A straight line is 180°.
The sum of all the angles in a triangle is also 180°.
Let the missing angle be x°.
For the straight line:
x + 2x²+ 3x+ 6 = 180
x = 180 - (2x² + 3x + 6)
x = 180 - 2x² - 3x - 6
x = 174 - 2x² - 3x
For the missing angle in the triangle:
(174 - 2x² - 3x) + 8x + 3x² - 6x = 180
174 - 2x² - 3x + 8x + 3x² - 6x = 180
174 + x² - x = 180
x² - x + 174 - 180 = 0
x² - x - 6 = 0
(x + 2)(x - 3) = 0
x + 2 = 0 or x - 3 = 0
x = -2 or x = 3
The answer is x = -2 or x = 3
Answer:
h=6 feet
Step-by-step explanation:
Given: 1. The base of a rectangle is three feet longer than its height.
2.Are of the rectangle=54 square meters
Let us say the rectangle has height h and base(breadth) b.
Since, the base of the rectangle is three feet longer than the height, we have b=h+3.
Also, Area of the Rectangle= hb
therefore, 54=h(h+3)
54= h2+ 3h
h2+3h-54=0 (Subtract 54 from both the sides)
To find the value of h we have to solve the quadratic equation.
[We have the equation in the form ax2+bx+c=0, to factorise the equation-
Step1. Find two numbers such that their multiplication is equal to ac and their addition is equal to b.
Step2. Replace b with these numbers.
Step3. Simplify the equation]
So, h2+3h-54=0
h2+9h-6h-54=0
h(h+9)-6(h+9)=0
(h+9)(h-6)=0
Which gives-
h= -9 or h= 6
As h is the height of the rectangle, h can not be -9.
so h=6 feet
and b=h+3=9 feet
So the dimensions of the rectangle are 6 feet for the height and 9 feet for the base.
Answer:
C). Nonrigid transformation.
F). Stretch
Step-by-step explanation:
Transformation in mathematics is defined as the alteration or variation in the shape of an object without altering the lengths by using a flip, turn, slide, or resizing.
The transformation 'Hexagon ABCDEF → hexagon A'B'C'D'E'F'' would best be described as the 'non-rigid' and 'stretch' transformation. Non-rigid because it alters the shape or size of the figure both vertically as well as horizontally. It would be considered a stretch transformation as it is resized by a pull from both the vertical and horizontal angles. Thus, <u>options C and F</u> are the correct answers.
Answer:
In order to simplify improper fractions
1. Multiply the denominator and the whole number.
2. Add the numerator to the product.
3. Keep the denominator the same.
4. Easily simplify your solution
Step-by-step explanation:
And for proper fractions, just simplify by finding the GCF and divide Numerator by denominator.
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Treat this as if the inequality sign was the same thing as an equal sign. Most of the equality rules apply to inequalities (with a few exceptions)

Subtract both sides by 4


Multiply both sides by 2


We want the unknown variable on the left side (because it looks nicer)
