551.985 in expanded notation

Answer:

The length is 10 inches, and the width is 4 inches.

By creating a quadratic equation using the known facts and algebra, we can determine that the dimensions of the rectangle with an area of 40 square inches are length= 10 inches and width= 4 inches.

This problem is a classic example of using algebra to solve for unknown dimensions. Given that the area (A) of a rectangle equals its length (L) times its width (W), written as A = L x W, you can substitute the given values into this formula. You're told the length is 6 inches longer than the width, which you can denote in algebra as L = W + 6. Secondly, you're given that the area is 40 square inches. Substituting these values gives us the following equation: 40 = W(W + 6).

Solving this equation will give us the width, and substituting the width into the formula L = W + 6, gives us the length.

First, distribute the width on the right side of the equation to get 40 = W^2 + 6W. Re-arranging terms gives W^2 + 6W - 40 = 0. Factoring this quadratic equation yields (W - 4)(W + 10) = 0. Setting each factor equal to zero and solving for W gives W = 4 and W = -10. Because a width cannot be negative, the width of the rectangle is 4 inches. Substituting W = 4 into the length equation results in L = 4 + 6 = 10 inches. Hence, the dimensions of the rectangle are Length = 10 inches and Width = 4 inches.

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Each of Tasha's friends receives one-quarter (¼) of the whole snack after she eats half and divides the remainder equally between them.

To determine what portion of the whole snack each of Tasha's two best friends gets, let's first understand the portions.

Tasha eats half of the snack, leaving the other half to be shared equally between her two friends.

Since there are two friends, the remaining half is divided into two equal parts.

Mathematically, when the remaining half (½) of the snack is divided equally among two people, this half is further divided by 2, which is the same as multiplying by ½ (since dividing by a number is the same as multiplying by its reciprocal).

So, the calculation would be ½ (remaining portion) × ½ (each friend's share) = ¼.

Therefore, each of Tasha's friends gets one-quarter (¼) of the whole snack.

We can visualize this through a drawing not included here, but imagine a circle (representing the snack) divided into 4 equal parts. Tasha eats 2 parts (half), and each friend gets 1 part (one-quarter).

The portion of the whole snack each friend gets is 1/4

What portion of the whole snack does each friend get?

From the question, we have the following parameters that can be used in our computation:

Proportion eaten = 1/2

Proportion to friends = 1/2

There are  2 friends

So, the portion of the whole snack each friend gets is

Each friend = 1/2 ÷ 2

Rewrite as

Each friend = 1/2 * 1/2

Evaluate

Each friend = 1/4

Hence, the portion of the whole snack each friend gets is 1/4

Answer:

x = 5

Step-by-step explanation:

Screenshot below will explain the answer

Answer:

nineteen and thirty - eight hundredths

Step-by-step explanation:

The total cost Abe needs to pay is the cost of one loaf, which is $2.50. Hence, the correct answer is $2.50.

Let's solve this question step by step:
Step 1: We know Abe has a coupon that allows him to buy one loaf and get the second free.
Step 2: The cost of a single loaf of bread is given as $2.50.
Step 3: As per the coupon, if Abe buys two loaves of bread, he is only required to pay for one. This means he needs to pay for one loaf only.
Step 4: Therefore, the total cost Abe needs to pay is the cost of one loaf, which is $2.50.
Hence, the correct answer is $2.50.

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Answer:

35000

Step-by-step explanation:

Multiply 7 by 5 and you would get 35, then add the zeros

Answer:

70*500= 35000

Step-by-step explanation:

Hey!

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Answer:

w = -12 or w = 12

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Explanation:

The lines on each side of the w stands for "absolute value". This means that whatever number is inside the two lines is positive regarding its sign.

|12| = 12

|-12| = 12

Since the equation has the negative symbol outside the two lines, it means that the absolute value will remain negative.

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Hope This Helped! Good Luck!

Answer:4(y+6)

Step-by-step explanation: y from -9 to 9

go to wolfram math to see the graph because i cant draw it

I hope this helps you.

[tex]\text{Hello there!}\\\\\text{We're trying to find the area of the shape}\\\text{We can do this by finding the area for the different shapes, then adding}\\\text{them together}\\\\\text{We can find the area of the rectangle,} \,\,84\cdot66=5,544\\\\\text{To find the area of the half circle, we would use the equation:}\,\,A=\frac{3.14r^2}{2}\\\\\text{The radius is half of the diameter, therefore it is 33. Plug 33 in r}\\\\A=\frac{3.14(33)^2}{2}\\\\\text{Solve:}\\\\A=\frac{3.14(33)^2}{2}\\[/tex]

[tex]A=\frac{3.14(1089)}{2}\\\\A=\frac{3419.46}{2}\\\\\text{Divide by 2}\\\\A=1709.73\\\\\text{Since there's two half circles, we would add 1709.73 twice}\\\\\text{Add all the areas together}\\\\1709.73+1709.73+5,544=8963.46\\\\\large\boxed{\text{Area:}\,\,8963.46\,\,\text{m}^2}}[/tex]

Answer:

Possible values of a =  2.58 and  -6.58.

Step-by-step explanation:

Using the distance formula

√(3- 1)^2 + (-2-a)^2) = 5

(3- 1)^2 + (-2-a)^2 = 25

4 + 4a + a^2 + 4 = 25

a^2  + 4a - 17 = 0

a = [-4 +/- √(4^2 - 4*1*-17) ] / 2

a =  -2 +/- √84 / 2

a =  2.58, -6.58.

Answer:

x = 8

Step-by-step explanation:

First distribute the -2 to (x - 4), -2 × x is -2x and -2 × -4 is 8. The equation should now look like this, -2x + 8 = -8. Then subtract the positive 8 from both sides, giving you, -2x = -16. Then divide both sides by -2 and you should get 8 as your answer.

Answer: x=8

Step-by-step explanation:

-2(x-4)=-8

divide both sides

x-4=4

move constant to the right

x=4+4

add the number

x=8

I hope it helped!

Answer: S+8

Step-by-step explanation:

The score increased by 8

Let S represent the score

Increased means additional

Hence the equation is

S+8

Algebraic expression:

S = Score

S+8

Increased means add 8. Then, add 8 to the score which is "S" S would be the more common variable in which you will use here.

Answer:

x = -1 , y = -4

Step-by-step explanation by elimination:

Solve the following system:

{8 y - 5 x = -27 | (equation 1)

7 y - 8 x = -20 | (equation 2)

Swap equation 1 with equation 2:

{-(8 x) + 7 y = -20 | (equation 1)

-(5 x) + 8 y = -27 | (equation 2)

Subtract 5/8 × (equation 1) from equation 2:

{-(8 x) + 7 y = -20 | (equation 1)

0 x+(29 y)/8 = (-29)/2 | (equation 2)

Multiply equation 2 by 8/29:

{-(8 x) + 7 y = -20 | (equation 1)

0 x+y = -4 | (equation 2)

Subtract 7 × (equation 2) from equation 1:

{-(8 x)+0 y = 8 | (equation 1)

0 x+y = -4 | (equation 2)

Divide equation 1 by -8:

{x+0 y = -1 | (equation 1)

0 x+y = -4 | (equation 2)

Collect results:

Answer:  {x = -1 , y = -4

Answer:

The rocket will take 6.49 seconds to fall back to the ground

Step-by-step explanation:

* Lets explain how to solve the problem

- A rock is thrown upward from the top of  a 25 foot tower with an initial

 upward  velocity of 100 ft/sec

- That means at t = 0 the height of the rock is 25 feet above the ground

- A function of time can  be modeled by the equation:

 h(t) =  - 16t² + 100t + 25, where h is the height of the rocket from the

 ground at time t

∵ h(t) = -16t² + 100t + 25

- The height of the rocket is 25 feet above the ground when it

  is thrown up

∴ h(t) = 25 at t = 0 ⇒ initial position of the rocket

- The height of the rocket when hits the ground is zero

∴ h(t) = 0 when the rocket hits the ground ⇒ final position of it

- We need to find the time that the rocket takes to fall back to

 the ground

∵ h(t) = 0

∵ h(t) = -16t² + 100t + 25

∴ -16t² + 100t + 25 = 0

- Lets solve it to find the value of t

∵ -16t² + 100t + 25 = 0

- Multiply both sides by -1 to make the coefficient of t² positive

∴ 16t² - 100t - 25 = 0

- Use your calculator to find the values of t

∴ t = 6.49 sec and t = -0.24 sec

∵ We will reject the value of t = -0.24, because time can not be

   negative value

∴ The rocket will take 6.49 seconds to fall back to the ground

Move 5 units left and 4 units up

Final answer:

To plot the point (-5, 4) from the origin, move 5 units to the left and 4 units up in a standard Cartesian coordinate system.

Explanation:

To plot the point (-5, 4) starting from the origin in a standard Cartesian coordinate system, you would need to move 5 units left and 4 units up. This is because the x-coordinate is negative, indicating a movement to the left of the origin, and the y-coordinate is positive, indicating a movement above the origin.

The correct steps are as follows:

This method adheres to the standard convention that in an xy-coordinate system, right and up are positive directions, while left and down are negative.

7(x - 2) = 5(x + 4)

Multiply the first bracket by 7

(7)(x)=7x

(7)(-2)=-14

Multiply the second bracket by 5

(5)(x)=5x

(5)(4)=20

7x-14=5x+20

Move 5x to the other side. Sign changes from -5x to +5x.

7x-5x-14=5x-5x+20

7x-5x-14=20

2x-14=20

2x-14+14=20+14

2x=34

Divide both sides by 2

2x/2=34/2

Answer: x=17

Answer:

7(x-2)=5(x+4)

7x-14=5x+20

7x-5x=20+14

2x=34

x=17

Answer:

[tex]\frac{x^2}{9}[/tex] - 4x + 36

Step-by-step explanation:

([tex]\frac{x}{3}[/tex] - 6)² = ([tex]\frac{x}{3}[/tex] - 6)([tex]\frac{x}{3}[/tex] - 6)

Each term in the second factor is multiplied by each term in the firs t factor, that is

[tex]\frac{x}{3}[/tex]([tex]\frac{x}{3}[/tex] - 6) - 6([tex]\frac{x}{3}[/tex] - 6)

Distribute both parenthesis

= [tex]\frac{x^2}{9}[/tex] - 2x - 2x + 36 ← collect like terms

= [tex]\frac{x^2}{9}[/tex] - 4x + 36

Answer:

Part 1) The value of x is 21

Part 2 The value of y is 8

Step-by-step explanation:

step 1

Find the value of x

we know that

[tex](10x-61)\°+(x+10)\°=180\°[/tex] ------> by supplementary angles (linear pair)

[tex]11x-51=180[/tex]

[tex]11x=180+51[/tex]

[tex]11x=231[/tex]

[tex]x=21[/tex]

step 2

Find the value of y

we know that

[tex](10x-61)\°=(18y+5)\°[/tex]  ----> by vertical angles

substitute the value of x and solve for y

[tex](10(21)-61)\°=(18y+5)\°[/tex]

[tex](149)\°=(18y+5)\°[/tex]

[tex]18y=149-5[/tex]

[tex]18y=144[/tex]

[tex]y=8[/tex]

Answer:

x=21 y=8

Step-by-step explanation:

Answer:

0.0362

Because the exponent is negative, you move the decimal to the left 2 times.

Final answer:

The time to complete a load of laundry ranges from a minimum of 42 minutes to a maximum of 58 minutes, combining the shortest and longest durations for both washing and drying cycles respectively.

Explanation:

The question asks about calculating the minimum and maximum total times for completing a load of laundry, including washing and drying cycles. The minimum time for washing is 22 minutes, and the minimum time for drying is 20 minutes. Therefore, the minimum total time to complete a load of laundry is 22 + 20 = 42 minutes.

On the other end, the maximum time for washing is 28 minutes, and the maximum time for drying is 30 minutes. The maximum total time to complete a load of laundry is 28 + 30 = 58 minutes.

In conclusion, the entire process of doing laundry, including both washing and drying, takes between 42 and 58 minutes in total.

[tex]\huge\boxed{\text{1. False}}[/tex]

Integers are the numbers in the set [tex]{..., -3, -2, -1, 0, 1, 2, 3, ...}[/tex]. This means that you can add two opposite integers to get [tex]0[/tex].

For example, [tex]-3+3=0[/tex].

[tex]\huge\boxed{\text{2. True}}[/tex]

When you add a negative number to another negative number, the only thing that can happen is that the result goes down.

For example, [tex](-3)+(-2)\ =\ -3-2\ =\ -5[/tex].

[tex]\huge\boxed{\text{3. 6}}[/tex]

Let's write this as an equation, where [tex]x[/tex] represents the unknown value. [tex]-6+x=0[/tex]

We need to isolate the variable by adding [tex]6[/tex] on both sides of the equation. [tex]x=\boxed{6}[/tex]

Answer:

1) false example -1+1=0

2) true

3) 6

Final answer:

Upon examining the prices of the three cars and calculating the potential original price before rounding, we find that all three cars could have a maximum price change of £49 when rounded to the nearest £100. Therefore, all cars have the same greatest potential change in price.

Explanation:

To determine which car's price changes by the greatest amount when rounded to the nearest £100, we need to consider the possible original prices before rounding. The original price could be up to £49 above or £50 below the rounded price, as values are rounded up when they reach the halfway point (£50).

Car A

Price: £12,380. Possible price range before rounding: £12,350 to £12,429.

Car B

Price: £16,760. Possible price range before rounding: £16,750 to £16,809.

Car C

Price: £14,580. Possible price range before rounding: £14,550 to £14,629.

Now, we must calculate the maximum changes in price. The greatest amount of change occurs when the original price is at the extreme end of the range.

With each car having a possible maximum change of £49, it means that all cars could potentially have the same greatest amount of change.

Answer:

64-5 divided by 64-3 is 59 divided by 61. 59

8 squared is equal to 64.                           -----

                                                                     61

Step-by-step explanation:

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{8^{-5}}{8^{-3}}\implies \cfrac{1}{8^{-3}\cdot 8^5}\implies \cfrac{1}{8^{-3+5}}\implies \cfrac{1}{8^2}\implies \cfrac{1}{64}[/tex]

Answer:

- 1050

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], thus

[tex]S_{20}[/tex] = [tex]\frac{20}{2}[/tex] [ (2 × - 74) + (19 × - 3) ]

= 10 ( - 148 - 57) = 10 × - 105 = - 1050

Answer:

16 pizza's

Step-by-step explanation:

you multiple 8 x 2 which is 16

Answer:

5/8

Step-by-step explanation:

0.625

625/1000

125/200

25/40

5/8

Answer:

there are many possible answers, but some samples are 625/1000, 125/200, 25/40, and 5/8.

Step-by-step explanation:

I just turned the decimal into a fraction using a simple method where, say, if the decimal went to the thousandths place value, like this one does, we put the decimal over 1000. If the number goes to the hundredths place, we put it over 100, etc. Then I simplified it a few times (by dividing both the numerator and denominator by 5) to get some more equivalent fractions (although you could multiply upwards and get fractions like 3125/5000 which would still be equivalent because I multiplied both the numerator and denominator, though that's besides the point) and ended up with the fully simplified fraction of 5/8.

Hope this helps! :3

The simplified equation from the given 3x + 9 + 4x + x = _x + _ is 8x + 9 = _x + _. This equation cannot be solved further without the values for the variables represented by the underscores.

The first step to solving the equation is to simplify it. Your original equation is 3x + 9 + 4x + x = _x + _. When we simplify the left side of the equation by combining like terms we get 8x + 9 = _x + _. However, the variables in the blanks on the right side of equation are unknown, so we can't solve it fully. But now you have a simpler equation to work with, and if you receive any additional information, you can substitute those values into your simplified equation.

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Answer:

6<x>54 ASK YOUR TEACHER

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Let's see...

It's a cube, so the total volume will be one length cubed or 10^3 which is 1000.

(2500 g)/(1000 cm^3) = [tex]2.5 g/cm^3[/tex]

I'm pretty sure the answer is A because it's the only one with correct scientific notation.