Help please pre calculus

Answers

Answer 1

put 7.6*10^-4 into the given formula as the denominator of the fraction:

10log(1/7.6*10^-4) = 31.19

Related Questions

What are the steps for using a compass and straightedge to construct a square? Drag and drop the steps in order from start to finish.

Use the straightedge to draw FD ¯ ¯ ¯ ¯ ¯ and FE ¯ ¯ ¯ ¯ ¯ .

Keeping the same compass width, place the compass on point E and draw an arc in the interior of ∠DBE to intersect the previously drawn arc. Label the point of intersection as point F.

Use a straightedge to draw line t and label a point on the line as point B.

Without changing the compass width, place the compass point on point D and draw an arc in the interior of ∠DBE .

With the compass open to the desired side length of the square, place the compass point on point B and draw an arc on line t and an arc on BC ← → . Label the points of intersection as points D and E.

Construct a line perpendicular to line t through point B. Label a point on this line as point C.

Answers

Is this from Flvs? if so i can help you

Answer:

See explanation below.

Step-by-step explanation:

To construct a square using only a compass and a straightedge first we need to:

Use a straightedge to draw a line (we will name the line t) and label a point on the line as point B.Then, you will draw a perpendicular line to the segment that passes through point B ( To remember how to draw a perpendicular line through a segment see the note at the end of the explanation), label a point on this line as point C.With the compass open to the desired side length of the square (meaning the measure of the side of the square you need), place the compass point on point B and draw an arc on line t and an arc on BC. Label the points of intersection as points D and E.Without changing the compass width, place the compass point on point D and draw an arc in the interior of ∠DBE .Keeping the same compass width, place the compass on point E and draw an arc in the interior of ∠DBE to intersect the previously drawn arc. Label the point of intersection as point F.Finally, use the straightedge to draw FD and FE (the other two sides of the square are DB and DE)

*Note: To draw a perpendicular line through a segment follow the next steps:

Place the compass point at point B Draw an arc of ANY size that crosses line t twice (one to the left of point B and one to the right)Stretch the compass larger than you first did and place the point at one of the points where the previous arc crossed the line. Draw an arc above the line.Using the same width you used on step 3, place the compass point at the other point in the line.From there draw an arc above the line that crosses the other arc from step 4.Using your straightedge draw a line from the intersection of both arcs and point B and this line will be perpendicular to the line and it will pass through point B.

Rajan climbed to a height of 10 ft from the bottom of a climbing wall. He then climbed up an additional 5 ft. What must he do to return to the bottom of the climbing wall?

Select from the drop-down menus to correctly complete the statement.
Rajan must climb _____ _____ ft to return to the bottom of the climbing wall.

1. Rajan must climb up, down, left, right? (Which way is it)

2. 5 ft, 10 ft, 15 ft, 20 ft

Answers

I'm assuming this is a Pythagorean theorem problem. If so the answer would be √125

Answer:

Rajan must climb down 15 feet to return to the bottom of the climbing wall.

Step-by-step explanation:

Rajan climbed to a height of 10 ft from the bottom of a climbing wall.

He then climbed up an additional 5 ft.

So, in total he climbed [tex]10+5=15[/tex] feet

If Rajan wants to return to the bottom, he must climb down 15 feet.

Answer:

Rajan must climb down 15 feet to return to the bottom of the climbing wall.

Please help with these questions and show all work.

Answers

a. FE is parellel to AB
b. EG
c.DH and CG

2.Opposite angles formed by two intersecting lines are equal, so angle 1 is the same as angle 4. That means angle 1 = angle 5 as well.

a)one line segment that is parallel to AB is EF
b)one line segment that is skew to AB is CG
c)parallel planes: BDHF

if m<4 = m<5 (Alternate Interior Angles )
r and s are parallel

what are the domain range and asymptote of h(x)=(1.4)^x+5

Answers

the range is the set of all valid y values. (5,)

domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5

What is A rational number? square root of 15, square root of 16 square root of 17, square root of 18

Answers

Answer:

B. [tex]\sqrt{16}[/tex]

Step-by-step explanation:

We have been given 4 numbers. We are asked to find the rational number from our given choices.

We know that a number is a rational number, when it could be written as a fraction.

Let us check our given choices one by one.

A. [tex]\sqrt{15}[/tex]

[tex]\sqrt{15}=3.8729833462074169[/tex]

Since our given number has non-terminating decimal, therefore, [tex]\sqrt{15}[/tex] is not a rational number.

B. [tex]\sqrt{16}[/tex]

[tex]\sqrt{16}=\sqrt{4^2}=4[/tex]

Since our given number is an integer and we can write it as a fraction [tex]\frac{4}{1}[/tex], therefore, [tex]\sqrt{16}[/tex] is a rational number.

C. [tex]\sqrt{17}[/tex]

[tex]\sqrt{17}=4.1231056256176605[/tex]

Since our given number has non-terminating decimal, therefore, [tex]\sqrt{17}[/tex] is not a rational number.

D. [tex]\sqrt{18}[/tex]

[tex]\sqrt{18}=4.2426406871192851[/tex]

Since our given number has non-terminating decimal, therefore, [tex]\sqrt{18}[/tex] is not a rational number.

It is to be noted that from the options given, the rational number is √16

What is a rational number?

A rational number is any number that can be expressed as a fraction, where the numerator and denominator are integers.

Among the given numbers, the √16 is a rational number.

The √16 equals 4, which can be expressed as the fraction 4/1.

The square roots of 15, 17, and 18 are irrational numbers because they cannot be expressed as fractions or terminate or repeat in decimal form.

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A crew of ten workers was hired to complete a job in 8 days. After working for two days, there was a new request to complete this job in two days. How many more workers need to be hired to finish this job in 2 days?

Answers

They would need to hire 20 more workers because they are 1/4 of the way done after the first two days. And that means they need to be 3/4 of the way done in the next 2 days, that means they have to be 3 times as productive from the first day and 10 times 3 equals 30, but they already have 10, so 30 - 10 = 20
THEY NEED 20 more workers
I hope it helps

Answer:

29 more workers are needed.

Step-by-step explanation:

Let us assume that the 10 workers, working at their normal rate would finish the job in exactly 8 days.

The rate of working for 1 worker is:

[ 1/10 of the job ] / [ 8 days ] = [ 1 job ] / [ 80 days ]

This is also [ 1/80 of the job ] / [ 1 day ]

In 2 days, the fraction of the job that gets done is:

[tex]2\times \frac{1}{80}=\frac{1}{40}[/tex]

Job left = [tex]1-\frac{1}{40} =\frac{39}{40}[/tex]

Now the rate has to be :

[tex]\frac{\frac{39}{40} }{2} =\frac{39}{80}[/tex]

Now, let w be the additional number of workers needed.

We get:

[tex]\frac{10+w}{80}=\frac{39}{80}[/tex]

Solving for w;

[tex]10+w=39[/tex]

[tex]w=39-10[/tex]

w = 29

Therefore, 29 more workers are needed.

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

There can be another approach as well.

Fraction of the job done by 10 workers in 2 days = 1/4

Remaining fraction = 1-1/4 = 3/4

Lets say W workers are needed more.

So, we can say that 3/4 of the work is to be done by 10+W workers.

Hence, it will take a total of 30 workers to complete the job.

Making it additional 20 workers.

Which of the following statements is true?

All trapezoids are parallelograms.
All parallelograms are trapezoids.
All rectangles are squares.
All rhombuses are rectangles.

Answers

Answer:

The answer is B. All parallelograms are trapezoids.

Step-by-step explanation:

The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. That makes the opposite of facing sides are parallel to each other. The the definition of trapezoid is a convex quadrilateral with at least one pair of parallel sides. Therefore, all parallelograms are trapezoids.

The true statement among the given options is, B. All parallelograms are trapezoids.

A trapezoid is a quadrilateral with at least one pair of parallel sides, but it doesn't require all sides to be parallel. Therefore, not all trapezoids are parallelograms. (Statement A is false)

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Every trapezoid has at least one pair of parallel sides, so it can be considered a special case of a parallelogram. Therefore, all trapezoids are parallelograms. (Statement B is true)

A rectangle is a quadrilateral with all four angles equal to 90 degrees. It has opposite sides that are parallel and equal in length. A square is a special type of rectangle with all sides of equal length. However, not all rectangles have all sides of equal length, so statement C is false.

A rhombus is a quadrilateral with all four sides of equal length. It has opposite sides that are parallel, making it a parallelogram. Since a rectangle is a parallelogram with right angles, and a rhombus is a parallelogram with equal sides. Therefore, statement D is also false.

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Which of the following is an example of gameplay in a video game
A: the art of a game

B: the player interacting with the game world and game mechanics

C: the personalities of all the characters

D:all of the above

Answers

i would think B, since that describes playing a game.

Answer:

B: the player interacting with the game world and game mechanics

Step-by-step explanation:

Simplify.

(-5.12) - (-4.7) + (7.021)

6.79
6.601
-2.799

Answers

The answer is 6.601, and therefore, the second option.

The answer is 6.601

(-5.12)-(-4.7)+(7.021)

= -0.42+7.021
= 6.601

Change each fraction to a decimal. If the division doesn’t end, round your answer to the nearest hundredth. a. 3⁄4 b. 7⁄16 d. 3⁄5 e. 7⁄40 f. 51⁄20

Answers

a. 0.75
b. 0.44
d. 0.6
e. 0.18
f. 2.55

Answer:

the other person forgot to answer c

Step-by-step explanation:

a 0.75

b 0.44

c 0.6

d 0.6

e 0.18

Ariel was told the x intercept and the y intercept of a line with a positive slope. Yet, it was impossible for Ariel to find the slope of the line. What can you conclude about this line?

Answers

A line has the following standard equation form:

y = m x + b

where m is the slope and b is the y intercept

So if Ariel cannot find the slope, then this would only mean that m = 0, there is no slope. And hence the line is either a straight vertical line or straight horizontal line.

Answer:

There is no slope

Final answer:

Given only the information that a line has x and y intercepts and a positive slope, Ariel cannot directly calculate the slope without knowing the exact values of the intercepts. Knowledge of two distinct points on the line is necessary for calculating the slope.

Explanation:

Ariel was told the x intercept and the y intercept of a line with a positive slope. Yet, it was impossible for Ariel to find the slope of the line. What can you conclude about this line? If given only the x and y intercepts without the exact numeric values or additional points, determining the slope directly is challenging because the slope formula, Δy/Δx (change in y over change in x), requires knowledge of at least two distinct points on the line (other than the intercepts without their exact values). However, knowing that a line has both an x and a y-intercept implicitly indicates it is neither vertical nor horizontal, and stating it has a positive slope provides a general direction of the line's angle relative to the axes.

To find the slope, you generally need the coordinates of two distinct points on the line. For instance, if the y-intercept is given as (0, b) and the x-intercept as (a, 0), the slope m can be found by the difference in y values divided by the difference in x values, or (0 - b) / (a - 0) = -b/a. But without knowing a and b's exact values, Ariel cannot calculate the numeric value of the slope. This indicates a limitation in calculating slope with incomplete information about the intercepts' exact numerical values but not an inherent impossibility of the line to have a determinable slope if such values were known.

NEED ASAP!!!!
In quadrilateral ABCD, diagonals AC and BD bisect one another:

What statement is used to prove that quadrilateral ABCD is a parallelogram?
Angles ABC and BCD are congruent.
Sides AB and BC are congruent.
Triangles BPA and DPC are congruent.
Triangles BCP and CDP are congruent.

Answers

Answer:Triangles BPA and DPC are congruent is used to prove that ABCD is a parallelogram.

Explanation:Here, we have given a quadrilateral ABCD in which diagonals AC and BD bisect each other.

If P is a an intersection point of these diagonals

Then we can say that, AP=PC and BP=PD ( by the property of bisecting)

So, In quadrilateral ABCD,

Let us take two triangles, [tex]\triangle BPA[/tex] and [tex]\triangle DPC[/tex].

Here, AP=PC

BP=PD,

[tex]\angle APB=\angle DPC[/tex] ( vertically opposite angles.)

So, By SAS postulate,[tex]\triangle BPA\cong \triangle DPC[/tex]

Thus AB=CD ( CPCT).

Similarly, we can prove, [tex]\triangle APD\cong \triangle BPC[/tex]

Thus, AD=BC (CPCT).

Similarly, we can get the pair of congruent opposite angle for this quadrilateral ABCD.

Therefore, quadrilateral ABCD is a parallelogram.

Note: With help of other options we can not prove quadrilateral ABCD is a parallelogram.

The congruence of triangles BPA and DPC, proven through the Side-Angle-Side postulate or other congruency postulates, can be used to prove that quadrilateral ABCD is a parallelogram when diagonals AC and BD bisect one another.

The statement used to prove that quadrilateral ABCD is a parallelogram when diagonals AC and BD bisect one another is that triangles BPA and DPC are congruent. The congruence of these triangles can be shown through the Side-Angle-Side (SAS) postulate or other congruency postulates depending on a given figure, and this property that diagonals bisect each other is a defining trait of a parallelogram. Therefore, by showing the congruence of triangles BPA and DPC, we can deduce that ABCD is a parallelogram.

Match the following items.

1. 2x + x + 4 = -17
subtraction
2. 3x + 4 =-17
division
3. 3x =- 21
combine like terms

4. x = -7 Given

Answers

Answer and explanation:

To find : Match the following items.

Solution :

We arrange all steps by steps,

Step 1 - Given

[tex]2x + x + 4 = -17[/tex]

Step 2 - Combine like terms,

[tex]3x+ 4 = -17[/tex]

Step 3 - Subtract 4 both side,

[tex]3x=-21[/tex]

Step 4 - Divide by 3 both side,

[tex]x=-7[/tex]

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The following are matched:

1. 2x + x + 4 = -17 ------------ ( Given )

2. 3x + 4 =-17 ----------(combine like terms)

3. 3x =- 21 -----------( subtraction )

4. x = -7 -------------( division )

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Given,

2x + x + 4 = -17

We will combine the like terms.

3x + 4 = -17

We will subtract 4 on both sides.

3x = -17 - 4

3x = -21

Divide both sides by 3.

x = -21/3

x = -7

Thus,

1. 2x + x + 4 = -17 ------------ ( Given )

2. 3x + 4 =-17 ----------(combine like terms)

3. 3x =- 21 -----------( subtraction )

4. x = -7 -------------( division )

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Drag an answer to each box to complete this paragraph proof.

Given: ∠PQR and ∠RQS are supplementary angles and m∠PQR=115°

Prove: ∠RQS is an acute angle.

It is given that ∠PQR and ∠RQS are supplementary angles. So, m∠PQR+m∠RQS=180° using the ________ . It is also given that m∠PQR=115° . Using the substitution property of equality, ________ + m∠RQS=180° . Using the subtraction property of equality, m∠PQR=65° . Therefore, ∠RQS is an acute angle by ________ .

A. definition of complementary angles
B. definition of supplementary angles
C. definition of acute angle
D. definition of obtuse angle
E. 180°
F. 115°

Image uploaded below:
V V V

Answers

definition of acute angle

Answer: The correct options for blank 1,2 and 3 are B, F and C respectively.

Explanation:

It is given that the ∠PQR and ∠RQS are supplementary angles and ∠PQR=115°.

The two angles are called supplementary angles if they are lies on the same arc of a straight line and their sum is 180 degree.

Since it is given that ∠PQR and ∠RQS are supplementary angles, so by the definition of supplementary angles we can say that their sum is 180 degree.

[tex]\angle PQR+\angle RQS=180^{\circ}[/tex] .... (1)

Therefore, the correct option for first blank is option B.

It is given that ∠PQR=115°.

Using the substitution property of equality, the equation (1) can be written as,

[tex]115^{\circ}+\angle RQS=180^{\circ}[/tex]

Therefore, the correct option for second blank is option F.

Using the subtraction property of equality, ∠PQR=65° .

An angle less that 90 degree is called an acute angle and the an angle more than 90 degree but not more that 180 degree is called an obtuse angle.

Since 65 is less than 90, so by the definition of acute angle the ∠RQS is an acute angle.

Therefore, the correct option for third blank is option C.

What is 55 x 10 to the power of 4 in scientific notation

Answers

55*10 power of 4

5.500

At the beginning of an experiment, there are 400 grams of contaminants. Each hour, three-fourths of the contaminants are filtered out.

A. Formulate a recursive sequence modeling the number of grams after "n" hours.

B. Use the model to calculate the amount of contaminants after the third hour of the experiment.

Answers

The recursive sequence is:[tex]T_n = \frac 14T_{n-1}[/tex] and there are 25 contaminants left after the third hour of the experiment

The recursive sequence

The initial number of contaminant is 400.

If 3/4 contaminants are filtered out, there are 1/4 contaminants left.

So, the recursive sequence is:

[tex]T_n = \frac 14T_{n-1}[/tex]

Where T1 = 400

The number of contaminants after the third hour

This means that n = 3.

So, we have:

[tex]T_3 = \frac 14 * T_2[/tex]

[tex]T_2 = \frac 14 * T_1[/tex]

Substitute [tex]T_2 = \frac 14 * T_1[/tex] in [tex]T_3 = \frac 14 * T_2[/tex]

[tex]T_3 = \frac 14 * \frac 14 * T_1[/tex]

Substitute 400 for T1

[tex]T_3 = \frac 14 * \frac 14 * 400[/tex]

Evaluate

[tex]T_3 = 25[/tex]

Hence, there are 25 contaminants left after the third hour of the experiment

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Final answer:

A recursive sequence can be formulated to model the number of grams of contaminants after "n" hours. After plugging in the values, the amount of contaminants after the third hour is 168.75 grams.

Explanation:

A. To formulate a recursive sequence modeling the number of grams after "n" hours, we can start with the initial amount of contaminants of 400 grams and then multiply it by three-fourths each hour. This can be represented by the formula: an = (3/4) * an-1. This formula tells us that to find the amount of contaminants after "n" hours, we multiply the amount after the previous hour by three-fourths.

B. To calculate the amount of contaminants after the third hour of the experiment, we can use the recursive formula. Let's plug in the values: a0 = 400 grams, a1 = (3/4) * a0 = (3/4) * 400 = 300 grams, a2 = (3/4) * a1 = (3/4) * 300 = 225 grams, a3 = (3/4) * a2 = (3/4) * 225 = 168.75 grams.

Therefore, the amount of contaminants after the third hour of the experiment is 168.75 grams.

explain quantum physics and math

Answers

2+2 is 4 minus 1 thats 3 quick maths

Final answer:

Quantum physics is the branch of physics that deals with small objects and the quantization of various entities, including energy and angular momentum. Mathematics plays a crucial role in explaining quantum physics. It has various applications and impacts our understanding of the universe and technology.

Explanation:

Quantum physics is the branch of physics that deals with small objects and the quantization of various entities, including energy and angular momentum. It focuses on understanding the behavior of subatomic particles and the strange submicroscopic world they inhabit. Quantum mechanics, a part of quantum physics, describes the motion of objects that are atomic or subatomic in size and demonstrates wave-particle duality.

Mathematics plays a crucial role in explaining quantum physics. The mathematics of probability is used to describe the behavior of complex quantum systems. Additionally, equations and mathematical models are used to calculate and predict the behavior of subatomic particles.

Quantum physics has many applications and impacts our understanding of the universe and technology. It helps explain phenomena such as why some materials conduct electricity while others do not. It is also vital in areas such as atomic and nuclear physics, where it is used to study and manipulate the behavior of particles and systems at the quantum level.

Jack purchases 12 gallons of gas on Monday. He uses 2/3 of the amount purchased commuting to and from work during the week and an additional 2 gallons running errands. How many gallons of gas does john use from work and errands?

Answers

10 gallons because 2/3 of 12 is 8 and 8+2 is ten.

Answer: Using operations with fractions, John uses 10 gallons from work and errands.

Solution:

Jack purchases 12 gallons of gas on Monday.

He uses 2/3 of the amount purchased commuting to and from work during the week:

(2/3)(12)=(2/3)(12/1)=(2*12)/(3*1)=24/3=8

Then John uses 8 gallons commuting to and from work during the week.

And an additional 2 gallons running errands.

John uses in total from work and errands= 8 gallons+2 gallons

John uses in total from work and errands= 10 gallons

$8 euros were worth $9 and $24 euros were worth $27 write an equation of the form y=kx to show the relationship between the number of euros and the value in dollars.

Answers

Sent a picture of the solution to the problem (s).

Solve an equation to answer the question

Jose bought 2 movie tickets and a box of popcorn. The popcorn cost $6, and he spent a total of $24. How much did each ticket cost? Use m to represent the cost of each movie ticket.

A. 6m+2=24 m=3 ; each ticket cost $3.

B. 2m+6=24 m=9 ; each ticket cost $9.

C. 2m+6=24 m=15 ; each ticket cost $15.

D. 6m+2=24 m=4 ; each ticket cost $4.

Answers

2m + 6 = 24

Subtract 6 from both sides.

2m = 18

Divide both sides by 2.

m = 9

Hope this helps!

Answer:

B) 2m+6=24 m=9 ; each ticket cost $9.

Step-by-step explanation:

Given: Jose bought 2 movie tickets and a box of popcorn. The popcorn cost $6, and he spent a total of $24.

Here "m" represents the cost of each movie ticket.

Now let's form an equation.

2m + box of popcorn = $24

Box of popcorn cost $6

So,

2m + 6 = 24

Now, we have to solve for m.

Subtract 6 from both sides, we get

2m + 6 - 6 = 24 - 6

2m = 18

Dividing both sides by 2, we get

2m/2 = 18/2

m = 9

So, the cost of movie ticket is $9 each.

Therefore, the answer is B) 2m+6=24 m=9 ; each ticket cost $9.

Sylvia has 6 1/2 boxes of chocolate to share at a family picnic. if she gives eacah person 1/3 of a box, how many people can receive chocolate

Answers

Answer:

The correct Answer is 19

The number of people who will receive the chocolate will be equal to 19.

What is a fraction?

In mathematics, a fraction is represented by a specific number that designates a portion of an entire. A fraction is a piece or section of a whole, whereby a can have been any number, a particular value, or an object.

As per the provided data in the question,

Total boxes of chocolate = 13/2

Chocolate received by each person = 1/3 of a box

Then, the number of people who receive the chocolate is,

13/2 ÷ 1/3 = 19.5 or,

A total of 19 people will receive the chocolate.

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What is the point slope form of the line with slope −3/7 that passes through the point (5, 8)?

Answers

They are asking for point slope form, so we need to grab the equation:
y - y1 = m(x - x1)

Then just plug in what we already know:
m = -3/7 , y1 = 5 , x1 = 8

y - 5= -3/7(x - 8)

Then solve for Y

Final Answer: y = -3/7x + 71/7

Answer:y−8=−[tex]{\frac{3}{7}[/tex](x−5)

Step-by-step explanation:

Leanne is trying to choose between two party dresses that originally cost $120 one dress is on 1/4 off and the $40 what is the price of less expensive dress

Answers

the dress thats $40 off is less expensive. 1/4 of 120 is 30.

Front-row tickets for a concert cost $60. After every 5 rows, the ticket price goes down by $5. What is the total amount of money generated by a full house? Info: There are 20 rows that increase by 3 seats each time starting with 18.

Answers

I think I got it, but just in case...tell me the whole thing again. I wasn't listening.

n a 20 row theater, the number of seats increases by 3 with each successive row.  The first row has 18 seats.

a. Write an arithmetic series in summation notation to represent the number of seats in the theater,∑n=12018+3(n−1)b. What is the total seating capacity of the theater?
930 seats

c. Front row seats cost $60.  After every 5 rows, the price drops $5.  What is the amount generated by a full house?
$46950

2.  An arithmetic series has a first term of 4.  The sum of the first 40 terms is 6080.  Find the value of the 40th term?
use the formula
sum of first n terms = n/2 * (s1 + sn)
6080 = 40/2 * (4 + sn)

Solve for x.

89(54x−36)+2=−34(−40+16x)+90x

Answers

c:
..................

Of all rectangles with a fixed perimeter of p, which one has the maximum area? (give the dimensions in terms of p.)

Answers

For all rectangles with a fixed perimeter of p the rectangle with the maximum area is one where the length is p/4 and the width is p/4, in other words a square. The area of such a rectangle would be (p*p) /16.

For a rectangle with a fixed perimeter P, the one with maximum area has dimensions L = P/4 and W = P/4 obtained by optimizing the area expression.

To find the rectangle with the maximum area given a fixed perimeter P, we can use optimization techniques. Let L represent the length and W represent the width of the rectangle. The perimeter is given by P = 2L + 2W, and the area is given by A = LW.

Since P is fixed, we can express one of the variables in terms of the other using the perimeter equation. Solving for L, we get L = (P/2) - W. Substituting this expression into the area equation, we have A = ((P/2) - W)W.

To find the dimensions that maximize A, we take the derivative of A with respect to W, set it equal to zero to find critical points, and check for endpoints (since we are dealing with real-world dimensions).

(dA/dW) = (P/2) - 2W = 0.

Solving for W, we get W = P/4. Substituting this value back, we find L = P/4.

Therefore, the rectangle that maximizes the area for a fixed perimeter P has dimensions L = P/4 and W = P/4.

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The question probable may be:

What are the dimensions of the rectangle with the maximum area given a fixed perimeter P?

Which ordered pairs are solutions to the inequality 2y−x≤−6 ?

Select each correct answer.

(0, −3)

(2, −2)

(1, −4)

(6, 1)

(−3, 0)

Answers

try plugging them in, might seem tedious, but it's the best way to practice. if you plug in a pair and the left side of the equation is less than or equal to 6, it's the right answer.

we have

[tex]2y-x\leq -6[/tex]

we know that

if a ordered pair is a solution of the inequality

then

the ordered pair must satisfy the inequality

we will proceed to verify each case to determine the solution of the problem

case A) [tex](0,-3)[/tex]