The function g(x) is the height of a football x seconds after it is thrown in the air. The football reaches its maximum height of 30 feet in 4 seconds, and hits the ground at 10 seconds.

What is the practical domain for the function f(x)

Write your answer in interval notation.

Answer:

1) In fig. (1) there are 2 shapes:

So,

Area of Rectangle = l × b

where,

➮ 12 × 14

➮ 168

Hence, the area of rectangle is 168cm².

Now,

Area of Triangle = ½bh

where,

➮ ½ × 8 × 12

➮ ½ × 96

➮ 48

Hence, the area of triangle is 48cm².

Thus, Area of the whole fig. :

Area of Rectangle + Area of Triangle

➮ 168 + 48

➮ 216cm² (Ans)

2) In fig. (2) there are also 2 shapes :

So,

Area of Semicircle = ½ (πr²)

where,

➮ ½ × 3.14 × (5)²

➮ ½ × 3.14 × 25

➮ ½ × 78.5

➮ 39.25

Hence, the area of semicircle is 39.25 in².

Now,

Area of Rectangle = l × b

where,

➮ 10 × 15

➮ 150

Hence, the area of rectangle is 150 in².

Thus, Area of whole fig. :

Area of Semicircle + Area of Rectangle

➮ 39.25 + 150

➮ 189.25 in² (Ans)

[tex]\bold{\huge{\underline{ Solutions }}}[/tex]

Given :-

We have,

We know that,

Area of rectangle

[tex]\bold{ = Length {\times} Breath}[/tex]

Subsitute the required values,

[tex]\sf{ = 12 {\times} 14}[/tex]

[tex]\sf{ = 168 \: cm^{2}}[/tex]

For triangle

Area of triangle

[tex]\bold{=}{\bold{\dfrac{ 1}{2}}}{\bold{ {\times} b{\times}h}}[/tex]

Subsitute the required values,

[tex]\sf{=}{\sf{\dfrac{ 1}{2}}}{\bold{ {\times}8{\times}12}}[/tex]

[tex]\sf{=}{\sf{\dfrac{ 1}{2}}}{\bold{ {\times} 96}}[/tex]

[tex]\sf{ = 48 \:cm^{2}}[/tex]

Thus, Area of triangle is 48 cm² .

The total area of the composite figure

= Area of rectangle + Area of triangle

[tex]\sf{ = 168 + 48}[/tex]

[tex]\bold{ = 216\: cm^{2}}[/tex]

Hence, The area of given composite figure is 216 cm²

Given :-

Here, we have

We know that,

Area of rectangle

[tex]\bold{ = Length {\times} Breath}[/tex]

Subsitute the required values,

[tex]\sf{ = 10 {\times} 15}[/tex]

[tex]\sf{ = 150 \: cm^{2}}[/tex]

For hemisphere

Area of semicircle

[tex]\bold{ = 1/2{\pi}r^{2}}[/tex]

Subsitute the required values,

[tex]\sf{ =}{\sf{\dfrac{ 1}{2 }}}{\sf{ {\times} 3.14 {\times} (5)^{2}}}[/tex]

[tex]\sf{ = }{\sf{\dfrac{1}{2}}}{\sf{ {\times}3.14 {\times} 25}}[/tex]

[tex]\sf{ = 1.57 {\times} 25}[/tex]

[tex]\sf{ = 39.25\: in^{2}}[/tex]

Thus, The area of semicircle is 39.25 in².

Total area of the given composite figure

= Area of hemisphere + Area of rectangle

= [tex]\sf{ = 150 + 39.25}[/tex]

[tex]\bold{ = 189.25\: in^{2}}[/tex]

Hence, The total area of the given composite figure is 189.25 in² .

Answer:

Are there any measurements for the size of the prisms? I think we need more info for this. I'll delete this when you answer and upload a new one :)

Step-by-step explanation:

The amount of sand left after building the sand castle is 290 inches³.

Rectangular prism is a three dimensional shape which consist of six faces. The two faces are at the top and bottom and the other faces are lateral faces.

We have to find the volume of each of the rectangular prism to know how much sand is used to make the castle.

Volume of a rectangular prism = l × w × h

where l, h and w are length, height and width of the prism respectively.

Volume of larger prism = 15 × 15 × 6

                                       = 1350 inches³

Volume of smaller prism = 9 × 8 × 5

                                         = 360 inches³

Total volume of the castle = 1350 + 360 = 1710 inches³

Remaining sand = 2000 - 1710 = 290 inches³

Hence the sand that remains is 290 inches³.

Learn more about Volume here :

https://brainly.com/question/21308574

#SPJ2

Answer:

8+5 and 8--5

Step-by-step explanation:

minus and minus is plus and 5+8 =8+5

Answer: B, because when we factor in each term it all checks out

Answer:

11+ 9 = 20

Step-by-step explanation:

=> 21-9=11

21 - 9 equals to 11 is actually a wrong answer

So in order to find the subtraction problem that will help us truly know whether the equation is wrong

=> 11+ 9 = 20

OR THE SECOND EQUATION IS

=> 21 - 11 = 10

Answer:

  (3x +2w)/(2x -3w)

Step-by-step explanation:

The usual rules for adding and dividing fractions apply:

  (a/b) +(c/d) = (ad +bc)/(bd) . . . . . . . use a common denominator

  (a/b)/(c/b) = a/c . . . . . . . . . . . . same denominators "cancel"

__

  [tex]\dfrac{\dfrac{3}{w}+\dfrac{2}{x}}{\dfrac{2}{w}-\dfrac{3}{x}}=\dfrac{\dfrac{3x+2w}{wx}}{\dfrac{2x-3w}{wx}}=\boxed{\dfrac{3x+2w}{2x-3w}}[/tex]

Answer:

y=4x-6

Step-by-step explanation:

That is how you would graph it.

Hope this helps!

The first step is to find any two sets of points on the line to find the slope. Let's use (0, -6) and (4,10).

   [tex]Slope=\frac{y2-y1}{x2-x1} =\frac{10--6}{4-0} =\frac{16}{4} =4[/tex]

Ok, now we found the slope. Now let's put it into the point-slope form which requires any one point on the line and the slope. Lets use the point (0,-6)  

        [tex](y-y0)=m(x-x0)\\(y+6)=4(x-0)\\y=4x-6[/tex]

The last equation is the slope-intercept form.

Hope that helped!

Answer: The length of the rectangle would be 20 inches and the width would be 14 inches.

Step-by-step explanation:

If the length is 20, first, it’s 6 more than 14, and second it would add up to 40. If the width is 14, it’s 6 less than 20, and adds up to 28. If you add those two together, you’d get your total of 68 inches for the perimeter!

Answer:

First one

Step-by-step explanation:

When he works 0 hr then he will make $0. So the line will intersect y axis at y= 0

He makes $11 an hr. So the earning increases by 11 for every 1 hr

The diameter of the ball in real life given the scale of the drawing is 150cm.

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

Scale of the drawing = original dimensions / dimensions of the scale drawing

10cm x 15 cm - 150cm

To learn more about scale drawings, please check: https://brainly.com/question/26388230

Answer:

The answer should be 7

Step-by-step explanation:

2³ = 8

4 x 1.5 = 6

8 + 6 = 14

14 ÷ 2 = 7

Answer:

Base 10 is always the decimal system which is from (0-9).

There is one input being mapped into two different outputs, so this is not a function. The correct option is D.

A function is a relation that maps elements from one set (the domain) into elements from another set (the range). Such that each element from the domain can be mapped into only one element from the range.

In this case, the table is:

So, the input "12" appears twice, the first time is mapped into 300 miles, and the second time is mapped into 350.

So the same value from the domain is being mapped into two different values of the range, meaning that this is not a function. So the correct option is D.

If you want to learn more about functions, you can read:

https://brainly.com/question/13136492

Answer:

[-1, 1]

Step-by-step explanation:

The range will be all y-values that the function reaches. Here, we see that the function is periodic which goes through a pattern of waves. It will go forever in both directions of the x-axis. However, in the y-dimension, it ranges from -1 to 1. It will have brackets as it touches 1 and -1 instead of approaching.

Answer:

Solving method

360°÷8 (number of sides)

= 45°

Answer:

D. 10π

Step-by-step explanation:

To find the circumference of a circle, use the equation:

circumference = 2πr

We can substitute the radius into this equation: c = 2 × π × 5. This is equal to 10π.

Hope this helps!

Answer:

A) 4+10i

Step-by-step explanation:

(7+3i)-(3-7i)

7+3i-3-(-7i)

7+3i-3+7i

7-3+3i+7i

4+3i+7i

4+10i

Answer:

Step-by-step explanation:

Answer: In 4 HOURS they will be 468 miles apart.

Step-by-step explanation:

1st car DATA:

rate = 59 mph ; time = x hrs. ; distance = 59x miles

2nd car DATA:

rate = 58 mph ; time = x hrs. ; distance = 58x miles

EQUATION:

distance + distance = 385

59x + 58x = 468

117x = 468

x = 4 hours.

Answer:

12

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Straight away, we can see there is some sort of reflection over the y-axis.

Then, we can see that, there is a reflection over the x-axis.

This matches up with A.

Answer:

5.928 liters is the correct answer

Step-by-step explanation:

Since 1 milliliter is 0.001 liters

Multiply both values by 5928.

Therefore... 5928 milliliters equals 5.928 which is letter D

Answer:

The answer is 0.5928 liters

Step-by-step explanation:

1 liter is made of 1000 milliliters

So 5,929 ÷ 1000

gives us 0.5928

Answer:

13

Step-by-step explanation:

Given:

13, 6, 24, 18, 33, 5, 13, 48, 9, 11, 36, 28, 15, 6, 13

To Find:

Median

Note:

Finding Median:

⇒ Arrange data values from lowest to highest value

⇒ The median is the data value in the middle of the set

⇒ If there are 2 data values in the middle the median is the mean of those 2 values.

Solve:

5, 6, 6, 9, 11, 13, 13, 13, 15, 18, 24, 28, 33, 36, 48

5, 6, 6, 9, 11, 13, 13, 13, 15, 18, 24, 28, 33, 36, 48

5, 6, 6, 9, 11, 13, 13, 13, 15, 18, 24, 28, 33, 36, 48

5, 6, 6, 9, 11, 13, 13, 13, 15, 18, 24, 28, 33, 36, 48

5, 6, 6, 9, 11, 13, 13, 13, 15, 18, 24, 28, 33, 36, 48

5, 6, 6, 9, 11, 13, 13, 13, 15, 18, 24, 28, 33, 36, 48

5, 6, 6, 9, 11, 13, 13, 13, 15, 18, 24, 28, 33, 36, 48

5, 6, 6, 9, 11, 13, 13, 13, 15, 18, 24, 28, 33, 36, 48

As you can see now.. Median is 13

[RevyBreeze]

Answer:

Median Arrayed Data :From ascending order; 5,6,6,9,11,13,13,13,15,18,24,28,33,36,48

Now,

Median= n+1/2

=15+1/2

=16/2

=8

5,6,6,9,11,13,13,13,15,18,24,28,33,36,48

Median = 8 th term= 13.

Hence the median is 13.

Answer:

12:35

Step-by-step explanation:

the first bus is at 10:35 so 10:35 + 2:00 = 12:35

Answer:

12:35 p.m.

Step-by-step explanation:

I mean it's pretty simple tbh. If the bus departs every two hours, then two hours from 10:35 is 12:35 p.m.

Answer:

58 Hours

Step-by-step explanation:

Given:

Martin~114 hours

Esperanza~56

Explanation:

The questions asks "How much longer". When this is asked, we know that we must subtract.

114-56=58

Answer: 58

For problems 1, 2, and 4, check out this link

https://brainly.com/question/27021415

as they were answered there earlier.

=======================================================

Problem 3

A triangle cannot be constructed with these parameters.

----------------------------

Explanation:

Use the Law of Sines to find angle B

sin(A)/a = sin(B)/b

sin(120)/12 = sin(B)/13

sin(B) = 13*sin(120)/12

sin(B) = 0.93819419

B = arcsin(0.93819419) or B = 180 - arcsin(0.93819419)

B = 69.75047247 or B = 180 - 69.75047247

B = 69.75047247 or B = 110.24952753

These angle values are approximate.

-----------

If B = 69.75047247, then,

A+B+C = 180

C = 180 - (A+B)

C = 180 - (120 + 69.75047247)

C = -9.75047247000001

We get a negative result which isn't valid.

This means B = 69.75047247 isn't valid either.

-----------

If B = 110.24952753, then,

A+B+C = 180

C = 180 - (A+B)

C = 180 - (120 + 110.24952753)

C = -50.24952753

We get a similar conclusion here as well.

-----------

No matter what value of B we go with, we end up with a negative value for angle C.

Negative angles are not allowed.

Therefore, we cannot construct a triangle with sides a = 12, b = 13 and angleA = 120 degrees.

This is one example of an SSA triangle leading to no possible solutions. Refer to the SSA ambiguous case for more info.

-----------

Check out the diagram below. Imagine that point B can be anywhere on the dotted circle. Imagine it can rotate around as in an animation. This circle is centered at point C and has radius a = 12. No matter where point B is placed, we cannot get it to land on the horizontal line to therefore form a triangle. Simply put: side a = 12 is too short.

I used GeoGebra to make the diagram and make sure it's to scale. This is to visually verify that we cannot construct such a triangle with these parameters.

Answer:

1/2 split into 4 parts

Step-by-step explanation:

i cant draw it

Answer:

dz/dt = -(3x + 9y)/z

Step-by-step explanation:

x² + y² + z² = 9

2x dx/dt + 2y dy/dt + 2z dz/dt = 0

x dx/dt + y dy/dt + z dz/dt = 0

x * 3 + y * 9 + z dz/dt = 0

so

dz/dt = -(3x + 9y)/z

Answer:

D

Step-by-step explanation:

it is d because you have to subtract that to get 35