Use synthetic division to find the result when x³ + 7x² - 12x + 14 is divided by a 1. If there is a remainder, express the result in the form q(x) + b(x)*

Answer:

d ≈ 8.5 units

Step-by-step explanation:

calculate the distance using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = A (2, - 1 ) and (x₂, y₂ ) = B (- 4, 5 )

d = \(\sqrt{(-4-2)^2+(5-(-1))^2}\)

   = \(\sqrt{(-6)^2+(5+1)^2}\)

   = \(\sqrt{36+6^2}\)

   = \(\sqrt{36+36}\)

   = \(\sqrt{72}\)

   ≈ 8.5 units ( to 1 decimal place )

Answer:

1/12πx³

Step-by-step explanation:

Given that :

Base diameter = x

Height, (h) = x

Volume of a cone (V) :

1/3 πr²h

Where r = radius = diameter / 2 = x/2

Hence,

V = 1/3 * π * (x/2)² * x

V = 1/3 * π * x²/4 * x

V = 1/12 * π * x³

V = 1/12πx³

We were given 12 functions and we are to determine which of the 12 functions obey the following rule:

We will proceed to test how the functions:

Hence, option d is the correct answer

Answer:

38.11 cm^2

Step-by-step explanation:

DEF is larger than ABC

therefore find the height of ABC

7 = 1/2 * 3 * h

h = 7 * 2/3

h = 14/3

So, lets find height for DEF, 7/3 = H/ 14/3

H = 98/9

A = 1/2 * 7 * 98/9

A = 38.11 cm^2

Answer:

42 ft²

Step-by-step explanation:

You need the total surface area of the box which is shaped like a rectangular prism.

surface area = area of bases + lateral area

Let length = 3 ft, width = 2 ft, height = 3 ft.

The base is a rectangle 3 ft by 2 ft.

The perimeter of the base is 2(3 ft + 2 ft) = 10 ft

The lateral area is (perimeter of the base) × height = 10 ft × 3 ft = 30 ft²

The area of the two bases is 2 × (3 ft × 2 ft) = 12 ft²

The total surface area is 30 ft² + 12 ft² = 42 ft²

The correct graph that models this exponential decay would show a decreasing trend as x (the number of years) increases. we need to consider the information given regarding its decrease in value.

The piece of machinery decreases in value by 22.5% each year. This means that its value after one year is \(100\% - 22.5\% = 77.5\%\) of its original value. In other words, its value is 0.775 times its original value.

To model the value of the machinery after x years, we need to consider the exponential decay function. The general form of an exponential decay function is:

y = \(a(1 - r)^x\)

Where:

- y represents the value after x years.

- a represents the initial value.

- r represents the decay rate (expressed as a decimal).

In this case, the initial value (a) is $150,000 and the decay rate (r) is 22.5% or 0.225.

Therefore, the equation representing the value of the piece of machinery after x years would be:

y = \(\$150,000 * (1 - 0.225)^x\)

Simplifying the equation further, we have:

y = \(\$150,000 * (0.775)^x\)

From this equation, we can see that the value of the machinery decreases exponentially over time. The correct graph that models this exponential decay would show a decreasing trend as x (the number of years) increases.

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Answer:

$6.50 per hour

Step-by-step explanation:

6 pm-1:30pm=4.5 hrs

29.25/4.5=6.5

$6.50 per hour

Answer: -4 because 2(-6)2 = -24 and 5(2)2 = 20 so -24 + 20 is -4.

Answer:-4

Step-by-step explanation:

2(-6)2

2 x -6 x 2=-24

5 x 2 x 2=20

-24+20=-4

Answer:

\(\huge\boxed{Option \ D:f(g(x)) = (x-7)^3}\)

Step-by-step explanation:

\(f(x) = x -1\\g(x) = x^3\)

We've to find \(f(g(x))\)

Which will be \(f(x-7)\)

Putting x in f(x) as x-7

So,

\(f(g(x)) = (x-7)^3\)

See attachment for math work and answer.

Answer:

2 and -3

Step-by-step explanation:

The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.

Given the expression in the question;

-6w + (–8.3) + 1.5+ (–7w)

To simplify, first remove the parenthesis

Note that;

-6w + × - 8.3 + 1.5 + × - 7w

-6w - 8.3 + 1.5 - 7w

Next collect and add like terms

-6w - 7w - 8.3 + 1.5

Add -6w and -7w

-13w - 8.3 + 1.5

Add -8.3 and 1.5

-13w - 6.8

Therefore, -13w - 6.8 is the simplified form.

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Answer:

it will increase to about 26,214,400 rabbits.

Step-by-step explanation:

the number doubles every 6 months,

first of all we have to convert the 10 yrs to months ,,, which will be 10 × 12 months to get = 120 months in total.

divide 120 by 6 months to get the number of times the rabbits will increase to get the answer as = 20.

so we will have to double 20 times.

there are 25 rabbits now. I n the next 6 months, we will have 25 × 2 = 50...... that is i time.......19 times to go. the numbers will go as follows:

50, 100, 200, 400, 800, 1600, 3200, 6400, 12800, 25600, 102400, 204800, 409600, 819200, 1638400, 3276800, 6553600, 13107200, 26214400.

Answer:

it's says that it is ×=1

Step-by-step explanation:

3×-5=2(x-2)

3x-5=2x-4

3x-5+5=2x-4+5

3x=2x+1

3x=2x + 1

3x-2x=2x+1-2x

Answer x=1

Answer:

The answer is "2.4 units "

Step-by-step explanation:

Please find the complete question:

\(EC = x\\\\\frac{5}{3} = \frac{4}{x}\\\\5x = 4(3)\\\\5x = 12\\\\x = \frac{12}{5}\\\\x = 2.4\)

Answer:

B. 2.4

Step-by-step explanation:

5/3 = 4/EC

EC = 4 (3/5) = 12/5 = 2.4

For the simple harmonic motion equation d=2 sin(pi/3t), the period is 6 seconds.

The period of a simple harmonic motion is the time taken for one complete cycle of the motion. In this equation, d represents the displacement or position of the object at time t. The equation is in the form of sin function with the argument (pi/3)t. The general form of the equation for simple harmonic motion is d=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. To determine the period of this motion, we can use the formula T=2π/ω, where T is the period and ω is the angular frequency. In this case, ω=pi/3, so the period is T=2π/(pi/3)=6 seconds (rounded to the nearest second). Therefore, the object completes one full cycle of motion every 6 seconds.

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Answer:

9.38%

Step-by-step explanation:

First this is the solution I used:

Percentage change = actual change/original amount x 100

Hope this helps.

Answer:

D. I and II only

Step-by-step explanation:

Give:- C= 5/9( f - 32 )

--> F = 9/5c + 32

(I) If F' = F + 1

C' = 5/9( F' - 32)

C' = 5/9( F - 32) + 5/9 x 1

C' = C + 5/9

The temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius

THEREFORE, STATEMENT | IS TRUE.

(II) If C'= C + 1

F' = 9/5C' + 32

F' = ( 9/5C + 32 ) + 9/5

F' = F + 9/5

F' = F + 1.8

The temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

THEREFORE, STATMENT || IS TRUE

(III) If F' = F + 5/9

C' = 5/9 (F' - 32)

C' = 5/9 ( F - 32 ) + 5/9 x 5/9

C' = C + 25/81

The temperature increase of 5/9 degrees Fahrenheit is equivalent to a temperature increase of 25/81 degree Celsius.

THEREFORE, STATEMENT ||| IS FALSE

Answer:

Step-by-step explanation:

For two side measures and one angle measure to form one distinct triangle, the given angle must be between the given sides, or opposite the longest side.

When the given measures are ...

The given angle is opposite the longest side, so one distinct triangle can be formed.

No triangle can be formed if the given angle is opposite the shorter given side, and either of ...

__

Additional comment

As we can see from the above, the only ambiguous cases arise when the given angle is opposite the shorter given side. When that happens, the ratio of the shorter to longer given side relative to the sine of the given angle determines the nature of the solution:

Answer:

1

0

Step-by-step explanation:

14.81 radians/second

Step-by-step explanation:

Answer:

The area of the shaded parts is 160 cm².

Step-by-step explanation:

To find the area of the shaded parts, subtract the area of the unshaded triangle from the area of the outer rectangle.

The formula for the area of a rectangle is:

\(\boxed{A= w \cdot l}\)

where:

Therefore, the area of the outer rectangle is:

\(\begin{aligned}\implies A_{\sf rectangle}&=14 \cdot 16\\&= 224\; \sf cm^2\end{aligned}\)

The formula for the area of a triangle is:

\(\boxed{A=\dfrac{1}{2} bh}\)

where:

From inspection of the given diagram, the base of the unshaded triangle is 16 cm, and the height is (14 - 6) cm.

Therefore, the area of the unshaded triangle is:

\(\begin{aligned}\implies A_{\sf triangle}&=\dfrac{1}{2} \cdot 16 \cdot (14-6)\\\\&=\dfrac{1}{2} \cdot 16 \cdot 8\\\\&=8 \cdot 8\\\\&=64\; \sf cm^2\end{aligned}\)

Finally, to calculate the area of the shaded parts, subtract the area of the unshaded triangle from the area of the outer rectangle:

\(\begin{aligned} \implies A_{\sf shaded}&=A_{\sf rectangle}-A_{\sf triangle}\\&=224-64\\&=160\; \sf cm^2\end{aligned}\)

Therefore, the area of the shaded parts is 160 cm².

To determine if the LCM of two numbers is the product of the two numbers using their prime factorization, you need to check if the numbers are coprime.

Coprime numbers have no common prime factors except for 1. If the numbers are coprime, their LCM will be equal to the product of the two numbers.

To tell if the LCM of two numbers is the product of the two numbers, you need to compare the prime factorization of the two numbers. If the prime factors of both numbers are unique (meaning they do not share any common factors), then the LCM will be the product of the two numbers. However, if the two numbers share some common prime factors, then the LCM will have to include those factors at their highest power. So, to find the LCM of the two numbers, you need to take the highest power of each prime factor that appears in either number and multiply them together. If the product of these highest powers matches the product of the two numbers, then the LCM is equal to the product of the two numbers.

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Answer:

9

Step-by-step explanation:

if we divide it my 9 we will get 927,998.666667

Answer: greatest number which should be replace m= 8

Except number 9, ; 2,5.and 8 can replace m so that the number 5567m92 is divisible by 6( Here greatest among all is 8 so 8 is your answer)

Step-by-step explanation:

5567292 is divisible by 6.

5567592 is divisible by 6.

5567892 is divisible by 6.

Answer:

Step-by-step explanation:

13/40 it can not be simplified any further.

The solution set of a homogeneous system of 18 linear equations in 20 variables lies in the null space of the coefficient matrix.

To know that every associated nonhomogeneous equation has a solution, we need to ensure that the homogeneous system has a nontrivial solution.

This means that we need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, i.e., whether there exist free variables.

If the rank is less than the number of variables, then there are infinitely many solutions to the homogeneous system, and thus every associated nonhomogeneous equation has a solution.

However,

We also need to ensure that the particular solution to the nonhomogeneous equation does not lie in the null space of the coefficient matrix.

This is equivalent to checking whether the null space of the coefficient matrix is orthogonal to the vector on the right-hand side of the nonhomogeneous equation.

If it is, then the nonhomogeneous equation has a solution.

So, in summary, to know that every associated nonhomogeneous equation has a solution.

We need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, and we need to check whether the particular solution lies in the null space of the coefficient matrix.

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Answer:

3.9

Step-by-step explanation:

a^2+b^2=c^2

a^2+7^2=10^2

a^2+49=100

100-49=a^2

\(\sqrt{51}\)=a

x^2+6^2=a^2

x^2+36=\(\sqrt{51}\)^2

x^2+36=51

51-36=x^2

15=x^2

\(\sqrt{15}\)=x

x=3.9

Answer:

value decrease: 1000

Percent decrease: 2

Step-by-step explanation:

Answer:

\( \frac{x}{4} + \frac{1}{2} = \frac{1}{8} \)

\( \frac{x}{4} = - \frac{3}{8} \)

\(x = - \frac{3}{2} = - 1 \frac{1}{2} \)

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

Consider the equation, we have only one x term, so taking all the terms without x to the other side and terms with x on one side.

x/4 + 1/2 = 1/8

Take the 1/2 term on the other side,

x/4=1/8 - 1/2

Taking the LCM on the Right side,

x/4 = (1-4) / 8

x/4 = -3/8

Now, we have x/4 so what we can do is, shift the 4 to the other side too, we get,

x = ( -3/8) * 4

x = -3/2

The solution to the equation x/4 + 1/2 = 1/8 is x = -3/2.

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The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. In science, observation can also entail the perception of information and the recording of that information using tools.

Because of ethical considerations or practical limitations, an observational study infers information from a sample to the population even when the researcher has no control over the independent variable.

An experiment is a technique used to confirm or deny a hypothesis, as well as assess the possibility or effectiveness of something that has never been done before. Experiments show what happens when a certain component is modified, which sheds light on cause-and-effect relationships.

The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

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