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3 years ago

Simplify the expression −2.3(4.1a−1.7a)+1.9(−5.4b)

Mathematics

1 answer:

Thepotemich [5.8K]3 years ago

7 0

Answer:

-5.52a-10.26b

Step-by-step explanation:

2.3*4.1=9.43

2.3*1.7=3.91

1.9*5.4=10.26

-------------------

-9.43a+3.91a-10.26b

-5.52a-10.26b

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Can someone answer this question please?

tester [92]

Answer:

(6, 1)

Step-by-step explanation:

plug in 6 for x and 1 for y in the given equation.

(6) - 3(1) = 3

then use PEMDAS to solve the equation.

-3 x 1 = -3

6 - 3 = 3

3 = 3

this ordered pair is correct because both 6 and 1 make the equation true.

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3 years ago

F(x)=3x+5/c what is f(a+2) ?

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Hello :
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3 years ago

After selling one third of his apple crop, a farmer sold the remainder at the same price per bushel for $600. What was the value

shtirl [24]

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3 years ago

Use the given information to write the equation of each line

Pachacha [2.7K]

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have two points (1, -4) and (-2, 5).

Substitute:

$m=\dfrac{5-(-4)}{-2-1}=\dfrac{5+4}{-3}=\dfrac{9}{-3}=-3$

Substitute the value of a slope and the coordinates of the point (1, -4) to the equation of a line:

$-4=-3(1)+b$

$-4=-3+b$ add 3 to both sides

$-4+3=-3+3+b$

$-1=b\to b=-1$

Finally:

$y=-3x-1$

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3 years ago

Use the limit definition of the derivative to find the slope of the tangent line to the curve

ale4655 [162]

Answer:

$\displaystyle f'(4) = 63$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Distributive Property

Algebra I

Expand by FOIL (First Outside Inside Last)
Factoring
Function Notation
Terms/Coefficients

Calculus

Derivatives

The definition of a derivative is the slope of the tangent line.

Limit Definition of a Derivative: $\displaystyle f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Step-by-step explanation:

Step 1: Define

f(x) = 7x² + 7x + 3

Slope of tangent line at x = 4

Step 2: Differentiate

Substitute in function [Limit Definition of a Derivative]: $\displaystyle f'(x)= \lim_{h \to 0} \frac{[7(x + h)^2 + 7(x + h) + 3]-(7x^2 + 7x + 3)}{h}$
[Limit - Fraction] Expand [FOIL]: $\displaystyle f'(x)= \lim_{h \to 0} \frac{[7(x^2 + 2xh + h^2) + 7(x + h) + 3]-(7x^2 + 7x + 3)}{h}$
[Limit - Fraction] Distribute: $\displaystyle f'(x)= \lim_{h \to 0} \frac{[7x^2 + 14xh + 7h^2 + 7x + 7h + 3] - 7x^2 - 7x - 3}{h}$
[Limit - Fraction] Combine like terms (x²): $\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7x + 7h + 3 - 7x - 3}{h}$
[Limit - Fraction] Combine like terms (x): $\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7h + 3 - 3}{h}$
[Limit - Fraction] Combine like terms: $\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7h}{h}$
[Limit - Fraction] Factor: $\displaystyle f'(x)= \lim_{h \to 0} \frac{h(14x + 7h + 7)}{h}$
[Limit - Fraction] Simplify: $\displaystyle f'(x)= \lim_{h \to 0} 14x + 7h + 7$
[Limit] Evaluate: $\displaystyle f'(x) = 14x + 7$