Multiply the following using the vertical multiplication method:
x² + 5x+1
x3x2 - 2x + 4

Answer:

Step-by-step explanation:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.

Answer: 0.3

Step-by-step explanation:

A percent that is equivalent to 3/10 is: D.) 30%.

In Mathematics, a percentage is any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

By multiplying both the numerator and denominator by a common number such as 10, we have the following:

3/10 × 10/10

30/100

30%

Based on the information provided, we can logically deduce that 30% is equivalent to 3/10. Therefore, the correct answer option is: D.) 30%.

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The expression for the original rational number is; x/(x + 10)

Let the numerator be x

Therefore, according to given condition, the denominator will be expressed as; (x + 10)

According to question If the numerator is increased by 1  and the denominator is decreased by 1, then new numerator is; x + 1

New denominator is (x + 10 - 1) = (x + 9)

Thus, the original rational number will be expressed as;

x/(x + 10)

The new rational number will be : (x + 1)/(x + 9)

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Answer:

20

Step-by-step explanation:

complex conjugate of 10+5i = 10-5i

10+5i + 10-5i = 20

Answer:

False

Step-by-step explanation:

The given function, f(x) = x⁴ - 2x², is even function.

The nature of the function, whether it is even or odd can be determined by applying the following rules.

Even function, f(x) = f(-x)

Odd function; f(x) = -f(-x)

The given function, f(x) = x⁴ - 2x²

Test of for even function;

f(-x) = (-x)⁴ - 2(-x)²

f(-x) = x⁴ - 2x²

so f(x) = f(-x), the function is even.

Test for odd function;

-f(-x) = - [(-x)⁴ - 2(-x)²]

-f(-x) = -x⁴ + 2x²

so, f(x) ≠ -f(-x), the function is not odd.

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Answer:

Here you go with your answer

Mark me as brainlist may your parents live long life

The disadvantages of the mode are: For many sets of data there is no mode.

The mode is a measure of central tendency that represents the most frequently occurring value in a dataset.

However, one of the disadvantages of the mode is that for many sets of data, there may not be a distinct mode. In such cases, the data may have a uniform distribution where all values occur with equal frequency, or it may have multiple modes with similar frequencies.

The mode is not affected by extremely large or small values. It only considers the frequency of values and not their magnitude. Therefore, extreme values do not influence the mode.

The statement that the mode can only be computed for interval-level data or higher is incorrect. The mode can be computed for any type of data, including nominal, ordinal, interval, and ratio data. It is applicable to categorical as well as numerical data.

The main disadvantage of the mode is that for many datasets, there may not be a distinct mode.

The correct option is: For many sets of data there is no mode.

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Answer:

I think it is 4:3

Step-by-step explanation:

From $960,000 take away $720,000 and you get $240,000 and that $960,000 divide by $240,000 and you get 4 and you do the same with $720,000 and you get 3

The requried ratio of candidate A's campaign spending to candidate B's campaign spending is 4 : 3.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

here,
During a mayoral election, candidate A spent $960,000 on her campaign, and candidate B spent $720,000 on her campaign.

The ratio of candidate A's campaign spending to candidate B's campaign spending,

= 960000 / 720000

= 96 / 72
= 4 / 3

Thus, the requried ratio of candidate A's campaign spending to candidate B's campaign spending is 4 : 3.

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\(x = - 5\)

\(y = 3\)

_________________________________

\( {x}^{2} \times y = ({ - 5})^{2} \times 3 = 25 \times 3 = 75 \\ \)

Done♥️♥️♥️♥️♥️

Using the concept of the word problem and utilizing the provided conditions and values, The answer is 18, 20, and 22.

A word problem in mathematics is a problem or exercise that is expressed in a natural language, rather than in mathematical notation. These types of problems often present a real-world situation that involves mathematical concepts, such as numbers, operations, or measurements. They typically require the use of mathematical reasoning and problem-solving skills to understand the problem and find a solution. Examples of word problems include: "If a train travels 60 miles per hour and you want to know how far it will travel in 4 hours", "If a rectangle is 6 meters long and 4 meters wide, what is its area?", "If a bag contains 3 red balls and 4 blue balls, what is the probability of picking a blue ball?"

In a mathematical problem, the conditions refer to the specific information or constraints provided in the problem statement that must be taken into account in order to find a solution. These conditions can include information about the quantities involved in the problem, the operations that need to be performed, or the specific requirements that the solution must meet.

Let x be the smallest of the three consecutive even integers. Then the next two integers are x+2 and x+4. We know that:

x + (x+4) * 3 = 84

Expanding and solving for x:

x + 3x + 12 = 84

4x = 72

x = 18

So the three consecutive even integers are 18, 20, and 22.

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Answer:

\(\frac{4}{5}\)

Step-by-step explanation:

Knowing that \({-\frac{3}{5}}^{2} + {\frac{4}{5}}^{2} = 1, {-\frac{3}{5}}^{2} + {-\frac{4}{5}}^{2} = 1\),

so x can be positive or negative 4/5,

and we know that x coordinate of any point in quadrant IV is positive,

so x = 4/5.

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

26.7 miles

Step-by-step explanation:

if 1 inch equals 10 miles then 2 2/3 x 10 will give you the answer but convert   2 2/3 to be 2.67 before multiplying by 10

Answer:

214 cubic feet (rounded to the nearest cubic foot)

Step-by-step explanation:

Step 1  Determine the volume of 1 box

Volume of a box or rectangular prism = dimensions multiplied by each other

Here, the given dimensions are 11 in by 8 in by 12 in

So the volume of one box would be 11 x 8 x 12 = 1056 cubic inches

Step 2 Determine volume of all 350 boxes

Volume of 1 box = 1056

So volume of all 350 boxes = 1056 x 350 = 369600 cubic in

Step 3 Convert cubic in to cubic ft

To convert to cubic feet we divide the amount of cubic inches by 1728 (this is because there are 1728 cubic inches in 1 cubic foot)

369600 / 1728 = 214 cubic feet (to the nearest cubic foot)

214 cubic feet of warehouse space is required for 350 boxes with the dimensions of 11in by 8in by 12in

Using the probability concept, it is found that there is a

a) 0.2 = 20% probability that 3 is obtained.

b) 0.3333 = 33.33% probability that 6 is obtained.

c) 0.6667 = 66.67% probability of a number greater than 3.

d) 0.6667 = 66.67% probability of an even number.

A probability is the number of desired outcomes divided by the number of total outcomes.

Item a:

There are 5 numbers greater than 1, one of which is 3, hence:

\(p = \frac{1}{5} = 0.2\)

0.2 = 20% probability that 3 is obtained.

Item b:

There are 3 numbers greater than 3, one of which is 6, hence:

\(p = \frac{1}{3} = 0.3333\)

0.3333 = 33.33% probability that 6 is obtained.

Item c:

There are 3 even numbers, two of which are greater than 3, hence:

\(p = \frac{2}{3} = 0.6667\)

0.6667 = 66.67% probability of a number greater than 3.

Item d:

There are 3 numbers greater than 3, two of which are even, hence:

\(p = \frac{2}{3} = 0.6667\)

0.6667 = 66.67% probability of an even number.

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using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

The simplified expression of 4√6/√30 by rationalizing the denominator is (8√5) / 15.

To rationalize the denominator, multiply both the numerator and denominator by a factor that will eliminate the radical from the denominator.

In this case, multiply both the numerator and denominator by the radical conjugate of the denominator, which is also √30.

(4√6)/√30 = (4√6/√30) × (√30/√30)

= (4√6√30) / 30

= (4√(630)) / 30

= (4√180) / 30

= (4√365) / 30

= (4 x 6√5) / 30

= (8√5) / 15

Therefore, the simplified expression is (8√5) / 15.

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Answer:

4\(y^{\frac{3}{2} }\)

Step-by-step explanation:

using the rule of exponents/ radicals

\(\sqrt[n]{a^{m} }\) = \(a^{\frac{m}{n} }\)

then

4 \(\sqrt{y^{3} }\)

= 4\(y^{\frac{3}{2} }\)

Answer:

10miles I think

Step-by-step explanation:

The required distance between, Nate's house and the restaurant is 7.5 miles.

From the graph,

Consider point C on the graph, which is 6  and 8 units apart from A and B respectively.

The distance between, Nate's house and the restaurant is given as,
AB = √[AC² + BC²]
AB = √[6² + 8²]
AB = 10 units

Now 1 unit = 3/4 miles
AB = 10 * 3/4
AB = 7.5 miles

Thus, the required distance between, Nate's house and the restaurant is 7.5 miles.

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Answer:

i think c or b I D K

Step-by-step explanation:

Answer:

38.88in²

Step-by-step explanation:

Area of shaded region = Area of square - Area of semi circle

First lets find the area of the square and semi circle

Area of square = s²

Where s = side length

Here we have a given side length of 8in

So s = 8

This means area = 8² = 64in²

Area of semicircle = (πr²)/2

Where r = radius

Here, the side length of the square and the diameter of the semicircle is shared meaning they are congruent. This means the diameter of the semicircle = 8in

To convert from diameter to radius we simply divide by 2

So radius = 8 / 2 = 4

Now we have Area = (πr²)/2

==> plug in r = 4 and π = 3.14

Area = (3.14(4)²))/2

==> simplify exponent

Area = (3.14(16))/2

==> multiply 3.14 and 16

Area = 50.24/2

==> simplify division

Area = 25.12in²

Area of shaded region

We now subtract the two areas

Area of shaded region = Area of square - Area of semi circle

Area of square = 64in² and Area of semicircle = 25.12in²

Area of shaded region = 64in² - 25.12in² = 38.88in²

By solving linear inequation, it can be calculated that

x < 8 is the solution of the inequality -5x+30 >-10

What is linear inequation?

At first, it is important to know about algebraic expression.

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Now, algebraic expressions are of different types. They are-

Monomial, Binomial and trinomial.

Algebraic expression with only one term is called monomial

Algebraic expression with two terms are called binomial

Algebraic expressions with three terms are called trinomial.

Algebraic expressions with more than three terms are called polynomial.

Based on degree, algebraic expression may be called as linear, quadratic, cubic and so on

Algebraic expression of degree one is called linear

Algebraic expression of degree two is called quadratic

Algebraic expression of degree one is called cubic

Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by >,<, ≥, ≤

A one degree inequation is known as linear inequation.

Here the given inequality is-

-5x+30 >-10

Now,

-5x + 30 > -10

-5x > -10 - 30

-5x > -40

x < \(\frac{-40}{-5}\)

x < 8

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Simplifying this fraction gives us 1/4. The answer is (D) 1/4.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

Let's start by finding the fraction of Michelle's patients who are under 12 or over 65. We know that one-third of her patients are under 12, so two-thirds must be 12 or older. Similarly, five-twelfths of her patients are over 65, so seven-twelfths must be 65 or younger.

Now, we want to find the fraction of Michelle's patients who are between 12 and 65. To do this, we need to subtract the fraction of patients who are under 12 or over 65 from 1 (since these are the only two age groups we're considering).

Fraction of patients under 12: 1/3

Fraction of patients over 65: 5/12

Fraction of patients 12 to 65: 1 - 1/3 - 5/12

We can simplify this expression by finding a common denominator:

Fraction of patients 12 to 65: 12/12 - 4/12 - 5/12

Fraction of patients 12 to 65: 3/12

Simplifying this fraction gives us 1/4. Therefore, the answer is (D) 1/4.

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The correct statement regarding the inverse function of f(x) = 4x^4 is given as follows:

\(f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}\); f^(-1)(x) is not a function.

The function in this problem is defined as follows:

f(x) = 4x^4.

To obtain the inverse of a function y = f(x), first the variables y and x are exchanged, as follows:

x = 4y^4.

Isolating the variable y, we have that:

y^4 = (x/4).

The inverse operation of the fourth power is the fourth root, hence:

\(y = \pm \sqrt[4]{\frac{x}{4}}\)

\(f^{-1}(x) = \pm \sqrt[4]{\frac{x}{4}}\)

\(f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}\)

The plus/minus symbol means that for each input of x, the inverse function gives two outputs, meaning that there are multiple outputs mapped to each input, and thus the inverse is not a function.

This means that the second statement is correct.

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Answer:

B -1-tan(2x)/1+(-1)(tan(2x))

Step-by-step explanation:

Edge 2020

the original expression listed in the question can be simplified to -1+tan(2x)/1-tan(2x). expression B can also be simplified to -1+tan(2x)/1-tan(2x)

The expression equivalent to tan(3π/4 -2x) is  -1-tan(2x)/1+(-1)(tan(2x))

It is the trigonometric identity.

Using the trigonometric formula , tan (A-B) = tanA - tanB/ (1+tanA tanB )

tan(3π/4 -2x) = tan(3π/4) - tan2x / 1+ tan(3π/4)tan2x

tan(3π/4 -2x) = -1-tan(2x)/1+(-1)(tan(2x))

Thus, the expression equivalent to tan(3π/4 -2x) is  -1-tan(2x)/1+(-1)(tan(2x))

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The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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