Which of the following is the equation for the line perpendicular to the line 3x−2y=10 that passes through the point (7, 5)

Answer:3/2

Step-by-step explanation:

The ordered pair (2,3) is not a solution of the system

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

−8x + 4y > 3

6x - 7y < −5

The solution is given as

(2, 3)

Next, we test this value on the system

So, we have

−8(2) + 4(3) > 3

-4 > 3 --- false

This means that (2,3) is not a solution of the system

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The slope of the line that contains these points is 0.75.

The slope of a line is the change in y-values divided by the change in x-values. In other words, it is the rise over the run. We can use the points given to calculate the slope.

Let's take the first two points (9, -24) and (13, -21) and use the formula for slope:

slope = (y2 - y1) / (x2 - x1)

slope = (-21 - (-24)) / (13 - 9)

slope = (3) / (4)

slope = 0.75

We can do the same with the other two points (17, -18) and (21, -15):

slope = (-15 - (-18)) / (21 - 17)

slope = (3) / (4)

slope = 0.75

Since the slope is the same for both sets of points, we can conclude that the slope of the line that contains these points is 0.75.

The slope of the line that contains these points is 0.75.

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The top priority during physical activity in the classroom is the safety and well-being of the students.

Ensuring a safe environment for physical activity helps prevent injuries and promotes the overall health and engagement of the students.

1. Supervision: Adequate adult supervision should be provided to monitor the students' activities, ensuring they are engaged in safe and appropriate physical exercises.

2. Proper Warm-up and Cool-down: Encouraging students to perform warm-up exercises before engaging in more vigorous activities and cool-down exercises afterward helps prevent injuries and promotes proper muscle recovery.

3. Suitable Physical Activities: The chosen physical activities should be age-appropriate, taking into account the students' physical abilities and limitations. Activities should be designed to minimize risks and promote participation for all students.

4. Clear Instructions and Demonstration: Teachers should provide clear instructions and demonstrate proper techniques for exercises or activities to ensure students understand how to perform them safely and effectively.

5. Equipment and Environment Safety: Regular inspection of equipment and ensuring the physical environment is free from hazards (such as tripping hazards or obstacles) is essential for maintaining a safe setting.

6. Individual Needs and Modifications: Teachers should consider any individual needs or limitations of students, such as physical disabilities or health conditions, and make necessary modifications or adaptations to ensure their safety and inclusion.

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the top priority during physical activity in the classroom is?

Based on the passage you provided, it seems like you are being asked to apply principles of logic and construct a truth table based on the premises and conclusion presented in the passage. To accomplish this, you need to follow the three steps outlined:

Step 1: Break the premises into several statements (usually denoted by p, q, r, etc.)

From the passage, we can identify the following statements:

- Statement 1: Water is fundamental for life and the environment.

- Statement 2: Water crisis is one of the most important challenges of the 21st century.

- Statement 3: Ensuring that we use water more wisely, more productively, and less profligately will be one of the defining challenges of this century.

- Statement 4: If all public services collaborate to address the water scarcity problem, then the governments will be able to provide a planning framework to manage water usage and boost awareness of the water crisis.

- Statement 5: There is a lack of planning frameworks or there are not enough campaigns to raise awareness of the water crisis.

- Statement 6: Therefore, there is no efficient collaboration among various public sectors to address the water shortage problem.

Step 2: Express the premises and conclusion symbolically.

Using the statements identified above, we can symbolically represent them as follows:

- p: Water is fundamental for life and the environment.

- q: Water crisis is one of the most important challenges of the 21st century.

- r: Ensuring that we use water more wisely, more productively, and less profligately will be one of the defining challenges of this century.

- s: All public services collaborate to address the water scarcity problem.

- t: Governments will be able to provide a planning framework to manage water usage and boost awareness of the water crisis.

- u: There is a lack of planning frameworks or there are not enough campaigns to raise awareness of the water crisis.

- v: There is no efficient collaboration among various public sectors to address the water shortage problem.

Step 3: Construct a truth table.

To construct a truth table, assign truth values (T or F) to each statement and evaluate the truth value of the conclusion based on the truth values of the premises

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Answer:

C.

explanation:

I just know.

Answer:

c

Step-by-step explanation:

y=-8x

Okay, here we have this:

Considering the provided information, and figures, we are going to find the requested length, so we obtain the following:

Let us remember that if two figures are proportional, then they are proportional between corresponding segments, therefore we have:

Finally we obtain that the measure of PS is 21 units.

Answer:

4 yards

Step-by-step explanation:

11 1/2 feet is equal to 3.833333 and 4 yards is more than that.

Answer:

11 1/2 ft. < 4 yd

Step-by-step explanation:

I'm not sure if thats what your asking.

But 1 yard is 3 ft, so 4 yards is equal to 12 ft. Therfore 11 1/2 ft. < 4 yd.

Answer

The one of the top right, bottom left, and bottom right.

Explanation

All of these have lines that intersect with the coordinates (0,3).

A factory inspector found flaws in 3 out of 18 wooden boxes. What is the experimental probability that the next wooden box will be flawed?

Write your answer as a fraction or whole number.

-------------------------------------------------------------------------------------------------------------

Remember, The experimental probability is the number of times an event occurs out of the total number of trials.

-------------------------------------------------------------------------------------------------------------

Flawed Boxes / Total

=3/18

=1/6

So The Answer is 1/6

The experimental probability that the next wooden box will be flawed is 1/6=0.167.

The experimental probability of an event is the ratio of the number of outcomes in which a specified events occurs to the total trials.

Mathematically, Experimental probability= f/n, where f is the number of times an event occurs, n is the total number of trials.

Total number of wooden boxes= 18

Total number of boxes that are flawed= 3

Therefore, required experimental probability = 3/18

                                                           =1/6

Hence, the experimental probability that the next wooden box will be flawed= 1/6

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Answer:

0.5 minutes

Step-by-step explanation:

Since we are provided the equation and the current height of the candle (which would be 25 inches) we can simply replace this current height with the variable h and then solve the rest of the equation to find out the value of m when the height of the candle is at 25 inches.

h = 32−14m

25 = 32−14m ... subtract both sides by 32

-7 = -14m ... divide both sides by -14

0.5 = m

Finally, we can see that after 0.5 minutes the candle would have melted down to 25 inches.

Answer:

slope = 2 , y- intercept = -8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

- 4x + 2y = - 16 ( add 4x to both sides )

2y = 4x - 16 ( divide both sides by 2 )

y = 2x - 8 ← in slope- intercept form

with slope m = 2 and y- intercept c = - 8

Answer:

the slope is 2 and y-intercept is (0,-8)

Step-by-step explanation:

Step 1: is to subtract 2y from both sides, -4x+2y-2y=-16-2y

Step 2: Simplify, -4= -16-2y

Step 3: Divide both sides by -4, -4x/4=-16/-4-2y/-4

4x/4=x=1

By using the concept of Depreciation, it is obtained that

Warrem's body  metabolize half of the 84 mg of caffeine in 4.71 hours

What is Depreciation?

Depreciation is the reduction in the value of a product at a certain rate over a certain period of time.

Here the concept of Depreciation has been used

Let the time taken to metabolize half of the 84 mg of caffeine be t hours

Damien's body metabolizes caffeine at a rate of 13.7% per hour

By the problem,

\(84(1 - \frac{13.7}{100})^t = 42\\\\(1 - \frac{13.7}{100})^t = \frac{42}{84}\\\\(1 - \frac{13.7}{100})^t = \frac{1}{2}\\\\(\frac{100 -13.7}{100})^t = \frac{1}{2}\\\\(\frac{86.3}{100})^t = \frac{1}{2}\\\\(\frac{863}{1000})^t = \frac{1}{2}\\\\t(ln(\frac{863}{1000}) = -0.693\\\\-0.147t = -0.693\\\\t = \frac{0.693}{0.147}\\\\t = 4.71 \ hours\)

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Answer:

/2 each time

Step-by-step explanation:

8,4,2

8/2=4

4/2=2

etc

option third is correct answer

In parallelogram ,opposite sides are equal.

x+3=2x-6

solve the value you will get x=9

Answer:

10x-22

Step-by-step explanation:

((x+2)(x-1))-((x-4)(x-5))

(x^2-x-2)-(x^2-9x+20)

     x^2 + x - 2

+  (-x^2+9x-20)

_______________

       10x-22

To solve the given linear programming (LP) problem using the graphical LP approach, we will plot the feasible region, identify the corner points, and determine the optimal solution.

Here are the steps:

Step 1: Plot the constraints:

- Plot the line 5x + y = 32, which represents the constraint 5x + y ≤ 32. To do this, find two points that lie on this line by assigning values to x and solving for y. For example, when x = 0, y = 32, and when x = 6, y = 2. Connect these points to draw the line.

- Plot the line x + 3y = 12, representing the constraint x + 3y ≥ 12. Again, find two points on this line and connect them. For instance, when x = 0, y = 4, and when x = 12, y = 0.

- Draw the lines representing x = 20 and y = 20 as vertical and horizontal lines passing through x = 20 and y = 20, respectively.

Step 2: Identify the feasible region:

- Shade the area that satisfies all the constraints. The feasible region is the intersection of the shaded regions.

Step 3: Identify the corner points:

- Find the coordinates of the corner points of the feasible region. These points are the intersections of the lines representing the constraints.

Step 4: Evaluate the objective function:

- Calculate the objective function Z = 3x + 12y for each corner point.

Step 5: Determine the optimal solution:

- Identify the corner point that gives the minimum value of the objective function Z. This point corresponds to the optimal solution of the LP problem.

Once you have completed these steps, you will have the complete solution to the LP problem using the graphical LP approach.

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Answer:

4^30

Step-by-step explanation:

multiply the exponent

Using system of linear equations he will require 20kg of 15% copper and 30kg of 70% copper to produce an alloy of 48% in 50kg

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.

To solve this problem, we need to write a system of linear equations and find the equivalent amount of the metal required to make the desired amount of the alloy.

0.15x + 0.7y = 0.48(50) ..eq(i)

0.15x + 0.7y = 24 ...eq(i)

x + y = 50 ...eq(ii)

solving equation (i) and (ii)

x = 20, y = 30

He needs 20kg of 15% copper and 30kg of 70% copper to get 48% of 50kg of alloy.

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The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.

1. Place the graduated pipet on a flat surface and make sure it is level

2. Draw the liquid up until the meniscus is level with the etched line that corresponds to the desired volume

3. Make sure the liquid is not touching the etched line above it

4. Observe the bottom of the meniscus and take the reading at the point where the liquid level is between the two etched lines

The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.

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The next three terms of the sequence will be 4,10,16.

What is a sequence?

A sequence is a list of numbers (or elements) that exhibits a particular pattern. For example, Olivia has been offered a job with a starting monthly salary of $1000 with an annual increment of $500. Can you calculate her monthly salary in the first three years? It will be $1000, $1500, and $2000. Observe that Olivia's salary over a number of years forms a sequence as they follow a pattern where the numbers are increasing by an amount of $500 every time.

Some of the most common examples of sequence are:

Arithmetic Sequences

A sequence in which every term is created by adding or subtracting a definite number from the preceding number is an arithmetic sequence.

Geometric Sequences

A sequence in which every term is obtained by multiplying or dividing a definite number with the preceding number is known as a geometric sequence.

Harmonic Sequences

A series of numbers is said to be in harmonic sequence if the reciprocals of all the elements of the sequence form an arithmetic sequence.

Fibonacci Numbers

Fibonacci numbers form an interesting sequence of numbers in which each element is obtained by adding two preceding elements and the sequence starts with 0 and 1. Sequence is defined as, F0 = 0 and F1 = 1 and Fₙ = Fn-1 + Fn-2

Now,

Given first term=-2

difference is =6

Therefore,

               The next three terms of arithmetic sequence will be -2+6,-2+6+6,-2+6+6+6  i.e. 4,10,16.

Hence,

          The next three terms of the sequence will be 4,10,16.

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The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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Answer:

F which gives you \(14^6=7529536\) and A it will give you \(7,529,536\) which is equal to \(14^6\)

Step-by-step explanation:

it's the only one that ends up with \(14^6\) as an answer

D is wrong bc it will give you \(14^8\)

E is wrong bc it will give you 1

C is wrong bc it will give you \(14^5=537824\)

B is wrong bc it will give you \(=14^{15}\)

                                    \(\huge\boxed{F,14^-^5*14^1^1}\)

\(\boxed{------------------------------------}\)

Explanation...

\(14^6\;gives\;us\;7,529,536.\\14^-^5*14^1^1\;also\;gives\;us\;7,529,536.\\\\If\;you\;simplify\;7,529,536\;to\;an\;exponent\;it\;will\;give\;you\;14^6.\\\\Therefore,\;this\;is\;your\;answer...\\\\\\\boxed{F,\;14^-^5*14^1^1}\)

\(\boxed{------------------------------------}\)

Hope i helped!

\(\huge\boxed{Thanks,\;Plip.}\)

Answer:

going up by 2 numbers

Step-by-step explanation:

Answer:

no. 4

Step-by-step explanation:

=25x - 125/x^2 - 25

=25(x-5) / x^2 - 5^2

=25(x-5) / (x-5) (x+5) <use of formula a^2 - b^2=(a-b) (a+b)>

=25/x+5 <cut (x-5) on both side>

From the information, the correct value that expresses the division will be 300 ÷ 75 = R

From the information given, the thing to do is simply to use the number in the box to divide the number beside it and get the information.

This will be:

= 3000 ÷ 75 = 40

= 300 ÷ 75 = 4

Therefore, the expression is 300 ÷ 75 = R.

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Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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Answer:

She should first perform the operation in the parentheses, you can reference the order of the operations based on PEMDAS.

Step-by-step explanation:

1. parentheses operations

2. multiply 4 x 3

3. add the value you get from the parentheses with -7

4. with that value add it to the product of 4 and 3

Hope that helped! :)

Answer:

Subtraction

Explanation:-

\(( 1.25 -0.4) \div7+ 4 \times 3\)

Using BODMAS Rule:-

In bracket, the operation subtraction should be performed first .