A box contains $7.45 in nickels, dimes, and quarters. There are 43 coins in all, and the sum of the numbers of nickels and dimes is 3 less than the number of quarters. How many coins of each kind are there?

Answers

Answer 1

Answer:

Number of nickels = 6

Number of dimes = 14

Number of quarters = 23

Step-by-step explanation:

Total number of coins = 43

Let number of nickels = n

Let number of dimes = d

Let number of quarters = q

[tex]n+d+q=43 ...... (1)[/tex]

Money in n nickels = [tex]n \times 0.05[/tex]

Money in d dimes = [tex]d \times 0.10[/tex]

Money in q quarters = [tex]q \times 0.25[/tex]

Total money = $7.45

[tex]0.05n +0.10d+0.25q = 7.45\\\Rightarrow 5n +10d+25q = 745 .... (2)[/tex]

The sum of the numbers of nickels and dimes is 3 less than the number of quarters.

i.e.

[tex]n+d=q-3[/tex]

Let us put the value  in (1):

[tex]q-3+q=43\\\Rightarrow 2q= 43+3\\\Rightarrow q =23[/tex]

Putting the value of q in (1) and (2):

n+d = 20 .... (3)

[tex]5n+10d+575 =745\\\Rightarrow 5n+10d =170\\\Rightarrow n+2d =34 .... (4)[/tex]

(4) - (3):

d = 14

Now, from (3):

n = 6

Number of nickels = 6

Number of dimes = 14

Number of quarters = 23


Related Questions

can you help me find this ans​

Answers

Answer:

28%

Step-by-step explanation:

100%-72%

=28%

So,about 28% of the earth surface is covered by dry land.

Answer = 28%

Explanation:

If 72% = water then dry land =

100% - 72% =

28%

40% of one spig is a spoog. 25% of a speeg is a spoog. 70% of a speeg is a spug. what percent of 1 spig is 5 spugs?

Answers

Answer:

            5 spugs is 560% of 1 spig

Step-by-step explanation:

a - spig

b - speeg

c - spoog

d - spug

40% of one spig is a spoog:  40%a = c

25% of a speeg is a spoog:    25%b = c

70% of a speeg is a spug:       70%b = d

what percent of 1 spig is 5 spugs?:     x%a = 5d

40%a = c  and  25%b = c

40%a = 25%b

[tex]b=\frac{40\%a}{25\%}=1.6a[/tex]

d = 70%b = 70%•1.6a = 112%a

x%a = 5d

x%a = 5•112%a

÷a         ÷a

x% = 560%      

1 point
Given –12 = 2(_5n + 11), What would be your first step?
O Distribute the 2 times the 5n and 11
Subtract 11 on both sides
Add the 5 and 11 because they are Like Terms.
O Divide by -5

Answers

Distribute the 2 is the first step

Which expression means 9 less than twice n?
O A. 2n -9
B. 2 (n - 9)
C. 9 - 211
D. 9–2+n
E. (9 - 2)

Answers

Answer:

The answer is A, 2n - 9

Step-by-step explanation:

9 less than (-9)             twice n  (2n)

2n - 9

Leon and Cisco are each making snack mix. Leon’s recipe calls for 8 parts pretzels to 3 pets peanuts. Cisco’s recipe calls for 6 parts pretzels to 2 part peanuts. Which recipe has higher concentration of peanuts? ASAP 15 pts +brainliest!

Answers

Answer:

  Leon's

Step-by-step explanation:

Since we're interested in peanuts, we can rewrite the ratios with peanuts first:

  L: peanuts : pretzels = 3 : 8

  C: peanuts : pretzels = 2 : 6 = 1 : 3 = 3 : 9

Leon's recipe has a higher proportion of peanuts. (3/8 > 3/9)

Write 2x+4y=8 slope intercept form (solve for y)

Answers

Answer:

[tex]\boxed{y=-\frac{1}{2}x+2}[/tex]

Step-by-step explanation:

[tex]2x+4y=8\\\\2x-2x+4y=8-2x\\\\4y=8-2x\\\\\frac{4y=8-2x}{4}\\\\y=2-\frac{2}{4}x\\\\ y=2-\frac{1}{2}x\\\\\boxed{y=-\frac{1}{2}x+2}[/tex]

Hope this helps.

Answer:

y=4-x/2

Step-by-step explanation:

A river discharges 4 x 106 cubic feet of water into the
Pacific Ocean each second. There are 86,400 seconds in
one day. To find the amount of water discharged each day,
a scientist multiplied 4 x 106 by 86,400 on his calculator.
The display showed:
3456E+14
Explain what 3.456E + 14 means.
OA) 3.456^14
OB) 3.456 *10^6
OC) 3.456 x 10^14
OD) 3.456 x 10^-14

Answers

Answer:

C

Step-by-step explanation:

Here, we want to know what what the display on the calculator means.

Well, the expression has to do with how scientific calculators display powers of 10.

So what this means is that the value 3.456 is raised to the power of 14.

This is a way in which the screen of the scientific calculators maximizes the space on their screens.

Perhaps, we have the result of a multiplication to the powers of 27. It would be quite funny seeing 27 zeros lying on the screen of the calculator right? isn’t it?

So the calculator makes a better way of this by just printing E 27 and this automatically means 10 raised to the power of 27

This makes our answer C

Kindly note that the + sign indicates that the power of the 10 is positive 14.

What is 3 3/5x(-8 1/3)=

Answers

Answer:-30

Step-by-step explanation:

h - 20
Solve for j in the literal equation
=k.

Answers

h - 20/j = k solve for j

isolate each term individually [tex]-\frac{20}{j}[/tex] then [tex]h[/tex] then [tex]-20[/tex]

[tex]h-\frac{20}{j}=k\\-\frac{20}{j}=k-h\\j=-\frac{20}{k-h}[/tex]

what is 123 round to the nearest hundered

Answers

123 rounded to the nearest hundred is 100 i believe

123 rounded to the nearest 100 is 100

Daniel hosted a party in which 15 to 45 people could attend and he charged $7 per person for admission. What is the range of admission with respect to the number of people that attended the party?

A. (105,315)
B. [15,45]
C. [105,315]
D. (15,45)​

Answers

Answer:

c. [105,315]

Step-by-step explanation:

where does the parentheses go in 3+6 ×9+3 to made a total of 84​

Answers

Answer:

Around the 3 + 6:-

(3 + 6) x 9 + 3

Step-by-step explanation:

(3 + 6) x 9 + 3

= 9 x 9 + 3

= 84.

Answer:

[tex](3+6) \cdot 9+3 = 9 \cdot 9 + 3 = 81 +3 = 84[/tex]

what is the solution to this equation
x+8=-3 ​

Answers

Answer:

x+8=-3.

x=-3-8.

x= -11.

Answer:

x=−11

Step-by-step explanation:

Ship A receives a distress signal from the north, And ship B receives a distress signal from the same vessel from the southeast. At what location is the vessel in distress located? Describe how you arrived at your conclusion using compete sentences. You must show all work in order to receive credit.

Answers

The coordinates of Ship A and B are missing, so i have attached it

Answer:

The vessel in distress is located at the coordinate (1, 2)

Step-by-step explanation:

The coordinates attached shows that;

Coordinates of A are (3, 4) while that of B are (1, 1).

We are told that Ship A receives a distress signal from the north, And ship B receives a distress signal from the same vessel from the southeast.

Now, from the image attached, If we imagine extending the line of ship A that is getting distress signal from southeast and also same thing for ship B that is getting signal from north,we'll discover that the lines intersect at a point with co-ordinates of approximately; (1, 2)

someone please help me

Answers

Answer: 64f^24

Steps:
(2f^4)^6
=2f^4 * 2f^4 * 2f^4 * 2f^4 * 2f^4 * 2f^4
=64f^24
Where ^4 means to the power of 4 and so on

3(x+4)=7x
Solving linear equations

Answers

Answer:

x = 3

Step-by-step explanation:

To solve this equation, we can use basic algebraic techniques as illustrated.

3(x + 4) = 7x Distribute the 3.

3x + 12 = 7x Subtract 3x from both sides of the equation.

12 = 4x Rearrange the equation so the variables are on the left.

4x = 12 Divide by 4 on both sides of the equation.

x = 3

Answer:

3(x+4)=7x3x+12=7x7x=3x+127x-3x=124x=12x=12/4x=3

rationalize the denominator ​

Answers

Answer:

The answer is

[tex]\frac{84 - 31 \sqrt{6} }{30} [/tex]

Step-by-step explanation:

[tex] \frac{5 \sqrt{3} - 4 \sqrt{2} }{4 \sqrt{3} + 3\sqrt{2} } [/tex]

To rationalize the denominator multiply both the numerator and the denominator by

4√3 - 3√2

That's

[tex] \frac{5 \sqrt{3} - 4\sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} } [/tex]

So we have

[tex] \frac{(5 \sqrt{3} - 4 \sqrt{2})(4 \sqrt{3} - 3 \sqrt{2}) }{(4 \sqrt{3} + 3 \sqrt{2} )(4 \sqrt{3} - 3 \sqrt{2} ) } \\ = \frac{60 - 15 \sqrt{6} - 16 \sqrt{6} + 24 }{16(3) - 9(2)} \\ = \frac{84 - 15 \sqrt{6} - 16 \sqrt{6} }{48 - 18} \\ = \frac{84 - 31 \sqrt{6} }{48 - 18} [/tex]

We have the final answer as

[tex] \frac{84 - 31 \sqrt{6} }{30} [/tex]

Hope this helps you

Find all the complex roots of the equation x4 − 16 = 0.

Answers

Answer:

4+16=0

4=−16=162

2=±4

Case 1  2=+4

=±2√

√=±(12√+12√)

=±2‾√+2‾√

Case 2  2=−4=43

=±23/2=±2()1/2

∵√=±(12√+12√)

=±(2‾√+2‾√)

So in all,

=2‾√+2‾√

=−2‾√+2‾√

=2‾√−2‾√

=−2‾√−2‾√

Let  √=+

Squaring both sides, we have

=(+)2

0+1=2−2+2⟹

2−2=0(1)

2=1

=12

Plugging in  (1)  … ⟹

2−1(2)2=0

4=14

2=12

∴=±12‾√

∴=±12‾√

∴√=+=±(12+12)

This can also be shown as below

√=12+12

Or

√=−12−12 \


12. If f(5) = 20.58 and f(6)= 2.94

f(7) = __. f(8) = Recursive Function:

Answers

Answer:

What's the answer

Step-by-step explanation:

The recursive function f(7) is = 7.f(8).

What is a recursive function ?

A recursive function is a form of arithmetic or geometric sequence which repeats.

According to the given question f(5) = 20.58 and f(6) = 2.9.

Given it is a recursive function so it could be in form of arithmetic sequence or geometric sequence.

We have asked f(7) is how many times of f(8) from here we can conclude that it is in the form of geometric sequence.

f(5) = 20.58 and f(6) = 2.94 so the common ratio of n/(n-1) is

= 20.58/2.94

= 7.

Or we can say that f(5) is 7 times of f(6) which is 7.f(6) = f(5).

∴ f(7) = 7.f(8) = (1/7)f(6) = 0.42.

learn more about recursive function here :

https://brainly.com/question/23896867

#SPJ2

Whats the least common denominator of the expression g to the second power over 9 minus g to the second power plus 14 plus g over 24g plus 8g to the second power

Answers

Answer:

The least common denominator of the expression is 72g.

Step-by-step explanation:

First, let us write the expression out mathematically

[tex]\frac{g^{2} }{9} - g^{2} + 14 + \frac{g}{24g} + 8g^{2}[/tex]

The denominators in the expression are 9 and 24g. To find the least common denominator, we will determine the least common multiple of the numbers (9 and 24) first, and then find the least common multiple of the result and g (since it is the only letter).

Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...

Multiples of 24 = 24, 48, 72, 96, ...

The least common multiple of 9 and 24 is 72.

Then, the least common multiple of 72 and g is 72g

Hence, the least common denominator of the expression is 72g.

Name three collinear points.
Type your answer as follows:

Answers

Answer:

A, B, E

Step-by-step explanation:

Three or more points are said to be collinear, if they lie on a single straight line

-7x-11x>26-x+9x
Help plis

Answers

Answwer:

x<−1

Step-by-step explanation:

Pull out like factors :

  -26x - 26  =   -26 • (x + 1)

Divide both sides by  -26

Remember to flip the inequality sign

Subtract  1  from both sides

           x < -1

Hope it helped!!!

Name the decimal by writing it in word form
0.48

Answers

Answer:

forty-eight hundredths

Step-by-step explanation:

pleas help me Solve- 8/0.5 ​

Answers

Answer:

The answer to the question is -16.

Answeryou should get 16 as uyour answer

Step-by-step explanation: i hope it helps :)

plus u have to simplfy if necssary

The back of Tom's property is a creek. Tom would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 920 feet of fencing available, what is the maximum possible area of the pasture

Answers

Answer:

Max Area = 105,800 sq.ft

Step-by-step explanation:

A square will always give us the maximum area.

Thus, one side would be;

920/4 = 230 feet

So, we want a square 230 ft by 230 ft

however, from the question, we are to use the creek as one side. So, we'll take the 230 ft that we don't need because of the creek and then add it to the opposite side to get 230 + 230 = 460 ft.

Thus,we now have a rectangle with dimensions: 230 ft by 460 ft

Area is given by;

area = length × width

Maximum Area = 230 × 460

Max Area = 105,800 sq.ft

Find the coordinates of the midpoint of the segment given its endpoints. A(5, 8) and B(-1, -4)

Answers

Answer:

(2,2)

Step-by-step explanation:

(5+(-1))/2. (8+(-4))/2

4/2 4/2.

(2,2)

whats the area of the rectangle? ​

Answers

Answer:

24x^2-13x-2

Step-by-step explanation:

Area of rectangle = Length ×Breadth

[tex]Length =8x+1\\Breadth = 3x-2\\\\A =\left(8x+1\right)\left(3x-2\right)\\\\=8x\times\:3x+8x\left(-2\right)+1\times\:3x+1\times\left(-2\right)\\\\=8\times\:3xx-8\times \:2x+1\times \:3x-1\times\:2\\\\=24x^2-13x-2[/tex]

find the equation of the line that is parallel to y = 3x - 2 and contains the points ( 2,11 )

Answers

Answer:

Below

Step-by-step explanation:

Let y' = mx + b be the equation of the second line

● m is the slope

● b is the y-intercept

The lines are parallel so they have the

same slope.

● y' = 3x + b

The second line crosses the point with the coordinates (2,11)

Replace y' by 11 and x by 2 to find b

● 11 = 3×2 + b

● 11 = 6 + b

Substract 6 from both sides

● 11 - 6 = 6 + b -6

● b = 5

So

● y' = 3x + 5

how many square feet of grass are there on a trapezoid field with a height of 75ft. and bases of 125ft. and 81ft?
formula: A=h(b1+b2/2)

Answers

Answer:

area= 7725

Step-by-step explanation:

A = 75((125+81)/2) A = 75(206/2) A = 75(103) A = 7725 The area is 7725 square feet

please someone help me...​

Answers

Answer:  see proof below

Step-by-step explanation:

Use the following Sum Identities:

cos (A + B) = cosA · cosB - sinA · sinB

sin (A + B) =  sinA · cos B - cosA · sinB

Use the Unit Circle to evaluate the following:

cos 30 = √3/2                            sin 30 = 1/2

cos 45 = √2/2                            sin 45 = √2/2

cos 120 = -1/2                             sin 120 = √3/2

cos 240 = -1/2                             sin 240 = -√3/2                        

cos 315 = √2/2                           sin 315 = -√2/2        

cos 330 = √3/2                          sin 330 = -1/2

Proof LHS → RHS

[tex]\text{LHS:}\qquad \qquad \dfrac{\cos 285+\cos 345}{\sin 435-\sin 375}[/tex]

[tex]\text{Expand:}\qquad \quad \dfrac{\cos (240+45)+\cos (315+30)}{\sin (315+120)-\sin (330+45)}[/tex]

[tex]\text{Sum Identity:}\qquad \dfrac{\cos 240\cdot \cos 45-\sin 240\cdot 45+\cos 315\cdot \cos 30-\sin 315\cdot 30}{\sin 315\cdot \cos 120+\cos315\cdot \sin 120-(\sin330\cdot \cos45+\cos 330\cdot \sin 45) }[/tex]

[tex]\text{Unit Circle:}\quad \dfrac{(\frac{-1}{2}\cdot \frac{\sqrt2}{2})-(\frac{-\sqrt3}{2}\cdot \frac{\sqrt2}{2})+(\frac{\sqrt2}{2}\cdot \frac{\sqrt3}{3})-(\frac{-\sqrt2}{2}\cdot \frac{1}{2})}{(\frac{-\sqrt2}{2}\cdot \frac{-1}{2})+(\frac{\sqrt2}{2}\cdot \frac{\sqrt3}{2)}-(\frac{-1}{2}\cdot \frac{\sqrt2}{2})-(\frac{\sqrt3}{2}\cdot \frac{\sqrt2}{2})}[/tex]

[tex]\text{Simplify:}\qquad \dfrac{-\sqrt2+\sqrt6+\sqrt6+\sqrt2}{\sqrt2+\sqrt6+\sqrt2-\sqrt6}\qquad =\dfrac{2\sqrt6}{2\sqrt2}\qquad =\sqrt3[/tex]

LHS = RHS: [tex]\sqrt3 = \sqrt3\qquad \checkmark[/tex]

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