Determine whether 7^2m · 6^2m is equivalent to each of the following expressions:
42^6m
42^m
42^9m

To be honest, I don't think it has anything to do with the exponent part at all. Instead, I think it has to do with the fact that integers are inherently easier to grasp compared to fractions (which is exactly what rational numbers are).

For instance, it's much easier to say 2+3 = 5 than it is to say 1/2 + 1/4 = 3/4

So going back to the exponent example, it's easier to say

x^2*x^3 = x^(2+3) = x^5

than it is to say

x^(1/2)*x^(1/4) = x^(1/2+1/4) = x^(3/4)

So that's my opinion as to why rational exponents are more tricky to grasp compared to integer exponents. Of course, everyone learns math differently so maybe some find fractions easier than others.

Answer:

C

Step-by-step explanation:

b=360-2(65)=360-130=230

Answer:

230

Step-by-step explanation:

b= 360-2(65)

=360-130

=230

Hi there!

[tex]\large\boxed{(n - 8)(n + 5)}[/tex]

n² - 3n - 40

Find two numbers that sum up to -3 and multiply into -40. We get:

-8, 5

Thus:

(n - 8)(n + 5)

The point [tex](-2,2)[/tex] is a solution of the system given by [tex]y<2x+8[/tex] and [tex]y \geq -x-3[/tex]

Given point: [tex](-2,2)[/tex]

Given systems:

To find: The system to which the given point is a solution

If a point is a solution of a system, then the coordinates of the point satisfies all the equation(s) or inequation(s) of the system. So, we can substitute the x & y coordinates of the given point into the inequalities of each of the given systems and check if the inequalities are satisfied by the coordinates of the point.

(1) [tex]y>-2x+2[/tex] and [tex]y>x+5[/tex]

Substitute the coordinates of the point [tex](-2,2)[/tex] into the inequalities of the system.

Put [tex]x=-2,y=2[/tex] in [tex]y>-2x+2[/tex] to get,

[tex]2>-2(-2)+2[/tex]

[tex]2>4+2[/tex]

[tex]2>6[/tex]

The above inequality is clearly impossible and thus, the coordinates of the given point does not satisfy this inequality.

This implies that the given point is not a solution of this system.

(2) [tex]y<x+2[/tex] and [tex]y>x-1[/tex]

Substitute the coordinates of the point [tex](-2,2)[/tex] into the inequalities of the system.

Put [tex]x=-2,y=2[/tex] in [tex]y<x+2[/tex] to get,

[tex]2<-2+2[/tex]

[tex]2<0[/tex]

The above inequality is clearly impossible and thus, the coordinates of the given point does not satisfy this inequality.

This implies that the given point is not a solution of this system.

(3) [tex]y<2x+8[/tex] and [tex]y \geq -x-3[/tex]

Substitute the coordinates of the point [tex](-2,2)[/tex] into the inequalities of the system.

Put [tex]x=-2,y=2[/tex] in [tex]y<2x+8[/tex] to get,

[tex]2<2(-2)+8[/tex]

[tex]2<-4+8[/tex]

[tex]2<4[/tex]

This is a true inequality. Then, the given point satisfies the first inequality of the system.

We will now check if the point satisfies the second inequality of the system.

Put [tex]x=-2,y=2[/tex] in [tex]y \geq -x-3[/tex] to get,

[tex]2 \geq -(-2)-3[/tex]

[tex]2 \geq 2-3[/tex]

[tex]2 \geq -1[/tex]

This is also a true inequality. Then, the given point also satisfies the second inequality of the system.

Thus, the given point is a solution of this system.

(4) [tex]y<2x+3[/tex] and [tex]y \geq -2x-5[/tex]

Substitute the coordinates of the point [tex](-2,2)[/tex] into the inequalities of the system.

Put [tex]x=-2,y=2[/tex] in [tex]y<2x+3[/tex] to get,

[tex]2<2(-2)+3[/tex]

[tex]2<-4+3[/tex]

[tex]2<-1[/tex]

The above inequality is clearly impossible and thus, the coordinates of the given point does not satisfy this inequality.

This implies that the given point is not a solution of this system.

Thus, we can see that the coordinates of the given point [tex](-2,2)[/tex] satisfies the inequalities of the third system only.

Then, the point [tex](-2,2)[/tex] is a solution of the system given by [tex]y<2x+8[/tex] and [tex]y \geq -x-3[/tex].

Learn more about geometric solutions of system of linear inequalities here:

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Answer:

B 19,000

Step-by-step explanation:

;------------------------;

Answer:

Last option= 30 minutes

Step-by-step explanation:

cos(90) = 0

around this point the cos function "mirrors" with opposite signs. cos(<90) is positive and cos(>90) is negative.

but |cos(90-a)| = |cos(90+a)| for 0 <= a <= 90

75 = 90 - 15

105 = 90 + 15

so, a = 15

and because of

|cos(90-a)| = |cos(90+a)| for 0 <= a <= 90

cos (90-15) = cos(75) = -cos(90+15) = -cos(105)

[tex]\\ \sf\longmapsto 2x+y=2[/tex]

[tex]\\ \sf\longmapsto 2x=2-y[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2-y}{2}\dots(1)[/tex]

And

[tex]\\ \sf\longmapsto x+1=y+2[/tex]

[tex]\\ \sf\longmapsto x=y+2-1[/tex]

[tex]\\ \sf\longmapsto x=y+1[/tex]

[tex]\\ \sf\longmapsto \dfrac{2-y}{2}=y+1[/tex]

[tex]\\ \sf\longmapsto 2-y=2(y+1)[/tex]

[tex]\\ \sf\longmapsto 2-y=2y+2[/tex]

[tex]\\ \sf\longmapsto 2-2=2y+y[/tex]

[tex]\\ \sf\longmapsto 3y=0[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{0}{3}[/tex]

[tex]\\ \sf\longmapsto y=\infty[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2-y}{2}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2-\infty}{2}[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{2}{2}[/tex]

[tex]\\ \sf\longmapsto x=1[/tex]

Answer:

x=1 , y=0

Step-by-step explanation:

2x+y=2.......1

x+1=y+2

x-y=2-1

x-y=1...... 2

from equation 2 we get ,

x-y=1

x=1+y

putting the value of x in equation 1 we get,

2*(1+y) +y=2

2+2y+y=2

2+3y=2

3y=2-2

3y=0

y=0/3

y=0

putting the value of y in equation 2 we get,

x-0=1

x=1+0

x=1

hence x=1 , y=0

Answer:

28125    

Step-by-step explanation:

Refer to the image below.

Answer:

x=2  true solution

x=-3 extraneous

Step-by-step explanation:

sqrt(x+7) -1 = x

Add 1 to each side

sqrt(x+7) -1+1 = x+1

sqrt(x+7)  = x+1

Square each side

(sqrt(x+7))^2  = (x+1)^2

x+7 = x^2 +2x+1

Subtract x from each side

7 = x^2 +x +1

Subtract 7 from each side

0 = x^2 +x - 6

Factor

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

Using the zero product property

x+3 = 0   x-2 =0

x=-3  x=2

Check solutions

x=-3

sqrt(-3+7) -1 = -3

sqrt(4) -1 = -3

3 =-3  extraneous

x=2

sqrt(2+7) -1 = 2

sqrt(9) -1 = 2

3 -1 =2

2 =2  true

we observe that this figure could be divided into a triangle and a rectangle.

for the area of the triangle, bxh/2, we have 15 x 12/2 = 90

and for the rectangle, we have 5 x 12 = 60

so, 90 + 60 = 150

hope it helps :)

Answer:

A: population

Step-by-step explanation:

Um its just the definition of the word i think.

Population: a collection of persons, things, or objects under study.

Step-by-step explanation:

I need help to...

I keep putting it in and no one has ever answered it and I'm struggling and getting stressed.

Answer:

Angelica's house is 11 miles away from the gas station.

Step-by-step explanation:

The most simple path from Angelica's house is 11 blocks away from the gas station and each unit/block is 1 mile. So 11 miles.

Answer: 7m⁵ -3m³ - 3

Working:

= (6m⁵ + 3 - m³ - 4m) -(-m⁵ + 2m³- 4m +6)

= 6m⁵ + 3 - m³ - 4m +m⁵-2m³+4m - 6

= 6m⁵ + m⁵-m³ -2m³ -4m + 4m - 6 +3

= 7m⁵ -3m³ - 3

Answered by Gauthmath must click thanks and mark brainliest

Answer:

Hello,

Step-by-step explanation:

In order to cut off ( pour couper court)

all multiple of 20 are divisible by 20, so they are not primes.

Answer:

D

Step-by-step explanation:

x^2=y^3

Then x^6=y^9 but x^3z=z^9 so 3z=6, z=2

Answer:

z = 2

Step-by-step explanation:

[tex]x^{3z} = y^{9}\\\\x^{3z} =y^{3*3} \\\\x^{3z}= (y^{3})^{3}\\\\x^{3z}=(x^{2})^{3}\\\\x^{3z} = x^{6}[/tex]

As bases are same, compare the powers

3z = 6

z = 6/3

z = 2

Answer:

A (3,3)

J (5,2)

L (0,0)

Step-by-step explanation:

.........................

The choices :

Three

B , E , D

Answer:

36 ft²

Step-by-step explanation:

equilateral means all sides are equally long.

a triangle has 3 sides.

in our case they are all equally long.

and their sum (all 3 sides together) is the perimeter

P = 18 = 3 × side length

side length = 18/3 = 6 ft

a square with the same side length (6) had then an area of

side length × side length = 6×6 = 6² = 36 ft²

it is important to remember : a length is measured e.g. in feet (ft). an area is then meshed in square-feet (ft²). it is important to add this to the calculated numbers to express the right dimension of these numbers.

Answer:

Step-by-step explanation:

The easiest way to explain this is to use slope and then writing equations for lines. The reason for that is because we are told that the production uniformly increases. That "uniform increase" is the rate of change, and since the rate of change is constant, we are talking about the slope of a line, where the rate of change is constant throughout the whole length of the line.

Create coordinates from the info given:

In the third year, 600 units were made. Time is always an x thing, so the coordinate is (3, 600). Likewise for the other bit of info. Time is always an x thing, so the coordinate is (7, 700). Applying the slope formula:

[tex]m=\frac{700-600}{7-3}=\frac{100}{4}=25[/tex]  which means that 25 units per year are produced. Write the equation to find the number of units produced in any year. I used the point-slope form of a line to do this:

y - 600 = 25(x - 3) and

y - 600 = 25x - 75 so

y = 25x + 525

If we want to know the number of units in the first year, we will replace x with 1 and do the math:

y = 25(1) + 525 so

y = 550 units, choice C.

y............. xnxnxnxnxnccncncncnnncncjcjnf

Answer:

x = 10

Step-by-step explanation:

7(x+1+7)=6(x+5+6)

or, 7(x+8)=6(x+11)

or, 7x+56=6x+66

or, 7x-6x=66-56

or, x=10

Answered by GAUTHMATH

Answer:

a(n)= 1/2 * (-8) n-1

Step-by-step explanation:

In a geometric sequence, the ratio between successive terms is constant. This means that we can move from any term to the next one by multiplying by a constant value. Let's calculate this ratio over the first few terms:

\dfrac{-256}{32}=\dfrac{32}{-4}=\dfrac{-4}{\frac12}=\blue{-8}  

32

−256

​

=  

−4

32

​

=  

2

1

​

−4

​

=−8start fraction, minus, 256, divided by, 32, end fraction, equals, start fraction, 32, divided by, minus, 4, end fraction, equals, start fraction, minus, 4, divided by, start fraction, 1, divided by, 2, end fraction, end fraction, equals, start color #6495ed, minus, 8, end color #6495ed

We see that the constant ratio between successive terms is \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed. In other words, we can find any term by starting with the first term and multiplying by \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed repeatedly until we get to the desired term.

Let's look at the first few terms expressed as products:

nn 111 222 333 444

h(n)\!\!\!\!\!h(n)h, left parenthesis, n, right parenthesis \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large0}\!\!\!\!\!\!  

2

1

​

⋅(−8)  

0

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, start superscript, 0, end superscript \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large1}\!\!\!\!\!\!  

2

1

​

⋅(−8)  

1

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, start superscript, 1, end superscript \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large2}\!\!\!\!\!\!  

2

1

​

⋅(−8)  

2

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, squared \red{\dfrac12}\cdot\!\!\!\left(\blue{-8}\right)^{\,\large3}  

2

1

​

⋅(−8)  

3

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, cubed

We can see that every term is the product of the first term, \red{\dfrac12}  

2

1

​

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, and a power of the constant ratio, \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed. Note that this power is always one less than the term number nnn. This is because the first term is the product of itself and plainly 111, which is like taking the constant ratio to the zeroth power.

Thus, we arrive at the following explicit formula (Note that \red{\dfrac12}  

2

1

​

start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030 is the first term and \blue{-8}−8start color #6495ed, minus, 8, end color #6495ed is the constant ratio):

a(n)=\red{\dfrac12}\cdot\left(\blue{-8}\right)^{\large{\,n-1}}a(n)=  

2

1

​

⋅(−8)  

n−1

a, left parenthesis, n, right parenthesis, equals, start color #df0030, start fraction, 1, divided by, 2, end fraction, end color #df0030, dot, left parenthesis, start color #6495ed, minus, 8, end color #6495ed, right parenthesis, start superscript, n, minus, 1, end superscript

Note that this solution strategy results in this formula; however, an equally correct solution can be written in other equivalent forms as well.

Answer:

20 and 55

Step-by-step explanation:

Let's assume, we have two numbers 'x' and 'y'.

Now, all we know is:

So we form two equations:

x + y = 75_____(i)

and x - y =  35

so, x = y+35 _____(ii)

Put the value of x from (ii) into (i)

x + y = 75

y + 35 + y = 75

2y = 40

y = 20

Put value of y back in (ii)

x = y+35

x = 20 + 35

x = 55

The first number is 20, and the second number is 55.

Given that the sum of two numbers is 75, one exceeds the other by 35, we need to find the numbers.

Let's assume the first number is x.

According to the problem, the second number exceeds the first by 35, so the second number can be expressed as (x + 35).

The sum of the two numbers is given as 75, so we can set up the equation:

x + (x + 35) = 75

Simplifying the equation, we get:

2x + 35 = 75

Subtracting 35 from both sides:

2x = 40

Dividing both sides by 2:

x = 20

Therefore, the first number is 20, and the second number is (20 + 35) = 55.

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Answer : -5a² + 10a

It was way easy ikr ~w~

Answer:

-5a2+10a

Step-by-step explanation:

distribute

-5a(a-2)

-5a2+ 10

Answer:

5, 12, 13

Step-by-step explanation:

let x be the longer leg then x + 1 is the hypotenuse and x - 7 the shorter leg

Using Pythagoras' identity in the right triangle

x² + (x - 7)² = (x + 1)² ← expand using FOIL

x² + x² - 14x + 49 = x² + 2x + 1

2x² - 14x + 49 = x² + 2x + 1 ( subtract x² + 2x + 1 from both sides )

x² - 16x + 48 = 0 ← in standard form

(x - 4)(x - 12) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x - 12 = 0 ⇒ x = 12

x = 4 , then x - 7 = 4 - 7 = - 3 ← not possible

x = 12, then x - 7 = 12 - 7 = 5 and x + 1 = 12 + 1 = 13

The lengths of the 3 sides are

longer leg = 12 m , shorter leg = 5 m and hypotenuse = 13 m

Answer:

Explanation:

Step 1

Multiply the denominator by the whole number

7 × 7 = 49

Step 2

Add the answer from Step 1 to the numerator

49 + 6 = 55

Step 3

Write answer from Step 2 over the denominator

Answer = 55/7

Answer:

55/7

Step-by-step explanation:

To convert 7 6/7 to an improper fraction

Answer:

A

Step-by-step explanation:

Note the expansion

tan(a - b) = [tex]\frac{tana-tanb}{1+tanatanb}[/tex]

We are given the right side of the expansion , then left side is

tan([tex]\frac{\pi }{7}[/tex] - [tex]\frac{\pi }{8}[/tex] )

= tan([tex]\frac{8\pi -7\pi }{56}[/tex] )

= tan ([tex]\frac{\pi }{56}[/tex] ) → A