180 = 65 + (x-5) + x
-65 -65
115 = x - 5 + x
115 = 2x - 5
2x = 120
x = 60
The angle measures are 65, 60, and 55 degrees.
Answer: B
<u>Step-by-step explanation:</u>
x³ - 3x² + 16x - 48 = 0
→ x²(x - 3) + 16(x - 3) = 0
→ (x² + 16) (x - 3) = 0
→ (x² - (-16)) (x - 3) = 0
→ (x - 4i)(x + 4i)(x - 3) = 0
→ x - 4i = 0 x + 4i = 0 x - 3 = 0
→ x = 4i x = -4i x = 3
2 imaginary roots and 1 real root
We know that<span>
<span>Figures can be proven similar if one, or more,
similarity transformations (reflections, translations, rotations, dilations)
can be found that map one figure onto another.
In this problem to prove circle 1 and circle 2 are similar, a
translation and a scale factor (from a dilation) will be found to map one
circle onto another.
we have that</span>
<span> Circle 1 is centered at (5,8) and has a
radius of 8 centimeters
Circle 2 is centered at (1,-2) and has a radius of 4 centimeters
</span>
step 1
<span>Move the center of the circle 1 onto the
center of the circle 2
the transformation has the following rule</span>
(x,y)--------> (x-4,y-10)
so
(5,8)------> (5-4,8-10)-----> (1,-2)
so
center circle 1 is now equal to center circle 2
<span>The circles are now concentric (they have the
same center)
</span>
step 2
<span>A dilation is needed to decrease the size of
circle 1 to coincide with circle 2
</span>
scale factor=radius circle 2/radius circle
1-----> 4/8----> 0.5
radius circle 1 will be=8*scale factor-----> 8*0.5-----> 4 cm
radius circle 1 is now equal
to radius circle 2
<span>A
translation, followed by a dilation will map one circle onto the other,
thus proving that the circles are similar
the answer is
</span></span>The circles are similar because you can translate Circle 1 using the transformation rule (x-4,y-10) and then dilate it using a scale factor of (0.5)
Answer:
22
Step-by-step explanation:
Answer:
The fraction of one pound of cheese to be used in each sandwich is 1/8
Step-by-step explanation:
Here, we have a question that requires the method of dealing with the division of fractions.
To divide a fraction by a whole number, we multiply the denominator of the fraction by the whole number as follows;
Quantity of cheese Shane has = 1/2 pound
Number of sandwiches to be made = 4
Amount of cheese per sandwich = 1/2÷4 = 1/8.
