Owen's bedroom has a perimeter of 46 feet. If the length of the bedroom is 11 feet, what is the width of the bedroom?

QUESTION POSTED AT 05/12/2019 - 11:59 AM

Answered by admin AT 05/12/2019 - 11:59 AM

46-11+11 which equals 24. Then you divide 24 by 2 to get the legth of one side of the width. Which is 12. So the width is 12.
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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

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

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

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

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

Alexei wants to hang a mirror in his boat, and put a frame around it. The mirror and frame must have an area of 19.25 square feet. The mirror is 3 feet wide and 5 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

The first part is already in squared terms. "19.25 sq ft" Taking the measurements for the mirror 3ft and 5ft, you'd get: "15 sq ft." Subtract that answer from the previous number to get "4.25 sq ft.

Hope this helps out a little lol :)

ANSWERED AT 18/01/2020 - 12:38 PM


QUESTION POSTED AT 18/01/2020 - 12:38 PM

Mary is making some shirts for her school's drama department. The fabric store has 3 1/6 yards of the fabric she wants in stock. But this quantity of fabric can make only 1 1/3 shirts. What length of fabric does Mary need to buy if she wants to sew 2 shirts?

The answer is 4 3/4 yards of the fabric.

This can be calculated using the proportion.
If the 3 1/6 yards of the fabric is enough for 1 1/3 shirts, how many yards are necessary of 2 shirts:
3 \frac{1}{6} yards :1 \frac{1}{3}shirts =xyards:2shirts

Let's express 3 1/6 as 19/6:
3 \frac{1}{6} =3+ \frac{1}{6} = 3* \frac{6}{6}+ \frac{1}{6} = \frac{18}{6} + \frac{1}{6} = \frac{18+1}{6} = \frac{19}{6}

Similarly, 1 1/3 = 4/3:
1 \frac{1}{3} =1+ \frac{1}{3} = 1* \frac{3}{3}+ \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{3+1}{3} = \frac{4}{3}<span>

ANSWERED AT 18/01/2020 - 12:37 PM


QUESTION POSTED AT 18/01/2020 - 12:37 PM

Laurie is trying to stay within 10 feet of her current diving depth of –30 feet (with regard to sea level) so that the light is still good but she can be close to the sea life during her scuba dive. Which two equations can be used to find the minimum and maximum depths Laurie wants to stay between? A. x + 30 = 10 and x + 30 = –10 B. x – 30 = 10 and x – 30 = –10 C. x + 10 = 30 and x + 10 = –30 D. x – 10 = 30 and x – 10 = –30

ANSWER
A. x + 30 = 10 and x + 30 = –10

EXPLANATION
If x represents the depth of Laurie at a given moment, then the distance between his current depth and -30 feet is given by

   | x - (-30) |

which can be simplifed into

   | x + 30 |

We use absolute value because distance cannot be negative.

Laurie must stay within 10 feet. Therefore, the distance x is from -30 feet has to be equal to 10 to find the maximum and minimum depths that Laurie can stay between:

   | x + 30 | = 10

When we solve this absolute value equation, we work with two cases.

Case 1: When x + 30 is positive, then |x+30| = x+30 (no change) and we have the equation
   x + 30 = 10

Case 2: When x + 30 is negative, then |x+30| = -(x+30) so as to force the distance into a positive number. Then this gives us the equation
   -(x+30) = 10
which we can multiply both sides by -1 to get
   x + 30 = -10

ANSWERED AT 18/01/2020 - 12:35 PM


QUESTION POSTED AT 18/01/2020 - 12:35 PM

In right ∆ABC, m B = 90°, m C = 40°, and BC = 10. What are the other two side lengths of the triangle?

It could be alot the easest is 20° and 20°

ANSWERED AT 18/01/2020 - 12:32 PM


QUESTION POSTED AT 18/01/2020 - 12:32 PM

Xz is 15 and the perimeter of triangle xwz is 50 what is the length of wz

Well if you have a congruent lines, and you have P = 50 and xz = 15 P = xz + 2 * wz so to find wz you need to subtract xz and divide by 2 50 - 15 = 35 and then divide by 2 to get 17.5

ANSWERED AT 18/01/2020 - 12:26 PM


QUESTION POSTED AT 18/01/2020 - 12:26 PM

B is the midpoint of ZA. find the length of ZA

If it was more details, it would be easier to solve. But I can suggest a logical way. ZB + BA = ZA. If B is the midpoint it devides line on two equal lines.

ANSWERED AT 18/01/2020 - 12:25 PM


QUESTION POSTED AT 18/01/2020 - 12:25 PM

What is A2 – (B + C) in simplest form? A=8x2 – 25x + 7 B=8x2– 25x + 11 C=10x2 – 25x + 7 D=10x2 – 25x + 11 A, B, and C are polynomials, where: A = 3x – 4 B = x + 7 C = x2 + 2

Answer: 8x^2 - 25x + 7

Step-by-step explanation:

Here, A = 3x - 4, B = x + 7 and C = x^2 + 2

A^2 - (B + C)= (3x-4)^2-(x+7+x^2+2)     ( By putting the values)

=  (3x)^2+ (4)^2- 2\times 3x\times 4- x- 7 - x^2 -2    ( solving the brackets)

=   9x^2+ 16 - 24x - x- 7 - x^2 -2

=   8x^2- 25x + 7        ( By operating like terms)

A^2 - (B + C) = 8x^2- 25x + 7

Thus, Option A is correct.

ANSWERED AT 18/01/2020 - 12:15 PM


QUESTION POSTED AT 18/01/2020 - 12:15 PM

Miriam has 62 feet of fencing to make a rectangular vegetable garden. Which dimensions will give Miriam the garden with greatest area

6 feet by 10 feet would use 60 feet of fencing. that's the biggest I can think of without going over 62 feet


ANSWERED AT 18/01/2020 - 12:15 PM


QUESTION POSTED AT 18/01/2020 - 12:15 PM

Miriam has 62 feet of fencing to make a rectangular vegetable garden. Which dimensions will give Miriam the garden with greatest area.

Given: 
62 feet of fencing = perimeter

P = 2 (L + W)

62/2 = 31
16 + 15 = 16 * 15 = 240 ft²
17 + 14 = 17 * 14 = 238 ft²
18 + 13 = 18 * 13 = 234 ft²
19 + 12 = 19 * 12 = 228 ft²
20 + 11 = 20 * 11 = 220 ft²

The best dimensions that will give the greatest area is to have a length of 16 feet and a width of 15 feet.

ANSWERED AT 18/01/2020 - 12:15 PM


QUESTION POSTED AT 18/01/2020 - 12:15 PM

The length of a rectangle is twice its width. The perimeter of the rectangle is 24 inches. Write a system of equations in 2 variables. Use substitution to solve the problem

Let us assume the width of the rectangle = w
Let us assume the length of the rectangle = l
Then
l = 2w
Also 
Perimeter of the rectangle = 2 (l + w)
24 = 2 (2w + w)
24 = 2 (3w)
24 = 6w
w = 24/6
    = 4 inches
Now 
The length of the rectangle = 2w
                                            = 2 * 4 inches
                                            = 8 inches
So the length of the rectangle is 8 inches and the width is 4 inches.

ANSWERED AT 18/01/2020 - 12:13 PM


QUESTION POSTED AT 18/01/2020 - 12:13 PM

Which expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign? A square shaped traffic sign is shown with length of one side labeled as 8x minus 2.

Given:
square shaped traffic sign. side measure of 8x - 2

A square has 4 equal sides. To find the area of a square, simply square the measure of 1 side. 

Area of a square = a²
A = (8x-2)²
A = (8x-2)(8x-2)
A = 8x(8x-2) - 2(8x-2)
A = 64x² - 16x - 16x + 4
A = 64x² - 32x + 4




ANSWERED AT 18/01/2020 - 12:13 PM


QUESTION POSTED AT 18/01/2020 - 12:13 PM

Denise is designing the seating arrangement for a concert an outdoor theater. To give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats. Help Denise plan the rest of the seating by solving for how many seats are in row 18. Then explain to Denise how to create an equation to predict the number of seats in any row. Show your work, and use complete sentences.

Given:
1st term = 11
common difference = 6

f(x) = 11 + 6(x - 1)
f(18) = 11 + 6(18-1)
f(18) = 11 + 6(17)
f(18) = 11 + 102
f(18) = 113 number of seats in row 18.

Row
1              11    11  
2       11     6    17
3       17     6    23
4       23     6    29
5       29     6    35
6       35     6    41
7       41     6    47
8       47     6    53
9       53     6    59
10     59     6    65
11     65     6     71
12     71     6     77
13     77     6     83
14     83     6     89
15     89     6     95
16     95     6    101
17   101     6    107
18   107     6    113

ANSWERED AT 18/01/2020 - 12:08 PM


QUESTION POSTED AT 18/01/2020 - 12:08 PM

Find the perimeter of a quadrilateral with vertices at C (−1, 2), D (−2, −1), E (2, −2), and F (1, 1). Round your answer to the nearest hundredth when necessary.

To get the perimeter of the quadrilateral, the distance formula can be used. We simply have to subtract the y coordinate of one point to another and the same for the x coordinate. The square root of the sum of the squares of the difference is the distance.The results can then be added to get the perimeter. So,
CF = sqrt ( (2-(-1))^2 + (-1-(-2))^2 ) = sqrt(10)
FE = sqrt ( (-2-1)^2 + (2-1)^2 ) = sqrt(10)
ED = sqrt ( (-1-(-2))^2 + (-2-2)^2 ) = sqrt(17)
DC = sqrt ( (2-(-1)^2 + (-1-(-2))^2 ) = sqrt(10)

P = CF + FE + ED + DC = sqrt(10) + sqrt(10) + sqrt(17) + sqrt(10) = 13.61

ANSWERED AT 18/01/2020 - 11:59 AM


QUESTION POSTED AT 18/01/2020 - 11:59 AM

The area of a square is 36 square feet. Each side of the square measures

6 because 6x6=36
-------------------

ANSWERED AT 18/01/2020 - 11:57 AM


QUESTION POSTED AT 18/01/2020 - 11:57 AM

Solve the problem. If a lawn sprinkler sprays 15 feet in every direction, what is the area of the yard that gets watered?

Hello,

A=πR²=3.141592...*15²=706,8583470...( ft²)
===================================

ANSWERED AT 18/01/2020 - 11:57 AM


QUESTION POSTED AT 18/01/2020 - 11:57 AM