The length of a rectangle is 9 inches more than three times the width. the perimeter is 98 inches. find the length and width

QUESTION POSTED AT 05/12/2019 - 08:23 AM

Answered by admin AT 05/12/2019 - 08:23 AM

Here is the equation:

Your goal is to get a number variable

2w+2(3w+9)=98

Solve the parentheses first, namely "w" by itself on one side

2w+6w+18=98

Add common  values

8w+18=98

Minus 18 from both sides

8w+18-18=98-18

It is now

8w=80

Now, divide 80 by 8

80÷8=10

w=10

Lets check:

2(10)+ 2(30+9)=98

20+60+18=98

Which is correct

So that means each side of the width is 10 inches
and each length side is 39 inches

Answer: So that means that width side is 10 inches each and each length side is 39 inches each. 10+10+39+39=98 inches

 
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Related questions

The formulas for area of a rectangle and area of a parallelogram are the same. State the formulas and write about why they are the same.

Area of rectangle A = l*w so area equal length time width 
in case of a parallelogram A = length what is base time height what is the width corresponding of rectangle case 

hope this is understandably sure easy 

ANSWERED AT 18/01/2020 - 01:14 PM


QUESTION POSTED AT 18/01/2020 - 01:14 PM

Find the quotient. (6x 2 + 23x + 20) ÷ (5 + 2x) 3x - 4 3x + 4 3x +19

\frac{6x^{2} + 23x + 20}{2x + 5} = \frac{6x^{2} + 15x + 8x + 20}{2x + 5} = \frac{3x(2x) + 3x(5) + 4(2x) + 4(5)}{2x + 5} = \frac{3x(2x + 5) + 4(2x + 5)}{2x + 5} = \frac{(3x + 4)(2x + 5)}{2x + 5} = 3x + 4

The answer is B.

ANSWERED AT 18/01/2020 - 01:13 PM


QUESTION POSTED AT 18/01/2020 - 01:13 PM

The Martin family is considering building a new house. On the blueprints, the dimensions of the outside of the house are 18 inches wide by 26 inches long. If the house is actually going to be 45 feet wide, what will the actual length of the house be?

This can be answered through simple ratio and proportion

 

Let x = width

y = height

x/y = x2/y2 = x3/y3

 

since

for 18 inches width we have 26 inches as length, therefore

 

18/26 = 45/y2

y2 = 65 ft

 

there is no need to convert the units for the smaller dimensions since we are dealing with definite ratios thus unitless. 

ANSWERED AT 18/01/2020 - 01:12 PM


QUESTION POSTED AT 18/01/2020 - 01:12 PM

If a cylinder’s radius and height are each shrunk down to a third of the original size, what would be the formula to find the modified surface area?

We let

r1 = the original radius of the cylinder

r2 = the new radius of the cylinder

h1 = the original height of the cylinder

h2 = the new height of the cylinder

SA = surface are of the cylinder

 

the radius and the height are shrunk down to a third of their value therefore

 

r2 = r1/3

h2 = h1/3

 SA = 2(PI)r^2 + 2(PI)rh

SA = 2(PI)[(r1^2)/9] +2(PI)(r1/3)(h1/3)

 

Simplifying

SA = [2(PI)r]/9 * (r1 + h1)

ANSWERED AT 18/01/2020 - 01:12 PM


QUESTION POSTED AT 18/01/2020 - 01:12 PM

A lizard needs to stay a safe distance from a cactus. The diameter of the cactus is 12 inches. If the lizard is 8 inches from a point of tangency, find the direct distance between the lizard and the cactus (x). If necessary, round to the hundredths place.

Answer:

10 in

Step-by-step explanation:

We are given that

Diameter of cactus=d=12 in

Radius of cactus=\frac{d}{2}=\frac{12}{2}=6 in

Distance of lizard from point of tangency=8 in

We have to find the direct distance between lizard and cactus.

In triangle OAB,

OA=6 in

AB=8 in

Pythagorous theorem: (Hypotenuse)^2=(base)^2+(perpendicular\;side)^2

Using pythagorous theorem

OB^2=(6)^2+(8)^2=100

OB=\sqrt{100}=10 in

Hence, the direct distance of lizard from cactus=10 in

ANSWERED AT 18/01/2020 - 01:11 PM


QUESTION POSTED AT 18/01/2020 - 01:11 PM

How does this model demonstrate the Pythagorean Theorem? Three squares whose corners touch so that the respective edges form a triangle. The smallest square has a side labeled six and is made up of thirty-six smaller squares. The largest square has a side labeled ten and is made up of one hundred smaller squares. The third square has a side labeled eight and is made up of sixty-four smaller squares. A. The sum of the lengths of the shortest and the longest sides is equal to twice the length of the middle side. So double the length of the longer leg of any right triangle is equal to the sum of the shorter leg and the hypotenuse. B. The sum of the area of the two smaller squares is equal to the area of the larger square. So the sum of the lengths of the two legs of any right triangle squared is equal to the length of the hypotenuse squared. C. The sum of the area of the smallest and the largest squares is equal to the area of the middle square. So the sum of the lengths of the shorter leg and the hypotenuse of any right triangle squared is equal to the length of the middle leg squared. D. The length of the longest side minus two equals the length of the middle side. The length of the middle side minus two equals the length of the shortest side. So the length of the short leg of any right triangle is equal to the length of the middle leg minus 2, and the length of the hypotenuse is equal to the length of the middle leg plus 2.

"  B is your best choice but it is very badly stated. this gives an Example of the Pythagorean theorem. it does Not demonstrate it. B is written incorrectly, it should say "sum of squares of the lengths of the legs" Not "sum of the lengths of the two legs of any right angle squared"

ANSWERED AT 18/01/2020 - 01:07 PM


QUESTION POSTED AT 18/01/2020 - 01:07 PM

Triangle ABC has side lengths 18,24, and 30. Do the side lengths form a Pythagorean triple? Yes or No?

Answer:  Yes, the side lengths form a pythagorean triple.

Step-by-step explanation:  Given that the side lengths of triangle ABC are as follows :

AB=18,~~BC=24,~~CA=30.

We are to check whether the side lengths form a pythagorean triple or not.

For making a pythagorean triple, the side lengths must satisfy the following :

AB^2+BC^2=CA^2.

We have

AB^2=18^2=324,\\\\BC^2=24^2=576,\\\\CA^2=30^2=900.

So,

AB^2+BC^2=324+576=900=CA^2.

Thus, the side lengths will form a pythagorean triple.

ANSWERED AT 18/01/2020 - 01:06 PM


QUESTION POSTED AT 18/01/2020 - 01:06 PM

You began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period. Time (weeks) 0 1 2 3 4 5 6 7 8 Weight (lb) 150 144 143 141 140 137 137 132 129. If you lost 13 pounds in the first five weeks, what is the average rate of change of weight with respect to time over the first five weeks of the program?

Time (weeks) 0     1     2      3      4    5      6      7     8 
Weight (lb) 150 144 143 141 140 137 137 132 129

Change in time (weeks) =      5 - 0      =   5    = -0.3846 
Change in weight (lbs)       137 -150      -13

The average rate of change of weight with respect to time over the first five weeks of the program is -0.3846. It is a negative sign because the weight is decreasing.

ANSWERED AT 18/01/2020 - 01:04 PM


QUESTION POSTED AT 18/01/2020 - 01:04 PM

Part A: The area of a square is (16x2 − 8x + 1) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)

16x2−4x−4x+1=4x(4x−1)−1(4x−1)=(4x−1)(4x−1)=(4x−1)2 Length of each side=4x-1

ANSWERED AT 18/01/2020 - 12:54 PM


QUESTION POSTED AT 18/01/2020 - 12:54 PM

Part B: The area of a rectangle is (81x2 − 4y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

Hello,

if the aim is to factorise:
81x²-4y²=(9x)²-(2y)²=(9x-2y)(9x+2y)

But the sides may also be and an other expression....

ANSWERED AT 18/01/2020 - 12:54 PM


QUESTION POSTED AT 18/01/2020 - 12:54 PM

Find the GCF of the following literal terms. m^7 n^4 p^3 and mn^12 p^5

Do you have the 4th problem typed correctly? The two given numbers have no factor (other than 1) in common (i.e., they are relatively prime) so the GCF is 1. 

48 = 2^4 * 3 

Therefore, GCF of 16a^4 b^4 + 32a^3 b^5 - 48a^2 b^6 is 16a^2 b^4, so 
16a^4 b^4 + 32a^3 b^5 - 48a^2 b^6 = (16a^2 b^4)(a^2 + 2ab - 3b^2) = (16a

ANSWERED AT 18/01/2020 - 12:53 PM


QUESTION POSTED AT 18/01/2020 - 12:53 PM

Find the value of y when x equals -11, 5x+6y=-37

5(-11)+6y=-37
-55+6y=-37
6y=18
y=3

ANSWERED AT 18/01/2020 - 12:51 PM


QUESTION POSTED AT 18/01/2020 - 12:51 PM

Arrange the equations in the correct sequence to find the inverse of f(x)=y=3x/8+x

To find the inverse of the the function, it must be arranged in such a way that the independent variable be on the left side and the dependent variable on the right. So,
f(x) = y = 3x/ (8 + x)
y (8 + x) = 3x
8y + xy = 3x
8y = 3x - xy
8y = x (3 - y)
8y / (3-y) = x
x = 8y / (3 -y)

Therefore,
f-(x) = f(y) = x = 8y/ (3 - y)

ANSWERED AT 18/01/2020 - 12:50 PM


QUESTION POSTED AT 18/01/2020 - 12:50 PM

In order to raise money for holiday gifts for your family, you are planning on starting a dog walking and car wash business. You earn $12 per hour while dog walking and $18 per hour washing cars. You need to earn at least $600 during the month of November. 1.Assign a variable to represent the number of hours that you will spend dog walking in November. Write an expression to represent the amount of money you need to earn while dog walking. 2.Assign a variable to represent the number of hours that you will spend washing cars in November. Write an expression to represent the amount of money you need to earn while washing cars. 3.Write an algebraic model using inequalities that represents the total amount of money earned by dog walking and washing cars during the month of November. 4.Graph the algebraic model in the first quadrant only. Let the x-axis be the number of hours spent dog walking and the y-axis be the number of hours spent washing cars. Click here for a sheet of graph paper to print.. 5.Use the graph and algebraic model to answer the following: a.Why does the graph exist only in the first quadrant? b.Are you able to earn exactly $600? Use the solutions of the system to find possible combinations of outcomes that equal exactly $600. Where do all of the combinations occur in the graph? c.Is it possible to earn more than $600? Use the solutions of the system to find possible combinations of outcomes that are greater than $600. Where do all of the combinations occur in the graph? d.If you work for 10 hours walking dogs and 10 hours washing cars, will you have earned enough money for the holiday gifts? Where does 10 hours walking dogs and 10 hours washing cars fall on the graph? Is this location representative of the solution to the algebraic model? Click here for a sheet of graph paper to print.. 6.How would the algebraic model be different if you needed to earn more than $600? Adjust your algebraic model to show that you must earn more than $600. Would the graph of the model be different from the original? Would you include the line in the solution? What type of line represents "more than"? Graph your new algebraic model . 7.In complete sentences, explain the difference between a solid line and a dashed line when graphing an inequality. When graphing the two algebraic models, how did you determine which type of line to use? 8.How did you determine which part of the graph of the inequality to shade? What does the shaded area tell you? What does the area that is not shaded tell you?

#1. Let x be the number of hours spent dog walking, then the amount of money earned dog working is 12x.
#2. Let y be the number of hours spent washing cars, then the amount of money earned washing cars is 18y.
#3. 12x+18y \geq 600

ANSWERED AT 18/01/2020 - 12:50 PM


QUESTION POSTED AT 18/01/2020 - 12:50 PM

The sum of a number and two times a smaller number is 98. The bigger number is 22 less than three times the smaller number.

Hello,

Let y the smaller
x the greater
x+2y=98 ==>x+2y=98 (1)
x=3y-22 ==> x-3y=-22 (2)

(1)-(2)==>5y=98+22==>y=120/5==>y=24
(2)==>x=3*24-22==>x=72-22==>x=50



ANSWERED AT 18/01/2020 - 12:49 PM


QUESTION POSTED AT 18/01/2020 - 12:49 PM

Jane has a 5 × 7-inch photograph that she wants enlarged to a 10 × 14-inch photograph.

Jane would double it in order to get her enlarged photograph? what is the question? 

ANSWERED AT 18/01/2020 - 12:48 PM


QUESTION POSTED AT 18/01/2020 - 12:48 PM

Find the value of y when x equals 4, -3x+9y=-57

-3(4)+9y=-57
-12+9y=-57
9y=-45
y=-5

ANSWERED AT 18/01/2020 - 12:48 PM


QUESTION POSTED AT 18/01/2020 - 12:48 PM

The lengths of three line segments are 4 centimeters, 5 centimeters, and 9 centimeters. Using this information, triangles can be constructed.

Answer:

No triangles can be constructed

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

In this problem

4+5>9------> is not true

therefore

No triangles can be constructed with the given side lengths



ANSWERED AT 18/01/2020 - 12:46 PM


QUESTION POSTED AT 18/01/2020 - 12:46 PM

Find the value of y when x equals 1, 9x+7y=-12

9(1)+7y=-12
9+7y=-12
7y=-12-9
7y=-21
y=-3

ANSWERED AT 18/01/2020 - 12:46 PM


QUESTION POSTED AT 18/01/2020 - 12:46 PM

Two sides of an obtuse triangle measure 10 inches and 15 inches. The length of longest side is unknown. What is the smallest possible whole-number length of the unknown side?

Answer – 19 inches
 The smallest possible whole-number length of the longest side of an obtuse triangle is the next integer greater than the Pythagorean distance of the other two sides.
 Given,
A = 10
 B = 15
Pythagoras theorem;
C^2 = A^2 + B^2
C^2 = 15^2 + 10^2
C^2 = 225 + 100
C^2 = 325
C = 18.03
 Therefore, the smallest possible whole-number length of the longest side is the next integer greater than 18.03 inches.
The smallest possible whole-number length of the longest side is 19 inches

ANSWERED AT 18/01/2020 - 12:45 PM


QUESTION POSTED AT 18/01/2020 - 12:45 PM

A computer simulation tossed a 10-faced die 5 times. How many possible outcomes exist?

Answer:  There exists 100000 possible outcomes.

Step-by-step explanation:  Given that a computer simulation tossed a 10-faced die 5 times.

We are to find the number of possible outcomes that exists.

Since there are 10 faces of the die, so we have 10 possible options for each of the 5 tosses.

Therefore, the total number of possible outcomes is

n=10\times10\times10\times10\times10=10^5=100000.

Thus, there exists 100000 possible outcomes.

ANSWERED AT 18/01/2020 - 12:42 PM


QUESTION POSTED AT 18/01/2020 - 12:42 PM