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Ede4ka [16]
2 years ago
10

A change jar contains nickels dimes and quarters totaling and amount of $1.90 the amount of nickels is one more than twice the n

umber of Dimes the number of quarters is one half the total number of nickels and dimes find the number of each coin in the change jar
Mathematics
2 answers:
Anit [1.1K]2 years ago
5 0
Nickel- 15
Dime- 7
Quarters- 2
Lilit [14]2 years ago
4 0

Answer:Given below

Step-by-step explanation:

We know Nickel is 5% of a dollar and dime is 10% of dollar

while quarter is 25% of dollar

Given

Let x be the no. of Dimes

therefore nickels be 2x+1

Quarter=\frac{1}{2}(2x+1+x)=\frac{1}{2}(3x+1)

Also total worth of coins is $1.90

x(0.1)+(2x+1)0.05+\frac{1}{2}(3x+1)(0.25)=1.9

115x+35=380

x=3

therefore no of nickels =2*3+1=7

Quarter=5

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Which statements are true regarding the relationships between central, inscribed, and circumscribed angles of a circle? Check al
mamaluj [8]

Answer:

# A circumscribed angle is created by two intersecting tangent segments ⇒ true (1st answer)

# The measure of a central angle will be twice the measure of an inscribed angle that intercepts the same arc ⇒ true (3rd answer)

# The measure of a central angle will be equal to the measure of an inscribed angle when the arc intercepted by the inscribed angle is twice as large as the arc intercepted by the central angle ⇒ true (6th answer)

Step-by-step explanation:

* Lets revise the types of angles in a circle

- A circumscribed angle is the angle made by two intersecting

 tangent lines to a circle (it's out side the circle)

- Its measure is half the difference of the measures of the two

 intercepted arcs

- Ex:

∵ AB and AC are tangent to circle M at B and C

∴ ∠A is a circumscribed angle

∴ m∠A = 1/2(m major arc BC - m minor arc BC)

- An inscribed angle is an angle formed by two chords in a circle

  which have a common endpoint, this common endpoint is the

  vertex of it

- Its measure is half the measure of the intercepted arc

Ex:

∵ XY and XZ are two chords in circle M

∴ ∠YXZ is an inscribed angle subtended by arc YZ

∴ m∠YXZ = 1/2 (m arc YZ)

- A central angle is an angle with endpoints located on the

 circumference of the circle and its vertex is the center of the circle

- Its measure is the measure of the intercepted arc

- Ex:

∵ MA and MB are two radii of circle M

∴ ∠AMB is a central angle subtended by the opposite arc AB

∴ m∠AMB = m of arc AB

- The measure of an inscribed angle is half the measure of the

  central angle which subtended by the same arc

- Ex:

∵ ∠ABC is an inscribed angle in circle M subtended by arc AC

∵ ∠AMC is a central angle subtended by arc AC

∴ m∠ABC = 1/2 m∠AMC

∴ m∠AMC = 2 m∠ABC

* Lets solve the problem

- From the facts above:

# A circumscribed angle is created by two intersecting tangent

  segments ⇒ true

# The measure of a central angle will be twice the measure of an

   inscribed angle that intercepts the same arc ⇒ true

- Lets prove the last statement

∵ AMC is a central angle of circle M subtended by arc AC

∴ m∠AMC = m of arc AC ⇒ (1)

∵ XYZ is an inscribed angle of circle M subtended by arc XZ

∴ m∠XYZ = 1/2 m of arc XZ

∵ m of arc XZ is twice m of arc AC

∴ m∠XYZ = m of arc AC ⇒ (2)

- From (1) and (2)

∴ m∠AMC = m∠XYZ

∴ The statement down is true

# The measure of a central angle will be equal to the measure of

   an inscribed angle when the arc intercepted by the inscribed

   angle is twice as large as the arc intercepted by the central

   angle ⇒ true

8 0
2 years ago
Read 2 more answers
Which will result in a difference of squares? (negative 7 x + 4)(negative 7 x + 4) (negative 7 x + 4)(4 minus 7 x) (negative 7 x
nevsk [136]

Answer:

(negative 7 x + 4)(negative 7 x minus 4)

Step-by-step explanation:

Consider two real numbers a and b. A difference of squares involving a and b is usually given as;

a^{2}-b^{2}

The difference of the two squares above can be factored to yield;

(a-b)(a+b)

This implies that in order to have the difference of squares we must have a product involving the difference and the sum of the numbers.

The expression;

(negative 7 x + 4)(negative 7 x minus 4) can also be written as ( 4 - 7x) ( -4 - 7x)

( 4 - 7x) ( -4 - 7x) = ( 4 - 7x) (-1( 4 + 7x)) = -1 *( 4 - 7x) ( 4 + 7x)

Expanding the last expression yields;

-1 (16 + 28x -28x - 49x^2) = -1 (16 - 49x^2) = 49x^2 - 16 which is in deed a difference of squares

3 0
2 years ago
Read 2 more answers
Adam lived a quarter of his life as a boy as fifth as a young man, a third in middle-age and 13 years in retirement. How old was
Anika [276]

ANSWER

Find out the how old was we when he died.

To proof

Let us assume that the age of the Adam be x

As given

Adam lived a quarter of his life as a boy as fifth as a young man, a third in middle-age and 13 years in retirement.

x =\frac{x}{4} +\frac{x}{5} +\frac{x}{3} + 13

L.C.M of denominator i.e ( 4,5,3) =60

than the equation becomes

60x = 15x + 12x +20x +780

60x - 47x = 780

13x = 780

x =\frac{780}{13}

x = 60 years

therefore the Adam age  when he died is 60 years.

Hence proved




5 0
2 years ago
Given right triangle XYZ, what is the value of tan(60°)?
Svetlanka [38]

we know that

Step 1

in the right triangle XYZ

Applying the Pythagorean Theorem

Find the value of ZY

XY^{2}=XZ^{2} +ZY^{2} \\   ZY^{2}=XY^{2}-XZ^{2}\\ ZY^{2}=42^{2}-21^{2}\\ ZY^{2}=1,323\\ ZY=\sqrt{1,323}\ units

ZY=21\sqrt{3}\ units

Step 2

in the right triangle XYZ

Find tan60°

we know that

tan\ 60=\frac{opposite\ side\ angle\ 60}{adjacent\ side\ angle\ 60}

in this problem

opposite side angle 60 is ZY

adjacent side angle 60 is XZ

so

tan\ 60=\frac{ZY}{XZ} \\ \\ tan\ 60=\frac{21\sqrt{3}}{21}  \\ \\  tan\ 60=\sqrt{3}

therefore

the answer is

\sqrt{3}


3 0
2 years ago
Read 2 more answers
a car travels 30 1/2 miles in 2/3 of an hour. what is the average speed, in miles per hour, of the car ?
Contact [7]

Answer:

speed=225.75 miles per hour

Step-by-step explanation:

given:

s=301/2

t=2/3

we have,

v=s/t

v=(301/2)/(2/3)

=(301/2)×3/2

=903/4

v=225.75

therefore, speed of car will be 225.75 miles per hour

6 0
1 year ago
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