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gregori [183]
3 years ago
7

9x – 5 < –41 or 3x + 13 > 7

Mathematics
2 answers:
aev [14]3 years ago
5 0
9x - 5 < -41
    +5      +5
9x < -36
x < -4

3x + 13 > 7
       -13   -13
3x      > -6
x > -2

x < -4 OR x >2
Elis [28]3 years ago
4 0
9x-5<-41                  or          3x+13>7
9x-5+5<-41+5                        3x+13-13>7-13 
9x/9<-36/9                             3x/3>-6 /3 
x<-4                                      x>-2
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3 years ago
What’s equivalent to 1/3 with the denominator of 6
podryga [215]

Answer:

2/6

Step-by-step explanation:

Ok, so if the fraction is 1/3 and the denominator needs to be 6, then what you do is figure out what would turn 3 into 6. So, 3 x 2 would equal 6 and then you would have to also keep that two and multiply that 2 with the 1 and you would get 2. That would lead to the numerator being 2 and the denominator being 6, or 2/6.

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3 years ago
Read 2 more answers
2 points) Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One
Stells [14]

y'=(t+y)^2-1

Substitute u=t+y, so that u'=y', and

u'=u^2-1

which is separable as

\dfrac{u'}{u^2-1}=1

Integrate both sides with respect to t. For the integral on the left, first split into partial fractions:

\dfrac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)=1

\displaystyle\int\frac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm dt=\int\mathrm dt

\dfrac12(\ln|u-1|-\ln|u+1|)=t+C

Solve for u:

\dfrac12\ln\left|\dfrac{u-1}{u+1}\right|=t+C

\ln\left|1-\dfrac2{u+1}\right|=2t+C

1-\dfrac2{u+1}=e^{2t+C}=Ce^{2t}

\dfrac2{u+1}=1-Ce^{2t}

\dfrac{u+1}2=\dfrac1{1-Ce^{2t}}

u=\dfrac2{1-Ce^{2t}}-1

Replace u and solve for y:

t+y=\dfrac2{1-Ce^{2t}}-1

y=\dfrac2{1-Ce^{2t}}-1-t

Now use the given initial condition to solve for C:

y(3)=4\implies4=\dfrac2{1-Ce^6}-1-3\implies C=\dfrac3{4e^6}

so that the particular solution is

y=\dfrac2{1-\frac34e^{2t-6}}-1-t=\boxed{\dfrac8{4-3e^{2t-6}}-1-t}

3 0
3 years ago
At the local gas station gasoline costs $2.75 for per gallon and diesel costs $3.02 per gallon. Gabriel needs to purchase 15.2 g
Ainat [17]

Answer:

The total amount paid by Gabriel at the local gas station is $70.49.

Step-by-step explanation:

Cost of gasoline per gallon = $2.75

Cost of diesel per gallon = $3.02

Amount of gasoline Gabriel needs = 15.2 gallons

Amount of diesel Gabriel needs = 9.5 gallons

Compute the total amount paid by Gabriel at the local gas station as follows:

Total Cost = Cost of gasoline × Amount of gasoline

                           + Cost of diesel × Amount of diesel

                =(2.75\times 15.2)+(3.02\times 9.5)\\\\=41.8+28.69\\\\=70.49

Thus, the total amount paid by Gabriel at the local gas station is $70.49.

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