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MissTica
3 years ago
5

How long is a line segment that has endpoints at (5, -7) and (5, 2.5)

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
3 0

Answer:

9.5 units

Step-by-step explanation:

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What is:<br> <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B4x%5E%7B2%7D%20-20x%2B25%20" id="TexFormula1" title=" \sqrt{4x^{2} -
Firdavs [7]

We are given :

\sqrt{4x^{2}-20x+25}

Step 1: factor the part inside square root

The function given inside square root is of quadratic form.

So let us try to factorise it using AC method.

Here A*C = 4*25 = 100

so we have to find factors of 100 that add up to give -20.

the two factors are -10 and -10.

Rewriting the function :

4x^{2} -20x+25

=4x^{2} -10x-10x+25

=2x(2x-5) - 5(2x-5)

=(2x-5)^{2}

Step 2:

Now we take square root of the factorised form

\sqrt{(2x-5)^2}

= 2x-5

Answer : (2x-5)

3 0
3 years ago
When the expression 10^2021 − 2021 is evaluated, the result is a very large number.
Dafna11 [192]

Answer:

18,176

Step-by-step explanation:

Figure out an easier thing to do: 1000 - 2021 = 9,797.

Therefore, our answer will be like 9999999999999999999999997979. Out of all of these digits, there are only 2 that arent nines. We know the amount of digits since it's 10^2021 power. We will have one less since we are subtracting 2021. Therefore, 2020 digits in total. Now we know of those 2020 digits, 2 of them are 7, therefore 2018 of them are 9s. That means do 2018(9) + 2(7) = 14 + 18,162 =  18,176.

6 0
3 years ago
The verticles of a triangle are the points R(3,c),Q(9,2) and R(3c,11) where c is constant. Given that angle PQR is 90​
IceJOKER [234]

Answer:

Step-by-step explanation:

Find c if ∠PQR = 90°?

I will ASSUME you mean point P is at (3. c)

slope of PQ is (2 - c) / (9 - 3) = (2 - c) / 6

slope of QR is (11 - 2) / (3c - 9) = 9 / (3c - 9)

perpendicular lines have negative reciprocal slopes.

(2 - c) / 6 = -1(3c - 9)/9

9(2 - c) = -6(3c - 9)

18 - 9c = -18c + 54

       9c = 36

         c = 4

5 0
3 years ago
Write an equation in point slope form that passes through the given point and has the given slope.
stich3 [128]
Y+2=4(x-5) pretty sure
7 0
3 years ago
Please help me to solve all the questions would appreciate it if its with full working
Degger [83]

∠ KGH is equal to 77°. This is arrived at by using the knowledge of the total angles in Parallel Lines.

<h3>What are the total angles on a straight line?</h3>

According to the laws of lines and angles, the total number of angles that can exist on a straight line is 180°.

If ∠CED = 25° and ∠BFL = 78°, then: ∠KGH = 180-(25+78), which is equals 77°. This is because the total angles on a straight-line total 180°

<h3>What is ∠LKJ?</h3>

Recall that in angles in parallel lines:

  • Corresponding Angles are always congruent,  
  • Alternate Angles are always congruent, and
  • Interior According always sum up to 180°

Hence,

We can derive ∠LKJ because it is congruent with ∠BGJ.

To get ∠BGJ, we must get ∠LFH because both of them are interior angles and sum up to 180°.

To get ∠LFH, we must subtract ∠BFL from 180° because they are both angles on a straight line.

Hence ∠LFH = 180 - 78 = 102°

Recall that ∠LFH and ∠BGJ are interior angels. Hence

∠BGJ = 180 - 102 = 78°.

Since ∠BGJ is a corresponding ∠ with ∠LKJ, therefore

∠LKJ = 78°

<h3>What is ∠ALM?</h3>

∠ALM is ∠BFL because they are both corresponding angles and are therefore congruent.

<h3>What are the solutions to section B?</h3>

  1. Because ∠ACB and ∠BAC are equal, therefore sides AB and BC are equal in length. We can tell that  ∠ACB and ∠BAC are equal because the total angles in the triangle are equal to 180°

     2. The name given to the triangle mentioned above is Obtuse      

          Triangle. This is because one of the angles exceeds 90°.

Learn more about angles in parallel lines at:
brainly.com/question/24607467
#SPJ1

4 0
2 years ago
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