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The function rule for g(x) is h(x) = (x - 0)² - 7.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the vertex (0, -7) and other points (-3, 2), we can determine the value of a as follows:

f(x) = a(x - h)² + k

2 = a(-3 - 0)² - 7

2 + 7 = 9a

9 = 9a

a = 1

Therefore, the required quadratic function in vertex form is given by:

h(x) = a(x - h)² + k

h(x) = (x - 0)² - 7

h(x) = x² - 7

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Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

Step-by-step explanation:

-5x-1>9

add 1 to both sides

-5x>10

divide by negative 5

x<-2

the sign flips since you divided by a negative

and your answer is x<-2

Answer:

20√5 - 10√10

Step-by-step explanation:

6√20 + 8√5 - 5√45

first, 6√20 and 5√45 need to be simplified. 8√5 cannot be simplified any further:

6√20 = 6√4•5 = 6√2•2•5 = 6•2√5 = 12√5

5√45 = 5√8•5 = 5√2•2•2•5 = 5•2√2•5 = 10√10

now:

12√5 + 8√5 - 10√10

then, add the coefficients of 12√5 and 8√5

20√5 - 10√10

the left over numbers cannot be combined because they do not have a common radical, making 20√5 - 10√10 the final answer

Answer:

Step-by-step explanation:

considering A). hemisphere diameter = 48 yd

volume of hemisphere = (2/3)*pi*(r)^3

the radius of hemisphere = diameter/2 = 48/2 = 24 yd

hence, the volume of hemisphere = (2/3)*pi*(24)^3  yd^3

taking pi = 3.14

volume = 28938.24 yd^3 approximately volume = 28940 yd^3

considering B). Circumference of a great circle = 26 m

circumference of sphere = 2*pi*r

therefore r = 4.14 m

volume of sphere = (4/3)*pi*(r)^3

volume of sphere = 297.077 m^3

Answer:

24. A. 28952.9 yd²

B. 297.2 m³

Step-by-step explanation:

24.

A.

diameter=48 yd

radius (r)=diameter/2=48/2=24yd

We have

Volume of Hemisphere= ⅔*πr³=⅔*π*r³

Substituting value

Volume of Hemisphere=⅔*π*24³=28952.9 yd³

B.

Circumference of great circle=2πr=26m

2πr=26

r=26/(2π)

r=4.14

Now

Volume of sphere = 4/3*πr³

Volume of sphere=4/3*π*4.14³=297.2 m³

Correct option is D, The equation which is equivalent to the expression be (x - 3)² = 14.

If two systems of equations have the same solution, they are equivalent (s).

Equations can be made equal in a variety of ways: An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of the equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.

Equivalent fractions are those that, despite their visual differences, reflect the same value. If two or more fractions simplify to the same fraction, they are said to be equivalent.

Given,

x² - 6x = 8

Using completing the square method,

x² - 6x - 8 = 0

x² - 6x + 9 - 9 - 8 = 0

(x - 3)² = 17

Therefore, the correct answer is option D.

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Answer: B. (6, ∞)

Step-by-step explanation:

    The domain of the function is all of the inputs. On a graph, it is the x-values.

    See the attached image for a visual and further explanation.

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Answer: b

Step-by-step explanation:

Observe that

\(\displaystyle \frac1{e^{2\pi x} - 1} = \frac{e^{-\pi x}}{e^{\pi x} - e^{-\pi x}} = \frac{\cosh(\pi x) - \sinh(\pi x)}{2\sinh(\pi x)} = \frac{\coth(\pi x) - 1}2\)

We have the following series expansion due to Mittag-Leffler:

\(\displaystyle \pi \coth(\pi z) = \frac1z + 2 \sum_{n=1}^\infty \frac z{z^2+n^2}\)

The proof of this is easy to follow. (I'll try to include a link)

With some simple rearrangement, we get the desired result.

\(\displaystyle \sum_{n=1}^\infty \frac1{n^2 + x^2} = -\frac1{2x^2} + \frac{\pi \coth(\pi x)}{2x} \\\\ ~~~~~~~~ = -\frac1{2x^2} + \frac\pi{2x} + \frac\pi{x(e^{2\pi x}-1)}\)

Answer:

m = 5

Explanation:

The given expression is

First, we need to apply the distributive property, so

Then, subtract 30 from both sides

Add 7m to both sides

Finally, divide both sides by 8

Therefore, the answer is m = 5

Therefore, the freight train traveled for 16.67 + 10 = 26.67 hours before the passenger train caught up with it.

let's call the time it took for the passenger train to catch up with the freight train "t" (in hours).

During this time, the freight train traveled at its average speed of 45 km/h for t + 10 hours, while the passenger train traveled at its average speed of 72 km/h for t hours.

We know that the distance both trains traveled is the same, since the passenger train caught up with the freight train. So, we can set up the following equation:

distance traveled by freight train = distance traveled by passenger train

\((45 km/h) x (t + 10 h) = (72 km/h) x t\)

Simplifying this equation, we get:

\(45t + 450 = 72t\)

\(27t = 450\)

t = 16.67 hours

Therefore, the freight train traveled for 16.67 + 10 = 26.67 hours before the passenger train caught up with it.

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Answer:

6xy² + 104y²

Step-by-step explanation:

Distribute the 2y² over the two numbers in the parentheses.

The answer selections in the question seem to be typos, none exactly right.

Answer:

green line or "b"

Step-by-step explanation:

we can set this up into the slope intercept form

y=mx+b

where m is the slope and b is y intercept

12=3x+4y

-3x -3x

-3x+12=4y

/4.  /4.  /4

-3/4x+3=y

we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"

hopes this helps please mark rainliest

Answer:

Slopes of parallel lines are equal

Step-by-step explanation:

On a coordinate plane, quadrilateral ABCD is shown. Point A is at (-2, -2), point B is at (-3, 4), point C is at (2, 2), and point D is at (3, -4).

The slope of the line segment BC is:  

\(\dfrac{4-2}{-3-2} =-\dfrac{2}{5}\)

The slope of the line segment AD is:

\(\dfrac{-4-(-2)}{3-(-2)} =\dfrac{-4+2}{3+2}=-\dfrac{2}{5}\)

The slope of the line segment CD is:

\(\dfrac{2-(-4)}{2-3} =\dfrac{2+4}{2-3}=\dfrac{6}{-1}=-6\)

The slope of the line segment BA is:

\(\dfrac{4-(-2)}{-3-(-2)} =\dfrac{4+2}{-3+2}=\dfrac{6}{-1}=-6\)

Because the slopes of parallel lines are equal. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.

Answer:

c.) on edg.

Step-by-step explanation:

got it right :)

Answer:

Above sea level (positive)

Below sea level (negative)

Temperature (can be both)

Money loans (can be both)

science (protons have both negative and positive charge)

Step-by-step explanation:

Answer: c

Step-by-step explanation:

i got it right

Answer:

C) Yes, because substituting these values into both equations forms two true statements.

Step-by-step explanation:

Answer:

1. A. 4 terms

There are 4 different values in the expression, so therefore there are 4 terms.    

2. D. 3x^2 + 6x + 10

To get the answer...

start with the original expression: 3x^2 + x + 10 + 5x

add the like terms together, in this case you'd add x + 5x

you'll get: 3x^2 + 6x + 10

I hope I could help :)

Answer: 9

Step-by-step explanation: It's nine because she makes 24 and puts 5 of each in three bags so that's 15. Now you do 24 - 15 which equals 9.

The characteristic that is representative of a FUSION reaction is: B. The reaction happens predominantly in stars, like our sun.

A reaction is a process that involves the transformation of one or more substances into new substances with different physical and/or chemical properties. Reactions can be classified as either physical or chemical depending on the nature of the change that occurs. In a physical reaction, the identity of the substances remains the same, but their physical properties, such as size, shape, or phase, may change. Examples of physical reactions include melting, freezing, boiling, and condensation.

Here,

Fusion reactions involve the joining together of two atomic nuclei to form a heavier nucleus, releasing a large amount of energy in the process. These reactions occur naturally in stars, including our sun, where the high temperatures and pressures allow the atomic nuclei to overcome their mutual repulsion and come close enough to fuse. While scientists are working on developing fusion reactors for use on Earth, the technology is still in the experimental stage and is not yet cost-effective for widespread use. However, fusion reactions do not produce long-lasting radioactive waste as in the case of nuclear fission reactions.

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Answer:

The expression (6 × 10^7) × 0.007 simplified is 4.2 x 10^5.

Step-by-step explanation:

Answer:

Answer is 160.00

Step-by-step explanation:

*proportion*

3hours/12cars

8hours/ (x) cars

X=32

Answer:

I think they would earn $40 buckeroos in 8 hours

Step-by-step explanation:

$5.00 x 8 hours = $40.00

I hope this was right & helpful ^w^

The simplification of the given expression on the basis of identity is given as  144 - 24y +  y².

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is (12 - y)².

It can be expanded on the basis of the algebraic identity (a - b)² = a² - 2ab + b² as follows,

(12 - y)²

= 12²- 2×12y + y²

= 144 - 24y +  y²

Hence, the given expression can be simplified as 144 - 24y +  y².

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The equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.

Given points:

Point 1: (1, 0)

Point 2: (3, 6)

Step 1: Calculate the slope (m) using the formula:

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

Substituting the coordinates:

m = (6 - 0) / (3 - 1)

m = 6 / 2

m = 3

Step 2: Substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).

Using Point 1 (1, 0):

0 = 3(1) + b

0 = 3 + b

b = -3

Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):

y = 3x - 3

Therefore, the equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

This equation represents a line with a slope of 3, indicating that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 3 units. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). By substituting any x-value into the equation, we can determine the corresponding y-value on the line.

Hence, the equation of the line passing through (1, 0) and (3, 6) is y = 3x - 3.

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The absolute value function for this problem is given as follows:

y = |x - 4| - 6.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The coordinates of the vertex of the function are given as follows:

(4, -6).

The slope of 1 determines the leading coefficient a as follows:

a = 1.

Hence the function is given as follows:

y = |x - 4| - 6.

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Step-by-step explanation:

Step 1: Find the mean x of the data values.

X = (ix₁) / n

x = (12 + 3 + 9 + 2 + 0 + 0 + 3) / 7

x = 29 / 7

x ≈ 4.14 (rounded to two decimal places)

Step 2: Calculate the squared differences from the mean for each data value [(x₁ - x)²].

For each data value, subtract the mean and square the result.

Squared Differences:

(12 - 4.14)² ≈ 53.43

(3 - 4.14)² ≈ 1.31

(9 - 4.14)² ≈ 23.09

(2 - 4.14)² ≈ 4.34

(0 - 4.14)² ≈ 17.11

(0 - 4.14)² ≈ 17.11

(3 - 4.14)² ≈ 1.31

Step 3: Calculate the variance (s²) of the data values.

s² = ((x₁ - x)²) / (n - 1)

s² = (53.43 + 1.31 + 23.09 + 4.34 + 17.11 + 17.11 + 1.31) / (7 - 1)

s² ≈ 117.70 / 6

s² ≈ 19.62 (rounded to two decimal places)

Step 4: Calculate the standard deviation (s) of the data values.

s = √s²

s = √19.62

s ≈ 4.43 (rounded to two decimal places)

Step 5: Find the range of the data values.

Range = Maximum value - Minimum value

Range = 12 - 0

Range = 12

Therefore, the results are:

The standard deviation is approximately 4.43 (rounded to two decimal places).

The variance is approximately 19.62 (rounded to two decimal places).

The range is 12.

The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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The summarized sample is do not reject the hypothesis because the test value 2.31 is less than the critical value 3.01, the correct option is D.

We are given that;

a = 0.05

s1^2 = 4.1 and s2^2 = 2.7,

Now,

The degrees of freedom for the F-test are df1 = n1 - 1 and df2 = n2 - 1, where n1 and n2 are the sample sizes of sample 1 and sample 2, respectively. In this case, df1 = 19 - 1 = 18 and df2 = 8 - 1 = 7. We can use an F-table or a calculator to find the critical value for the F-test at α = 0.05 and these degrees of freedom. The critical value is F0.05(18,7) = 3.55.

We compare the test statistic to the critical value to make a decision about the hypothesis. If F > F0.05(18,7), we reject the null hypothesis and conclude that the variances are different. If F ≤ F0.05(18,7), we fail to reject the null hypothesis and conclude that there is not enough evidence to say that the variances are different.

F = 1.52 < F0.05(18,7) = 3.55, so we fail to reject the null hypothesis and conclude that there is not enough evidence to say that the variances are different at α = 0.05.

Therefore, by the sample the answer will be do not reject the hypothesis because the test value 2.31 is less than the critical value 3.01.

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Julio will be 30 years old when his father is twice his age.

To determine the age at which Julio will be twice his father's age, we need to find the age difference between them and then add that difference to Julio's current age.

Currently, Julio is 12 years old, and his father is 42 years old. The age difference between them is 42 - 12 = 30 years.

For Julio to be twice his father's age, the age difference needs to remain the same as it is currently. Therefore, when Julio is x years old, his father will be x + 30 years old.

Setting up an equation to solve for x:

x + 30 = 2x

Simplifying the equation, we subtract x from both sides:

30 = x

Thus, when Julio is 30 years old, his father will be 30 + 30 = 60 years old. At this point, Julio will indeed be twice his father's age.

Therefore, Julio will be 30 years old when his father is twice his age.

Note : the translated question is Julio is 12 years old and his father is 42 years old. How old will Julio be when his father is twice his age?

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