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2 years ago

Determine whether the solutions to the equations are rational or irrational.

Mathematics

1 answer:

statuscvo [17]2 years ago

8 0

Answer:

Step-by-step explanation:

x^3 = -216 yields 1 real, rational solution: 6

x^3 = 25 yields 1 real solution, but this solution is irrational:

∛-25 = -∛25 ≈ -2.92

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I need help with problem

pychu [463]

Answer:

f(x)=4x(x-3)

Vertex=3/2, -9

Step-by-step explanation:

First, factorize it.

That is equal to 4x(x-3)

Therefore, x intercepts are 0 and 3, as at least one of them need to be 0.

To find the vertex, first find the x of the vertex, which you can do by finding the average of the x intercepts, so it will be 3/2

Then, find the y, by making x in the original equation equal 3/2. This will give us -9 as the y.

The vertex will by 3/2, -9

4 0

2 years ago

Hi, Could anyone help me with my homework

tatiyna

Answer:

$\hookrightarrow \sf x^6+24x^5+240x^4+1280x^3+3840x^2+6144x+4096$

solving steps:

$\rightarrow \sf (x + 4)^6$

$\bold{rewrite \ the \ following}$

$\rightarrow \sf (x + 4)^2 (x + 4)^2 (x + 4)^2$

$\bold {formula \ used : \sf (x+a)^2 = (x^2 + 2xa + a^2)}$

$\rightarrow \sf (x^2 + 8x+16) (x^2 + 8x+16) (x^2 + 8x+16)$

$\bold{simplify \ by \ removing \ parenthesis}$

$\rightarrow \sf (x^4 +8x^3 + 16x^2 + 8x^3 +64x^2 + 128x+16x^2+128x+256 ) (x^2 + 8x+16)$

$\bold{basic \ addition \ of \ integers }$

$\rightarrow \sf (x^4+16x^3+96x^2+256x+256) (x^2 + 8x+16)$

$\bold{remove \ parenthesis}$

$\rightarrow \sf (x^6 + 16x^5 + 96x^4 + 256x^3 + 256x^2 + 8x^6 + 128x^4 + 768x^3 + 2048x^2 + 2048 + 16x^4 + 256x^3 + 1536x^2 + 4096x + 4096)$

$\bold {final \ answer:}$

$\rightarrow \sf x^6+24x^5+240x^4+1280x^3+3840x^2+6144x+4096$

8 0

1 year ago

in a hotel ,100 bulbs each of 60W are lightened for 6 hours a day and 40 fans each of 50Wvate run for 10 hours a day . calculate

alekssr [168]

Answer:

1680 kwhr

Step-by-step explanation:

See attached for explanation. I converted watt*hr to kW*hr by dividing by 1000.

Fans Bulbs

40 100

50 60 W

10 6 hours/day

20000 36000 W*hr/day

30 30 days/month

600000 1080000 W*hr/month

600 1080 kWhr/month

Total = 1680 kWhr/month

5 0

2 years ago

Madeleine can type 3 pages in one hour. How many pages will it take her to type a 123- page report?

Maurinko [17]

It would be 41 because 123/3 =41

4 0

2 years ago

Read 2 more answers

Write the slope-intercept form of the equation of each line given the slope and y-intercept.

saul85 [17]

Answer:

4b. −6x + y = −4

4a. 7x + 4y = −12

3b. y = ½x + 3

3a. y = −6x + 5

2b. y + 2 = −⅔(x + 3)

2a. y - 3 = ⅘(x - 5)

1b. y = -x + 5

1a. y = 5x - 3

Step-by-step explanation:

Plug the coordinates into the Slope-Intercept Formula first, then convert to Standard Form [Ax + By = C]:

2 = 6[1] + b

−4 = b

y = 6x - 4

-6x - 6x

_________

−6x + y = −4 >> Standard Equation

4 = −7⁄4[-4] + b

−3 = b

y = −7⁄4x - 3

+7⁄4x +7⁄4x

____________

7⁄4x + y = −3 [We do not want fractions in our Standard Equation, so multiply by the denominator to get rid of it.]

4[7⁄4x + y = −3]

7x + 4y = −12 >> Standard Equation

__________________________________________________________

Plug both coordinates into the Slope-Intercept Formula:

5 = ½[4] + b

3 = b

y = ½x + 3 >> EXACT SAME EQUATION

−1 = −6[1] + b

−6

5 = b

y = −6x + 5

* Parallel lines have SIMILAR RATE OF CHANGES [SLOPES].

__________________________________________________________

b. y + 2 = −⅔(x + 3)

a. y - 3 = ⅘(x - 5)

According to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE TERMS OF WHAT THEY REALLY ARE, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT SIGNS.

__________________________________________________________

b. y = -x + 5

a. y = 5x - 3

Just write out the Slope-Intercept Formula as it is given to you.

I am joyous to assist you anytime.

3 0

2 years ago