Answer:
m∠B = 157°
Step-by-step explanation:
Cyclic quadrilateral is the quadrilateral whose vertices lie on the edge of the circle
In the cyclic quadrilateral each two opposite angles are supplementary (the sum of their measures is 180°)
∵ Quadrilateral ABCD is inscribed in a circle
- That means its four vertices lie on the edge of the circle
∴ ABCD is a cyclic quadrilateral
<em>Each two opposite angles in the cyclic quadrilateral are supplementary (The sum of their measures is 180°)</em>
∵ ∠B and ∠D are opposite angles in the quadrilateral ABCD
∴ m∠B + m∠D = 180° ⇒ opposite ∠s in a cyclic quadrilateral
∵ m∠B = (6x + 19)°
∵ m∠D = x°
- Substitute them in the rule above
∴ (6x + 19) + x = 180
- Add the like terms in the left hand side
∴ (6x + x) + 19 = 180
∴ 7x + 19 = 180
- Subtract 19 from both sides
∴ 7x = 161
- Divide both sides by 7
∴ x = 23
<em>Substitute the value of x in the expression of the measure of ∠B to find its measure</em>
∵ m∠B = 6(23) + 19
∴ m∠B = 138 + 19
∴ m∠B = 157°
If Marcus monthly salary is $1,500 plus 10% of sale, then he could earn 1500 + 0.09x per month with salary and 9% sales
Monthly salary of Marcus = $1500
The percentage incentives for sales = 10%
If the percentage of incentive for sales is 9 %
Consider the amount of sales is $x
Therefore the monthly salary of Marcus = Monthly salary of Marcus + (The amount of sales × 9/100)
Substitute the values in the equation
The monthly salary of Marcus = 1500 + (x×9/100)
Divide the numbers in the equation
= 1500 + (x × 0.09)
Multiply the numbers the numbers
= 1500 + 0.09x
Therefore, the monthly salary of Marcus will be 1500 + 0.09x
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Answer: The value of the integer that was removed = 4
Step-by-step explanation:
Sum of <em>n</em> values= Mean x <em>n</em>
Given: n = 7 , Mean = 16
Let x= integer removed.
Sum of remaining 6 integers = 6
Hence, the value of the integer that was removed = 4
Answer:
The solution of this system is (9, 2).
Step-by-step explanation:
Substitute x - 7 for 'y' in the first equation. We get:
x - 3(x - 7) = 3 Doing this temporarily eliminates the variable 'y'.
Now perform the indicated multiplication, and then combine like terms:
x - 3x + 21 = 3, or
-2x = -18
so that x = 9. Substituting 9 for x in the second equation, we get:
y = 9 - 7, or y = 2.
The solution of this system is (9, 2).
1. [(3)(-2)(5)] = -30
2. [(3)^2 - |-5|] = 4
3. [(5)^3 - (4)(3)(-2)^2] = 48
4. [(-2)(3+5)] = -16
After these, I'm not to sure what the new variable's value is for m, n, w, x and y.