MATHEMATICS HIGH SCHOOL

A rectangular painting measures 15 inches by 18 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 90 inches. Determine the width of the frame.

Answers

Answer 1

Answer:

3 inches

Step-by-step explanation:

Lenght = 18 inches

Width =15 inches

Perimeter of the rectangular painting and frame = 90 inches

Let X be the width of the frame

The width of the framed picture = 15 + 2x

The length of the framed picture = 18 + 2x

Perimeter = 2 (L + W)

90 = 2(15 + 2x + 18+ 2x)

90 = 2(33 + 4x)

90 = 66 + 8x

8x = 90 - 66

8x = 24

x = 24/8

x = 3 inches

the width of the frame is 3 inches

Answer 2

Answer:

Final answer:

To determine the width of the frame, subtract twice the frame width from the length and width of the outer rectangle and set up an equation based on the perimeter.

Explanation:

To determine the width of the frame, we need to first find the dimensions of the inner rectangle formed by the painting. If we subtract twice the frame width from the length and width of the outer rectangle, we get the length and width of the inner rectangle. Let's call the width of the frame 'x'.

The length of the inner rectangle is 15 inches - 2 inches, and the width of the inner rectangle is 18 inches - 2 inches. The perimeter of the inner rectangle is the sum of its four sides, which can be calculated using the

formula P = 2l + 2w. We know that the perimeter of the inner rectangle is 90 inches, so we can set up the equation:

90 = 2(15 - 2x) + 2(18 - 2x)

Solving this equation will give us the value of 'x', which represents the width of the frame.

Learn more about the Dimensions of a rectangular frame here:

brainly.com/question/32613996

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The director of marketing at a large company wants to determine if the amount of money spent on internet marketing is a good predictor of company profit. She fits a least-squares regression line to 20 months of data and computes the following regression line:Profit = 372.6 + 17.2(advertising dollars)

What is the value of the residual for advertising dollars spent equal to $1,020 and Profit equal to $17,500? Round to the nearest integer.

Answers

Given:
Profit = 17,500
advertising dollar = 1,020

regression line:

Profit = 372.60 + 17.2(advertising dollar)
17,500 = 372.60 + 17.2(1020)
17,500 = 372.60 + 17,544
17,500 = 17,916.60

There is a residual value of 416.60.

17,916.60 - 17,500 = 416.60

Equation:cosθ= -12/13 for π <θ<3π /2
prompt:
find sin 2θ, cos 2θ, and tan 2θ

Answers

Cosθ = -12/13.
For π <θ<3π /2 means 180° <θ< 270°. That is the third quadrant.

Let us just have the positive value of Cosθ = 12/13

Cosθ = Adjacent / Hypotenuse = 12 / 13

So we imagine a right angled triangle with adjacent side = 12, and Hypotenuse = 13.

To get the opposite side we apply Pythagoras' Theorem. Let the opposite side be x.

x² + 12² = 13²
x² + 144 = 169
x² = 169 - 144
x² = 25
x = √25
x = 5.

Sinθ = Opposite / Hypotenuse = 5 / 13

Tanθ = Opposite / Adjacent = 5 / 12

Recall the angle is in the third quadrant, and in the third quadrant, only Tangent is positive, Cosine and Sine are both negative.

Therefore
Cosθ = -12/13 Sinθ = -5/13 Tanθ = 5/12

Solving:

i) Sin2θ = 2SinθCosθ. By Trigonometric Identity.

= 2*(-5/13)*(-12/13)

= 120/169

ii) Cos2θ = 2Cos²θ - 1

= 2*(-12/13)(-12/13) - 1

= 288/169 - 1

= (288 - 169) / 288

    = 119/288

Tan2θ = 2Tanθ /(1 - Tan²θ)

   = 2*(5/12) / ( 1- (5/12)²)

   = (5/6) / ( 1 - 25/144)

   = (5/6) / ( (144 -25)/144)

   = (5/6) / (169/25)

   = (5/6) * (25/169)

   = 125/1014

I hope this helps.

One number is 16 more than a second number. The sum of the first number and twice the second number is 139. What is the answer ?

Answers

Answer first number = 57 second number = 41
x= 16 + y
x + 2y = 139

16+ y + 2y =139
16 + 3y =139
16-16 +3y = 139-16
3y = 123
3/3y = 123/3
y= 41

x= 16+y
x = 16+41
x= 57

M/2+m evaluate if m 14

Answers

Answer:

Step-by-step explanation:

To add fractions find the LCD and then combine

Factor out 12x^2- 4x = 0

Answers

12x^2-4x=0
144x^2-4x=0
140x^2=0
/140 /140
x=0

12x^2-4x=0.
Factor it out.
4x(3x-1)=0
4x=0 or 3x-1=0

x=0 or x=1/3

a money bag contains ten 5-dollar notes and thirty 10-dollar notes. if a note is randomly selected from the bag, what is the probability of a 5-dollar note being selected?

Answers

Total no. of notes = 10+30 =40
5 dollars note = 10

probability = 10/40 =1/4

$67 answer from my oppinon

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