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Daniele has 33 quarters and dimes in her piggy bank. The piggy bank contains a total of $4.95. Write and solve a system of equat

3241004551 [841]

Answer:the number of dimes is 22

the number of quarters is 11

Step-by-step explanation:

A dime is worth 10 cents. Converting to dollars, it becomes 10/100 = $0.1

A quarter is worth 25 cents. Converting to dollars, it becomes 25/100 = $0.25

Let x represent the number of dimes.

Let y represent the number of quarters.

Daniele has 33 quarters and dimes in her piggy bank. This means that

x + y = 33

The piggy bank contains a total of $4.95. This means that

0.1x + 0.25y = 4.95 - - - - - - - - -1

Substituting x = 33 - y into equation 1, it becomes

0.1(33 - y) + 0.25y = 4.95

3.3 - 0.1y + 0.25y = 4.95

- 0.1y + 0.25y = 4.95 - 3.3

0.15y = 1.65

y = 1.65/0.15 = 11

Substituting y = 11 into x = 33 - y, it becomes

x= 33 - 11 = 22

5 0

3 years ago

One month ruby worked six hours more than Isaac and svetlana worked four times as much hours as ruby together they worked 126 ho

natulia [17]

R=I+6 S=4R I

I+(I+6)+4(I+6)=126

Basic algebra (I dont know how to show it) leaves you with: 6I = 90, divide both sides by 6 and I=15

4 0

3 years ago

Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (3, 1, 0) and perpendicu

iren2701 [21]

Answer with Step-by-step explanation:

We are given that a point (3,1,0)

Two vectors are

A=<1,1,0>

B=<0,1,1>

$A\times B=\begin{vmatrix}i&j&k\\1&1&0\\0&1&1\end{vmatrix}$

$A\times B=i-j+k$

Let v $=A\times B=i-j+k$

$v==$

$r_0==$

$r=r_0+vt$

Substitute the values then we get

$r=+t$

$r=$

The parametric equation of the line

$x=x_0+at,y=y_0+bt,z=z_0+ct$

Using the formula

The parametric equation of the line which is passing through the point (3,1,0) and perpendicular to both i+j and j+k is given by

$x=3+t,y=1-t,z=t$

The symmetric equation of the line is given by

$\frac{x-x_0}{a}=\frac{y-y_0}{b}=\frac{z-z_0}{c}$

Using the formula

The symmetric equation of the line which is passing through the point (3,1,0) and perpendicular to both i+j and j+k is given by

$\frac{x-3}{1}=\frac{y-1}{-1}=z$

8 0

3 years ago

HELPPPP

Shalnov [3]

$y = 0.25x + 40$

$60 = 0.25x + 40$

$60 - 40 = 0.25x + 40 - 40$

$20 = 0.25x$

$\frac{20}{0.25} = \frac{0.25x}{0.25}$

$80 = x$

She can buy a maximum of 80 cups.

5 0

3 years ago

He oblique prism has a rectangular base with a width of 10 units and a length of 13 units. the top base extends 8 units to the r

kumpel [21]

Answer:

The correct option is 3.

Step-by-step explanation:

It is given that the oblique prism has a rectangular base with a width of 10 units and a length of 13 units. The top base extends 8 units to the right of the bottom base.

From the figure the height of prism is

$h=\sqrt{(17)^2-8^2}=\sqrt{225}=15$

The height of prism is 15.

The volume of prism is

$V=(\text{base area })\times h$

$V=(10\times 13)\times 15$

$V=1950$

The volume of prism is 1950 unit². Therefore the correct option is 3.

4 0

3 years ago

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