-1.4 repeating as a fraction in simplest form

The real zeros of the following function [tex]$\quad f(x)=\left(x^4-16\right)\left(x^2+3 x-18\right)$[/tex] are

2,-2,3,-6, and the graph is attached below

This is further explained below.

[tex]$\quad f(x)=\left(x^4-16\right)\left(x^2+3 x-18\right)$[/tex]

as we know the formula a^2-b^2=(a-b)(a+b)

[tex]\begin{aligned}x^4-16 &=\left[\left(x^2\right)^2-(4)^4\right]=\left(x^2-4\right)\left(x^2+4\right) \\&=\left((x)^2-(2)^2\right)\left(x^2+4\right) \\x^4-16 &=(x-2)(x+2)\left(x^2+4\right)\end{aligned}[/tex]

substituting it in equation (1) we get.

[tex]\begin{gathered}f(x)=(x-2)(x+2)\left(x^2+4\right)\left(x^2+3 x-18\right) \\\\\left(x^2+3 x-18\right)=x^2+6 x-3 x-18=x(x+6)-3(x+6) \\\\f(x)=(x-2)(x+2)(x-3)(x+6)\left(x^2+4\right) \\\\x^2+4=(x+2 i)(x-2 i)=\left[(x)^2-(2 i)^2\right] \\\\f(x)=(x-2)(x+2)(x-3)(x+6)(x+2 i)(x-2 i)\end{gathered}[/tex]

Real zuoes =2,-2,3,-6

imaginary zuroes =2 i,-2 i

In conclusion, In the question, we have to answer the real zeroes of the function f(x)

which is 2,-2,3,-6

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Reason:

The angles shown must add to 180 degrees if we want the top and bottom lines to be parallel. These angles are same side interior angles.

(x+4)+(3x) = 180

4x+4 = 180

4x = 180-4

4x = 176

x = 176/4

x = 44

Answer:

x=42because of 3x and f or g

The probability that the exactly 5 are white and 2 are red is126/1716 and,

the probability that at least 5 of the balls are white is 133/1716

Given that:-

Total number of balls in the urn = 13

Number of white balls = 6

Number of red balls = 7

Number of randomly selected balls = 7

We have to find the probability that the exactly 5 are white and 2 are red and the probability that at least 5 of the balls are white.

Probability that exactly 5 balls are white and  2 are red, P(x = 5) = [tex]\frac{^6C_5*^7C_2}{^{13}C_7}[/tex] = 126/1716 = 21/286

We know that,

Probability that atleast 5 balls are white = P(x = 5) + P(x = 6)

We know that,

P(x = 6) = [tex]\frac{^6C_6*^7C_1}{^{13}C_7}[/tex] = 7/1716

Hence,

Probability that atleast 5 balls are white = 126/1716 + 7/1716 = 133/1716.

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Step 1. Find the volume of just one box.

To find the volume V of one box, we multiply all of the dimensions of the box:

In this case, the volume of one box is:

The result is:

Step 2. We are told that Ying bought 12 boxes, so the total volume that the boxes occupy will be the volume of one box multiplied by 12:

Answer:

Answer:

$27

Step-by-step explanation:

[tex] \frac{3}{4} (20) + \frac{3}{5} (20) = 15 + 12 = 27[/tex]

Answer:

option 3

It has a zero a set of whole no has 0 in it and it start after the no 3 as it says GREATER then 3.

The most appropriate choice for fraction will be given by -

Each person get [tex]1\frac{5}{6}[/tex] baskets of apples.

What is fraction?

Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

Here,

Number of person = 3

Total baskets of apple picked = [tex]5\frac{1}{2}[/tex] = [tex]\frac{11}{2}[/tex] baskets

Number of baskets each person got =

                                                                 [tex]\frac{11}{2} \div 3\\\frac{11}{2} \times \frac{1}{3}\\\frac{11}{6}\\1\frac{5}{6}[/tex]

Each person got [tex]1\frac{5}{6}[/tex] baskets of apples

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The number of days it will take the crew to lay all the track is; 27 days

The number of miles of track the crew has left to lay after 18 days is; 65 miles

We are given the equation that represents the length L (in miles) that is left to lay after d days as;

L(d) = 189 - 7d

where;

L is length in miles

d is number of days

Thus, the number of days it will take to lay all the tracks is;

Number of days = 189/7

Number of days = 27 days

The length L (in miles) that is left to lay after 18 days is;

L= 189 - 7(18)

L= 189 - 126

L= 65 miles

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Complete question is;

A railroad crew can lay 7 miles of track each day. They need to lay 189 miles of track. The length, L (in miles), that is left to lay after d days is given by the following function. L(d) = 189 - 7d​

(How many days will it take the crew to lay all the track?)

(How many miles of track does the crew have left to lay after 18 days?)

When two lines are perpendicular, their slopes have the following relation:

If we rewrite this expression, we have:

The product of each slope is equal to -1.

Therefore the correct option is the fourth one.

An estimated answer is 237.44 and the exact answer is 237.475.

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The most appropriate choice for percentage will be given by- Percentage change in cost = 37.09 %

What is percentage?

A number or ratio which can be expressed as just a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a portion per hundred. Per 100 is what the word percent means. The letter "%" stands for it. As in 0.6%, 0.25%, etc., percentages can also be expressed as decimals or fractions. The grades earned in any subject have been calculated in terms of percentages in academics. Ram, for instance, scored 78% on his final exam. This rate is computed based on Ram's overall grade point average (GPA) across all subjects.

For example 2% means [tex]\frac{2}{100}[/tex].

Here,

Cost last year = 24500

Cost today = 14300

Change in cost = 24500 - 14300

                         = 10200

Percentage change in cost = [tex]\frac{10200}{24500} \times 100[/tex]

                                              = 37.09 %

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answer:

vertical

explanation:

vertical angles are angles opposite each other.

g(x) is a dilation of scale factor 1/2 of f(x), and the rule is:

g(x) = 2x + 3

Here we have the function f(x) = 4x + 6 and the function g(x) that is defined as:

g(x) = (1/2)*f(x)

So g(x) is a vertical dilation of scale factor k = 1/2 of f(x).

Replacing f(x) in there we get:

g(x) = (1/2)*(4x + 6) = (4/2)*x + 6/2 = 2x + 3

The rule for g is:

g(x) = 2x + 3

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Using the normal distribution, it is found that:

a) The sampling distribution is approximately normal, with mean 45 and standard deviation 4.

b) The answer is not dependent on the sample size, as the underlying distribution is normal.

c) 0.0001 = 0.01% probability that the average is less than half an hour.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the parameters are given as follows:

[tex]\mu = 45, \sigma = 12, n = 9[/tex]

Hence the standard error of the approximately normal sampling distribution of sample means of size 9 is:

s = 12/sqrt(9) = 12/3 = 4.

As stated in the problem, the underlying distribution is normal, hence this is not dependent on the sample size.

For item c, the probability is the p-value of Z when X = 30, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (30 - 45)/4

Z = -3.75

Z = -3.75 has a p-value of 0.0001.

Hence the probability is of 0.0001 = 0.01%.

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The image of the point is (0, -5) after applying the geometric transformation, the answer is (0, -5).

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that:

The point is (0, 5)

As we know, the

The rule for the above transformation:

(x, y) → (-x, -y)

(0, 5) → (0, -5)

Thus, the image of the point is (0, -5) after applying the geometric transformation, the answer is (0, -5).

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Answer:

they filter the air coming into the body

Answer:

[tex]y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]

Step-by-step explanation:

The genera slope-intercept equation of a line is

y = mx + 8 where m is the slope and b the y-interecept

A perpendicular line will have a slope = -1/m ie the negative of reciprocal of the first line such that m x (-1/m ) = -1

The equation of the tangent line is

3x + 2y = 28.

1. Convert to slope-intercept form:

So slope = -3/2

Reciprocal of -3/2 = -2/3
Negative of reciprocal = +2/3

Slope of a perpendicular line should be -1/3 and the resultant equation of the line(the support arm) should be:

y = (2/3)x + b

To calculate b for the complete line equation plug in the point B(4, 8) and solve for B

y = 8 when x = 4

=> 8 = (2/3)(4) + b

Switch sides: (does not change any signs)
8/3 + b = 8

Subtract  8/3 on both sides
b =  8 - 8/3

b = 24/3 -  8/3

b = 16/3

So equation of the support arm is

[tex]\boxed{y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]

A. The number of beds that are at the hostel will be 700 beds.

B. The planned capacity will be 105 beds.

C. The box of silver is heavier.

A. In a hostel , 30% of the beds are vacant and T

there are 210 guest beds at the hostel currently. The number of beds will be:

= 30% of x = 210

0.3x = 210

x = 210/0.3

x = 700

The number of beds is 700.

B. The planned capacity will be:

= 15% × 700

= 0.15 × 700

= 105 beds.

C. When the jeweler is trying to determine which box has the greatest weight and a box of gold weighs 0.55 kilograms and a box of silver weighs 14/25 kilograms. It should be noted that 14/25 = 0.56. Therefore, the silver is heavier.

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Answer:

7-x

Step-by-step explanation:

If one piece is x, and the whole is 7, the missing piece would be 7-x

Hope this helps :)

Answer:

[tex]y=4x[/tex]

Step-by-step explanation:

Slope-intercept form:

[tex]y=mx+b\\[/tex]

m is the slope

b is the y-intercept

Parallel lines have the same slope, therefore we know that our new line will have the slope m = 4.

Since the point is the origin (0,0) we also know that the y-intercept will be 0.

Using this information, write the equation of the line:

[tex]y=4x+0[/tex]

Simplify:

[tex]y=4x[/tex]

Using a system of equations, a possible set of values for a, b and c such that it results in an integer number is given by:

a = 6, b = 3, c = 2.

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.

In the context of this problem, the variables are the given ones of:

a, b and c.

An integer number is a number that has no decimal part, hence the easiest way to solve this is making the sum of 1.

Attributing a = 6, we have that:

[tex]\frac{1}{6} + \frac{1}{b} + \frac{1}{c} = 1[/tex]

[tex]\frac{1}{b} + \frac{1}{c} = \frac{5}{6}[/tex]

This is possible with these two fractions:

[tex]\frac{1}{2} + \frac{1}{3} = \frac{3 + 2}{6} = \frac{5}{6}[/tex]

Hence the other possible values are given by:

b = 2, c = 3.

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The value of f(1/2) for the given function f(x) = -3(4x² + 12) + 3/4(8x) - 2x is:  -37. (None of the options are correct).

If given a function, to evaluate the function for a given value of x, input the value of x in the equation and solve to evaluate the function.

Given the function, f(x) = -3(4x² + 12) + 3/4(8x) - 2x, to find the value of f(1/2), substitute x = 1/2 into the equation:

f(1/2) = -3(4(1/2)² + 12) + 3/4(8(1/2)) - 2(1/2)

Evaluate

f(1/2) = -3(4(1/4) + 12) + 3/4(4) - 1

f(1/2) = -3(1 + 12) + 3 - 1

f(1/2) = -3(13) + 2

f(1/2) = -39 + 2

f(1/2) = -37

The value of the function f(1/2) is: -37. (none of the given options are correct).

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Answer:

I hope the deadline hasn't passed!

Your last question got deleted

Answer:

Mai made 10 successful free throws yesterday.
(25%=1/4  40/4=10)

Today Priya made 18 successful free throws.

(150%=1 1/2  12/2=6  12+6=18)

Lmk if u didn't understand my explanation :')

Answer: the property needed to find this is negative exponents

Step-by-step explanation: find the reciprocal of g to the -7th power which would be 1 over g to the 7th power

The given quadrilateral RSTV is a kite.

The following characteristics apply to quadrilaterals, which are polygons.

To classify the quadrilateral calculate the length of its sides using the distance formula given as follows:

[tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} }[/tex]

In the given quadrilateral RSTV,

RS = [tex]\sqrt{(2 - (-5))^{2} + (6 - 7)^{2} }[/tex] = [tex]\sqrt{50 }[/tex]

RV = [tex]\sqrt{(-4 - (-5))^{2} + (0- 7)^{2} }[/tex] = [tex]\sqrt{50}[/tex]

ST = [tex]\sqrt{(5 - 2)^{2} + (-3- 6)^{2} } = \sqrt{90}[/tex]

VT = [tex]\sqrt{(-3 - 0)^{2} + (5- (-4))^{2} } = \sqrt{90}[/tex]

The two adjacent sides of the quadrilateral are equal i.e. RS = RV and ST = VT.

A kite is a quadrilateral with two pairs of sides that are both the same length and are next to one another.

Therefore, the quadrilateral is a kite.

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The statement that are true about the equations − 3 ⁢ x − 8 = 19  and − 3 ⁢ x − 2 = 25 is that he equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.

From the first equation, we were given,  − 3 ⁢ x − 8 = 19

then if we add 6 to the both sides of the equation then we will have

− 3 ⁢ x − 8 + 6 = 19 + 6

Then if we perform the simplification on this equation we have,

− 3 ⁢ x − 2 = 25

Which is the given equation i.e the second equation, hence the statement in the third option is correct.

Therefore, option C is correct.

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