Which measurement is the best estimate for the length of a clothespin?

9 cm
9 km
9 mm
9 m

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:

Ok this is multiplication so its 30.25

Step-by-step explanation:

5.50 X 5.50 = 30.25

Answer:

25

Step-by-step explanation:

180-130=50

50/2=25

Answer:

x = 25 degrees

Step-by-step explanation:

the figure is an isosceles triangle

x + x + 130 = 180

2x + 130 = 180

2x = 180 - 130

2x = 50

x = 25 degrees

Answer:

[tex]f(x) = -3x+4[/tex]

Step-by-step explanation:

We can use the form [tex]y=mx+b[/tex] to find the linear function.

From [tex]f(2)=-2[/tex] , we can write:

[tex]-2=2m+b[/tex]

From [tex]f(1)=1[/tex] , we can write:

[tex]1=m+b[/tex]

To find for [tex]m[/tex], we can substract the second equation from the first:

[tex]2m+b-(m+b) = -2-1[/tex]

[tex]2m+b-m-b=-3[/tex]

[tex]m=-3[/tex]

To find for [tex]b[/tex], we can use substitution:

[tex]1 = m+b[/tex]

[tex]1 = -3+b[/tex]

[tex]b=4[/tex]

∴ [tex]f(x) = -3x+4[/tex] is the linear function.

Hope this 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:36+2 divided by x=A

Step-by-step explanation:

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:

$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:

-y=5-x

Step-by-step explanation:

Answer:

f(2) = -3

Step-by-step explanation:

This is the answer because:

1) The question is basically asking what the y-cordinate is.

2) In order to find the y-cordinate, look at the graph and find where 2 is on the x-axis. Then, see wheree the y-coordinate is on the same line a the x-cordinate which is 2.

3) When you line up the cordinates, you can see that where x is 2, y is -3.

Therefore, the answer is -3.

Hope this helps! :D

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:

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

do eat popcorn in a tub

:)

poopy face

Answer:

20

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

:P

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:

18

Step-by-step explanation:

so all you have to do is divide 54 by 3

Answer:

Concept: Mathematical Representation

Answer:

there are a total of 120 + 96 = 216, 5 digit numbers divisible by '3' that can be formed using the digits 0 to 5.

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:

16.27

Step-by-step explanation:

if 1000m rep 1km

therefore :

58.6km/h in ms = 58.6km×1000/3600

=16.277 ms

Answer:

multiple choice?

Step-by-step explanation:

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:

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:

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:

64 cupcakes

Step-by-step explanation:

Tray 1 = 2 cupcakes

Tray 2 = 4 cupcakes

Tray 3 = 8 cupcakes

Tray 4 = 16 cupcakes

Tray 5 = 32 cupcakes

Tray 6 = ?

This is a geometric progression

First term, a = 2

Common ratio, r = 4/2

= 2

6th term = ar^n-1

= 2 × 2^6-1

= 2 × 2^5

= 2 × 32

= 64

The 6th tray will have 64 cupcakes

Answer:

49

Step-by-step explanation:

28-21=7

7 to the power of two is the same as 7(7)

7(7)=49