Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more quarters than dimes. The coins have a total value $10.90. How many dimes and how many quarters does she have? [hint: use the decimal values of the c coins to write an equation.]

Answers

Answer 1

Since you have two unknowns, you must formulate 2 equations in order to solve the system. Let x be the numbers of dimes and y be the number of quarters. The equations are:

x + y = 61
y = x + 3

Since a dime is 1/10 of a dollar and a quarter is 1/4 of a dollar,
(1/10)x + (1/4)y = 10.90

We made 3 equations. The system is overspecified. Let's just use the first two equations and apply it to the third for verification.

x + (x + 3) = 61
Solving for x,
x = 29
y = 29 + 3 = 32

Verifying,
(1/10)(29) + (1/4)(32) = 10.90

Hence, there are 29 dimes and 32 quarters.

Related Questions

a movie club charges a one time fee of $25 it allows members to purchase movies for $7 each another club does not charge a membership fee and sells movies $12 how many movies must a member purchase for the total cost of the two clubs to be equal

Answers

Club Members = $25 + $7 per movie(x)
No membership club = $12 per movie(x)
We need to know how many movies must each purchase to equal in costs.
Set up both equations to equal each other and solve for x=movies.
25 + 7x= 12x
25 + 7x -7x = 12x - 7x
25= 5x
25/5=5x/5
5=x it will take them both 5 movies each to have equal costs.

The number of movies in which the total cost of the two clubs should be equal is 5.

Given that,

The one-time fee is $25.The other club should be $7.The selling price of the movies should be $12.Let us assume the number of movies be x.

25 + 7x= 12x

Now put -7x in both sides

So,

25 + 7x -7x = 12x - 7x

25= 5x

x = 5

Therefore we can conclude that the number of movies in which the total cost of the two clubs should be equal is 5.

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You are a contractor and charge $45 for a site visit plus an additional $24 per hour for each hour you spend working at the site.Write and solve an equation to determine how many total hours you have to work

Answers

so lemme ...
45+(24x)=h

I feel this is the best I can do with the given information ... hope this helps

99 Point question - Consider the graph of f(x) below. (See attachment)

Write the equation of f(x), and classify the function as linear, quadratic, cubic, exponential, or logarithmic.

Answers

A linear function is a straight line, so that's clearly not it

A quadratic function has one point where is switches from going up to going down (or down to up), but this has two, so that's not it.

A cubic function has 2 points where it goes from down to up or up to down, so this may just work.

An exponential function has a constant to the power of something, so it's either staying constantly up or down after 0 or jumping up and down with every x value, which it isn't doing.

Logarithmic functions are similar to exponential functions in that it usually stays either going up or down the whole time.

Using our definitions, a cubic function is the only one that fits

What's the answer to 2z-31=-9z+24

Answers

2z-31=-9z+24
add 9z to both sides
11z-31=24
add 31 to both sides
11z=55
divide by 11 on both sides
z=5

the answer is to this is z=5

3x^2-5x-1 from 8x^2+2x-9

Answers

8x^2 + 2x - 9 - (3x^2 - 5x - 1) =
8x^2 + 2x - 9 - 3x^2 + 5x + 1 =
5x^2 + 7x - 8 <===

[tex](3x^2-5x-1)-(8x^2+2x-9) =3x^2-5x-1-8x^2-2x+9 =3x^2-8x^2-5x-2x-1+9 =-5x^2-7x+8 [/tex].

The entrance fee for an exhibition is $6 for an adult and $4 for a child. $700 was collected from the sale of tickets. There were 5 more adults than children. How many adults were there?

Answers

The answer should be 55 adults.

The price of a dozen roses in the united states is about $30. if $0.559 u.s. dollars can purchase 1.00 turkish lira, how much does the same dozen roses cost in turkey, if purchasing power parity holds?

Answers

Sent you a picture of the solution.

Answer:

16.77

Step-by-step explanation:

MA BRAIN

Nine coins are placed in a 3x3 matrix with some face up and some face down. you can represent the state of the coins using a 3x3 matrix with values 0 (heads) and 1 (tails). here are some examples: 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 each state can also be represented using a binary number. for example, the preceding matrices correspond to the numbers: 000010000 101001100 110100001 there are a total of 512 possibilities, so you can use decimal numbers 0, 1, 2, 3,...,511 to represent all the states of the matrix. write a program that prompts the user to enter a number between 0 and 511 and displays the corresponding matrix with the characters h and t.

Answers

Hello,

Here is the program in QB64

CONST Ordre = 3
DIM SHARED mat(1 TO Ordre, 1 TO Ordre) AS INTEGER, n AS INTEGER
CALL ReadN
CALL MakeMat
CALL SeeMat
END

SUB ReadN
SHARED n AS INTEGER
DIM k AS INTEGER
INPUT "0<=n<=511"; k
IF k < 0 OR k > (2 ^ (Ordre * Ordre)) - 1 THEN PRINT "erreur de valeur de n"; n: END
n = k
END SUB

SUB MakeMat
SHARED mat() AS INTEGER, n AS INTEGER
DIM i AS INTEGER, j AS INTEGER, x AS INTEGER
x = n
FOR i = 1 TO Ordre
    FOR j = 1 TO Ordre
        mat(i, j) = x MOD 2
        x = INT(x / 2)
    NEXT j
NEXT i
END SUB

SUB SeeMat
SHARED mat() AS INTEGER
DIM i AS INTEGER, j AS INTEGER
FOR i = 1 TO Ordre
    FOR j = 1 TO Ordre
        IF mat(i, j) = 0 THEN
            PRINT "h|";
        ELSE
            PRINT "t|";
        END IF
    NEXT j
    PRINT " "
NEXT i
END SUB

You are baking cookies for your class. There are 23 total students in your class and you have baked 12 cookies. Write and solve an equation to find the additional number x of cookies you need to bake in order to have 2 cookies for each student. Write your equation so that the units on each side of the equation are cookies per student.

Answers

Your equation must look like the following:

(something) = 2 cookies/student.

12+x cookies 2 cookies
--------------------- = ---------------
23 students 1 student

Solve the following equation: 12+x 2
--------- ----
23 1

Cross-multiplying: (1)(12+x) = (2)(23) = 46

12+x = 46
x = 46-12=34

Must make 34 more cookies to ensure that every student receives 2 cookies.

find the equation of the circle where (-9,4),(-2,5),(-8,-3),(-1,-2) are the vertices of an inscribed square.

Answers

check the picture below, so, that'd be the square inscribed in the circle.

so... hmm the diagonals for the square are the diameter of the circle, and keep in mind that the radius of a circle is half the diameter, so let's find the diameter.

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ 5}})\quad % (c,d) &({{ -8}}\quad ,&{{ -3}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{[-8-(-2)]^2+[-3-5]^2} \\\\\\ d=\sqrt{(-8+2)^2+(-3-5)^2}\implies d=\sqrt{(-6)^2+(-8)^2} \\\\\\ d=\sqrt{36+64}\implies d=\sqrt{100}\implies d=10[/tex]

that means the radius r = 5.

now, what's the center? well, the Midpoint of the diagonals, is really the center of the circle, let's check,

[tex]\bf \textit{middle point of 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ 5}})\quad % (c,d) &({{ -8}}\quad ,&{{ -3}}) \end{array}\qquad \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left( \cfrac{-8-2}{2}~,~\cfrac{-3+5}{2} \right)\implies (-5~,~1)[/tex]

so, now we know the center coordinates and the radius, let's plug them in,

[tex]\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{ k}})\qquad radius=&{{ r}}\\ &-5&1&5 \end{array} \\\\\\\ [x-(-5)]^2-[y-1]^2=5^2\implies (x+5)^2-(y-1)^2=25[/tex]

Final answer:

The equation of the circle where the vertices of an inscribed square are (-9,4),(-2,5),(-8,-3),(-1,-2) is (x+5)² + (y-1)² = 25. This is found by getting the average x and y coordinates to find the center of the circle, calculating the radius, and applying it to the standard equation of a circle.

Explanation:

To find the equation of the circle where the vertices of an inscribed square are located at (-9,4),(-2,5),(-8,-3),(-1,-2), first, you need to find the center of the circle. In the case of a square inscribed in a circle, the center of the square is the same as the center of the circle. This can be found by averaging the x and y coordinates of the vertices of the square.

The average x-coordinate = [(-9) + (-2) + (-8) + (-1)] / 4 = -5
The average y-coordinate = [4 + 5 - 3 - 2] / 4 = 1

So, the center of the circle is at (-5, 1).

Next, you need to calculate the radius of the circle. The radius in an inscribed square is the half of the square's diagonal. Calculate the distance between two opposite vertices of the square - for example (-9,4) and (-1,-2). Apply the distance formula: √[(-1 - (-9))^2 + (-2 - 4)^2 ]. That's √[64 + 36], giving a distance of √100 = 10. As this is the diagonal of the square, the radius would be half of this, giving us a radius of 5.

Finally, the equation of the circle in its standard form (x-h)² + (y-k)² = r² can be written as (x+5)² + (y-1)² = 5².

Thus, the equation of the circle is (x+5)² + (y-1)² = 25.

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1 point) the solution of a certain differential equation is of the form y(t)=aexp(3t)+bexp(4t), y ( t ) = a exp ⁡ ( 3 t ) + b exp ⁡ ( 4 t ) , where a a and b b are constants. the solution has initial conditions y(0)=3 y ( 0 ) = 3 and y′(0)=3. y ′ ( 0 ) = 3 . find the solution by using the initial conditions to get linear equations for a a and

Answers

y(t) = a exp(3t) + b exp(4t) conditions, y(0) = 3 y'(0) = 3 y(0) = a exp(3 x 0) + b exp(4 x 0) = a exp(0) + b exp(0) = (a x 1) + (b x 1) = a + b y'(0) = 0 so the linear equation is, a + b = 3

sin α = 21/29, α lies in quadrant II, and cos β = 15/17, β lies in quadrant I Find sin (α - β).

Answers

[tex]\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta[/tex]

[tex]\sin\alpha=\dfrac{21}{29}\implies \cos^2\alpha=1-\sin^2\alpha=\dfrac{400}{841}[/tex]

Since [tex]\alpha[/tex] lies in quadrant II, we have [tex]\cos\alpha<0[/tex], so

[tex]\cos\alpha=-\sqrt{\dfrac{400}{841}}=-\dfrac{20}{29}[/tex]

[tex]\cos\beta=\dfrac{15}{17}\implies\sin^2\beta=1-\cos^2\beta=\dfrac{64}{289}[/tex]

[tex]\beta[/tex] lies in quadrant I, so [tex]\sin\beta>0[/tex] and

[tex]\sin\beta=\sqrt{\dfrac{64}{289}}=\dfrac8{17}[/tex]

So

[tex]\sin(\alpha-\beta)=\dfrac{21}{29}\dfrac{15}{17}-\left(-\dfrac{20}{29}\right)\dfrac8{17}=\dfrac{475}{493}[/tex]

Final answer:

The value of sin (α - β), where sin α = 21/29 and α is in the 2nd quadrant, and cos β = 15/17 and β is in the 1st quadrant, is calculated to be 379/493.

Explanation:

In trigonometry, the formula for sin (α - β) is defined as sin α cos β - cos α sin β. Given the problem, we know sin α is 21/29 and cos β is 15/17.

However, we need to determine cos α and sin β. In these cases, we use the identity sin² α + cos² α = 1, and its counterpart for β. For α being in the second quadrant, cos α would be negative. Therefore, cos α = -√(1 - (21/29)²), which simplifies to -8/29. Similarly, for β in the first quadrant (where sin β is positive), sin β = √(1 - (15/17)²), which simplifies to 8/17.

Substitute these values into the formula for sin (α - β), we have sin (α - β) = (21/29 * 15/17) - (-8/29 * 8/17) = 315/493 + 64/493 = 379/493.

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Express 192 as a prime factors in order

Answers

You can write this two ways - as a list of prime factors, or combine like factors and represent their quantity with an exponent.
If you begin by dividing by two, you can do that six times, with a three as the remaining prime factor.
2·2·2·2·2·2·3
OR
2∧6 · 3

Matt plans to put concrete on a rectangular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Matt needs is $58.07. Which of the following is closest to the width of the portion of the driveway on which Matt plans to put concrete?

[1 foot = 12 inches; 1 yard = 3 feet]

0.5 feet
1.5 feet
3 feet
6 feet

any help is appreciated offering 15 points ;)

Answers

Hey! Hope that I can help.

DVD cases are sold in packages of 20 padded mailing envelopes or so in packets of 12 what is the least number of cases and envelopes you could buy so that there is one case for each envelope with none left over

Answers

The least number of cases and envelopes so that there would be no remainder can be determined by finding their least common multiple. The solution is as follows

4 | 20 12
---------------
| 5 3
-------------------

Multiplying 4*5*3 = 60. The least common multiple is 60. Thus, there should be at least 60 each of the envelopes and the packets.

Number of mailing envelopes = 20x = 60
x = 3
Number of packets = 12y = 60
y = 5

That would be 3 packs of the envelopes, and 5 packs of the packets.

or parallelogram ABCD, A(0, 0), B(a, b), and D(c, 0) are three of its vertices. Find the coordinates of C in terms of a, b, c.

Answers

Refer to the diagram below.

Because ABCD is a parallelogram, therefore
(i) AD = BC, so that
x - a = c - 0
x = a + c

(ii) AB = DC, so that
y - 0 = b - 0
y = b

he coordinates of C are (a+c, b).

Answer: (a+c, b)

Answer:

(a + b, c)

Step-by-step explanation:

I did this is school and this was the correct answer!

If you need extra security just look at this brainly question. (below ) It is the same question asked by a diffrerent person. And these people got this answer also!

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What number can be written as 40 plus 5

Answers

I am pretty sure it's 45, but it might be more complex and I just don't understand.

add them together: 40+5 = 45

the number is 45

8.51 is what percent of 18.5

Answers

dive the two numbers:

8.51 / 18.5 = 0.46

0.46 = 46%

Should the quotient of an integer divided by a nonzero integer always be a rational number? Why or Why not?

Answers

YES , it is a rational number

a rational number is defined as

a/b , where a and b are integers, with bâ‰ 0

when you divide two integers you get exactly that form

I am not sure how to solve this

Answers

2x + 1 - 4 = -2x - 3

We're simply just trying to get "x" by itself :)

So, we have to add 2x to both sides.

2x + 2x + 1 - 4 = -3

Add like terms.

(2x + 2x) + (1 - 4) = -3

Simplify.

4x - 3 = -3

Then, we must add 3 to both sides.

4x = -3 + 3

Simplify.

4x = 0

Divide both sides by 4.

x = 0 ÷ 4

Simplify.

x = 0

~Hope I helped!~

You have been able to do the dishes in 30 minutes and vacuum in 15 minutes. youer roomate takes 40 minutes to do the dishes and 60 minutes to vacuum. based on this scenario

Answers

yours d+v=45minutes and roommate d+v=100minutes

What is 9 X 10 to the fifth?

Answers

900,000 should be correct. :)

9,000,000 juss add 5 zeros to 90... I'm pretty sure

Select the answer for this number showing three significant figures. Remember to round. 566 (1)600 (2)570 (3)566(4) 500

Answers

The answer is (1)600! I'm taking the same course, and I know this gets confusing. Hope I helped!

We have to round 566, such that , it has three significant figures.

→ Option 1

600=It has only one Significant figure.Zeroes which lie on right side of digit ,if there is no decimal after zeroes are not significant.

→ Option 2

570=Two Significant figure.

→ Option 3

566=Three Significant figure.

→ Option 4

500=One Significant figure.

⇒Option 3 ,which is equal to 566, is most appropriate ,among given Options, that is when this number is rounded , it has three significant figures.

What is the relationship between the measure of angle and the reflex measure of the angle

Answers

The relationship between the measure of an angle and its reflex angle is their sum is 360 degrees

Angles are measured in degrees and their reflex measures can be obtained by adding 180 degrees to their measures.

In mathematics, an angle is a measure of the amount of turn between two lines or rays that share a common endpoint. The measure of an angle is given in degrees, and it represents the amount of rotation needed to move from one ray to the other.

The reflex measure of an angle is the sum of the angle's measure and 180 degrees. It represents the amount of rotation needed to move from one ray to the other while going in the opposite direction. For example, if an angle has a measure of 30 degrees, its reflex measure would be 30 degrees + 180 degrees = 210 degrees.

So, the relationship between the measure of an angle and its reflex measure is that the reflex measure is obtained by adding 180 degrees to the measure of the angle.

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f(t)=10t2+5t+1 . Find the value of t for which the tangent line to the graph of f(t) has slope 1.

Answers

[tex]\bf f(t)=10t^2+5t+1\implies \stackrel{\textit{slope of tangent}}{\cfrac{df}{dt}}=20t+5\implies 1=20t+5 \\\\\\ -4=20t\implies -\cfrac{4}{20}=t\implies -\cfrac{1}{5}=t[/tex]

The value of t for which the tangent line to the graph of f(t) has slope 1 is -1/5.

The given function is f(t)=10t²+5t+1.

We need to find the value of t for which the tangent line to the graph of f(t) has slope 1.

What is the tangent line to the graph?

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve.

Now, f'(t) = slope of the tangent line to the curve at the point (t, f(t)).

Given, f'(t) = 1

f(t)=10t²+5t+1

⇒f'(t)=20t+5

⇒1=20t+5

⇒20t=-4

⇒t=-4/20

⇒t=-1/5

Therefore, the value of t for which the tangent line to the graph of f(t) has slope 1 is -1/5.

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Which product is negative

Answers

One thing for sure it is not b,d,c its a

1st one -*- =+,+*- = -,-*- = +

2nd one = 0

3rd one-*-=+,+*+=+,+*+=+

4th one +*-=-,-*-=+,+*- = -

4th one is negative

The initial population of a town is 2600, and he grows with the doubling time of 10 years. What will the population be in 12 years?

Answers

I think it would be 5,720, because if you figure every year the population grows 260, then 2600x2 would be doubled then add the 2 years missing so add 260+260. It would equal 5,720.

Solve for x. 4−(2x+4)=5 x=32 x=−52 x=−10 x=6

please help

Answers

If you asked about solving this:

4−(2x+4)=5
4-2x - 4 =5
-2x = 5

x= -5/2 = -2.5

Done!

Final answer:

The solution to the equation 4−(2x+4)=5 is x = -2.5. None of the provided suggestions x = 32, x = -52, x = -10, x = 6 are correct.

Explanation:

To solve for x in the equation 4−(2x+4)=5, you first simplify the expression in the parentheses, which creates the equation 4 - 2x - 4 = 5. This simplifies to -2x = 5. You then divide each side by -2 which results in x = -5/2 or x = -2.5. So the solution to this equation is not any of the provided x = 32, x = -52, x = -10, x = 6 but rather x = -2.5.

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What is 121.6 in word form

Answers

One-Hundred and Twenty-One point Six

one hundred twenty-one and six tenths

Housing expenses are commonly referred to as PITI. What does PITI stand for?

Answers

PITI: principal, interest, taxes, and insurance

Answer:

Step-by-step explanation:

PITI: principal, interest, taxes, and insurance

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