Write an inequality to show: The population of China (p) is at least 1,000,000,000 people.
I'll try to mark brainiest

(x • (y³)) - 32xyz²

Pull out like factors :

xy³ - 9xyz² = xy • (y² - 9z²)

Factoring: y² - 9z²

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A² - AB + BA - B² =

A² - AB + AB - B² =

A² - B²

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3

Check : y² is the square of y¹

Check : z² is the square of z¹

Factorization is : (y + 3z) • (y - 3z)

Final result :

xy • (y + 3z) • (y - 3z)

Answer:

A and B

Step-by-step explanation:

They both have the same numbers and at least one of the given numbers is negative.

Hope this helps :)

Answer:

use this equation: GPE=mgh

Step-by-step explanation:

GPE = gravitational potential energy = J

m = mass = Kg

g = gravitational field = N/kg = world's gravitational field is 9.8N/kg

h = height = m

Answer:

40

Step-by-step explanation:

Answer:

x = 24°

Step-by-step explanation:

Using 180-degree formula, we can find x.

=> 84 + 4x = 180°

=> 4x = 180 - 84

=> 4x = 96

=> 24°

Therefore, x = 24°

Hoped this helped.

Answer:

[tex] {\boxed {\sf{x = 24 \degree}}}[/tex]

Step-by-step explanation:

In the given figure we have two consecutive interior angles.

We know that each pair of consecutive interior angles is supplementary.

So,

Therefore, x = 24°

Answer:

Step-by-step explanation:

Translate the given into two pairs of coordinates:

Work out the equation of the line passing through both of the points.

Find the slope:

Find the y-intercept:

The line is:

Find the value of y when x = 1500:

Answer:

the answer is expkained below

Answer:

Evans dog would weigh 39 pounds

Step-by-step explanation:

117= 3 × X

Take 117 and divide it by 3 and the answer we would get is 39

117 ÷ 3 = 39

To double check the answer we could multiply 39 by 3 to see if we 117.

39 × 3 = 117

X= 39 pounds, so Evans dog is 39 pounds

Answer:

(-5,-9)

Step-by-step explanation:

Answer:

C(-1, -4)

Step-by-step explanation:

see the point reflected over the line through the vertex point

Answer:

D. Q′ (−4, −3)

Step-by-step explanation:

From looking at the graph it looks like the answer would be

Q= (3, -4) if the X-axis goes first

Q= (-4, 3) if the Y-axis goes first

[tex]xy =-21~~.....(i)\\\\x+ y=20~~....(ii)\\\\\text{From equation (i):}\\\\xy = -21 \implies y = -\dfrac{21}x~~.....(iii)\\\\\text{Substitute y in equation (ii):}\\\\x - \dfrac{21}x = 20\\\\\implies x^2 -20x -21= 0\\\\\implies x^2 - 21x + x-21=0\\\\\implies x(x-21) +(x-21) =0\\\\\implies (x+1)(x-21)=0\\\\\implies x = -1 ~~\text{or}~~ x =21\\\\\text{Substitute x in equation (iii):}\\\\y = 21 ~~ \text{or}~~ y = -1\\\\\text{Hence,}~ (x,y)=(21,-1) ~~ \text{or}~~ (x,y) = (-1,21)[/tex]

If she read 52 pages in one hour, then she'll continue at a rate of 52 pages per hour.

Answer:

52 pages

Step-by-step explanation:

Since she reads 52 pages in 1 hour we multiply 52 by the amount of hours she reads.

52 pages times 1 hour equals 52 pages.

52 x 1 = 52

Answer:

3 / (3t+4) is the answer

the straight up answer is -12/5

Answer:

Your answer would be x=2±√5

Step-by-step explanation:

Answer:

17.5

Step-by-step explanation:

i solved it and got that answer. hope this helps =)

Answer:

x=10

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

6x-7 = 26+2x+7

Combine like terms

6x-7 = 2x+33

Subtract 2x

6x-7-2x =2x+33-2x

4x-7 = 33

Add 7 to each isde

4x-7 +7 = 33+7

4x=40

Divide by 4

4x/4 = 40/4

x=10

Answer:

Answered is x= 55x

Step-by-step explanation:

13x+10 * 12x+20

soln:

or, 13x+12x+10+20

or, 25x+30

:., therefore, x=55x

"Find all real solutions of" basically means solve for x. You're looking for the real numbers x such that the given equation is satisfied. "Zeros" is synonymous with "solutions".

It looks like the first equation is

3x³ + x² - 38x + 24 = 0

It's not immediately obvious whether this can be factorized, so we first carry out the rational zero test to see if there are any rational solutions. *If* this equation has any rational solutions, then they must take the form of (divisor of 24)/(divisor of 3). That is, take any divisor of the constant coefficient and divide it by any divisor of the leading term's coefficient.

We have

• divisors of 24 : ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

• divisors of 3 : ±1, ±3

Sadly, there are 64 possible roots to test, but we only need one to make the rest of the problem easier.

• Let x = +1 / +1 = 1. Then plugging x = 1 into the equation gives

3•1³ + 1² - 38•1 + 24 = -10 ≠ 0

so x = 1 is *not* a solution

• Let x = +2 / +1 = 2. If x = 2, then

3•2³ + 2² - 38•2 + 24 = -24 ≠ 0

so x = 2 is *not* a solution.

• Let x = +3 / +1 = 3. If x = 3, then

3•3³ + 3² - 38•3 + 24 = 0

so x = 3 is a solution.

By the remainder theorem, this means that x - 3 divides 3x³ + x² - 38x + 24. Using long or synthetic division,

(3x³ + x² - 38x + 24) / (x - 3) = 3x² + 10x - 8

so that

3x³ + x² - 38x + 24 = 0

is the same as

(x - 3) (3x² + 10x - 8) = 0

We factorize the remaining quadratic to get

3x² + 10x - 8 = (3x - 2) (x + 4)

and so the original equation is equivalent to

(x - 3) (3x - 2) (x + 4) = 0

Solve for x :

x - 3 = 0   or   3x - 2 = 0   or   x + 4 = 0

x = 3   or   x = 2/3   or   x = -4

The other equations can be solved similarly, though some of the others you included are much simpler.

For the second problem (note that you left out an exponent), we solve the equation

x³ - 2x² - 23x + 60 = 0

Again, not immediately obvious how to factorize this. But using the rational root test, we have

• divisors of 60 : ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60

• divisors of 1 : ±1

If you follow the same steps as before, you'll find the first rational solution with x = 3. So x - 3 divides x³ - 2x² - 23x + 60, and long division gives

(x³ - 2x² - 23x + 60) / (x - 3) = x² + x - 20

and the resulting quadratic is easily factored,

x² + x - 20 = (x - 4) (x + 5)

So, we have

x³ - 2x² - 23x + 60 = (x - 3) (x - 4) (x + 5) = 0

which means

x - 3 = 0   or   x - 4 = 0   or   x + 5 = 0

x = 3   or   x = 4   or   x = -5

For the third problem, we can factor by grouping.

x³ - 4x² - x + 4 = 0

x² (x - 4) - (x - 4) = 0

(x² - 1) (x - 4) = 0

(x - 1) (x + 1) (x - 4) = 0

Then

x - 1 = 0   or   x + 1 = 0   or   x - 4 = 0

x = 1   or   x = -1   or   x = 4

For the fourth problem, we use the rational root test again, but twice this time.

x⁴ - 6x³ + 7x² + 6x - 8 = 0

• divisors of -8 : ±1, ±2, ±4, ±8

• divisors of 1 : ±1

We find that x = 1 and x = 2 are both rational roots, so both x - 1 and x - 2 divide x⁴ - 6x³ + 7x² + 6x - 8. By long division,

(x⁴ - 6x³ + 7x² + 6x - 8) / ((x - 1) (x - 2)) = x² - 3x - 4

and factoring this gives

x² - 3x - 4 = (x + 1) (x - 4)

So, we have

x⁴ - 6x³ + 7x² + 6x - 8 = (x - 1) (x - 2) (x + 1) (x - 4) = 0

which means

x - 1 = 0   or   x - 2 = 0   or   x + 1 = 0   or   x - 4 = 0

x = 1   or   x = 2   or   x = -1   or   x = 4

For the last problem,

x⁴ + 4x³ + 7x² + 16x + 12 = 0

we use the rational root test again.

• divisors of 12 : ±1, ±2, ±3, ±4, ±6, ±12

• divisors of 1 : ±1

We find that both x = -1 and x = -3 are rational solutions, and dividing gives

(x⁴ + 4x³ + 7x² + 16x + 12) / ((x + 1) (x + 3)) = x² + 4

which we cannot factorize further over the real numbers. So we end up with

x⁴ + 4x³ + 7x² + 16x + 12 = (x + 1) (x + 3) (x² + 4) = 0

so that

x + 1 = 0   or   x + 3 = 0   or   x² + 4 = 0

x = -1   or   x = -3

(We omit the third equation here because it has no real solution since x² + 4 ≥ 4 for all real x.)

Answer:

A- 8x+9

Step-by-step explanation:

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

5x + 3 (x + 2) + 3

5x + 3x + 6 + 3

8x + 6 + 3

8x + 9

<3

Answer:

Step-by-step explanation:

Answer:

16 I guess.

Step-by-step explanation:

lolololololol?

Answer:

1

Step-by-step explanation:

gradient M= change in Y / change in X

= (-16--6)/(-6-4)

= -10/-10

M therefore= 1

Answer:(x-3)² + (y-2)² = 25

Step-by-step explanation:

A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².

So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.

Answer:

(x - 3)² + (y - 2)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Here (h, k ) = (3, 2 ) and r = 5 , then

(x - 3)² + (y - 2)² = 5² , that is

(x - 3)² + (y - 2)² = 25 ← equation of circle

Answer:

sorry i can answer that the asy

Answer:

Q1 - 10080

(sorry couldn't do q2 haha)

step by step;

By isosceles triangle theorem,

Angle ZXY = Angle ZYX

The sum of the angles in a triangle is 180 degrees.

106 + 2 same angles (-106) = 180 (-106)  (Subtract 106 by both sides)

2 same angles (/ 2) = 74 (/ 2)   (Divide 2 by both sides)

V = 37

Answer:

The value of v is 37°.

Step-by-step explanation:

Given that △ XYZ is an isosceles triangle where both sides have the equal angles. The total angle of △ is 180°. Let ∠ZXY and ∠ZYX be the same angles:

Let ∠ZXY = v, ∠ZYX = v, ∠ XZY = 106°,

∠ZXY + ∠ZYX + ∠XZY = 180°

v + v + 106° = 180°

2v + 106° = 180°

2v = 180° - 106°

2v = 74°

v = 74 ÷ 2

v = 37°

Answer: $113.89

Step-by-step explanation:

108.99 * 0.045

= 4.90455

108.99 + 4.90455

= 113.89455

$113.89

Answer:

Total Cost = $113.89

Step-by-step explanation:

Total Cost = Cell phone cost + sale Tax % ( cell phone cost)

Total Cost = $108. 99 + .045 × $108.99

Total Cost = $108.99 + $4.90455

Total Cost = $108.99 + $4.90

Total Cost = $113.89

Answer:

D,no if you graph both inequalitiesvon thevsame geaph ,you will get b =16

Step-by-step explanation:

i think this is the answer

Answer:

Step-by-step explanation:

Obtuse angle is the angle greater than 90°.

A right triangle has one 90° and the sum of remaining angles is 90°.

It means a right triangle can't have an obtuse angle.