Nancy and bill collect coins. Nancy has x coins. Bill has 6 coins fewer than times the number of coins nancy has. Write and simplify an expression for the total number of coins nancy and bill have

Answer:

d ≈ 6.41

Step-by-step explanation:

Given that F is inversely proportional to d² then the equation relating them is

F = [tex]\frac{k}{d^2}[/tex] ← k is the constant of proportion

To find k use the condition when F = 8, d = 6 , then

8 = [tex]\frac{k}{6^2}[/tex] = [tex]\frac{k}{36}[/tex] ( multiply both sides by 36 )

288 = k

F = [tex]\frac{288}{d^2}[/tex] ← equation of proportion

When F = 7 , then

7 = [tex]\frac{288}{d^2}[/tex] ( multiply both sides by d² )

d² × 7 = 288 ( divide both sides by 7 )

d² = [tex]\frac{288}{7}[/tex] ( take the square root of both sides )

d = ± [tex]\sqrt{\frac{288}{7} }[/tex] ≈ ± 6.41

The positive value of d is 6.41 ( to 2 dec. places )

Answer:

when F = 7, d = 6.41

Step-by-step explanation:

We know that when 'y' varies inversely with 'x', we get the equation

y ∝ 1/x

y = k/x

where 'k' is called the constant of proportionality

Given that F is inversely proportional to d.

F ∝ 1/d

F = k /d²

When F = 8, d = 6, we need to find k

k = Fd²

k = 8×(6)²=288

Now, we need to find d when F = 7

so substitute k = 288, F = 7 in the equation

F = k /d²

d² = k/F

d² = 288/7

[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]d=\sqrt{\frac{288}{7}},\:d=-\sqrt{\frac{288}{7}}[/tex]

but, we need to take the positive value of d, so

[tex]d=\sqrt{\frac{288}{7}}[/tex]

[tex]d=6.41[/tex]

Therefore,

when F = 7, d = 6.41

Answer:

D

Step-by-step explanation:

(3, 9) (-3, 5)

 0 is in the middle       7 is in the middle

for x: 3 2 1  0  -1 -2 -3   for y: 9 8  7  6 5

Thus, (0, 7) is the midpoint between (3, 9) and (-3, 5)

Answer:

16.27

Step-by-step explanation:

if 1000m rep 1km

therefore :

58.6km/h in ms = 58.6km×1000/3600

=16.277 ms

Answer:

18

Step-by-step explanation:

so all you have to do is divide 54 by 3

Answer:

do u go to dutchtown

Step-by-step explanation:c

Answer:

Ok this is multiplication so its 30.25

Step-by-step explanation:

5.50 X 5.50 = 30.25

Answer:

D

Step-by-step explanation:

To find the system of equations that is satisfied by the solution shown on the graph, we will simply need to find the equations of our two lines.

So, we will begin by finding the slope of each line and then proceed to find the entire equation.

Red Line:

To find the slope, we will first pick any two points from the red line.

Two sample points include (-5, 5) and (-4, 6).

The slope formula is given by:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Lett (-5, 5) be (x₁, y₁) and (-4, 6) be (x₂, y₂). Substitute:

[tex]\displaystyle m=\frac{6-5}{-4-(-5)}=\frac{1}{1}=1[/tex]

Hence, the slope of the red line is 1.

Now, we can find the entire equation. We will use the slope-intercept form:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

We know that the slope m is 1. Hence:

[tex]y=x+b[/tex]

We need to find our y-intercept b. For the red line, we know that when x is -5, y is 5. Hence:

[tex](5)=(-5)+b[/tex]

Solving for b yields:

[tex]b=10[/tex]

Therefore, our entire equation is:

[tex]y=x+10[/tex]

Blue Line:

Again, we will find the slope first.

Picking two points, we get (0, 6) and (1, 5).

Using the slope formula by letting (0, 6) be (x₁, y₁) and (1, 5) be (x₂, y₂), we acquire:

[tex]\displaystyle m=\frac{5-6}{1-0}=\frac{-1}{1}=-1[/tex]

Hence, the slope of the blue line is -1.

Again, we can use the slope-intercept form:

[tex]y=mx+b[/tex]

Fortunately, we already know the y-intercept in this case. Since we have the point (0, 6), the y-intercept b is 6.

Therefore, our equation is:

[tex]y=-x+6[/tex]

So, our two equations are:

[tex]y=x+10\text{ and } y=-x+6[/tex]

Our answers are in standard form, so we will convert the two equations to standard form. Standard form is given by:

[tex]Ax+By=C[/tex]

Where A, B, and C are integers and A is positive.

For the first equation, we can subtract x from both sides to get:

[tex]-x+y=10[/tex]

Since A should be positive, we multiply both sides to get:

[tex]x-y=-10[/tex]

For the second equation, we can add x to both sides:

[tex]x+y=6[/tex]

Hence, our two equations in standard form is:

[tex]x+y=6\text{ and } x-y=-10[/tex]

Therefore, our final answer is D.

Answer: D x + y = 6 and x − y = -10

Step-by-step explanation:

Answer:36+2 divided by x=A

Step-by-step explanation:

Step-by-step explanation:

f(x) = 9 - 2|x + 2|

When x = 7, f(-7) = 9 - 2|(-7) + 2|

= 9 - 2|(-5)|

= 9 - 2(5)

= 9 - 10

= -1.

9514 1404 393

Answer:

  -1

Step-by-step explanation:

Put -7 where x is and do the arithmetic.

 f(-7) = 9 -2|-7+2|

  = 9 -2|-5| = 9 -2·5 = 9 -10

  f(-7) = -1

Answer:

Becky is 5 1/4 ft tall

Answer:

It's option B

= - 1/3 -(-5/12)

= - 1/3 +5/12

Because minus and minus is plus

- - = =

Hope it's help ^_^

Answer:

0.01809955% or about 0.018%

Step-by-step explanation:

You do the multiplication of 4/52 by 3/51 by 2/50

Answer:

I agree with both.

Step-by-step explanation:

If it's $3 per dozen that would be $0.25 per muffin because

3÷ 12 = 0.25

And if Andre has $2 than he can only afford 8 muffins because

0.25 x 8 = 2

And if Elena wants 16 muffins

16 x 0.25 = 4

So she will have to pay $4.

Hope this makes sense and helps!

Answer:

The value of uxd=4

Step-by-step explanation:

since  y=u, y=d, y=y

y=1/2 and 8

2y-1=0

2y=1

y=1/2

8-y=0

8=y

1/2*8=4

Answer:

4

Step-by-step explanation:

0=(2y−1)(8−y)

Using the zero product property

2y-1 =0    8-y =0

2y =1     8=y

y =1/2  y= 8

Let y=u, y=d

u = 1/2    d = 8

We want the value of u*d

u*d = 1/2 *8 = 4

Answer:

$6.50 per candle

Step-by-step explanation:

19.50 / 3 = 6.50

Answer:

$6.50

Step-by-step explanation:

$19.50 divided 3 is 6.50

Answer:

a−4b

Step-by-step explanation:

=4a+−6b+−3a+2b

Combine Like Terms:

=4a+−6b+−3a+2b

=(4a+−3a)+(−6b+2b)

=a+−4b

I like your cut g ;)

Answer:

63+48= 3(21+16)

Step-by-step explanation:

Check answer:

Distribute 3(21+16)

3(21)+3(16)

63+48

#19 - amphibians do not produce amniotic eggs. Therefore they must lay their eggs in water so they don't dry out

Answer:

-y=5-x

Step-by-step explanation:

Answer:

wait wut!!!?????????

Step-by-step explanation:

i hope this helps you somehow

Answer:

Concept: Mathematical Representation

Answer:

70,000

Step-by-step explanation:

Answer:

The correct answer is 73,000.

Step-by-step explanation:

This is because, we know that the number 7 or 70,000 represents the ten-thousands in this number. Therefore, the number 2 or 2,000 represents the thousands place, which is what we are trying to round.

In order to do so, we have to look at the number behind it, which, in this case, is 6.

Rule: If the number is 4 or less, the number before it stays the same. If the number is 5 or more, the number before it goes up 1.

Since 6 is larger than 5, the 2 will become a 3, while the other numbers become 0s.

Therefore, the correct answer is 73,000.

Hope this helps! :)

Answer:   36/[tex]K^{2}[/tex]

Step-by-step explanation:

The k on top will cancel the k to the second power.

So the only number in the numerator is 1.

Then the 1 qill go away because you cant divide anything by 1.

The expoenet -2 that was at the top near K will become positive.

Then distribute

Answer:

216$

Step-by-step explanation:

Answer:

41.2%

Step-by-step explanation:

[tex]Percentage\ change = (\frac{Final\ Price\ - Initial\ Price}{Final\ Price})100\\\\Percentage\ change=(\frac{238-140}{238})100\\\\Percentage\ change=(\frac{98}{238})100\\\\Percentage\ change=(0.412)100\\Percentage\ change=41.2\\[/tex]

So the percentage increase was 41.2%

Answer:

12 weeks

Step-by-step explanation:

Make an inequality equation with x being the number of weeks:

200 > 500 - 25x

*subtract 500 from both sides*

-300 > -25x

*divide both sides by -25*

12 > x