Solve for x by using the quadratic formula. If you have multiple solutions, list them separated by comma 9x^(2)+12x=-6 x

If the pth term of an arithmetic progression is q and qth term is p then the (p+q) th term is 0.

Given that the p th term of an A.P is q aand q th term is p.

We are required to find the (p+q) th term of that A.P.

Arithmetic progression is a sequence in which all the terms have common difference between them.

N th term of an A.P.=a+(n-1)d

p th term=a+(p-1)d

q=a+(p-1)d-------1

q th term=a+(q-1)d

p=a+(q-1)d---------2

Subtract equation 2 by 1.

q-p==a+(p-1)d-a-(q-1)d

q-p=pd-qd-d+d

q-p=d(p-q)

d=(p-q)/(q-p)

d=-(p-q)/(p-q)

d=-1

Put the value of d in 1.

q=a+(p-1)(-1)

q=a-p+1

a=q+p-1

(p+q) th term=a+(n-1)d

=q+p-1+(p+q-1)(-1)

=q+p-1-p-q+1

=0

Hence if the pth term of an A.P is q and qth term is p then the (p+q) th term is 0.

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Answer:

any number equal to or less than -4

Step-by-step explanation:

x - 1 < -4

< represents that -4 is a larger number than x - 1. we know that -4 is a negative number, so anything below -4 would be less. x = -4 would be a good solution, but the reality is that any number equal to or less than -4 is the correct answer. I hope this helps!

The unit circle can be divided into 6 equal arcs using t-values that are multiples of π/3.

To determine the number of equal arcs that can be formed by dividing the unit circle using t-values that are multiples of π/3, we need to consider the angular measure between each division point.

A circle has a total angular measure of 360 degrees or 2π radians. Since we are using t-values that are multiples of π/3, each division point will have an angular measure of π/3.

To find the number of equal arcs, we divide the total angular measure of the circle (2π radians) by the angular measure between each division point (π/3 radians):

Number of equal arcs = (Total angular measure of the circle) / (Angular measure between each division point)

Number of equal arcs = (2π radians) / (π/3 radians)

Simplifying the expression, we get:

Number of equal arcs = (2π radians) * (3/π radians)

Number of equal arcs = 6

Therefore, the unit circle can be divided into 6 equal arcs using t-values that are multiples of π/3. Each arc will have an angular measure of π/3.

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Answer: When something is decreasing by 30%, the growth factor is 0.7 (1 - 0.3).

When something is increasing by 200%, the growth factor is 3 (1 + 2).

When something is decreasing by 8%, the growth factor is 0.92 (1 - 0.08).

When something is decreasing by 0.12%, the growth factor is 0.99988 (1 - 0.0012).

The function of the town's population is an exponential growth

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

Initial population = 3800

Growth  rate = 2% every year

From the above, we understand that

There is a growth in the population by 2% every year

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

This means that the function is an exponential growth

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According to the question this equation represents a single point in the xy-plane, and does not have a constant rate of change. It doesn't have a linear function as a result.

When the roots and solutions of two equations match, they are said to be equivalent. The same number, symbols, or expression must be added to or subtracted from both the equation's two sides to produce an equivalent equation. By multiplying or dividing both sides of an equation by a nonzero number, we can also obtain an analogous equation.

Equation representing a linear function:

Y is equivalent to x plus 5 times the negative one-fourth.

Linear functions have a constant rate of change, which means that as x increases or decreases by a certain amount, y also changes by a constant amount. The equation y equals negative one fourth times x plus 5 has a constant slope of negative one fourth, which means that for every increase of one in x, y will decrease by one fourth. This is a characteristic of a linear function.

The equation y equals two thirds times x squared represents a quadratic function, which has a curved graph.

The equation x = 5 is a linear equation, but it only represents a vertical line passing through x = 5. It does not have a slope or a y-intercept, which are necessary for a linear function.

The equation 2x + 7 = 12 can be simplified to a linear equation of the form y = mx + b by solving for y:

2x + 7 = 12

2x = 5

x = 5/2

Substituting x = 5/2 back into the equation gives:

y = 2(5/2) + 7 = 12

This equation represents a single point in the xy-plane, and does not have a constant rate of change. Therefore, it is not a linear function.

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Answer:

price is now $24.64

and it was $3.36 off

Step-by-step explanation:

Answer:

f(x) = \(\frac{1}{16}\) (x - 2)² + 2

Step-by-step explanation:

From any point (x, y ) on the parabola the focus and the directrix are equidistant.

Using the distance formula

\(\sqrt{(x-2)^2+(y-6)^2}\) = | y + 2 | ← square both sides

(x - 2)² + (y - 6)² = (y + 2)² ← subtract (y + 2)² from both sides

(x - 2)² + (y - 6)² - (y + 2)² = 0 ← subtract (x - 2)² from both sides

(y - 6)² - (y + 2)² = - (x - 2)² ← expand left side using FOIL and simplify

y² - 12y + 36 - y² - 4y - 4 = - (x - 2)²

- 16y + 32 = - (x - 2)² ← subtract 32 from both sides

- 16y = - (x - 2)² - 32 ← divide all terms by - 16

y = \(\frac{1}{16}\) (x - 2)² + 2

Answer:

3

Step-by-step explanation:

The gradient of the line can be calculated using the \(\frac{rise}{run}\) between two points.

\(\frac{rise}{run}\) = \(\frac{-8-(-2)}{3-5}\)

     = \(\frac{-8+2}{3-5}\)

     = \(\frac{-6}{-2}\)

     = 3

Answer:

  a.  1080

  b.  405

Step-by-step explanation:

Function evaluation is often conveniently done using a calculator. Many calculators know about the order of operations, so can be used without fear of an incorrect evaluation.

Put the value where the variable is and do the arithmetic.

  f(x) = 40(3^x)

  f(3) = 40(3^3) = 40(27) = 1080

  g(x) = 5(3^(x+1))

  g(3) = 5(3^(3+1)) = 5(3^4) = 5(81) = 405

Answer:

Step-by-step explanation:

Sum of angle in a triangle = 180°

<A+<B+<C = 180

Given <B = 50°

Substituting into the formula

<A+50+<C = 180

<A+<C = 180-50

<A+<C = 130°

Since the ∆ABC is an acute triangle, the angles <A and <C must be angles less than 90° since acute angles are angles less than 90°

The possible values of <A and <C that will be acute and give a sum of 130° are;

∠A= 58° and ∠C= 72°

∠A= 80° and ∠C= 50°

∠A= 60° and ∠C= 70°

You can see that all the Angles are less than 90° and their sum is 130°

Answer:

A scale is a way to resize drawings or figures to make them fit into a particular size.

Step-by-step explanation:

In 2D drawing or diagrams, a  scale factor greater than 1 enlarges the object, while a scale factor between 0 and 1 shrinks the objects, also using a scale factor of 1 changes nothing or leaves the drawing the way it is.

Furthermore, scales are represented in ratio form 1:2, telling us that say 1cm in the virtual environment or paper represents 2km in reality

When giving a sales presentation based on performance statements and charts,trend analysis,outperformance,volatility,consistency,historical and relative  Performance observations may a registered representative.

When giving a sales presentation based on performance statements and charts, a registered representative may make the following observations:

Trend Analysis: The representative may analyze the trend of performance over time, noting if it is consistently improving, declining, or fluctuating.

Outperformance: The representative may highlight instances where the investment or product being presented has outperformed relevant benchmarks or competitors.

Volatility and Risk: The representative may comment on the volatility or risk associated with the investment based on the performance statements and charts.

Consistency: The representative may note if the investment's performance has been consistent over time or if there are periods of significant fluctuations.

Historical Performance: The representative may discuss the investment's historical performance, comparing it to previous periods or market conditions.

Relative Performance: The representative may compare the investment's performance to similar investments or industry averages.

The observations made by a registered representative should be based on accurate and reliable data, and any claims or statements should comply with relevant regulations and disclosures.

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By solving a system of two simultaneous linear equations, it can be calculated that

Dan and Camille spent $150 altogether

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here a system of two simultaneous linear equations needs to be solved

Let Dan had $x and Camille had $y

Both cards combined hava a balance of $350

x + y = 350 ..... (1)

Amount of money Dan spent = $\(\frac{x}{2}\)

Amount of money Dan left with = $(\(x - \frac{x}{2}\)) = $\(\frac{x}{2}\)

Amount of money Camille spent = $\(\frac{y}{3}\)

Amount of money Camile left with = $\((y - \frac{y}{3})\) = $\(\frac{2y}{3}\)

By the problem,

\(\frac{x}{2} = \frac{2y}{3}\)

3x = 4y

3x - 4y = 0 .... (2)

Multiplying (1) by 4

4x + 4y = 1400 ..... (3)

Adding (1) and (3)

7x = 1400

\(x = \frac{1400}{7}\)

x = $200

Putting the value of x in (1)

200 + y = 350

y = 350 - 200

y = $150

Amount of money Dan spent = $\(\frac{1}{2}\times 200\) = $100

Amount of money Camille spent = $\(\frac{1}{3} \times 150\) = $50

Total money spent altogether  = $(100 + 50) =$150

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Answer:

Step-by-step explanation:

20049 IS YOUR ANSWER

Answer:

5(x-6)/3

Step-by-step explanation:

1. Let f(x) be y

2. Switch x and y

3. Make y the subject

4. Change y become f(x)^-1

Answer:

26:26

Step-by-step explanation:

I hope I've helped :)

Answer:

\(k=-8\)

Step-by-step explanation:

We have the two points: (2, -3) and (k, 7).

And we want to find the value of k such that the slope between these two points is -1.

So, we can use the slope formula:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Let (2, -3) be (x₁, y₁) and let (k, 7) be (x₂, y₂). Let's also substitute the slope m for -1. This gives us:

\(-1=\frac{7-(-3)}{k-2}\)

So, let's solve for k. Add in the numerator:

\(-1=\frac{10}{k-2}\)

Notice that we can rewrite the left side as:

\(\frac{-1}{1}=\frac{10}{k-2}\)

Now, we can cross-multiply:

\(-(k-2)=10\)

Divide both sides by -1. This removes the negative on the left:

\(k-2=-10\)

Finally, add 2 to both sides. So, the value of k is:

\(k=-8\)

And we're done!

This option correctly describes that the function is defined for x-values that satisfy the inequality x - 5 < x < 3. It also states that the range of the function is {-2}, which is not accurate since the range of the function includes multiple values from 1 to 6, inclusive.

Based on the given information, it seems that the linear function is represented by the points (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). To determine the domain and range of the function, we need to analyze the set of possible inputs (x-values) and the set of possible outputs (y-values) in the function.

The domain of a function refers to the set of all possible input values for the function. In this case, it appears that the function is defined for all values of x between 1 and 6, inclusive. Therefore, the domain can be represented as: Domain: {x | 1 ≤ x ≤ 6}.

The range of a function, on the other hand, refers to the set of all possible output values. Looking at the given points, we can observe that the y-values range from 1 to 6. Therefore, the range can be represented as: Range: {y | 1 ≤ y ≤ 6}.

From the given answer choices, the option that accurately represents the domain and range of the linear function is:

G Domain: {x | x - 5 < x < 3}

Range: {-2}

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Answer:

Step-by-step explanation:

I can tell you what it represents, but not what it means. Or maybe the units.

V(5/7) means that wherever you see an r on the right hand side, you put in 5/7 where the R is.

V = 4/3 * pi * r^3

V(5/7) = 4/3 * 3.14 * (5/7)^3

V(5/7) = 4/3 * 3.14 * 125 / 343

V(5/7) = 4/3 * 3.14 * 0.3644

V(5/7) = 1.526 cubic units (of whatever the units of 5/7 were to begin with)

The percentage by which the price of the car went up from the original price is 60% (third option)

The first step is to determine the price of the car after the percentage increase. Percentage is the fraction of a number as a value out of 100. The sign that is used to represent percentage is %.

Price of the car after the percentage increase = (1 + percent increase/100) x original cost of the car

Price of the car after the percentage increase = (1 + 20/100) x 20,000

Price of the car after the percentage increase = (1 + 0.2) x 20,000

Price of the car after the percentage increase = 1.2 x 20,000 = $24,000

Price after the $8,000 increase = $24,000 + 8,000 = $32,000

Percentage of the original price = (32,000 / 20,000) - 1 = 0.60 = 60%

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To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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The total bill, after a 30% price increase and a 6% tax applied to a $160 initial bill, is $208.32.

To calculate the total bill, we need to consider the price increase and the tax applied to the initial bill amount of $160.

First, we calculate the price increase by multiplying the initial bill amount by 30%:

Price increase = $160 * 30% = $48.

Adding the price increase to the initial bill amount, we get the new bill amount before tax:

New bill amount before tax = $160 + $48 = $208.

Next, we calculate the tax amount by multiplying the new bill amount before tax by 6%:

Tax amount = $208 * 6% = $12.48.

Finally, we add the tax amount to the new bill amount before tax to find the total bill:

Total bill = New bill amount before tax + Tax amount = $208 + $12.48 = $208.32.

Therefore, the total bill, after the price increase and tax, is $208.32.

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Answer:36

Step-by-step explanation:

Let h be the number of hats and s be the number of scarves that Alex can bring to the art fair. Then, the system of inequalities can be written as:

h ≤ 20 (since he can make at most 20 hats)

s ≤ 30 (since he can make at most 30 scarves)

h + s ≤ 40 (since he can make no more than 40 items altogether)

h + s ≥ 25 (since he wants to bring at least 25 items)

To graph this system of inequalities, we can plot the lines h = 20, s = 30, h + s = 40, and h + s = 25, and shade the region that satisfies all the inequalities. The resulting graph will be a quadrilateral with vertices at (20, 0), (0, 30), (10, 15), and (20, 5). The shaded region will be the area inside this quadrilateral that is above the line h + s = 25.

Answer:

n ≥ 6.24/x

Step-by-step explanation:

Given that :

Amount spent is atleast $6.24

Let price spent = p

p ≥ $6.24

If cost of granola bar = x

The number of granola bars, n purchased will be :

n ≥ 6.24/x

Since cost of granola bar isn't given, we represent it as x.

The hypothesis regarding the convincing evidence that the average number of colleges students apply to is accepted because  p-value is more than the chosen significance level.

The null hypothesis will be that the average number of colleges students apply to is equal to or less than 8. The alternative hypothesis would be that the average number of colleges students apply to is greater than 8.

We can apply a one-sample t-test to test this hypothesis. By doing so we can evaluate the t-statistic
t = (x'- μ) / (s / √n)
here
x' = sample mean,
μ = hypothesized population mean,
s = sample standard deviation,
n = sample size
(x'- μ) / (s / √n)
Staging values
(9.7 - 8) /(7) /√206)
=( 0.3) /( 7/ 14.35)
= (0.3) /(0.4)
= 0.75


Now, the p-value associated with this t-statistic using a t-distribution . The p-value in this case is  greater than the chosen significance level (usually 0.05), we will accept  the null hypothesis.

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