Are the equations 6x-6=3x and x-1=3x equivalent?​

Answer:

x = 16

Step-by-step explanation:

Let the second number be x.

The first number = 2x

The third number = 2×2x = 4x

2x + x + 4x = 112

7x = 112

x = 112/7

x = 16

Answer:

4×(x+1)(3x-8)(x+4)= (4x²+4)(3x-8)(x+4)= (12x³-32x²+12x²-32)(x+4)= (12x³-20x²-32)(x+4)= 12x⁴+48x³-20x³-80x²-32x²-128x= 12x⁴+28x³-112x²-128x

Answer:

105

Multiples of 35:
35, 70, 105, 140, 175

Multiples of 21:
21, 42, 63, 84, 105, 126, 147

Answer:

105

Step-by-step explanation:

Given the following question:

We are given two numbers and we are trying to find the least common multiple (LCM) of the two. In order to find the LCM we have to find the GCM or the greatest common multiple.

[tex]35\div7=5[/tex]
[tex]21\div7=3[/tex]
[tex]GCM=7[/tex]

Now that we have the GCM we multiply 35, and 21 then divide it by the GCM.

[tex]35\times21=735[/tex]
[tex]735\div7=105[/tex]
[tex]LCM=105[/tex]

The least common multiple is "105."

Hope this helps.

Answer:

x= 0.21428571428 or x=0.2

Step-by-step explanation:

-7x+7x^2=9  1. simplify 7x^2

-7x+ 7x(7x)=9   2. combine like terms

-7x+49x=9    3. combine like terms

42x=9           4. /42 on both sides

x= 0.21428571428 or x=0.2

=========================================================

Explanation:

Points Q and R have the same y coordinate of 6.

This means they're on the same horizontal level and we can form a number line through these points. Think of Q and R being on the x axis.

Going from -4 to 8 is a distance of 12 units because either

-4-8 = -12 which flips to +12 or 12

8-(-4) = 8+4 = 12

Effectively I used absolute value for the first part to go from -12 to 12. Distance cannot be negative.

Alternatively, you can count out the number of horizontal spaces from -4 to 8 and you should count out 12 units.

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

If you need to use the distance formula, then this is what the steps may look like:

[tex]Q = (x_1,y_1) = (-4,6) \text{ and } R = (x_2, y_2) = (8,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-8)^2 + (6-6)^2}\\\\d = \sqrt{(-12)^2 + (0)^2}\\\\d = \sqrt{144 + 0}\\\\d = \sqrt{144}\\\\d = 12\\\\[/tex]

In my opinion, the distance formula is overkill because we can simply apply subtraction or count out the number of spaces. It's up to you which you prefer you like better. Of course be sure to follow all instructions your teacher mentions.

If the two points weren't on the same horizontal level, then we would have no choice and have to use the distance formula. Or you could use the pythagorean theorem which is effectively what the distance formula is derived from.

The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth if  you have $1000 and need to buy 10 chairs worth $5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that you have $1000 and need to buy 10 chairs worth $5. Let x represent the money that can be spent on the booth, hence:

x + 10(5) ≤ 1000

The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth, if you have $1000 and need to buy 10 chairs worth $5.

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Answer:

3

Step-by-step explanation:

blue, white, and red colors

Answer:

[tex] 4x^2y\sqrt[4]{3y} [/tex]

Step-by-step explanation:

[tex] \sqrt[4]{768x^8y^5} = [/tex]

[tex] = \sqrt[4]{256 \times 3(x^2)^4y^4y} [/tex]

[tex] = \sqrt[4]{4^4 \times 3(x^2)^4y^4y} [/tex]

[tex] = 4x^2y\sqrt[4]{3y} [/tex]

Answer:

  B.  0.95

Step-by-step explanation:

The probability that the value of the random variable is in the given range is the area under the normal probability distribution curve over that range. The value of this area is conveniently provided by any number of calculators, apps, or spreadsheets. It can also be determined using the "empirical rule" that tells you the probability over certain normalized ranges.

__

A standard normal probability density function (PDF) has a mean of 0 and a standard deviation of 1. The range in this problem can be normalized to some number of standard deviations above or below the mean. The mean is given as 46, and the standard deviation is given as 22.

In this problem, the lower limit of the range is ...

  z = (2 -46)/22 = -2

standard deviations from the mean.

Similarly, the upper limit is ...

  z = (90 -46)/22 = +2

standard deviations from the mean.

The empirical rule tells us that 95% of the area of the PDF lies between -2 and +2 standard deviations from the mean.

  P(2 < X < 90) ≈ 0.95

_____

Additional comment

The empirical rule for other ranges is ...

  ± 1 standard deviation: 68%

  ±2 standard deviations: 95%

  ±3 standard deviations: 99.7%

Answer:

300+(300 + 0.23x)

Step-by-step explanation:

I'm not sure what you are asking but this is the only equation I can get

Answer:

Step-by-step explanation:

Comment

There was a flat fee of 10 dollars

Each 1/4 hour brought in 3,75

The total charge was 55 dollars.

Equation

Charge = 10 + 4*3.75*x                     as an hourly rate,

Solution

55 = 10 + 4*3.75x                                Combine

55 = 10 + 15x                                       Subtract 10 from both sides

55-10= 10-10 + 15x

45 = 15x                                               Divide by 15

45/15 = 15x/15

x = 3 hours

Answer 3 hours  

Answer:

(2x-11)(2x+11)

Step-by-step explanation:

2x-11 × 2x+11 yields

4x^2 + 22x -22x +121

22x subtracts itself and final result is

4x^2 -121

Answer:

height = 7

Step-by-step explanation:

[tex]2\cdot\frac{42}{8.7 + 3.3} = 7[/tex]

A major arc is an arc that is greater than 180 degrees.

A minor arc is an arc less than 180 degrees.

An acute angle is an angle less than 90 degrees.

A central angle is an angle created in the center of a circle with 2 sides being the radius.

Thus, we can see in the figure that we are talking about the angle so we can eliminate the major arc and minor arc.

Now, we clearly see that the angle is greater than 90 degrees so it cannot be an acute angle.

The correct answer is the central angle as it goes with the definition.

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Answer:

Slope is undefined.

Step-by-step explanation:

Answer:

[tex]\frac{\left(3x^2-6x+3\right)}{\left(x-1\right)3x-93x^2-3x^3x-33x^2-6}: -\frac{\left(x-1\right)^2}{x^4+41x^2+x+2}[/tex]
[tex]\frac{3x^2-6x+3}{\left(x-1\right)\cdot \:3x-126x^2-3x^3x-6}[/tex]
[tex]\frac{3\left(x-1\right)^2}{\left(x-1\right)\cdot \:3x-126x^2-3x^3x-6}[/tex]
[tex]\frac{3\left(x-1\right)^2}{-3\left(x^4+41x^2+x+2\right)}[/tex]
[tex]\frac{\left(x-1\right)^2}{-\left(x^4+41x^2+x+2\right)}[/tex]
[tex]-\frac{\left(x-1\right)^2}{x^4+41x^2+x+2}[/tex]

Answer:

3x-3

Step-by-step explanation:

use synthetic division

Answer:

[tex]x = 2, 4[/tex]

Step-by-step explanation:

Given :

[tex]\frac{4-x}{x^{2} -5x+4} + \frac{2}{x-1} =1[/tex]

=============================================================

Factorize the denominator of the first term :

⇒ x² - 5x + 4

⇒ x² - x - 4x + 4

⇒ x(x - 1) - 4(x - 1)

⇒ (x - 4)(x - 1)

============================================================

Hence, the equation now is :

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

============================================================

Multiply the second term by (x - 4) in the numerator and denominator :

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

============================================================

Combine the numerator of both terms and bring the denominator to the other side :

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

[tex]4 - x+2x-8 = x^{2} - 5x + 4[/tex]

[tex]x - 4 = x^{2} - 5x + 4[/tex]

[tex]x^{2} -5x-x+4+4=0[/tex]

[tex]x^{2} -6x+8=0[/tex]

[tex](x-4)(x-2)=0[/tex]

[tex]x = 2, 4[/tex]

The volume of the rectangular piece with sides of lengths of 7.08 × 10–3 m, 2.18 × 10–2 m, and 4.51 × 10–3m is 6. 96 × 10^ -7 m

Volume is defined as the amount of space or capacity occupied by a three-dimensional shape.

It is represented in cubic units.

Formula:

Volume, V = length × breadth × height

Given the values;

7. 08 × 10 ^-3m , 2.18 × 10^ -2m and 4. 51 × 10^-3m

Multiply all the lengths

Volume = 7. 08 × 10 ^-3 × 2.18 × 10^ -2 × 4. 51 × 10^-3

= 69.6 × 10^-8

= 6. 96 × 10^ -7 m

Therefore, the volume of the rectangular piece is 6. 96 × 10^ -7 m

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Answer:

A

Step-by-step explanation:

trust

Answer:

290

Step-by-step explanation:

Formula :

Number of action figures on wall = Total number of figures × % of figures on wall

=============================================================

Given :

⇒ Total number of action figures = 500

⇒ % of action figures on wall = 58%

=============================================================

Solving :

⇒ Action figures on wall = 500 × 58%

⇒ Action figures on wall = 500 × 58/100 (all % are ratios of 100%)

⇒ Action figures on wall = 5 × 58

⇒ Action figures on wall = 290

Total action figures

Done!

A parallel line has the same slope as the original line. So in this case the slope of the line is also 3/4. Now how do we know if it intersects the point? We need to adjust the y intercept.



Currently, we know the equation of the line is y= 3/4 x + b, where b is the thing we are looking for. We also have a point, which supplies the x and y. Plug that in and solve for b

-2 = (3/4)*(12) + b

You'll get b= -11

So the equation of the parallel line intersecting the point given is y= 3/4x -11.

I am assuming that the slope is 3/4 based on the way you formatted the original equation, but it's the same steps if the slope is different.

Answer:

2 1/6

Step-by-step explanation:

The answer is 2 1/6 because you should start by adding 3 1/2 + 2 1/3. This equals 5 5/6 feet. You should then subtract 8 - 5 5/6 because you are figuring out how much is left. When you subtract 8 - 5 5/6, you get 2 1/6. So 2 1/6 feet of the board is left.

Hope this helps!

The material wasted is 7915.375 sq cm.

The product of its length and breadth.

Area = length* breadth

Given:

length= 150 ac, breadth = 100 cm

d= 0.9m 5cm

r= 47.5 cm

Area of rectangle,

= l * b

= 150*100

= 15000 sq. cm

Area of Circular cloth,

= πr²

=3.14*47.5*47.5

=7084.625 sq cm.

Hence, the wasted material is = 15000-7084.625

                                                  = 7915.375 sq cm

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Answer:

y= -1/2x+5

Step-by-step explanation:

The factorization is  [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³

To answer the question, w e need to know what factorization is

Factorization is the breaking down of a larger expression into smaller expression by grouping it into its factors.

So, [{(a² - 25b²}³ + {25b² - 9c²}³ + {9c² - a²}³)/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

= [{(a² - (5b)²}³ + {(5b)² - (3c)²}³ + {(3c)² - a²)})/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

Using the fact that x² - y² = (x + y)(x - y) in the terms in the numerator, we have

[{(a - 5b)(a + 5b)}³ + {(5b - 3c)(5b + 3c)}³ + {(3c - a)(3c + a)}³/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

Factorizing out the denominator, we have

= [{(a + 5b)/(a - 5b)}³ + {(5b + 3c)/(5b - 3c)}³ + {(3c + a)/(3c - a)}³[(a - 5b)³ + (5b - 3c)³ + (3c - a)³]/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

Cancelling out the denominator, we have

= [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³

So, the factorization is  [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³

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Answer:

What is the value of x in the equation?

Step-by-step explanation:

A correct answer is option A which is x² + (y – 3)² = 36 is the equation of the circle that has a diameter of 12 units and a center that lies on the y-axis.

A circle is a two-dimensional geometry on the plane having a center point and the circular line is drawn equidistant from the center point.

The general form of the equation of a circle is given as:-

( x - h )² + ( y - k )² = r²

By comparing the given equation we can see the following results:-

x² + (y – 3)² = 36

( x - ( 0 ))² + ( y - 3 )² = 6²

We can see that the coordinate of the center are ( 0, 3 ) and the radius is 6 so the diameter is 12.

Therefore the correct answer is option A which is x² + (y – 3)² = 36 is the equation of the circle that has a diameter of 12 units and a center that lies on the y-axis.

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Answer:

A and E (first and last, ending in "=36")

x2 + (y – 3)2 = 36

x2 + (y + 8)2 = 36

Step-by-step explanation:

just took the quiz

Answer:

2(7x-4) = 7x(2)-4(2) = 14x-8

but

(7x-4)^2 = (7x-4) (7x-4)

Answer:

122.5 degrees

Step-by-step explanation:

A six sided polygon's interior angles sum to

  (n-2)(180) =  (6-2) (180) = 720 degrees

then   x + x + x +     x+10    + 130   + 90 = 720

                          4x = 490        so x = 122.5 degrees