How can you use a number line to add and subtract like fractions?

The height of the plant after it grows 1 7/8 inches is 81/8 inches.

To find the height of the plant after it grows 1 7/8 inches, we need to add 1 7/8 to the current height of 8 1/4. First, we can convert 8 1/4 to an improper fraction by multiplying the whole number (8) by the denominator (4) and then adding the numerator (1). This gives us 33/4 inches. Next, we can add 1 7/8 by finding a common denominator (8) and adding the numerators (1+7=8). So, 1 7/8 is equivalent to 15/8. Adding 33/4 and 15/8, we first need to find a common denominator which is 8. Multiplying the numerator and denominator of 33/4 by 2 gives us 66/8. Now, we can add 66/8 and 15/8 to get a total of 81/8 inches. Therefore, the height of the plant after it grows 1 7/8 inches is 81/8 inches.

Final answer:

After adding the growth of 1 7/8 inches to the original plant height of 8 1/4 inches, the new height of the plant is calculated to be 10 1/8 inches.

Explanation:

To calculate the new height of the plant after it grows an additional 1 7/8 inches, we simply need to add this growth to the plant's original height of 8 1/4 inches. The sum of these two measurements will give us the plant's total height.

Begin by converting the mixed numbers to improper fractions to make addition easier: 8 1/4 inches becomes 33/4 inches and 1 7/8 inches becomes 15/8 inches. Next, find a common denominator and add the two fractions.

Now, convert the improper fraction back to a mixed number to determine the plant's new height:

Therefore, after growing an additional 1 7/8 inches, the plant's new height is 10 1/8 inches.

Factors that 28 and 44 have in common are 1, 2, and 4.

Factors that 28 and 44 have in common:

1. List of Factors for 28:

1, 2, 4, 7, 14, 28

2. List of Factors for 44:

1, 2, 4, 11, 22, 44

Common Factors: 1, 2, 4

Answer:

The y-coordinate of the solution is approximately 7.2.

Explanation:

To solve the system of equations:

1. [tex]\( 5x + 2y = 7 \)[/tex]

2. [tex]\( -2x + 6 = 9 \)[/tex]

We'll start by solving the second equation for [tex]\( x \):[/tex]

[tex]\[ -2x + 6 = 9 \][/tex]

Subtract 6 from both sides:

[tex]\[ -2x = 9 - 6 \][/tex]

[tex]\[ -2x = 3 \][/tex]

Divide both sides by -2:

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

Now that we have the value of [tex]\( x \)[/tex], we can substitute it into the first equation to find [tex]\( y \):[/tex]

[tex]\[ 5x + 2y = 7 \][/tex]

[tex]\[ 5(-\frac{3}{2}) + 2y = 7 \][/tex]

[tex]\[ -\frac{15}{2} + 2y = 7 \][/tex]

Add [tex]\( \frac{15}{2} \)[/tex] to both sides:

[tex]\[ 2y = 7 + \frac{15}{2} \][/tex]

[tex]\[ 2y = \frac{14}{2} + \frac{15}{2} \][/tex]

[tex]\[ 2y = \frac{29}{2} \][/tex]

Divide both sides by 2:

[tex]\[ y = \frac{29}{4} \][/tex]

Now, let's convert the fraction into a decimal rounded to the nearest tenth:

[tex]\[ y \approx 7.2 \][/tex]

The given difference of two numbers which we have to estimate is

  920,026-535,722

Actual Difference=384,304

→Estimation Using Ones

 920,030-535,720=384,310

→Estimation Using Tens

 920,000-535,700=384,300

Estimation using Tens is Closer to Actual Difference.

So, Answer=384,300

24 -18 = 6

24/6 =4

18/6 =3

6 bundles with 4 balls and 3 clubs each

Final answer:

The notation f'(x) represents the derivative of the function f with respect to x, signifying the rate of change of the function or the slope of the tangent to its curve at a specific point.

Explanation:

The notation f prime of x, often written as f'(x), represents the derivative of the function f with respect to x. This concept is a fundamental part of calculus, which deals with the rate at which quantities change. The derivative f'(x) is the instant rate of change of the function f(x) at a particular value of x, or the slope of the tangent line to the curve f(x) at that point.

For example, if f(x) = x2, then the derivative f'(x) would equal 2x, as the rate of change of x2 with respect to x is 2x. This means that for every unit increase in x, the value of x2 increases by an amount corresponding to 2x.

The derivative can also be understood in the context of physics, where it might represent things like velocity, which is the derivative of position with respect to time. Regardless of the context, f'(x) is about understanding how a function changes at a specific point.

r= 5% = 0.05

t = 5 years

I= 20

P=20÷(0.05×5)
P=$80

Food, clothing, and medical are variable expenses because they occur regularly but can change from month to month.

The Porters’ food, clothing, and medical expenses are variable expenses.

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It can be deduced that the value of angle GDC is 110°.

The value of minor arc DG will be;

= 2 × 55°

= 110°

The value of AC will be:

= 230° + AC = 360°

AC = 360° - 230°

AC = 130°

Lastly, since segment CO is congruent to segment HZ, CO is congruent to HZ.

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Answer:

False.

Step-by-step explanation:

If an item is [tex]\frac{1}{3}[/tex] off thats how much you are not paying from the original price of the item, to calculate how much are you paying after the disccount you can do 2 things.

The first one is multiplying the price by [tex]\frac{1}{3}[/tex] and then substracting that from the original price, that will give you the final price.

Or you can simply multiply the original price by 2/3 which is what you have to pay for the item in terms of fractions, and you´d get the final price.

Final answer:

The rate of change of the surface area of a sphere with respect to its radius is 8πr. For a sphere with a radius of 6, this rate is 48π square units per unit of radius.

Explanation:

The surface area S of a sphere is given by the formula S = 4πr², where r is the radius of the sphere. To find the rate of change of the surface area with respect to the radius, we need to differentiate the surface area formula with respect to r. This calculation gives us dS/dr = 8πr. When r = 6, the rate of change, or the derivative evaluated at this radius, is dS/dr = 8π(6) which equals 48π.

So, the rate of change of the surface area of a sphere with respect to its radius when r = 6 is 48π square units per unit of radius.

The three consecutive even integers are 10, 12, and 14.

Given that three consecutive even number the sum of the smallest integer and twice the median is 20 more than the largest integer.

Let's represent the three consecutive even integers as follows:

The smallest integer: x

The median integer: x + 2 (since it's consecutive and even)

The largest integer: x + 4 (since it's consecutive and even)

Now, we can set up the equation based on the given information:

"The sum of the smallest integer and twice the median is 20 more than the largest integer."

This can be expressed as:

x + 2(x + 2) = (x + 4) + 20

Now, we can solve for x:

x + 2x + 4 = x + 24

Combine like terms:

3x + 4 = x + 24

Subtract x from both sides:

2x + 4 = 24

Subtract 4 from both sides:

2x = 20

Now, divide by 2:

x = 10

So, the smallest integer is 10, the median integer is x + 2 = 12, and the largest integer is x + 4 = 14.

Therefore, the three consecutive even integers are 10, 12, and 14.

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Answer: Set goals higher than what you feel you can achieve.

Step-by-step explanation:

Answer:

D. A skipped check has not been cashed or deposited.

Step-by-step explanation:

We can say that a skipped check number means the check has not been cashed yet.

If we see the check book and there is a gap between the check numbers that you have written, then that means the missing number checks are not processes yet. The processing can be depositing or withdrawing/cashing.

So, the correct answer here is D. A skipped check has not been cashed or deposited.

Answer: 13

25 3/2 = 26.5

26.5 is basically 26 1/2

26 1/2 = 13

At a value of 2, the graph of F(x) = 2/x-2 has a vertical asymptote.