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

Determine Whether 7^2m 6^2m Is Equivalent To Each Of The Following Expressions:42^6m42^m42^9m

Answers

Answer 1

Answer:

Not equivalent to any of the options

Step-by-step explanation:

Given:

7^2m * 6^2m

Since, they both have different bases, multiply the bases and add the powers

7^2m * 6^2m

= (7 * 6)^(2m + 2m)

= 42^4m

Therefore,

7^2m * 6^2m is equivalent to 42^4m

A. 42^6m

Not equivalent

B. 42^m

Not equivalent

C. 42^9m

Not equivalent


Related Questions

A brick is in the shape of a rectangular prism with a length of 6 inches, a width of 3 inches, and a height of 5.5 inches. The brick has a density of 2.7 grams per cubic centimeter. Find the mass of the brick to the nearest gram.

pls pls pls help

Answers

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

What is the intersecting point of these two lines?
1. y = 3/4x + 6
2. y = x + 1

Answers

The answer is Y=3/4x + 6

Can someone help me on this please

Answers

The choices :

Three

B , E , D

please someone help me! asap!!

Answers

Answer:

Last option= 30 minutes

Find an explicit formula for the geometric sequence \dfrac12\,,-4\,,\,32\,,-256,.. 2 1 ​ ,−4,32,−256,..start fraction, 1, divided by, 2, end fraction, comma, minus, 4, comma, 32, comma, minus, 256, comma, point, point. Note: the first term should be \textit{a(1)}a(1)start text, a, left parenthesis, 1, right parenthesis, end text. a(n)=a(n)=a, left parenthesis, n, right parenthesis, equals

Answers

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.

Can someone help me with this please !!

Answers

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.

round to the nearest underlined place 18 904 A. 18,000 B. 19,000 C. 20,000 D. 18,920

Answers

Answer:

B 19,000

Step-by-step explanation:

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

Evaluate the expression. Question 9 options: A) tan π∕56 B) tan 17π∕56 C) –tan 17π∕56 D) –tan π∕56

Answers

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

Convert 7 6/7 into an improper fraction.

Answers

Answer:

55/7

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

I hope you are enjoying your day and that this helps you out! Brainliest would be appreciated :)

Answer:

55/7

Step-by-step explanation:

To convert 7 6/7 to an improper fraction

Start by multiplying the whole number with the denominator 7 x 7 = 49Then add the numerator to the number you get 49 + 6 = 55 The 55 will be your numerator for your improper fraction. 55/7 The denominator will remain the same

Find the coordinate of J' after a reflection of the triangle about the y-axis. Write your answer in the form (a,b)

Answers

Answer:

A (3,3)

J (5,2)

L (0,0)

Step-by-step explanation:

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

Find: (6m5 + 3 – m3 – 4m) – (–m5 + 2m3 – 4m + 6)

Answers

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

An equilateral triangle has a perimeter of 18 feet. If a square whose sides have the same length as one side of the triangle is built, what will be the area of the square?

Answers

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.

Find the area of the figure.

Answers

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 :)

What is the smallest prime number that is also a multiple of 20?

Answers

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.

Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

square root of the quantity x plus 7 end quantity minus 1 equals x

Answers

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

Factor the polynomial and explain answer

Answers

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)

-8, 5 hope this helps!

Will Mark Brainlest Help Please ,,,, ​

Answers

[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]

Put the value

[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]

Put in eq(1)

[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

Given that cos 75 = X, show that cos 105 = −X

Answers

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)

Please Help Asap Its Pre-Calculus

The point (−2, 2) is a solution to which of the following systems?

y > −2x + 2 and y > x + 5
y < x + 2 and y > x − 1
y < 2x + 8 and y ≥ −x − 3
y < 2x + 3 and y ≥ −2x − 5

Answers

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:

[tex]y>-2x+2[/tex] and [tex]y>x+5[/tex] [tex]y<x+2[/tex] and [tex]y>x-1[/tex] [tex]y<2x+8[/tex] and [tex]y \geq -x-3[/tex] [tex]y<2x+3[/tex] and [tex]y \geq -2x-5[/tex]

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:

https://brainly.com/question/17174433


A manufacturer of radio sets produced 600 units in the third year and 700 units in the
seventh year. Assuming the production uniformly increases by a fixed number every year,
the production in the first year is
b) 530
d) 570
a) 500
c) 550

Answers

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.

I could really use a hand

Answers

Answer : -5a² + 10a

It was way easy ikr ~w~

Answer:

-5a2+10a

Step-by-step explanation:

distribute

-5a(a-2)

-5a2+ 10

please help, i don't understand the subject so i need an answer to help me out:) i will give brainliest to a good answer.

Answers

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.

The sum of two numbers is 75. If one exceeds the other by 35, find the numbers.

Answers

Answer:

20 and 55

Step-by-step explanation:

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

Now, all we know is:

one number exceeds the other by 35 (i.e  their difference is 35)sum of two numbers is 75

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.

Learn more about numbers click;

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PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU K NOW THE ANSWER!!
The entire group of objects or individuals under consideration in a survey is the ________________.
A. population
B. establishment
C. corporation
D. entity

Answers

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.

Question 10 The hypotenuse of a right triangle is I m longer than the longer leg. The other leg is 7 m shorter than the longer leg. Determine the lengths of the three sides of the triangle. (3 marks)​

Answers

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

Find the value of b. PLEASE HELP ASAPPPP!!!!
A. 56
B. 140
C. 230
D. 65

Answers

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

solve for x.
solve for x.
solve for x.

Answers

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

WILL MARK BRAINLIEST!!
Angelica uses the point 4,3 to represent the location of her house and uses the point 10,8 to represent the location of a gas station. Each unit on the graph represents 1 mi. How far is the gas station from Angelica’s house? Show your work.

Answers

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.

Find the 6th term of each geometric sequence. 9, 45, 225, 1125

Answers

Answer:

28125    

Step-by-step explanation:

Refer to the image below.

Answer pls……………………….

Answers

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

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