Answer:
Part A
12 pieces
Part B
Tara can cut Twelve 2/5 foot pieces can be cut from 4 4/5 feet of rope.
Step-by-step explanation:
Part A: How many 2/5 foot pieces can Tara cut from the 4 4/5 feet of rope?
This is calculated as:
4 4/5 feet of rope ÷ 2/5 foot pieces
= 24/5 ÷ 2/5
= 24/5 × 5/2
= 12
Part B: Using the information in Part A, interpret the meaning of the quotient in terms of the two fractions given
The quotient in Part A is 12
Therefore, this can be interpreted as:
Tara can cut Twelve 2/5 foot pieces can be cut from 4 4/5 feet of rope.
Answer:
Check explanation
Step-by-step explanation:
I'll give you my way of solving it and you can figure it out from there.
<CEA = <DEB due to vertical angles
AE = ED due to midpoint theorem
<CAD = <ADB due to alternating angles theorem
thus two triangles congruent due to ASA
Answer:
w= 9
Step-by-step explanation:
Square both sides:
-4w +61= (w -4)²
Expand:
-4w +61= w² -2(w)(4) +4²
-4w +61= w² -8w +16
Simplify:
w² -8w +16 +4w -61= 0
w² -4w -45= 0
Factorize:
(w -9)(w +5)= 0
w -9= 0 or w +5= 0
w= 9 or w= -5 (reject)
Note:
-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.
<u>Why </u><u>do </u><u>we </u><u>use </u><u>negative </u><u>square </u><u>root?</u>
When solving an equation such as x²= 4,
we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.
In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.
However, back to our question, we did not introduce the square root so we should not consider the negative square root value.
Answer:
45°
Step-by-step explanation:
Let's understand "supplement" and "complement" -- basics of geometry of angles.
- When we say two angles, a & b, are supplementary, we mean that both ADD up to 180.
- When we say two angles, a & b, are complementary, we mean that both ADD up to 90.
<em><u>If we have given an angle, such as "x", to find its supplement, we subtract the angle from 180. Similarly, we would need to subtract the angle x from 90 if we were to find the complement of the angle.</u></em>
<em><u /></em>
We want to find complement of 45, so we subtract 45 from 90 to get:
90 - 45 = 45°
Hence, the complement of a 45° angle = 45°
Answer:
26°
Step-by-step explanation:
An obtuse triangle is a triangle that has one obtuse angle. Obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees.
An isosceles triangle is a triangle that has two equal sides and angles.
Therefore, an obtuse isosceles triangle is a triangle with an obtuse angle and two equal sides that have two equal acute angles (angle less than 90° ).
Given:
The three angles of the triangle are given to be x°, x° and (10x−2) = 128°. The obtuse angle is 128°, the two x° are acute angles. We are not using equation 10x − 2 since the value of the obtuse angle has been given as 128°
The sum of angles in a triangle is 180°
∴ x° + x° + 128° = 180°
2x° = 180° - 128°
2x° = 52°
x° = 52° / 2
x° = 26°
The measurement of one of the acute angles is 26°
