Answer:
x=9
Step-by-step explanation:
2x+12=5x-15
3x=27
x=9
Answer: A; 6.3%
Step-by-step explanation:
Problem 1
For the first problem, we first want to find y so that we can plug it into the expression.
We can use elimination method for the system of equations to solve.
3x+3y=21
3x-y=5
We subtract both equations to eliminate x.
4y=16 [divide both sides by 4]
y=4
Now that we know y, we can plug it into the expression.
[divide]
[subtract]
We know that the answer is A.
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Problem 2
For the second problem, we need to know how to calculate percent error. The formula for precent error is 
. We know that the exact value is 80 because the buyer was supposed to given 80. 75 is the measured value because that was what the buyer was given.
[subtract]
[solve absolue value]
[divide]
[multiply]
Since the problem said to round to one decimal place, we know that the answer is 6.3%.
AB = 6 cm, AC = 12 cm, CD = ?
In triangle ABC, ∠CBA = 90°, therefore in triangle BCD ∠CBD = 90° also.
Since ∠BDC = 55°, ∠CBD = 90°, and there are 180 degrees in a triangle, we know ∠DCB = 180 - 55 - 90 = 35°
In order to find ∠BCA, use the law of sines:
sin(∠BCA)/BA = sin(∠CBA)/CA
sin(∠BCA)/6 cm = sin(90)/12 cm
sin(∠BCA) = 6*(1)/12 = 0.5
∠BCA = arcsin(0.5) = 30° or 150°
We know the sum of all angles in a triangle must be 180°, so we choose the value 30° for ∠BCA
Now add ∠BCA (30°) to ∠DCB = 35° to find ∠DCA.
∠DCA = 30 + 35 = 65°
Since triangle DCA has 180°, we know ∠CAD = 180 - ∠DCA - ∠ADC = 180 - 65 - 55 = 60°
In triangle DCA we now have all three angles and one side, so we can use the law of sines to find the length of DC.
12cm/sin(∠ADC) = DC/sin(∠DCA)
12cm/sin(55°) = DC/sin(60°)
DC = 12cm*sin(60°)/sin(55°)
DC = 12.686 cm
Answer:
33
Step-by-step explanation:
10+23 according to my sense
