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2 years ago

Explain why 82.5 + 8(0.25x) = 338.5 is equivalent to 82.5 + 2x = 338.5

Mathematics

2 answers:

VARVARA [1.3K]2 years ago

7 0

Answer:

Multiply 0.25x by 8

Step-by-step explanation:

82.5 + 8(0.25x) = 338.5

Multiply 0.25x by 8 we get,

8 × 0.25x = 2x

Thus, 82.5 + 2x = 338.5

<u>-TheUnknownScientist 72</u>

gtnhenbr [62]2 years ago

7 0

Commutative property states out that in multiplication, changing the order of the numbers still have the same product (the product remains the same)

So, we can rewrite 8(0.25x) as (8 x 0.25)x = 2x

So, 82.5 + 8(0.25x) = 82.5 + 2x

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A parking lot charges $3 to park a car for the first hour and $2 per hour after that. If you use more than one parking space, th

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Given, a parking lot charges $3 for first hour and $2 per hour after that.

So for t hours, the parking lot charges $3 for the first hour and after first hour there is $(t-1)$ hours left.

So for $(t-1)$ hours it will charge $2 per hour.

The charges for $(t-1)$ hours = $ $2(t-1)$ .

Total charges for t hours for one car = $ $(3+2(t-1))$

Now for the second car, it will charge 75% of the first car.

So the charges for second car

=$[ $(3+2(t-1))(75/100)$ ]

=$ $0.75(3+2(t-1))$

There are 3 cars. That parking charges for the third car is also 75% of the first car.

So for third car the parking charges are same as for the second car.

Total parking charges for 3 cars

= $ $(3+2(t-1))+(0.75(3+2(t-1))+(0.75(3+2(t-1))$

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We have got the required answer here.

The correct option is option C.

8 0

3 years ago

Please help! With explanation, thanks!

Ber [7]

45.6%, I think

If the angle was 45 degrees, then 50% of the circumference of the ice cream would be inside the cone.
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3 years ago

The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the ge

Leno4ka [110]

Answer:

Infinite number of solutions.

Step-by-step explanation:

We are given system of equations

$5x+4y+5z=-1$

$x+y+2z=1$

$2x+y-z=-3$

Firs we find determinant of system of equations

Let a matrix A= $\left[\begin{array}{ccc}5&4&5\\1&1&2\\2&1&-1\end{array}\right]$ and B= $\left[\begin{array}{ccc}-1\\1\\-3\end{array}\right]$

$\mid A\mid=\begin{vmatrix}5&4&5\\1&1&2\\2&1&-1\end{vmatrix}$

$\mid A\mid=5(-1-2)-4(-1-4)+5(1-2)=-15+20-5=0$

Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.

We are finding rank of matrix

Apply $R_1\rightarrow R_1-4R_2$ and $R_3\rightarrow R_3-2R_2$

$\left[\begin{array}{ccc}1&0&1\\1&1&2\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\1\\-5\end{array}\right]$

Apply $R_2\rightarrow R_2-R_1$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&-1&-3\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\-5\end{array}\right]$

Apply $R_3\rightarrow R_3+R_2$

$\left[\begin{array}{ccc}1&0&1\\0&1&1\\0&0&-2\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\6\\1\end{array}\right]$

Apply $R_3\rightarrow- \frac{1}{2}$ and $R_2\rightarrow R_2-R_3$

$\left[\begin{array}{ccc}1&0&1\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-5\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$

Apply $R_1\rightarrow R_1-R_3$

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$ : $\left[\begin{array}{ccc}-\frac{9}{2}\\\frac{13}{2}\\-\frac{1}{2}\end{array}\right]$