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3 years ago

Explain how knowing that 5÷8 = 0 .625 helps you write the decimal for 4 5/8

Mathematics

1 answer:

ivolga24 [154]3 years ago

8 0

Answer:

because an integer divided by an integer is equal to integer and the answer isn't up to one so it is zero

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Tom bought a book that originally costs $35. The book was on sale for ⅕ off. Write an expression to represent the scenario Write

dezoksy [38]

Answer:

Step-by-step explanation:

1. 1/5 = 2/10

2. 2/10 = 20%

3. 20% = 0.2

4. 35 x 0.2 = 7

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2 years ago

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Isaiah is having his house painted. He paid $525 for the required materials, and he will pay $30 an hour for the painters to com

alukav5142 [94]

Answer:

Step-by-step explanation:

x is the amount of hours it will take. Since he pays $30 per hour, your answer would be 30x + 525

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2 years ago

The half-life of a certain radioactive material is 78 hours. An initial amount of the material has a mass of 790 kg.. Write an e

adoni [48]

<span> half life i= 78 hours
amount after 78 hours is 395 kg:
395 = 790e^(k*78)

Dividing by 790 and taking natural log
ln (395/790) = (k*78)
-0.6931 = 78k
-0.00888 = k

lets calculate how much is left after 18 hours:
Amount(18)
= 790e^(-0.00888*18)
Amount = 673.301 kg
hope this helps</span>

4 0

2 years ago

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Write an explicit formula for a_n, the nth term of the sequence 4, -20, 100, ...

saw5 [17]

Answer:

$a_{n}$ = 4 $(-5)^{n-1}$

Step-by-step explanation:

There is a common ratio r between consecutive terms , that is

r = - 20 ÷ 4 = 100 ÷ - 20 = - 5

This indicates the sequence is geometric with nth term ( explicit formula )

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio

Here a₁ = 4 and r = - 5 , then

$a_{n}$ = 4 $(-5)^{n-1}$

3 0

2 years ago

The vertices of a square CDEF are C(1,1), D(3,1), E(3,-1) and F(1,-1). What formulas prove that the diagonals are congruent perp

Oxana [17]

To prove that the diagonals are congruent, you need to formula to compute the distance between two points:

$d(A,B) = \sqrt{(A_x-B_x)^2 + (A_y-B_y)^2}$

Using that formula, you may prove that $d(C,E) = d(D,F)$ , which means that the two diagonals have the same length.

To prove that they are perpendicular, you need the formula to compute the slope of a segment. The slope, knowing the enpoints, is given by

$m = \cfrac{\Delta y}{\Delta x} = \cfrac{A_y-B_y}{A_x-B_x}$

You can use this formula to prove that

$m_{CE} = -\cfrac{1}{m_{DF}}$

In fact, if one slope is the opposite of the reciprocal of the other, the two segments are perpendicular.

Finally, to prove that they bisect each other, you first need to find the point where they meet. First of all, you need to find the line the segments lie on: the formula is

$y-y_0 = m(x-x_0)$

where $(x_0,y_0)$ is one of the points belonging to the line, and you already know how to find the slope. Then, you find the point of intersection, say A, by solving the system involving the two lines:

$\begin{cases} y= m_{CE}x+q_{CE}\\ y = m_{DF}x+q_{DF} \end{cases}$

And use again the formula for the distance between two points to prove that

$d(A,C) = d(A,D) = d(A,E) = d(A,F)$

4 0

2 years ago