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3 years ago

If the range of the function f(x) = 4x – 3 is {11.4, 15, 17, 29}, what is its domain?

1 answer:

5 0

The range of the function is the y-component or the ordinate of the sets of points. The domain of the function meanwhile is the x-component ot the abscissa of the sets of points. In this case, we have the function f(x) = 4x – 3 and given each y, we get the x. Subsituting each y to the function we get the domain equal to {3.535, 4.5, 5, 8}.

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Barb is going to cover a rectangle area 8 feet by 10 feet with rectangle paving blocks that are 4 inches by 8 inches by 2 inches

soldier1979 [14.2K]

Step-by-step explanation:

First, transform 8 feet and 10 feet into inches so we can work with the same measurements

8 * 12 = 96 in

10 * 12 = 120 in

Next find the patio rectangle area.

96 * 120 = 11520 in^2

Now find the paving block area

4 * 8 = 32 in^2

Now, find out how many paving blocks will go into the patio rectangle area.

11520 / 32 = 360

The minimum number is 360 paving blocks

5 0

3 years ago

Given a circle with a radius of 6, what the the length of an arc measuring 30 degrees

Mazyrski [523]

$\bf \textit{arc's length}\\\\
s=\cfrac{\theta \pi r}{180}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=6\\
\theta =30
\end{cases}\implies s=\cfrac{30\cdot \pi \cdot 6}{180}\implies s=\pi$

6 0

3 years ago

The negative effects of a recession would be reduced by which fiscal policy decision?

Elis [28]

Answer:

The negative effects of a recession would be reduced by which fiscal policy decision?

A. incurring a budget deficit which is used to retire debt held by the public

<h3>B. incurring a budget surplus and allowing that surplus to accumulate as idle Treasury balances</h3>

C. incurring a budget surplus, which is used to retire debt held by commercial banks

D. incurring a budget deficit by borrowing from the public and increasing expenditures

Step-by-step explanation:

#CarryOnLearning

3 0

3 years ago

How many terms of the arithmetic sequence {1,22,43,64,85,…} will give a sum of 2332? Show all steps including the formulas used

MA_775_DIABLO [31]

There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by

• a (1) = 1

• a (n) = a (n - 1) + 21 … … … for n > 1

We can find the explicit rule for the sequence by iterative substitution:

a (2) = a (1) + 21

a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21

a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21

and so on, with the general pattern

a (n) = a (1) + 21 (n - 1) = 21n - 20

Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is

a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332

or more compactly,

$\displaystyle\sum_{n=1}^N a(n) = 2332$

It's important to note that N must be some positive integer.

Replace a (n) by the explicit rule:

$\displaystyle\sum_{n=1}^N (21n-20) = 2332$

Expand the sum on the left as

$\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332$

and recall the formulas,

$\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n$

$\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2$

So the sum of the first N terms of a (n) is such that

21 × N (N + 1)/2 - 20N = 2332

Solve for N :

21 (N ² + N) - 40N = 4664

21 N ² - 19 N - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

N = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer N for which the first N terms of the sum add up to 2332.

4 0

2 years ago

Please help! I'm stuck:(

irina [24]

Answer:

1st graph is Y=1x+0

2nd Graph is Y=-2/1x + 0

Step-by-step explanation:

Your slope is 1 for the 1st graph

Your slope is -2/1 for the second graph

3 0

3 years ago