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2 years ago

Find the rate of change of the linear function shown in the graph. Then find the initial value.

Mathematics

1 answer:

EastWind [94]2 years ago

3 0

rate of change is change in y / change in x

(-1 - -3)/ (0 - -6) = 2/6 = 1/3

initial value is the y value when x is 0 , which is -1

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What is the solution of the system of equations?

Elis [28]

Answer:

The answer to your question is:

x = 4

y = -1

z = -3

Step-by-step explanation:

3 x + 2 y + z = 7

5 x + 5 y + 4 z = 3

3 x + 2 y + 3 z = 1

$\left[\begin{array}{ccc}3&2&1\\5&5&4\\3&2&3\end{array}\right]$

= 45 + 10 + 24 - (30 + 24 + 15)

= 79 - 69

Δ = 10

$\left[\begin{array}{ccc}7&2&1\\3&5&4\\1&2&3\end{array}\right]$

= 105 + 6 + 8 - (18 + 56 + 5)

= 119 - 79

Δx = 40

$\left[\begin{array}{ccc}3&7&1\\5&3&4\\3&1&3\end{array}\right]$

= 27 + 5 + 84 - ( 105 + 12 + 9)

= 116 - 126

Δy = -10

$\left[\begin{array}{ccc}3&2&7\\5&5&3\\3&2&1\end{array}\right]$

= 15 + 70 + 18 - (10 + 18 + 105)

= 103 - 133

= -30

Δz = -30

x = Δx /Δ = 40/10 = 4

y = Δy/Δ = -10/10 = -1

z = Δz/Δ = -30/10 = -3

8 0

3 years ago

Read 2 more answers

Solve the inequality.<br> 4│x + 5│ - 2 ≤ 10

castortr0y [4]

Step-by-step explanation: To solve this absolute value inequality,

our goal is to get the absolute value by itself on one side of the inequality.

So start by adding 2 to both sides and we have 4|x + 5| ≤ 12.

Now divide both sides by 3 and we have |x + 5| ≤ 3.

Now the the absolute value is isolated, we can split this up.

The first inequality will look exactly like the one

we have right now except for the absolute value.

For the second one, we flip the sign and change the 3 to a negative.

So we have x + 5 ≤ 3 or x + 5 ≥ -3.

Solving each inequality from here, we have x ≤ -2 or x ≥ -8.

6 0

3 years ago

Read 2 more answers

Estimate 43% of 117. (2 points)<br> Show your work to

finlep [7]

Answer:

Let's say 50

Step-by-step explanation:

40% of 100 is 40

50% of 117 is about 59

so number should be a somewhere in between.

8 0

2 years ago

Algebra help. Zoom in if you can

Artist 52 [7]

Answers:

Pair-1: $log_{2}x = 5$ ↔ 32
Pair-2: $log_{10}x = 3$ ↔ 1000
Pair-3: $log_{4}x = 2$ ↔ 16
Pair-4: $log_{5}x = 4$ ↔ 625

Explanation:

Pair-1:
$log_{2}x = 5 \\ \frac{ln(x)}{ln(2)} = 5 \\ ln(x) = 5 * ln(2) \\ x = e^{5*ln(2)} \\ x = 32$

Pair-2:
$log_{10}x = 3 \\ \frac{ln(x)}{ln(10)} = 3 \\ ln(x) = 3 * ln(10) \\ x = e^{3*ln(10)} \\ x = 1000$

Pair-3:
$log_{4}x = 2 \\ \frac{ln(x)}{ln(4)} = 2 \\ ln(x) = 2 * ln(4) \\ x = e^{2*ln(4)} \\ x = 16$

Pair-4:
$log_{5}x = 4 \\ \frac{ln(x)}{ln(5)} = 4 \\ ln(x) = 4 * ln(5) \\ x = e^{4*ln(5)} \\ x = 625$

7 0

3 years ago

3q(p-q)+2r(p-q)-S(q-p)<br> Can u solve it step by step

Artyom0805 [142]

Answer:

-3q² + 3qp + 2rp - 2rq + Sq - Sp

Step-by-step explanation:

first part

3q(p-q) = 3qp - 3q²

second part

2r(p-q) = 2rp - 2rq

third part

S(q-p) = Sq - Sp

then we put it all together

3qp - 3q² + 2rp - 2rq + Sq - Sp

in the right place possibly

-3q² + 3qp + 2rp - 2rq + Sq - Sp

8 0

2 years ago