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3 years ago

Parallel to y = 3x – 1 and passes through the point ( – 4, – 11)

1 answer:

7 0

If the line is parallel, you know it’s going to have the same slope, which in this case is 3

Using the format y= mx + b, plug in your x and y values to find b (m is the slope)
-11 = 3(-4) + b
-11= -12 + b
b = 1

You now have all the needed values to write the equation in slope-intercept form:

y = 3x + 1

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4x square+ 8 x - 5=0 <img src="https://tex.z-dn.net/?f=4%20%7Bx%7D%5E%7B2%7D%20%20%2B%208x%20-%205%20%3D%200" id="TexFormula1

Damm [24]

Answer:

$x = \frac{1}{2}$

$x = -\frac{5}{2}$

Step-by-step explanation:

Solve Using the Quadratic Formula

4x^2 + 8x − 5 = 0

Use the quadratic formula to find the solutions.

−b ± √b^2 − 4 (ac)

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

Substitute the values a = 4, b = 8, and c = −5 into the quadratic formula and solve for x.

−8 ± √82 − 4 ⋅ (4 ⋅ −5)

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

2 ⋅ 4

Simplify the numerator.

Raise 8 to the p ower of 2.

−8 ± √64 − 4 ⋅ 4 ⋅ −5

x= ---------------------------

2 ⋅ 4

Multiply −4 by 4.

−8 ± √64 − 16 ⋅ −5

x = -------------------------

2 ⋅ 4

Multiply −16 by −5.

−8 ± √64 + 80

x = -------------------

2 ⋅ 4

Add 64 and 80.

−8 ± √144

x = --------------

2 ⋅ 4

Rewrite 144 as 12^2.

−8 ± √122

x = ------------

2 ⋅ 4

Pull terms out from under the radical, assuming positive real numbers.

multiply 2 by 4

−8 ± 12

x= ------------

simplify

−2 ± 3

x= ---------

The final answer is the combination of both solutions.

x= 1/2, -5/2

Hope this helped!

6 0

3 years ago

Read 2 more answers

Determine the value of k

KATRIN_1 [288]

Answer:

$\displaystyle k = 6$

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

Algebra I

Functions
Function Notation

Algebra II

Piecewise Functions

Calculus

Limits
Continuity

Step-by-step explanation:

Step 1: Define

Identify

Continuous at x = 2

$\displaystyle f(x) = \left \{ {{2x^2 \ if \ x < 2} \atop {x + k \ if \ x \geq 2}} \right.$

Step 2: Solve for k

Definition of Continuity: $\displaystyle \lim_{x \to 2^+} 2x^2 = \lim_{x \to 2^-} x + k$
Evaluate limits: $\displaystyle 2(2)^2 = 2 + k$
Evaluate exponents: $\displaystyle 2(4) = 2 + k$
Multiply: $\displaystyle 8 = 2 + k$
[Subtraction Property of Equality] Subtract 2 on both sides: $\displaystyle 6 = k$
Rewrite: $\displaystyle k = 6$

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

Unit: Limits - Continuity

Book: College Calculus 10e

4 0

3 years ago

Read 2 more answers

Wes measures the floor area of his rectangular living room to replace the carpet with tiles.The room is 12.4 feet long and 9.8 f

Zina [86]

Answer: 121.52 square feets

Step-by-step explanation:

The room has the shape of a rectangle and its dimensions are 12.4 feet long and 9.8 feet wide. This means that dimension of the carpet is also 12.4 feet long and 9.8 feet wide. To replace the rectangular carpet with tiles, the area of the tiles must be equal to the area of the carpet. The area of the carpet is determined by length × width.

Length of the room or carpet = 12.4 feets

Width of the room or carpet = 9.8 feets

The number of square feets of tiles that Wes will need

=12.4 ×9.8 = 121.52 square feets

7 0

3 years ago

Suppose a square garden represented by 16x squared foot squared what is the length of each side

allochka39001 [22]

Answer: 4

Step-by-step explanation:

Area of a square is side*side, which is s^2

So, s^2=16

s=squareroot(16)=4

4 0

3 years ago

Help me please!The perimeter of a rectangle is 40 inches.find its length if its width is 4 inches

rusak2 [61]

Answer:

Length: 10 inches

Step-by-step explanation:

Because we know that the total perimeter of the rectangle is 40, we can just divide the perimeter by the width, which gets us 10 inches (length).

40/4=10 inches

6 0

3 years ago