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2 years ago

Factor completely. 81x^2+180x+100=81x

Mathematics

1 answer:

Ilya [14]2 years ago

3 0

Answer:

There is no solution :/

Step-by-step explanation:

81x^2+180x+100=81x

Step 1: Subtract 81x from both sides.

81x^2+180x+100−81x=81x−81x

81x^2+99x+100=0

For this equation: a=81, b=99, c=100

81x^2+99x+100=0

Step 2: Use quadratic formula with a=81, b=99, c=100.

x= −b±√b2−4ac/ 2a

x= −(99)±√(99)2−4(81)(100) / 2(81)

x= −99±√−22599/162

So you see... no solution

Hope this helps!

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Solve the system of equations. −5x−3y−9=0 4x−18y−54=0 y=? x=?

Darina [25.2K]

Answer:

Step-by-step explanation:

Eq. 1 ) −5x−3y−9=0

Eq. 2) 4x−18y−54=0

there are two routes to solve this, Substitution or elimination, I'll go for the 2nd one because I can see that the y values are a multiple of each other :)

6 *( −5x−3y−9=0 )

Eq. 3) -30x -18y =54

subtract Eq. 2 from Eq. 3 :)

-30x -18y =54

-( 4x−18y=54)

-34x = 0

so according to the equations then x =0 but, that's not really a full answer, so now we should go back and try the other method, substitution,

then:

-5x = 9 +3y

x = - 9/5 + (-3/5)y

now plug that into Eq. 2

4( - 9/5 + (-3/5)y ) - 18y = 54

-36/5 + (-12/5)y -18y = 54

(-12/5)y - (90/5)y = 54+36/5

-(102/5)*y =270/5+36/5

-(102/5)y = 306/5

y = (-5/102)*(306/5)

y = -306/102

y = -3

then plug in for either equation

-5x-3( -3) = 9

-5x + 9 = 9

-5x = 0

x = 0

now we have the full answer

check it by plugging in both x and y into the 2nd equation

4(0) - 18(-3) = 54

54= 54

this seems good

3 0

3 years ago

A cable company charges $70 per month for cable service. Please help ASAP Check screenshot pleasee (20 points) Thank youu! :)) &

LiRa [457]

Answer:

for #1: 70x = y

for #2: 70x + 100 = y

Step-by-step explanation:

you pay $70 for x amount of time with will equal your total therefore it's 70x = y

if you have to pay a one-time fee of $100.00 then you have to add that to your equation giving you 70x + 100 = y

hope this is right

hope it helps too :)

8 0

2 years ago

Answers: a/b= 8/2 B: 3.2/2= a/b C: b/6.4 = 8/5 D: 2/ 3.2= b/a

scoundrel [369]

Answer:

b/6.4 = 8/5

Step-by-step explanation:

6 0

3 years ago

What is the value of x in the equation 2.5(5x-5)=10+4(1.5+0.5x)

Alexus [3.1K]

Answer:

x= 19/7

Step-by-step explanation:

7 0

2 years ago

A student carried out an experiment to determine the amount of vitamin C in a tablet sample. He performed 5 trials to produce th

ivolga24 [154]

Answer:

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

P-value = 0.166.

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\$

Then, we can perform the hypothesis t-test for the mean.

The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.

Then, the null and alternative hypothesis are:

$H_0: \mu=500\\\\H_a:\mu< 500$

The significance level is 0.05.

The sample has a size n=5.

The sample mean is M=496.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1$

The degrees of freedom for this sample size are:

$df=n-1=5-1=4$

This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.166) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

4 0

2 years ago