38 degrees 2x degrees +6 degrees

Answer:

Step-by-step explanation:

here is an solution

Answer:

Yes, because the products of means is equal to the product of extreme

Step-by-step explanation:

The term that must be added to the equation x2+4x=1 to make it into a perfect square is 4.

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. Since there is no ax2 term, the equation is linear if a = 0, not quadratic.

This is true because the Latin word quadratum, which means "square," plus the fact that the area of a square with side length x is equal to x2, make up what is known as the quadratic (or "square-like") definition of a polynomial equation with exponent two.

x²+4x=1

as, the x has coefficient 4.

so,

half the coefficient of x and add and subtract the square of the remaining.

x²+4x + 2 ² - 2² =1

Now,

make the whole square term

x²+4x + 2 ² - 4 - 1=0

( x + 2)² -5= 0

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The unknown angle x in the triangle is 80 degrees

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

The triangle

The unknown angle x is calculated using the sum of angles in a triangle theorem

So, we have

x + 60 + 40 = 180

Evaluate the like terms

x + 100 = 180

So, we have

x = 80

Hence, the unknown angle x is 80 degrees

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Answer:

x=-y/4 +6

Step-by-step explanation:

First, y to each side.

-4x=y+24

Second, leave the x by itself by dividing both sides by - 4.

x=-y/4 +6

The equation with 'n' as the independent variable is m = -2n - 13.

To rearrange the equation so that n is the independent variable, you can start by moving all of the terms with n on one side of the equation and all of the other terms on the other side.

You can start by subtracting 1 from both sides of the equation to get

m = -2(n + 6) - 1.

Then, you can distribute the -2 on the right side of the equation to get

m = -2n - 12 - 1.

Finally, you can combine the constants on the right side of the equation to get m = -2n - 13.

Therefore, the equation with 'n' as the independent variable is m = -2n - 13.

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Answer:

  an = 1/2n² -1/2n -2

Step-by-step explanation:

You want a formula for the n-th term of the quadratic sequence -2, -1, 1, 4.

Using x = 1, 2, 3 and y = -2, -1, 1 we can write equations for the coefficients a, b, c of the quadratic expression ax² +bx +c.

  a(1²) +b(1) +c = -2

  a(2²) +b(2) +c = -1

  a(3²) +b(3) +c = 1

Subtracting the first equation from the other two, we get ...

  3a +b = 1

  8a +2b = 3

Subtracting twice the first from the second of these, we get ...

  (8a +2b) -2(3a +b) = (3) -2(1)

  2a = 1

  a = 1/2

Then b can be found from ...

  b = 1 -3a = 1 - 3/2 = -1/2

And c can be found from ...

  -2 -b -a = c = -2 -(-1/2) -(1/2) = -2

The formula is ...

  an = 1/2n² -1/2n -2

__

Additional comment

For systems of equations, the solver used in the second attachment works well. It tells us (a, b, c) = (1/2, -1/2, -2) as we found above.

Alternate solution

The first differences of the given terms are ...

  1, 2, 3

And their differences are ...

  1, 1

The coefficient of n² is half this second-difference value: 1/2.

If you subtract 1/2n² from the given terms, you get ...

  -5/2, -3, -7/2, -4

This arithmetic sequence has the formula ...

  a1 +d(n -1)

  -5/2 +(-1/2)(n -1) = -1/2n -2

Adding this to the term we subtracted gives ...

  an = 1/2n² -1/2n -2 . . . . . as above

Answer:

The ball takes 5 seconds to hit the ground

Step-by-step explanation:

The equation to model the height of a golf ball in time t is:

\(h(t)=80t-16t^2\)

There are two moments when the height is zero: At launch time and when it hits the ground. To find the last time, we equate:

\(80t-16t^2=0\)

Factoring out t:

\(t(80-16t)=0\)

It gives us two solutions:

t=0

\(80-16t=0\)

Solving:

\(-16t=-80\)

\(t=-80/(-16)=5\)

t = 5 sec

Thus, the ball takes 5 seconds to hit the ground

Answer:

6) a

7) c

Step-by-step explanation:

question 6 is incorrect because you have to find the distance between the two points. for question 6, you are finding the distance between -2 and 1. that is three!

The domain of function f(x)=(x)/(8x+9) is given by D = (-∞, -9/8) ∪ (-9/8, ∞).

To determine the domain of a function, we need to find the values of x for which the function is defined. Here, we have the function f(x) = x/(8x + 9).The denominator of f(x) cannot be equal to zero.

If it were, the function would be undefined. So, we have:8x + 9 ≠ 0 ⇒ 8x ≠ -9 ⇒ x ≠ -9/8Thus, x cannot be equal to -9/8. Other than that, the function is defined for all real numbers.

Therefore, the domain of the function f(x) = x/(8x + 9) is all real numbers except x = -9/8. This can be written as: D = (-∞, -9/8) ∪ (-9/8, ∞). The domain of f(x) is given by D = (-∞, -9/8) ∪ (-9/8, ∞).

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Answer:

$1.80

Step-by-step explanation:

The statement "The empirical rule assumes that the distribution of data follows a normal curve." is True.

The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that states that for a normal distribution, approximately 68% of the data will fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This implies that the distribution of data follows a normal curve.

A normal distribution is a type of probability distribution that follows a symmetrical bell-shaped curve. It is also known as the Gaussian distribution and is a continuous probability distribution. The normal distribution is defined by its mean, which is the average of the values, and its standard deviation, which is a measure of the spread of the values from the mean.

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Answer:

x <  3

Step-by-step explanation:

A 40 gram sample of a substance that’s used for drug research has a k-value of 0.1472. The substance's half-life, in days, is approximately 4.7 days.

The half-life of a substance is the time it takes for half of the substance to decay or undergo a transformation. The half-life can be determined using the formula:

t = (0.693 / k)

where t is the half-life and k is the decay constant.

In this case, we are given that the sample has a k-value of 0.1472. We can use this value to calculate the half-life.

t = (0.693 / 0.1472) ≈ 4.7 days

Therefore, the substance's half-life, rounded to the nearest tenth, is approximately 4.7 days.

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The answer is D. 95th percentile is not needed for constructing a box-plot.

A box plot, also known as a box-and-whisker plot, provides a visual representation of the distribution of a dataset. It consists of several key measures, including the following:

A. First quartile (Q1): This is the 25th percentile, which marks the lower boundary of the box.

B. 50th percentile: This is the median, which is the middle value of the dataset when it is ordered from smallest to largest. It is represented by a line within the box.

C. 75th percentile (Q3): This is the upper quartile, marking the upper boundary of the box.

D. 95th percentile: This measure is not typically used in constructing a box plot. It provides information about the value below which 95% of the data falls, but it is not necessary for constructing the basic elements of a box plot.

Therefore, the correct answer is D. 95th percentile.

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The formula becomes ½(10cos(θ)² - 5²)dθ, integrated from θ = π/3 to θ = 5π/3. Simplifying, we have ½(100cos²(θ) - 25)dθ.

The area of the region that lies inside the first curve (r = 10cos(θ)) and outside the second curve (r = 5) can be found by evaluating the definite integral of ½(r₁² - r₂²)dθ, where r₁ represents the outer curve and r₂ represents the inner curve.

To find the limits of integration, we need to determine the values of θ where the two curves intersect. Setting r₁ equal to r₂, we have 10cos(θ) = 5. Solving this equation, we find cos(θ) = ½, which corresponds to θ = π/3 and θ = 5π/3.

Now we can calculate the area using the definite integral. The formula becomes ½(10cos(θ)² - 5²)dθ, integrated from θ = π/3 to θ = 5π/3. Simplifying, we have ½(100cos²(θ) - 25)dθ.

Integrating this expression will give us the exact area of the region. Evaluating the integral over the given limits will provide the desired result.

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The data set that shows a nonlinear association is the third set.

The easiest way to check this is to graph the sets on an x-y plane, and see which of these graphs does not behave like a line.

But let's do another thing.

For each of the sets identify the increase in the independent variable, x, and then the increase in the y-variable.

For example, in the first table, we have the pairs:

(2, 3), (3, 4), (4, 5), etc...

This is clearly a linear relation of the form:

y = x + 1

So, writing each set in increasing order of the elements allows us to identify if it is linear or not.

Now let's go to the third option, the elements in order are:

(2, 2), (5, 4), (8, 10), ....

Notice that between the first two pairs, x increases by 3 and y increases by 2.

Between the second two pairs, x increases by 3 again, but y increases by 6.

Thus, this is not a linear relation.

We conclude that the correct option is the third set.

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For each pound of potatoes, the number of cups of cheese is,

⇒ 1/2 pounds

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The graph shows the relationship between the number of pounds of potatoes and the number of cups of shredded cheese used to make the recipe.

Hence, Two points on the graph are (3, 1 1/2) and (9, 4 1/2).

Thus, The equation of line is,

⇒ y - 3/2 = (9/2 - 3/2) / (9 - 3) (x - 3)

⇒ y - 3/2 = 3/6 (x - 3)

⇒ y - 3/2 = 1/2 (x - 3)

⇒ y - 3/2 = 1/2x - 3/2

⇒ y = 1/2x

Thus, For each pound of potatoes, the number of cups of cheese is,

⇒ y = 1/2 × 1

⇒ y = 1/2 pounds

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Complete question is shown in figure.

B. Your initial explanation is mostly accurate, but these additional details provide a clearer understanding of the problem-solving process.

A. The process you described is commonly known as problem-solving or decision-making. Here's a breakdown of the steps involved: Identify the problem, Generate alternative solutions, Evaluate alternatives, Select the best solution, Implement the solution.

Identify the problem: The first step is to clearly identify and define the problem at hand. This involves understanding the nature of the problem, its causes, and its consequences or effects. Without a clear understanding of the problem, it would be difficult to find an appropriate solution.

Generate alternative solutions: Once the problem is identified, the next step is to brainstorm and generate multiple possible solutions or approaches to address the problem. This step encourages creativity and exploration of different options.

Evaluate alternatives: After generating alternative solutions, each option should be evaluated carefully. Factors such as feasibility, cost, time, resources required, and potential risks or benefits should be considered. This evaluation helps in narrowing down the options to those that are most viable.

Select the best solution: Based on the evaluation, one or more solutions may stand out as being the most effective or suitable for solving the problem. The best solution is selected based on its ability to address the problem efficiently and meet the desired objectives.

Implement the solution: Once the best solution is chosen, it is put into action. Implementation may involve planning, executing tasks, allocating resources, and managing the necessary steps to bring the solution to fruition.

It's important to note that the order of the steps may vary depending on the context and the complexity of the problem. While it's generally logical to evaluate and select the best solution before implementing it, sometimes it may be necessary to iterate through the steps, re-evaluate options, or make adjustments during the implementation phase.

Regarding the other options you mentioned:

A. This option suggests starting with identifying the best solution without understanding the nature of the problem or considering other possible solutions. As you correctly pointed out, this approach is flawed because it skips important steps in the problem-solving process.

C. This option implies evaluating and selecting the best solution before understanding the problem or considering other alternatives. Again, this is incorrect because a thorough understanding of the problem and exploration of multiple solutions should precede the evaluation and selection stage.

D. This option suggests implementing the solution before evaluating and selecting the best one. However, it's generally more effective to assess the potential effectiveness of different solutions before committing to their implementation.

In summary, your initial explanation is mostly accurate, but these additional details provide a clearer understanding of the problem-solving process.

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Answer:

1 and 3

Step-by-step explanation:

The equation can be arranged to form equations 1 and 3.

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Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

The equation in slope-intercept form for the line that passes from the points (-7,2) and (5,8) is y = (1/2)x -3/2.

We know that, the slope intercept form is given by:-

y = mx + b

Where,

(x,y) is the ordered pair of every point on the line

m is the slope of the line

b is the y-intercept of the line

We know that, slope = (8-2)/(5-(-7)) = 6/12 = 1/2

Putting (-7,2) in (x,y) and m = 1/2 in the slope intercept form, we get,

2 = (1/2)(-7) + b

2 = -7/2 + b

b = -3/2

Hence, the slope intercept form of the line is y = (1/2)x -3/2.

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Answer:

x=-14 and x=-1

Step-by-step explanation:

x+6=-7                 x-6=-7

x=-14                      x=-1

Using proportions, it is found that it's value before the 2-day drop was of 264 points.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the value dropped by 25%, that is, it was 75% of the original amount, and the dropped value was of 198 points, hence the original amount was:

0.75x = 198

x = 198/0.75

x = 264

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Explanation:

First we have to see that there's a first transformation from triangle ABC to triangle A'B'C'. This first transformation is a translation. Since the units are not shown in the graph I can only tell the direction of the translation: it's a translation to the right and down (more units to the right than down).

Then there's a final transformation from triangle A'B'C' to triangle A''B''C'', which is a reflection over the y-axis

Answer:

0. Translation to the right and down

1. Reflection over the y-axis

The number of square yards that is the area of the composite figure is 38 square yards

The composite figure is made up of a trapezium and a right angled triangle. We can therefore find the area by finding the area of the two figures and then summing them up.

Area of triangle :

= 1/ 2 x base x height

= 1 / 2 x 3 x 2

= 3 square yards

Area of trapezium :

= ( a + b ) / 2 x height

= ( (3 + 2 ) + 9 ) / 2 x 5

= ( 5 + 9 ) / 2 x 5

= 14 / 2 x 5

= 35 square yards

The area of the figure is:

= 3 + 35

= 38 square yards

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Answer:

BELOW is the answer

Step-by-step explanation:

fm = 15.2m + 58

step 1; add -15.2m to both sides.

fm + -15.2m = 15.2m + 58

fm - 15.2m = 58

step 2; Factor out variable m.

m(f - 15.2) = 58

step 3; Divide both side by f-15.2

\(\frac{mf - 15.2)}{f - 15.2}\) = \(\frac{58}{f - 15.2}\)

answer will be; m = \(\frac{58}{f - 15.2}\)

a) The solution for b in the equation 2b × 3 = 6 is b = 1.

b) The solution for b in the equation 32 - 3b = 2 is b = 10.

c) The solution for b in the equation 6 + 7b = 41 is b = 5.

d) The solution for b in the equation 100/5b = 2 is b = 10.

a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.

2b × 3 = 6

(2b × 3) / 2 = 6 / 2

3b = 3

b = 3/3

b = 1

Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.

c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.

6 + 7b - 6 = 41 - 6

7b = 35

b = 35/7

b = 5

Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.

b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.

32 - 3b - 32 = 2 - 32

-3b = -30

b = (-30)/(-3)

b = 10

Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.

d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.

(100/5b) × 5b = 2 × 5b

100 = 10b

b = 100/10

b = 10.

Therefore, the solution for b in the equation 100/5b = 2 is b = 10.

In summary, the solutions for b in the given equations are:

a) b = 1

c) b = 5

b) b = 10

d) b = 10

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The partial sum of the given series -3 + (-6) + (-12) + ... + (-192) can be calculated using the formula for the sum of an arithmetic series. The sum is -2016.

To find the partial sum of the series -3 + (-6) + (-12) + ... + (-192), we can use the formula for the sum of an arithmetic series.

The given series is an arithmetic series where each term is obtained by multiplying the previous term by -2. We can observe that each term is obtained by multiplying the previous term by -2. Therefore, the common ratio of this series is -2.

To find the partial sum of an arithmetic series, we can use the formula:

Sn = (n/2)(a + L),

where Sn is the sum of the first n terms, a is the first term, and L is the last term.

In this series, the first term a = -3, and we need to find the last term L. We can use the formula for the nth term of an arithmetic series:

Ln = a * r^(n-1),

where r is the common ratio.

We need to find the value of n that corresponds to the last term L = -192. Setting up the equation:

-192 = -3 * (-2)^(n-1).

Dividing both sides by -3, we get:

64 = (-2)^(n-1).

Taking the logarithm base 2 of both sides:

log2(64) = n - 1,

6 = n - 1,

n = 7.

Now we can substitute the values into the formula for the partial sum:

Sn = (n/2)(a + L) = (7/2)(-3 + (-192)) = (7/2)(-195) = -1365/2 = -682.5.

Therefore, the partial sum -3 + (-6) + (-12) + ... + (-192) equals -682.5.

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