Brenda's class took a field trip to the science museum. It took them 50 minutes to drive to the museum. They stayed at the museum for 3 hours and 45 minutes, and it took them 56 minutes to drive back to school. When the class arrived back at school, it was 3:47 P.M. What time did Brenda's class leave for the field trip?

Check the picture below.

so the maximum height will occur at its vertex y-coordinate.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{+48}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 48}{2(-4.9)}~~~~ ,~~~~ 6-\cfrac{ (48)^2}{4(-4.9)}\right) \implies \left( - \cfrac{ 48 }{ -9.8 }~~,~~6 - \cfrac{ 2304 }{ -19.6 } \right)[/tex]

[tex]\left( \cfrac{ 48 }{ 9.8 } ~~~~ ,~~~~ 6 +\cfrac{ 2304 }{ 19.6 } \right) ~~ \approx ~~ (4.89~~,~~\text{\LARGE 124})[/tex]

The solution is,  the domain is: x ∈ (-∞, ∞).

Here, we have,

When we have two functions, f(x) and g(x), the composite function:

(f°g)(x)

is just the first function evaluated in the second one, or:

f( g(x))

And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:

f(x) = 1/(x + 1)

where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.

Now, we have:

f(x) = x^2

g(x) = x + 9

then:

(f ∘ g)(x) = (x + 9)^2

And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:

x ∈ (-∞, ∞)

(g ∘ f)(x)

this is g(f(x)) = (x^2) + 9 = x^2 + 9

And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:

x ∈ (-∞, ∞)

(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4

And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:

x ∈ (-∞, ∞)

(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18

And again, there are no values of x that cause a problem here,

so the domain is:

x ∈ (-∞, ∞)

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complete question:

Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat

The equation of the dilated line is 9x + 15y = 10.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects, which can be used to either vertically or horizontally enlarge (increase) or reduce (compress) a function representing their size.

Generally speaking, the transformation rule for the dilation of a geometric object or equation based on a specific scale factor of 3 is given by this mathematical expression:

(x, y)      →    (SFx, SFy)

Where:

Therefore, the transformation rule for this dilation is given by;

(x, y)      →    (3x, 3y)

3(3x + 5y) = 10

9x + 15y = 10.

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Answer:

The answer to this question is --> f(x) = -4x^2-8x+32

Hope this helps

Answer: Given the following equations, determine the x value(s) that result in an equal output for both functions. f(x) = 3* g(x)=4x+1. C0 and 2.

Step-by-step explanation:

Given the following equations, determine the x value(s) that result in an equal output for both functions. f(x) = 3* g(x)=4x+1. C0 and 2.

The value of the unknown perimeter is derived to be 96 cm using the ratio of the known side of the similar figures.

A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It can be used to express one quantity as a fraction of the other ones.

By comparison using the variable x to represent the unknown perimeter, and the ratio of the known side lengths;

24/32 = 72cm/x

x = (32 × 72cm)/24 {cross multiplication}

x = 2304cm/24

x = 96 cm

Therefore, the value of the unknown perimeter is derived to be 96 cm using the ratio of the known side of the similar figures.

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The velocity of the two cars are 50km/hr and 60km/h

Velocity is the rate of change of distance with time. it is measured in meter per second and it is a vector quantity.

let the faster car be A and slower car be B

V(A) = V(B) +10

S( A) = v × t

S(B) = v(b) × t

S( A) = 5( v(b) +10)

S(A) +S(B) = 550

5v(b) +50+5vb = 550

10v(b) = 550-50

v(b) = 500/10

v(b) = 50km/h

v(a) = 50 +10

v(a) = 60km/h

Therefore the velocity of the two cars are 50km/h and 60 km/h

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Answer: the inequalities for which 0 is a solution are x - 5 ≤ -3 and x/-2 ≥ 0.

Step-by-step explanation: x - 5 ≤ -3 (0 is less than or equal to 2)

x/-2 ≥ 0 (0 is greater than or equal to 0)

In mathematical form, this can be written as:

0 ≤ x - 5 ≤ -3 or x - 5 ≤ 0 and x ≤ -3

Answer:

C is correct because parallel lines cut by a transversal form congruent alternate interior angles.

The essay, "I, Pencil," illustrates that production of an ordinary wood pencil used for writing d. involves the cooperative efforts of millions of people, whose actions are directed through markets.

I, Pencil, an essay by Leonard Read portrays that the manufacture of a common wood pencil utilized for writing necessitates the collective efforts of millions of human beings whose activities are strictly regulated through markets.

The paper conveys that though an ordinary pencil looks like such a straightforward item, it is actually created from a complex system of people, procedures, and materials from far and wide. From timber harvesters who procure the wood, to the miners who take graphite out from the ground, to the employees in manufacturing plants who produce the finished article, the lead holder necessitates the orderly collaboration of multiple individuals and enterprises.

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Answer:

Step-by-step explanation:

9 * 9 = 81

4 * 4 = 16

81 + 16 = 97

Answer:

The common ratio is 5.

30 ÷ 5 = 6.

Let n = 1 be the first term of this sequence.

[tex]a(n) = 6( {5}^{n} )[/tex]

Answer:

see explanation

Step-by-step explanation:

given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

then the equation of the axis of symmetry is

x = - [tex]\frac{b}{2a}[/tex]

f(x) = 2x² + 8x - 4 ← is in standard form

with a = 2, b = 8 , then equation of axis of symmetry is

x = - [tex]\frac{8}{2(2)}[/tex] = - [tex]\frac{8}{4}[/tex] = - 2

that is equation of axis of symmetry is x = - 2

the axis of symmetry passes through the vertex of the parabola

substitute x = - 2 into f(x) for corresponding y- coordinate

f(- 2) = 2(- 2)² + 8(- 2) - 4 = 2(4) - 16 - 4 = 8 - 20 = - 12

vertex = (- 2, - 12 )

the y- intercept is on the y- axis, where the x- coordinate is zero

substitute x = 0 into f(x)

f(0) = 2(0)² + 8(0) - 4 = 0 + 0 - 4 = - 4

y- intercept = - 4

Answer:To solve this problem, we need to use the formulas for the area and perimeter of a triangle.

Let's start by using the formula for the area of a triangle:

Area = (base x height) / 2

where base and height are the length and height of the triangle's base, respectively.

Let's assume that the base of the triangle is x meters, and the height is y meters. Then we have:

Area = (x*y)/2 = 0.45 m²

Solving for y, we get:

y = (2*0.45)/x

y = 0.9/x

Now, let's use the formula for the perimeter of a triangle:

Perimeter = a + b + c

where a, b, and c are the lengths of the three sides of the triangle.

Since we know that the perimeter is about 325 cm, we can assume that the three sides are close to each other in length. Let's assume that each side has a length of 325/3 = 108.33 cm.

Converting to meters, we get:

a = b = c = 108.33/100 = 1.0833 m

Now, we can use the formula for the area of a triangle again to solve for x:

Area = (base x height) / 2

0.45 = (x * 0.9/x) / 2

0.9 = x²

x = √0.9 = 0.9487 m

Therefore, the base of the triangle is approximately 0.9487 meters, and the height is approximately 0.9/0.9487 = 0.9487 meters.

So the triangle has sides of length 1.0833 meters and a base of length 0.9487 meters, which gives us a perimeter of approximately 3.215 meters (rounded to three decimal places).

Step-by-step explanation:

6,000 mL is equal to 6 litres

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

We know that 6,000 mL  is equal to 6L

One litre is equal to 1000 ml

1 l = 1000 ml

6 l=6000 ml

Hence,  6,000 mL is equal to 6 litres

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Answer:

If 2:3 = x:12, then:

2/3 = x/12

Multiplying both sides by 12, we get:

x = 2/3 x 12 = 8

Therefore, the value of x is 8.

Answer:θ≈2.15

θ≈4.13 are correct

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

3u^2 - 2u - 2 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 3, b = -2, and c = -2. Substituting these values, we get:

u = (2 ± sqrt(4 + 24)) / 6

u = (2 ± 2sqrt(7)) / 6

Simplifying this expression, we get:

u = (1 ± sqrt(7)) / 3

Therefore, either:

Answer: it’s C, cubic

Step-by-step explanation:

Answer:

[C] Cubic

Step-by-step explanation:

Let find define all the answer choices:

Linear- Straight Line

Quadratic -  shape of a U or an upside down U

Cubic - trivalent graphs, are graphs all of whose nodes have degree 3

Exponential- curve that has a horizontal asymptote and it either has an increasing slope or a decreasing

As a result, the graph given is a Cubic graph.

RevyBreeze

Answer:

I am not sure if you wanted the answer in mm or m.  I gave the answer is m

v =  0.58875[tex]m^{3}[/tex]

Step-by-step explanation:

v = 1/3[tex]\pi r^{2} h[/tex]

v = 1/3 (3.14)([tex].075^{2}[/tex])(100)    The diameter 150mm is .0150m  Take have of that to find the radius

v =  0.58875[tex]m^{3}[/tex]

Answer:

Step-by-step explanation:The function y=log(x) is translated 1 unit right and 2 units down.

The volume of the image is given as follows:

10626 ft³.

The volume of a prism is calculated as the multiplication of the base area of the prism by the height of the prism.

The bottom of the prism in this problem square base of side length 23 ft, along with height of 18 ft, hence:

Bottom volume = 18 x 18 x 23

Bottom volume = 7452 ft³.

The top of the prism also has square base of side length 23 ft, along with triangular height of 12 ft, hence:

Top volume = 0.5 x 12 x 23 x 23 (multiplies by 0.5 as the top is a triangle).

Top volume = 3174 ft³.

Hence the total volume of the prism is given as follows:

7452 + 3174 = 10626 ft³.

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Answer:

One.

Step-by-step explanation:

This polynomial has only one variable, which is x*. We can treat z and 7 as constants. Therefore, the polynomial is linear and can be written as:

5x* + c

where c = 7 - 3z.

A linear polynomial has either one root (when the coefficient is non-zero) or zero roots (when the coefficient is zero). Therefore, the given polynomial has exactly one root, which is:

x* = -c/5 = -(7 - 3z)/5 = (3z - 7)/5

Answer:

  15

Step-by-step explanation:

You want the remainder from division of f(x) = 2x³ +5x² -12x by x -(-1).

The table used for synthetic division is built by listing the zero of the divisor at upper left, and the coefficients of the polynomial across the top to the right of that. They are listed in order of decreasing degree, with any necessary zero coefficients put in the appropriate place(s).

The attachment shows the table and the instructions for filling it out. The value at the bottom in the rightmost column is the remainder from the division.

The remainder theorem tells you that is also the value of the function for x = k.

The remainder from f(x) ÷ (x +1) is 15.

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Answer:

It is a function

Step-by-step explanation:

It's a function because it does not over lapp

Answer: 54

Step-by-step explanation:

Start from the middle of the equation and work your way out.

First find g(3) :

g(3) = 3+7 = 10

Then plug g(3) into the f equation:

f(g(3)) = 5(10) + 4 = 54

Transformation is a function that takes points on the plane and maps them to other points on the plane.

Transformations can be applied one after the other in a sequence where you use the image of the first transformation as the pre image for the next transformation.

Find the image for each sequence of transformations.

 Using geometry software, draw a triangle and label the

vertices A, B, and C. Then draw a point outside the

triangle and label it P.

Rotate △ABC 30° around point P and label the image as

△A′B′C ′. Then rotate △A′B′C ′ 45° around point P and

label the image as △A″B″C ″. Sketch your result.

 Make a conjecture regarding a single rotation that will map △ABC to △A″B″C″.

Check your conjecture, and describe what you did.

 Using geometry software, draw a triangle and label the

vertices D, E, and F.

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To calculate the three-sigma control limits, we first need to find the mean and standard deviation of the sample.

Here, we have,

The mean is:

μ = (4 + 12 + 16 + 8 + 9 + 6 + 5 + 12 + 15 + 7 + 6 + 4 + 2 + 11) / 14 = 8.071

The standard deviation is calculated using the standard deviation formula and is arrived at:

σ = 4.319

The three-sigma control limits are:

Upper control limit = μ + 3σ = 8.071 + (3 × 4.319) = 20.027

Lower control limit = μ - 3σ = 8.071 - (3 × 4.319) = -3.886

b. We can check if the process is in control by looking at whether any of the data points fall outside of the control limits.

From the given data, we can see that the maximum number of complaints is 16, which is well within the upper control limit of 20.027. The minimum number of complaints is 2, which is also well within the lower control limit of -3.886.

Therefore, based on the given data, we can conclude that the process is in control.

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The simplest form of the expression (2x-3)(3x²+2x-1) is 6x³ - 5x² - 8x + 3.

Given the expression in the question:

( 2x - 3 )( 3x² + 2x - 1 )

To simplify the expression (2x-3)(3x²+2x-1), we need to use the distributive property of multiplication,

which states that: a(b+c) = ab + ac

Using this property, we can expand the expression as follows:

(2x-3)(3x²+2x-1)

2x(3x²+2x-1) - 3(3x²+2x-1)

6x³ + 4x² - 2x - 9x² - 6x + 3

Add like terms

= 6x³ - 5x² - 8x + 3

Therefore, the simplest form is 6x³ - 5x² - 8x + 3.

Option A) 6x³ - 5x² - 8x + 3 is the correct answer.

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