MATHEMATICS HIGH SCHOOL

Proportions in Triangles (5)

Answers

Answer 1

Answer:

Answer:

3 1/3

Step-by-step explanation:

Right side segments are proportional to left side segments:

5/6 = x/4

x = 4·5/6 = 3 1/3 . . . . . multiply by 4

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A recipe calls for 2 cups of flour and 1 cup of milk. What is the ratio of milk to flour in this recipe?

Answers

Answer:

1:2

Step-by-step explanation:

1:2 I believe, maybe 1/2 or 1 and 2.

Solve for x: 3 − (2x − 5) < −4(x + 2)

Answers

3 − (2x − 5) < −4(x + 2)
3-2x+5< -4x-8
-2x+4x< -8-3-5
2x< -16
x< -16/2
x< -8
x∈(-∞ -8)

IS -9 + 14 the same as -14 + 9

Answers

Answer:

Step-by-step explanation:

no because -9 plus 14 would be 5 because your technically takeing away from 14 -14 plus 9 would be -23

A square and a rectangle have the same area. The length of the rectangle is twelve more than twice times the side of the square. The width of the rectangle is eight less than the side of the square. Let x be the length of the side of the square. Using the information above, what is the value of x?

Answers

Answer:

$x = 12$

Step-by-step explanation:

Given

Shapes: Square and Rectangle

Square:

$Length = x$

Rectangle:

$Length = 12 + 2x$

$Width = x- 8$

Required

Find x

First, we calculate the area of the square.

$Area = x * x$

$Area = x^2$

Next, we calculate the area of the rectangle

$Area = (12 + 2x) * (x - 8)$

$Area = 12x -96 + 2x^2 - 16x$

$Area = 2x^2 - 16x + 12x -96$

$Area = 2x^2 -4x -96$

Since both areas are equal, we have:

$x^2 = 2x^2 -4x -96$

Equate to 0

$2x^2 -x^2 -4x -96= 0$

$x^2 -4x -96= 0$

Expand:

$x^2 - 12x + 8x -96 = 0$

$x(x - 12) + 8(x - 12) = 0$

$(x + 8)(x - 12) = 0$

$x + 8 = 0$ or $x - 12 = 0$

$x = -8$ or $x = 12$

But x can't be negative.

Hence:

$x = 12$

A 4-pound bag of sugar contains 454 one-teaspoon servings and costs $3.49. A batch of muffins uses 1/4 cup of sugar. How many batches can you make if you use all the sugar? What is the cost of sugar for each batch? (1 cup = 48 teaspoons)

Answers

About 9 times with a remainder of 22 teaspoons

Solve the system of equations.2.5y + 3x = 27
5x – 2.5y = 5

What equation is the result of adding the two equations?

What is the solution to the system?

Answers

If you put them together, +2.5y and -2.5y neutralize themselves while 5x and 3x become 8x.

2.5y + 3x = 27
5x – 2.5y = 5

8x = 32
x = 4

2.5y + 3x4 = 27
2.5y + 12 = 27
2.5y = 27-12
2.5y = 15
y = 15/2.5
y = 6

X = 4
Y = 6

Answer:

x=4 Y=6

Step-by-step explanation:

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Two large numbers of the Fibonacci sequence are F49 = 7,778,742,049 and F50 = 12,586,269,025. What is the approximate value of the quotient ?