LESSON 3.2 (C) - Rates of Change and Slope
Directions: Find the slope of the line each each graph. Leave the slope as a fraction instead of converting
them to decimals.
1)
2)
Slope =
Slope =

Answer:

9/15

Step-by-step explanation:

Answer:

I think its b

i hope you pass

Answer:

Area of rectangle = 216 square mm

Step-by-step explanation:

Base (b ) = 18 mm

width = 'x' mm

Perimeter of rectangle = 2*(base + width)

Perimeter = 60 mm

2*(base + width) = 60 mm

2 *(18 + x )  = 60

2*18 + 2*x = 60

36   + 2x  = 60

         2x = 60 - 36

         2x = 24

          x = 24/2

    x = 12

Width = 12 mm

Area of rectangle = base * width

                             = 18 * 12

                             = 216 square mm

Answer:

[tex]\frac{60}{11}[/tex] feet

Step-by-step explanation:

Rectangle 1:

6 x Width = Area

Rectangle 2:

5 x Width = Area

Total Area = Area of Rectangle 1 + Area of Rectangle 2 = 60 square feet

Take Width as [tex]x[/tex] as the widths of both rectangles are the same:

[tex]5x + 6x = 60\\\\11x = 60\\\\x = \frac{60}{11}[/tex]

Answer:

A) -3/4

B) 1/4

Step-by-step explanation:

A) m = y2-y1 / x2-x1

B) rise / run

Hope this helps. Pls give brainliest.

Answer:

-13

Step-by-step explanation:

If a = -7 and y = 3, then all we have to do is plug in the given values to the expression we were given!

-2(3) + (-7)

-6 - 7

-13

Answer:

Step-by-step explanation:

-2(3)+-7

-6+(-7)

-13

Answer: 17.25

Step-by-step explanation:

An additional expression in the form Descent + Ascent to represent this situation is -13.7 + 15.2. The sum will be 1.5 meters.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Eric started at sea level. He descended 13.7 meters and then ascended 15.2 meters.

The expression will be written as,
E = -13.7 + 15.2.

E = 1.5 meters

Therefore, the additional expression in the form Descent + Ascent to represent this situation is -13.7 + 15.2. The sum will be 1.5 meters.

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Answer:

I think it's zero or positive

Answer:

a.

[tex]Length = 25[/tex]

[tex]Width = 14[/tex]

[tex]Perimeter = 78ft[/tex]

b.

[tex]Length = 25.2[/tex]

[tex]Width = 13.6[/tex]

[tex]Perimeter = 77.6ft[/tex]

c.

[tex]Perimeter = 77.54ft[/tex]

Estimate (b) is closer to the actual measurement.

Step-by-step explanation:

Given

[tex]Length = 25.15[/tex]

[tex]Width = 13.62[/tex]

Solving (a): Approximate measurements to whole numbers then estimate the perimeter.

When approximated to whole numbers (i.e. no decimal place), the new measurement is:

[tex]Length = 25[/tex]

[tex]Width = 14[/tex]

The perimeter is calculated as thus:

[tex]Perimeter = 2(Length + Width)[/tex]

[tex]Perimeter = 2(25 + 14)[/tex]

[tex]Perimeter = 2*39[/tex]

[tex]Perimeter = 78ft[/tex]

Solving (b): Approximate measurements to tenth then estimate the perimeter.

When approximated to tenth (i.e. to 1 decimal place), the new measurement is:

[tex]Length = 25.2[/tex]

[tex]Width = 13.6[/tex]

The perimeter is calculated as thus:

[tex]Perimeter = 2(Length + Width)[/tex]

[tex]Perimeter = 2(25.2 + 13.6)[/tex]

[tex]Perimeter = 2*38.8[/tex]

[tex]Perimeter = 77.6ft[/tex]

Solving (c): Exact Perimeter.

Given measurements are:

[tex]Length = 25.15[/tex]

[tex]Width = 13.62[/tex]

The perimeter is calculated as thus:

[tex]Perimeter = 2(Length + Width)[/tex]

[tex]Perimeter = 2(25.15 + 13.62)[/tex]

[tex]Perimeter = 2*38.77[/tex]

[tex]Perimeter = 77.54ft[/tex]

To determine which is nearest, we calculate the absolute difference between each estimate from the actual measurement.

For estimate a

[tex]Difference = |77.54 - 78|[/tex]

[tex]Difference = |-0.46|[/tex]

[tex]Difference = 0.46ft[/tex]

For estimate b

[tex]Difference = |77.54 - 77.6|[/tex]

[tex]Difference = |-0.06|[/tex]

[tex]Difference = 0.06ft[/tex]

The closest to the exact is the one with the smallest difference.

Hence, estimate (b) is closer to the actual measurement.

Answer: y = -2x

M is the midpoint of PQ

=> M(0;0)

the line PQ passes through P(2;1) and Q(-2;-1)

=> (PQ): 2x - 4y = 0

have:

(d): perpendicular (PQ)

     passes throgh M(0;0)

=> (d): 4x + 2y = 0 ⇔ y = -2x

Step-by-step explanation:

The equation of the perpendicular bisector of PQ is,

⇒ y = - 2x

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point P has coordinates (2, 1) and the point Q has coordinates(-2, -1).

Hence, The slope of line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - 1) / (- 2 - 2)

m = - 2 / - 4

m = 1/2

Thus, The slope of perpendicular line is,

⇒ m = - 2

The midpoint of coordinates (2, 1) and (- 2, - 1) is,

⇒ (- 1 + 1) / 2 , (- 2 + 2) / 2

⇒ (0, 0)

Hence, The equation of line is,

⇒ y = mx + b

⇒ 0 = - 2 × 0 + b

⇒ b = 0

Hence, The equation of the perpendicular bisector of PQ is,

⇒ y = - 2x

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Answer:

8x + 128??

Step-by-step explanation:

Answer:

To start off, lets label this triangle ABC where A is the top right vertical, the top left verticle is B, and the bottom one is C. Now lets label the 2 points of intersection from the line segment 8x-23 D and E where the left intersection is E and the right is D.

Notice how CE and AE have an arc and that AC was split to get AE and CE. The 2 arcs show us that the intersection E is located at half the line segment.

This is the same on the other line segment BC. So if E and D are half of those line segments then the line segment ED must be half of the parallel segment above it. Because this is true, 2(8x-23)=10x+44

Now we have an equation and we can solve:

2(8x-23)=10x+44

16x-46=10x+44

6x-46=44

6x=90

x=15

Step-by-step explanation:

Answer: A) 5 x 1/2

Step-by-step explanation: 5 x 1/2 yields 2.5, which is also the answer to 5 / 2.

Answer: A. 5 x 1/2

5 divided by 2 is 2.5, and 5 x 1/2 is also 2.5

(a)1/10

(b)4/5

(c)1/20

Answer:

a) [tex]\frac{2}{18}[/tex] or 1/9

b) [tex]\frac{14}{18}[/tex]

c)[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Answer:

-5/24

Step-by-step explanation:

-3/8 =

-9/24

1/6 =

4/24

-9/24+4/24=-5/24

Answer:

-3

Step-by-step explanation:

multiply to make it a common number so -3/8 times 6/6 and 1/6 times 8/8

so -18/48 times 8/48. Then you multiply the top numbers to get 144/48. Then you simplify or divide so -3.

Answer:

729

Step-by-step explanation:

If you multiply 9x9x9 which is for the largest number and the 3 digits you would get 729.

Answer:

6A7C8B

Step-by-step explanation:

Add them in and try to solve for 7 and 6, for 8. I usually put all number on one side and all x on other side.

(blue) y= 1/2x -2

(green) y= 9-5x

Answer:

7

Step-by-step explanation:

Answer:

5 (12+3)

75

Step-by-step explanation:

so you multiply 5 with the inside of paranthesis. So 5 x 12 and 5 x 3

So its 60 + 15 which is 75. Hope this helps!

Answer:

The x-intercept is : (22, 0)

Step-by-step explanation:

Given the table

x                 y

48              30

61               45

74               60

From the table, it is clear that every y value is changing 15 units, and every x is changing 13 units. Hence, it is a straight line.

Hence, we can find the other values of this straight line as well.

so

When the value of y = 15 i.e. (30-15), then the value of x will

be 35 i.e. (48 - 13).

as

y = 30 - 15 = 15, and x = 48 - 13 = 35.

Similarly,

When the value of y = 0 i.e. (15-15), then the value of x will be 22 i.e. (35-13).

as

y = 15-15 = 0, and x = 35 - 13 = 22.

As we know that the x-intercept is the point where the line crosses the x-axis. At this point y = 0.

so, as we have checked that when the value of y = 0, then the value of x = 22.

Therefore, the x-intercept is : (22, 0)

Answer:

3 > x > − 4 and your welcome bud

Answer:

yea u got it right my dude

9514 1404 393

Answer:

Step-by-step explanation:

The absolute extremes will be at one of two locations:

Here, the absolute maximum occurs where the derivative is zero (and the second derivative is negative).

  f'(x) = 3x^2·e^-x -x^3·e^-x = x^2·e^-x·(3 -x)   ⇒   f'(3) = 0

The absolute minimum occurs at the left end of the interval, where both x^3 and e^-x have large magnitude.

The minimum is ...

  (-4)^3×e^-(-4) ≈ -3494.21 . . . . six significant figures

__

A graph can show you the function tends toward -∞ as x goes to large negative values. Hence, the absolute minimum on an interval beginning in the left half-plane will be at the left end of the interval.

Answer:

[tex]x\geq 6\text{ or } x<-3[/tex]

Step-by-step explanation:

We have the compound inequality:

[tex]2(x-1)\geq10\text{ or } 3-4x>15[/tex]

Let's solve each of them individually first:

We have:

[tex]2(x-1)\geq10[/tex]

Divide both sides by 2:

[tex]x-1\geq5[/tex]

Add 1 to both sides:

[tex]x\geq6[/tex]

We have:

[tex]3-4x>15[/tex]

Subtract from both sides:

[tex]-4x>12[/tex]

Divide both sides by -4:  

[tex]x<-3[/tex]

Hence, our solution set is:

[tex]x\geq 6\text{ or } x<-3[/tex]

Answer:

x ≥ 6 or x < -3

Step-by-step explanation:

2(x-1) ≥ 10 or 3 - 4x > 15

2x - 2 ≥ 10 4x < -12

x ≥ 6 or x < -3

Topic: Inequalities

If you would like to venture further into mathematics, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!

Answer:

x=4

Step-by-step explanation:

multiply first eq. by 3 and second by 4 to get rid of y

15x+12y=24

8x-12y=68

add the equations

23x = 92

divide both sides by 23

x=92/23=4

Answer:

x = 4

Step-by-step explanation:

Given the 2 equations

5x + 4y = 8 → (1)

2x - 3y = 17 → (2)

Multiplying (1) by 3 and (2) by 4 then adding will eliminate the y- term

15x + 12y = 24 → (3)

8x - 12y = 68 → (4)

Add (3) and (4) term by term to eliminate y, that is

23x = 92 ( divide both sides by 23 )

x = 4

Answer:

Vertex:  (−2,7)

Step-by-step explanation:

May I have brainliest please? :)