What is the quotient of 78.3 ÷ 3.48?
1 answer:
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The slope intercept form is given as y = 2x + 6
The general expression for slope intercept form is given as:
y = mx + c
where, m = slope
c = intercept
The formula for slope intercept form when we have been given the coordinates of a point and slope is given as :
(1)
where ( = the coordinates of a point
m = slope of the line
putting the required values in equation (1) we get
(y - 4) = 2(x- (-1))
(y - 4) = 2(x+1) [As (-)*(-) = +]
y - 4 = 2x + 2
y = 2x + 2 + 4
y = 2x + 6
Thus the slope intercept form is y = 2x + 6
Learn more about slope intercept form here : brainly.com/question/19440459
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m∠1 = 30° (by Vertical angle theorem)
m∠A = 80° (by Triangle sum theorem)
m∠D = 80° (by Triangle sum theorem)
The value of x is 7.5 and y is 9.
Solution:
∠ACB and ∠DCE are vertically opposite angles.
Vertical angle theorem:
<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>
⇒ m∠DCE = m∠ACB
⇒ m∠1 = 30° (by Vertical angle theorem)
In triangle ACD,
Triangle sum property:
<em>Sum of the interior angles of the triangle = 180°</em>
⇒ m∠A + m∠C + m∠B = 180°
⇒ m∠A + 30° + 70° = 180°
⇒ m∠A + 100° = 180°
⇒ m∠A = 100° – 180°
⇒ m∠A = 80° (by Triangle sum theorem)
Similarly, m∠D = 80° (by Triangle sum theorem)
In ΔACD and ΔDCE,
All the angles are congruent, so ΔACD and ΔDCE are similar triangles.
<em>In similar triangle corresponding sides are in the same ratio.</em>
Do cross multiplication.
90 = 12x
7.5 = x
Now, to find y:
Do cross multiplication.
9y = 72
Divide by 9, we get
y = 8
Hence the value of x is 7.5 and y is 9.
Using probabilities, it is found that the expected profit of one round of this game is of $0.
A probability is the <u>number of desired outcomes divided by the number of total outcomes</u>.
- One of the two sides of the coin are heads.
- 2 of the 6 sides of the dice are 3 or 6.
Hence, since the coin and the dice are independent, the <em>probability </em>of winning is:
The expected value is the <u>sum of each outcome multiplied by its respective probability</u>.
In this problem:
probability of earning $30.
probability of losing $6.
Then:
The expected profit of one round of this game is of $0.
A similar problem is given at brainly.com/question/24855677