<u>Part 1) which angle is congruent to Angle 1?</u>
we know that
When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called <u>corresponding angles</u>
m∠5=m∠1 ----------> by corresponding angles postulate
therefore
<u>the answer Part 1) is </u>
Angle 
Part 2) Which can be used to directly prove that Angle 1 =~ Angle 8?
we know that
<u>Alternate exterior angles</u> are defined as two exterior angles on opposite sides of a transversal which lie on different parallel lines.
in this problem
m∠1=m∠8 -------> by alternate exterior angles theorem
therefore
<u>the answer part 2) is the option </u>
Alternate Exterior Angles Theorem
<u>Part 3) If m Angle 5 = 42 degrees, what is m Angle 4?</u>
we know that
<u> Alternate interior angles</u> are two interior angles which lie on different parallel lines and on opposite sides of a transversal
m∠4=m∠5 --------> by alternate interior angles theorem
so
m∠4=
therefore
<u>the answer Part 3) is</u>
Answer:
A dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
Step-by-step explanation:
To graph the solution set of the inequality 2x - 3y < 12, first plot the dashed line 2x - 3y = 12 (dashed because the inequality has sign < without notion "or equal to"). This line passes through the points (0,-4) and (3,-2) (their coordinates satisfy the equation of the line). this line has positive slope because
and the slope of the line is 2/3.
Now, identify where the origin is (in the region or outside the region). Substitute (0,0) into the inequality:
This means coordinates of the origin satisfy the inequality, so origin belongs to the shaded region. Thus, shade that part which contains origin.
Width of the rectangle is 9 units
Step-by-step explanation:
- Step 1: Let the width of the rectangle be x. Then the length = x - 3. Find dimensions of the rectangle if its area = 54 sq. units
Area of the rectangle = length × width
54 = x (x - 3)
54 = x² - 3x
x² - 3x - 54 = 0
x² + 6x - 9x - 54 = 0 (Using Product Sum rule to factorize)
x(x + 6) - 9(x + 6) = 0
(x + 6)(x - 9) = 0
x = -6, 9 (negative value is neglected)
x = 9 units
Given:
A quadratic function has a line of symmetry at x = –3.5 and a zero at –9.
To find:
The other zero.
Solution:
We know that, the line of symmetry divides the graph of quadratic function in two congruent parts. So, both zeroes are equidistant from the line of symmetry.
It means, line of symmetry passes through the mid point of both zeroes.
Let the other zero be x.
Multiply both sides by 2.
Add 9 on both sides.
Therefore, the other zero of the quadratic function is 2.
Answer: i explained
Step-by-step explanation: Just do
8 times 11 = *your answer*
then
*your answer* times/subtract/divided by 108
