Describe the translations applied to the graph of y= xto obtain a graph of the quadratic function g(x) = 3(x+2)2 -6

Step-by-step explanation:

See image:

Answer:

The answer is; the snail moved 1 inch every 20 minutes.

Step-by-step explanation:

120 divided by 6 is 20

Answer:

A) 1 Over 20 of an inch per minute

Step-by-step explanation:

I took this test and got 100

to determine the likelihood of good weather in Columbus in the long run, it is essential to consider historical climate data, seasonal changes, and weather patterns.

In the long run, the likelihood of good weather in Columbus on a given day depends on various factors, such as historical climate data, seasonal changes, and weather patterns.
Examine historical climate data
To determine the likelihood of good weather, we can look at historical climate data for Columbus. Generally, Columbus experiences a mix of sunny, cloudy, and rainy days throughout the year.
Consider seasonal changes
Weather in Columbus varies across different seasons. Spring and fall typically have milder temperatures and a mix of sun and clouds. Summer can be hot and humid, while winter is cold with snow and ice. Knowing the season can help predict the likelihood of good weather.
Analyze weather patterns
Weather patterns can also play a role in determining the likelihood of good weather. For example, if a high-pressure system is present, it generally results in clear skies and good weather. Conversely, low-pressure systems often bring clouds and precipitation.
to determine the likelihood of good weather in Columbus in the long run, it is essential to consider historical climate data, seasonal changes, and weather patterns. By analyzing these factors, you can get a better idea of how likely it is for the weather to be good on a given day. However, it's important to remember that weather predictions are not always accurate, and unexpected changes can occur.

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Complete Question:

Refer to Exercise 4. In the long run, how likely is it for the weather in Columbus to be good on a given day? 4. The weather in Co on any given day. If the a 60% chance the eather in Columbus is either good, indifferent, or bad ny given day. If the weather is good today, there is of chance the weather will be good tomorrow, a 30% are the weather will be indifferent, and a 10% chance the other will be bad. If the weather is indifferent today, it will he good tomorrow with probability 40 and indifferent with probability .30. Finally, if the weather is bad today, it will be good tomorrow with probability .40 and indifferent with probability .50. a. What is the stochastic matrix for this situation? b. Suppose there is a 50% chance of good weather today and a 50% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 40% in- different weather and 60% bad weather. What are the chances for good weather on Wednesday?

If the width of the border is equal and was made from 7 feet² of clear glass , then the width of the border is 0.5  feet .

the border is = (2 sides) × (4 tall) × (w)  on the long sides  

and on the top and bottom will be =  (2 sides) × (2 feet + 2w) × (w)

since the width of the border is made out of 7 square feet ,

So,  adding  together = 7 ;

we get ; 2×4×w + 2×(2 + 2w)w = 7  ;

⇒ 8w  + 2(2w + 2w²) = 7 ;

⇒ 8w + 4w + 4w² = 7  ;

⇒ 4w² + 12w - 7 = 0    

solving the above quadratic ,

We get ; w = 0.5    or   w = -3.5 ;

Since the width of border cannot be negative ;

So ; w = 0.5 ft .

Therefore , the width of the border is 0.5 feet  .

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The given question is incomplete , the complete question is

A rectangle stained glass window is 2 feet by 4 feet. A clear glass border is constructed around the stained glass window. The width of the border is equal and was made out of 7 square feet of clear glass. What is the width of the border ?

Answer:

its four fifteenths

Step-by-step explanation:

3/5 = 9/15

1/3 = 5/15

9/15 - 5/15 = 4/15

4/15 = four fifteenths

Answer:

A.)

B.)

If Idil drove 12 miles in 1/5an hour on average, then she drove at an average speed of 60 miles per hour.

To calculate the average speed of Idil's car in miles per hour, we need to divide the distance she drove (12 miles) by the time it took her to drive that distance (1/5 hour):

Average speed = distance ÷ time

Average speed = 12 miles ÷ (1/5) hour

To divide by a fraction, we can multiply by its reciprocal, so:

Average speed = 12 miles × 5/1 hour

Average speed = 60 miles per hour

Therefore, Idil drove at an average speed of 60 miles per hour.

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The solution to the equation is x = 0.

Option D is the correct answer.

We have,

The equation is:

(1 - 3x)^{1/3} - 1 = x

Let's start by isolating the radical term by adding 1 to both sides:

(1 - 3x)^(1/3) = x + 1

Next, we'll cube both sides to eliminate the radical:

[(1 - 3x)^(1/3)]^3 = (x + 1)^3

1 - 3x = (x + 1)^3

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

0 = x^3 + 3x^2 + 6x

Now we have a cubic equation, which we can solve by factoring out an x:

x(x^2 + 3x + 6) = 0

The quadratic factor doesn't have any real roots (since its discriminant is negative),

So the only solution is x = 0.

i.e

(1 - 3x)^(1/3) - 1 = 1^(1/3) - 1 = 0.

Thus,

The solution to the equation is x = 0.

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Answer:

d) y = -1/2 + 3

Step-by-step explanation:

Looking at the graph, we can use y = mx + b to find the equation. m is the slope and for slope, we go 1 unit down and 2 units to the right. b is the y variable and our b would be 3.

y = mx + b

y = -1/2x + 3

Hope this helps and stay safe, happy, and healthy, thank you :) !!

The given polynomial f(x) = x^4 + 6x^2 - 27 is to be written as the product of factors that are irreducible over the rationals.        

Let's factorize the given polynomial as follows:f(x) = x^4 + 6x^2 - 27Since there are no possible rational roots of the given polynomial, we can use substitution to factorize it.Let's substitute x^2 = y; therefore, we have f(y) = y^2 + 6y - 27We can now factorize f(y) = y^2 + 6y - 27 as follows:f(y) = (y + 9)(y - 3)Therefore, x^4 + 6x^2 - 27 = (x^2 + 9)(x^2 - 3)If we continue the factorization, then we have x^4 + 6x^2 - 27 = (x + 3i)(x - 3i)(x + sqrt(3))(x - sqrt(3))Hence, the polynomial as the product of factors that are irreducible over the rationals is (x + 3i)(x - 3i)(x + sqrt(3))(x - sqrt(3)).          

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Answer:

A = 196 units²

Step-by-step explanation:

the area (A) of a regular polygon is

A = \(\frac{1}{2}\) perimeter × apothem

here perimeter = 56 and apothem = 7 , then

A = \(\frac{1}{2}\) × 56 × 7 = 28 × 7 = 196 units²

Answer:

The expression (8-i)/(2+i) in standard form is, 3 - 2i

Step-by-step explanation:

The expression is,

(8-i)/(2+i)

writing in standard form,

\((8-i)/(2+i)\\\)

Multiplying and dividing by 2+i,

\(((8-i)/(2+i))(2-i)/(2-i)\\(8-i)(2-i)/((2+i)(2-i))\\(16-8i-2i-1)/(4-2i+2i+1)\\(15-10i)/5\\5(3-2i)/5\\=3-2i\)

Hence we get, in standard form, 3 - 2i

The expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

To write the expression (8-i)/(2+i) in standard form a+bi, we need to eliminate the imaginary denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator.

The conjugate of 2+i is 2-i. So, we multiply the numerator and denominator by 2-i:

(8-i)/(2+i) * (2-i)/(2-i)

Using the distributive property, we can expand the numerator and denominator:

(8(2) + 8(-i) - i(2) - i(-i)) / (2(2) + 2(i) + i(2) + i(i))

Simplifying further:

(16 - 8i - 2i + i^2) / (4 + 2i + 2i + i^2)

Since i^2 is equal to -1, we can substitute -1 for i^2:

(16 - 8i - 2i + (-1)) / (4 + 2i + 2i + (-1))

Combining like terms:

(15 - 10i) / (3 + 4i)

Therefore, the expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

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Answer:

we will have a negative number

Answer:

i think their were 17 do you have any answer choices

The value of k from the equation is k = -20

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = kx   be equation (1)

Let the first point be P ( 4 , -80 )

Substituting the values in the equation , we get

-80 = 4k

Divide by 4 on both sides of the equation , we get

k = - ( 80/4 )

On simplifying the equation , we get

k = -20

Hence , the equation is k = -20

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Answer:

X=200

First your going to add all sides together. Once you finish you should get

50+55+90=195

after you got your answer your going to round to the tenths if it's higher than 5 your going to make it 200 but if it's lower than 5 than your going to make it 180.

So in our case because it's 195 we're going to turn it into a 200.

I hope this helps

We need to find the derivative which is the rate of change

So, when x is infinite, the function g(x) has the greatest rate of change

The probability of getting at least one nun in three spins of a dreidel is approximately 0.578

The probability is the ratio of number of favorable outcomes to the total number of outcomes

The probability of getting no nuns in a single spin is 3/4, since there are three non-nun letters (Gimel, Hei, Shin) and four total letters.

The probability of getting no nuns in three spins is then (3/4)^3, since the spins are independent and we can multiply probabilities of independent events.

So the probability of getting at least one nun in three spins is

= 1 - (3/4)^3

= 1 - 0.421875

= 0.578125

Therefore, the probability of getting at least one nun is 0.578

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The given question is incomplete, the complete question is:

A dreidel is a four-sided spinning top with the Hebrew letters nun, gimel, hei, and shin, one on each side. Each side is equally likely to come up in a single spin of the dreidel. Suppose you spin a dreidel three times. Calculate the probability of getting (a) at least one nun?

To find the correct equations for the missing boxes, we need more information about the relationships between the different activities in Jake's Gems. However, based on the given context, we can make some assumptions and suggest potential equations:

Mining and Cutting activities produce diamonds, rubies, and other gems. Let's assume that the production of each gem type is represented by a variable: D (diamonds), R (rubies), and G (other gems).

Maintenance supports the Mining and Cutting activities. We can assume that the maintenance effort required for each activity is represented by the variable M (maintenance).Since the question mentions five missing boxes, we can suggest additional equations to represent relationships between these variables, such as:

Mining + Cutting = D + R + G (the sum of all gem types produced equals the total production from Mining and Cutting activities).

Maintenance = M (maintenance effort required).

The relationships between these variables might include equations like D = f(M), R = g(M), G = h(M), where f, g, and h represent some functions or formulas that relate gem production to maintenance effort.

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The simplified expression for √6x • √15x³ without a perfect square factor in the radicand is 3x√10x.

To simplify the expression √6x • √15x³ without a perfect square factor in the radicand, we can follow these steps:

Step 1: Use the product rule of square roots, which states that

√a • √b = √(a • b). Apply this rule to the given expression.

√6x • √15x³= √(6x • 15x³)

Step 2: Simplify the product inside the square root.

√(6x • 15x³) = √(90x⁴)

Step 3: Rewrite the radicand as the product of perfect square factors and a remaining factor.

√(90x⁴) = √(9 • 10 • x² • x²)

Step 4: Take the square root of the perfect square factors.

√(9 • 10 • x² • x^2) = 3x • √(10x²)

Step 5: Combine the simplified factors.

3x • √(10x²) = 3x√10x

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Answer:

c = -4

Step-by-step explanation:

If f(x) = 2x^3 - x + c and f(2) = 10, plug in 2 for the x values in the function and make the function output 10.

10 = 2(2^3) - 2 + c    Now, we only have to deal with one variable, that is c.

10 = 2(8) - 2 + c

10 = 16 - 2 + c

10 = 14 + c

-4 = c    After simplifying, we get that c is -4.

To check this, plug in 2 for x, and -4 for c in the function. If the function produces 10 as the result, the halleluja!

f(2) = 2(2^3) - 2 - 4

f(2) = 2(8) - 2 - 4

f(2) = 16 - 2 - 4

f(2) = 10

\(\\ \tt\hookrightarrow 2x^3-x+c=10\)

\(\\ \tt\hookrightarrow 2(2)^3-2+c=10\)

\(\\ \tt\hookrightarrow 2(8)-2+c=10\)

\(\\ \tt\hookrightarrow 16-2+c=10\)

\(\\ \tt\hookrightarrow 14+c=10\)

\(\\ \tt\hookrightarrow c=-4\)

Answer:

x=10

Step-by-step explanation:

Reason:

Rewrite the given equation into \((x-6)^2 + (y-(-5))^2 = 5^2\)

I changed the y+5 into y-(-5), and also replaced 25 with \(5^2\)

Then compare that to the circle template of \((x-h)^2 + (y-k)^2 = r^2\)

We see that h = 6 and k = -5 to give a center of (h,k) = (6, -5)

Side note: the radius is r = 5 units

1. The solution to the first differential equation is given by e^2yx - ysin(xy) + y^2 + C = 0, where C is an arbitrary constant.

2. The general solution to the second differential equation is x(3x - y^2) = C, where C is a positive constant.

To solve the first-order differential equations, let's solve them one by one:

1. (e^2y - ycos(xy))dx + (2xe^2y - xcos(xy) + 2y)dy = 0

We notice that the given equation is not in standard form, so let's rearrange it:

(e^2y - ycos(xy))dx + (2xe^2y - xcos(xy))dy + 2ydy = 0

Comparing this with the standard form: P(x, y)dx + Q(x, y)dy = 0, we have:

P(x, y) = e^2y - ycos(xy)

Q(x, y) = 2xe^2y - xcos(xy) + 2y

To check if this equation is exact, we can compute the partial derivatives:

∂P/∂y = 2e^2y - xcos(xy) - sin(xy)

∂Q/∂x = 2e^2y - xcos(xy) - sin(xy)

Since ∂P/∂y = ∂Q/∂x, the equation is exact.

Now, we need to find a function f(x, y) such that ∂f/∂x = P(x, y) and ∂f/∂y = Q(x, y).

Integrating P(x, y) with respect to x, treating y as a constant:

f(x, y) = ∫(e^2y - ycos(xy))dx = e^2yx - y∫cos(xy)dx = e^2yx - ysin(xy) + g(y)

Here, g(y) is an arbitrary function of y since we treated it as a constant while integrating with respect to x.

Now, differentiate f(x, y) with respect to y to find Q(x, y):

∂f/∂y = e^2x - xcos(xy) + g'(y) = Q(x, y)

Comparing the coefficients of Q(x, y), we have:

g'(y) = 2y

Integrating g'(y) with respect to y, we get:

g(y) = y^2 + C

Therefore, f(x, y) = e^2yx - ysin(xy) + y^2 + C.

The general solution to the given differential equation is:

e^2yx - ysin(xy) + y^2 + C = 0, where C is an arbitrary constant.

2. x(yy' - 3) + y^2 = 0

Let's rearrange the equation:

xyy' + y^2 - 3x = 0

To solve this equation, we'll use the substitution u = y^2, which gives du/dx = 2yy'.

Substituting these values in the equation, we have:

x(du/dx) + u - 3x = 0

Now, let's rearrange the equation:

x du/dx = 3x - u

Dividing both sides by x(3x - u), we get:

du/(3x - u) = dx/x

To integrate both sides, we use the substitution v = 3x - u, which gives dv/dx = -du/dx.

Substituting these values, we have:

-dv/v = dx/x

Integrating both sides:

-ln|v| = ln|x| + c₁

Simplifying:

ln|v| = -ln|x| + c₁

ln|x| + ln|v| = c₁

ln

|xv| = c₁

Now, substitute back v = 3x - u:

ln|x(3x - u)| = c₁

Since v = 3x - u and u = y^2, we have:

ln|x(3x - y^2)| = c₁

Taking the exponential of both sides:

x(3x - y^2) = e^(c₁)

x(3x - y^2) = C, where C = e^(c₁) is a positive constant.

This is the general solution to the given differential equation.

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Marshall handed out more brochures per minute. He handed out 150 brochures per hour, which is equal to 2.5 brochures per minute. Silas handed out 240 brochures in 90 minutes, which is equal to 2.67 brochures per minute. Therefore, Marshall handed out more brochures per minute.

Marshall: 300 brochures in 2 hours = 150 brochures per hour = 2.5 brochures per minute

Silas: 240 brochures in 90 minutes = 2.67 brochures per minute

The marketing company is hiring two college students to hand out brochures near an event. Marshall hands out 300 brochures in 2 hours and Silas hands out 240 brochures in 90 minutes. To compare their performance, it is necessary to calculate the number of brochures handed out per minute. After doing the math, it is evident that Marshall handed out more brochures per minute. He handed out 150 brochures per hour, which is equal to 2.5 brochures per minute. Silas handed out 240 brochures in 90 minutes, which is equal to 2.67 brochures per minute. Therefore, Marshall handed out more brochures per minute. This data demonstrates that Marshall is more efficient in handing out the brochures, and the marketing company should take this into consideration when deciding who to hire for the job.

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it is going to be true

Answer: \(x\leq 0\)

Step-by-step explanation:

The first thing we need to do is to make the argument or the number inside the square root equal or larger than zero:

-2x ≥ 0

x ≤ 0/-2

x ≤ 0

So the given expression only makes sense for x that is less than or equal to zero.

The number that makes the equation 0.54 + 17/100 = x/100 + 17/100 true is 54.

To solve this equation, we want to isolate x on one side of the equation.

Starting with:

0.54 + 17/100 = x/100 + 17/100

We can first simplify the left side by finding a common denominator for 0.54 and 17/100:

0.54 = 54/100

54/100 + 17/100 = 71/100

Now, we can simplify the right side by combining like terms:

x/100 + 17/100 = (x + 17)/100

Substituting these simplifications back into the original equation, we get:

71/100 = (x + 17)/100

To isolate x, we can multiply both sides by 100:

71 = x + 17

Subtracting 17 from both sides, we get:

x = 54

Therefore, the number that makes the equation true is 54.

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The question is -

Enter the number that makes the equation true.

0.54 + 17/100 = x/100 + 17/100