Marc solves the equation Latex: (\sqrt[4]{x})^3=5\textsf{.} His work is shown below. Step 1: Latex: (\sqrt[4]{x})^3=5 ( √ [ 4 ] x ) 3 = 5 Step 2: Latex: x^{\frac{3}{4} }=5 x 3 4 = 5 Step 3: Latex: x^{\frac{3}{4} \cdot \frac{4}{3} }=5^{\frac{4}{3} } x 3 4 ⋅ 4 3 = 5 4 3 Step 4: Latex: x=\sqrt[3]{5 \cdot 5 \cdot 5 \cdot 5} x = √ [ 3 ] 5 ⋅ 5 ⋅ 5 ⋅ 5 Step 5: Latex: x=5\sqrt[3]{\not{5} \cdot \not{5} \cdot\not {5} \cdot 5} x = 5 √ [ 3 ] ¬ 5 ⋅ ¬ 5 ⋅ ¬ 5 ⋅ 5 Step 6: Latex: x=5\sqrt[3]{5} x = 5 √ [ 3 ] 5 Explain what Marc did in steps 4 and 5. Why did he do this? Create your own radical equation and explain how to solve it. Is there an extraneous solution to your equation?

Answer:

1

Step-by-step explanation:

1 is the first natural number because 0 is not a natural number.

All natural numbers are numbers from 1 onward.

Ex. 1.2.3.4.5.6...

[tex] \green{\large\underline{\sf{Solution-}}}[/tex]

Given expression is

[tex]\rm :\longmapsto\:\dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } [/tex]

can be rewritten as

[tex]\rm \:  =  \: \dfrac{5 \times { {(5}^{2} )}^{n + 1} - {5}^{2} \times {5}^{2n} }{5 \times {5}^{2n + 3} - {( {5}^{2} )}^{n + 1} } [/tex]

We know,

[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ {( {x}^{m} )}^{n} \: = \: {x}^{mn}}}} \\ [/tex]

And

[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ \: \: {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}} \\ [/tex]

So, using this identity, we

[tex]\rm \:  =  \: \dfrac{5 \times {5}^{2n + 2} - {5}^{2n + 2} }{{5}^{2n + 3 + 1} - {5}^{2n + 2} } [/tex]

[tex]\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 4} - {5}^{2n + 2} } [/tex]

can be further rewritten as

[tex]\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 2 + 2} - {5}^{2n + 2} } [/tex]

[tex]\rm \:  =  \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2} - 1)} [/tex]

[tex]\rm \:  =  \: \dfrac{4}{25 - 1} [/tex]

[tex]\rm \:  =  \: \dfrac{4}{24} [/tex]

[tex]\rm \:  =  \: \dfrac{1}{6} [/tex]

Hence,

[tex]\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } = \frac{1}{6} }}[/tex]

Answer:

88 blankets

Step-by-step explanation:

5 times 15 = 75

75 + 13 = 88

Answer:

(3,7) is not a solution

Step-by-step explanation:

You fill in the values x=3 and y=7 in both equations and see if you end up with something that is true.

-5·3 - 2·7 = 23 is not true, because it simplifies to -29 = 23

no need to look further, but if you would, the second equation is also false:

3 + 4·7 = -19 is also not true.

The real solution by the way is (-3, -4).

[tex]\large\underline{\sf{Solution-}}[/tex]

Given that

[tex] \purple{\rm :\longmapsto\:Dividend = {x}^{3} - {2x}^{2} - x + 2}[/tex]

and

[tex] \purple{\rm :\longmapsto\:Divisor = x + 1}[/tex]

So, By using Long Division Method, we have

[tex]\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\: {x}^{2} - 3x + 2\:\:}}}\\ {\underline{\sf{x + 1}}}& {\sf{\: {x}^{3}  -  {2x}^{2} - x + 2 \:\:}} \\{\sf{}}& \underline{\sf{- {x}^{3} - {x}^{2} \: \: \:  \:  \:  \:  \:  \:  \:  \: \:\:}} \\ {{\sf{}}}& {\sf{\: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  - 3{x}^{2} - x +2  \:  \:  \:  \:   \:  \:  \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  3{x}^{2} + 3x  \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 2x + 2 \:\:}} \\{\sf{}}& \underline{\sf{\: \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \: - 2x - 2\:\:}} \\ {\underline{\sf{}}}& {\sf{\:\: \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 0\:\:}}  \end{array}\end{gathered}\end{gathered}\end{gathered}[/tex]

So,

[tex]\bf\implies \:Remainder = 0[/tex]

Verification

[tex] \purple{\rm :\longmapsto\:Dividend = {x}^{3} - {2x}^{2} - x + 2}[/tex]

[tex] \purple{\rm :\longmapsto\:Divisor = x + 1}[/tex]

[tex] \purple{\rm :\longmapsto\:Remainder = 0}[/tex]

[tex] \purple{\rm :\longmapsto\:Quotient = {x}^{2} - 3x + 2}[/tex]

Now, Consider

[tex]\rm :\longmapsto\:Divisor \times Quotient + Remainder[/tex]

[tex]\rm \:  =  \: (x + 1)( {x}^{2} - 3x + 2) + 0[/tex]

[tex]\rm \:  =  \: {x}^{3} - {3x}^{2} + 2x + {x}^{2} - 3x + 2[/tex]

[tex]\rm \:  =  \: {x}^{3} - {2x}^{2} - x + 2[/tex]

[tex]\rm \:  =  \: Dividend[/tex]

Hence, Verified

CARRY ON LEARNING

CAN YOU BRAINLEST ME PLEASE

Answer:

25

Step-by-step explanation:

remember that the pythagorean theorem is a²+b²=c²

so this equation would be:

7²+24²=c²

solve the exponents

49 + 576 = c²

combine like terms

625 = c²

take the radical of each number

√625 = √c²

25 = c

have a lovely day <3

Answer:

hope it helps you..........

Answer:

y=2.5x

Step-by-step explanation:

We have been given a graph that shows numbers of servings (y) in different amounts (x) of frozen yogurt listed on a carton.

To write an equation that gives the number of servings y in x pints, we will have to find the slope (rate of change) of our given linear function.

Since we know that rate of change of a function can be found by vertical change of the function divided by horizontal change of the function.  

m= Slope (rate of change).

=Difference between two y-coordinates.

=Difference between corresponding x-coordinates of the y-coordinates.    

Upon substituting coordinates of two points (0,0) and (4,10) in slope formula we will get,  

The slope of our given line is 2.5.  

Now we will write equation of our given line is slope-intercept form. The equation of a line in slope-intercept form is: , where m=slope and b = y-intercept (initial value).

Upon substituting m=2.5 and coordinates of point (4,10) in slope-intercept form of equation we will get,

Upon substituting m=2.5 and b=0 in slope-intercept form of equation we will get,

Therefore, the equation  will give the number of servings y in x pints.

Answer:

No

Step-by-step explanation:

Answer:

No, it will not be the same shade of green.

Step-by-step explanation:

For the shade of green to be equivalent that person would need both of the proportions to be equal weather it is 6/4 and 12/8 or 8/5 16/10.

The ratios 8/5 and 6/4 do not match therefore the green the batches make will not be equal.

I hope this helps :D

Answer:

N=20

Step by Step:

First you add 17 to both of the sides:

N−17+17=3+17

Second, you simplify;

N=20

Brainiest please?

Answer:D

Step-by-step explanation:

Answer:

4(x + 1/4) ≤ 9 + 2x

Step-by-step explanation:

Answer:

1) y=3.5+(5•x)

2) 103.5

3) No, because 5•20 is 100 and 5•10 is 50, BUT with both you still have to add 3.5 no matter what because of the $3.50 to pick up the rider

Answer:

im gonna go with c

Answer:

(X+1) (x - 4) (x+2)

Step-by-step explanation:

All the coefficients are integers so apply the rational zeros theorem.

The coefficient of x^3 is 1.

Divide (x^3-x2-10x-8)(x+1) = x^2-2x-8 with remainder = 0

The remainder is 0. (x+1) is a factor.

(x + 1) ( x^2 - 2x - 8)

x^2 - 2x - 8 (-4 * 2= 8) and -4 + 2 = -2)

= (x -4) (x+2)

Answer:

4

Step-by-step explanation:

x= 18÷4.5=4

hope it helps

Answer:

Your answer is 506.093.

Step-by-step explanation:

Hope this helps!

13. M=4/3

14. m=-6

Step-by-step explanation:

Answer:

the answer is the third one 3

The answer is x=−4 and y=−3

Answer:

-2

Step-by-step explanation:

It's (x,y)

Here, (3,-2)

-2 is y

:)

[tex] \sf \underline{ \red{Solution - }} \\ [/tex]

Given,

[tex] \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} }} \\ [/tex]

The denominator is √11 - √5.

We know that

Rationalising factor of √a-√b is √a+√b.

Therefore, the rationalising factor of √11-√5 is √11+√5.

On rationalising the denominator them

[tex] \longrightarrow \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} \times \dfrac{(\sqrt{11} + \sqrt{5})}{(\sqrt{11} + \sqrt{5})} }} \\ [/tex]

Multiplying (√11 + √5) with both the numerator of the fraction.

[tex] \longrightarrow \sf{\quad { \dfrac{-7(\sqrt{11} + \sqrt{5}) }{(\sqrt{11} - \sqrt{5})(\sqrt{11} + \sqrt{5})} }} \\ [/tex]

Performing multiplication in the numerator and by using identity (a + b)(a - b) = a² - b², solving further in the denominator.

[tex] \longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{(\sqrt{11})^2 - (\sqrt{5})^2} }} \\ [/tex]

Writing the squares of the numbers in the denominator.

[tex] \longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{11 -5} }} \\ [/tex]

Performing subtraction in the denominator.

[tex] \longrightarrow \quad \underline{ \boxed{ \dfrac{ \textbf{ \textsf{-7 }}\sqrt{ \textbf{ \textsf{11 }}} - \textbf{ \textsf{7}}\sqrt{ \textbf{ \textsf{5 }}}}{ \textbf{ \textsf{ 6}}}} } \\ [/tex]

Hence, the denominator is rationalised.

Answer:

(5,-12)

(-3,0)

(-1,-1)

Step-by-step explanation:

For (4, −12): 2(4) - 12 = 8 - 12 = -4                  [false]

For (−3, 0): 2(-3) = -6 < -4                                [false]

For (5, −12): 2(5) - 12 = 10 - 12 = -2 > -4         [true]

For (0, 1): 2(0) + 1 = 1 > -4                              [true]

For (−1, −1): 2(-1) - 1 = -2 - 1 = -3 > -4            [true]

Therefore, (5, -12), (0, 1) and (-1, -1) satisfies the inequality 2x + y > -4

For (7, 12): 12 - 2(7) = 12 - 14 = -2 > -3                   [false]

For (0, −2): -2 - 2(0) = -2 > -3                                   [false]

For (5, −3): -3 - 2(5) = -3 - 10 = -13 < -3                   [true]

For (−6, −3): -3 - 2(-6) = -3 + 12 = 9 > -3                  [false]

For (1, −1): -1 - 2(1) = -1 - 2 = -3                              [true]

Therefore, (5, -3) and (1, -1) satisfy the inequality y - 2x ≤ -3

The situation is represented by 2.25x + 2.65y ≥ 8

Answer:

hope this helps

Answer:

perimeter-3+6+3+10+6+4=32m

area- 10×6=60m²

Answer:

y = 2x - 1

Step-by-step explanation:

Slope = (5-1) / (3-1) = 4/2 = 2

y-intercept = 1 - (2)(1) = - 1

y = 2x - 1

Answer:

$130.00

Step-by-step explanation:

674-284=390

390/3=130

what that person said :(

Answer:

the answer would be:

g(X)

and

m(X)

Step-by-step explanation:

make me as Brainliest sorry if I am wrong

Answer:

Step-by-step explanation:

Answer:

207 cm

Step-by-step explanation:

Because ΔPQR ≅ΔSTU and the longest side in the ΔPQR is RP then the longest side in ΔSTU must be SU = 92 cm

Perimeter of triangle PQR is

P(ΔPQR) = 36+48+24 = 108 cm

Because the triangles are are similar their sides are in proportion.

But how much bigger did the second triangle get?...is (92/48) times bigger

P(ΔSTU) = 180*(92/48) = 207 cm

...you can also use proportions to find each side and then find the perimeter

TU = 24*92 /48 = 46

TS = 36*92/48 = 69

SU = 92

P(ΔSTU) = 92+69+46 =207 cm

*the triangles are not drawn to scale

Answer:

m=-2/-1 or m=-2

Step-by-step explanation:

Find two points on the line, then use this formula:  m=rise/run  or m=y2-y1/x2-x1

m=0- 2/-3-(-2)

m=-2/-1 or m=-2