F(x)=3\cdot \left(\dfrac{7}{4}\right)^xf(x)=3⋅(

Solve for x.<br><br> −4/5x+3/10<8/10

Genrish500 [490]

Answer:

for (−4/5)x + 3/10 < 8/10: solution is x > -5/8

for −4/(5x) + 3/10 < 8/10: solution is x > -8/5

Step-by-step explanation:

I'm not exactly sure if you mean -4 divided by 5x or (-4/5)x, so I've done both! :)

$-\frac{4}{5}x+ \frac{3}{10} < \frac{8}{10}$

subtract 3/10 from both sides: $-\frac{4}{5}x < \frac{5}{10}$

Divide both sides by 4/5: $-x < \frac{5}{8}$

Divide both sides by -1 (reverse sign): $x > -\frac{5}{8}$

$-\frac{4}{5x}+ \frac{3}{10} < \frac{8}{10}$

subtract 3/10 from both sides: $-\frac{4}{5x} < \frac{5}{10}$

Multiply both sides by 5x: $-4 < \frac{5}{2}x$

Divide both sides by 5/2: $x>- \frac{8}{5}$

6 0

2 years ago

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Find the average rate of change of each function over the interval [0, 2]. Match each representation with its respective average

marishachu [46]

Average rate of change over interval [a,b]: r=[f(b)-f(a)]/(b-a)
In this case the interval is [0,2], then a=0, b=2
r=[f(2)-f(0)]/(2-0)
r=[f(2)-f(0)]/2

1) First function: h(x)
r=[h(2)-h(0)]/2
x=2→h(2)=(2)^2+2(2)-6
h(2)=4+4-6
h(2)=2
x=0→h(0)=(0)^2+2(0)-6
h(0)=0+0-6
h(0)=-6
r=[h(2)-h(0)]/2
r=[2-(-6)]/2
r=(2+6)/2
r=(8)/2
r=4

2) Second function: f(x)
A function, f, has an
x-intercept at (2,0)→x=2, f(2)=0
and a y-intercept at (0,-10)→x=0, f(0)=-10
r=[f(2)-f(0)]/2
r=[0-(-10)]/2
r=(0+10)/2
r=(10)/2
r=5

3) Third function: g(x)
r=[g(2)-g(0)]/2
From the graph:
g(2)=6
g(0)=2
r=(6-2)/2
r=(4)/2
r=2

4) Fourth function: j(x)
r=[j(2)-j(0)]/2
From the table:
x=2→j(2)=-8
x=0→j(0)=4
r=(-8-4)/2
r=(-12)/2
r=-6

Answer:
Pairs
1) h(x) 4
2) f(x) 5
3) g(x) 2
4) j(x) -6

8 0

4 years ago

PLEASE HELP

valkas [14]

Do you have to multiply 6 x 6 which equals 36

7 0

4 years ago

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Ava opens an account with $400. She deposits $200/month for 20 years. The interest rate is 2.15%. How much interest will she hav

artcher [175]

Answer:

d. None of the above

Step-by-step explanation:

We assume the sequence of deposits is ...

month 0: $400

month 1: $200

month 2: $200

...

month 240: $200 . . . . accumulated interest is determined at this point

That is, no interest is earned on the last deposit.

_____

The value of the initial $400 deposit after 20 years at 2.15% interest compounded monthly is ...

$400×(1 +.0215/12)^(12×20) = $400×1.536666 ≈ $614.67

The value of the $200 annuity at the same interest rate is ...

$200((1 +.0215/12)^(12×20) -1)/(.0215/12) = $200×299.534612 ≈ $59,906.92

So, the total account value is ...

$614.67 +59,906.92 = $60521.59

The total amount deposited was ...

$400 +$200×240 = $48,400

The interest earned is the difference between the account value and the total of deposits:

$60,521.59 -48,400 = $12,121.59 . . . . interest earned

This value does not match any numerical answer choice, so we conclude the appropriate answer is ...

None of the above

3 0

3 years ago

The mechanics at Giuseppe’s Auto House specialize in changing fuel injection units and transmissions. Last week, they changed 5

Lemur [1.5K]

Answer:

The solution is (2,6)

Step-by-step explanation:

Let

x-----> the number of hours to change a fuel injection unit

y-----> the number of hours to change a transmission

we know that

5x+10y=70 -----> equation A

8x+8y=64 -----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (2,6)

see the attached figure

4 0

3 years ago

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