[tex] {3}^{x} = 243[/tex]

Answer:

x = 4

Step-by-step explanation:

4x+41=3x+45

Subtract 3x from both sides

x + 41 = 45

Subtract 41 from both sides

x = 4

The equation[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4)[/tex]  is a representation of the Difference of Powers formula in algebra. This formula can be proven accurate by expanding the expression on the right hand side and simplifying.

Your question essentially asks about the proof of a formula in algebra known as the Difference of Powers. This formula is applied when you have a difference of two terms, each raised to the same power.

Let us prove[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4):[/tex]

This demonstrates that the original formula you asked about is accurate.

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The distributive property: a(b + c) = ab + ac

Answer:

c) -3 · (6.48) = -3 · (6 + 0.4 + 0.08) = (-3 · 6) + (-3 · 0.4) + (-3 · 0.08)

Step-by-step explanation:

Answer:

He paid $6,000 in taxes.

Step-by-step explanation:

His final amount after taxes is $24000.  In order to obtain this number we had to tax 20% of the total (Note that 100%-20%=80%).  In other words if he was taxed 20% he took home 80% of what he was paid.  Therefore mathematically we have:

[tex]0.8A_{pre-tax}=A_{taxed}[/tex]

Since we know he was left with $24000 after taxes then:

[tex]0.8A_{pre-tax}=24000\\\\\frac{0.8A_{pre-tax}}{0.8}=\frac{24000}{0.8}\\\\A_{pre-tax}=\frac{24000}{0.8}\\\\A_{pre-tax}=30000[/tex]

So originally he had $30,000.  So how much did he pay in taxes? We can calculate the difference of both pretax and after tax and we get:

$30,000 - $24,000= $6,000 taxed

Answer:

D) x ≤ -2

Step-by-step explanation:

The dot is at -2 = -2

the dot is filled in = ≤ or ≥ because its means equal too

think of ≤ or ≥ like arrows = it points left.  

so its x ≤ -2

Note on using the  ≤ or ≥  like pointing arrows

this only works if its written:

variable <   constant form,

which is the way they are usually seen, like x < 5

but it could be 5 > x which means the > points the opposite way

Hello! :)

Answer:

D. x≤-2

*The answer must have a negative sign and less than or equal to.*

Step-by-step explanation:

Lesson: It's about the graphing inequalities

An inequality is a statement that compares mathematical expressions that are not equal. The expressions are separated by an inequality symbol (<,>, ≤, ≥, or ≠).

The arrow points to the left. The circle is closed.

Hope this helps!

Have a nice day! :)

:D

-Charlie

Thanks!

Answer:

x = .140741

Step-by-step explanation:

0.7(3x−0.2)=0.3(0.8−2x)

Distribute

.7 * 3x - .7*.2 = .3*.8 - .3 * 2x

2.1x - .14 = .24 - .6x

Add .6x to each side

2.1x +.6x -.14 = .24 -.6x+.6x

2.7x -.14 = .24

Add .14 to each side

2.7x -.14+.14 = .24+.14

2.7x = .38

Divide by 2.7 on each side

2.7x/2.7 = .38/2.7

x = .140741

Answer:

Step-by-step explanation:

lets say in the shown triangle x=165

so speed [tex]\frac{dx}{dt} =25[/tex]

and  [tex]\frac{dy}{dt} =35[/tex]

Also since distance = speed* time

time = pi minutes = pi/60 seconds

y = [tex]\frac{35\pi \pi }{60}[/tex]

y = [tex]\frac{7\pi }{12}[/tex]

Now using the pythagorean :

[tex]x^2+y^2=z^2\\so \\165^2+(\frac{7\pi }{12} )^2 =z^2[/tex]

derivate the equation so  we get :

[tex]x\frac{dx}{dt} +y\frac{dy}{dt} =z\frac{dz}{dt} \\[/tex][tex]165*25+35*\frac{7\pi }{12}=\sqrt{165^2+(\frac{7\pi }{12})^2} *\frac{dz}{dt}[/tex]

[tex]\frac{dz}{dt} =25.387[/tex] m/s

So Rate of change = 25.387 m/s

Answer:

Step-by-step explanation:

35 x .08 = $2.80

35 + 2.80 = 37.80

Answer:

T = 0.08 × 35

Step-by-step explanation:

The cost of a jacket = $35

The tax rate on the jacket = 8% =  [tex]\frac{8}{100}[/tex]

                                           = 0.08

The expression to find the cost of the tax on the jacket would be

T = 0.08 × 35

Two lines perpendicular to a third line are parallel to each other because they both inherit the slope from their perpendicularity. The resulting lines only differ in their y-intercepts, indicating they run parallel.

The theorem you're referring to essentially relates to the slope of the lines. If two lines are each perpendicular to the same line, this means the slope of all three lines are related. This occurs because the slope of any line perpendicular to y=-1/3x is 3, the negative reciprocal of -1/3. For example, if we have two lines L1: y = 3x + b1 and L2: y = 3x + b2 which are both perpendicular to y= -1/3x (and thus parallel to each other), their formulas would only differ by their y-intercepts (b1 and b2). Since the coefficient of x (the slope) remains the same (3), we can conclude that these two lines are indeed parallel to each other which confirms the mentioned geometric theorem.

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Answer:

The expression represents

[tex]a\geq\frac{1}{4}\times (10^{-2})[/tex] and solution is   [tex]a \geq 0.0025[/tex]  

Step-by-step explanation:

Given : Expression represents a number one fourth as great as [tex]10^{-2}[/tex]

To find : What is the expression?

Solution :

Let the number be 'a'.

According to question,

A number one fourth as great as [tex]10^{-2}[/tex]

i.e.  [tex]a\geq \frac{1}{4}\times (10^{-2})[/tex]

Now, we solve the expression

[tex]a \geq \frac{1}{4}\times\frac{1}{100}[/tex]

[tex]a \geq\frac{1}{400}[/tex]

[tex]a \geq 0.0025[/tex]

Therefore, The expression represents

[tex]a\geq\frac{1}{4}\times (10^{-2})[/tex] and solution is   [tex]a \geq 0.0025[/tex]

Answer:

97/100

Step-by-step explanation:

9/10 = 90/100

90/100 + 7/100 = 97/100

Answer:

The given sequence is neither arithmetic not geometric.

Step-by-step explanation:

A sequence is in arithmetic if it has a common difference.

i.e., a sequence a, b, c is in arithmetic if

b - a = c - b

Let's check if the given sequence is in arithmetic.

[tex]\frac{4}{3} -\frac{4}{9} =\frac{12}{9} -\frac{4}{9}[/tex]

[tex]= \frac{8}{9}[/tex]

[tex]4-\frac{4}{3} =\frac{12-4}{3}[/tex]

[tex]=\frac{8}{3}[/tex]

So, [tex]\frac{4}{3} -\frac{4}{9} \neq 4-\frac{4}{3}[/tex]

Hence, the given sequence is not arithmetic.

Let's check if the given sequence is in geometric.

A sequence is in geometric if it has a common ratio.

i.e., a sequence a, b, c is in geometric if

[tex]\frac{b}{a} =\frac{c}{b}[/tex]

[tex]\frac{4/3}{4/9} =\frac{4}{3} (\frac{9}{4} )[/tex]

= 3

[tex]\frac{4}{4/3} =4(\frac{3}{4} )[/tex]

= 3

Clearly, [tex]\frac{12}{4} =\frac{36}{12} =3[/tex]

But, [tex]\frac{0}{36} =0[/tex]

Therefore, the given sequence is not in geometric.

Hence, the given sequence is neither arithmetic not geometric.

Answer:

55 + 14 sqrt(6)

Step-by-step explanation:

(7+√6)(7+√6)

We can figure out this problem by FOILing

First : 7*7 = 49

Outer: 7* sqrt(6) = 7 sqrt(6)

Inner:  7* sqrt(6) = 7 sqrt(6)

Last: sqrt(6) * sqrt(6) = 6

Add these together

49+ 7 sqrt(6)+ 7 sqrt(6)+6

55 + 14 sqrt(6)

Answer:

X=28

Step-by-step explanation:

3x-8=2x+20. So x=28

I would say B. The mean is a good measure of central tendency.

I hope this helps!

Answer:

y-2 = 2/3(x-8)

Step-by-step explanation:

We have the line 6x-9y = -7

Let's rewrite it in the form y=mx+b

6x-9y = -7

Subtract 6x from each side

6x-6x-9y = -7 -6x

-9y = -6x-7

Divide by -9

-9y/-9 = -6x/-9 -7/-9

y = 2/3 x + 7/9

The slope is 2/3

If the line is parallel, the slope will be the same so the slope will be 2/3

We have the slope and a point (8,2) on the new line, so we can use the point slope form of a line

y-y1 = m(x-x1)

y-2 = 2/3(x-8)

Answer:

40

Step-by-step explanation:

5+1 3/8n=60

Subtract 5

1 3/8n=55

11/8n=55

8/11(55/1)  

n=40

Answer:

She gave away 24 cards

Step-by-step explanation:

(36)*([tex]\frac{2}{3}[/tex])=24

Answer:

Consider the following cases

Case 1: In n first gear,  an automobile's engine runs about three times as fast as the drive shaft.

So, if Speed of Engine = 1,850 r.p.m

Then Speed of Drive Shaft  [tex]=\frac{1850}{3}=616.67[/tex] r.p.m

Case 2 : In second gear, the engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft.

 So, if Speed of Engine = 1,850 r.p.m

Then Speed of Drive Shaft  [tex]=\frac{1850}{1.6}=1156.25[/tex] r.p.m

Case 3:  Finally, in third, or high gear, the engine runs at the same speed as the drive shaft.

So, if Speed of Engine = 1,850 r.p.m

Then Speed of Drive Shaft is also equal to 1,850 r.p.m

Answer:

y = [tex]\frac{1}{2}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y-intercept )

here m = [tex]\frac{1}{2}[/tex] and b = 4, hence

y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line

Answer:

where is the question?

Answer: B - 3/40

Step-by-step explanation: in order to find their difference, set up their common denominators equally, resulting in them having 5/40 and 8/40. subtract and you will get 3/40 as your final answer.

Answer:

D

Step-by-step explanation: 1/3 x 3 = 1/9 same with 2/3

Answer:

B is the one here as well

Answer:

0.707 to nearest thousandth

Step-by-step explanation:

People who go at least 2 times a month = 219 + 180 + 96

= 495

So the required probability = 495 / 700

= 0.707 14

Answer: -2,0,2,4,6

The solution of the inequality is x<1

Step-by-step explanation:

Answer:

x < 1

Step-by-step explanation:

2x < 2

Divide 2 on both sides

x < 1

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

Table: (I think)

-2 , 0 , 2 , 4 , 6

Answer: The answer is 12 days

Step-by-step explanation: miles total=miles per day times number of days

3000=250 times days

divide both sides by 250

12=days

Answer:

r= -5 , r= 17

Step-by-step explanation:

5|-6+r|=55

solve for 'r'

First we isolate absolute function

We divide both sides by 5

|-6+r| = 11

for absolute function we consider two cases, one with positive and one with negative. Now we make two equations

-6+r = 11   or -6+r = -11

Now solve both equations

-6 + r= 11

Add 6 on both sides

so , r= 17

-6 + r= -11

add 6 on both sides , so r= -5

Answer:

2/25 chance for both.

Step-by-step explanation:

There is a total of 25 students = 25 as my denominator.

11 + 12 = 23.

25 -23 = 2

Therefore my numerator is 2.

----> 2/25

Answer:

x=12

Step-by-step explanation:

Solve for x:

(3 (x/6 + 16))/4 = (3 ((4 + 3/8) x - 21))/7

Put 4 + 3/8 over the common denominator 8. 4 + 3/8 = (8×4)/8 + 3/8:

(3 (x/6 + 16))/4 = (3 ((8×4)/8 + 3/8 x - 21))/7

8×4 = 32:

(3 (x/6 + 16))/4 = (3 ((32/8 + 3/8) x - 21))/7

32/8 + 3/8 = (32 + 3)/8:

(3 (x/6 + 16))/4 = (3 ((32 + 3)/8 x - 21))/7

32 + 3 = 35:

(3 (x/6 + 16))/4 = (3 ((35 x)/8 - 21))/7

Put each term in x/6 + 16 over the common denominator 6: x/6 + 16 = x/6 + 96/6:

3/4 x/6 + 96/6 = (3 ((35 x)/8 - 21))/7

x/6 + 96/6 = (x + 96)/6:

3/4 (x + 96)/6 = (3 ((35 x)/8 - 21))/7

3/6 = 3/(3×2) = 1/2:

(x + 96)/(2×4) = (3 ((35 x)/8 - 21))/7

Put each term in (35 x)/8 - 21 over the common denominator 8: (35 x)/8 - 21 = (35 x)/8 - 168/8:

(x + 96)/(2×4) = 3/7 (35 x)/8 - 168/8

(35 x)/8 - 168/8 = (35 x - 168)/8:

(x + 96)/(2×4) = 3/7 (35 x - 168)/8

2×4 = 8:

(x + 96)/8 = (3 (35 x - 168))/(8×7)

8×7 = 56:

(x + 96)/8 = (3 (35 x - 168))/56

Multiply both sides by 56:

(56 (x + 96))/8 = (56×3 (35 x - 168))/56

56/8 = (8×7)/8 = 7:

7 (x + 96) = (56×3 (35 x - 168))/56

(56×3 (35 x - 168))/56 = 56/56×3 (35 x - 168) = 3 (35 x - 168):

7 (x + 96) = 3 (35 x - 168)

Expand out terms of the left hand side:

7 x + 672 = 3 (35 x - 168)

Expand out terms of the right hand side:

7 x + 672 = 105 x - 504

Subtract 105 x from both sides:

(7 x - 105 x) + 672 = (105 x - 105 x) - 504

7 x - 105 x = -98 x:

-98 x + 672 = (105 x - 105 x) - 504

105 x - 105 x = 0:

672 - 98 x = -504

Subtract 672 from both sides:

(672 - 672) - 98 x = -672 - 504

672 - 672 = 0:

-98 x = -672 - 504

-672 - 504 = -1176:

-98 x = -1176

Divide both sides of -98 x = -1176 by -98:

(-98 x)/(-98) = (-1176)/(-98)

(-98)/(-98) = 1:

x = (-1176)/(-98)

The gcd of -1176 and -98 is -98, so (-1176)/(-98) = (-98×12)/(-98×1) = (-98)/(-98)×12 = 12:

Answer:  x = 12

30/2 =15. So 182 times 15 is 2730, or D.