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
Anna [14]
3 years ago
14

3 geometry questions, 30 points!

Mathematics
2 answers:
polet [3.4K]3 years ago
8 0

Answer:

A ) The value of x for  the given circle with chords and center is 8.3

B) The circumference of circle with chords 1.2 cm and 0.5 cm is 4.082

Step-by-step explanation:

Given two figures :

<u>For Figure first  </u>

A circle with center y ,  having two chords FM and NM

FM = 5 x

MN = 2 x + 25

Now from theorem of circle ,

Chords equidistant from center of circle are equal in length

I.e distance of chord MN from center y  and distance of FM from center y are equal

So, FM = MN

Or, 5 x = 2 x + 25

Or, 5 x - 2 x = 25

Or, 3 x = 25

∴       x = \frac{25}{3} = 8.33

<u>For figure second</u>

The length of two adjacent chords of circle is 1.2 cm and 0.5 cm

Let the center of circle = O

Length of chord AB = 1.2 cm

Length of chord BC = 0.5 cm

As both chords are at 90° to each other

So The Length of diameter of circle AC = \sqrt{AB^{2}+BC^{2}}

Or, The Length of diameter of circle AC = \sqrt{1.2^{2}+0.5^{2}}

Or, The Length of diameter of circle AC = \sqrt{1.44+0.25}}

Or, The Length of diameter of circle AC = \sqrt{1.69}

∴ The Length of diameter of circle AC = 1.3 cm

So, Circumference of circle = \pi d

Or, Circumference of circle = 3.14 × 1.3

∴ Circumference of circle = 4.082 cm

Hence,

A ) The value of x for  the given circle with chords and center is 8.3

B) The circumference of circle with chords 1.2 cm and 0.5 cm is 4.082 Answer

Black_prince [1.1K]3 years ago
6 0

Answer:

○ \displaystyle 4,08\:cm.

○ \displaystyle 8,3

Step-by-step explanation:

\displaystyle \sqrt{[CB]^2 + [BA]^2} = d → \sqrt{0,5^2 + 1,2^2} = d \\ \\ \sqrt{0,25 + 1,44} = d → \sqrt{1,69} = d → 1,3 = d \\ \\

Now use the diameter in the circumference formula:

\displaystyle 2πr = C\:or\:πd = C \\ \\ 1,3π ≈ 4,08407045 ≈ 4,08

Two equidistant chords are congruent, therefore the two segments are congruent, so you would set them equal to each other:

2x + 25 = 5x

- 2x - 2x

___________

\displaystyle \frac{25}{3} = \frac{3x}{3} \\ \\ 8\frac{1}{3} = x \\ \\ 8\frac{1}{3} ≈ 8,3

I am joyous to assist you anytime.

You might be interested in
Divide a number by 7, and then subtract 4 from the quotient
Ronch [10]
Y = (x/7) - 4; this would be the equation, assuming x is the number.
3 0
3 years ago
Read 2 more answers
What r the formulas of Exponents and Powers​
lys-0071 [83]

Step-by-step explanation:

8 0
2 years ago
La suma dels quadrats de tres nombres naturals consecutius i múltiples de 3 és igual a 450. Planteja una equació de segon grau i
Firlakuza [10]

Answer:

The 3 numbers are 9, 12, and 15.

Step-by-step explanation:

I will answer in English, below the answer you can see a translation in Catalan.

This can be translated to:

The sum of the squares of three consecutive and multiple natural numbers of 3 is equal to 450. Pose a quadratic equation and calculate the three numbers.

First, a multiple of 3 can be written as:

3*n

The consecutive multiple of 3 is:

3*n + 3

The consecutive multiple of 3 is:

3*n + 3 + 3

Then the sum of their squares is:

(3*n)^2 + (3*n + 3)^2 + (3*n + 6)^2

And we know that this is equal to 450, then we need to solve the equation:

(3*n)^2 + (3*n + 3)^2 + (3*n + 6)^2 = 450

let's solve this:

9*n^2 + (9*n^2 + 2*(3*n)*3 + 9) + (9*n^2 + 2*(3*n)*6 + 36) = 450

27*n^2 + 54*n + 45 = 450

we can write this as:

27*n^2 + 54*n + 45 - 450 = 0

27*n^2 + 54*n - 405 = 0

The solutions of this equation are given by the Bhaskara's formula, and the solutions are:

n = \frac{-54 \pm \sqrt{54^2 -4*27*(-415)}  }{2*27} = \frac{-54 \pm 216 }{54}

we know that our numbers are naturals, then the numbers are positives, which means that we only care for the positive solution of n, which is:

n = (-54 + 216)/54 = 3

Then the 3 numbers are:

3*n = 3*3 = 9

(3*n + 3) = (3*3 + 3) = 12

(3*n + 6) = (3*3 + 6) = 15

In Catalan:

En primer lloc, es pot escriure un múltiple de 3 com:

3 * n

El múltiple consecutiu de 3 és:

3 * n + 3

El múltiple consecutiu de 3 és:

3 * n + 3 + 3

Llavors, la suma dels seus quadrats és:

(3 * n) ^ 2 + (3 * n + 3) ^ 2 + (3 * n + 6) ^ 2

I sabem que això és igual a 450, llavors hem de resoldre l’equació:

(3 * n) ^ 2 + (3 * n + 3) ^ 2 + (3 * n + 6) ^ 2 = 450

resolem això:

9 * n ^ 2 + (9 * n ^ 2 + 2 * (3 * n) * 3 + 9) + (9 * n ^ 2 + 2 * (3 * n) * 6 + 36) = 450

27 * n ^ 2 + 54 * n + 45 = 450

podem escriure això com:

27 * n ^ 2 + 54 * n + 45 - 450 = 0

27 * n ^ 2 + 54 * n - 405 = 0

Les solucions d’aquesta equació vénen donades per la fórmula de Bhaskara, i les solucions són:

n = \frac{-54 \pm \sqrt{54^2 -4*27*(-415)}  }{2*27} = \frac{-54 \pm 216 }{54}

sabem que els nostres nombres són naturals, aleshores els nombres són positius, cosa que significa que només ens importa la solució positiva de n, que és:

n = (-54 + 216) / 54 = 3

Llavors els 3 nombres són:

3 * n = 3 * 3 = 9

(3 * n + 3) = (3 * 3 + 3) = 12

(3 * n + 6) = (3 * 3 + 6) = 15

7 0
3 years ago
When converting between the mixed numbers and improper fractions, the ____always stays the same
Elena L [17]

Answer: Denominator ♥️

Step-by-step explanation:

6 0
3 years ago
During the 2005 football season team tackle the team sack by eight points if the combine scores total of 26 find the individual
Ierofanga [76]

Answer:

Team sack = 9

Team tackle = 17

Step-by-step explanation:

To start with, we'd assume that

Let x = the points scored by Team Sack

Let x + 8 = the points scored by Team Tackle

x + x + 8 = 26

So, go further and solve mathematically

2x + 8 = 26

if we subtract 8 from both sides, we have

2x = 18

Next, we then divide both sides by 2. So that,

x = 18/2

x = 9

Since we assumed the total points for Team Sack to be x, then Team Sack scored 9 points while Team Tackle scored x + 8 points, and that is 17

3 0
2 years ago
Other questions:
  • Which expressions are equivalent to 4(y − 3) + 9y
    13·2 answers
  • A set of data has a normal distribution with a mean of 29 and a standard deviation of 4. Find the percent of data within each in
    9·1 answer
  • Hellp mee pleeeease​
    12·2 answers
  • Given the function rule f(x)=^2-4x+3, which is the output of f(-3)?
    14·1 answer
  • 2. The population of a state A is 650 lakhs and that of
    10·1 answer
  • Two actors were rated by 11 casting directors on their audition performance.
    11·1 answer
  • Add or subtract the following mixed numbers using the first method. (Add the whole numbers; add the fractions; combine the parts
    15·1 answer
  • Increase 15837.77 by 8.5% give your answer rounded to 2 D.P
    10·1 answer
  • If g(x) = 1 - 3/4x, find g(0)
    13·1 answer
  • Which of these is NOT an arithmetic sequence?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!