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3 years ago

What is the slope of the line with the equation 16 + x = -4y

Mathematics

2 answers:

Eddi Din [679]3 years ago

7 0

Answer:

m= -1/4

Step-by-step explanation:

Radda [10]3 years ago

4 0

Answer:

- $\frac{1}{4}$

Step-by-step explanation:

You are looking for the slope of the equation. The easiest way to do this would be to look for the slop in slope-intercept form, y=mx+b. Lets start converting our equation!

16 + x = -4y

First, lets flip our equation around the '=', so we can already see the future flow of slope-intercept form!

-4y = x + 16

Now, we need to get rid of the -4 in front of the y value! Lets do this by dividing both terms on the right by -4. (Key tip: Remember, the x has a 1 in front of it!

y = -1/4x - 4

Finally, we can see that our slope is going to be -1/4.

Hope this helps!

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${16x}^{19}$

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3 years ago

Is 7.8 greater than 7.800

blsea [12.9K]

Answer:

Step-by-step explanation:

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3 years ago

The function f(x) varies inversely with x and f(x)=2 when x = 16.<br><br> What is f(x) when x = 4?

andrew-mc [135]

Answer: The correct answer is: [D]: "8" .

Step-by-step explanation:f y varies inversely with x; then y = k/x ; with "k" being the "constant" in this equation.

You can find the constant by substituting the values given: x = 16, f(x) = y = 2 ;

So, f(x) = y = 2 = k/16 ;

→ 2 = k / 16 ;

Solve for the constant; "k" ;

Multiply EACH SIDE of the equation by "16"

→ 16* (2) = (k / 16) * 16 ;

→ 32 = k ;

↔ k = 32 ;

As such, we can write the equation:

y = k/ x ; as:

→ y = 32/ x ;

Since we are given: "x = 4" ; Plug in that value; and solve for "y" ;

y = 32/4 = 8 .

y = 8 .

y = f(x) ;

So; f(x) = 8 ; which is: Answer choice: [D]: "8" .

8 0

3 years ago

An investor invested a total of $3 comma 500 in two mutual funds. One fund earned a 4% profit while the other earned a 2% pro

lesya [120]

Answer:

$2000 invested in first fund

$1500 invested in second fund

Step-by-step explanation:

An investor invested a total of $3,500 in two mutual funds.

Let x be the amount invested in first fund

first fund earned a 4% profit (4%= 0.04)

So interest is 0.04x for first fund

Let x be the amount invested in first fund

first fund earned a 4% profit (4%= 0.04)

So interest is 0.04x for first fund

Let y be the amount invested in second fund

second fund earned a =2% profit (2%= 0.02)

So interest is 0.02y for second fund

An investor invested a total of $3,500 in two mutual funds.

So x+y = 3500----> equation 1

y= 3500-x

the investor's total profit was $110

0.04x + 0.02y = 110----> equation 2

Plug in 3500 -x for y

0.04x + 0.02(3500-x) = 110

0.04x + 70 - 0.02x = 110

0.02x + 70 = 110

Subtract 70 onboth sides

0.02x = 40

Divide both sides by 0.02

x= 2000

y= 3500-x

so y= 3500 - 2000 = 1500

$2000 invested in first fund

$1500 invested in second fund

3 0

3 years ago

22. An employee joined a company in 2017 with a starting salary of $50,000. Every year this employee receives a raise of $1000 p

Setler79 [48]

Answer:

(a) The recurrence relation for the salary is

$S_{n+1}=1.05*S_n+1000\\\\S_0=50000$

(b) The salary 25 years after 2017 will be $217044.85.

Step-by-step explanation:

We can define the next year salary $S_{n+1}$ as

$S_{n+1}=S_n+1000+0.05*S_n=1.05*S_n+1000$

wit S0=$50000

If we extend this to 2 years from 2017 (n+2), we have

$S_{n+2}=1.05*S_{n+1}+1000=1.05*(1.05*S_n+1000)+1000\\S_{n+2} =1.05^2*S_n+1.05*1000+1000\\S_{n+2}=1.05^2*S_n+1000*(1.05^1+1)$

Extending to 3 years (n+3)

$S_{n+3}=1.05*S_{n+2}+1000=1.05(1.05^2*S_n+1000*(1.05^1+1))+1000\\\\S_{n+3}=1.05^3S_n+1.05*1000*(1.05^1+1)+1000\\\\S_{n+3}=1.05^3*S_n+1000*(1.05^2+1.05^1+1)$

Extending to 4 years (n+4)

$S_{n+4}=1.05*S_{n+3}+1000=1.05*(1.05^3*S_n+1000*(1.05^2+1.05^1+1))+1000\\\\S_{n+4}=1.05^4S_n+1.05*1000*(1.05^2+1.05^1+1))+1000\\\\S_{n+4}=1.05^4S_n+1000*(1.05^3+1.05^2+1.05^1+1.05^0)$

We can now express a general equation for S_n (salary at n years from 2017)

$S_n=1.05^nS_0+1000*\sum_{0}^{n-1}1.05^n$

The salary at 25 years from 2017 (n=25) will be

$S_{25}=1.05^{25}S_0+1000*\sum_{0}^{24}1.05^i\\\\S_{25}=3.386*50000+1000*47.72=217044.85$

8 0

4 years ago