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Example 2
17. OLYMPICS in the 2010 Winter Olympic Games, the
Winter Olympic Games, the United States won 1 more than
4 times the number of gold medals France won. The
old medals France won. The United States won 7 more
gold metals than France. Write and solve an equation
ce. Write and solve an equation to find the number of gold
medals each country won.

Final answer:

By rearranging the formula for the volume of a box to solve for width and substituting the given values, the width of the box is calculated to be 5 inches.

Explanation:

The student asks what the width of the box is, given that the volume of the box is 400 cubic inches (in³), the height is 10 inches (in), and the length is 8 inches (in). The formula to find the volume of a rectangular box is V = l × w × h, where V is the volume, l is the length, w is the width, and h is the height. Since we already have the volume, length, and height, we can rearrange the formula to solve for the width w as follows: w = V / (l × h). Substituting the given values, we get w = 400 in³ / (8 in × 10 in), which simplifies to w = 400 in³ / 80 in². After dividing 400 by 80, the result is w = 5 in. Therefore, the width of the box is 5 inches.

Answer:

c

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

x + y = 4 or y = -x + 4

Step-by-step explanation:

0 = -1[4] + b

4 = b

y = -x + 4

If you want it in Standard Form:

y = -x + 4

+x +x

_________

x + y = 4 >> Line in Standard Form

* Since the rate of change [slope] is -1 and that parallel lines have SIMILAR SLOPES, -1 remains the same.

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Good evening ,

___________________

Step-by-step explanation:

AO=[tex]\sqrt{p^{2}+q^{2} }[/tex]

AB=[tex]\sqrt{( p+2q-p)^{2} + (q+2p-q)^{2}[/tex]

=[tex]\sqrt{(2q)^{2}+(2p)^{2} }[/tex]

=[tex]\sqrt{4(q^{2}+p^{2} ) }[/tex]

=[tex]2\sqrt{p^{2}+q^{2} }[/tex]

=2AO.

:)

To find out the volume of water leaked per day by a leaking faucet, we convert the given rate from milliliters per minute to gallons per day. The faucet leaks at a rate of 4.2 milliliters per minute. By multiplying this rate by the number of minutes in a day, we find that it leaks 6048 milliliters per day. After converting milliliters to liters and liters to gallons using conversion factors, we determine that the faucet leaks 1.57328 gallons of water per day.

To find out how many gallons of water the faucet leaks per day, we need to determine the volume in milliliters and convert it to gallons. The given rate is 4.2 milliliters per minute, so we need to find the number of minutes in a day. There are 60 minutes in an hour and 24 hours in a day, so there are 60 x 24 = 1440 minutes in a day.

Multiplying the rate by the number of minutes in a day, we get 4.2 x 1440 = 6048 milliliters per day. To convert milliliters to liters, we divide by 1000, so 6048 / 1000 = 6.048 liters per day. Finally, to convert liters to gallons, we multiply by the conversion factor 0.26, resulting in 6.048 x 0.26 = 1.57328 gallons per day.

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Answer:

See explanation

Step-by-step explanation:

A dog owner records the weight of her dog. She finds that from the age of 20 weeks to the age of 48 weeks, the dog’s weight can be modelled by the equation

[tex]w = 0.92t-0.15\ \ \ (20\le t\le 48)[/tex]

where

w = weight

t = number of week from 20 weeks to 48 weeks

If we want to extend this model to the dog's weight at birth, then find the dog's weigth when it was born.

At t = 0,

[tex]w=0.92\cdot 0-0.15\\ \\w=-0.15\ kg[/tex]

We get the dog's weight -0.15 kilograms at the day the dog was born. But this is impossible, because the dog's weight cannot be negative.

The model cannot predict the dog's weight at birth due to negative values and unrealistic linear growth for early development.

The equation w = 0.92t - 0.15 describes the weight of the dog as a function of time t in weeks, specifically for the age range of 20 weeks to 48 weeks. When t is set to 20 weeks, we can calculate the weight:

w = 0.92(20) - 0.15

= 18.4 - 0.15

= 18.25 kg.

However, if we try to extend this model to predict the dog's weight at birth (t = 0 weeks), we would get:

w = 0.92(0) - 0.15

= -0.15 kg.

A negative weight is nonsensical in this context, as animals cannot have negative weight. Moreover, the biological growth of a dog does not follow a linear pattern from birth to maturity. The model is designed to represent a specific growth phase after the initial rapid growth and development that occurs in the early weeks of life.

Growth models typically start with an exponential phase during early life, which cannot be accurately captured by a linear equation.

Answer:

949 centimeters

Step-by-step explanation:

100 centimeters = 1 meter

We have to multiply by 100 to find the values

9.49 meters = 9.49 * 100 = 949 m

Answer:

949 cm.

Step-by-step explanation:

1 m. = 100 cm.

100 × 9,49 = 949

⤻⤻

According to the Power of 10 rule, whenever you divide by 10 [⅒], you move the decimal mark to the left each time, and of course, whenever you multiply by 10, you move the decimal mark to the right each time. In this case, since you are multiplying by 100, you move the decimal mark twice to the right to get 949.

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Answer:

[tex]\frac{19}{8}[/tex]

Step-by-step explanation:

As per definition of commutative property, the final output of addition remains same regardless to what order the number are added in i.e.

[tex]a + b + c = b + c + a = c + a + b[/tex]

∴[tex]\frac{1}{2}  + \frac{3}{8} + \frac{3}{2} = \frac{4 + 3 + 12}{8} = \frac{19}{8}[/tex]

Answer:

in a 140 meter spool there are 31 1/9 times 4 1/2 meters of ribbon

Step-by-step explanation:

To find out how many 4 1/2 meters of ribbon are there in a 140 meter spool, divide 140 meter by 4 1/2 meter, but first convert mixed number to an improper fraction

[tex]4\frac{1}{2}=\frac{4*2+1}{2}=\frac{9}{2}[/tex]

[tex]\frac{140}{(9/2)}=\frac{280}{9}[/tex]

Convert to mixed number

[tex]\frac{280}{9}=\frac{279}{9}+\frac{1}{9}=31\frac{1}{9}\ times[/tex]

therefore

in a 140 meter spool there are 31 1/9 times 4 1/2 meters of ribbon

Check the picture below.

notice, the car starts at 0 miles and 0 minutes, since it was at rest, wasn't moving, and off it went and in 10 minutes it has covered 55 miles.

Answer:

t = 8 t = 0

Step-by-step explanation:

The factored form is t(t + 8).

Certainly! Let's factor the given polynomial t^2 + 8t step by step.

So, the factored form of t^2 + 8t is t(t + 8).

Answer:

AB = 2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Calculate the length using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = A(- 3, - 4) and (x₂, y₂ ) = B(- 1, - 6)

AB = [tex]\sqrt{(-1+3)^2+(-6+4)^2}[/tex]

     = [tex]\sqrt{2^2+(-2)^2}[/tex]

     = [tex]\sqrt{4+4}[/tex]

     = [tex]\sqrt{8}[/tex] = 2[tex]\sqrt{2}[/tex] ≈ 2.83 ( to 2 dec. places )

Answer:

Step-by-step explanation:

AB= √((-6+4)²+(-1+3)²)² = √(4+4)= √8 =2√2

Answer:

n =  1.33 repeating

Step-by-step explanation:

first you distribute the -2 by everything in the parenthesis so then you get -12 + 1- = 26 the you subtract 10 from each side which leaves you with -12 = 16 then you devide -12 by both sides and you get the decimal 1.33 repeating.

The equation x + 3/6 = x - 6/3 cannot be solved for x, as simplification leads to 1/2 = -2, which is not possible, indicating a mistake in the provided equation.

To solve the equation x + 3/6 = x - 6/3 for x, let's first simplify each side of the equation by reducing the fractions. This gives us:

x + 1/2 = x - 2

At this point, we can see that the variable x appears on both sides of the equation. To solve for x, we would normally try to isolate x on one side. However, if we attempt to subtract x from both sides, we will get:

1/2 = -2

This statement is not true, indicating that the original equation was incorrect or improperly written. If the equation only involved x on one side, we could use algebraic techniques to solve for x, but as it stands with this impossible equality, we cannot find a value for x that satisfies the equation. Therefore, it seems there may be a mistake in the transcription of the original problem.

Answer:

The GCF for 15az and 25az is marked below.

15az = 3*5*a*z

25ab - 5*5*a*b

GCF = 5a

Step-by-step explanation:

Answers above! Hoped this helped :)

Answer:

GCF=5az.

Step-by-step explanation:

First, find a number that is the largest to be multiplied by something else to get both of these numbers. 5 is the correct number. az is also applicable, so therefore 5az is correct. you can multiply 5az by 3 to get 15az or by 5 to get 25az

Answer:

x = 4.75 or 19/4 or 4 and 3/4

Step-by-step explanation:

10 - 4x = -9

-10         -10

-4x = -19

----    -----

-4     -4

x = 4.75 or 19/4 or 4 and 3/4

Correct answer: x= - 3/2

Answer:

The total cost of book using array multiplication is 35$

Solution:

Jamie buys 5 books for 7$. So draw array multiplication table using 5 rows and 7 columns (see the figure attached below)

By counting the number of rows and number of objects in each row from the figure attached below, we get the total cost of the book.

Total cost = number of rows [tex]\times[/tex] total number of objects in each row

Total cost = 5 [tex]\times[/tex] 7 = 35

Answer:

See explanation

Step-by-step explanation:

A. Given the equation

[tex]3+9=12[/tex]

Using the subtraction property of equality (subtracting 5 from both sides of equation), we'll get an equivalent equation

[tex]3+9-5=12-5[/tex]

B. Given the equation

[tex]x-4=7[/tex]

Using the addtion property of equality (adding 4 to both sides of equation), we'll get an equivalent equation

[tex]x-4+4=7+4[/tex]

C. Given the equation

[tex]2(6)=12[/tex]

Using the division property of equality (dividing  both sides of equation by 2), we'll get an equivalent equation

[tex]\dfrac{2(6)}{2}=\dfrac{12}{2}[/tex]

D. Given the equation

[tex]\dfrac{x}{2}=5[/tex]

Using the multiplication property of equality (multiplying  both sides of equation by 2), we'll get an equivalent equation

[tex]2\cdot \dfrac{x}{2}=2\cdot 5[/tex]

The operation displayed in the equation change from '3 + 9 = 12' to '3 + 9 - 5 = 12 - 5' is subtraction. The number 5 is subtracted from both sides of the original equation, altering the values while keeping the equation fundamentally equivalent and balanced.

The operation that occurred between the two equations, 3 + 9 = 12 and 3 + 9 - 5 = 12 - 5, is called subtraction. This operation is depicted by the inclusion of the -5 in both sides of the second equation. Essentially, the number 5 is being subtracted from the results of the first equation, resulting in an altered but comparable equation.

Think of it as taking the entire set of operations in the first equation, and applying an additional step to it - the step of subtracting 5, denoted in the equation as '- 5'. This step is applied to both sides of the equation to maintain its balance, keeping it equivalent to the initial equation, albeit with different values.

Continuing from our first equation, the left-hand side which was '3 + 9' (equals to 12) would become '3 + 9 - 5' (equals to 7), and the right-hand side which was '12', becomes '12 - 5' (also equals to 7). The fundamental rule being employed here is that the same operation should be performed on both sides of an equation to keep it balanced. Adjusting only one side would result in a different, non-equivalent equation.

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Answer:

b=2

Step-by-step explanation:

Changing the y-intercept would move the graph down or up.

So we have the equation [tex]y=\frac{-2}{3}x+5[/tex].

We want to move the graph down 3 units.  We want the y-intercept to be 3 units lower than what is was.  Since 5-3 is 2, then the new y-intercept is 2.

The equation would  then be [tex]y=\frac{-2}{3}x+2[/tex].

So b=2.

Answer:

162 RPM

Step-by-step explanation:

Start by multiplying 9⁄10 by the Multiplicative Inverse of ⅓, which is 3:

9⁄10 ÷ ⅓ → 9⁄10 × 3 = 2 7⁄10

After this, multiply the result by sixty seconds, since there are sixty seconds in one minute:

60 × 2 7⁄10 = 162

So, it will make 162 RPM.

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Your Question: How to calculate ratio.

The Answer/Explanation: To find an equal ratio, you can either multiply or divide each term in the ratio by the same number (but not zero). For example, if we divide both terms in the ratio 3:6 by the number three, then we get the equal ratio, 1:2.

To calculate the ratio, the width will be divided by the GCD and the height will be divided by the GCD. A colon will be placed between those two numbers. The result is 4:3 -- the ratio for those screen dimensions.

Remember to check study guides, lessons and notes to rely on; working hard is the way to success. Good Luck!

To calculate a ratio, you compare two quantities and express their relationship as a fraction, a colon-separated pair, or a "to" statement. You usually divide the larger number by the smaller and simplify to whole numbers to find the smallest whole-number ratio.

To calculate a ratio, you compare two quantities to each other. Ratios can be represented in a few different ways, such as fractions, with a colon, or with the word "to". For example, a ratio might be 2/3, 2:3 or "2 to 3". If you're dealing with a scenario where you are given two different molar amounts, you would follow these steps:

For example, if you're looking at a chemical equation and need to determine the mole ratio, divide all numbers by the smallest value presented. So, if the molar amounts are 5.5, 1, and 1.2, dividing each by the smallest amount (1 in this case) gives you the mole ratio of 5.5:1:1.2. Simplified, it would become 55:10:12 as a ratio of whole numbers.

Answer:

54

Step-by-step explanation:

First you would distribute 6 into 4 and 5. 6 times 5 is 30, and 4 times 6 is 24. the equation is now (24 + 30), which equals 54.

Answer:

Step-by-step explanation:

Writing a system of equations is really just writing an equation for each part of the problem.  The parts here being the calories, and number of items.  It's not asking to solve it, so I will not unless you do want me to.

First variables, let's keep it simple.  O will be onion rings and M will be mozzarella sticks.

Now, I mentioned the two parts are the calories and number of items so we'll take it one at a time.  First calories.  

The total calories will equal 800, so we know the answer to the equation.  Now, how would we relate the variables?  if you had two of each item what would the total calories be?  it may be easy to figure out,  but for our purposes we want to think of it as multiplying the calories of each by the number of each item, or in other words 40*O+60*M, where O and M equal 2.  So for the general case we use the same thing, but we know what we want So our first equation is 40*O + 60*M = 800

The second is a bit simpler.  It just wants to know the total amount of things ordered.  So we are just adding O and M together.  So this gets us O + M = 14, since there are 14 things together.  Let me know if there's still something you don't understand though.  

The system of equations is: [tex]\( x + y = 14 \)[/tex] and [tex]\( 40x + 60y = 800 \)[/tex], where \( x \) represents the number of onion rings in the combination meal and \( y \) represents the number of mozzarella sticks in the combination meal.

Let's define:
- \( x \) as the number of onion rings in the combination meal.
- \( y \) as the number of mozzarella sticks in the combination meal.

The system of equations would be:

1. [tex]\( x + y = 14 \)[/tex] (since the combination meal has a total of 14 onion rings and mozzarella sticks altogether)
2. [tex]\( 40x + 60y = 800 \)[/tex] (since each onion ring has 40 calories and each mozzarella stick has 60 calories, and together they contain 800 calories)

Answer:

2.2360679775 or 2.24

Step-by-step explanation:

Because the square root of 180 is 13.416407865 and when you divide that by 6 you will get 2.2360679775 or 2.24

w= x + y/z

w-x = y/z

z= y/(w-x)

y = (w-x)z

Fractions are division problems, ex 1/2 is the same as one divided by 2, so if you multiply the denominator you solve for the numerator, and to solve for the denominator just substitute what's on the other side

Answer:

x = 5, -5

Step-by-step explanation:

Find the roots of [tex]x^{2} -25=0[/tex] by solving for x.

Add 25 to both sides

[tex]x^{2} =25[/tex]

Square root both sides

[tex]x = 5[/tex]

[tex]x=-5[/tex]

The solution to the quadratic equation x² - 25 = 0 is 5, -5 after using the identity a² - b² = (a + b)(a - b).

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

It is given that:

The quadratic equation:

x² - 25 = 0

As we know,

a² - b² = (a + b)(a - b)

Using the above identity:

x² - 5² = 0

(x + 5)(x -  5) = 0

x + 5 = 0  

x = -5

Or

x - 5 = 0

x = 5

We can also find the solution to the equation x² - 25 = 0 using the quadratic formula.

Thus, the solution to the quadratic equation x² - 25 = 0 is 5, -5 after using the identity a² - b² = (a + b)(a - b).

Learn more about quadratic equations here:

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Answer:

/\zlm is the correct answer for this kind of questions because the other answer over there aren't having any truth