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Diano4ka-milaya [45]
3 years ago
7

Last week Jennifer ran 7 1/2 blocks less than Sam. Jennifer ran 35

Mathematics
1 answer:
STatiana [176]3 years ago
7 0

Answer:

42.5

Step-by-step explanation:

35+7.5=42.5

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Solve for x. x + 4 = -12
Zina [86]

Answer:

x=-16

Step-by-step explanation:

Subtract 4 from both sides

x+4-4=-12-4

x=-16

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3 years ago
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2/5 of Janet's class prefers chocolate ice cream and 2/5 prefers vanilla ice cream. What part of the class prefers chocolate or
belka [17]
The answer is D, 4/5, because 2/5+2/5=4/5.
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Find four numbers that form a geometric progression such that the third term is greater than the first by 12 and the fourth is g
olchik [2.2K]

If x is the first number in the progression, and r is the common ratio between consecutive terms, then the first four terms in the progression are

\{x,xr,xr^2,xr^3\}

We want to have

\begin{cases}xr^2-x=12\\xr^3-xr=36\end{cases}

In the second equation, we have

xr^3-xr=xr(r^2-1)=36

and in the first, we have

xr^2-x=x(r^2-1)=12

Substituting this into the second equation, we find

xr(r^2-1)=12r=36\implies r=3

So now we have

\begin{cases}9x-x=12\\27x-3x=36\end{cases}\implies x=\dfrac32

Then the four numbers are

\left\{\dfrac32,\dfrac92,\dfrac{27}2,\dfrac{81}2\right\}

4 0
3 years ago
Find the 13th term of the arithmetic sequence -3x – 1,42 + 4,112 + 9, ...
Strike441 [17]

Answer:

The 13th term is 81<em>x</em> + 59.

Step-by-step explanation:

We are given the arithmetic sequence:

\displaystle -3x -1, \, 4x +4, \, 11x  + 9 \dots

And we want to find the 13th term.

Recall that for an arithmetic sequence, each subsequent term only differ by a common difference <em>d</em>. In other words:

\displaystyle \underbrace{-3x - 1}_{x_1} + d = \underbrace{4x + 4} _ {x_2}

Find the common difference by subtracting the first term from the second:

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

Distribute:

d = (4x + 4) + (3x + 1)

Combine like terms. Hence:

d = 7x + 5

The common difference is (7<em>x</em> + 5).

To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:

\displaystyle x_n = a + d(n-1)

Where <em>a</em> is the initial term and <em>d</em> is the common difference.

The initial term is (-3<em>x</em> - 1) and the common difference is (7<em>x</em> + 5). Hence:

\displaystyle x_n = (-3x - 1) + (7x+5)(n-1)

To find the 13th term, let <em>n</em> = 13. Hence:

\displaystyle x_{13} = (-3x - 1) + (7x + 5)((13)-1)

Simplify:

\displaystyle \begin{aligned}x_{13} &= (-3x-1) + (7x+5)(12) \\ &= (-3x - 1) +(84x + 60) \\ &= 81x + 59 \end{aligned}

The 13th term is 81<em>x</em> + 59.

3 0
3 years ago
To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line repr
BARSIC [14]
Hi there! The slope of the line is -2/5.

We can determine the slope of a line by dividing the change of y-coordinates by the change of x-coordinates.

In this situation we have a...
change of x-coordinates of (5 - 0) = 5
change of y-coordinates of (0 - 2) = -2

Therefore, the slope of this line is -2/5
6 0
3 years ago
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