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3 years ago

Find the area of the smaller sector

Mathematics

1 answer:

Digiron [165]3 years ago

3 0

Since the radius is 6 inches, the area is

$A=\pi r^2=36\pi$ squared inches.

Now, the full circle is a sector given by a 360° angle. So, the area of a 140° angle will be proportionate:

$140\div x = 360\div 36\pi$

Solving for $x$ , we have

$x=\dfrac{36\pi\cdot 140}{360}=14\pi$

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If two angles are complementary angles and they measure m ∠1=(x + 5) and m∠2=(5x + 13). Find x and the measure for both an

Korolek [52]

5X+13+X+5=90°(SUM OF COMPLEMENTRY ANGLE IS EQUAL TO 90°)

6+18=90°

6X=90°-18°

X=72°/6

X=12 °ANSWER

6 0

3 years ago

4x − 1 < 11 solve for x

kvv77 [185]

Answer:

$\huge \boxed{x < 3}$

Step-by-step explanation:

4x - 1 < 11

Add 1 on both sides.

4x - 1 + 1 < 11 + 1

4x < 12

Divide both sides by 4.

(4x)/4 < 12/4

x < 3

8 0

3 years ago

The ratio of boys to girls at King Middle school is 3:2. What is the ratio of girls to all students?

Dominik [7]

The answer is: " 2 :5 " ; or, write as: " 2/5 " .
________________________________________________________
The ratio of 'girls' to 'all students' is: "2: 5 " ; or, write as: " 2/5 ".
________________________________________________________
Explanation:
________________________________________________________
Given: The ratio of boys to girls is: " 3:2 " .

Problem: Find the ratio of "girls" to "all students:
________________________________________________________
Note: This ratio of "boys to girls", which is " 3 : 2 " ;
________________________________________________________
→ can be expressed as " 3x: 2x" ;

in which the total number of students is: " 3x + 2x " = 5x " .

→ The total number of students is represented as: " 5x " .
________________________________________________________
→ The ratio of "girls to boys" is: "2x : 3x" .

→ {that is; the "inverse" of the ratio of "boys to girls"} ;
→ {that is; the "inverse" of " 3x: 2x" } ; → which is: " 2x : 3x " .
________________________________________________________

The ratio of "girls" to "all students" is: "2x : 5x " ; or " 2x/5x " ;
→ Both "x" values cancel ; {since: " x/x = 1 "} ;
_________________________________________________________
→ and we have the answer: " 2 :5 " ; or, write as: " 2/5 " .
_________________________________________________________
The ratio of 'girls' to 'all students' is: " 2 :5 " ; or, write as: " 2/5 ".
_________________________________________________________

8 0

3 years ago

Yin wants to create figure Y′ that is similar to figure Y. Yin begins by reflecting figure Y across the y-axis.

Sholpan [36]

Answer: B) Dilate by scale factor of 2

====================================================

Explanation:

Your teacher isn't saying this directly, but I'm assuming s/he wants you to find a similar figure that isn't congruent to the original. Informally, your teacher seems to want you to find a figure that is the same shape but not the same size as the original.

If so, then any dilation will shrink or enlarge the image depending on the scale factor. So the new image will not be the same as the old one. In this case, a dilation with scale factor 2 means the new figure is twice as large (each side is twice as long). But the old image is similar to the new image. The angles keep their values and therefore we get the same shape. This is why choice B is the answer. Again this is assuming what I mentioned in the first paragraph.

Choices A, C, and D are all known as rigid transformations and they preserve the same size of the figure. Applying any of those operations will lead to the same figure (just rotated, reflected or shifted somehow). In other words, applying operations A,C, or D will have us get two congruent triangles. If two triangles are congruent, then they are automatically similar, but not vice versa. This is why we can rule out A,C, and D.

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3 years ago

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Which of the following is a solution to 2cos x + 1 = 0? 60° 120° 210° 300°

klasskru [66]

Rewrite 2cos x + 1 = 0 as:

2 cos x = -1, and then cos x = -1/2

x must be in Quadrant II or Quadrant III, since the adj. side is negative.

Note that the angle 120 has adj. side -1 and hyp 2. So 120 degrees is one solution.

Now what about a possible 2nd solution, to be found in Quadrant III? That would be -120 degrees, which has the same terminal line as does 240 degrees.

No soap.

So, the solution is 120 degrees.

6 0

3 years ago

Read 2 more answers

Find the area of the smaller sector ​

Find the area of the smaller sector