how to factorise 15x-10x^3

The x-intercepts of an equation are simply the zeros of the equation

The equation [tex]\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}[/tex] has 4 distinct x-intercepts

The equation is given as:

[tex]\mathbf{y = bx(x - a)(x -a)(x + b)(x - b)}[/tex]

Set the equation to 0; i.e. calculate the zeros

[tex]\mathbf{bx(x - a)(x -a)(x + b)(x - b) = 0}[/tex]

Divide both sides by constant b

[tex]\mathbf{x(x - a)(x -a)(x + b)(x - b) = 0}[/tex]

Split the above equation, as follows

[tex]\mathbf{x= 0\ or\ x - a = 0\ or\ x -a = 0\ or\ x + b = 0\ or\ x - b = 0}[/tex]

Solve for x in each of the equation

[tex]\mathbf{x= 0\ or\ x = a\ or\ x = a\ or\ x= -b\ or\ x = b}[/tex]

Remove repeated solutions

[tex]\mathbf{x= 0\ or\ x = a\ or\ x= -b\ or\ x = b}[/tex]

The count of solutions above is 4

Hence, the equation has 4 distinct x-intercepts

Read more about x-intercepts at:

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Answer:

hello

Step-by-step explanation:

Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. Generally, a line's steepness is measured by the absolute value of its slope, m.

m = slope

Answer:

(x^3y)/2

Step-by-step explanation:

Answer:

1.)47.022

2.)8.032

3.)2.436

4.)61.92

Step-by-step explanation:

Answer:

$57.84

Step-by-step explanation:

Balloons needed = 168

Cost of 36 balloons per pack = $11.88

Cost of 12 balloons per pack = $5.16

cost per balloon

36 per pack = $11.88 / 36

= $0.33

12 per pack = $5.16 / 12

= $0.43

In order to minimize cost, she should buy as many packs of 36 per pack balloon

36 per pack × 1 pack = 36

36 per pack × 2 packs = 72

36 per pack × 3 packs = 108

36 per pack × 4 packs = 144

36 per pack × 5 packs = 180

The required number of balloons is 168

So, the number of possible 36 packs to buy is 4, that is, 144 balloons

Balloons remaining = 168 - 144

= 24

Possible packs of 12 balloons per pack possible is

12 per pack × 1 pack = 12

12 per pack × 2 packs = 24

Therefore, Megan needs to buy 4 packs of 36 balloons per pack and 2 packs of 12 balloons per pack

Cost of 4 packs of 36 balloons per pack = 4 × $11.88

= $47.52

Cost of 2 packs of 12 balloons per pack = 2 × $5.16

= $10.32

Total cost = $47.52 + $10.32

= $57.84

Answer:

0

Step-by-step explanation:

-(-x) ^3-x^3

x^3-x^3

=0

Answer:

so

box1 = x

box2= 9

Step-by-step explanation:

5(x+9)  

distribute

5(x) + 5(9)

5x + 45

Answer:

[tex]\boxed {x = -\frac{1}{7}}[/tex]

Step-by-step explanation:

Solve for the value of [tex]x[/tex]:

[tex]6(4x + 5) = 3(x + 8) + 3[/tex]

-Use Distributive Property:

[tex]6(4x + 5) = 3(x + 8) + 3[/tex]

[tex]24x + 30 = 3x + 24 + 3[/tex]

-Combine like terms:

[tex]24x + 30 = 3x + 24 + 3[/tex]

[tex]24x + 30 = 3x + 27[/tex]

-Take [tex]3x[/tex] and subtract it from [tex]24x[/tex]:

[tex]24x + 30 -3x = 3x - 3x + 27[/tex]

[tex]21x + 30 = 27[/tex]

-Subtract both sides by [tex]30[/tex]:

[tex]21x + 30 - 30 = 27 - 30[/tex]

[tex]21x = -3[/tex]

-Divide both sides by [tex]21[/tex]:

[tex]\frac{21x}{21} = \frac{-3}{21}[/tex]

[tex]x = \frac{-3}{21}[/tex]

-Reduce the fraction to the lowest term by extracting and canceling out [tex]3[/tex]:

[tex]x = \frac{-3\div3}{21 \div 3}[/tex]

[tex]\boxed {x = -\frac{1}{7}}[/tex]

Therefore, the value of [tex]x[/tex] is [tex]-\frac{1}{7}[/tex].

Answer:

D.) y=-x-2

Step-by-step explanation:

Answer:

D.) y=-x-2

Step-by-step explanation:

Trust me I just know

Answer:

24

Step-by-step explanation:

Answer:

B. x = −3, x = −11

Step-by-step explanation:

−3|x + 7| = −12

-3x - 21 = -12 and -3x - 21 = 12

-3x - 21 = -12

      -3x = 9

          x = -3

-3x - 21 = 12

      -3x = 33

         x = -11

Answer:

81 cm square

Step-by-step explanation:

the answer is 121.5cm^2

Answer: 48

Step 1: Find how much 12 is of 48.

12 = 1/4 of 48

Step 2: Multiply 12 by 3 for 3/4.

12 x 3 = 36.

Step 3: Add the numbers.

12 + 36 = 48

Answer = 48

Approximately, 48 hot dogs did he eat during the 12-minute contest.

One strategy to promote uniformity in work efforts, costs, and time is to simplify procedures. It lessens diversity and variation that is damaging, unnecessary, or meaningless. PEMDAS stands for parenthesis, exponents, multiplication, division, addition, and subtraction. Given two or more operations in a single statement, the order of the letters in PEMDAS tells you what to compute first, second, third, and so on, until the computation is complete.

As a result, Takeru Kobayashi broke the record for eating the hottest dogs in a 12-minute period.

Since,

In the first three minutes, he consumed 12 hot dogs.

in three minutes, he ate = 12 hot dogs

in 1 minute, he ate = 12/3

in 1 minute, he ate = 4

So,

in 12 minutes, the total number of hot dogs he ate = 4*12

in 12 minutes, the total number of hot dogs he ate = was 48

therefore, Approximately, 48 hot dogs did he eat during the 12-minute contest.

Learn more about Simplification here:

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#SPJ6

Answer:

A, C, E, F

Step-by-step explanation:

Answer:

360 degrees

Step-by-step explanation:

We know that the sum of all the (ordered) exterior angles of any polygon is 360 degrees. As shown in the figure that, x,y and z recognise themselves as  the exterior angles of the given triangles, their sum will be 360 degrees as well.

Answer:

Step-by-step explanation:

for 2.2 you would still have 5^2 in brackets still

same kind of error for 2.1

Answer:

(7, -6)

Step-by-step explanation:

You will graph it at this point because the point is basically the origin and when you rotate it clockwise 90° it will end up in Quadrant IV.

9514 1404 393

Answer:

  x = 4c-3d

Step-by-step explanation:

Cross multiply, separate variables terms and constant terms.

  [tex]3(x-d)=4(x-c)\\\\3x-3d=4x-4c\\\\4c-3d=x\qquad\text{add $4c-3x$}\\\\\boxed{x=4c-3d}[/tex]

Answer:

C. None of these

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

When dividing two negative numbers, the negatives cancel out, leaving you with simply 21/3. As you probably know, 21/3 is 7.

Answer:

John: 18 years old

Mikayla: 6 years old

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

[tex]n = \frac{49}{2x}[/tex]

Step-by-step explanation:

1) Simplify [tex]\frac{4}{7}[/tex] xn to [tex]\frac{4xn}{7}[/tex]

[tex]\frac{4xn}{7}[/tex] = 14

2) Multiply both sides by 7.

4xn = 14 × 7

3) Simplify 14 × 7 to 98.

4xn=98

4) Divide both sides by 4.

[tex]xn = \frac{98}{4}[/tex]

5) Simplify [tex]\frac{98}{4}[/tex] to [tex]\frac{49}{2}[/tex]

[tex]xn = \frac{49 }{2}[/tex]

6) Divide both sides by x.

[tex]n = \frac{49}{2} / x[/tex]

7) Simplify [tex]\frac{49}{2} /x[/tex] into [tex]\frac{49}{2x}[/tex]

[tex]n = \frac{49}{2x}[/tex]

Angle GFJ = 56 degrees

Angle FGH = 124 degrees

Angle HFJ = 34 degrees

Angle HKJ = 101 degrees

Step-by-step explanation:

The measure of the angles are:

[tex]\mathbf{GFJ = 56}[/tex]

[tex]\mathbf{GFJ = 56}[/tex]

[tex]\mathbf{\angle HFJ = 34}[/tex]

[tex]\mathbf{\angle HKJ =101}[/tex]

The given parameters are:

∠GHF = 34°,

∠HJF = 124°,

∠FKJ = 79°.

(a) Angle ∠GFJ

This is calculated as:

[tex]\mathbf{GFJ = 180 - \angle HJF}[/tex] --- base angles of parallelogram add up to 180 degrees

So, we have:

[tex]\mathbf{GFJ = 180 - 124}[/tex]

[tex]\mathbf{GFJ = 56}[/tex]

(b) Angle ∠FGH

This is calculated as:

[tex]\mathbf{\angle FGH = \angle HJF}[/tex] --- opposite angles of parallelogram are equal

So, we have:

[tex]\mathbf{\angle FGH = 124}[/tex]

(c) Angle ∠HFJ

This is calculated as:

[tex]\mathbf{\angle HFJ = \angle GHF}[/tex] --- corresponding angles

So, we have:

[tex]\mathbf{\angle HFJ = 34}[/tex]

(d) Angle ∠HKJ

This is calculated as:

[tex]\mathbf{\angle HKJ =180 - \angle FKJ}[/tex] ---- supplementary angles

So, we have:

[tex]\mathbf{\angle HKJ =180 - 79}[/tex]

[tex]\mathbf{\angle HKJ =101}[/tex]

Read more about angles in a parallelogram at:

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Answer:

m=56kx-6

Step-by-step explanation:

Answer:

The radius of the track is 32 meters

Step-by-step explanation:

Circumference

The circumference of a circle can be defined as the distance around the circle or the length of a circuit along the circle.

Given a circle of radius r, the circumference of the circle can be calculated as follows:

[tex]L=2\pi r[/tex]

If we already know the length of the circle, we can solve the above expression for r:

[tex]\displaystyle r=\frac{L}{2\pi}[/tex]

The distance given around a circular running track is L=200 m, thus:

[tex]\displaystyle r=\frac{200}{2\pi}=31.830989\ m[/tex]

Rounding to the nearest meter:

r= 32 meters

The radius of the track is 32 meters

Answer:

Step-by-step explanation:

BD divides CBA into two angles. The add to 90 degrees. Therefore they are complementary.

The key word is complementary. The angles are <CBA and <DBA are complementary.

Answer:

Right angle or adjacent angle. I'm not sure if there was a vocabulary bank.

Step-by-step explanation:

Answer:

50 dollars an hour

Step-by-step explanation: