All categories

2 years ago

Use synthetic substitution to evaluate the polynomial P(x) = x^3-3x^2+4x-7 for x=3

Mathematics

1 answer:

Zina [86]2 years ago

3 0

Answer:

$\frac{x^3-3x^2+4x-7}{x-3} =(x^2+4)+\frac{5}{x-3}$

Step-by-step explanation:

We are given polynomial as

$P(x)=x^3-3x^2+4x-7$

and it is divided by x=3 or x-3

we can use synthetic division

so, we got

Remainder =5

Quotient is

$=x^2+0x+4$

$=x^2+4$

we can write as

$\frac{x^3-3x^2+4x-7}{x-3} =(x^2+4)+\frac{5}{x-3}$

You might be interested in

A line passes through the points (5, –7.5) and has a y-intercept of 10.

brilliants [131]

Answer:y=0.5x+10

Step-by-step explanation:

need help with explanation?

4 0

3 years ago

Can someone help me the 2nd problem I don’t understand it

Galina-37 [17]

Answer:

So this means the bus B covered 390-120=270 miles when bus A has already reached 390 miles.

270 miles

Step-by-step explanation:

So is A is going faster than B so A will reach the destination first.

When will A reach it's destination?

Let's find out.

To solve this problem, the following will come in handy:

Speed=distance/time or time*Speed=distance or time=distance/speed .

time=distance/speed

$T_A=\frac{390}{S_A}$

$T_A=\frac{390}{65}$

$T_A=6$

So it will take bus A 6 hours to cover the distance of 390 miles.

How much time would have it taken bus B to reach that same distance?

$T_B=\frac{390}{45}$

$T_B=8.\overline{6}$

So it would have taken bus B $8.\overline{6}$ hours to cover a distance of 390 miles.

So the time difference is $8.\overline{6}-6=2.\overline{6}$ hours.

It will take $2.\overline{6}$ more hours than bus A for bus B to complete a distance of 390 miles.

So bus B traveled $2.\overline{6} \cdot 45=120$ miles (used the time*speed=distance) after bus A got to it's destination.

So this means the bus B covered 390-120=270 miles when bus A has already reached 390 miles.

4 0

3 years ago

The cost per week of running a boarding house is partly constant and partly

patriot [66]

Answer:

the cost of running the boarding

house for 600 students is N61,000

Step-by-step explanation:

Let C represents cost

K1 represents first constant

K2 represents second constant

C= k1+k2n

3500 = k1 + 25 k2............. Eqn(1)

6000= k1 + 50 k2 .............. Eqn(2)

Subtract eqn(1) from eqn(2)

2500= 25k2

K2= 2500/25

K2= 100

To get k1 from eqn(1)

3500 = k1 + 25 k2

Substitute the value of k2

3500 = k1 + 25 (100)

3500= k1 +2500

K1= 3500- 2500

K1= 1000

The equation connecting them;

C= 1000+ 100n

The cost of running the boarding

house for 600 students is

n= 600

C= 1000+ 100(600)

C= 1000+60000

C= N 61,0000

6 0

2 years ago

What are all the exact solutions of -3tan^2(x)+1=0? Give your answer in radians.

goldenfox [79]

$\displaystyle\\
 -3\tan^2x + 1 = 0\\\\
 -3\tan^2x = -1\\\\
\tan^2x = \frac{-1}{-3} \\\\
\tan^2x = \frac{1}{3} ~~~~~ \Big|~\sqrt{~~~} \\\\
\sqrt{\tan^2x} = \sqrt{\frac{1}{3}} \\\\
\tan x = \Big| \frac{1}{ \sqrt{3} } \Big|\\\\
\tan x = \Big| \frac{\sqrt{3}}{ 3 } \Big|\\\\
\tan x = \frac{\sqrt{3}}{ 3 }~~~\Longrightarrow~~x_1= \frac{\pi}{6} + k\pi,~~k \in N \\\\ 
\tan x = -\frac{\sqrt{3}}{ 3 }~~~\Longrightarrow~~x_2= \pi-\frac{\pi}{6} + k\pi = \frac{5\pi}{6} + k\pi,~~k \in N \\\\ 
$

4 0

3 years ago

Read 2 more answers

DESCRIBE DOMAIN WITH ALGEBRA in my screenshot (sorry caps)

bogdanovich [222]

Answer:

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

3 0

2 years ago

Read 2 more answers