Use the point-slope formula to write an equation of the line that passes through 4, 5 and −6, −4 . Write the answer in slope-intercept form (if possible).
The equation of the line is _________ .

Answer:

a) (2x + 1)(3x - 4)

b) 546

Step-by-step explanation:

a)

We need to try to factor the polynomial.

6(-4) = -24

6x² - 8x + 3x - 4 = 2x(3x - 4) + 1(3x - 4) =

= (2x + 1)(3x - 4)

b)

6(10)² - 5(10) - 4 = 600 - 50 - 4 = 546

Answer:

(a) when x = 2:    width = 2 units   and     length = 5 units

(b) 546 units²

Step-by-step explanation:

Given expression:

[tex]6x^2-5x-4[/tex]

Part (a)

To factor a quadratic in the form [tex]ax^2+bx+c[/tex]

Find 2 two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]

Two numbers that multiply to -24 and sum to -5:  -8 and 3

Rewrite [tex]b[/tex] as the sum of these 2 numbers:

[tex]\implies 6x^2+3x-8x-4[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 3x(2x+1)-4(2x+1)[/tex]

Factor out the common term [tex](2x+1)[/tex]:

[tex]\implies (3x-4)(2x+1)[/tex]

Therefore:

[tex]\implies x=\dfrac{4}{3}, \: x=-\dfrac{1}{2}[/tex]

As distance is positive, [tex]x > \dfrac{4}{3}[/tex]

Let [tex]x=2[/tex]

[tex]\implies (3(2)-4)(2(2)+1)[/tex]

[tex]\implies (2)(5)[/tex]

Therefore, possible dimensions of the rectangle are:

width = 2 units

length = 5 units

Part (b)

Substitute [tex]x=10[/tex] into the equation:

[tex]\begin{aligned}\implies 6(10)^2-5(10)-4&=600-50-4\\&=546\end{aligned}[/tex]

Answer:

Help with what, I may be able to help. :)

Answer:

Slope formula:

RISE: y2(second y-coordinate) - y1(first y-coordinate)

        ____________________________________

RUN: x2(second x-coordinate) - x1(first x-coordinate)

y2 - y1 / x2 - x1

Plug in what we have in the order given in the formula:-

 12 - 6           6

______ = ______, which simplifies to 2.

  7 - 4            3

Therefore, 2 is the slope of this equation.

Answer:

Slope: 2

Step-by-step explanation:

Given points:

Slope formula: (y₂ - y₁)/(x₂ - x₁)

1. Substitue the coordinates of the points in the formula, which will determine the slope of the two points:

2. Simplify the fraction. The quotient will be the slope of the line.

Thus, the slope of the line is 2.

Answer:

x = 0.5

Step-by-step explanation:

2-5x/-3+4 < -x is simplified to 2-5x/1<-x because -3+4 is 1.

Answer:

y = 2/3x - 1 (or y = 2/3x + -1 to fit the graphic)

Step-by-step explanation:

Slope intercept form is written as (y = mx + b) where m is slope and b is the y intercept.

First you need to find the slope, m. We'll use the two points (-3, -3) and (3, 1)

m = (y2 - y1) / (x2 - x1)

m = (1 - (-3)) / (3 - (-3))

m = 4/6

m = 2/3

Next we need the y intercept, b. On the graph we can see that is -1 but we can also find it substituting the known slope and one point on the line for our values to solve for b. We'll use (3, 1) as the point.

y = mx + b

1 = 2/3 * 3 + b

simplify 2/3 * 3

1 = 2 + b

subtract 2 from both sides

-1 = b

Now we have all the values we need to plug into our slope intercept equation (m = 2/3, b = -1)

y = mx + b

y = 2/3x - 1

[tex]\sf{y=\displaystyle\frac{2}{3} x-1[/tex]

Hope it helps.

Do comment if you have any query.

Answer:

90

Step-by-step explanation:

There are 15 packa of 6 cards in each pack. You could either do it the long way and count it out on paper or just times 15x6 and it equals 90.

Answer:

A = 28 cm²

Step-by-step explanation:

area of square = 4 × 4 = 16 cm²

area of trapezium = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the height and b₁ , b₂ the parallel bases

here h = 2 , b₁ = 8 , b₂ = 4

area of trapezium = [tex]\frac{1}{2}[/tex] × 2 × (8 + 4) = 1 × 12 = 12 cm²

area of the logo (A) = 16 + 12 = 28 cm²

Answer:

a)  y = (x - 3)²

b)  y = x² - 4

c)  y = (x + 2)²

d)  y = x² + 5

e)  y = (x + 6)² - 7

f)  y = (x - 2)² + 5

Step-by-step explanation:

Parent equation:  y = x²

Transformed equation:  y = (x - h)² + k

h translates the parabola horizontally

If h > 0 then the translation is h units to the right.

If h < 0 then the translation is h units to the left.

If h = 0 then there is no horizontal translation.

k translates the parabola vertically

If k > 0 then the translation is k units up.

If k < 0 then the translation is k units down.

If k = 0 then there is no vertical translation.

a) The parabola moves 3 units to the right:  

⇒ y = (x - 3)² + 0

⇒ y = (x - 3)²

b) The parabola moves 4 units down:

⇒ y = (x - 0)² - 4

⇒ y = x² - 4

c) The parabola moves 2 units left:  

⇒ y = (x + 2)² + 0

⇒ y = (x + 2)²

d) The parabola moves 5 units up:  

⇒ y = (x - 0)² + 5

⇒ y = x² + 5

e) The parabola moves 7 units down and 6 units left:  

⇒ y = (x + 6)² - 7

f) The parabola moves 2 units right and 5 units up:  

⇒ y = (x - 2)² + 5

#a

Equation

#b

4 units down in y axis

#c

2 units left in x axis

#d

5 units up in. y axis

#e

7units down in y axis and 6 units left in x axis

Answer:

15

Step-by-step explanation:

The range from Q1 to Q3 is the interquartile range (IQR).

The interquartile range is the difference between the third and first quartiles.

The third quartile is 17.5.

The first quartile is 2.5.

The interquartile range = 17.5 - 2.5 = 15.

Q1: Solutions: x = 2 and x = 4, Axis of symmetry: x = 3.

Q3: (x, y) = (-3, 5).

Q4: A parabola cannot have both a minimum and maximum point because it is only bounded by its vertex.

Q5: [tex]x \in \mathbb{R}[/tex]

Q6: [tex]y \in [-5, + \infty)[/tex]

Graphically speaking, second order polynomials are represented by parabolas. In this question we must interpret the graphs to find all the required information.

The solutions to the graph are those values of x such that the graph goes through the x-axis and the axis of symmetry is a line that goes through the vertex ot the parabola and is perpendicular to the width of the curve.

Thus, the solutions to the graph are x = 2 and x = 4 and the axis of symmetry is x = 3. [tex]\blacksquare[/tex]

The vertex is the extreme point of a parabola, which may be a minimum or a maximum, but never both. The vertex of the parabola is located at (x, y) = (-3, 5). [tex]\blacksquare[/tex]

A parabola cannot have both a minimum and maximum point because it is only bounded by its vertex. [tex]\blacksquare[/tex]

The domain of the function is defined by the set of x-values such that the function exists. Thus, the domain of the quadratic function is [tex]x \in \mathbb{R}[/tex]. [tex]\blacksquare[/tex]

The range of the function is defined by the set of y-values such that the function exists. Thus, the range of the quadratic function is [tex]y \in [-5, + \infty)[/tex].  [tex]\blacksquare[/tex]  

To learn more on parabolas, we kindly invite to check this verified question: https://brainly.com/question/4074088

Answer:

2/3

Step-by-step explanation:

2/9+4/9=6/9

6/3=2   9/3=2

6/9=2/3

Answer:

the answer is 0.062

Step-by-step explanation:

i hope this helps pls make as brainliest

Answer:

A C F G H J ARE THE FIGURES WHERE AB IS AN ALTITUDE

Answer:

the real awnser is b

Step-by-step explanation:

The statement that best describes why author of "Water Efficiency Strategies" organized the text into two main sections is to show readers that thinking about both the supply side and the demand side are important for water efficiency.

Efficient use of water is necessary so as to prevent the wastage of water. Although 3/4th of the earth is covered with water, the sustainable use of water is necessary so as to preserve the pure water for the future generations. The statement that best describes why the author of "Water Efficiency Strategies" organized the text into two main sections is to show readers that thinking about both the supply side and the demand side are important for water efficiency.

Therefore, the statement that best describes why author of "Water Efficiency Strategies" organized the text into two main sections is to show readers that thinking about both the supply side and the demand side are important for water efficiency.

To solve more questions on Water Efficiency Strategies, visit the link-

https://brainly.com/question/23634600

#SPJ2

Answer:

Some vocabulary we should know:

mx = slope while b is the y-intercept.

-3x = x

6y = y

BRAINLIEST is APPRECIATED. This is based on speculation! Good luck in your future studies.

- daintysword

Step-by-step explanation:

IF THE TEMPERATURE WAS -5° AT 5:00 am., WHAT WAS THE TEMPERATURE AT 9:00 am?

To find the area of the triangle

  ⇒ must know the area of the triangle's formula

     ⇒ [tex]\frac{1}{2} *base*height[/tex]

Let's look at the information given:

Let's solve:

 [tex]Area=\frac{1}{2} *base*height=\frac{1}{2} *\frac{61}{4} *18 = 137.55in^2[/tex]

Thus the area is 137.55 square inches

Hope that helps!

Answer:

76 Square Feet

Step-by-step explanation:

First, add all the numbers you see up. Your final answer of square feet will be the total you added up as a whole.

24+14+4+6+5+3+15+5= 76

Answer:

IM NOT. NNOT SURE BUT I THINK... the area may be 177? if i did it right, please check my equations though!

Step-by-step explanation:

so we first have to find the area of alllll the rectangles/squares in that weird squiggly shape

lets do the top

the width is 15 ft and the length is 5ft

so to find the area you have to do length times with so

A = lw

A = 15(5)

A = 75

so the first shape is 75

now lets do something real quick (im sorry this is all messed up infromation i have a dba (call) in like 16 mins and i gotta hurry. but illl come back if you need more explinations)

let first shape be f

let second shape be s

let third shape be t

let R be the area of the total shape

f + t + s = R

75 + t + s = R

now to find t

so the width would be 9ft and the length would be 8ft

A = lw

A = 9(8)

A = 72

75 + 72 + s = R

now to find s

the width is 5fth and the length is 6ft

A = lw

A = 6(5)

A = 30

now i think we add?

75 + 72 + 30 = R

75 + 102 = R

177 = R

i think the area is 177? (if i remeber how to do this correctly)

btw I will come back later and upload a pic of how i did it if you like. i must go now cause my teacher is gonna ask me civics questions and im so bad at that subject!!!!  

Answer:

GDP decreases and Debt increases

Step-by-step explanation:

Answer:

13.5

Step-by-step explanation:

total boxes of granola is = 3 + 2 + 1

                                         =  6 boxes

6 boxes = 57 bars

1 box  =  57 / 6

1 box  = 9.5 + 3

           = 13.5 (ANS)

i hope my ans is correct if not i apologise.

Answer:

900 trucks on a highway with 3600 vehicles

Step-by-step explanation:

3 out of 12 is also 1/4  (one quarter)

so 3600 ÷ 4 = 900 trucks on a highway with 3600 vehicles

hope this helps :))

The domain of the function in interval form is (-∞, -8) U (-8, ∞)

The domain of a function is the point where the real value of the function exists.

Given the funciton

f(x) = x - 7/x+8

The function will exist on all real values except the point where the denominator is zero.

x + 8 = 0

x = -8

The domain of the function in interval form is (-∞, -8) U (-8, ∞)

Learn more on domain here: https://brainly.com/question/25959059

Step-by-step explanation:

mean = sum of all data points / number of data points

median = the number, where half of the other numbers is larger, and the other half is smaller.

4 4 5 6 6

2 2 3 9 9

both mean values are 5.

the median of the 1st is 5, if the second is 3.