The length of a rectangle is 4 times its width. The perimeter of the rectangle is 150 cm. Find the dimensions of the rectangle.​
it should contain step by step and understandable explanation.

Answer:

a) £60

b) 6 weeks

Step-by-step explanation:

Phil is paid £240 per week

He saves 1/4 ie., 1/4 x 240 = 60

Cost of new bike = £349

No. of weeks savings = 349 / 60 = 5.816666 werks

To maintain the CG and balance in the system, the third box weighing 20 pounds should be placed 4 feet forward of the CG.  The CG is the point where the weight of the object is evenly distributed, and it is crucial for maintaining balance.

First, let's calculate the total weight of the system. We have two boxes weighing 15 pounds and 10 pounds, and a third box weighing 20 pounds. The total weight is 15 + 10 + 20 = 45 pounds.
Next, we need to find the moment caused by the two boxes already placed. The moment is the product of the weight and its distance from the CG.
For the 15-pound box, the moment is 15 pounds * 4 feet = 60 pound-feet.
For the 10-pound box, the moment is 10 pounds * 2 feet = 20 pound-feet.

To keep the CG unchanged, the total moment of the system must be zero. This means that the moment caused by the third box must balance out the moments of the other two boxes.

Let's denote the distance from the CG to the third box as 'x' feet. The moment caused by the third box is 20 pounds * x feet.
So, to maintain balance, the equation becomes:
60 pound-feet + 20 pound-feet = 20 pounds * x feet.
Simplifying this equation, we get:
80 pound-feet = 20x feet.
To solve for 'x', we divide both sides by 20:
4 = x.
Therefore, the third box should be placed 4 feet forward of the CG to maintain balance.

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To find 2a + 5b, we multiply each component of vector a by 2, and each component of vector b by 5, and then add the corresponding components together.

a = (-5, 12)

b = (7, 3)

2a + 5b = (-10, 24) + (35, 15) = (25, 39)

|a| = sqrt((-5)^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13

|a - b| = sqrt((-5 - 7)^2 + (12 - 3)^2) = sqrt((-12)^2 + 9^2) = sqrt(144 + 81) = sqrt(225) = 15

To find 2a + 5b, we multiply each component of vector a by 2, and each component of vector b by 5, and then add the corresponding components together. So we have:

2a + 5b = (2(-5), 2(12)) + (5(7), 5(3)) = (-10, 24) + (35, 15) = (25, 39)

To find |a|, we need to calculate the magnitude (or length) of vector a. This is done by taking the square root of the sum of the squares of its components. So we have:

|a| = sqrt((-5)^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13

To find |a - b|, we need to calculate the magnitude of the difference between vectors a and b. This is done by subtracting the corresponding components of the vectors, squaring them, summing the squares, and taking the square root of the result. So we have:

|a - b| = sqrt((-5 - 7)^2 + (12 - 3)^2) = sqrt((-12)^2 + 9^2) = sqrt(144 + 81) = sqrt(225) = 15

Therefore:

2a + 5b = (25, 39)

|a| = 13

|a - b| = 15

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Answer:

15.26

Step-by-step explanation:

By using a^2+b^2=c^2, we can plot the numbers into the equation, 8^2+13^2=c^2. Then answering the exponents, it will equal 64+169=c^2. Add that together to get 233=c. Lastly, we have to square-root 233, which equals 15.26. Hope this helped!

Answer:

-12

Step-by-step explanation:

3q-6=x q=-2

(3(-2))-6

-6-6=x

-12=x

An equation for C is C = 0.1t + 4.

An interpretation of the slope of the graph is that the total cost of using a computer increases by 0.1 per minute.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 4.5)/(10 - 5)

Slope (m) = 0.5/5

Slope (m) = 0.1

At data point (10, 5) and a slope of 0.1, a linear equation for C can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 0.1(x - 10)

y = 0.1x + 5 - 1

y = 0.1x + 4 ≡ C = 0.1t + 4

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Answer:

4.07

Step-by-step explanation:

2.50+1.75+4.80+12.88=4.07 EZ

A regular hex decagon's measure of one internal angle is 7.5 degrees more than a regular dodecagon's measure of one interior angle.

We must ascertain the measure of each individual angle in each polygon in order to compare the differences in one inside angle between a regular hex decagon and a regular dodecagon.

The following formula can be used to determine the size of each interior angle in a regular polygon with n sides:

Interior Angle = (n - 2) x 180 / n

Regular hex decagon:

Interior Angle = (16 - 2) * 180 / 16

= 14 * 180 / 16

= 2520 / 16

= 157.5 degrees

Regular dodecagon:

Interior Angle = (12 - 2) * 180 / 12

= 10 * 180 / 12

= 1800 / 12

= 150 degrees

Difference = Measure of hexadecagon angle - Measure of dodecagon angle

= 157.5 degrees - 150 degrees

= 7.5 degrees

Therefore, the measure of one interior angle of a regular hex decagon is 7.5 degrees greater than the measure of one interior angle of a regular dodecagon.

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The correct answer would be "A. $2,075 = $1,500 + (.0575*s)" total sales.

A sale is a deal in which two or more parties trade products or services for cash or other assets, usually between a buyer and a seller. It is an agreement between a buyer and seller on the price of a security and the delivery of the security to the buyer in exchange for the agreed-upon compensation constitutes a sale in the financial markets. The transaction is not regarded as a sale if the product or service in issue is given by one party to the other without receiving payment, but rather as a gift or donation.

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if you do 24 x 4 you get 96  so that mean multiply 3 x 4 too and you get 12 so the answer is he can run 12 miles in 96 minutes

Answer:

Hello!!

Alan can run 3 miles in 24 minutes. If he maintains the same pace, what the greatest number of miles he can run in 96 minutes is 12 miles.

Step-by-step explanation:

\(96\) ÷ \(24=4\)

\(4\) × \(3=12\)

Hope this helps!!

Answer:

Step-by-step explanation:

\(\begin{array}{c|c|c|c}&D&E&Sum\\---&---&---&---\\A&10&20&30\\B&15&5&20\\C&30&15&45\\---&---&---&---\\Sum&55&40&95\\\end {array}\\\\\\1) P(E)=\dfrac{40}{95} =\dfrac{8}{19} \\\\2) P(B \cup D)=P(B)+P(D)-P(B \cap D)=\dfrac{20}{95} +\dfrac{55}{95} -\dfrac{15}{95} =\dfrac{60}{95} =\dfrac{12}{19} \\\\3) P(A \cap E)=\dfrac{20}{95}=\dfrac{4}{19} \\\\4) P(B | E)=\dfrac{P(B \cap E )}{P(E)} =\dfrac{\dfrac{5}{95} }{\dfrac{40}{95} } =\dfrac{5}{40}= \dfrac{1}{8} \\\\5) P(D|E)=0\)

Supplementary = 180 Degrees

So the measure of angle U + the measure of angle V = 180 Degrees

The measure of angle V is 3 times the measure of angle U, so

U+3U=180 Degrees, which can be written as 4U=180

You can find the value of U by dividing both sides by 4

U=180/4=45 Degrees

Since you are trying to find the value of x that makes U and V supplementary, you would sustitute the value of 45 Degrees that was calculated for U into the equation given for x.

45 Degrees = 3x

To solve you divide both sides by 3

x=45/3=15

x = 15 Degrees

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form

Slope-intercept form is written as y=mx+b, where m is the slope and b is the y-intercept. Using the information given we can plug in the numbers to get the correct equation. This looks like y=-3x+4.

Slope-intercept form is helpful because we can use it to find coordinate points and graphs. By graphing the y-intercept and then using the slope to count out points, you can find the function. Additionally, by plugging in values for x or y, you can find coordinate pairs.

The standard form is Ax + By = C

Where, if at all possible, A, B, and C are integers, and A is non-negative.  Our linear equation in standard form is:

x - 5y = -12  or 1x - 5y = -12

where A = 1, B = -5, and C = -12  

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Answer:b

Step-by-step explanation:

Answer:

? question ?

Step-by-step explanation:

Answer:

I think the answer is A if its not im sorry

Step-by-step explanation:

The value of length JK is 11

A tangent is a straight line that touches any part of the circumference. A circumference is the outer body of a circle.

A theorem of tangency states that if lines comes from thesame point of a circumference and meet at a point , then the lines are equal.

Therefore we can say that;

JA = JB = 5

AL = LC = 9

CK = LK - LC

= 15 -9

= 6

BK = LK = 6

therefore ;

JK = BK + JP

= 6+5

= 11

Therefore the value of JK is 11

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Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:3x100=300+75=$375.00

Step-by-step explanation:

Answer:

$375 to install 100 square ft of carpet

Step-by-step explanation:

you would do (3.00 x 100 ft) which would get you to 300. then since there’s a flat fee of 75 you would add 300 + 75 = 375

Answer:

She earned $42,000 in the previous year

Step-by-step explanation:

9% can be rewritten as 0.09

0.09x is 4050

divide both sides by 0.09

0.09x becomes x

4050 becomes 45,000

then we subtract 3,000 from 45,000 to find the previous years salary

Answer:

Step-by-step explanation:

\(tan\theta =\frac{12}{5}\\ \\ \theta =tan{-1}\frac{12}{5}\\ \\ \theta =67.38^o\\ \\ \theta \approx 67^o\)

Answer: b) The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞.

Step-by-step explanation:

It will take Joe 5 hours to reach Chicago.

To calculate the time it will take for Joe to reach Chicago, we can use the formula:

Time = Distance / Rate

Given that Joe drives 325 miles at a constant rate of 65 mph, we can plug these values into the formula:

Time = 325 miles / 65 mph = 5 hours

The correct answer is:

C) 5 hrs.

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Answer:

Y=2/3x - 3

Gradient is 2/3

y=mx+c

Answer:

4

Step-by-step explanation:

4x + 15 = x - 3

4x - x = 3 - 15

3x = 12

x = 12 : 3

x = 4

According to recent studies, an accurate assessment of how much time we spend with the most important people in our lives reveals that:

Research shows that while we may know hundreds or even thousands of people, only a few of them are truly important to us. These important individuals may include family members, close friends, and romantic partners. Despite the limited number of people who fall into this category, we tend to spend a significant amount of our social time with them, reflecting the quality of our relationships with them.

This information highlights the importance of building and nurturing meaningful relationships with those who matter most to us. By investing time and energy in these important connections, we can enhance our well-being and build a strong support system to help us navigate life's challenges.

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The following is an accurate assessment of how much time we spend with the most important people in our lives:

On average, we devote 40 percent of our limited social time with the five most important people we know, who represent just 3 percent of our social world.

The notion of "social worlds" is used here to refer to a form of social organization which cannot be accurately delineated by spatial, territorial, formal, or membership boundaries.

Rather, boundaries of social worlds must be determined by interaction and communication which transcend and cross over the more formal and traditional delineators of organization.

The term "social world" is used here to develop a common referent for a number of related concepts which refer to similar phenomena.

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To find the function to which the given series converges, we can rewrite it as a power series. The series is:

x - x^5 + x^5 + x^6 - x^2 + 28 - x^8 - x^9

We can simplify this by grouping like terms:

(x - x^5) + (x^5 + x^6) - x^2 + 28 - (x^8 + x^9)

Now, we can express each term as a power series:x(1 - x^4) + x^5(1 + x) - x^2 + 28 - x^8(1 + x)

Expanding each term further:

x - x^5 + x^6 + x^6 + x^7 - x^2 + 28 - x^8 - x^8

Combining like terms:

x + x^6 + x^7 - x^2 + 28 - 2x^8 - x^5

This power series represents the function to which the given series converges within its interval of convergence.

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Answer:

6.4 units

Step-by-step explanation:

c = √(x1 - x2)^2 + (y1 - y2)^2

c = √(3 - 7)^2 + (-3 + 8)^2

c = √(-4)^2 + (5)^2

c = √16 + 25

c = √41

c = 6.4031...

c = 6.4

1. From the given data in the question,

Decrease in city population = 25000 – 24500 = 500

Therefore, change in population = 500

Initial population = 25000

Percentage decrease = (Change in population / Initial population) × 100

On substituting the values, we get

= (500 / 25000) ×100

= 2%

2.

Increased in price of a car from Rs. 3,50,000 to Rs. 3,70,000

Amount change = Rs.3,70,000−Rs.3,50,000=Rs.20,000

Therefore, Increased percentage =

Amount of change/Original Amount × 100

\( \tt{ = \frac{20000}{350000} × 100} \\ \)

\( \tt = {5 \frac{5}{7}\%.} \\ \)

Answer:

D) 10y+10

E) 10(y+1) = 10y+10

Step-by-step explanation:

8y+y+y+10

9y+y+10

10y+10

Answer:

D, E

Step-by-step explanation:

D. 10y + 10

E. 10 (y+1) = 10y+10