Write the equation of the line fully simplified slope-intercept form.

Answer:

-9=b

Step-by-step explanation:

1. combine multiple turns into a single fraction.

2. multiple all terms by the same value to eliminate

fraction denominators.

3. simplify

4. divide both sides of the equation by the same term

5. simplify

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:

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.

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:

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:

272/-13 or −20.923

Step-by-step explanation:

To solve this equation you need to isolate the variable.

First, add 71 to both sides

-13x-71+71=201+71

-13x=272

Then, divide both sides by -13

-13x/-13=272/-13

So, x=272/-13 or −20.923

(blue) y= 1/2x -2

(green) y= 9-5x

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

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Answer:

I think it's zero or positive

Answer:

[tex]\displaystyle y=\frac{16-9x^3}{2x^3 - 3}[/tex]

[tex]\displaystyle y=-\frac{56}{13}[/tex]

Step-by-step explanation:

Equation Solving

We are given the equation:

[tex]\displaystyle x=\sqrt[3]{\frac{3y+16}{2y+9}}[/tex]

i)

To make y as a subject, we need to isolate y, that is, leaving it alone in the left side of the equation, and an expression with no y's to the right side.

We have to make it in steps like follows.

Cube both sides:

[tex]\displaystyle x^3=\left(\sqrt[3]{\frac{3y+16}{2y+9}}\right)^3[/tex]

Simplify the radical with the cube:

[tex]\displaystyle x^3=\frac{3y+16}{2y+9}[/tex]

Multiply by 2y+9

[tex]\displaystyle x^3(2y+9)=\frac{3y+16}{2y+9}(2y+9)[/tex]

Simplify:

[tex]\displaystyle x^3(2y+9)=3y+16[/tex]

Operate the parentheses:

[tex]\displaystyle x^3(2y)+x^3(9)=3y+16[/tex]

[tex]\displaystyle 2x^3y+9x^3=3y+16[/tex]

Subtract 3y and [tex]9x^3[/tex]:

[tex]\displaystyle 2x^3y - 3y=16-9x^3[/tex]

Factor y out of the left side:

[tex]\displaystyle y(2x^3 - 3)=16-9x^3[/tex]

Divide by [tex]2x^3 - 3[/tex]:

[tex]\mathbf{\displaystyle y=\frac{16-9x^3}{2x^3 - 3}}[/tex]

ii) To find y when x=2, substitute:

[tex]\displaystyle y=\frac{16-9\cdot 2^3}{2\cdot 2^3 - 3}[/tex]

[tex]\displaystyle y=\frac{16-9\cdot 8}{2\cdot 8 - 3}[/tex]

[tex]\displaystyle y=\frac{16-72}{16- 3}[/tex]

[tex]\displaystyle y=\frac{-56}{13}[/tex]

[tex]\mathbf{\displaystyle y=-\frac{56}{13}}[/tex]

Reciprocal is reversing the given fraction.

1. Would be 8/3

2. 2 2/3 as in improper fraction is 8/3, reciprocal would be 3/8

3. -3/8 x 8/3 = -24/24 = -1

4. 3/8 / -8/3 =3/8 x -3/8 = -9/64

5. - 8/3 - -3/8 = -8/3 + 3/8 = -2 7/24

6. Only answer left: 2 7/24

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:

729

Step-by-step explanation:

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

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

Answer:

[tex] Slope (m) = -\frac{3}{4} [/tex]

Step-by-step explanation:

Using any two pairs from the table of values given, (-2, 5) and (2, 2):

[tex] Slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Where,

[tex] (-2, 5) = (x_1, y_1) [/tex]

[tex] (2, 2) = (x_2, y_2) [/tex]

Plug in the value into the slope formula:

[tex] Slope (m) = \frac{2 - 5}{2 -(-2)} [/tex]

[tex] Slope (m) = -\frac{3}{4} [/tex]

Given:

Scale factor is [tex]\dfrac{1}{144}[/tex].

Length of wingspan of the airplane = 1152 inches

To find:

The length of wingspan of the model airplane.

Solution:

Scale factor is [tex]\dfrac{1}{144}[/tex]. It means,

1 inches of airplane [tex]=\dfrac{1}{144}[/tex] inches of model airplane.

1152 inches of airplane [tex]=1152\times \dfrac{1}{144}[/tex] inches of model airplane

                                       [tex]=8[/tex] inches of model airplane

Therefore, the length of wingspan of the model airplane is 8 inches.

Answer:a

Step-by-step explanation:hhehenndherndur

Answer

$7

Step-by-step explanation:

10-8= 2

9-2=7

Answer: 17.25

Step-by-step explanation:

Answer:

I think its b

i hope you pass

Answer:

yea u got it right my dude

Answer:

Vertex:  (−2,7)

Step-by-step explanation:

May I have brainliest please? :)

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:

4960 miles

Step-by-step explanation:

Answer:

3 > x > − 4 and your welcome bud

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.