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = -\frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= -\frac{1522\sqrt{41}}{41} \approx -238\end{aligned}$ .

Similarly, assume that $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = \frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= \frac{1522\sqrt{41}}{41} \approx 238\end{aligned}$ .

4 0

2 years ago

Really need help with my aleks

tatiyna

Answer:

(4x -4)° +x° +(6x-3)° = 180°
J = 99°
K = 64°
L = 17°

Step-by-step explanation:

The relation that helps you write an equation for x is, "the sum of angles in a triangle is 180°."

<h3>equation</h3>

(4x -4)° +x° +(6x -3)° = 180° . . . . . sum of angles in this triangle

<h3>solution for x</h3>

11x -7 = 180 . . . . . . . divide by °, collect terms

11x = 187 . . . . . . . . add 7

x = 17 . . . . . . . . . divide by 11

<h3>angle values</h3>

m∠J = (6x -3)° = (6(17) -3)° = 99°

m∠K = (4x -4)° = (4(17) -4)° = 64°

m∠L = x° = 17°

5 0

1 year ago

Identify the angle measures of PQRS.

kap26 [50]

The opposite angles of an inscribe quadrilateral are supplementary.

angle P + angle R = 180
6x + 7 + 12x + 11 = 180
18x + 18 = 180
18x = 162
x = 9

Now we will substitute in the value of x to find angle P and R.

angle P = 6(9)+7 = 61
angle R = 12(9)+11 = 119

Now we will find the value of y.

angle Q + angle S = 180
10y + 7 + 3(3y + 7) = 180
10y + 7 + 9y + 21 = 180
19y + 28 = 180
19y = 152
y = 8

Now substitute in the value of y to find angle Q and S.

angle Q = 10(8)+7 = 87
angle S = 3(3*8+7) = 93

Hope this helps :)

7 0

2 years ago

Linda has d dollars in an account that pays 1.4% interest, compounded weekly. She withdraws w dollars. Express her first week’s

Fittoniya [83]

Answer:

If the 1.4% rate of interest is the weekly rate of interest, Then, total first week interest = 1.4(d - w)/100 = 0.014(d - w)

But if the 1.4% rate of interest is a yearly rate of interest compounded weekly, then her total first week interest = 7(d - w)/2600 = 0.00269 (d - w)

Step-by-step explanation:

The interest, I = PRT

P = initial amount of dollars in account = (deposit - withdrawal) = (d - w)

R = rate of interest = 1.4% = 0.014/week

T = time = 1 week

If the 1.4% rate of interest is the weekly rate of interest

I = PRT = (d - w) × 0.014 × 1 = 0.014(d - w)

But if the 1.4% rate of interest is a yearly rate if interest compounded weekly,

P = initial amount of dollars in account = (deposit - withdrawal) = (d - w)

R = rate of interest = 1.4% = 0.014/year

T = time = 1 week = (1/52) years

I = PRT = (d - w) × 0.014 × (1/52) = 7(d - w)/2600 = 0.00269 (d - w)

Hope this Helps!!!

7 0

3 years ago

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