All categories

3 years ago

Two lines, C and D, are represented by the following equations:

Mathematics

2 answers:

guapka [62]3 years ago

8 0

Answer:

(−2, 3), because both lines pass through this point

Step-by-step explanation:

The meaning of "solution to the system of equations" is that both lines intersect at the solution point. That is, they both pass through that point.

Natasha2012 [34]3 years ago

3 0

Answer:

(−2, 3), because both lines pass through this point

Step-by-step explanation:

Line C: y = x + 5

Line D: y = −2x − 1

Substitute x+5 for y in second equation

x + 5 = -2x -1

add 2x on both sides

3x + 5= -1

subtract 5 from both sides'

3x = -6

divide both sides by 3

x= -2

Now plug in -2 for x in y=x+5

y=-2+5= 3

so x= -2, y= 3

both lines satisfies the point (-2,3) (intersection point)

(−2, 3), because both lines pass through this point

You might be interested in

Pls help fast !! Thanks

Pavlova-9 [17]

Answer:

A. 8fg + 3h

Step-by-step explanation:

$4f × 2g + 3h \\ \\ = 4 \times 2 \times f \times g + 3h \\ \\ = 8fg + 3h$

8 0

3 years ago

Read 2 more answers

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

3 years ago

You want to calculate the value of your car each year when it depreciates by 15%. What does the term y mean in the exponential f

insens350 [35]

Answer:

Value of the car after x years

Step-by-step explanation:

Exponential functions are generally expressed in the form: $y=a(b)^x$ and since this function is decreasing, meaning it has an exponential decay, it can be expressed as: $y=a(1-r)^x$ where r=rate of decay.

In this case the a represents the initial value or y-intercept, since when x=0, (1-r)^0 = 1, so we just have y=a(1) or y=a

The r represents the rate of decay

the x usually represents the time in seconds, days, months, or whatever unit is being used

The y value represents the value of whatever your measuring, and in this context it represents the value of the car after x years.

This is because a represents the initial value

After one year it's only 85% worth it's initial value or 15% less which is represented as 0.85(a)

After two years it's only 85% worth the previous year or 15% less the previous year, which is represented as 0.85(0.85(a))

This will continue to decrease the number of years increase

4 0

2 years ago

Read 2 more answers

What is the lowest common denominator of 5 and 9

lozanna [386]

It is 45 . Just simply multiply both numbers. You will get the smallest denominator

6 0

3 years ago

Find the missing value.

denis-greek [22]

Answer:

-7

Step-by-step explanation:

x + 5 = -2

<h2>I hope this helped! :)</h2>

8 0

3 years ago