1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
blagie [28]
3 years ago
6

PLEASE HELP ME

Mathematics
1 answer:
olga_2 [115]3 years ago
7 0

The measure of the angles are ∠A = 91°, ∠C = 89° and ∠D = 34°

Explanation:

Given that the quadrilateral ABCD is inscribed in a circle.

The given angles are ∠A = (2x + 3), ∠C  = (2x + 1) and ∠D = (x - 10)

We need to determine the measures of the angles A, C and D

<u>The value of x:</u>

We know that, the opposite angles of a cyclic quadrilateral add up to 180°

Thus, we have,

\angle A+\angle C=180^{\circ}

Substituting the values, we have,

2x+3+2x+1=180

             4x+4=180

                   4x=176

                     x=44

Thus, the value of x is 44.

<u>Measure of ∠A:</u>

Substituting x=44 in ∠A = (2x + 3)°, we get,

\angle A=(2(44)+3)^{\circ}

     =(88+3)^{\circ}

\angle A=91^{\circ}

Thus, the measure of angle A is 91°.

<u>Measure of ∠C :</u>

Substituting x=44 in ∠C = (2x + 1)°, we get,

\angle C=(2(44)+1)^{\circ}

     =(88+1)^{\circ}

\angle C=89^{\circ}

Thus, the measure of angle C is 89°.

<u>Measure of ∠D :</u>

Substituting x=44 in ∠D = (x - 10)°, we get,

\angle D=(44-10)^{\circ}

\angle D=34^{\circ}

Thus, the measure of angle D is 34°.

Hence, the measure of the angles are ∠A = 91°, ∠C = 89° and ∠D = 34°

You might be interested in
Amalia used 8 lemons to make a picture of lemonade that served six people. How many lemons would she need to make enough lemonad
11111nata11111 [884]
28 lemons is the answer to your question
8 0
3 years ago
Here are some values of sequence Q. Write a recursive definition for the sequence.
Rashid [163]

Answer: Q(n) = Q(n - 1) + 2.5

Step-by-step explanation:

We have 3 values of the sequence Q(n)

These values are:

Q(1) = 3

Q(3) = 8

Q(7) = 18

I would think that this is a geometric sequence.

Remember that the equation for the n-th term of a geometric sequence is:

A(n) = A(1)*r^(n-1)

where r is a constant, and A(1) is the first term of the sequence.

If we rewrite the terms that we know of Q(n) in this way we get:

Q(3) = Q(1)*r^(3 - 1) = 3*r^2 = 8

Q(7) = Q(1)*r^(7 - 1) = 3*r^6 = 18

Then we have two equations:

3*r^2 = 8

3*r^6 = 18

We should see if r is the same for both equations:

in the first one we get:

r^2 = 8/3

r = (8/3)^(1/2) = 1.63

and in the other equation we get:

r^6 = 18/3

r = (18/3)^(1/6) = 1.34

Then this is not a geometric sequence.

Now let's see if this is an arithmetic sequence.

The n-th term of an arithmetic sequence is written as:

A(n) = A(1) + (n - 1)*d

where d is a constant.

If we write the terms of Q(n) that we know in this way we get:

Q(3) = Q(1) + (3 - 1)*d = 3 + 2*d = 8

Q(7) = Q(1) + (7 - 1)*d = 3 + 6*d = 18

We need to see if d is the same value for both equations.

in the first one we get:

3 + 2*d = 8

2*d = 8 - 3 = 5

d = 5/2 = 2.5

In the second equation we get:

3 + 6*d = 18

6*d = 18 - 3 = 15

d = 15/6 = 2.5

d is the same for both terms, then this is an arithmetic sequence.

An arithmetic sequence is a sequence where the difference between any two consecutive terms is always the same value (d)

Then the recursive relation is written as:

A(n) = A(n - 1) + d

Then the recursive relation for Q is:

Q(n) = Q(n - 1) + 2.5

4 0
3 years ago
3/5x=52 is the answer 120 or 130
postnew [5]
The direct answer to your question is: "No".
because in that equation, 'x' is not 120 or130.

Let's find out what 'x' actually is:

<u>3/5 x  =  52</u>

Multiply each side by  5 :      3x  =  260

Divide each side by  3 :       <em>  x  =  86 and 2/3 </em>
8 0
3 years ago
Noelle and karina both leave the Internet cafe at the same time, but in opposite directions. If karina travels 9 mph faster than
Vesna [10]
Noelle goes east at N mph.
Karina travels west at N + 9
then their velocity between them is (N + N + 9)
After 8 hours they travel 8(2N + 9) = 232
(2N + 9) = 29
2N = 20
N = 10 mph for Noelle
N+9=19 mph for Karina

7 0
3 years ago
A certain star is 2.6×102 light years from the Earth. One light year is about 5.9×1012 miles. How far from the earth​ (in miles)
navik [9.2K]

Answer:

2.5 x 10^{15} miles

3 0
2 years ago
Read 2 more answers
Other questions:
  • Find the​ slope-intercept form of the line whose slope is 66 and that passes through the point (negative 5 comma 10 )(−5,10).
    12·1 answer
  • timeless toys builds tricycles and wagons. the owner noticed that there are several diffrent ways that a customer could place an
    8·2 answers
  • Necesito ayuda en esta
    9·1 answer
  • Help another easy question guys please help me
    7·1 answer
  • ¿Cuál es el sexto término en la secuencia entre 4, -8,16, -32,​
    10·2 answers
  • You are responsible for insuring that 5550 finished goods are delivered to the new store in Springfield, MO. However, you are al
    14·1 answer
  • sally needs $ 20,000 in 4 years, she has $ 10,000 to invest. if interest is compounded continuously, what rate is required for s
    12·1 answer
  • What is the number of terms in this geometric series?<br> 1+2+4...+128
    12·1 answer
  • -6/13 - (-7/15)<br> pls solve it for me !!! :)
    13·2 answers
  • A spinner has 6 equal sections marked 1 through 6. You spin and land on a number less than 6?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!