Given f(x)=4x^2+9x+9, find f(−1)​

After adding and subtracting the rational expressions , the simplified rational expression is 4x - 4/x² - 5/x³ + 9  .

We first simplify each expression inside the parentheses :

that means :

⇒ (2x + 5/x² -3x) = (2x - 3x + 5/x²) = (-x + 5/x²) ;

⇒ (3x + 5/x³ - 9x) = (-6x + 5/x³)  ;

⇒ (x + 1/x² - 9) = (-9 + x + 1/x²)  ;

Now we substitute these expressions into original equation/expression :

we get ; (-x + 5/x²) - (-6x + 5/x³) - (-9 + x + 1/x²)

Simplifying further ,

we get ;

⇒ -x + 5/x² + 6x - 5/x³ + 9 - x - 1/x²  ;

On Combining the like terms, we get ;

⇒ 4x - 4/x² - 5/x³ + 9

Therefore, the simplified rational expression is 4x - 4/x² - 5/x³ + 9.

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The given question is incomplete , the complete question is

Adding and subtracting rational expressions, Simplify the rational expression  (2x + 5/x² -3x) - (3x + 5/x³ - 9x) - (x + 1/x² - 9)  .

Answer:

9°

Step-by-step explanation:

x + 4x + 5x + 6x + 7x + 8x + 9x = 360

40x = 360

x = 9

The smallest angle measures x, and x = 9, so its measure is 9°.

Answer: 9°

The binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

Given that binomial  (x+5) is a factor of x² + 8x + 15.

We need to find the other factor.

Let us solve x² + 8x + 15=0

x² + 5x +3x+ 15=0

x(x+5)+3(x+5)=0

(x+3)(x+5)

So the other binomial factor is x+3.

Hence, the binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.

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Answer:

y-2x=11

Step-by-step explanation:

y+3=2(x-4)

y+3=2x-8

y-2x=-3-8

y-2x=-11

The missing number in the sequence is 64

From the question, we have the following parameters that can be used in our computation:

1, 4, 16, ____, 256, 1024, ...​

Using the above as a guide, we have the following:

To obtain the next term, we can multiply the previous term by 4:

So, we have

Next term = 16 * 4

Next term = 64

Therefore, the next term in the sequence is 64.

The completed sequence is: 1, 4, 16, 64, 256, 1024, ...

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The length of points IJ given the total length of HJ and length HI is 8

The line HJ is measured as 20

If HI = 12

Then, subtract to find IJ

IJ = HJ - HI

= 20 - 12

IJ = 8

Therefore, length of points IJ is 8

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A reflection over the x-axis.

A vertical stretch by 11 units.

A translation left by 5 units.

A translation up 4 units.

The reflection of a function across the x- or y-axis is another transformation that may be used. In contrast to a horizontal reflection, which reflects a graph horizontally across the y-axis, a vertical reflection reflects a graph vertically across the x-axis.

An illustration of a transformation is a reflection, which flips a shape (referred to as the pre image) over a line (referred to as the line of reflection) to produce a new shape (called the image). Imagine what would happen if you flipped the form over the line in order to graph a reflection.

Here, f(x) = 1/x²

Now, reflect the graph over the x-axis to obtain the graph of:

f(x) = -1/x²

Now, stretch the graph vertically by 11 units to get the graph of:

f(x) = -11/x²

Again, translate the graph left by 5 units to obtain the graph of:

f(x) = - 11 / (x + 5)²

Now, translate the graph up by 4 units to obtain the graph of:

f(x) = 4 - {11 / (x + 5)²}

Hence,

A reflection over the x-axis. A vertical stretch by 11 units. A translation left by 5 units. A translation up 4 units.

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Answer:

2.57 square meters

Step-by-step explanation:

r = Radius of circle

Area of shaded region = Area of semi-circle:

[tex]= \frac{1}{2}(\pi r^{2})[/tex]

= [tex]\frac{\pi}{2} r^{2}[/tex]

= [tex]\frac{\pi }{2} (1.28m)^{2}[/tex]

= 2.57 [tex]m^{2}[/tex] (Rounded to 2 decimal places)

The correct statement regarding the probabilities is given as follows:

c. The experimental probability is 4% higher than the theoretical probability.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For the theoretical probability, we have that the coin is equally as likely to fall heads or tails, hence:

p = 1/2

p = 0.5 = 50%.

For the experimental probability, we have that on 100 trials, 54 resulted in heads, hence:

p = 54/100

p = 0.54 = 54%.

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Step-by-step explanation:

173 bagels left after the first hour.

The smallest sample size that will result in a margin of error of no more than 5% for a 95% confidence interval is given as follows:

385.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error is modeled as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

We have no estimate, hence we consider that:

[tex]\pi = 0.5[/tex]

The minimum sample size is obtained as n when M = 0.05, hence:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96 \times 0.5[/tex]

[tex]\sqrt{n} = 1.96 \times 10[/tex] (0.5/0.05 = 10).

[tex](\sqrt{n})^2 = (1.96 \times 10)^2[/tex]

n = 384.16

Hence rounded to 385, as a sample size of 384 would have a margin of error slightly above 0.05.

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Answer: 7/10

Step-by-step explanation:

multiply 4/5 by 7/8=28/40 or 7/10

To represent Brandon's total collection of quarters and dimes, let's use variables.

Let:

q be the number of quarters

d be the number of dimes

The following equations can be used to represent the given information:

The quarters and dimes are worth a total of $9.6:

0.25q + 0.10d = 9.6

The quantity of quarters is 348 less than 8 times that of dimes.

q = 8d - 348

To get a solution for one of the variables, we can use substitution. We may solve for d by substituting the expression for q from equation 2 into equation 1:

0.25q + 0.10d = 9.6

0.25(8d - 348) + 0.10d = 9.6 (substitute q = 8d - 348)

2d - 87 + 0.10d = 9.6

2.10d = 96.6

d = 46

Now that we know d = 46, we can use equation 2 to solve for q:

q = 8d - 348

q = 8(46) - 348

q = 16

Therefore, There are 46 dimes and 16 quarters in Brandon.

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Answer:

the answer is x=23.84 which is A

Step-by-step explanation:

using SOH CAH TOA

tan0 =opp/adj

where 0=40,opposite =20,adjacent =x

tan 40=20/x

0.8391=20/x

0.8391x=2

divide both sides by 0.8391

x=23.84

Answer:

The probability of choosing 2 girls from a list of 6 girls and 6 boys can be calculated using combinations.

The number of combinations of choosing 2 girls out of 6 girls is given by the formula: C(6,2) = 6! / (6-2)!2! = 15.

So, the probability of choosing 2 girls is 15 / (C(12,2) = 66) = 15/66 = 5/22.

Therefore, the probability of Mr. Mackinson choosing 2 girls to lead the class field trip is 5/22 or approximately 0.227.

Answer:

258cm

it is the vertex's hieght as well as the length of the sides to multiply together and also divide since there is 5 sides

On the z-table with a 90% confidence interval, the value 1.645 is called the critical value. The critical value is used to determine the boundary values for the confidence interval.  Correct option is A.

In a confidence interval, we use sample data to estimate the true population parameter with a certain degree of certainty or confidence. The critical value is determined based on the desired confidence level and the degrees of freedom (sample size - 1) of the distribution.

For example, if we want a 90% confidence interval, we use the z-table to find the critical value that corresponds to a probability of 0.05 in the tail of the distribution. The critical value represents the number of standard errors that correspond to the probability in the tail of the distribution.

Once we have determined the critical value, we can use it to find the margin of error for the confidence interval, which represents the range of values within which the true population parameter is likely to lie. The margin of error is calculated by multiplying the critical value by the standard error of the sample statistic.

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Complete question is:

On the z table with a 90% confidence interval, what is 1.645 called? group of answer choices

a. critical value

b. confidence interval

c. margin of error point

d. estimate

Answer:

24.67

Step-by-step explanation:

6 x 3 = 18

18 plus 6 = 24

X-M=0.60

P-3=7

24.67

The expression is a summation formula, representing the sum of a series of values. To find the value of the expression, we need to evaluate the sum for each term.

The general formula for each term is:

900(1.04)^n

where n is the term number and 1.04 is the common ratio.

For the first term (n = 1), the formula is:

900(1.04)^1 = 900 * 1.04 = 937.6

For the second term (n = 2), the formula is:

900(1.04)^2 = 900 * 1.04^2 = 976.9792

And so on, for each term. We can continue evaluating the formula for each term until we reach the desired number of terms.

Let's evaluate the expression for n = 10 terms.

The sum of the first 10 terms is:

937.6 + 976.9792 + 1018.057312 + ... + 1412.14803883

The value of the expression is approximately 1412.15.

Rounding to the nearest integer, the answer is 1412.

Answer:

85.71% chance of randomly selecting a student who owns at least one laptop or one desktop

Step-by-step explanation:

Out of a total of 70 students, only 10 own neither a laptop nor a desktop. This means that the probability of selecting a student with at least one of the two is [tex]\frac{60}{70}[/tex] or [tex]\frac{6}{7}[/tex].

If we convert this fraction into a percentage and round to the nearest hundredth, it equals:

85.71%

The amount of money that the items will cost you to send through United States Postal Service would be = $13.3

The dimensions of the first envelope = 20 L, 10°H and 4"W

The weight of the first envelope = 10 ounce.

The first envelope is a parcel because the dimensions are larger than 11.5 L, 6.125" H, 0.25"W.

The price per ounce = $1.22

10 ounce = 1.22×10 = $12.2

The dimensions of the second envelope = 8 L, 5" H and 0.20 W.

The weight of the second envelope = 2.5 ounce.

The second letter is of normal letter size because of the dimensions (min. dimension: 5" L, 3.5" H, 0.007" W; max. dimension: 11.5 L, 6.125" H, 0.25 W, max. weight 3.5 oz)

The price per ounce = $0.44

2.5 ounce = 2.5× 0.44 = $1.1

The total price = 12.2+1.1 = $13.3

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Answer:

s^2 + n^2 = 116

Step-by-step explanation:

s^2 + n^2 = ?

s^2 = 80

n = 6

n^2 = 36

s^2 +n^2 = 80 + 36

s^2 +n^2 = 116

The cost of spending the fencing around will be $1312.5.

The perimeter of any two-dimensional figure is defined as the sum of all the sides of the figure. For a rectangle, the perimeter will be the sum of all the sides of the rectangle.

Given that the graph of rectangle ABCD depicts Kenny's intentions for erecting a safety fence to surround a construction site. The units on the graph each correspond to 25 ft.

Kenny decides to construct a fence that encloses a wider region after carefully reviewing the drawings. Given that fencing costs $5.25 per foot and Kenny enlarges rectangle ABCD by a scale factor of 2.5

Perimeter = 4 x side x scale factor

Perimeter = 4 x 25 x 2.5

Perimeter = 250 feet.

The cost of fencing will be,

Cost = 250 x $5.25

Cost = $1312.5

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The expression when completed is 0.9 [<] 0.95

From the question, we have the following parameters that can be used in our computation:

9 10 19 20​

Rewrite the expression properly

So, we have the following representation

9/10 [ ] 19/20​

Next, we evaluate the expressions

This gives

0.9 [ ] 0.95

0.9 is less than 0.95

So, we have

0.9 [<] 0.95

The above represents the complete statement

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A histogram would be the most appropriate graphical display to present data by grouping the results into groups of 25 cm.

A histogram is a graphical representation of data that shows the distribution of a set of continuous data by dividing the data into bins (or intervals) and showing the frequency of observations within each bin. The histogram provides a visual representation of the distribution of data, showing the shape, central tendency, and spread of the data.

In this case, the farmer has measured the height of every tree in a large orchard in centimeters and wants to present the data in groups of 25 cm. To create a histogram for this data, the first step would be to divide the data into bins, or intervals, of 25 cm.

Once the bins are created, the next step is to count the number of observations (tree heights) that fall within each bin. This information can be represented as a bar graph, where the height of each bar represents the frequency of observations within the corresponding bin.

By presenting the data in this way, the farmer can easily see the distribution of tree heights in the orchard. The shape of the histogram can indicate whether the data is symmetrical, skewed, multimodal, or uniform.

The central tendency of the data can be determined by looking at the peak of the histogram, which represents the most frequent range of tree heights. The spread of the data can be determined by looking at the width of the histogram and the range of tree heights represented.

In conclusion, a histogram is the most appropriate graphical display to present the results of the tree heights in groups of 25 cm because it provides a visual representation of the distribution of the data and allows the farmer to see the shape, central tendency, and spread of the tree heights in the orchard.

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Answer:

1.  2^n + 1.

2. (n +1)/(n + 4)

Step-by-step explanation:

1. 3 5 9 17....

3 = 2^1 + 1

5 = 2^2 + 1

9 = 2^3 + 1

17 = 2^4 + 1

Therefore the nth term is

2^n+ 1 .

2. Looking at the fractions we see that:

Numerators are 2, 3, 4 ,5..

and denominators are  5, 6, 7, 8

So the nth term is

(n + 1) / (n + 4)

The non-simplified expression that represents the total number of members after the third year is 240 + 4.5x.

The simplified expression that represents the total number of members after the third year is 4.5(53 + x).

Let's call the number of members from the other club "x".

After the first year, the total number of members is 20 + x, and it doubles to 2(20 + x) = 40 + 2x.

After the second year, half of the members from the other club leave, so there are 0.5x members left from the other club. And another 40 members join, so the total number of members is (40 + 2x - 0.5x) + 40 = 80 + 1.5x.

After the third year, the total number of members triples, so we have 3(80 + 1.5x) = 240 + 4.5x.

Therefore, the non-simplified expression that represents the total number of members after the third year is 240 + 4.5x.

To simplify, we can factor out 4.5 from the expression to get 4.5(53 + x). So the simplified expression that represents the total number of members after the third year is 4.5(53 + x).

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The nth term of the given quadratic sequence is expressed as; aₙ = 2n²

To find the nth term, we have to find the relation between the given terms.

Here we see that;

1st term = 2 = 2 × 1 × 1 = 2 × 1²

2nd term = 8 = 2 × 2 × 2 = 2 × 2²

3rd term = 18 = 2 × 3 × 3 = 2 × 3²

4th term = 32 = 2 × 4 × 4 = 2 × 4²

5th term = 2 × 5² = 2 × 50 = 100

Thus, we clearly see a pattern that can represent the nth term as;

aₙ = 2 × n²

aₙ = 2n²

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The equation of the graph is y = (5x + 10)/(x²-1).

The correct option is c.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

The graph of the equation is given in the image.

From the graph:

When x = 0, then y = -10.

And when y = 0, then x = -2.

y = (5x + 10)/(x²-1)

Substituting the values,

we get,

when x = 0, then y = -10.

And when y = 0, then x = -2.

From the given choices:

The equation,

y = (5x + 10)/(x²-1) satisfies the points.

Hence, the equation is y = (5x + 10)/(x²-1).

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