From Mason's house, it takes 10 1⁄2 hours to drive to Los Angeles. If Mason has already driven for 7 1⁄4 hours, how many hours remain until he reaches Los Angeles?

The sum of the two consecutive positive integers, approximated to be 51 and 52, is 103.

If the quotient of two consecutive positive integers is 1.02, it indicates a very small difference between the two integers.

However, since integers cannot have fractional parts, the quotient cannot be exactly 1.02. If we assume the quotient is approximately 1.02, it means the two consecutive integers are very close to each other.

Let's solve it:

Let's denote the smaller integer as x, then the larger one would be x + 1.

So, we have:

[tex]\[\frac{x}{x + 1} \approx 1.02\][/tex]

Now, we can cross multiply:

[tex]\[x \approx 1.02(x + 1)\][/tex]

[tex]\[x \approx 1.02x + 1.02\][/tex]

Subtract 1.02x from both sides:

[tex]\[0.02x \approx 1.02\][/tex]

Now, divide both sides by 0.02:

[tex]\[x \approx \frac{1.02}{0.02}\][/tex]

[tex]\[x \approx 51\][/tex]

So, one integer is approximately 51. The next consecutive integer would then be 52.

The sum of these two integers is 51 + 52 = 103.

Thus, the sum of the two consecutive positive integers is approximately [tex]\(\boxed{103}\).[/tex]

Answer:

The correct answer is 1. 2d + 1 = 3d + 5

Step-by-step explanation:

The factorization of given expression is 4(3a+2b).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given expression is 12a+8b.

In the given expression there are two terms 12a and 8b

Now, 12a=2×2×3×a and 8b=2×2×2×b

So, from both the terms common is 2×2=4

Thus, 4(3a+2b)

Therefore, the factorization of given expression is 4(3a+2b).

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Answer:

4.47

Step-by-step explanation:

Given : [tex]\sqrt{20}[/tex]

To Find : Which is a better approximation

Solution:

20 lies between two perfect squares i.e. 16 and 25

Square root of 16 = 4

Square root of 25 = 5

So, Square root of 20 must lie between 4 and 5

Using calculator

The [tex]\sqrt{20}=4.47[/tex]

Hence a better approximation of the square root of 20 is 4.47.

2.135 meters rounded to the nearest hundredth is 2.14 meters. Decimal conversion for centimeters to meters involves moving the decimal two places to the left. A ruler measuring in millimeters allows for more precise measurement.

To round 2.135 meters to the nearest hundredth, you should look at the third digit after the decimal point, which is 5. Because the third digit is 5 or greater, you round the second digit up. Therefore, 2.135 meters rounded to the nearest hundredth is 2.14 meters when placed on a number line.

When considering decimal conversion from centimeters to meters, you need to move the decimal point two places to the left (e.g., 100 cm is equal to 1.00 meters). For precise measurements, it's important to have a ruler that can measure at least to the nearest tenths of a centimeter, which is also known as millimeters, so you can then estimate to the hundredths.

To round 2.135 meters to the nearest hundredth, we look at the digit in the hundredths place, which is 3 in this case. Since 3 is less than 5, we round down the digit in the tenths place. Therefore, the rounded value of 2.135 meters to the nearest hundredth is 2.13 meters.

On a number line, you can mark this value between 2.12 and 2.14, closer to 2.13.

The points T and S will have the same abscissa, and the points Q and R have the same abscissa. Then the correct options are A and D.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

The pair of points that have equal X coordinates that is abscissa will be

From the diagram, the coordinate of the points R, Q, S, and T will be

R ⇒ (-5, -7)

Q ⇒ (-5, 6)

S ⇒ (5, -6)

T ⇒ (4, 6)

The points Q and R have the same abscissa.

Then the correct options are A and D.

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9.125×10² is 100000 times the [tex]9.125\times10^{-3}[/tex].

We need to find what is the relationship between [tex]9.125\times10^{-3}[/tex] and 9.125×10².

The scientific notation helps us to represent the numbers that are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small.

9.125×10² can be written as [tex]9.125\times10^{-3+5}=9.125\times10^{-3}\times10^{5}[/tex]

= [tex]9.125\times10^{-3+5}=9.125\times10^{-3}\times100000[/tex]

Therefore, 9.125×10² is 100000 times the [tex]9.125\times10^{-3}[/tex].

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There were 340,000 cattle placed on feed

How many of the 340,000 cattle placed on feed were between 700 and 799 pounds?

Given the fraction of total cattle for 700 - 799 pounds is 2/5

Let x be the number of cattle between 700 - 799 pounds

We make a proportion using the fraction

[tex]\frac{2}{5} = \frac{x}{340,000}[/tex]

Cross multiply it and solve for x

340000* 2 = 5x

680000 = 5x

Divide by 5 on both sides

So x= 136,000

There were 136,000 cattle between 700 and 799 pounds

Answer:

it is 40 f to -3 f

Step-by-step explanation:

so i just subtracted and got 3 supposedly. than ad another 37 and got 40 so it is 40 f to - 3 f