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4 years ago

13

Evaluate the piecewise function at the given values of the independent variable solver

1 answer:

Goryan [66]4 years ago

5 0

X | x ≤ 1} and {x | x ≥ 1}{x | x < 1} and {x | x > 1}<span>{x | x ≤ 1} or {x | x ≥ 1}

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If the temperature at the North Pole is -12 degrees how many degrees would the temperature have to increase for it to be 0 degre

ch4aika [34]

12 degrees

Think of a number line -12 is 12 spaces away from 0.

6 0

3 years ago

Sophia determined that the expression Negative (4 x minus 5) + 2 (x minus 3) is equivalent to –2x – 5 by using the steps below.

strojnjashka [21]

Answer:

She is not correct because she did not substitute the same number in both expressions in Step 1

Step-by-step explanation:

CASE 1: substitute 1 for x to both sides of the equations

L.H.S

-(4x-5)+2(x-3)

-(4 (1) - 5)+ 2(1-3) = - (-1) + 2(-2) = 1 - 4 = -3

R.H.S

-2x - 5

-2(1) - 5 = -2-5 = -7

Hence for x= 1

-(4x-5)+2(x-3) ≠ -2x -5

Because -3 ≠ -7

CASE 2: substitute -1 for x to both sides of the equations

L.H.S

-(4x-5)+2(x-3)

-(4 (-1) - 5)+ 2(-1-3) = - (-9) + 2(-4) = 9 - 8 = 1

R.H.S

-2x - 5

-2(-1) - 5 = 2-5 = -3

Hence for x= -1

-(4x-5)+2(x-3) ≠ -2x -5

Because 1 ≠ -3

Answer:

She is not correct because she did not substitute the same number in both expressions in Step 1

6 0

3 years ago

Read 2 more answers

Solve for x in the equation x² + 14x + 17 = - 96

gavmur [86]

Answer:

Solutions of x are;

x = -7 + 8i and x = -7 -8i

Step-by-step explanation:

Given the equation: $x^2+14x+17 = -96$

Add 96 both sides we get;

$x^2+14x+17+96 = 0$

$x^2+14x+113= 0$

Using quadratic formula $ax^2+bx+c = 0$ then the solution is given by:

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

On comparing we have;

a= 1, b =14 and c =113

$x = \frac{-14\pm\sqrt{(14)^2-4(1)(113)}}{2(1)}$

$x = \frac{-14\pm\sqrt{196-452}}{2}$

or

$x = \frac{-14\pm\sqrt{-256}}{2}$

Simplify:

$x = \frac{-14\pm 16i}{2}$ ; where i is the imaginary, $i^2= -1$

or

$x = -7 \pm 8i$

Therefore, the solution of x are; x = -7 + 8i and x = -7 -8i

4 0

3 years ago

Determine the number of terms n in each arithmetic series.

natta225 [31]

We're given an arithmetic sequence $\{a_n\}_{n\ge1}$ that starts with $a_1=14$ and a common difference between terms of $d=10$ . Recursively, this sequence is given by

$\begin{cases}a_n=a_{n-1}+10&\text{for }n>1\\a_1=14\end{cases}$

We can find an explicit formula for the $n$ -th term $a_n$ :

$a_2=a_1+10$

$a_3=a_2+10=a_1+2(10)$

$a_4=a_3+10=a_1+3(10)$

and so on, with the general pattern of

$a_n=a_1+(n-1)(10)=4+10n$

We're given that the sum of the first $N$ consecutive terms is

$S_N=\displaystyle\sum_{n=1}^Na_n=\sum_{n=1}^N(4+10n)=1260$

Recall that

$\displaystyle\sum_{n=1}^N1=N$

$\displaystyle\sum_{n=1}^Nn=\dfrac{N(N+1)}2$

So we solve for $N$ :

$1260=\displaystyle\sum_{n=1}^N(4+10n)$

$1260=\displaystyle\sum_{n=1}^N4+\sum_{n=1}^N10n$

$1260=\displaystyle4\sum_{n=1}^N1+10\sum_{n=1}^Nn$

$1260=4N+10\dfrac{N(N+1)}2$

$1260=5N^2+9N$

$5N^2+9N-1260=0\implies N=15$

(there are two solutions, but only one is a positive integer)

7 0

3 years ago

every summer I drive to Pennsylvania it is 895 km to get there. if I average 100km/hr how much time will I spend driving?

Jobisdone [24]

<span><span>1. </span>Every summer you are driving to Pennsylvania. It is 895 km to get there.
Now, you drive at the average speed of 100 km/h.
Let’s solve how much time will take you to get there.
=> Distance of the place is 895 km.
=> Speed is 100 km/h
Formula
=> D/s = time
=> Time = 895 km / 100 km/h
=> Time = 8.95h
Thus, it will take you about 8.95 or 9 hours to be able to get in Pennsylvania.</span>

3 0

4 years ago