Answer:
x° = 149°
Step-by-step explanation:
According to the <u>Triangle Sum Theorem</u>, the sum of the measures of the angles in every triangle is 180°. Since we are given two angles with measures of m < 86° and m < 63°, then the third angle must be:
m < 86° + m < 63° + m < (angle 3) = 180°
149° + m < ? = 180°
Subtract 149° from both sides to solve for m < (angle 3)
149° - 149° + m < (angle 3) = 180° - 149°
m < ? = 31°
Therefore, the measure of the third angle is 31°.
To find x°, we can reference the <u>Triangle Exterior Angle Postulate</u>, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
In other words, the measure of x° = m < 86° + m < 63°
x° = 149°
By the way, m< (angle 3) and x° are also supplementary angles whose sum equal 180°:
x° + m < (angle 3) = 180°
149° + 31° = 180°
Step-by-step explanation:
Let's say b is the rate of the boat in still water, and c is the rate of the current.
Distance = rate × time
Going upstream:
100 = (b − c) (5)
20 = b − c
Going downstream:
100 = (b + c) (2)
50 = b + c
Solve the system of equations using substitution or elimination. Using elimination, add the equations together:
70 = 2b
b = 35
c = 15
The boat's speed is 35 km/h, and the current's speed is 15 km/h.
2x-15=3(x-15)
2x-15=3x-45
2x+30=3x
30=x
Let's check this work!
2(30)-15=3(30-15)
60-15=3(15)
45=45
She worked 45 hours each week
*the reason it is 2x-15 and not 15+2x is because "more than" is considered a "turn around word" meaning it is the opposite
Answer:
The two linear equations are the same line
Step-by-step explanation:
two different linear equations can only possibly intersect at one point. once the two lines intersect, they cannot curve back to intersect once again.
The transformation of a function may involve any change. The correct option is D.
<h3>How does the transformation of a function happen?</h3>
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
- Left shift by c units, y=f(x+c) (same output, but c units earlier)
- Right shift by c units, y=f(x-c)(same output, but c units late)
Vertical shift
- Up by d units: y = f(x) + d
- Down by d units: y = f(x) - d
Stretching:
- Vertical stretch by a factor k: y = k \times f(x)
- Horizontal stretch by a factor k: y = f(\dfrac{x}{k})
Given the function f(x)=2ˣ, while the h(x)=-3(2ˣ), therefore, the function f(x) is a reflection and a translation of a function. Hence, the correct option is D.
Learn more about Transforming functions:
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