Using the given information, which lines, if any, can you conclude are parallel? Justify your conclusion with a theorem or postulate.

Answer:

b

Step-by-step explanation:

To write the equation of a line in slope-intercept form given two points, calculate the slope from the points, use one point and the slope to find the y-intercept, then write the equation as y = mx + b.

To write the equation of a line in slope-intercept form, given two points, follow these steps:

For example, if the two points given are (1, 3) and (4, 11), the slope would be (11 - 3) / (4 - 1) = 8 / 3. Then choosing the point (1, 3), we would substitute to find the y-intercept: 3 = (8/3)(1) + b, resulting in b = 3 - 8/3 = 1/3. So the equation of the line is y = (8/3)x + 1/3.

Answer:

3.

Step-by-step explanation:

We are asked to find the estimated digit in the measurement 0.503 L.

We know that in each measurement the estimated digit is always the last digit.

We can see that the first digit in the given measurement is 5, the second digit is 0 and the last digit is 3.

Since the last digit is in our given measurement 3, therefore, the estimated digit is 3.

Option B is correct, y≤1/3x-4 is the  linear inequality which is represented by the graph

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The equation of line passing through points (3, -3) and (0, -4)

Slope = -4+3/0-3

=1/3

Now let us find y intercept

-4=1/3(0)+b

b=-4

Equation is y=1/3x-4

y≤1/3x-4 is the required inequality of the graph

Hence, y≤1/3x-4 is the  linear inequality which is represented by the graph

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The time it takes the rock to hit the water is 6 seconds

Data;

To find the time it takes for the rock to hit the ground, we have to use the and assume that the given equation represents the height at which the rock attained.

[tex]f(x) = -16(x^2 - 3x -18)\\0 = -16x^2 + 48x + 288\\16x^2 - 48x - 288 = 0\\x^2 - 3x - 18 = 0[/tex]

Solving the above quadratic equation,

x = - 3 or x = + 6

The time it takes the rock to hit the water is 6 seconds

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[tex]\[ w = 7 \][/tex]

The given equation is [tex]\(\log(w^2+21)=\log(10w)\)[/tex]. To find the solution, we can set the arguments of the logarithms equal to each other, giving [tex]\(w^2 + 21 = 10w\)[/tex].

Rearranging, we get a quadratic equation [tex]\(w^2 - 10w + 21 = 0\).[/tex] Factoring or using the quadratic formula yields the solutions  

However, we need to check for extraneous solutions. Substituting [tex]\(w = 3\)[/tex] back into the original equation results in taking the logarithm of a negative number, which is undefined in the real number system. Therefore, [tex]\(w = 3\)[/tex] is extraneous, and the valid solution is [tex]\(w = 7\).[/tex]

In the detailed explanation, we used the property of logarithms that states [tex]\(\log(a) = \log(b)\)[/tex] implies [tex]\(a = b\)[/tex]. By setting the arguments of the logarithms equal to each other, we obtained a quadratic equation.

Factoring or applying the quadratic formula allowed us to find the solutions. However, we must always check for extraneous solutions by substituting them back into the original equation and ensuring the logarithms are defined for the real number system.

In this case, only [tex]\(w = 7\)[/tex] satisfies the equation without resulting in undefined logarithms.

Answer:

First find the unit price for each. Then compare the unit prices. The item that has the lesser unit cost is the better buy.

Step-by-step explanation:

When comparing the costs of two items that are different sizes, use ratios to make a comparison and consider the unit size.

When comparing the costs of two items that are different sizes, you can use ratios to make a comparison. Let's say Item A costs $10 and Item B costs $20. Item A is twice as expensive as Item B. To make the comparison fair, you can also consider the size or quantity of the items. For example, if Item A is twice as expensive but also twice as large as Item B, then the cost per unit size is the same. However, if Item A is half the size of Item B, then Item B is a better deal in terms of size.

Answer with explanation:

Total number of vacant seats = 4 seat

Number of students Looking for Seats = 12 Student

We have to fill the four Seats and there are 12 students.

First Seat can be filled in 12 ways,11 students are left,So, second seat can be filled in 11 ways ,Now,there are 10 students left ,So, third seat can be filled in 10 ways,Now there are 9 students left,so last seat can be filled in 9 ways.

Total number of ways of filling 4 seats if there are 12 number of students

               =12 × 11 × 10 × 9

              =132 × 90

             =  11880 ways

Or ,you can solve it directly by the concept of Permutation.

Total ways of filling 4 vacant seats if there are 12 students in all

           [tex]= _{4}^{12}\textrm{P}=\frac{12!}{(12-4)!}=\frac{12\times 11\times 10\times 9\times 8!}{8!}=12\times 11\times 10\times 9=11880[/tex]  

The argument is valid by the law of detachment.

Answer:

The argument is valid by the law of detachment.

Step-by-step explanation:

We first verify that the first statement, "if p, then q" is correct.  If a parallelogram has a right angle, this means that the angle opposite that angle must also be right; this is because the opposite angles of a parallelogram are congruent.

This also means that the adjacent angle to this right angle must also be right; this is because the adjacent angles in a parallelogram are supplementary.

Thus "if p, then q" is true.

The law of detachment states that if I have two statements, one of the form "if p, then q" and the other "p", then the conclusion, "q," is valid.

 82=6482=64choices for that.

Now, for the second one, we can't be in the row or column of that first one, so leaving us with 72=4972=49 choices.

Then so on, we have 62=3662=36 for the third one, 2525 for the fourth one, and so on ……

But, however, we have to remember the rooks are not labeled, thus it doesn't matter specifically about a specific rook's position.

Thus, we have a total of (8!)28!=40320(8!)28!=40320 ways.