A. The relationship of <7 and <8 are that they are vertical angles, and are congruent.
B. Since vertical angles are congruent, you can form an equation where the two measurements equal each other.
C. 5y-29=3y+19 then plug y into your equation: 5*24-29=91
2y=48 and so: <7 = 180-91=89 (and since <8 is congruent)
y=24 <8 also equals 89
Your second problem:
complementary are two angles that add up to 90 degrees.
<B=x, <A=2x
2x+x=90
3x=90
x=30 so: <B=30 degrees, <A=60 degrees
Your third problem:
1. Since A and B are parallel, angle 3x+7 and angle 4x+5 are same-sided exterior angles. That means that they both add up to 180 degrees. So if you should add the two and make it equal 180
2. 3x+7+4x+5=180
7x+12=180
7x=168
x=24
3. <6 is a corresponding angle with angle 3x+7, meaning that they are congruent. So plug x into 3x+7: 3*24+7=79 and since <6 is congruent to 3x+7, <6=79 degrees
1/2 = 8/16 . . . so there are (<u><em>8</em></u>) - 1/16 pounds servings of chocolate in a 1/2 pound chocolate bar
The answer is: " 128 oz. " .
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There are: " 128 oz. " (in " 8 lbs." ) .
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Explanation:
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Set up a proportion; as a fraction; as follows:
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400/ 25 = x / 8 ;
in which: "x" = the number of "ounces [oz.] there are in "8 lbs." ;
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We shall solve for "x" , the answer to the problem:
Cross-factor multiply:
25x = (400) * 8 ;
→ 25x = 3200 ;
Divide each side of the equation by "25" ; to isolate "x" on one side of the equation; & to solve for "x" ;
→ 25x / 25 = 3200 / 25 ;
→ x = 128 .
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Answer: " 128 oz. " .
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There are: " 128 oz. " (in " 8 lbs." ) .
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Note of interest: " 16 oz. = 1 lb. " (exact conversion).
So; "8 lbs. <span>= ?</span> oz. " ;
→ " 8 lbs. * (16 oz/ 1 lb) = ( 8 * 16) oz. = 128 oz. ; → which is our answer!
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Answer:
The vertical one is the y axis and the horizontal one is the x axis.
Step-by-step explanation:
Answer:
Claim 2
Step-by-step explanation:
The Inscribed Angle Theorem* tells you ...
... ∠RPQ = 1/2·∠ROQ
The multiplication property of equality tells you that multiplying both sides of this equation by 2 does not change the equality relationship.
... 2·∠RPQ = ∠ROQ
The symmetric property of equality says you can rearrange this to ...
... ∠ROQ = 2·∠RPQ . . . . the measure of ∠ROQ is twice the measure of ∠RPQ
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* You can prove the Inscribed Angle Theorem by drawing diameter POX and considering the relationship of angles XOQ and OPQ. The same consideration should be applied to angles XOR and OPR. In each case, you find the former is twice the latter, so the sum of angles XOR and XOQ will be twice the sum of angles OPR and OPQ. That is, angle ROQ is twice angle RPQ.
You can get to the required relationship by considering the sum of angles in a triangle and the sum of linear angles. As a shortcut, you can use the fact that an external angle is the sum of opposite internal angles of a triangle. Of course, triangles OPQ and OPR are both isosceles.