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Answer: A) 6.4</h3>
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Explanation:
Refer to the diagram below. I've added the points A, B, C, D, and E. Point A is the center of the circle while points B, C and D are along the circle's edge. The radius AC and chord BD intersect at point E.
Recall that whenever we have a radius perpendicular to a chord like this, it means that the radius bisects the chord. So that means chord BD is cut into two equal pieces BE and ED. The diagram given to you tells us that ED = x, so BE is also x units long as well. Overall, BD = BE+ED = x+x = 2x units.
Since BE = ED, the arcs formed are congruent as well. Minor arc BC is the same measure as minor arc CD. Both are 45 degrees. They combine to 90 degrees. In turn, this leads to central angle DAB to be 90 degrees.
Note how triangle DAB is an isosceles right triangle. The two equal legs are the two radii AB and AD, both which are 9 units long. The hypotenuse BD is equal to sqrt(2) times the leg length, so BD = 9*sqrt(2) units long.
Earlier I mentioned that BD = 2x also. We'll equate the two right hand side expressions and solve for x like so:
2x = 9*sqrt(2)
x = (9*sqrt(2))/2
x = (9/2)*sqrt(2)
x = 4.5*sqrt(2)
x = 6.36396103067892
That value is approximate. Rounding to the nearest tenth leads to the final answer of 6.4; therefore, the answer is choice A.
Answer:
4 students
Step-by-step explanation:
As shown in the diagram, let U=[The total number of students questioned]
![\implies n(U) = 10](https://tex.z-dn.net/?f=%20%5Cimplies%20n%28U%29%20%3D%2010)
A=[Those who liked peanut butter ]
![\implies n(A) =18](https://tex.z-dn.net/?f=%5Cimplies%20n%28A%29%20%3D18)
B=[Those who liked jam ]
![\implies n(B) = 10](https://tex.z-dn.net/?f=%20%5Cimplies%20n%28B%29%20%3D%2010)
x = those who like both peanut butter and jam.
Also 6 liked neither peanut butter nor jam.
From the diagram we can write the mathematical equation as follow and solve for x
![30 = 18 - x + x + 10 - x + 6](https://tex.z-dn.net/?f=30%20%3D%2018%20-%20x%20%2B%20x%20%2B%2010%20-%20x%20%2B%206%20)
![\implies 30 = 34- x](https://tex.z-dn.net/?f=%20%5Cimplies%2030%20%3D%2034-%20x%20)
We add x and subtract 30 to both sides.
![\implies 30 - 30 + x = 34- x + x - 30](https://tex.z-dn.net/?f=%20%5Cimplies%2030%20-%2030%20%2B%20x%20%3D%2034-%20x%20%2B%20x%20-%2030)
![\implies x = 4](https://tex.z-dn.net/?f=%5Cimplies%20x%20%3D%204)
Therefore 4 students like both peanut butter and jam.
Answer:
Step-by-step explanation:
Remark
If the horizontal lines are parallel, then 2x + 20 = 3x - 10
Equation
2x + 20 = 3x - 10
Add 10 to both sides
2x + 20 + 10 = 3x
Subtract 2x from both sides
30 = x
2x + 20 = 2*30 + 20 = 80
the solution to the equation is x=12
The distributive property is defined as
Let us now solve the equation.
5(x - 6) = 2(x + 3)
Using the distributive property, simplify the parentheses on both sides.
5(x - 6) = 2(x + 3)
5x - 30 = 2x + 6
The parenthesis was simplified. However, we have one x term on one side and another x term on the other.
5x - 30 - 2x = 2x + 6 - 2x
3x - 30 = 6
We only have an x term on one side of the equation now.
To begin, reverse the subtraction by adding 30 to either side of the equation.
To keep an equation balanced or true, we do the identical operation on both sides.
3x - 30 + 30 = 6 + 30
3x = 36
We're getting close to an answer. Only one more step.
The x term is multiplied by 3.
We can undo the multiplication operation by dividing both sides by 3.
3x / 3 = 36 / 3
x = 12
So, x is equal to 12.
Learn more about Equations here: brainly.com/question/2972832
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