What’s The Value Of X as A Decimal

The simplified expression for -27z^3-9z^4+18z^6, using the greatest common factor, is given as follows:

9z³(-3 - z + 2z³).

To find a symbolic expression by the greatest common factor, we have to:

Then we multiply these GCFs.

For this problem, the numeric coefficients are given as follows:

27, 9 and 18, hence the GCF is of 9.

The exponents are given as follows:

z³, z^4 and z^6, hence the GCF is of z³, which is the expression with the lowest exponent.

Then the GCF of the expression is given as follows:

9z³.

To simplify the expression, each term of the expression is divided by 9z³, hence the factored expression is:

9z³(-3 - z + 2z³).

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Using linear function concepts, it is found that:

The slope-intercept representation of a linear function is:

y = mx + b.

In which:

For this problem, we will use a calculator from the points on the table to build a linear function of best-fit. The points are given as follows:

(5, 17.9), (10, 18.7), (15, 19.7), (20, 20.5), (25, 21.3).

Then the function is:

y = 0.172x + 17.04.

Then:

The table is missing, and is given by the image at the end of the answer.

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Answer:

Answer down below!

Step-by-step explanation:

It is not prime!!

10,000,000,001 is an odd eleven-digits composite number following 10000000000 and preceding 10000000002. In scientific notation, it is written as 1.0000000001 × 10^10. The sum of its digits is 2. It has a total of 3 prime factors and 8 positive divisors. There are 9,897,840,000 positive integers (up to 10000000001) that are relatively prime to 10000000001.

The decomposition of 240 - 135 = 105 will be 15(16 - 9) = 15(7) = 105

It should be noted that decomposition simply means breaking down of the numbers that are given or illustrated.

It should be noted that the numbers 240 - 135 = 105 all have a common factor of 15. This will be broken down as:

240 - 135 = 105

15(16 - 9)

= 15(7)

= 105

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The expression 8 ( 3x - 7 ) when expanded gives 24xx - 56.

The cornerstone of mathematics is the theory of operations; we use it to compute and remember fundamental truths. The subsequent three characteristics are applied to addition and multiplication: Commutative Property, Associative Property, and Distributive Property.

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.

Consider the expression 8( 3x - 7 ),

Let's say y is equal to 8( 3x - 7 ).

By using the distributive property:

y = 8 × 3x - 8 × 7

y = 24x - 56

Therefore,

8( 3x - 7 ) = 24x - 56

Therefore, when the expression 8( 3x - 7 ) is expanded we obtain the expression 24x - 56.

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Answer:

a = - 2

Step-by-step explanation:

since the point (3, 2 ) lies on the parabola, then it makes the equation true.

substitute x = 3, y = 2 into the equation and solve for a

y = ax² + 3x + 11

2 = a(3)² + 3(3) + 11

2 = 9a + 9 + 11

2 = 9a + 20 ( subtract 20 from both sides )

- 18 = 9a ( divide both sides by 9 )

- 2 = a

Answer:

a = -2

Step-by-step explanation:

Given quadratic equation:

[tex]y=ax^2+3x+11[/tex]

In order to find "a", substitute the given point on the curve (3, 2) into the equation and solve for a:

[tex]\begin{aligned}y&=ax^2+3x+11\\\textsf{Substitute $(3,2)$} \implies 2&=a(3)^2+3(3)+11\\2&=9a+9+11\\2&=9a+20\\2-20&=9a+20-20\\-18&=9a\\9a&=-18\\\dfrac{9a}{9}&=\dfrac{-18}{9}\\\implies a&=-2 \end{aligned}[/tex]

Therefore, the value of "a" so that parabola y = ax² + 3x + 11 goes through the point (3, 2) is:

[tex]\large \boxed{a=-2}[/tex]

Proved [tex]Cos^{4}x - Sin^{4}x + 1[/tex] = 2Cos²x

We will use the Pythagorean Theorem:

Sin²x + Cos²x = 1

from which we can get:

Sin²x = 1 - Cos²x

Also, note that the difference in the similarity of squares can be written:

A² - B² = (A - B)

We can use this with A = Sin²x and B = Cos²x as follows:

[tex]Sin^{4}x - Cos^{4}x[/tex]

= (Sin²x)² - (Cos²x)²

= (Sin²x - Cos²x) (Sin²x + Cos²x)

= Sin²x - Cos²x

= (1 - Cos²x) - Cos²x

= 1 - 2Cos²x

Now move the 1 and negative symbols to the left.

[tex]Cos^{4}x - Sin^{4}x + 1[/tex] = 2Cos²x

The trigonometric ratios are related to each other by equations called trigonometric identities.

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Answer:

13.3 liters of petrol left

Step-by-step explanation:

80 ÷ 6 = 13.3

Answer:

Your number written in expanded form is: 80000 + 4000 + 700 + 80 + 7

Answer:

(5, 4)

Step-by-step explanation:

What is Orthocenter?

A point where the altitudes of the triangle meet is known as the point of concurrency or simply the orthocenter of the triangle

Answer: The answer would be  12 39/72

Step-by-step explanation:

903 divided by 72, you'd get 12.5417. You could also express 903/72 as a mixed fraction: 12 39/72.

Answer:

[tex]-9k-7[/tex]

Step-by-step explanation:

Replace n with -9k.

The solution of given inequalities are x > -3 and x ≤ 5.

When resolving an inequality, you can do one of the following: add the same amount to each side; deduct the same amount from each side; multiply or divide each side by the same positive amount. You must flip the inequality sign if you multiply or divide each side by a negative number.

Given inequalities are 2x - 5 > -11 and -10x - 6 ≥ 44.

To solve the first inequality,

2x - 5 > -11

Adding 5 on both sides,

2x - 5 + 5 > -11 + 5

2x > -6

Divide both sides by 2,

x > -3

To solve the second inequality,

-10x - 6 ≥ 44

Adding 6 on both sides,

-10x - 6 + 6 ≥ 44 + 6

-10x ≥ 50

Divide both sides by -10, and change the inequality sign

x ≤ 5

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Answer:

see explanation

Step-by-step explanation:

the volume (V) of the container is

V = 10 × 4 × 5 = 200 m³

change the dimensions of the box to m , to be same as container

l = 50 cm = 0.5 m , b = 40 cm = 0.4 m , h = 20 cm = 0.2 m

then

volume of box = 0.5 × 0.4 × 0.2 = 0.04 m³

Number of boxes that can be stored in container is

200 ÷ 0.04 = 5000

thus no more than 5000 boxes can be placed in the container

The solutions of the quadratic equation  x² = 16x - 65 are:

x = 1/2 +  1/32i

x = 1/2 - 1/32i

We know that a quadratic equation is an equation that is of the sort ax^2 + bx + c = 0. Hence, the equation would be solved and it could have a complex root. By this I mean that the root of the equation could be a complex number as we have in the case of the equation here.

x² = 16x - 65 = 0

x² - 16x + 65 = 0

When we solve by the formula method;

x = -b ±√b^2 - 4ac/2a

x = -(-16) ±√(-16)^2 - 4 (1) (65)/2(16)

x = 16 ±√256 - 260/32

x = 16/32 ±√-4/32

x = 1/2 ± 1/32i

Thus

a =  1/2

b = 1/32

We then obtain;

x = 1/2 +  1/32i

x = 1/2 - 1/32i

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∠6 and ∠12 are supplementary angles. That means, they add up to 180°

Substitute ∠6 by 53° to find ∠12.

Subtract 53 from both sides to find ∠12.

Answer: ∠12 = 127°.

√134 is the number which is located between 11 and 12 on a number line.

A number line is a horizontal straight line on which real numbers are arranged in equal intervals. This line extends both sides at infinity.

Comparison and operations of numbers can be better explained using number lines.

Taking consecutive perfect squares of integers which lies above and below the given numbers on the number line and taking it's square root, we can find the answer.

The perfect squares below and above 150 are 144 = 12² and 169 = 13². So √150 lies in between 12 and 13.

The perfect squares below and above 134 are 121 = 11² and 144 = 12². So √134 lies in between 11 and 12.

The perfect squares below and above 115 are 100 = 10² and 121 = 11². So √115 lies in between 10 and 11.

The number 121 is itself a perfect square. √121 = 11.

Hence √134 is the number which lies in between 11 and 12.

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The frequency of the 10 inch violin string will be 630 cycles per second or Hertz if the violin string 14 inches long vibrates at a frequency of 450 cycles per second.

As per the question statement, A violin string 14 inches long vibrates at a frequency of 450 cycles per second and we are supposed to find out the  frequency of a 10-inch violin string.

We should be knowing that the length of a violin string varies inversely as the frequency of its vibrations.

f = m/l, where "f" is the frequency and "l" is the length and "m" is the constant number

450 = m / 14

m = 6300

Therefore New frequency = 6300 / 10 = 630 cycles per second

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julia wants to purchase a pair of headphones that are on sale for $42.79. the sales tax rate in her county is 6%. then Julia have to pay $2.57 as sales tax on purchase of headphones.

Given,

The cost of headphones which Julia wants to purchase on sale = $ 42.79

The sales tax in Julia's country = 6%

We have to calculate the amount of sales tax Julia will pay on the purchase:

That is,

Sales Tax Value = Percentage of sales tax × Price of headphones

Sales Tax Value = (6 / 100) × 42.79

Sales Tax Value = 0.06 × 42.79

Sales Tax Value = 2.5674

Sales Tax Value ≈ 2.57

Therefore, Julia have to pay $2.57 as sales tax on purchase of headphones.

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Answer:

Value of x is 22 because there are alternative angles

Step-by-step explanation:

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.

The statement that is best supported by the graph is; Jillian's car holds more gasoline, but Nikki's car gets better gas mileage.

The total amount of gasoline each car tank can hold is shown on the left of each graph on the y-axis.

Jillian's car holds 22 gallons.

Nikki's car holds 20 gallons.

Jillian's car holds more gasoline.

Now we need to see which car gets better gas mileage. Getting better gas mileage means you can go farther with each gallon of gas.

With Jillian's car, after using 22 gallons of gas, you have gone 350 miles, and the gas tank is empty.

350 miles with 22 gallons is 350/22 = 15.9 miles per gallon.

With Nikki's car, you start with only 20 gallons. By the time you drive 350 miles, you still have some gas left. Not only did you start with less gas, 20 gal vs. 22 gal, but after driving the same distance, 350 miles, there is still some gas left in the tank, 6 gallons.

That means Nikki's car used 20 - 6 = 14 gallons to drive 350 miles. 350/14 = 25 miles per gallon.

The more miles per gallon you get, the better the mileage. Thus;

25 miles per gallon is better mileage than 15.9 miles per gallon.

Nikki's car has a smaller gas tank, but it gets better mileage.

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25.42 marked down by 33 % is 17.0314.

This is a question of percentages.

Percentage

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Percentages have no dimension. Hence it is called a dimensionless number.

33 % of 25.42 is given by:-

(33/100)*(25.42) = (33*25.42)/100 = 838.86/100 = 8.3886

25.42 marked down by 33 % = 25.42 - 8.3886 = 17.0314.

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The value of AC when BD= 12 and AC = x+ 23 is 28

A line segment can be defined as the part of a straight line that is being bounded by two different end points, and also contains all the points on the line between its endpoints.

From the information given, we have that line AD is a line with segments, line AB, line BC, line CD with B and C as the midpoints.

Given the points as;

We have that;

AC + BC = AD

But line BD = 14 + x, we have;

Line AC = x + 23 - 14 + x

Line AC = 2x + 9

substitute the values into the equation

2x + 9 +12 = 26 + x

collect like terms

2x - x = 26 - 21

Add or subtract like terms

x = 5

But, we have that;

Line AC = x + 23

Line AC = 5 + 23

Add the values

Line AC = 28

Hence, the value is 28

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The equation for the line that is parallel to the given line y=3/4x + 7 and that passes through the given point G (8,3) is y= (3/4)x -3.

As given in the question,

Equation of the given line :

y=3/4x + 7

Slope of the given line = (3/4)

Equation of line with slope (3/4) & passing through point (8, 3) is given by:    

y - 3 = [tex]\frac{3}{4}[/tex] (x - 8)      

⇒ 4 (y - 3) = 3 (x - 8)

⇒ 4y - 12 = 3 x - 24

⇒ 4 y = 3 x - 24 + 12

⇒ 4 y = 3 x - 12

⇒ y = (3/4)x - 3

Therefore, the equation for the line that is parallel to the given line

y=3/4x + 7 and that passes through the given point G (8,3) is y= (3/4)x -3.

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Answer: m = (3/2)r

Step-by-step explanation:

2/3m+a=a+r, for m

----

(2/3)m + a = a + r

---

(2/3)m = r

Answer:

The probability is 5/8

Step-by-step explanation:

Equation is y= 56x that models the relationship between x ,the number of hours Mark reads, and y, the number of pages of the book he reads.

The term rate of change (ROC) describes the rate at which something changes over time. Thus, it is not the amount of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate). Rate of change is a tool used in finance to comprehend price returns and spot trend momentum.

Given Data

The hours are indicated by = x

The calculation for the number of pages is =y

Read 42 pages every [tex]\frac{3}{4}[/tex] hour

You can model the equation as follows:

y = mx +b

Rate of change = [tex]\frac{change in y}{change in x}[/tex]

Rate of change = 42 ÷[tex]\frac{3}{4}[/tex]

Rate of change = 42 ×[tex]\frac{4}{3}[/tex]

Rate of change = 56

Equation y= 56x

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A man's taxable income is $3060 if tax is paid at 12%, then the man's net income is $3477.27

The taxable income = $3060

The tax percentage = 12%

Income tax is the a type of tax impose on income generated by businesses and individuals by the government

Consider the net income as x

Then,

12% of the income = x×(12/100)

Therefore the equation will be

x -  x×(12/100) = 3060

x(1-(12/100) = 3060

x(1-0.12) = 3060

0.88x = 3060

x = 3060/0.88

x = $3477.27

Hence, a man's taxable income is $3060 if tax is paid at 12%, then the man's net income is $3477.27

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Answer:

24

Step-by-step explanation:

it just is, I don't know how I get this. I just did.

[tex]\frac{2n+48}{3}[/tex]

This how we change 23 out of 25 to a percentage

The numerator of a question is the number that appears above the bar; in this case, the numerator is 23.

The denominator is the number beneath the bar, and in this question, it is 25.

To calculate the value of a fraction, divide the numerator by the denominator.

Therefore, we must divide 23 by 25.

23/25 = 0.92

To determine the percentage, multiply the outcome by 100.

The percentage value will be obtained by multiplying 0.92 by 100.

0.92 x 100 = 92%

As a result, 92% is the answer to the question.

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