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3 years ago

If a gradient of line a is 4 what is the gradient of the line perpendicular to a

1 answer:

5 0

$\bf \textit{perpendicular, negative-reciprocal slope for}\quad 4\implies \cfrac{4}{1}\\\\
negative\implies -\cfrac{4}{ 1}\qquad reciprocal\implies - \cfrac{ 1}{4}$

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Please answer and explain the link below

Leviafan [203]

Answer:

See explanation.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Functions
Function Notation

Calculus

Limits

Right-Side Limit: $\displaystyle \lim_{x \to c^+} f(x)$
Left-Side Limit: $\displaystyle \lim_{x \to c^-} f(x)$

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = \left \{ {{\sqrt{x + 1}, \ x < 3} \atop {5 - x, \ x \geq 3}} \right.$

Step 2: Find Right Limit

Substitute in variables [Right-Side Limit]: $\displaystyle \lim_{x \to 3^+} 5 - x$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle \lim_{x \to 3^+} 5 - x = 5 - 3$
Subtract: $\displaystyle \lim_{x \to 3^+} 5 - x = 2$

∴ the right-side limit equals 2.

Step 3: Find Left Limit

Substitute in variables [Left-Side Limit]: $\displaystyle \lim_{x \to 3^-} \sqrt{x + 1}$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{3 + 1}$
[√Radical] Add: $\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = \sqrt{4}$
[√Radical] Evaluate: $\displaystyle \lim_{x \to 3^-} \sqrt{x + 1} = 2$

∴ the left-side limit equals 2.

Step 4: Find Limit

The right and left-side limits are equal.

∴ $\displaystyle \lim_{x \to 3} f(x) = 2$

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

Unit: Limits

Book: College Calculus 10e

4 0

3 years ago

Create a linear equation in slope intercept form that contains the points (1,4) and (4,7).

S_A_V [24]

Answer:

y = x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (4, 7)

m = $\frac{7-4}{4-1}$ = $\frac{3}{3}$ = 1, hence

y = x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation.

Using (1, 4), then

4 = 1 + c ⇒ c = 4 - 1 = 3

y = x + 3 ← equation in slope- intercept form

4 0

4 years ago

You buy 3 pairs of pants at an original cost of $24.99 and the sale is buy 1 get the 2nd pair half off. The sales tax is 6%. How

Finger [1]

Answer:

D. $66.23

Step-by-step explanation:

The sale discounts your purchase by half the price of a pair of pants, so you pay for 2.5 pairs of pants. The sale price of the pants is then ...

$24.99 × 2.5 = $62.48

The added tax multiplies this value by 1.06, so you pay ...

1.06 × $62.48 = $66.23

_____

Comment on the answer

Whether you pay $66.23 or $66.22 depends on how the discount is calculated. If you get the benefit of the half-penny (the discount is rounded up), then the sale price is $62.47 and the total is $66.22.

4 0

3 years ago

What are the zeros of the fuction f(x)=x2-13x-30

uysha [10]

X²-13x-30=0
(x-15)(x+2)=0
x = -2 or 15

3 0

3 years ago

Driven any two two number witch is greater the lcm of the number or gcf of the the number?why?

avanturin [10]

Lcm because a multiple is always greater then a factor.

4 0

3 years ago