A spring with spring constant 0.5 m has a force of 40 newtons applied to it. How much does the spring
stretch? Use Hooke's law F = kx
N
O A 1,600 cm
OB. 100 cm
O C. 80 cm
O D. 40 cm

Answer:

Step-by-step explanation:

The area of the wall is the sum of the areas of the different sections of the wall. The cost to paint it will be the product of the cost of a tin of paint and the number of tins required.

__

Here, the shape of the wall can be divided into two trapezoids and a rectangle. Each shape has a corresponding area formula. Left-to-right, their areas are ...

Left Trapezoid

  A = 1/2(b1 +b2)h

  A = 1/2(10 m +11 m)(4 m) = 42 m²

Middle Rectangle

  A = LW

  A = (13 m)(11 m) = 143 m²

Right Trapezoid

  A = 1/2(b1 +b2)h

  A = 1/2(11 m +8 m)(10 m) = 95 m²

Wall Area

The total area to be painted is the sum of the above areas:

  total area = 42 m² +143 m² +95 m² = 280 m²

The area that needs to be painted is 280 m².

__

A tin of paint covers 15 m², so the number of tins needed is ...

  (15 m²)t = 280 m²

  t = 280/15 = 18 2/3 . . . . . . divide by the coefficient of t

We can only buy whole tins, so we need to buy 19 tins. Their cost will be ...

  (£7 /tin)(19 tins) = £133

It will cost £133 to paint the wall.

Answer: [tex]\frac{6}{5}[/tex]x + 6

Step-by-step explanation:

       We will use the order of operations, also known as PEMDAS. See attached. Please note that we cannot do what is in the parentheses first because we have a variable, so we will distribute the 2 into it. Since this is an expression, I do not believe we can fully solve for x, but can only simplify.

       Given:

2(3/5x+3)

       Distribute:

2 * (3/5x) + (2 * 3)

6/5x + 6

       Answer:

[tex]\frac{6}{5}[/tex]x + 6

Answer:

Late because 12 were on time so 5 would be late

Answer:

28620

Step-by-step explanation:

→ Find the multiplier

( 100 + 6 ) ÷ 100 = 1.06

→ Multiply by the original amount

27000 × 1.06 = 28620

Answer:

66

Step-by-step explanation:

It's given that

Tn = 5n + 16

The 10th term is

T10 = 5(10) + 16

= 66

The 10th term of the sequence is 66.

In mathematics, a sequence is a list of numbers arranged in a specific order. Each number in the sequence is called a term. Sequences can be finite, meaning they have a specific number of terms, or they can be infinite, continuing indefinitely.

We have the rule: 5n + 16

Now, To find the 10th term of the sequence, we can substitute n = 10 into the given rule:

5n + 16 = 5(10) + 16 = 50 + 16 = 66

Therefore, the 10th term of the sequence is 66.

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The number of marbles in the bag illustrates probability

The conclusion about the number of marbles in the bag is that the bag can only contain one type of marble

The probabilities are given as:

P(Red) = 1

P(Green) = 1

For a distribution, the sum of all probabilities must equal to 1.

This means that:

P(Red) + P(Green) = 1

So, we have:

1 + 1 = 1

This gives

2 = 1

The above equation is false because 2 does not equal to 1.

So, the conclusion about the number of marbles in the bag is that the bag can only contain one type of marble i.e. either red marbles are in the bag or blue marbles are in the bag

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Answer:

Step-by-step explanation:

Finding the angles of quadrilateral:

Sum of all angles of quadrilateral = 360

2x + 10 + 3x + 3x + 5 + 5x +20 =360

2x + 3x + 3x + 5x + 10 + 5 + 20 = 360

Combine like terms

                    13x + 35 = 360

Subtrace 35 from both sides

                            13x = 360 - 35

                           13x  = 325

Divide both sides by 13

                               x = 325/13

                               x = 25

5x +20 = 5*25 +20

            = 125 +20

             = 145°

Measeure of largest angle : 145°

Answer:

p = 4

Step-by-step explanation:

Given equation:

[tex]x^2+(p-3)y^2-4x+6y-16=0[/tex]

Standard equation of a circle:

[tex](x-a)^2+(y-b)^2=r^2[/tex]

(where [tex](a,b)[/tex] is the centre of the circle, and [tex]r[/tex] is the radius)

If you expand this equation, you will see that the coefficient of [tex]y^2[/tex] is always one.

Therefore, [tex]p-3=1[/tex]

[tex]\implies p=1+3=4[/tex]

Additional information

To rewrite the given equation in the standard form:

[tex]\implies x^2+y^2-4x+6y-16=0[/tex]

[tex]\implies x^2-4x+y^2+6y=16[/tex]

[tex]\implies (x-2)^2-4+(y+3)^2-9=16[/tex]

[tex]\implies (x-2)^2+(y+3)^2=16+4+9[/tex]

[tex]\implies (x-2)^2+(y+3)^2=29[/tex]

So this is a circle with centre (2, -3) and radius √29

The length of the hypothenuse or the value of x is equal to 19.53

This is a right angle triangle and since we have a missing side, we should list our data first and find an option to solve this.

Data;

To solve this problem, we have to use Pythagoras's theorem which is used to find the missing side in a right angle triangle if we have at least two sides.

The formula for this is

x^2 = y^2 + z^2

Let's substitute the values and solve for the missing side.

[tex]x^2 = 16^2 + 11.2^2 \\x^2 = 256 + 125.44\\x^2 = 381.44\\x = \sqrt{381.44} \\x = 19.53[/tex]

The length of the hypothenuse or the value of x is equal to 19.53.

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Answer:

What's the complex name

Pd(co2) (me3p)2

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =80 \end{cases}\implies \begin{array}{llll} A=\cfrac{(80)\pi (8)^2}{360}\implies A=\cfrac{128\pi }{9} \\\\\\ A\approx 44.68~in^2 \end{array}[/tex]

Answer:

∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE  are the additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS.

The additional information to prove that ΔXYZ ≅ ΔFEG using ASA or AAS

is ∠Z ≅ ∠G and XY ≅ FE

Option E is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

ΔXYZ ≅ ΔFEG

We see that,

∠X and ∠F are equal

To prove that ΔXYZ ≅ ΔFEG using ASA or AAS.

We need one more congruent angle and one corresponding side.

∠Z ≅ ∠G and XY ≅ FE can be used to prove this.

Now,

∠X = ∠F (angle)  (given)

∠Z ≅ ∠G (angle)

XY ≅ FE (side)

ΔXYZ ≅ ΔFEG

Thus,

The additional information is:

∠Z ≅ ∠G and XY ≅ FE

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Answer:

14.28%

Step-by-step explanation:

I'm not sure if it's right but this is how I worked it out,

the box's contents are 4.2 pounds in total,

therefore in a fraction it would be 6/42

you turn a fraction into a percentage you do the numerator divided by the denominator

6÷42=0.142857(decimal form)

now you just turn it into a percentage

14.28%

please correct me if I'm wrong

Answer:

-2.1

Step-by-step explanation:

its a 0.1 step.

hope you understand

Answer:

Set 1: 6

Set 2: 4.5

Step-by-step explanation:

To find the mean you would add them all up and divide by the total number of points, found by counting the x's. You have one 4; three 5's, two 6's, three 7's, and one 8. You would then add this up. This adds up to 60, and there are 10 points. The mean for set one is 6.

Repeat this process for set b. For this one you would get 4.5

The equation that can be used to determine when each cooler would contain the same amount of water is 2.5 = 0.75t.

Equation that can be used to determine the amount of water in the first cooler at time t : 4.5 + 0.1t

Equation that can be used to determine the amount of water in the second cooler at time t : 7 + 0.25t

Where t represents seconds

When they have the same amount of water, the two above equations would be equal

4.5 + 0.1t = 7 + 0.25t

Combine similar terms

7 - 4.5 = 0.1t - 0.25t

2.5 = 0.75t

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Answer:

16

Step-by-step explanation:

Use the method of PEMDAS (Parenthesis, Exponent, multiplication, division, addition and then subtraction.)

When using this order you would do 10-9 first

23 + 5 * (10-9) - 12

23+ 5 * 1 - 12

then 5 times 1

23 + 5 * 1 - 12

23 + 5 - 12

then 23 + 5 and subract 12 from the solution

23 + 5 - 12

28 - 12 =

16

Answer:

3861444226895040

Step-by-step explanation:

You do not want to know.

Answer:

~6.534653% of randomly selected a book from his bag (I don't know how many decimals you need)

Step-by-step explanation:

Basically you just do (66 (books) /1010 (total items)) * 100 to find your answer because out of the total 1010 items in that bag there is only 66 that are books so its (66/1010)*100 to find your answer, the *100 is added to find the percentage.

Answer:  Choice C

The fraction 1/16

In other words the "StartFraction 1 Over 16 EndFraction"

=============================================================

Work Shown:

[tex]\displaystyle L = \lim_{x \to -2}4^x\cos(\pi x)\\\\\\L = 4^{-2}\cos(\pi (-2))\\\\\\L = \frac{1}{4^2}\cos(-2\pi)\\\\\\L = \frac{1}{16}\cos(2\pi)\\\\\\L = \frac{1}{16}(1)\\\\\\L = \frac{1}{16}\\\\\\[/tex]

The limit of the function f(x)=[tex]4^{x}[/tex]cos(πx) is 1/16 which is start fraction 1 over 16 end fraction.

The limit is the extent to which the value of function exists.

The function which is given is f(x)=[tex]4^{x}[/tex]cos(πx) and we have to find the limit of f(x).

L.H.L of f(x)

[tex]\lim_{x \to \-2} 4^{x}cos([/tex]πx)

Put x=-2-h

[tex]\lim_{h \to \0} 4^{-2-h}cos([/tex]π(-2-h)

put h=0

=[tex]4^{-2} cos(2[/tex]π)

=[tex]4^{-2}*1[/tex]  {cos(2π)=1}

=1/16

R.H.L of f(x)

[tex]\lim_{x \to \-2} 4^{x}[/tex] cos(πx)

Put the value of x=-2+h

=[tex]\lim_{h \to \0}4^{-2+h}[/tex] cos{π(-2+h)}

Put the value of h=0

=[tex]4^{-2}*cos(2[/tex]π)

=1/16

L.H.L=R.H.L

Hence the limit of the function [tex]4^{x}cos([/tex]πx) is 1/16.

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The voltage difference for an outlet will be 140 volts.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

For an outlet,

Current (I) = 10 ampere

Resistance (R) = 14 ohms

Now,

Since, We know that;

The current is the ratio of the potential difference and resistance.

That is,

⇒ I = V / R

⇒ V = I R

Thus, Substitute all the values, we get;

⇒ V = I R

⇒ V = 10 x 14

⇒ V = 140 Volts

Therefore, The voltage difference for an outlet will be 140 volts.

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Answer:

5/18

Step-by-step explanation:

Here,

total numbering balls n(S) = 18

total number of winning balls n(B) = 5

Therefore,

Probability or winning chances P(B)=

n(B)/n(S)

= 5/18

Not sure about Angle. 13

Answer:

6 * 1.2 = 7.2

7 * 1.2 = 8.4

8 * 1.2 = 9.6

now find the Area and Perimeter of the enlarged triangle:

A = 1/2bh

A = 1/2 * 9.6 * 8.4

A = 40.32

P = a + b + c

P = 7.2 + 7.2 + 9.6

P = 24

So, the Area is 40.32 and the Perimeter is 24.

Answer:

7AM was 8PM for a few days but 3the 3only 3and 3and 3and 3was is a little too much to me because I am not a fan of the cold and cold 4th

Answer: D. Subtraction property of equality

Step-by-step explanation:

They are subtracting 6 from both sides of the equality.

Answer:

look it up

Step-by-step explanation:

The solution of system of equations is (3.5, 3.5).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

1) 1/2 (12x+8) -1/3 (24)=1/4 (16x+40)

6x+4-8=4x+10

6x-4=4x+10

6x-4x=10+4

2x=14

x=7

Therefore, the value of x is 7.

3) y=3x-7 -------(i) and -y=x-7 -------(ii)

Substitute equation (i) in equation (ii), we get

-(3x-7)=x-7

-3x+7=x-7

x+3x=7+7

4x=14

x=14/4

x=3.5

Substitute x=3.5 in equation (i), we get

y=3×3.5-7

y=10.5-7

y=3.5

So, the solution is (3.5, 3.5)

4) Production of chairs from Anthony

(2, 10) and (5, 25)

Here, m=(25-10)/(5-2)

= 15/3

= 5

Substitute m=5 and (x, y)=(2, 10) in y=mx+c, we get

10=5(2)+c

c=0

Substitute m=5 and c=0 in y=mx+c, we get y=5x

Production of chairs from Billy

(1, 2) and (4, 8)

Here, m=(8-2)/(4-1)

= 6/3

= 2

Substitute m=2 and (x, y)=(1, 2) in y=mx+c, we get

2=2(1)+c

c=0

Substitute m=2 and c=0 in y=mx+c, we get y=2x

When y=18

Production of chairs from Billy 18=5x

x=3.6

When y=18

Production of chairs from Anthony

18=2x

x=9

Therefore, the solution of system of equations is (3.5, 3.5).

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Answer:2x+(x+17)+(x-21)=180

Step-by-step explanation:

Angles in a triangle add to 180 degrees.

The equation that can be used to find the measure of each angle is 2x + x + 17 + x - 21 = 180

The given parameters are:

P = 2x

Q = x + 17

R = x - 21

The sum of angles in a triangle is 180.

So, we have:

P + Q + R = 180

Substitute known values

2x + x + 17 + x - 21 = 180

Hence, the equation that can be used to find the measure of each angle is 2x + x + 17 + x - 21 = 180

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