3x^3+2x-4 divided by 2x^2-x-4

To find the other angles in a parallelogram if only one is given then you need to subtract the number with 180 to find the consecutive angles. With the theorem 6-5 opposite angles are congruent, so the opposite side would have the same value.

The answer is 25

25x1 is 25

anything multiplied by 1 Is itself

Answer:

Step-by-step explanation:

There are 108 feet in 36 yards.what is the constant of proportionality that relates y, the number of yards to x, the number of feet?

Answer:

1/3 im pretty sure this is the right answer wish you good luck

A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

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Answer:

100

Step-by-step explanation:

Evaluate the function when x=3 (third bounce)

Answer: 0.86 ft

Determining whether each statement implies correlation or causation between two variables is as follows:

Correlation indicates that one independent variable causes another dependent variable to change.

Causation indicates that one dependent variable or event is the direct result of the occurrence of the other event or independent variable.

Causation shows cause and effect - unlike correlation which points out two events simultaneously occur or two variables change at the same time.

Thus, correlation is a test of association in relationship, while causation focuses on cause and effect.

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Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

The asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

What is the standard position of angles?

Standard position simply means that the vertex of the angle is at the origin of the circle and that one ray of the angle is on the positive x-axis. The other ray of the angle is placed at the angle measure formed by traveling counter-clockwise along the circle.

To draw an angle in standard position with measure 8/3 π, follow these steps:

Start with the positive x-axis.

Counterclockwise, rotate the initial side of the angle until it coincides with the positive x-axis.

Starting from the initial side on the positive x-axis, rotate the terminal side of the angle in a counterclockwise direction until the angle measures 8/3 π.

The resulting angle will have a measure of 8/3 π and will look like the following:

       |

       |

--------*-----------

       |

       |

Here, the asterisk (*) represents the vertex of the angle, the initial side is the positive x-axis, and the terminal side is the red line segment that forms an angle of 8/3 π with the positive x-axis.

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The Average rate of change of the function f(x) = 2x² + 3 in the interval [1 , 5]  is 12  .

In the question ,

the function is given as f(x) = 2x² + 3 ,

the interval in which we have to find the average rate of change is [1,5] .

So , f(1) = 2 + 3  = 5

and ,  f(5) = 2(5)² + 3 = 50 + 3 = 53

we know that the the average rate of change for the function f(x) over the interval [a,b] is calculated using the formula .

Rate Of Change is \(=\) (f(b) - f(a))/(b - a)

Substituting the required values in the formula , we get

Rate Of Change is  \(=\) (f(5) - f(1))/(5 - 1)

= (53 - 5)/4

= 48/4  = 12

Therefore , Average Rate Of Change is 12 .

The given question is incomplete , the complete question is

What is the average rate of change in f(x) = 2x² + 3 between x = 1 and x = 5 ?

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The Probability is 0.750 .

What is probability explain with an example?

                           Did not lie lied Total

Positive test results  15          45   60

Negative test results 32           12    44

Total                          47           57   104

The probability that the subject lied given that the test yield a positive result is given by

P = P( Subject lied and the test yield a positive result) / P( test yields a positive results)

P=  45/104/60/104  = 45/60 = 3/4 = 0.750

So the Probability is 0.750

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Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

Answer:

28. B

29. D

30. A

Step-by-step explanation:

28.

2 5/8 yd × 5/6 yd =

= 21/8 × 5/6 yd²

= 105/48 yd²

= 35/16 yd²

= 2 3/16 yd²

Answer: B

29.

2641 becomes 6241.

In 6241, the 6 is in the thousands place.

6 × 1000 = 6000

Answer: D

30.

90 + 7 × (7 - 1) =

Use the correct order of operations.

= 90 + 7 × 6

= 90 + 42

= 132

Answer: A

Answer:

21.9mm

Step-by-step explanation:

6.2+ 15.7 = 21.9

hope this helps....

Answer:

711001392

321000759

Step-by-step explanation:

hope it helps ^o^

Type such digits that's are correlated to both numbers but they are not present in both rather than present in one.

They can be 2 and 7 or 5 and 9

You can write other one also

The value of x for each item is given as follows:

28. x = 5.

29. x = 3.44.

For item 28, we apply the crossing chord theorem, which states that the products of the parts of the chords are equal, hence the value of x is obtained as follows:

16x = 10 x 8

16x = 80

x = 5.

For item 29, we apply the two secant theorem, hence the value of x is obtained as follows:

10(x + 10) = 12(12 + 25)

10x + 100 = 444

10x = 344

x = 3.44.

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The exponential function that can model the county population, y, x decades after Tiana was born, is:

\(y = 641000(0.99)^x\)

The population will fall below 600,000 in 6.6 decades after Tiana was born.

The definition of the exponential function is presented as follows:

\(y = a(b)^x\)

In which the parameters of the exponential function are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the function is:

\(y = 641000(0.99)^x\)

The population will fall below 600,000 when y = 600000, hence:

\(y = 641000(0.99)^x\)

\(600000 = 641000(0.99)^x\)

\((0.99)^x = \frac{600000}{641000}\)

\(\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}\)

\(x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}\)

\(x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}\)

x = 6.6 decades.

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In equation 7(5x + 2) = -4(6 - 5x), Using the Distributive Property, we get 35x + 14 = -24 + 20x. So, the correct option is D).

To solve the equation 7(5x + 2) = -4(6 - 5x), a good first step is to use the Distributive Property to simplify both sides of the equation. Distributing the 7 and -4 on the left and right sides, respectively, we get

35x + 14 = -24 - 20x.

Next, we can combine like terms by adding 20x to both sides to get 55x + 14 = -24. Then, subtracting 14 from both sides, we get 55x = -38. Finally, we can solve for x by dividing both sides by 55, giving us x = -38/55. Therefore, the solution to the equation is x = -38/55.

The evaluation process involves performing arithmetic operations in a logical order to simplify the equation step-by-step until a solution is reached. So, the correct answer is D).

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b. four fifths plus two fourths

Step-by-step explanation: Change the fractions to their equivalents in 20ths-- like finding the common denominator.

Divide the original denominator into 20, then multiply the result by the original numerator to get the new numerator.

4/5  20/5 = 4    4×4 = 16   so 4/5 is equivalent to 16/20

2/4   20/4 = 5    5×2 = 10   so  2/4 is equivalent to 10/20  

Add:    16/20 + 10/20 = 26/20

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The solutions to the nearest tenth are x = -0.1 and x = 1.3

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

5x² - 2x - 1 = 4x

Evaluate the like terms

So, we have

5x² - 6x - 1 = 0

Next, we solve using a graph

The graph of 5x² - 6x - 1 = 0 is added as an attachment

From the attached graph, we can see that the curve intersects with the x-axis at x = -0.1 and x = 1.3

This means that the solutions are x = -0.1 and x = 1.3

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Answer:

The solutions to the equation 5x^2-2x-1=4x to the nearest tenth are x ≈ 1.3 or x ≈ -0.4.

Step-by-step explanation:

To solve the equation 5x^2-2x-1=4x to the nearest tenth, we can start by moving all the terms to one side of the equation.

5x^2-2x-1=4x

5x^2-6x-1=0

Next, we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 5, b = -6, and c = -1.

Plugging these values into the formula gives:

x = (-(-6) ± sqrt((-6)^2 - 4(5)(-1))) / 2(5)

x = (6 ± sqrt(56)) / 10

The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).

We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.

From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:

243 = (9/2)(2(11) + (9-1)d)

243 = 9(22 + 8d)

243 = 198 + 72d

45 = 72d

d = 45/72 = 5/8

Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:

tₙ = a + (n-1)d

t₄ = 11 + (4-1)(5/8)

t₄ = 11 + 3(5/8)

t₄ = 11 + 15/8

t₄ = 88/8 + 15/8

t₄ = 103/8

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The numeric values of the piecewise function in this problem are given as follows:

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

A piecewise function is a function that has different definitions, based on the input x of the function.

For values of x that are of 1 or less, the function is defined as follows:

f(x) = x.

Hence the numeric values in this interval are given as follows:

For values of x that are greater than 1, the function is defined as follows:

f(x) = -x + 4.

Hence, at x = 3, the numeric value of the function is given as follows:

f(3) = -3 + 4 = 1.

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Answer:  The correct answer is 9x+36

Step-by-step explanation:

Area of the rectangle:

short side: 12

long side: 3/4x + 3

area = 12 * (3/4x + 3)

area = 12*3/4x + 12*3

area = 36/4x +36

area = 9x + 36

Answer: 9x+36

Step-by-step explanation:

Area=length times width which would be length: 3/4x+3 times width which is 12.

12 times 3/4x is 9x

Then you need to do the same for 12 times 3 which is 36.

So I believe it is 9x+36.

One role of plants in the carbon cycle is the process of carbon dioxide (CO2) absorption during photosynthesis. Plants are able to take in atmospheric CO2 and convert it into organic carbon compounds through the process of photosynthesis.

During photosynthesis, plants utilize sunlight, water, and CO2 to produce carbohydrates and release oxygen as a byproduct.This absorption of CO2 by plants helps in reducing the concentration of greenhouse gases in the atmosphere, thus playing a crucial role in mitigating climate change.

By capturing carbon from the atmosphere, plants act as natural carbon sinks, storing carbon in their tissues, including leaves, stems, roots, and woody structures. Some carbon is stored temporarily, such as in leaves or as plant biomass, while other carbon can be stored for longer periods when plants die and decay, leading to the formation of fossil fuels over millions of years.

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Answer:

0

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-5)/(-4-2)

m=0/-6

m=0

Answer:

\(P(X\cap Y\cap Z)=0.05\)

Step-by-step explanation:

From the question we are told that:

Percentage of audience in first concert \(P(X)=0.28\)

Percentage of audience in second concert \(P(Y)=0.42\)

Percentage of audience in third concert \(P(Z)=0.30\)

Audience Percentage at at-least one concert \(P(X \cup Y \cup Z)=0.80\)

Percentage of audience at first & second concert \(P(X \cap Y)=0.10\)

Percentage of audience in first & third concert \(P(X \cap Z)=0.08\)

Percentage of audience in second & third concert \(P(Y\cap Z)=0.07\)

Generally the equation for probability of attending all concerts \(P(X\cap Y\cap Z)\)is mathematically given by

\(P(X \cup Y \cup Z)=P(X)+P(Y)+P(Z)-P(X \cap Y)-P(X \cap Z)-P(Y\cap Z)+P(X\cap Y\cap Z)\)

\(P(X\cap Y\cap Z)=P(X \cup Y \cup Z)-P(X)-P(Y)-P(Z)+P(X \cap Y)+P(X \cap Z)+P(Y\cap Z)\)

\(P(X\cap Y\cap Z)=0.80-0.28-0.42-0.30+0.10+0.80+0.70\)

\(P(X\cap Y\cap Z)=0.05\)

Therefore the probability that a randomly selected audient attended all the concerts

\(P(X\cap Y\cap Z)=0.05\)

Answer:

c

Step-by-step explanation:

The third function has a range of y that is greater than or equal to 0.

A function is a kind of rule that, for one input, gives you one output.

For the first function, it contains negative values for y, so it was eliminated.

The second function did not start from zero, so it was eliminated.

The third function obeys the given condition, but the last function contains negative values for y.

Hence, the third function satisfies the condition that y is greater than or equal to 0. 

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The values greater than -3, such as 0, 2, and 4 are solutions to the inequality.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

-3x-3 less than or equal to 6

This can be written as -3x-3≤6

Add 3 on both the sides

-3x≤6+3

-3x≤9

Divide both sides by 3

-x≤3

x≥-3

Hence, the values greater than -3, such as 0, 2, and 4 are solutions to the inequality.

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Answer: 0,2,4

Step-by-step explanation:

just did the test

Answer:

1st option

Step-by-step explanation:

Complementary angles sum to 90°

∠ BFC and ∠ AFB form a right angle and sum to 90°

These angles are therefore complementary

The sine and cosine of the angle of point P are sin θ = 143/145 and cos θ = -24/145 respectively. Option b. is the answer

Given the coordinate of the point as P (-24/145, 143/145)

This implies x = -24/145 and y =  143/145

To determine the sine and cosine of the angle of point P, we can make a sketch using this information (see attached image).

opposite = 143/145, adjacent = -24/145

hypotenuse = √[(-24/145)² + (143/145)²] = √1 = 1

Using trigometric ratios:

sin θ =   (143/145) / 1 = 143/145    [sin θ = opposite/ hypotenuse]

cos θ =  (-24/145) / 1 = -24/145    [cos θ = adjacent/ hypotenuse]

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