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2 years ago

Write an equation to represent the relationship shown in the graph. Use the graph below

Mathematics

1 answer:

Lostsunrise [7]2 years ago

6 0

Answer:

$y=x+3$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

First, we could determine the slope (m). The slope is the $\displaystyle\frac{rise}{run}$ of the line, or the number of units it travels up over the number of units it travels to the right.

Notice how each consecutive point moves up 1 unit and right 1 unit. This makes the slope of the line 1/1, which is just 1:

$y=1x+b\\y=x+b$

Now, to find the y-intercept, we must identify the value of y when the line crosses the y-axis.

The line crosses the y-axis at y=3, so therefore, the y-intercept is 3:

$y=x+3$

I hope this helps!

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If anyone knows about definite integrals for calculus then please I request help! I

kicyunya [14]

Answer:

$\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u: $\displaystyle u = 4x^{-2}$
[u] Differentiate [Basic Power Rule, Derivative Properties]: $\displaystyle du = \frac{-8}{x^3} \ dx$
[Bounds] Switch: $\displaystyle \left \{ {{x = 9 ,\ u = 4(9)^{-2} = \frac{4}{81}} \atop {x = 5 ,\ u = 4(5)^{-2} = \frac{4}{25}}} \right.$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^9_5 {\frac{-8}{x^3}e^\big{4x^{-2}}} \, dx$
[Integral] U-Substitution: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^{\frac{4}{81}}_{\frac{4}{25}} {e^\big{u}} \, du$
[Integral] Exponential Integration: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}(e^\big{u}) \bigg| \limits^{\frac{4}{81}}_{\frac{4}{25}}$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8} \bigg( e^\Big{\frac{4}{81}} - e^\Big{\frac{4}{25}} \bigg)$
Simplify: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

4 0

2 years ago

Please awnser for brainlyest awnser btw I don’t like emojis ✌️✌️✌️✌️✌️✌️✌️

nexus9112 [7]

Answer:

7. Mean = 48

Median = 47.5

Mode = 72

Range = 66

8. Mean= 59.625

Median = 61

Mode = 90

Range = 79

9. Mean = 31.57

Median = 32

Mode = 46

Range = 34

10. Mean = 42.11

Median = 36

Mode = 51

Range = 51

Step-by-step explanation:

Mean is the average. Mode is the number that appears the most. Median is the middle number. Range is the biggest number minus the smallest number.

Hope this helps.

3 0

3 years ago

Read 2 more answers

Can someone help me simplify this?

ziro4ka [17]

=(14+3i) - (-12-7i) + (6+2i)
=14 + 3i +12 + 7i + 6 + 2i
=32 + 12i

7 0

2 years ago

Can you solve -3(y-5)=24

garri49 [273]

Answer:y=-3

Step-by-step explanation:yes firs multiply everything by -3 in parenthesies

Then you would subtract 15 from both sides

Next you would divide 9 by -3 and you would get -3

So y =-3

7 0

3 years ago

Read 2 more answers

Kathi's order at the diner cost $12.75. She had to pay 6% tax on the bill. How much is her tax?

Talja [164]

$\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 12.75}}{\left( \cfrac{6}{100} \right)12.75}\implies 0.765~~\approx 0.77~~\textit{about 77 cents}$

3 0

2 years ago