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Answer:

Simplify ans: 3 x^2 y^-4

a no = x( x+2)

b no = 2x(x- 3)

c no = 5x(3- 2x^2)

d no.= 3x^2( 3+ x)

Hope this helps you

Answer:

see explanation

Step-by-step explanation:

Using the rules of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex] ( m > n)

[tex]\frac{a^{m} }{a^{n} }[/tex] ⇒ [tex]\frac{1}{a^{(n-m)} }[/tex] ( n > m )

Given

[tex]\frac{21x^6y^5}{14x^2y^9}[/tex]

= [tex]\frac{21}{14}[/tex] × [tex]x^{(6-2)}[/tex] × [tex]\frac{1}{y^{(9-5)} }[/tex]

= [tex]\frac{3}{2}[/tex] × [tex]x^{4}[/tex] × [tex]\frac{1}{y^{4} }[/tex]

= [tex]\frac{3x^4}{2y^4}[/tex] ← with positive exponents

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

(a)

x² + 2x ← factor out x from each term

= x(x + 2)

(b)

2x² - 6x ← factor out 2x from each term

= 2x(x - 3)

(c)

15x - 10x³ ← factor out 5x from each term

= 5x(3 - 2x²)

(d)

9x² + 3x³ ← factor out 3x² from each term

= 3x²(3 + x)

Answer:

position         1             5             8                12               19             25

term              -8            8             20             36               64            88

Step-by-step explanation:

(n - 1) is position ( n ∈ N)

d is the distance between the numbers in the sequence

a1 is the first number in the sequence

we have the fuction: a(n) = a1 + (n - 1)d

see in the table, with position = 1, term = -8 => a1 + d = -8

                                    position = 25, term = 88 => a1 + 25d = 88

=> we have: a1 + d = -8

                     a1 + 25d = 88

=> a1 = -12

    d = 4

=> a(n) = -12 + 4(n - 1)

=> term = 8, position = (8 + 12)/4 = 5

    position = 8, term = -12 + 4.8 = 20

    term = 36, position = (36 + 12)/4 = 12

    position = 19, term = -12 + 4.19 = 64

Answer:

The required table is:

Position   1     5       8      12      19      25

Term      -8     8      20     36     64     88  

Step-by-step explanation:

The general formula for arithmetic sequence is:

[tex]a_n=a_1+(n-1)d[/tex]

where n is the nth term, a₁ is the first term and d is the difference.

Looking at the table, we know that

a₁ = -8 and

a₂₅ = 88

We can find the common difference d:

[tex]a_n=a_1+(n-1)d\\n=25, a_1=-8, a_{25}=88\\a_{25}=a_1+(25-1)d\\88=-8+24(d)\\88+8=24\:d\\96=24\:d\\d=\frac{96}{24}\\d=4[/tex]

So, we have d = 4

Now we can fill the remaining table.

We have to find position n, when term (a_n) is 8

[tex]a_n=a_1+(n-1)d\\8=-8+(n-1)4\\8=-8+4n-4\\8=-12+4n\\8+12=4n\\20=4n\\n=\frac{20}{4}\\n=5[/tex]

So, when term is 8, position is 5

We have to find term a_n when position n is 8

[tex]a_n=a_1+(n-1)d\\a_8=-8+(8-1)4\\a_8=-8+7(4)\\a_8=-8+28\\a_8=20[/tex]

So, when position is 8 term is 20

We have to find position n, when term (a_n) is 36

[tex]a_n=a_1+(n-1)d\\36=-8+(n-1)4\\8=-8+4n-4\\8=-12+4n\\36+12=4n\\48=4n\\n=\frac{48}{4}\\n=12[/tex]

So, when term is 36, position is 12

We have to find term a_n when position n is 19

[tex]a_n=a_1+(n-1)d\\a_{19}=-8+(19-1)4\\a_{19}=-8+18(4)\\a_{19}=-8+72\\a_{19}=64[/tex]

when position is 19 term is 64

So, the required table is:

Position   1     5       8      12      19      25

Term      -8     8      20     36     64     88  

Answer:

marked price = $69,000

Step-by-step explanation:

cost price = $60,000

profit

= 15%

= 15% × cost price

= 15/100 × $60,000

= $9000

marked price

= cost price + profit

= $60,000 + $9000

= $69,000

Answer:

i think its 36!

Step-by-step explanation:

6 x 6+36

Answer:

27.999999993 or 27.9 or 28 (rounded) miles.

Step-by-step explanation:

Find out how many miles he goes every minute.

(1.6 ÷ 12 = 0.13 recurring (0.1333333333)

3.5 hours = (60 × 3) + 30 = 210 minutes

Multiply 0.13 recurring (0.1333333333) by 210 mins.

210 × 0.13 recurring (above number) = 27.999999993 (You can round this up to the nearest whole number), which is 28 if the question asks you to but as it uses 1.6 miles, you can leave it as 27.9 or even leave the long decimal if you're not entirely sure.

Hope this helps. :)

Answer:

1,000,000,000,000,001,111,111

Answer:

9 + 4x = 101

Step-by-step explanation:

9 + 4x = 101        Equation

( +9 - 9 ) + 4x = ( 101 - 9 )          Subract 9 on both sides

4x = 92                     Simplify

x = 23                       Divide 4 on both sides

23 people in art class

Given:

The graph passes through the points (0,-20) and (4,10).

To find:

The equation of line that most closely represents the line depicted in the graph.

Solution:

If a line passing through two points, then the equation of line is

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The given line passes through the points (0,-20) and (4,10). So, the equation of line is

[tex]y-(-20)=\dfrac{10-(-20)}{4-0}(x-0)[/tex]

[tex]y+20=\dfrac{10+20}{4}(x)[/tex]

[tex]y+20=\dfrac{30}{4}x[/tex]

[tex]y+20=\dfrac{15}{2}x[/tex]

Subtracting 20 from both sides, we get

[tex]y=\dfrac{15}{2}x-20[/tex]

The function form is

[tex]f(x)=\dfrac{15}{2}x-20[/tex]

f of x equals fifteen halves times x minus 20.

Therefore, the correct option is B.

Answer:

Your answer is B

Step-by-step explanation:

f of x equals fifteen halves times x minus 20

The original height of the tree is 60 m

Answer:

Step-by-step explanation:

the base of the triangle that the fallen tree makes up is 12 and the up right is 5 the tree top is the hypotenuse of this triangle  :)

treeTop= [tex]\sqrt{12^2+5^{2} } }[/tex]

treeTop = [tex]\sqrt{169}[/tex]

treeTop = 13

13+5 = treeHeight

18 = treeHeight

Answer:

30m per gallon

Step-by-step explanation:

150m/5g= 30m/g

Answer:

$32.65

Step-by-step explanation:

To find the tax, multiply 29.95 by .09. This gets us 2.6955. We can round this to $2.70. Now, we add the tax to the cost of the pants. This gets us 32.65. This means the total cost, with tax, is $32.65.

Answer:

[tex]\huge y = \sin(q) = \sin(90°) = 1[/tex]

Answer:

one-third

Step-by-step explanation:

                                                         A          B

<-------+---------+---------+---------+--------+---------+---------+--------------->

         0                                   1       1 1/3     1 2/3        2

Since each unit is divided into three equal spaces, each space is 1/3 of a unit.

Between any two consecutive marks, the distance is 1/3 unit.

Answer: one-third

Answer: 266.66%

Step-by-step explanation:

(2/3)/(1/4) = (2/3)(4/1) = 8/3 = 2 2/3 = 2.6666 = 266.66%

Answer:

the first is 14cm and second is 20.4cm

Step-by-step explanation:

Answer:

First one

Step-by-step explanation:

Answer: Let, n(U) be=x only (p)=x/5 only(ca)=16 n(pnc)=?n(c)=60%ofx=0.6x

then,

Only (c)=n(c)-n(cnp)

16=0.6x-n(cnp)

n(cnp)=0.6x-16

again,

n(U)=only(p)+only (c)+n(cnp)+n(pUc)of complement

x=x/5+16+0.6x-16+8

5x=x+3x+40

x=40

n(cnp)=0.6x-16=0.6×40-16=8

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/2

Step-by-step explanation:

If 15 oranges were bought,

the total cost would be 15 * ¥90 = ¥1350.

¥1890 - ¥1350 = ¥540.

For every orange that switches to an apple,

the cost increases by ¥150 - ¥90 = ¥60.

Number of apples = ¥540 / ¥60 = 9.

Therefore there are 6 oranges and 9 apples.

Answer:

6 oranges and 9 apples.

Step-by-step explanation:

Let the number of oranges be x then the number of apples = 15 - x.

So  90x +  150(15 - x) = 1890

90x - 150x + 2250 = 1890

-60x = -360

x = 6

and number of apples = 15 - 6

So it's 6 oranges and 9 apples.

The triangle is an acute triangle

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of angles of the triangle are

The measure of ∠ABC = 50°

The measure of ∠BAC = 50°

The measure of ∠ACB = 80°

So , all the angles of the triangle are less than 90°

So , it is an acute triangle

Hence , the triangle is acute

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ5

Answer:

happy new year

Step-by-step explanation:

i am your biggest fan I am your teacher you fill

Answer:

The rule used to reflect Δ ABC to its image is Reflect over y = x ⇒ B

Step-by-step explanation:

From the given figure

∵ The coordinates of point A are (-4.5, 6)

∵ The coordinates of point A' are (6, -4.5)

→ The coordinates are switched ⇒ 3rd rule

∴ Point A is reflected over the line y = x

∴ Δ ABC is reflected over the line y = x

∴ The rule used to reflect Δ ABC to its image is Reflect over y = x

Note: Point B' on the graph should be C' and point C' should be B' (correct it)

Step-by-step explanation:

Given that,

For 4 weeks in June, Cameron biked 3 1/4 miles each week and swam 2 1/2 miles each week.

For 3 weeks in July, he biked 4 3/4 miles each week and swam 3 1/2 miles each week.

We need to find how much greater was the total distance Cameron bike and swim in July compared to the total distance he bike in swim in June.

In July, total distance is ,

[tex]4\dfrac{3}{4}\times 3+3\dfrac{1}{2}\times 3\\\\= \dfrac{19}{4}\times 3+\dfrac{7}{2}\times 3\\\\=24.75\ \text{miles}[/tex]

In June, total distance is :

[tex]=4\times 3\dfrac{1}{4}+4\times 2\dfrac{1}{2}\\\\=\dfrac{13}{4}\times 4+\dfrac{5}{2}\times 4\\\\=23\ \text{miles}[/tex]

Hence, in June total distance is 23 miles and in July total distance is 24.75 miles.

Answer:

Answer and steps in the picture

Answer:

143

Step-by-step explanation:

[tex]x + 120 = 180[/tex]

(linear pair of angles)

[tex]x = 180 - 120[/tex]

[tex]x = 60[/tex]

Answer:  He is not correct. The resulting will be in a different quadrant.

Step-by-step explanation:  This would be much easier to answer with a screen shot of the image.

For example, if the original image is in quadrant 1, the first reflection over the x-axis places the new image in quadrant 4, "upside-down" and the second reflection over the y=x line places the new image in quadrant 2 and "oblique" to the original.

Reflecting the original over the y=-x line places the new image in quadrant 3.

-1

Step-by-step explanation:

because looking at the graph it is negative, and it goes down one over one