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3 years ago

Linda's penny bank is 1/4full. After she adds 360 pennies, it is 5/8 how many pennies can Linda bank hold?

Mathematics

2 answers:

Leokris [45]3 years ago

6 0

The answer for your question is 480.
Hope it helps!

ZanzabumX [31]3 years ago

5 0

X=# of pennies the bank can hold(1/2)x+80=(2/3)x80=(2/3)x-(1/2)x80=(4/6)x-(3/6)x80=(1/6)xx=80*6x=480 pennies (how many pennies the bank can hold)check: 1/2 full means 240 penniesadd 80 pennies240+80=320320/480=32/48=2/3

hope that helps

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Two points in the Cartesian plane are A(2.00 m, −4.00 m) and B(−3.00 m, 3.00 m). Find the distance between them and their polar

Brrunno [24]

The distance between the two points is $d=8.6m$

The polar coordinate of A is $\left(4.47,296.57\right)$

The polar coordinate of B is $\left(4.24,135\right)$

Explanation:

The two points are $A(2,-4)$ and $B(-3,3)$

The distance between two points is given by,

$d=\sqrt{(2+3)^{2}+(-4-3)^{2}}\\d=\sqrt{(5)^{2}+(-7)^{2}}\\d=\sqrt{25+49}\\d=8.6$

Thus, the distance between the two points is $d=8.6m$

The polar coordinates of A can be written as $(Distance, tan^{-1} \frac{y}{x} )$

Distance = $\sqrt{x^{2} +y^{2} }$

Substituting $A(2,-4)$ , we get,

Distance = $\sqrt{2^{2} +(-4)^{2} }=\sqrt{4+16 }=4.47$

$tan^{-1} \frac{y}{x} =tan^{-1} \frac{-4}{2}=-63.43$

To make the angle positive, let us add 360,

$\theta=360-63.43=296.57$

The polar coordinate of A is $\left(4.47,296.57\right)$

Similarly, The polar coordinate of B can be written as $(Distance, tan^{-1} \frac{y}{x} )$

Distance = $\sqrt{x^{2} +y^{2} }$

Substituting $B(-3,3)$ , we get,

Distance = $\sqrt{(3)^{2}+(3)^{2}}=4.24$

$tan^{-1} \frac{y}{x} =tan^{-1} \frac{3}{-3}=-45$

To make the angle positive, let us add 360,

$\theta=180-45=135^{\circ}$

The polar coordinate of B is $\left(4.24,135\right)$

5 0

3 years ago

Solve x^4 y^4=706 given x y=8.........

lapo4ka [179]

<span>Maybe xy is also given ........................</span>

4 0

3 years ago

Multiply the additive inverse of (-7/8) by the reciprocal of (5 1/2)<br><br>PLEASE HELP!

EleoNora [17]

Answer:

$\bold {$\dfrac{7}{44}$}$

Step-by-step explanation:

<h3> Reciprocal:</h3>

$\sf \text{The reciprocal of any number $\dfrac{a}{b}$ is given by $\dfrac{b}{a}$}\\\\5\dfrac{1}{2}=\dfrac{11}{2}\\\\\text{Reciprocal of $\dfrac{11}{2}$ = $\dfrac{2}{11}$}$

<h3>Additive inverse:</h3>

$\text{Additive inverse of $\dfrac{-7}{8}$=$\dfrac{7}{8}$}$

Now multiply,

$\sf \dfrac{7}{8}*\dfrac{2}{11}=\dfrac{7}{4}*\dfrac{1}{11}\\$

$=\dfrac{7}{44}$

7 0

2 years ago

You place the spring vertically with one end on the floor. You then drop a book of mass 1.50 kg onto it from a height of 0.900 m

Alex777 [14]

Answer:

The value of the maximum distance the spring will be compressed

x = 0.143 m= 14.3 cm

Step-by-step explanation:

Given data

Mass m = 1.5 kg

h = 0.9 m

k = 1500 $\frac{N}{m}$

Since the book is released from a height h = 0.9 m above the top of the spring. so the total distance

y = h + x

Now in that case for the spring

$mg y= \frac{1}{2} k x^{2}$

$mg(h +x) = \frac{1}{2} k x^{2}$

By rearranging the above equation we get

$k x^{2} - 2mgx - 2mg h = 0$

Put all the values in above equation we get

$1500x^{2} - 29.43 x - 26.48 = 0$

By solving the above equation we get

x = 0.143 m= 14.3 cm

This is the value of the maximum distance the spring will be compressed.

8 0

3 years ago

The quantity a varies directly with b and c and inversely with d. The quantity d is tripled. Which of the following must be true

Vinvika [58]

Lets name the quantity Q
$Q=k* \frac{b*c}{d} 

When quantity d is tripled, we get




$
$Q=k \frac{b*c}{3d} 

To be the relationship the same, we see that we need to$ $
multiply /numerator / by /3 


$ $Q = k \frac{3bc}{3d} 

So the answer should be 
"The product of c and b must be tripled."$

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3 years ago