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Nostrana [21]
2 years ago
12

A. 70-74 B. 60-64 C.75-79 D.65-69 E.55-59 please answer will give brainliest

Mathematics
1 answer:
Leona [35]2 years ago
7 0

Answer:

C

Step-by-step explanation:

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Can someone help me with this? Please this would mean so much.
Paha777 [63]

Answers:

x = angle MLN = 35 degrees

angle FLJ = 55 degrees

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

Explanation:

This problem is fairly tricky if you're not sure what to look for. A slight clue is that they've marked a red point that strangely doesn't have a label on it. It's a fairly small point but it's definitely there if you look closely. While this point's location isn't exactly what we want, we're fairly close. Start at point L and draw a ray through the center point P. Ray LP will intersect the circle at point A, as shown in the diagram below.

From here, draw segments FA and MA. Now notice that inscribed angle LMF = 55 and inscribed angle FAL both subtend the same arc. The term "subtend" basically means "cut off". This arc that the inscribed angles subtend is minor arc FL. A minor arc is where you travel the shorter path around the circle, which indicates its measure is less than 180 degrees.

Since inscribed angles LMF and FAL subtend the same minor arc, this makes the inscribed angles to be congruent.

In short: angle FAL is 55 degrees

----------------------

Segment LA goes through the center P. Through Thales theorem, we know that inscribed angle LFA is 90 degrees. Consequently, we can determine that inscribed angle FLA is 90-55 = 35 degrees.

Segment JL is tangent to the circle, meaning that angle ALJ is 90 degrees. So angle FLJ is 90-35 = 55 degrees.

It's not a coincidence that angle FLJ, angle FAL, and angle LMF are the same measure.

----------------------

We found that angle FAL was 55 degrees. Applying Thales theorem again shows that angle MAF is 90 degrees. Therefore, angle LAM is 90-55 = 35 degrees.

Focus now on triangle LMA. This is also a right triangle (Thales Theorem). The upper acute angle we found was angle LAM = 35, so the lower acute angle is ALM = 55.

Then we can find angle MLN = (angle ALN) - (angle ALM) = 90 - 55 = 35

In short, angle MLN = 35 degrees

Similar to the previous section, it is not a coincidence that angles LFM, LAM and MLN are the same measure.

------------------------

As an alternative, since we know angle FLJ = 55, and angle FLM is 90 degrees, this means...

(angle FLJ)+(angle FLM) + (angle MLN) = 180

55 + 90 + angle MLN = 180

145 + angle MLN = 180

angle MLN = 180 - 145

angle MLN = 35 degrees

7 0
2 years ago
The area of sandbox in park is represented by 2X^2-5x-3 find the dimensions of the sandbox in terms of
lora16 [44]

Answer:

The dimension of the sandbox is (2x+1) by (x - 3)

Step-by-step explanation:

It seems the complete question will be:

The area of sandbox in park is represented by 2X^2-5x-3 find the dimensions of the sandbox in terms of x.

Step-by-step explanation:

From the question, the given expression is 2X^2-5x-3. This can be rewritten as

2x^{2} -5x-3

If the area of the sandbox in park is represented by this expression, then the dimensions of the sandbox will be the product of the factors. To determine the factors, we will factorize the given quadratic expression.

Factorizing the expression 2x^{2} -5x-3, we get

2x^{2} -6x+x-3

2x(x-3)+1(x-3)

(2x+1)(x-3)

Hence, the dimension of the sandbox is (2x+1) by (x - 3)

6 0
3 years ago
Of the following, which is the solution to 2x^2-5x=-8
Wittaler [7]

the answer is B these are the steps of getting your answer

6 0
3 years ago
What is the fraction for the following decimal expansion? 0.16
lozanna [386]

Answer:

<h2><em><u>D. 4/25</u></em></h2>

Step-by-step explanation:

As,

0.16

= 16/100

= <em>4/25.</em> [Taking common factor 4 from both 16 and 100]

6 0
2 years ago
The length of a bridge on a map is 1.5 cm. What is the actual length of the bridge in meters if the map is drawn at a scale of 1
Ilya [14]

Answer:

Step-by-step explanation:

If the length of a bridge on a map is 1 cm,then the actual length = 40,000

If the length of a bridge on a map is 1.5 cm,then the actual length= 1.5 * 40000

= 60000.0 = 60,000 m

3 0
3 years ago
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