Solve (9th grade math)

The function g(x) is obtained by stretching the logarithmic function f(x) vertically by 7, reflecting it over the x-axis and y-axis, and shifting it up by 2 units. The equation for g(x) is -7*log₆(-x) + 2.

To find the equation of the function g(x), we can apply a series of transformations step by step. First, we stretch the function vertically by a factor of 7 by multiplying it by 7. This gives us the function g₁(x) = 7*log₆(x).

Next, we reflect the function g₁(x) over the x-axis by multiplying it by -1. This results in the function g₂(x) = -7*log₆(x).

To reflect the function g₂(x) over the y-axis, we replace x with -x, giving us the function g₃(x) = -7*log₆(-x).

Lastly, we shift the function g₃(x) up by 2 units by adding 2 to it. This gives us the final equation for g(x) as g(x) = -7*log₆(-x) + 2.

In summary, the function g(x) is obtained by vertically stretching the logarithmic function f(x) by a factor of 7, reflecting it over the x-axis, reflecting it over the y-axis, and then shifting it up by 2 units.

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Answer:

it is too blury to read

Step-by-step explanation:

Answer:

An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.

To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.

Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is

20,18,16,14,12

In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.

The simplification of 3 hours : 45 m is 4 minutes : 1 minutes.

Ratio refers to a number representing a comparison between two named quantities.

3 hours : 45 m

Convert hours to minutes:

1 hour = 60 minutes

3 hours = 180 minutes

3 hours : 45 m = 180 minutes : 45 minutes

= 180/45

= 4 / 1

= 4 : 1

Ultimately, 3 hours : 45 m is 4 minutes ratio 1 minutes.

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A. The volume of the hemisphere with a diameter of 48 yards is approximately 1001.1 cubic yards.

B. The volume of the sphere with a circumference of a great circle approximately equal to 26 meters is approximately 359.4 cubic meters.

A. To find the volume of a hemisphere, we first need to calculate the radius. The diameter is given as 48 yards, so the radius is half of that, which is 24 yards.

The formula for the volume of a hemisphere is (2/3)πr^3, where r is the radius. Plugging in the values:

Volume = (2/3) * π * (24^3)

Volume ≈ 1001.1 cubic yards (rounded to the nearest tenth)

Therefore, the volume of the hemisphere is approximately 1001.1 cubic yards.

B. To find the volume of a sphere, we need to know the radius. Since the circumference of a great circle is given as approximately 26 meters, we can use the formula C = 2πr, where C is the circumference and r is the radius.

We can rearrange the formula to solve for the radius: r = C / (2π). Plugging in the circumference:

r = 26 / (2π)

r ≈ 4.134 meters (rounded to the nearest thousandth)

The formula for the volume of a sphere is (4/3)πr^3. Substituting the radius:

Volume = (4/3) * π * (4.134^3)

Volume ≈ 359.4 cubic meters (rounded to the nearest tenth)

Therefore, the volume of the sphere is approximately 359.4 cubic meters.

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The equation that represents the total cost of purchasing currency is 1.30x + 1.50y = 3200.00.

The equation that represents the relationship between the number of currency A and number of currency B is x = 5y.

x = 2000 and y = 400

There are 2000 of currency A and 400 of currency B

In order to write a system of linear equations to describe this situation, we would assign variables to the number of currency A and currency B, and then translate the word problem into an algebraic equation as follows:

Since she budgeted $3200.00 for spending money on an upcoming trip and currency A is trading at $1.30 per euro, and currency B is trading at $1.50 per pound, a system of linear equations to describe this situation is given by;

1.30x + 1.50y = 3200.00

x = 5y

1.30(5y) + 1.50y = 3200.00

8y = 3200

y = 3200/8

y = 400

x = 5y

x = 5(400)

x = 2000

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Answer:

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Step-by-step explanation:

To find the slope, we can use the slope formula.

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

    = ( 4-8)/(-5 - -5)

    = (4-8)/(-5+5)

   = -4/0

The slope is undefined.

The other side of the triangle is approximately 4.664 cm.

Let's denote the other side of the triangle as x. We know that the perimeter of the triangle is 22 cm, and one of the sides is 9 cm. The perimeter of a triangle is the sum of the lengths of its three sides. So, we can set up the equation:

9 + x + z = 22

where z represents the remaining side.

Now, we are given that the area of the triangle is 20.976 cm². The area of a triangle can be calculated using the formula:

Area = (1/2) * base * height

Since we know the area and one side (9 cm), we can rearrange the formula to solve for the height (which is the remaining side, z):

z = (2 * Area) / 9

Substituting the given values, we get:

z = (2 * 20.976) / 9

z ≈ 4.664 cm

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The discriminant of the quadratic equation -2x² + 6x + 13 is 140.

To find the discriminant of the quadratic equation 0 = -2x² + 6x + 13, we can use the formula for the discriminant, which is given by Δ = b² - 4ac. The quadratic equation is in the form ax² + bx + c = 0, with coefficients a = -2, b = 6, and c = 13.

Substituting these values into the discriminant formula, we have:

Δ = (6)² - 4(-2)(13)

Δ = 36 - (-104)

Δ = 36 + 104

Δ = 140

The discriminant provides valuable information about the nature of the solutions of a quadratic equation.

It can take on different values, and each value indicates a different scenario:

If the discriminant (Δ) is greater than zero (Δ > 0), then the quadratic equation has two distinct real solutions.

If the discriminant is equal to zero (Δ = 0), then the quadratic equation has a single real solution (a repeated root).

If the discriminant is less than zero (Δ < 0), then the quadratic equation has no real solutions, but rather two complex solutions.

The discriminant is 140 (Δ = 140), which is greater than zero, the quadratic equation -2x² + 6x + 13 has two distinct real solutions.

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The correct answer is C. 2.

To determine the slope of a line, we need to calculate the change in the y-coordinates divided by the change in the x-coordinates between two points on the line. In this case, we have the points (0, -5) and (3, 1).

The change in the y-coordinates is 1 - (-5) = 6, and the change in the x-coordinates is 3 - 0 = 3.

Therefore, the slope of the line is the ratio of the change in the y-coordinates to the change in the x-coordinates, which is 6/3 = 2.

Hence, the slope of the line graphed is 2.

Therefore, the correct answer is C. 2.

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The three dramatic techniques that make "Look Back in Anger" interesting are social realism, strong language and rhetoric, and character conflict and dynamic relationships.

"Look Back in Anger" by John Osborne is a play known for its compelling portrayal of post-war disillusionment and social critique. Here are three dramatic techniques used in the play that contribute to its enduring interest:

1. Social Realism: Osborne employed social realism, depicting the gritty realities of working-class life, alienation, and societal discontent. This authenticity and portrayal of relatable characters and situations engage the audience emotionally and intellectually.

2. Strong Language and Rhetoric: The play is characterized by sharp, biting dialogue and impassioned monologues. The use of strong language and rhetoric adds intensity, captures the characters' frustrations, and conveys their anger and disillusionment effectively.

3. Character Conflict and Dynamic Relationships: The play revolves around intense conflicts between characters, particularly the central couple, Jimmy and Alison. Their volatile relationship and the clash between Jimmy's anger-fueled rebellion and Alison's desire for a different life create tension and keep the audience engaged.

Overall, these dramatic techniques of social realism, powerful language, and dynamic relationships make "Look Back in Anger" interesting by effectively portraying societal issues, engaging the audience emotionally, and highlighting the complexities of human interactions.

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The equation of the tangent line at (3, 324) is y = 288x - 540.

To find y' (the derivative of y), we can differentiate the given function y = [tex](x^2 + 2x + 3)^2[/tex] using the chain rule.

y' = [tex]2(x^2 + 2x + 3) \times (2x + 2) = 4(x^2 + 2x + 3)(x + 1)[/tex]

Now, to find the slope of the tangent line at (3, 324), we substitute x = 3 into y' and evaluate it:

y' = [tex]4(3^2 + 2(3) + 3)(3 + 1) = 4(9 + 6 + 3)(4) = 4(18)(4) = 288[/tex]

So, the slope of the tangent line at (3, 324) is 288.

To find the y-intercept of the tangent line, we substitute the coordinates (3, 324) and the slope (288) into the point-slope form equation: y - y1 = m(x - x1).

Using (x1, y1) = (3, 324) and m = 288, we have:

y - 324 = 288(x - 3)

y - 324 = 288x - 864

y = 288x - 540

Therefore, the equation of the tangent line at (3, 324) is y = 288x - 540.

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Answer:

The given linear equation is -5x-3y=-7. To graph the equation, we need to find three points that satisfy the equation and then plot them on the graph.

Let's find the x and y intercepts first.

At x = 0, we have -3y = -7, which gives us y = 7/3. So the y-intercept is (0, 7/3).

At y = 0, we have -5x = -7, which gives us x = 7/5. So the x-intercept is (7/5, 0).

Now, let's choose another point. We can choose any value for x or y and solve for the other variable. Let's take x = 1.

-5(1) - 3y = -7

-3y = -2

y = 2/3

So the third point is (1, 2/3).

Now we can plot these three points on the graph and draw a line passing through them.

Here's the graph:

|

|

| . (1, 2/3)

|

| .

| (0, 7/3)

|

|_________________________

| |

7/5 -7/15

Step-by-step explanation:

Already explained

The measure of the length VT from the diagram is 5.4

From the given diagram, we can see that the triangle TSR and TUV are similar, hence the correct expressed needed to determine the value of x is given as:

6/x+2 = 14/4x-1

Cross multiply to have
6(4x - 1) = 14(x + 2)

24x - 6 = 14x + 28

24x - 14x = 28 + 6

Simplify to have:

10x = 34

x = 3.4

Determine the measure of VT

VT = x + 2

VT = 3.4 + 2

VT = 5.4

Hence the measure of VT from the diagram is 5.4

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The slope, "m," indicates the rate of change of the line, while the y-intercept, "b," represents the value of y when x equals zero.

I apologize, but as a text-based AI model I'm unable to directly view or analyze any attached images or graphs. However, if you provide me with the equation of the line in the slope-intercept form or describe the relevant details from the graph, I can certainly help you with a response within the given word limit.

The slope-intercept form of a linear equation is given by y = mx + b, where "m" represents the slope of the line and "b" represents the y-intercept, the point where the line intersects the y-axis.

Using this equation, you can determine the slope and y-intercept by comparing the given equation with the slope-intercept form.

Once you provide me with the equation or necessary information, I'll be able to assist you further in understanding the line and its characteristics.

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To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?

The two angles are related in that they are supplementary angles

Supplementary angles would add tuo to 180 degrees according to the angle Theorem.

Adding the two given angles :

These angles are supplementary

The angles aren't vertical in that , vertical angles should have the same vertex. Complementary angles on the other hand add to 90 degrees. While the angles doesn't share the same side, hence, they aren't adjacent.

Hence, the angles are related as they are supplementary angles .

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The graph with the upward parabola plotted in quadrant 1 of a coordinate plane, with the vertex at (3, -1), and left and right slopes at (2, 1) and (4, 1), matches the quadratic function f(x) = (x - 3)^2 - 1.T

To match the graph with the quadratic function it represents, we need to analyze the given information about the graph.
The graph shows an upward parabola plotted in quadrant 1 of a coordinate plane. This means that the parabola opens upwards.
The vertex of the parabola is given as (3, -1), which means that the axis of symmetry is a vertical line passing through x = 3, and the vertex is the lowest point on the parabola.
The left slope of the parabola is given as (2, 1), which means that the slope on the left side of the vertex is positive and equal to 1.
The right slope of the parabola is given as (4, 1), which means that the slope on the right side of the vertex is also positive and equal to 1.
Based on this information, we can determine the quadratic function that matches the graph.
The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) represents the vertex.
In this case, the vertex is (3, -1), so the equation can be written as f(x) = a(x - 3)^2 - 1.
Since the parabola opens upwards, the coefficient of a must be positive.
The left and right slopes of the parabola are both equal to 1, which means that the coefficient a must be equal to 1.
Therefore, the quadratic function that matches the graph is f(x) = (x - 3)^2 - 1.

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The value of x can be found by rearranging the formula S = 6[tex]x^2[/tex] to x = √(S/6).

1. The formula for the surface area of a cube is given as S = 6[tex]x^2[/tex], where S represents the surface area and x represents the side length.

2. To solve for x, we need to isolate it on one side of the equation.

3. Divide both sides of the equation by 6: S/6 = [tex]x^2[/tex].

4. To eliminate the exponent of 2, take the square root of both sides: √(S/6) = x.

5. Therefore, the value of x is given by x = √(S/6).

6. If you have a specific value for S, you can substitute it into the equation to find the corresponding value of x.

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The trigonometric ratios for this problem are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

The hypotenuse for this problem is of 34, and the sides are given as follows:

Hence the trigonometric ratios are given as follows:

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The amount invested in Scheme B is R6,000.

Let's assume that Mr Mangena invested "x" amount in Scheme A and "y" amount in Scheme B.So, as per the problem, the total amount invested by Mr Mangena in Scheme A and Scheme B is equal to R13,890. Hence,x + y = 13,890This is our first equation.

The second equation is that after 3 years, the total interest that Mr Mangena earned was R5,508. Now, we know that the interest earned is simply the product of principal, rate of interest and time. The rate of interest is given as 12% for Scheme A and 10% for Scheme B. Hence, we can write the following equation:0.12x * 3 + 0.10y * 3 = 5,508This is our second equation.

We have two equations and two variables. We can solve these equations simultaneously to get the values of x and y, and hence, we can find the amount invested in Scheme B.x + y = 13,890 ................... Equation 1 0.12x * 3 + 0.10y * 3 = 5,508 .............. Equation 2 Simplifying Equation 1, we get:x = 13,890 - ySubstituting this value of x in Equation 2, we get:0.12(13,890 - y) * 3 + 0.10y * 3 = 5,508Simplifying this equation, we get:y = R6,000.

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The line slants downward from left to right, indicating that as x increases, y decreases.

The given linear equation is -x = 2y + 1. To represent this equation graphically, we need to rearrange it into the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.Rearranging the given equation, we get:2y = -x - 1

Dividing both sides by 2:y = (-1/2)x - 1/2

The slope of the line is -1/2, which means that for every unit increase in x, y decreases by 1/2 unit. The y-intercept is -1/2, indicating that the line intersects the y-axis at (0, -1/2).

Based on this information, the best graph that represents the linear equation y = (-1/2)x - 1/2 is a straight line with a negative slope of -1/2, starting at the point (0, -1/2) and extending infinitely in both directions.

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The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 [tex]\geq[/tex] 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 [tex]\geq[/tex]  9p  +8

Taking p's on the same side we will get :

-7 - 8 [tex]\geq[/tex] 9p - 4p

-15 [tex]\geq[/tex] 5p

Divide by 5 into both sides

-3 [tex]\geq[/tex] p

i.e. p [tex]\leq[/tex] -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 [tex]\geq[/tex] 9p+8 true

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The exponential function giving the number of bacteria after x hours is given as follows:

[tex]y = 250(2)^x[/tex]

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 250, b = 2.

Hence the function is given as follows:

[tex]y = 250(2)^x[/tex]

The problem asks for the exponential function giving the number of bacteria after x hours is given as follows:

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The expanded expression equivalent to log6((2y-3y)/9) using the Quotient Rule of Logarithms is log6(2y) - log6(3y).

The Quotient Rule of Logarithms states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and the denominator. Using this rule, we can expand the given expression log6((2y-3y)/9) as follows:

log6((2y-3y)/9) = log6(2y/9) - log6(3y/9)

Now, let's simplify each logarithmic expression separately:

For the first term, log6(2y/9), we can write it as:

log6(2y/9) = log6(2y) - log6(9)

For the second term, log6(3y/9), we can write it as:

log6(3y/9) = log6(3y) - log6(9)

Combining these expressions, we have:

log6((2y-3y)/9) = (log6(2y) - log6(9)) - (log6(3y) - log6(9))

Now, let's simplify further by distributing the negative sign:

log6((2y-3y)/9) = log6(2y) - log6(9) - log6(3y) + log6(9)

Notice that log6(9) appears both as a subtraction and addition term. This cancels out, resulting in:

log6((2y-3y)/9) = log6(2y) - log6(3y)

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A. The area of the triangle is 108 mm².

B. The area of parallelogram is 286√2 in²

A. Area of a triangle (A) = 1/2 * Base (b) * Height (h)

We have:

b = 18 mm

h = 12 mm

Thus:

A = 1/2 * 18 * 12

A = 108 mm²

B. The area of parallelogram is given by:

A = b * h

where b is the base and h is the height

We have:

b = 26 in

Using trig.:

sin 45 = h/22

h = 22 * sin 45

h = 11√2 in

Thus,

A = 26 * 11√2

A = 286√2 in²

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The enough evidence to support the claim that the wait time to see an IRS representative is more than 50 minutes at a 0.100 level of significance.

The null hypothesis is, H0:

µ ≤ 50 minutes.

The alternative hypothesis is,

Ha: µ > 50 minutes.

The significance level is α = 0.100Sample size = 300

Sample mean (x) = 52 minutes

Sample standard deviation (s) = 4 minutes

We have to find whether there is enough evidence to support the claim that the waiting time to see an IRS representative is more than 50 minutes or not.

For that, we perform a one-sample t-test.

The test statistic is given by:

t = (x - µ) / (s/√n)t

= (52 - 50) / (4/√300)t

= 7.905

Critical t-value = t 0.100,299 = 1.646

Since the calculated t-value (7.905) is greater than the critical t-value (1.646), we can reject the null hypothesis.

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x = 4√3

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