Answer:
A = [tex]8\sqrt{110}[/tex] [tex]inches^{2}[/tex]
Step-by-step explanation:
In this question, we are tasked with calculating the area of a triangle given the length of its three sides
Mathematically, we can calculate this using the Heron's formula
For Heron's formula, A = [tex]\sqrt{S(S-A)(S-B)(S-C)}[/tex]
WHERE S = [tex]\frac{A+B+C}{2}[/tex]
we take the lengths of the triangle as A,B and C respectively as given
S = (12 + 14 + 18)/2 = 22
Plugging the values into the equation, we have;
A = [tex]\sqrt{22(22-12)(22-14)(22-18)}\\ \\\sqrt{22(10)(8)(4)} \\\\\sqrt{7040}[/tex]
A = [tex]8\sqrt{110}[/tex] [tex]inches^{2}[/tex]
Answer:
8*sqrt(110)
Step-by-step explanation:
Problem 2. (4 points) Given that A is a matrix of size 6 by 5. Which of the following statements must be TRUE? (I) The linear system Ax = b is consistent for all b in R 6 . (II) The linear system Ax = b is consistent for some b in R 6 . (III) If the linear system Ax = b is consistent for a fixed b in R 6 , then its solution must not be unique. (A) I only (B) II only (C) III only (D) II and III only (E) I and II
Answer:
Step-by-step explanation:
If the columns span R^6, this says that every b in R^6 is in the span of the columns, which is another way of saying that any b is a linear combination of the columns. Then the equation is consistent for some b or all b in R^6.
If an augmented matrix can be transformed by elementary row operations into reduced echelon form, then the equation Ax = b is consistent.
Any matrix can be transformed by elementary row operations into reduced echelon form, but not every matrix equation Ax = b is consistent
For example, after echelon reduction we have
1 6. 7. 8. 8.
0 1. 5. 4. 9
0. 0. 1. 3. 6
0. 0. 0. 1. 6.
0. 0. 0. 0. 1
0. 0. 0. 0. 0
In this case, the matrix doesn't have a solution, then the matrix is inconsistent
But if the matrix echelon reduction gives
1 6. 7. 8. 8.
0 1. 5. 4. 9
0. 0. 1. 3. 6
0. 0. 0. 1. 6.
0. 0. 0. 0. 1
0. 0. 0. 0. 1
Then, the system have a solution but not unique, the system have a solution for some b in R^6.
Then, the solution is II and III
So the correct option is D.
An Olympic runner set a record for the 100m dash.
The time was ten and sixty-two hundredths
seconds. How would you write this as a number?
To convert the word form of the time to decimal form, add 10.00 and 0.62 to get the final number representation of 10.62 seconds.
Explanation:To write the time of ten and sixty-two hundredths seconds as a number, we need to convert the word form into decimal form. The word form tells us that there are ten whole seconds and sixty-two hundredths of a second. To convert this to decimal form, we write 10 as 10.00 and 62 hundredths as 0.62. Then, we add the two decimal numbers together to get the final result: 10.00 + 0.62 = 10.62. Therefore, the number representation of the given time is 10.62 seconds.
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En un salon de la academia trilce hay 24 varones y 36 mujeres ¿Qué fracción de las mujeres son los varones?
Answer:
2/3
Step-by-step explanation:
To know the fraction of men over women, we just need to divide the total number of men in the academy by the total number of women in the academy. So, we have that:
Fraction = men / women = 24 / 36 = 2/3
So the fraction we want to know is 2/3, that is, for every 2 men, there are 3 women in the academy.
A card is 9 inches by 4 inches. A printing shop will enlarge it so that the longer side is any lengths up to 3 ft. Find the dimensions of the biggest enlargement
Answer:
3 ft by 4/3 feet.
Step-by-step explanation:
We have been given that a card is 9 inches by 4 inches. A printing shop will enlarge it so that the longer side is any lengths up to 3 ft. We are asked to find the dimensions of biggest enlargement.
We will use proportions to solve our given problem.
[tex]\frac{\text{Card width}}{\text{Card length}}=\frac{\text{Enlarged width}}{\text{Enlarged length}}[/tex]
Upon substituting our given values, we will get:
[tex]\frac{\text{4 inches}}{9 \text{ inches}}=\frac{\text{Enlarged width}}{\text{3 ft}}[/tex]
[tex]\frac{4}{9}=\frac{\text{Enlarged width}}{\text{3 ft}}[/tex]
[tex]\frac{4}{9}\times \text{3 ft}=\frac{\text{Enlarged width}}{\text{3 ft}}\times \text{3 ft}[/tex]
[tex]\frac{4}{3}\times \text{ft}=\text{Enlarged width}[/tex]
Therefore, the dimensions of the biggest enlargement would be 3 ft by 4/3 feet.
Izzy recently took a math test were each answer a on the main part of the test was worth 8.7 points she also correctly so the bonus question worth 10 points. Using the equation 8.7 A +10 equals 105.7 how many correct answers age is he have on the main part of the test
Answer:
11
Step-by-step explanation:
8.7A+10=105.7
8.7A=95.7
A=11
6q add 4 takeaway q add 5
Find the product: -4/7 (- 13/2)
Answer:
the answer is 3.71
Step-by-step explanation:
Answer:
3.71428571429
Step-by-step explanation:
NEED HELP ASAP!!!!!!!!!!!
The area of a parking lot is 600 square meters. A car requires 6 square meters. A bus requires 30 square meters. The attendant can handle only 60 vehicles. The parking lot also needs to be able to hold at least 3 buses and 10 cars. A car is charged $2.50 each day and a bus is charged $7.50 each day. They want to collect at least $75 each day.
Answer:
Step-by-step explanation:
Let the no of cars be x and no of buses be y.
x + y = 60 -> y = 60 - x
6x + 30y = 600
with the available equations let us calculate the values of x and y.
6x + 30 * (60-x) = 600
6x + 1800 - 30x = 600
24x = 1200
x cars = 50
y buses = 10
maximum profit = 50 * 2.5 + 10 * 7.5 = $200
a) The objective function to maximize profit is: 2.5C + 7.5B using constraints 6C + 30B ≤ 600 and C + B ≤ 60. b) The parking lot should accept 50 cars and 10 buses to maximize profit. The maximum profit will be $200.
We need to set up a linear programming model to maximize profit from parking cars and buses.
A. Model Formulation:
Let C represent the number of cars and B represent the number of buses.
Objective Function: Maximize Profit = 2.5C + 7.5B
Constraints:
Space constraint: 6C + 30B ≤ 600 (square meters)Vehicle limit: C + B ≤ 60 (vehicles)Non-negativity constraints: C ≥ 0, B ≥ 0B. Solution:
First, we convert the inequalities to equations and solve:
6C + 30B = 600 ⟶ C + 5B = 100 C + B = 60We solve these equations simultaneously:
1. C + 5B = 100 (Equation 1)
2. C + B = 60 (Equation 2)
Subtract Equation 2 from Equation 1:
(C + 5B) - (C + B) = 100 - 60
⟶ 4B = 40 ⟶ B = 10
From Equation 2, we get:
C + 10 = 60 ⟶ C = 50
Maximum Profit Calculation:
Substituting C = 50 and B = 10 into the objective function:
Profit = 2.5(50) + 7.5(10) = 125 + 75 = 200
Therefore, to maximize profit, the attendant should accept 50 cars and 10 buses.
Maximum profit is $200.
Complete question:
The area of a parking lot is 600 square meters. A car requires 6 square meters. A bus requires 30 square meters. The attendant can handle only 60 vehicles. If a car is charged $2.50 and a bus $7.50. How many of each should be accepted to maximize Profit?
a. Set up for the solution of this Linear Programming (LP) problem.
b. Using part (a), how many of each should be accepted to maximize Profit? What is the maximum profit?
Which graph has a rate of change equal to
1 in the interval between 0 and 3 on the x-axis?
bo
Answer: -2
Step-by-step explanation:
Because I know
What is the solution set for the following graph below?
The solution set is where the black dot is located, which is on the number 5.
The solution would be 5
Which is equivalent to (4 × 2) × 7?
6 × 7
8 + 5
8 × 7
4 × (2 + 7)
Answer:
8 × 7
Step-by-step explanation:
(4 × 2) × 7
We can multiply what is inside the parentheses
(8) × 7
Answer:
8*7
Step-by-step explanation:
Multiply what is inside the parentheses first, (PEMDAS)
(4*2)*7
8*7
Hope this helps! :)
Finding the Volume of a Pyramid
Find the volume of the square pyramid. The work has been started for you.
V = 1
3
Bh
B = 6.5(6.5) = 42.25 m2
A square pyramid. The square base has side lengths of 6.5 meters and the height of 6 meters.
What is the volume of the pyramid
Answer:
84.5 cubic meters
Step-by-step explanation:
You want the volume of a pyramid with a base area of 42.25 m² and a height of 6 m.
VolumeThe formula for the volume of a pyramid is ...
V = 1/3Bh
Using the given values, we find the volume to be ...
V = 1/3(42.25 m²)(6 m) = 84.5 m³
The volume of the pyramid is 84.5 cubic meters.
Find the volume of a cone with base area 36π ft2 and a height equal to twice the radius. Give your answers both in terms of π and rounded to the nearest tenth.
The volume in terms of π is _____ft3.
The volume rounded to the nearest tenth is _____ft3.
Answer:
The volume in terms of π is 144 ft³
The volume rounded to the nearest tenth is 452.4 ft³
Step-by-step explanation:
The formula of the volume of a cone is V = [tex]\frac{1}{3}[/tex] π r² h , where r is its radius and h is its height
The formula of the area of a circle is A = π r²
∵ The area of the base of the cone is 36π ft²
- Equate the formula of the area of the circle by 36π to find r
∵ πr² = 36π
- Divide both sides by π
∴ r² = 36
- Take √ to both sides
∴ r = 6 ft
∵ The height of the cone is equal to twice the radius
∵ The radius of the cone is 6 ft
- Multiply 6 by 2 to find the height
∴ h = 2(6) = 12 ft
∴ The height of the cone is 12 ft
Substitute the values of h and r in the formula of the volume of the cone to find it
∵ V = [tex]\frac{1}{3}[/tex] π(6)²(12)
∴ V = 144 π ft³
∴ V = 452.3893421 ft³
- Round it to the nearest tenth
∴ V = 452.4 ft³
Joey wants to buy strawberries and raspberries to bring to a party strawberries cost $1.60 per pound and raspberries cost $1.75 per pound if she only has $10 to spend on berries which any quality represents the situation where she buys X pounds of strawberries and why pounds of
Answer: 1.6x + 1.75y ≤ 10
Step-by-step explanation:
Let x represent the number of pounds of strawberries that Joey can buy.
Let y represent the number of pounds of raspberries that Joey can buy.
Strawberries cost $1.60 per pound and raspberries cost $1.75 per pound. It means that the cost of x pounds of strawberry and y pounds of raspberry is expressed as
1.6x + 1.75y
if she only has $10 to spend on berries, then the inequality that can be used to represent the situation is
1.6x + 1.75y ≤ 10
How do you know when a situation involves a percent increase or a
percent decrease?
Answer:
1. Subtract starting value minus final value.
2.divide that amount by the absolute value of the starting value.
3. Multiplt by 100 to get a percent decrease.
4. if the percentage is negative, it means there was an increase and not an decrease
Answer:
Step-by-step explanation:
A percent of increase (or decrease) is a ratio of the amount of increase (or decrease) to the original amount. To find the percent of increase (decrease): Determine the amount of increase (or decrease). Divide this result by the given original amount.
A recipe for beef stew calls for 1 pound of beef and 3 potatoes. The recipe is doubled to include 2 pounds of beef and 6 potatoes. Given that the proportion 1 3 = 2 6 represents the situation, which of these statements are true? Check all that apply.
Answer:
b and d
Step-by-step explanation:
Find the mode of the set of data 7, 2, 5, 8, 14, 8, 10, 2
Answer: The modes of that set of data are both 8 and 2
Step-by-step explanation: The mode is the number that appears most often in a data set and 8 and 2 are the only number that appear more than once in that set of data
Answer:
8 and 2
Step-by-step explanation:
I got this for a quiz and the answer was 8 and 2.
A gas pump fills 2^-3 gallon of gasoline per second. How many gallons does the pump fill in one minute?
Answer:
7.5 gallons
Step-by-step explanation:
2^-3= 0.125
0.125*60= 7.5
Final answer:
The gas pump fills 7.5 gallons of gasoline in one minute.
Explanation:
If a gas pump fills 2-3 gallon of gasoline per second, we first need to understand how much that is in gallons. 2-3 is the same as 1/23 or 1/8. Therefore, the pump fills 1/8 gallon per second.
To find out how many gallons the pump fills in one minute, we multiply the amount filled per second by the number of seconds in a minute:
Gallons per minute = gallons per second × seconds per minute
Gallons per minute = 1/8 gallon/second × 60 seconds/minute
Gallons per minute = 60/8 gallons
By reducing this fraction, we get:
Gallons per minute = 7.5 gallons
Thus, the gas pump fills 7.5 gallons of gasoline in one minute.
PL
(05.02)
Find the measure of angle x in the figure below: (5 points)
Answer:
the measure of angle x is 80
Step-by-step explanation:
What is the measure of each exterior angle of a regular 30-gon?
Answer:
Each Exterior Angle = (360 degrees) ÷ (Number of Sides)
Each Exterior Angle = 360 / 30
Each Exterior Angle = 12 degrees
Step-by-step explanation:
The measure of each exterior angle of a regular 30-gon will be 12°.
Based on the information, it should be noted that the value of the total angles will be 360°.
Therefore, the measure of each exterior angle of a regular 30-gon will be:
= 360/30
= 12°
Therefore, the measure of each exterior angle of a regular 30-gon is 12°.
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Oceanside Bike Rental Shop charges a 17 dollar fixed fee plus 6 dollars an
hour for renting a bike. Benny paid 59 dollars to rent a bike. How many
hours did he pay to have the bike checked out ?
Write the expression in standard form 6(-5r-4)-2(r-7s-3)
Final answer:
To write the expression 6(-5r-4)-2(r-7s-3) in standard form, distribute the numbers outside the parentheses across the terms within and combine like terms to get -32r + 14s - 18.
Explanation:
To write the expression 6(-5r-4)-2(r-7s-3) in standard form, we must distribute the numbers outside the parentheses to each term inside the parentheses and then combine like terms.
Distribute the 6: 6 × (-5r) = -30r and 6 × (-4) = -24, giving us -30r - 24.
Distribute the -2: -2 × r = -2r, -2 × (-7s) = +14s and -2 × (-3) = +6, giving us -2r + 14s + 6.
Combine the two resulting expressions: -30r - 24 - 2r + 14s + 6.
Combine like terms: The terms -30r and -2r combine to -32r, and the constants -24 and +6 combine to -18.
The standard form of the expression is -32r + 14s - 18.
Check the answer to see if it is reasonable.
1. The cities of Dallas, Charleston, and Indianapolis form a triangle. The distance from Dallas to
Charleston is 980 mies, Charleston to Indianapolis is 595 mies, and Indianapolis to Dallas is 764
mies. If Dallas and Charleston lie on the same latitude, find the bearing from Charleston to
Indianapolis.
Answer: 130 degree
Step-by-step explanation:
Given that
The distance from
Dallas to Charleston = 980 miles Charleston to Indianapolis = 595 miles,
Indianapolis to Dallas is 764 mies.
If Dallas and Charleston lie on the same latitude, find the bearing from Charleston to Indianapolis.
Let us use cosine formula to find the angle at Charleston
764^2 = 980^2+595^2-2(980)(595)cosØ
583696 = 1314425-1166200cosØ
-1166200cosØ = -730729
CosØ = 0.6266
Ø = 51.2
Let us also calculate the angle at Indianapolis by using sine rule
980/sinI = 764/sin 51.2
Reciprocal both sides
SinI/980 = sin 51.2/764
Sin I = 980 × sin52.1/764
Sin I = 0.9996
I = 88.5 degree
The bearing = 270 - ( 51.2 + 88.5)
= 270 - 140
= 130 degree.
In this exercise we have to use the knowledge of triangles to calculate the angle of this geometric figure, in this way we can say that:
130 degree
Given that the distance from dallas to Charleston and Charleston to Indianapolis and Indianapolis to Dallas, we can use the the cosine formula to find the angle at Charleston, so we have:
[tex]764^2 = 980^2+595^2-2(980)(595)cos\phi\\583696 = 1314425-1166200cos\phi\\-1166200cos\phi = -730729\\Cos\phi = 0.6266\\\phi = 51.2[/tex]
Let us also calculate the angle at Indianapolis by using sine rule:
[tex]980/sin\theta = 764/sin (51.2)\\Sin\theta/980 = sin 51.2/764\\Sin\theta = 980 * sin52.1/764\\Sin \theta = 0.9996\\\theta = 88.5 degree = 270 - ( 51.2 + 88.5)\\= 270 - 140\\= 130 degree.[/tex]
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It takes a smaller hose twice as long to fill a certain swimming pool as it does a larger hose. It takes both hoses working together 25 minutes to fill the pool. How long will it take the larger hose to fill the pool by itself?
Answer: it will take the larger hose 37.5 minutes to fill the pool.
Step-by-step explanation:
Let t represent the number of minutes it will take the larger hose to fill the pool by itself. It means that the rate at which larger hose fills the pool per minute is 1/t
It takes the smaller hose twice as long to fill the swimming pool as it does the larger hose. It means that the number of hours it takes smaller hose to fill the pool is 2t and it fills it alone, then the rate at which it fills the pool per minute is 1/2t
By working together, they would work simultaneously and their individual rates are additive. It takes both hoses working together 25 minutes to fill the pool. It means that the rate at which they fill the pool together per minute is 1/25. Therefore,
1/t + 1/2t = 1/25
3/2t = 1/25
Cross multiplying, it becomes
2t = 3 × 25 = 75
t = 75/2 = 37.5 minutes
Final answer:
To find the time it takes for the larger hose to fill the pool alone, we set up an equation based on their combined work rate and solve for the larger hose's time, finding that it would take 75 minutes.
Explanation:
The question is about determining how long it will take for the larger hose alone to fill the pool, given that it takes twice as long for a smaller hose to complete the same task, and together they can fill the pool in 25 minutes. To solve this problem, let's denote the time it takes for the larger hose to fill the pool by itself as x minutes. Therefore, the smaller hose takes 2x minutes to fill the pool by itself.
Since the problem involves rates of work, we can use the formula Work done = Rate × Time. The rate can be considered as the portion of the pool filled per minute. So, the larger hose's rate is 1/x and the smaller hose's rate is 1/(2x). Working together, their combined rate is 1/25 of the pool per minute, following the equation 1/x + 1/(2x) = 1/25.
By solving this equation: 2/2x + 1/2x = 1/25 ⇒ 3/(2x) = 1/25 ⇒ x = 75. Therefore, it would take the larger hose 75 minutes to fill the pool by itself.
An object is thrown up word from the top of 160 foot building with an initial velocity of 144 ft./s. The height H of the object after T seconds is given by the quadratic equation h= -16t^2 + 144t + 160. When will the object hit the ground?
Answer:
After 10 seconds
Step-by-step explanation:
In this problem, the height of the object after t seconds is described by the function
[tex]h(t)=-16t^2+144t+160[/tex]
where
160 ft is the initial height of the object at t = 0
+144 ft/s is the initial velocity
[tex]-32 ft/s^2[/tex] is the acceleration due to gravity (downward)
Here we want to find the time at which the object hits the ground, so the time t at which
[tex]h(t)=0[/tex]
Therefore we can write
[tex]-16t^2+144t+160 =0[/tex]
Simplifying (dividing each term by 16), we get
[tex]-t^2+9t+10=0[/tex]
This is a second-order equation in the form
[tex]ax^2+bx+c=0[/tex]
Which has solutions given by the formula
[tex]t_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] (2)
Here we have:
a = -1
b = 9
c = 10
Substituting into (2) we find the solutions:
[tex]t_{1,2}=\frac{-9\pm \sqrt{9^2-4(-1)(10)}}{2(-1)}=\frac{-9 \pm 11}{-2}[/tex]
Which gives:
[tex]t_1=10 s\\t_2 =-1 s[/tex]
Since time cannot be negative, the only solution is
t = 10 seconds
A cylinder has a radius of 8 centimeters and a height of 12 centimeters. A smaller cylinder has linear dimensions that are one-fourth the dimensions of the larger cylinder. Compare the surface area of the smaller cylinder to the surface area of the larger cylinder.
Answer:
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Answer: the surface area of the larger cylinder is 16 times that of the smaller cylinder.
Step-by-step explanation:
The formula for determining the total surface area of a cylinder is expressed as
Total surface area = 2πr² + 2πrh
Where
r represents the radius of the cylinder.
h represents the height of the cylinder.
π is a constant
Considering the larger cylinder,
radius = 8 cm
Height = 12 cm
Therefore,
Total surface area = (2 × π × 8²) + (2 × π × 8 × 12)
= 128π + 192π = 320π
Considering the smaller cylinder,
Total surface area = 56π
radius = 8/4 = 2cm
Height = 12/4 = 3 cm
Therefore,
Total surface area = (2 × π × 2²) + (2 × π × 2 × 3)
= 8π + 12π = 20π
Ratio of the surface area of the larger cylinder to the smaller cylinder is
320π/20π = 16
All 150 eighth grade students at a local middle school were asked how many hours they studied during the week. Each row of the table represents one sample from the population. Find the mean of each sample.
Population Data
Row 1
6
5
3
0
4
Row 2
4
5
3
5
6
Row 3
7
1
4
5
3
Row 4
4
2
5
6
3
Which row has the greatest mean?
1
2
3
4
Answer:
Row 2
Step-by-step explanation:
6+5+3+0+4=16
4+5+3+5+6=23
7+1+4+5+3=20
4+2+5+6+3=20
23 is bigger than all of those so it would be row two.
Answer:
Row 2
Explanation:
mark's dog needs 1 3/4 cups of dry food. Mark picks up one bag of dry food that contains 16 cups how many days will mark be able to feed his dog the specified diet?
Answer: I believe the answer is 9 days.
Step-by-step explanation: 16 divided by 1.75 (1 and three-fourths) is equal to 9.143, which is only enough to feed him 9 full days.
Answer:
The answer to your question is 9 days.
Step-by-step explanation:
Data
Food needed = 1 3/4 cups
Total food = 16 cups
Number of days = ?
Process
1.- Convert the mixed fraction into an improper fraction
1 3/4 = (4 + 3)/4 = 7/4
2.- Divide the total food by the food needed
16/1 ÷ 7/4 = 64/7
-Simplify 9 Quotient
7 64
1 Remainder
3.- Mark can feed his dog 9 days and there will be 1/7 of the bag left.
Alex, Benji, and Carmen collect shells they have found on the beach. When combined, they have a total of 308 shells. They also noticed that Benji has 20% more shells than Alex, while Carmen has 40% fewer shells than Alex.
How many shells does each friend have?
Answer:
Alex has 110 shells
Benji has 132 shells
Carmen has 66 shells
Step-by-step explanation:
In this question, we are tasked with calculating the number of shells each of the friends have.
We proceed as follows;
Since Alex is the linking point between the other two friends, we say that let the number of shells Alex has be A
Now, Benji has 20% more shells
This mathematically means that the number of shells owned by Benji = (20% × A) + A = 0.2A + A = 1.2A
Carmen has 40% fewer shells than Alex;
Mathematically, this means that the number of shells owned by Carmen is A - (40% × A) = A - 0.4A = 0.6A
To find A, we simply add all together and equate to 308
Mathematically, we have;
A + 1.2A + 0.6A = 308
2.8A = 308
Divide both sides by 2.8
A = 308/2.8
A = 110
This means Alex has 110 shells
Benji has 1.2A = 1.2 × 110 = 132 shells
Carmen has 0.6A = 0.6 × 110 = 66 shells
A rectangle is shown. All angles are right angles. The length of one side is 2 x and the length of another side is 3 x + 3. The perimeter of the rectangle is 146 units. What is the length of the longer side? 14 units 28 units 33 units 45 units Rhombus LMNO is shown with its diagonals. Rhombus L M N O is shown. Diagonals are drawn from point M to point O and from point L to point N and intersect at point P. All sides are congruent. The length of LN is 28 centimeters. What is the length of LP? 7 cm 9 cm 14 cm 21 cm
Answer: (A) The longer side in the rectangle is 45 units.
(B) The line LP measures 14 cm.
Step-by-step explanation: In the rectangle, two sides are given as 2x and 3x + 3, respectively. The perimeter is also given as 146 units. The formula to determine the perimeter is
Perimeter = 2(L + W)
We can now substitute for the values
146 = 2(2x + 3x + 3)
146 = 2(5x + 3)
146 = 10x + 6
Subtract 6 from both sides of the equation
140 = 10x
Divide both sides of the equation by 10
14 = x
With the value of x now known as 14, the sides of the rectangle are,
L = 2x
L = 2 x 14
L = 28
And the other side is
W = 3x + 3
W = 3(14) + 3
W = 42 + 3
W = 45
Therefore the longer side is 45 units.
In question B;
The rhombus has all sides congruent as one of its properties. This simply implies that the diagonal from point M to point O, is the same length as the diagonal from point L to point N. Hence, at point P, where both diagonals intersect, both diagonals are divided into two equal lengths each. If line LN is 28 cm, then line LP which is half of LN shall be 28 divided by 2, and that gives us 14 cm.