Carpet, padding, and installation costs $23.23 per sq. yd. how much would it cost to carpet both bedrooms.

Rewrite 12/17 as a decimal number. Round to the nearest thousandth.

boyakko [2]

Let's rewrite the given fraction 12/17 to a decimal number. Then Let's round to the nearest thousandth.
To do that, divide the numerator by the denominator.
=> 12 / 17
=> 0.7058
Le's round this to
=>0.706

8 0

3 years ago

Read 2 more answers

2. Factor f(x) = x4 + 10x3 + 35x2 + 50x + 24 completely showing all work and steps with synthetic division. Then sketch the grap

telo118 [61]

We need to use rational root theorem to find out roots here.

The rational root theorem states that if p(x) is a polynomial with integer coefficients and if $\frac{p}{q}$ is a zero of p(x) then p is a factor of constant term and q is a factor of leasing term coefficient.

Here factors of constant term are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12, and -24.

And factors of leading coefficient is -1,1.

Hence possible roots may be -1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-12,12,-24 and 24.

Let us plugin these in f(x) to find zeroes.

$f(-1)=(-1)^{4}+10(-1)^{3}+35(-1)^{2}+50(-1)+24 =1-10+35-50+24=0$

Hence x=-1 is a zero which means x-(-1)=x+1 is a factor.

Let us use synthetic division to find quotient.

-1 | 1 10 35 50 24

| 0 -1 -9 -26 -24

1 9 26 24 0

Hence quotient is $x^{3} +9x^{2} +26x+24$

Since all coefficients are positive, root must be negative. Let's plugin all remaining negative numbers in the quotient.

$(-2)^{3}+9(-2)^{2}+26(-2)+24 = 0$

Hence x+2 is another factor.

Let us find quotient again using synthetic division.

-2 | 1 9 26 24

| 0 -2 -14 -24

1 7 12 0

Hence quotient is $x^{2} +7x+12$

Again we got quotient with all positive coefficients, let us plugin remaining negative numbers from rational root theorem.

$(-3)^{2}+7(-3)+12=-9-21+12=0$

Hence x+3 is also a factor.

Let us find quotient using synthetic division.

-3 | 1 7 12

| 0 -3 -12

1 4 0

Hence quotient is x+4.

So, $f(x)=x^{4}+10x^{3}+35x^{2}+50x+24 =(x+1)(x+2)(x+3)(x+4)$

Please have a look at the graph attached.

4 0

3 years ago

Suppose that the functions s and t are defined for all real numbers x as follows.

PolarNik [594]

Answer:

(s-t)(-1) = -1

(s+t)(-1) = -7

Step-by-step explanation:

Given the following set of functions

s(x)=2x-2

t(x)=3x

(s-t)(x) = s(t) - t(x)

(s-t)(x) = 2x - 2 - 3x

(s-t)(x) = -x -2

(s-t)(-1) = -(-1) - 2

(s-t)(-1) = 1-2

(s-t)(-1) = -1

(s+t)(x) = s(t) + t(x)

(s+t)(x) = 2x - 2 + 3x

(s+t)(x) = 5x -2

(s+t)(-1) = 5(-1) - 2

(s+t)(-1) = -5-2

(s+t)(-1) = -7

8 0

3 years ago

1/3=4/12 Explain the reasoning in words.

nevsk [136]

1/3 is equal to 4/12.
1 goes into 3, 3 times, and 4 goes into 12 three times. Therefore 4/12 is also 1/3.

6 0

4 years ago

A 20-foot cable hangs from the top of a building that is 50 feet high. if the cable weighs 2 pounds per foot, how much work is d

pychu [463]

20*2=40
40*50=2000
2000/60=33.33
about 33 hours by lifting by hand

4 0

3 years ago