54 x 10 to the power of 4

The solutions of the rational equation x-1 / x+2 = x² + 2 x-3/x+2 are x = -2 and x = 1

In this question,

We have been given a rational equation.

x-1 / x+2 = x² + 2 x-3/x+2

We need to find the solution of given rational equation.

Here, the denominator is same on the both sides.

x-1 / x+2 = x² + 2 x-3/x+2

⇒ x - 1 = x² + 2 x-3

⇒ x² + 2x - 3 - x + 1 = 0

⇒ x² + x -2 = 0

We solve above quadratic equation.

⇒ x² + 2x - x - 2 = 0

⇒ x(x + 2) - (x + 2) = 0

⇒ (x + 2)(x - 1) = 0

⇒ x + 2 = 0                or          x - 1 = 0

⇒ x = -2        or         x = 1

Therefore, the solutions of the rational equation x-1 / x+2 = x² + 2 x-3/x+2 are x = -2 and x = 1

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Work Shown:

x = first integer

x+1 = second integer right after x

The two consecutive integers add to -207

(first) + (second) = -207

(x)+(x+1) = -207

2x+1 = -207

2x = -207-1

2x = -208

x = -208/2

x = -104 is the first integer

x+1 = -104+1 = -103 is the second integer

Check:

-104 + (-103) = -207

The answers are confirmed.

we  know she poured already 2 qts of a 62% sugar solution, hmmm how much will that be in quarts?  well, just (62/100) * 2 = 1.24 quarts.

we also know she wants to mixed say "x" quarts of a 38% sugar solution, how many quarts will that be?  well, (38/100) * x = 0.38x.

let's make a quick table from that as well as including the desired mixture.

[tex]\begin{array}{lcccl} &\stackrel{solution}{quarts}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{qts of }}{amount}\\ \cline{2-4}&\\ \textit{62\% solution}&2&0.62&1.24\\ \textit{38\% solution}&x&0.38&0.38x\\ \cline{2-4}&\\ desired~mixture&y&0.54&0.54y \end{array}\qquad \begin{cases} ~\hfill 2+x&=y\\\\ 1.24 + 0.38x &= 0.54y \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{substituting on the 2nd equation}}{1.24 + 0.38x ~~ = ~~ 0.54(\underset{y}{2 + x})}\implies 1.24+0.38x=1.08+0.54x \\\\\\ 0.16+0.38x=0.54x\implies 0.16=0.16x\implies \cfrac{0.16}{0.16}=x\implies \stackrel{qts}{1}=x[/tex]

Answer: 3

Step-by-step explanation:

Answer: A unit rate is when you need to convert between measurement systems. There is no picture for the points so this is all i can answer.

Step-by-step explanation:

Answer:

7th term = (-1)

rule for the nth term = an = a+(n-1)d

Step-by-step explanation:

a = 5, d = a2-a1 = 4-5 = -1, n = 7

an = a+(n-1)d

a7 = 5+(7-1)(-1)

a7 = 5-6

a7 = (-1)

Based on the elevation that the mountaineer has to climb of 6,282 meters, supplementary oxygen is needed because this distance is above 18,000 feet.

The limit for what is considered extremely high altitude is given in feet so the mountaineer's elevation of 6,282 meters needs to be converted to feet.

1 meter in feet is 3.28084 feet.

6,282 meters in feet is therefore:

= 6,282 x 3.28084

= 20,610.24 feet

This distance is more than the 18,000 feet above sea level which makes it extremely high altitude and so supplementary oxygen is needed.

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Answer:

Step-by-step explanation:

we cant see the question :)

Answer: If you have to fill in the chart I think you just add them together so aluminum would be +3, phosphide -3, iodide -1, and tin 0

Step-by-step explanation:

Answer: A. 4w+(-75)

B. 925

Step-by-step explanation:

The slope of the line with points (0,-1/2) and (7/5, 10) is 7.5

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope

We know that slope, slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

For the pairs of points (0,-1/2) and (7/5, 10)

⇒ m = [tex]\frac{10 - (-1/2)}{(7/5) - 0}[/tex]

⇒ m = [tex]\frac{21/2}{(7/5) }[/tex]

⇒ m = 15/2

⇒ m = 7.5

Hence, the slope of the line with points (0,-1/2) and (7/5, 10) is 7.5

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Answer:

14 to 8

Step-by-step explanation:

8 roses+6 daisies=14 is all the flowers in the vase

The division of given rational expression 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8 is 12x / x + 3 provided x ≠ -3

In this question,

we have been given a complex rational expression [tex]\frac{3x^{2} -9x}{x-2}\div \frac{x^2-9}{4x-8}[/tex]

We need to find the division of given rational expression.

We rewrite given rational expression as,

3x²-9 x / x-2 ÷ x² - 9 / 4 x-8

= 3x²-9 x / x-2 / x² - 9 / 4 x-8

= (3x²-9 x / x-2) × (4 x-8 / x² - 9 )

= [tex]\frac{3x(x-3)}{x-2}\times \frac{4(x-2)} {(x+3)(x-3)}[/tex]

= 12x / x + 3     .........(provided x ≠ -3)

Therefore, the division of given rational expression 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8 is 12x / x + 3 provided x ≠ -3

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Based on the information, it should be noted that the inequality to solve for m will be D. m + 6 < 8; m < 2.

It should be noted that in Mathematics, an inequality is used to show the expressions that are hot the same or equal.

Based on the information given about the triangle, it should be noted that the hypothenuse which is given as 8 is the longest side of the triangle.

Therefore, the inequality to solve for m will be:

m + 6 < 8.

Collect like term

m < 8 - 6

m < 2

Therefore, based on the information, it should be noted that the inequality to solve for m will be m + 6 < 8; m < 2.

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Answer:

The factor pairs of the number 48 are: 1 x 48, 2 x 24, 3 x 16, 4 x 12, and 6 x 8. When you multiply each of these factor pairs together, you get 48.

Step-by-step explanation:

1 x 48 = 48

2 x 24 = 48

3 x 16 = 48

4 x 12 = 48

6 x 8 = 48

HOPE IT'S HELP:)

Answer: X=3, Y=6 z=-1

Step-by-step explanation:

A triangle is a shape whose all three angles have a sum of 180 degrees. So from the above definition we know that:

P + Q + R = 180

Q=3P

T=P + 20

Therefore:

P + 3P + P + 20 = 180

5P + 20 = 180

5P = 160

P = 32

Q = 3(32) = 96

R = 32 + 20 = 52

To Additional Control P + Q + R = 32 + 96 + 52 = 180 °Degree

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Answer:

[tex]\displaystyle 25 = GQ[/tex]

Step-by-step explanation:

If point Q is the centre of GH, then QH and GQ are equivalent segments. So, double the length of GQ, set it equal to the length of GH, then solve for x:

[tex]\displaystyle \boxed{4x + 6} = 2[2x + 3] \\ \\ 5x - 5 = 4x + 6 \hookrightarrow -11 = -x \hookrightarrow \boxed{\boxed{11 = x}}[/tex]

Plug the result into the expression for the length of GQ to get twenty-five units.

I am joyous to assist you at any time.

Answer:

61 miles

Step-by-step explanation:

0.90 x 61 = 54.9

The fraction of the animals in chickens is 52/80 which is 0.65 in decimal form.

So, (A) The fraction of the animals is chickens: 52/80

Simplest form: 13/20

(B) In decimal form: 0.65

Therefore, the fraction of the animals in chickens is 52/80 which is 0.65 in decimal form.

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Answer: the midpoint of the segment is (6,5)

Step-by-step explanation:

(2,2)     (10,8)

[tex]\displaystyle\\ A_x=\frac{2+10}{2} \\\\A_x=\frac{12}{2} \\\\A_x=6[/tex]

[tex]\displaystyle\\A_y}=\frac{2+8}{2}\\ \\A_y=\frac{10}{2} \\\\A_y=5\\[/tex]

Thus, A(6,5)

The least common denominator for the rational expressions 1/x²-5x-6 and 1/x²-12 x+36 is  (x-6)(x+1)(x-6).

In the given question

[tex]=\frac{1}{x^{2} -5x-6} , \frac{1}{x^{2} -12x+36}[/tex]  ...(i)

First we will factor each denominator

So,

x²-5x-6

On splitting the factors of the above expression , we get

(x+1)(x-6)   ....(ii)

x²-12x+36

On splitting the factors of the above expression , we get

(x-6)(x-6)    ...(iii)

Substituting the value of (ii) and (iii) in (i) ,we get ;

[tex]=\frac{1}{(x+1)(x-6)} , \frac{1}{(x-6)(x-6)}[/tex]

As the LCM of denominator is the Least common denominator , we have

LCM of (x+1)(x-6) and (x-6)(x-6)

LCM=(x-6)(x+1)(x-6)

Hence the LCD is (x-6)(x+1)(x-6).

Therefore , the least common denominator for the rational expressions 1/x²-5x-6 and 1/x²-12 x+36 is  (x-6)(x+1)(x-6).

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Answer:

< 5 gigabytes

Step-by-step explanation:

Let the number of gigabytes be represented as: g

Under her cell phone plan, Nicole pays a flat cost of $35 per month and $5 per gigabyte. She wants to keep her bill under $60 per month.

Under $60 = less than (<) $60

Hence, our inequality equation is given as:

$35 + $5 × g < 60

35 + 5g < 60

Collect like terms

5g < 60 - 35

5g < 25

g < 25/5

g < 5 gigabytes

Therefore, the number of gigabytes she can use while staying within her budget less than 5 gigabytes

Answer: t=2

Step-by-step explanation:

[tex]1=t+\sqrt{2t} -3\\1-1=t+\sqrt{2t}-3-1\\0= t+\sqrt{2t} -4\\Thus,\\t+\sqrt{2t} -4=0\\Let`s\ \sqrt{t} =x\geq 0\\\Rightarrow\ x^2+\sqrt{2} x-4=0\\x^2-\sqrt{2} x+2\sqrt{2}x-4=0\\ x(x-\sqrt{2})+2\sqrt{2} ( x-\sqrt{2})=0\\ (x-\sqrt{2})(x+2\sqrt{2})=0\\\\x-\sqrt{2} =0\\ x-\sqrt{2}+\sqrt{2}=0+\sqrt{2} \\ x=\sqrt{2}\\ \Rightarrow\ t=(\sqrt{2})^2\\ t=2\\\\x+2\sqrt{2} =0\\x+2\sqrt{2} -2\sqrt{2} =0-2\sqrt{2} \\x=-2\sqrt{2} \notin(x\geq 0)[/tex]

⊂ Hey, ausemkattom2559 ⊃

Answer:

x = 1

Step-by-step explanation:

Solve each equation.

Check your solutions.

x /2 = x + 1/4

From the given: [tex]\frac{x}{2}=\frac{x+1}{4}[/tex]

Applying fraction cross multiply: [tex]\mathrm{if\;\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c}[/tex]

[tex]x\cdot \:4=2\left(x+1\right)[/tex]

Distribute:

[tex]x\cdot \:4=2x+2[/tex]

Subtract 2x from both sides:

[tex]x\cdot \:4-2x=2x+2-2x[/tex]

[tex]2x=2[/tex]

Divide both sides by 2:

[tex]\frac{2x}{2}=\frac{2}{2}[/tex]

x = 1

As a result, x = 1

We can substitute to check our solution:

1/2 = 1 + 1/4

1/2 = 1/2

Hence, x = 1

xcookiex12

9/12/2022

Answer:710.4

Step-by-step explanation:

Answer:

8xh h=hours

Step-by-step explanation:

8 times how ever much hour than that's all if there's tips well just add it to your answer

Answer:

= 0.377 liters

= 377 mililiters

Step-by-step explanation:

Volume of a regular cylindrical container = л r ² h

л = 3.1416   (aprox,)

r = radius

h = height = 15cm (half filled) = 15/2 = 7.5cm

then:

Volume = 3.1416 * (4cm)² * 7.5cm

volume = 3.1416 * 16cm² * 7.5cm

volume =  377 cm³      (aproximadly)

1 cm³ = 0.001 liters

377 cm³ = 0.001*377 = 0.377 liters = 377 mililiters

By using the fact that the two angles whose measures are expressed in terms of x are vertical angles, we will see that x = 8.

Then using that we will see that the measure of angle BAC is 63 degrees.

On the given diagram, we can see that the two angles whose measures are expressed in terms of x are vertical angles, thus, these two angles have the same measure, then we can write a linear equation that helps us to find the value of x, which is:

(2x + 3) = (4x - 5)

Solving the linear equation for x we get:

2x + 3 = 4x - 5

3 + 5 = 4x - 2x

8 = 2x

8/2 = x = 4

So we can see that the value of x is 4.

Now we want to find the measure of angle BAC.

We can see that the measure of angle BAC plus the measure of the angle to its right will be a right angle, then we can write:

m∠BAC + (4x - 5)° = 90°

Replacing the value of x we get:

m∠BAC + (4*8 - 5)° = 90°

m∠BAC + 27° = 90°

m∠BAC = 90° - 27° = 63°

We conclude that the measure of angle BAC is 63 degrees.

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The Simplified value is [tex]\frac{-3}{4} a^{2} +2b^{2}[/tex].

Like terms are defined as terms that have same variable and and same power.

For Example ; 2a² , 6a² are like terms.

In the given question ,

[tex]=-a^{2} +2b^{2} +\frac{1}{4} a^{2} \\ \\ =-a^{2} +\frac{1}{4} a^{2} +2b^{2}[/tex]

[tex]=a^{2}(-1+\frac{1}{4} )+2b^{2}[/tex]  ( taking a² common )

taking LCM and solving further we get

[tex]=a^{2} (\frac{-4+1}{4} )+2b^{2}[/tex]

[tex]=\frac{-3}{4} a^{2} +2b^{2}[/tex]

Therefore , The value by combining Like terms in -a² + 2b² + (1/4) a² is [tex]\frac{-3}{4} a^{2} +2b^{2}[/tex].

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