G(x) = 4x - 5, find g(3)

To solve this, we need to find the area of the ring-shaped path. We can find this area, by calculating the area of the whole circular garden and subtracting the area of the flower garden.

The whole garden has a diameter of 34yd for the flower garden, plus the ring-shaped path, which adds 10yd to the diameter, making a total of 44yd diameter circle.

The formula for the area of a circle is:

Where r is the radius,

Let's find the area of a circle of diameter 44yd. The radius is half the diameter, thus r = 22

And now, the area of the garden without the ring-shaped path. This is a circle of diameter 34yd. Thus, the radius is 17yd.

If we now rest the area of the smaller circle to the area of the bigger circle, we get the area of the path:

And to find out how many bags of san are needed, we divide the area of the path (612.3 sq yd) by the area that a single bag can cover (6 sq yd):

Since we can't buy a fraction of a bag,

The answer is 103 bags of sand.

Answer:

62%

Step-by-step explanation:

This one's easy to solve as a percentage because the total number was 100 to begin with. Simply divide the number of employed students by the total amount of students, 62/100, which gets 0.62, or 62%.

your answer is 1/36 because if you spin once it would be 1/18 and if spin x2 the answer would be 1/36

Answer:

x=45

Step-by-step explanation:

i hope its right good luck :)

i think im wrong

Find Geometric mean of

a) 2 and 8 . GM = √16 = 4

b) 9 and 36. GM= √324 = 18

c) 4 and 7. GM = √28= 2√7

d) 5 and 10. GM =√50 = 5√2

e) 2√2 and 5√2 . GM = √10•√2•√2= √20= 2√5

f)3√5 and 5√5 . GM= √(15•√5•√5) = √75 = 5√3

Answer:

$405,44

Step-by-step explanation:

First of all we have to find how much the tv cost after 15% of discount.

we can use this proportion

15 : 100 = x : 499.99

x = (15*499.99)/100 = $74.9985

then we have to subtract the initial value to the value of the discount

499.99-74.9985 = $424,9915

thanks to the card we can apply another 10%

10 : 100 = x : 424,9915

x = (424,9915 *10)/100 = $42,49915

424,9915-42,49915 = $382,49235

now we have to apply taxes

6:100 = x : 382,49235

x = $22,949541

382,49235 + 22,949541 = $405,441891

that can be rewrite as $405,44

If we want to write an equation to solve this problem we can use this

499.99 - (499.99 * 15/100) - 1/10[499.99-(499.99*15/100)] + 6/100{1/10[499.99-(499.99*15/100) = x

Answer:303.19

Step-by-step explanation: HOPE I HELPED

Answer:

I'm not sure for my answer but is B

I'm gonna put the steps

Step-by-step explanation:

x2−4x−12as(x+p)(x+q)

=−12apqs−12apsx−12aqsx−12asx2+x2−4x

Answer:

(gof)(x) = 14x + 1

Step-by-step explanation:

We can think of (gof)(x) as g(f(x)).  Writing it in this form shows that we must start with the inner function and work our way to the outer function.

Essentially, the input of the inner function yields an output and the output becomes the input of the outer function.

f(x) means that the input is x and since we're given no value for x (e.g. x = so and so), the output is the original function or 2x - 1

Now, this output becomes the input for g(x):

g(2x-1) = 7(2x - 1) + 8

14x -7 + 8

(gof)(x) = 14x + 1

Answer:

\(\textsf{12)} \quad \text{a.}\;\;m \angle 1 = 107^{\circ}, \quad \text{b.}\;\;m \angle 2 = 107^{\circ}, \quad \text{c.}\;\;m \angle 3 = 73^{\circ}\)

\(\textsf{13)} \quad EC = 6\)

\(\textf{14)}\quad \text{a.}\;\;x = 33, \quad \text{b.}\;\; x = 8\)

Step-by-step explanation:

As the base angles of an isosceles trapezoid are congruent, the measures of angles E and J are the same. Therefore:

\(m\angle 3 = 73^{\circ}\)

The opposite angles of an isosceles trapezoid sum to 180°. Therefore:

\(\implies m\angle 1 + m\angle 3 = 180^{\circ}\)

\(\implies m\angle 1 + 73^{\circ} = 180^{\circ}\)

\(\implies m\angle 1 = 107^{\circ}\)

Since the base angles of an isosceles trapezoid are congruent, the measures of angles A and N are the same. Therefore:

\(m\angle 2 = 107^{\circ}\)

\(\hrulefill\)

The diagonals of isosceles trapezoid ABCD are AC and BD.

Point E is the point of intersection of the diagonals. Therefore:

\(BE + ED = BD\)

\(AE + EC = AC\)

As the diagonals of an isosceles trapezoid are the same length, BD = AC. Therefore:

\(AE + EC = BD\)

Given BD = 20 and AE = 14:

\(\implies AE + EC = BD\)

\(\implies 14 + EC = 20\)

\(\implies 14 + EC - 14 = 20 - 14\)

\(\implies EC = 6\)

\(\hrulefill\)

The midsegment of a trapezoid is a line segment that connects the midpoints of the two non-parallel sides (legs) of the trapezoid.

The formula for the midsegment of a trapezoid is:

\(\boxed{\begin{minipage}{6 cm}\underline{Midsegment of a trapezoid}\\\\$M=\dfrac{1}{2}(a+b)$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the midsegment.\\ \phantom{ww}$\bullet$ $a$ and $b$ are the parallel sides.\\\end{minipage}}\)

a)  From inspection of the given trapezoid:

Substitute these values into the midsegment formula and solve for x:

\(x=\dfrac{1}{2}(18+48)\)

\(x=\dfrac{1}{2}(66)\)

\(x=33\)

Therefore, the value of x is 33.

b)  From inspection of the given trapezoid:

Substitute these values into the midsegment formula and solve for x:

\(15=\dfrac{1}{2}(22+x)\)

\(30=22+x\)

\(x=8\)

Therefore, the value of x is 8.

The triple integral of f(x,y,z) = x² + y² over G, using both spherical and cylindrical coordinates, is (16π/15)(√2 - √3).

To sketch the solid G, we first observe that the cylinder x² + y² = 2 is a circular cylinder with radius √2, centered at the origin.

The cone z = √(x² + y²) is a double-napped cone with vertex at the origin and axis along the z-axis. The cone intersects the xy-plane in a circle of radius 1, which is contained inside the cylinder.

The solid G is the region between the cylinder and the cone, enclosed by the xy-plane.

To visualize the solid, we can first plot the cylinder and the cone in the xy-plane, as shown in image attached.

To compute the triple integral of f(x,y,z) = x² + y² over G, we can use both spherical and cylindrical coordinates.

Cylindrical Coordinates:

In cylindrical coordinates, we can write the equations of the cylinder and the cone as follows:

Cylinder: r² = 2

Cone: z = r

The limits of integration for r, θ, and z are as follows:

r: 0 to √2

θ: 0 to 2π

z: 0 to r

The triple integral of f(x,y,z) = x² + y² over G in cylindrical coordinates is:

∫∫∫ f(r,θ,z) r dz dr dθ

= ∫₀^(√2) ∫₀^(2π) ∫₀^r (r² cos²θ + r² sin²θ) dz dr dθ

= ∫₀^(√2) ∫₀^(2π) r³/2 dr dθ

= (2π/5) [√2]^5

= 16π/5

Spherical Coordinates:

In spherical coordinates, we can write the equations of the cylinder and the cone as follows:

Cylinder: ρ sinφ = √2

Cone: ρ = r

The limits of integration for ρ, θ, and φ are as follows:

ρ: √2/sinφ to √2

θ: 0 to 2π

φ: 0 to π/4

The triple integral of f(x,y,z) = x² + y² over G in spherical coordinates is:

∫∫∫ f(ρ,θ,φ) ρ² sinφ dρ dθ dφ

= ∫₀^(π/4) ∫₀^(2π) ∫_(√2/sinφ)^(√2) (ρ⁴ sin²φ cos²θ + ρ⁴ sin²φ sin²θ) sinφ dρ dθ dφ

= 2π/3 ∫_(√2/sinφ)^(√2) ρ⁴ sinφ dρ ∫₀^(π/4) sin³φ dφ

= 2π/3 [ρ⁵/5]_(√2/sinφ)^(√2) [-cosφ]₀^(π/4)

= (2π/15) [(√2)⁵ - (2/√3)(√2)⁵]

= (4π/15) [(√2)⁵ - (√6)(√2)⁴]

= (4π/15) (√2)⁴ [(√2 - √3)(√2 + √3)]

= (16π/15) (√2 - √3)

Learn more about  triple integral here: https://brainly.com/question/17206296

#SPJ1

Answer:

510 minutes.

Step-by-step explanation:

i hope this helped you! :)

510 MINUTES!! :)

Hope this helped!

Answer: 475 adults paid admission

Step-by-step explanation:

1.50c+4a=5050 (1.50 per child and 4 per adult)

1.50(2100)+4c=5050 (2100 children times 1.5 each)

3130+4a=5050

4a=1900

a=475

Answer:51,000

Step-by-step explanation:

ther is 1000 grams every kilogram so 17x3 is 51 and 51x1000 is 51,000

Answer:

2 tickets because round

Step-by-step explanation:

make an equation: 100=40x+2 and solve

2.45 tickets so only two

40+40 =80

100-80=20

but 100-2=98 so there is only 18$ left so not enough for another ticket

Answer:

30 Tickets

Step-by-step explanation:

In the question, it said that $40 is the entrance fee. Then, it said that visitors purchase additional tickets for rides, games, and food. This means that EACH ticket is 2 dollars.

Hence, $40 (entrance fee) + $2 (each ticket price) x (the number of tickets spent) = 100 (total amount of money).

So, the equation should be 40 + 2x = 100, which means x = 30.

100 - 40 = 60

60/2 = 30

30 tickets can be purchased

Answer:

9×y

Step-by-step explanation:

the

answer

of

the

given

is 9y

Given:

8, 9, 5, 15, 12, 25, 4

To make a box-and-whisker plot.

Let us write it in ascending order,

4, 5, 8, 9, 12, 15, 25.

The median of the given data is 9.

The median of the first three numbers is 5.

The median of the last three numbers is 15.

Hence, the correct box-and-whisker plot is given the option he third one.

For the given logarithmic function, we have:

domain: (4, ∞).

range: (-∞, ∞).

For a function y = f(x), the domain is the set of the possible input values, and the range is the set of the possible output values.

Here we have the function:

f(x) = log(x - 4) - 3

First, we know that the range of logarithmic functions is the set of all real numbers.

We also know that the argument of logarithmic functions can only be larger than zero.

So the domain is defined by x > 4.

Then we have:

domain: (4, ∞).

range: (-∞, ∞).

If you want to learn more about domain and range.

https://brainly.com/question/10197594

#SPJ1

Answer:

\(tom = \frac{85}{100} \times 20 \\ = 17 \: questions\)

Melissa had a greater mark.

Answer:

Melissa

Step-by-step explanation:

Melissa: 18/20

Tom: 85/100

You need a common denomenater so multiply 18 and 20 by 5:

90/100>85/100

Melissa has the greater mark by 5%

The x-intercept of the function is (-1/3, 0) and (5, 0)

Given is a graph of a parabola having equation y = -3x²+14x+5, we need to find the x-intercept of the graph,

So to find the x-intercept put y = 0,

Therefore,

-3x²+14x+5 = 0

-3x²+15x-x+5 = 0

-3x(x-5)-1(x-5) = 0

(-3x-1)(x-5) = 0

Therefore,

x = -1/3 and x = 5

Hence the x-intercept of the function is (-1/3, 0) and (5, 0)

Learn more about x-intercept click;

https://brainly.com/question/14180189

#SPJ1

\(\huge\text{Hey there!}\)

\(\huge\textbf{Equation:}\)

\(\mathbf{7x + 2x + 27 = 180^\circ}\)

\(\huge\textbf{Solve:}\)

\(\mathbf{7x + 2x + 27 = 180^\circ}\)

\(\huge\textbf{COMBINE the LIKE TERMS:}\)

\(\mathbf{(7x + 2x) + 27 = 180^\circ}\)

\(\mathbf{7x + 2x + 27 = 180^\circ}\)

\(\mathbf{9x + 27 = 180^\circ}\)

\(\huge\textbf{SUBTRACT 27 to BOTH SIDES:}\)

\(\mathbf{9x + 27 - 27 = 180^\circ - 27}\)

\(\mathbf{9x + 27 - 27 = 180 - 27}\)

\(\huge\textbf{Simplify it!}\)

\(\mathbf{9x = 180 - 27}\)

\(\mathbf{9x = 153}\)

\(\huge\textbf{DIVIDE 9 to BOTH SIDES:}\)

\(\mathbf{\dfrac{9x}{9}=\dfrac{153}{9}}\)

\(\huge\textbf{Simplify it!}\)

\(\mathbf{x = \dfrac{153}{9}}\)

\(\mathbf{x = 17}\)

\(\huge\textbf{Answer:}\)

\(\huge\boxed{\textsf{Option D. 17}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

19 feet

Step-by-step explanation:

First we must make the scale make sense, that is, it is in the same unit, therefore, we will pass 3 inches to feet, we know 1 foot is 12 inches, therefore:

3 inches * 1 foot / 12 inches = 0.25 feet

Which means that the real equivalence is 0.25: 8, now they are 7 inches, therefore:

7 inches * 1 foot / 12 inches = 0.583333

Now, we calculate the number of actual feet using the scale.

0.583333 * 8 / 0.25 = 18.66 feet

that is to say that the length of the current Kitchen is 19 feet if we round

The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

For more such questions on segment

https://brainly.com/question/280216

#SPJ8

Answer:

Area: 113cm²

Circumference: 37.7cm

Step-by-step explanation:

to find area use the formula πr², π being Pi (3.14) and r being radius

radius = 6cm (half the diameter)

3.14 × 6² = 113.04cm²

to find the circumference use the formula πd

diameter = 12cm

3.14 × 12 = 37.68

Explanation:

Step 1. We are given the expressions for u(x) and v(x):

The first two parts of the problem consist of finding the derivative of these two expressions: u'(x) and v'(x).

Step 2. To derivate u(x) we use the following rule:

which means that in this case:

Step 3. To derivate v(x) we use the following rule:

In our case n=14, therefore, the derivative is:

simplifying the exponent:

Step 4. Now, to solve the third part of the problem, we consider the definition of f(x) given in the statement:

And to find the derivative of this function f'(x) or f', we use the quotient rule,

We already know u and v from the given definitions, and we found u' and v' in 2 and 3.

So now, we substitute the known values into the quotient rule formula:

Step 5. The last step is to simplify our result. We start by simplifying the exponent in the denominator:

and to simplify further, divide both the numerator and denominator by x^13

And that is the simplified solution.

Answer:

The effect that does NOT relate to one's driving ability is breathalyzer test results indicating a high BAC. Option B.

While the breathalyzer test measures the blood alcohol concentration (BAC), it is a method used to determine the level of alcohol in a person's system and is commonly used in assessing impairment for driving under the influence.

Therefore, it directly relates to one's driving ability and is not excluded from the effects on driving ability caused by a BAC of .2 percent.

On the other hand, options, lack of coordination, impaired gross motor skills, and impaired reactions all directly relate to one's driving ability as they affect the physical and cognitive abilities necessary for safe and efficient driving.

More on breathalyzers can be found here: https://brainly.com/question/26086547

#SPJ1