Simplify (5x3 + 7x – 8) + (2x3 – 5x2 – x + 3). Choose the standard form of the answer.

Answer:

f(x)=15 when: 0<x(less than or equal to)3

f(x)=22 when: 3<x<7

f(x)=30 when: 7(is less than or equal to)x

Part B- Evaluate the function for f(2): 15

Step-by-step explanation:

Algebra Nation; Section 8 topic 6

The domain of each function is the set of all possible values of t for which the function is defined. In this case, the domain of each function is:

For f(t) = 15: 0 < t ≤ 3

For f(t) = 22: 3 < t ≤ 7

For f(t) = 30: t > 7

The admission prices at the amusement park can be represented as functions of the amount of time a customer spends at the park. Let's denote the amount of time by t (in hours). Then we can define the following functions:

For t ≤ 3: f(t) = 15

For 3 < t ≤ 7: f(t) = 22

For t > 7: f(t) = 30

The domain of each function is the set of all possible values of t for which the function is defined. In this case, the domain of each function is:

For f(t) = 15: 0 < t ≤ 3

For f(t) = 22: 3 < t ≤ 7

For f(t) = 30: t > 7

Note that the domain for each function reflects the fact that customers can only be charged according to the specified rates for the corresponding time intervals.

Additionally, since the amusement park is open for 15 hours a day, 7 days a week, we can say that the total operating time is 15 x 7 = 105 hours per week.

To know more about the domain follow

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Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

2, -1

Step-by-step explanation:

add -7x to the other side so the equation is

y=7x-2

slope is 7

y-int is -2

Answer:

Part A

[tex]The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}[/tex]

Plugging in the given values we get;

[tex]The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12[/tex]

R = 12 inches

The radius of the circumscribing circle is 12 inches

Part B

The length of each side of the hexagon, 's', is;

[tex]s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)[/tex]

Therefore;

[tex]s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12[/tex]

s = 12 inches

The perimeter, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon is 72 inches

Step-by-step explanation:

The given parameters of the regular hexagon are;

The length of the apothem of the regular hexagon, a = 6·√3 inches

The relationship between the apothem, 'a', and the circumradius, 'R', is given as follows;

[tex]a = R \cdot cos \left(\dfrac{\pi}{n} \right)[/tex]

Where;

n = The number of sides of the regular polygon = 6 for a hexagon

'a = 6·√3 inches', and 'R' are the apothem and the circumradius respectively;

Part A

Therefore, we have;

[tex]The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}[/tex]

Plugging in the values gives;

[tex]The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12[/tex]

The circumradius, R = 12 inches

Part B

The length of each side of the hexagon, 's', is given as follows;

[tex]s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)[/tex]

Therefore, we get;

[tex]s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12[/tex]

The length of each side of the hexagon, s = 12 inches

The perimeter of the hexagon, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon = 72 inches

Answer: radius = 12, perimeter = 72

Step-by-step explanation:

We know that in 30-60-90 right triangles, the hypotenuse is exactly twice the length of the short leg and the long leg is the short leg times √3.

so therefore, if the long leg (apothem) is equal to 6√3, the short leg is equal to 6

long leg = 6√3

long leg = short leg √3

short leg = 6

hypotenuse (radius) = 2(short leg)

hypotenuse (radius) = 2(6)

hypotenuse (radius) = 12

The radius of hexagon ABCDEF = 12 inches

Perimeter = r (sides)

Perimeter = r (6)

Perimeter = 12 (6)

Perimeter = 72

The perimeter of hexagon ABCDEF = 72 inches

Answer:

V = 796 7/8 ft^3

Step-by-step explanation:

The storage unit has a rectangular shape.

Thus, the volume is V = (area of floor)(height)

                                  V = (106 1/4 ft^2)(7 1/2 ft)

                                   V = 796 7/8 ft^3

Converting 106 1/4 ft to 106.25 makes it easier to use a calculator here.  Same with 7 1/2 ft:  7.5 ft

Answer: 7.44

Step-by-step explanation: DeltaMath

Answer:

[tex]6[/tex]×[tex]\frac{1}{2} =3[/tex]

Step-by-step explanation:

Yeah.

(6x-5)-(-x-4)

6x-5=x+4

6x-x=4+5

5x=9

s.a=C.A xH

v of n.o.2 =lxwxh

Step-by-step explanation:

v of no.3=πr2h and s.a=πdh

no.1=area of cross section x area of all faces and v=area of cross section x length

try those ones

Answer:

380 students

Step-by-step explanation:

133 = 35%

[tex]\frac{133}{35}[/tex] = 1%

3.8 = 1%

3.8 * 100

= 380

Answer:

A.

Step-by-step explanation:

Answer:

oh I see. that's an interesting question but the problem is I hate maths

Answer: 40,260

Step-by-step explanation:

72,100-31,840=40,260

Answer:

201,300

Explanation

I got 100 so no worries

Answer:

b

Step-by-step explanation:

a translation is when it looks exactly the same but is on the other side of the line

Answer:

18,24,30

Step-by-step explanation:

hope this helps

Answer:

c

Step-by-step explanation:

because that the hypotenuse 30 adjacent 18 and opposite 24

Answer:

A≈153.94mi²

Step-by-step explanation:

A = πr2 = π · 72 ≈ 153.93804mi²

Answer:

15

Step-by-step explanation:

3/4(20/1) = (3*20)/(4*1)

60/4

15

Ok so I am not exactly sure if you want to know how many whole cups can be added or simply how many 2/3 cups make up 10, but heres what I found.

So to find how many 2/3 is in 10 cups you simply have to divide

10/(2/3) = 15

So 10 cups of flour is 15 (2/3) cups of flour.

Hope this helps :)

Answer:

f x

Step-by-step explanation:

the equqtion's y intercept is -4 , and f (x) has that intercept

Answer:

f(x)

Step-by-step explanation:

The equation says -4 meaning that it moved down 4 spaces on the y-axis.

Answer:

50 hours

Step-by-step explanation:

Given data

Time=40hr

Speed=10km/hr

Let us find the fixed distance first

Speed= distance/Time

10= distance/40

distance= 10*40

distance= 400miles

Now our speed= 8km/h

hence the time is

8= 400/time

time= 400/8

time=50 hours

Hence the time is 50 hours

9514 1404 393

Answer:

  222 cm²

Step-by-step explanation:

The surface area can be found using the formula ...

  A = 2(LW +H(L+W))

To minimize fraction nonsense, we'll let H be the fraction.

  A = 2(12·8 +(3/4)(12 +8)) = 2(96 +15) = 222

The surface area of the prism is 222 square centimeters.

Answer:

varied

square root of number never result negative number

Step-by-step explanation:

There will only be one real solution.

If [tex]x[/tex] is a real number, the square root function [tex]\sqrt x[/tex] will only have real solutions when [tex]x\ge0[/tex].

For [tex]x<0[/tex], we get imaginary solutions.

Also, when [tex]\sqrt x> 0[/tex], [tex]x>0[/tex]

In other words, when the square root of [tex]x[/tex] is a positive real number,  [tex]x[/tex] will be a unique positive number.

We can see this when trying to solve the equation given in the question

So, the equation

[tex]\sqrt x=c[/tex]

where [tex]c>0[/tex], when solved, will give

[tex]\sqrt x=c\\(\sqrt x)^2=c^2\\x=c^2[/tex]

We will have a unique solution because squaring a positive real number gives a single result.

Learn more here: brainly.com/question/24117016

Answer:

x=58 ; z=32

Step-by-step explanation:

Answer:

1.3

Step-by-step explanation:

Answer:

0.09

0.16

0.35

0.65

0.19

0.56

Step-by-step explanation: