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John had 2 apples, he got 3 more. more. How many apples does he have?

S_A_V [24]

Answer:

5

Step-by-step explanation:

2+3=5

4 0

4 years ago

The fraction 9/15 is an equivalent fraction of 6/20 1/2 3/5

Mama L [17]

Answer:

3/5

Step-by-step explanation:

3/5 is equal to 9/15.

7 0

3 years ago

Read 2 more answers

Point M is located in the third quadrant of the coordinate plane, as shown.

nevsk [136]

Answer:

It is in quadrant three

Step-by-step explanation:

The points of M means there x and y will both be negatives.

5 0

3 years ago

Read 2 more answers

Please help i am giving away brainliest

emmasim [6.3K]

Answer:

6,480in.3

Step-by-step explanation:

Hope this helps!

7 0

3 years ago

Integrating sums of functions

Andrei [34K]

Answer:

(a) -12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Calculus

Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Swapping Limits]: $\displaystyle \int\limits^b_a {f(x)} \, dx = -\int\limits^a_b {f(x)} \, dx$

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

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Integration Property [Splitting Integral]: $\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx$

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

Step-by-step explanation:

Step 1: Define

$\displaystyle \int\limits^6_4 {f(x)} \, dx = 5$

$\displaystyle \int\limits^4_{10} {f(x)} \, dx = 8$

$\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx$

Step 2: Solve Pt. 1

[Integral] Rewrite [Integration Property - Addition]: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = \int\limits^{10}_6 {4f(x)} \, dx + \int\limits^{10}_6 {10} \, dx$
[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4\int\limits^{10}_6 {f(x)} \, dx + 10\int\limits^{10}_6 {} \, dx$

Step 3: Redefine

Manipulate the given integral values.

[Integrals] Combine [Integration Property - Splitting Integral]: $\displaystyle \int\limits^6_4 {f(x)} \, dx + \int\limits^4_{10} {f(x)} \, dx = \int\limits^6_{10} {f(x)} \, dx$
[Integral] Rewrite: $\displaystyle \int\limits^6_{10} {f(x)} \, dx = \int\limits^6_4 {f(x)} \, dx + \int\limits^4_{10} {f(x)} \, dx$
[Integral] Substitute in integrals: $\displaystyle \int\limits^6_{10} {f(x)} \, dx = 5 + 8$
[Integral] Add: $\displaystyle \int\limits^6_{10} {f(x)} \, dx = 13$
[Integral] Rewrite [Integration Property - Swapping Limits]: $\displaystyle -\int\limits^{10}_6 {f(x)} \, dx = 13$
[Integral] [Division Property of Equality] Isolate integral: $\displaystyle \int\limits^{10}_6 {f(x)} \, dx = -13$

Step 4: Solve Pt. 2

[Integral] Substitute in integral: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10\int\limits^{10}_6 {} \, dx$
[Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(x) \bigg| \limits^{10}_6$
[Integral] Evaluate [Integration Rule - FTC 1]: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(10 - 6)$
[Integral] (Parenthesis) Subtract: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(4)$
[Integral] Multiply: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -52 + 40$
[Integral] Add: $\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -12$

Topic: AP Calculus AB/BC

Unit: Integration

Book: College Calculus 10e

8 0

3 years ago