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2 months ago

Fill in the blank. Given O below, you can conclude that OD is congruent to ___________.

Mathematics

2 answers:

zzz [12.3K]2 months ago

6 0

We can deduce that $\boxed{\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OB}}} }$ . Option (A) is the correct choice.

Detailed Explanation:

Provided:

The options are listed below,

A. $\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OB}}}.$

B. $\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{EF}}}.$

C. $\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{AB}}}.$

D. $\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OC}}}.$

Clarification:

The lengths of AB and EF are $9.07{\text{ units}}.$

AB and EF are chords of the circle that are of equal length.

OD and OB serve as the perpendicular bisectors of chords AB and EF.

The mentioned chords are equidistant from the center of the circle.

We can conclude that $\boxed{\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OB}}} }$ . Option (A) is the correct answer.

To Explore Further:

What would be the loss incurred by a clothing manufacturer who purchased 500 m2 of this fabric, priced at $1.00/yard if 0.9144m equals 1 yard? .
In a reference book, if the ocean's total volume is found to be 1.4×109km3, how can you find the mass utilizing the water's density included within, and first convert that volume to cubic meters? .

Response Information:

Grade: High School

Subject: Mathematics

Chapter: Lines and Rays

Tags: congruent, fill, blank, conclude, OH, OE, chord, tangent, displacement, two chords, radius, center, circle, equidistant,

Inessa [12.5K]2 months ago

4 0

In a circle centered at O, there are two chords, AC and EF, both measuring 9.07.

OD and OB are the perpendiculars from the center O to the chords AC and EF, indicating their distance from the center.

The theorem concerning circles states that chords of equal length are equidistant from the center.

This means that OD and OB are equal.

Thus, the correct answer is Option A.

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If m<9=97° and m<12=114°, find each measure. I have to show my work.

Leona [12618]

Solution/Step-by-step breakdown:

Information provided:

m<9 = 97°

m<12 = 114°

a. m<1 = m<9 because they are corresponding angles, which are equal.

m<1 = 97° (using substitution)

b. m<2 + m<1 = 180° (since they form a linear pair)

m<2 + 97° = 180° (substitute the value)

m<2 = 180 - 97 (subtracting 97 from both sides)

m<2 = 83°

c. m<3 = m<11 (as they are corresponding angles)

m<11 + m<12 = 180° (linear pair)

m<11 + 114° = 180° (substituting the known angle)

m<11 = 180 - 114

m<11 = 66°

m<3 = m<11 = 66°

d. m<4 + m<3 = 180° (linear pair)

m<4 + 66° = 180° (substituting the known angle)

m<4 = 180 - 66

m<4 = 114°

e. m<5 = m<2 as vertical angles are equal.

m<5 = 83° (using substitution)

f. m<6 = m<1 (vertical angles are equal)

m<6 = 97° (using substitution)

g. m<7 = m<4 (as vertical angles are equal)

m<7 = 114° (using substitution)

h. m<8 = m<3 (due to vertical angles being equal)

m<8 = 66° (using substitution)

i. m<10 = m<2 (corresponding angles are equal)

m<10 = 83° (using substitution)

j. m<11 = m<3 (because they are vertical angles)

m<11 = 66° (using substitution)

k. m<13 = m<5 (corresponding angles)

m<13 = 83° (applying substitution)

l. m<14 = m<9 (as vertical angles)

m<14 = 97° (applying substitution)

m. m<15 = m<12 (as vertical angles)

m<15 = 114° (applying substitution)

n. m<16 = m<11 (because they are vertical angles)

m<16 = 66° (applying substitution)

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2 months ago

A taxi company charges $3 per ride plus $1.50 fo each mile traveled. Andrea wants to spend no more than $24 on the taxi ride. Ho

AnnZ [12381]

The answer is C since 24-3=21, followed by 21/1.50=14

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1 month ago

P varies inversely with x. If P = 14 when x= 16, find the value of P when x = 21.

tester [12383]

Answer:

Option C. 32/3

Step-by-step explanation:

It is understood that

A relationship between two variables, x and y, signifies inverse variation if it can be represented as either $p*x=k$ or $p=k/x$

It is also known that

For p=14, x=16

Determine the value of k

$k=p*x$

By substituting these values

$k=(14)*(16)=224$

This shows that

The equation equals

$p=\frac{224}{x}$

Calculate the value of p when x=21

Substitute the given value of x into the equation

$p=\frac{224}{21}$

Simplify

Divide both the numerator and denominator by 7

$p=\frac{32}{3}$

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1 month ago

In a state where tax is 5%, Jane bought a telescope and paid $4.55 in tax. What is the price of the telescope?

tester [12383]

The telescope’s cost is $91

4.55 divided by 5% (0.05) equals 91.

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1 month ago

Read 2 more answers

An automobile manufacturer sold 30,000 new cars, one to each of 30,000 customers, in a certain year. The manufacturer was intere

babunello [11817]

A) To establish a sampling plan, follow these 5 steps:
1) Identify the sample population: which customers will you reach out to?
   Those who purchased a new car during a specific year.
2) Determine the population size: how many customers will you contact?
   From the 30,000 car buyers, select 1,000 customers to contact.
3) Select contact method: what is your means of contacting customers?
   Since you have a list with names and addresses, mailing questionnaires is feasible.
4) Define the sampling frame: what is the timeline or deadline for contacting customers?
   Send out questionnaires and allow two months for responses.
5) Decide on the analysis approach: is your research qualitative or quantitative?
   You aim for quantitative research, so you will use probabilistic sampling.

B) The 32.5% probability relates only to those customers who experienced mechanical issues, specifically power door lock problems, and does not account for those without any problems or those reporting issues after the first 5,000 miles.

C) To estimate the probability of power door lock problems among all customers within the first 5,000 miles, consider the entire sample:
P = 13 / 1000 = 0.013

Therefore,
N = 0.013 × 30,000 = 390

Thus, the estimated number of new cars that had power door lock issues within 5,000 miles is 390.

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3 months ago