Given ABCD is a cyclic quadrilateral.
To prove that ∠A + ∠C = 180° and ∠B + ∠D = 180°
Construction: Join AC and BD.
Proof:
<em>Angles in the same segment are equal.</em>
∠ACD = ∠ABD – – – – (1)
∠DAC = ∠DBC – – – – (2)
Add (1) and (2), we get
∠ACD + ∠DAC = ∠ABD + ∠DBC
⇒ ∠ACD + ∠DAC = ∠ABC (Since ∠ABD + ∠DBC = ∠ABC)
Add ∠ADC on both sides.
⇒ ∠ACD + ∠DAC + ∠ADC = ∠ABC + ∠ADC
We know that <em>sum of the angles of a triangle is 180°.</em>
In ΔABC, ∠ACD + ∠DAC + ∠ADC = 180°
Now, 180° = ∠ABC + ∠ADC
180° = ∠B + ∠C – – – – (3)
<em>Sum of all the angles of a quadrilateral = 360°</em>
∠A + ∠B + ∠C + ∠D = 360°
∠A + ∠C + 180° = 360° (using (3))
∠A + ∠C = 360° – 180°
∠A + ∠C = 180° – – – – (4)
Equation (3) and (4) shows that,
Opposite angles of a cyclic quadrilateral are supplementary.
Hence proved.
Let first number = X and 2nd number = Y
Equation 1: 5X + 8Y = -13
Equation 2: 5X + 10Y = -15
Multiply equation 1 by -1 to get: -5X + -8Y = 13
Now add the 2 equations together:
-5X + 5X = 0
-8Y + 10Y = 2Y
13 + -15 = -2
The total of the 2 equations is 2Y = -2
divide both sides by 2 to solve for Y
Y = -2 / 2
Y = -1
Now we know the 2nd number is -1, so replace Y in the 1st equation and solve for X
5X +8(-1) = -13
5x + -8 = -13
Add 8 to both sides:
5x = -5
Divide both sides by 5 to get x
X = -5 / 5
X = -1
Both numbers are -1
To check replace X and Y with -1 and solve:
1st equation: 5(-1) +8(-1) = -5 + -8 = -13 TRUE
2nd equation: 5(-1) +10(-1) = -5 + -10 = -15 TRUE
Both numbers are -1
Answer:
8 more players
Step-by-step explanation:
There are already 4 players including Jeff, so in order to have more players, they need from 1-8 more players.
Have a good day!!!!
Answer:
<u>-The independent variable is whether the motivational signs were posted, and the dependent variable is the amount of use of the stairs.</u>
<u>-Nominal scale. </u>
Step-by-step explanation:
<u>Independent variable:</u> In research methods, the term "independent variable" is described as the variable that is being altered, manipulated, or changed by an investigator to see its effects on the dependent variable in specific research or experiment.
<u>Dependent variable: </u>In research methods, the term "dependent variable" is described as the variable that is being measured, analysed, or tested in an experiment by the experimenter or researcher. The dependent variable is being directly affected by the independent variable.
<u>Nominal scale:</u> In research methods, the term "nominal scale" is determined as one the different measurement scales in which a specific number is being served as labels or tags only and to classify and identify an object.
[8] The hypotenuses must be congruent, DE and IJ
HL is hypotenuse-leg, or where the hypotenuse and one leg are congruent.
Since we see a leg is congruent, to prove they are congruent with HL we will need to know that the hypotenuses are congruent.
[9] Another leg, AC and YX
LL is leg-leg. Since we have one leg, we will need the other leg to prove the triangles are congruent by LL.
[10] A leg, DE and E? or FE and E?
LA means leg-angle. The angles by point E are vertical angles, so they will be congruent. To finish prooving the congruence using LA we will also need a leg.
-> The question marks are because the letters are too blurry to read.
