PART B: APPLICATIONS
5. A Pokéball's flight is described by the equation h = –20t2 + 120t + 140, where h is the
height of the ball in feet at time, t seconds.
a) When does the ball hit the ground? (show all work)
[3]
b) From what height is the ball thrown?
[1]
c) What is the maximum height reached by the ball? (show all work)
[3]
PLEASE HELP AND SHOW WORK I BEG

Answer: 12 minutes

Step-by-step explanation:

7 km ........ 4 minutes

21 km ...... ?

21/7 x 4= 12 minutes

Answer: 12 minutes.

Step-by-step explanation:

It is easy to put the numbers into a ratio form to work it out. So-

4 minutes for 7 km = 4 : 7

Then ? minutes for 21 km = ? : 21

You first divide the given value by the original value of that it is proportioned to (the number on the same side of the original ratio as 21). In this case divide 21 by 7 = 3. You now have to times the answer you got by the other original value which will be 4 x 3 = 12.

Therefore your answer is 12 minutes.

Answer:

The two inequalities are :

option B and option C.

Step-by-step explanation:

Explanation:

Daniel moves no more than 30 of his sheep and goats into another field. This means the summation of sheep and goats will be at maximum 30.

that is why it is s+g<30

And more than 7 of his animals are sheep means sheep are greater than 7. that is why =s>7

The right inequalities which corresponds to Daniel's animals are s+g<=30 and s>7 which are on option A and C.

It is a type of an equation in which we have to use greater than, less than, greater than or equal to , less than or equal to signs.

There are total 30 animals of Daniel and s represents the number of sheeps and g responds the number of goats so the first inequality will be

s+g<=30

There are more than 7 sheeps so the second inequality will be

s>7

Hence the right inequalities are s+g<=30, s>7.

Learn more about inequality at https://brainly.com/question/24372553

#SPJ2

Answer:

The amount one locust eats in a week is 420/30 = 14 grams so it eats 14/7 = 2 grams per day, therefore 21 locusts can eat 21 * 14 = 42 grams per day. 420 / 42 = 10 so the answer is 10 days or 1 week and 3 days.

Answer:

See the step-by-step

Step-by-step explanation:

This answer is based on the idea that magnitude is absolute value.

Absolute value is a number's distance from zero.

1. Magnitude is never negative. (True)

2. The magnitude of -1.9 is  |–1.9| which is 1.9. (True)

3. The absolute value of a number is greater than its magnitude. (False, they are the same (?, maybe)

4. The numbers –4 and 4 have the same magnitude. (True)

5. The magnitude of Negative two-thirds is less than the magnitude of Two-thirds. (False)

Answer:

Which statements are true? Check all that apply.

Magnitude is never a negative value.

The magnitude of –1.9 is |–1.9| which is 1.9

The numbers –4 and 4 have the same magnitude.

Step-by-step explanation:

Answer:

110

Step-by-step explanation:

example:

rounded 20+20+20+30 = 90

original 25+25+25+35 = 110

Answer:

21

Step-by-step explanation:

substitution

Answer:

21

Step-by-step explanation:

Plug in x as -2.

3(-2)² - 4(-2) + 1

3(4) - - 8 + 1

12 + 8 + 1

= 21

Answer:

x = 5

Step-by-step explanation:

5(x + 4) - 8 = x + 32

5x + 20 - 8 = x + 32

5x + 12 = x + 32

5x - x + 12 = 32

5x - x = 32 - 12

4x = 32 - 12

4x = 20

x = 5

Hope this helped! :)

Answer:

A

Step-by-step explanation:

Hours worked, probably because of commission or bonuses (the other ones seem to be proportional)

Answer:

521

Step-by-step explanation:

Composite figure.

Draw a straight down from C to line segment AB. This forms a triangle.

Now, the area of this figure=

Area of semicircle+area of rectangle+ area of triangle.

Rectangle area formula = l times w

Length - 20

Width =14

14 times 20 = 280

Area of rectangle = 280

Semicircle area = area of circle/2

Area of circle = π[tex]r^2[/tex]

Diameter =20= 2r

r=10

π[tex]r^2[/tex]= π 10^2 =100π

100 times 3.14 =314

314/2 = 157

Area of semicircle = 157

Area of triangle= bh/2

Triangle's base= 32-20=12

Triangles height = 14

14 times 12 = 168

168/2 = 84

Area of triangle: 84

Area of semicircle+area of rectangle+ area of triangle.

157+280+84 =521

Answer:

1.) 15,708cm^2/s

2) 47,124cm^2/s

3.) 109,956cm^2/s

Step-by-step explanation:

Given the following:

50cm/s is the radius of the ripple per second , that is, radius(r) of ripple after t seconds = speed * time(t)

Speed = 50cm/s

r = 50t

.area of a circle(A) = πr^2

Rate of change of area with radius :

dA/dt = π2r . dr/dt

Speed of ripple created = 50cm/s; this is the rate at which the radius changes with time (dr/dt)

dr/dt = 50cm/s

Rate at which area is increasing with time:

dA/dt = π2r . dr/dt

dA/dt = π2(50t).50

dA/dt = 5000πt

After 1 second:

dA/dt = 5000π(1)

= 15,707.963cm^2/s

After 3 second:

dA/dt = 5000π(3)

= 47,123.889cm^2/s

After 7 second:

dA/dt = 5000π(7)

= 109,955.74cm^2/s

Answer:

0.723 seconds

Step-by-step explanation:

Let h = 0

0 = -16t² + 6t + 4

Let’s solve by completing the square.

Subtract 4 from both sides.

-4 = -16t² + 6t

Since the coefficient of -16t² is -16, divide both sides by -16.

1/4 = t² - 3/8t

The coefficient of (-3)/8t is (-3)/8. Let b=(-3)/8.

Then we need to add (b/2)² = 9/256 to both sides to complete the square.

Add 9/256 to both sides.

73/256 = t² - 3/8t + 9/256

Factor right side.

73/255 = (t-3/16)²

Take the square root on both sides.

±√(73/255) = t-3/16

Add 3/16 to both sides.

3/16 ± √(73/255) = t

The answer has to be positive, not negative.

0.72254626884 = t

0.723 ≈ t

Answer:

Rounding to the nearest hundredth, it is 0.72

Answer:

For 75 g butter ≈ 27 fingers

Step-by-step explanation:

Using unitary method

For 20 fingers = 55 g butter

For 1 g butter = 20/55 fingers

=> For 1 g butter = 4/11 fingers (Simplified form)

Multiplying both sides by 75

=> for 75 g butter = [tex]\frac{4}{11} * 75 {fingers}[/tex]

=> For 75 g butter ≈ 27 fingers ( approximately )

Step-by-step explanation:

You could simply say the numbers in 0.7 one at a time like this:

=> zero point seven

OR

You can also see 0.7 as a fraction (7/10) and should therefore be said and written as follows:

=> seven tenths

Hope this helps.. Good Luck

0.7 means the same thing as 7 tenths.

Below, I have made a place value chart.

You will see that 0.7 means 0 units and 7 tenths.

Answer:

$776.96

Step-by-step explanation:

The computation of the average daily balance for August is shown below:

Particulars              Days         Days end balance   Total balance

                                                                                    for the period

                              (A)                   (B)                        (A × B)

Aug 1 to Aug 9         9            $728.15                     $6,533.35

Aug 10 to Aug 14     5            $864.15                     $4,321.70

                                      ($728.15 + $136.19)

Aug 15 to Aug 22    8           $572.34                     $4,578.72

                                     ($864.15 - $136.19)

Aug 23 to Aug 31    9           $959.12                      $8,632.08

                                    ($572.34 + $386.78)

Total                       31                                              $24,085.85

Now the average daily balance is

= $24,085.85 ÷ 31 days

= $776.96

Answer:  4 + (−5)

An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.

Step-by-step explanation:  The arrow from 0 running to 4 is the graph of  how the point on the line is a positive 4: Four added to 0

The "additive inverse" means start there and go in the opposite direction. The arrow is 5 units long, so they ended up at -1 . Adding -5 is the same as subtracting 5

4 + (-5) = -1  is the additive inverse of  4-5= -1  

The descriptions of the number lines are well done, but difficult to sort out.

Answer:

4 + (−5)

Step-by-step explanation:

it is got it correct

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

There are only r red counters and g green counters in a bag.  A counter is taken at random from the bag.  The probability that the counter is green is 3/7  The counter is put back in the bag.  2 more red counters and 3 more green counters are put in the bag.  A counter is taken at random from the bag.  The probability that the counter is green is 6/13

Find the number of red counters and the number of green counters that were in the bag originally.

Answer:

Total number of green counters = 9

Total number of red counters = 12

Step-by-step explanation:

Recall that probability is given by

P = number of desired events/total number of events

The probability that the counter is green is 3/7

P(green) = 3/7 = 3x/7x

Where 3x is the number of green counters

7x is the total number of counters

So then red counters are

red counters = 7x - 3x = 4x

4x is the number of red counters

P(green) = 3/7 = 3x/3x + 4x

The counter is put back in the bag.  2 more red counters and 3 more green counters are put in the bag. The probability that the counter is green is 6/13

So after addition of 3 green and 2 red new counters,

P(green) = 6/13 = (3x + 3)/(3x + 4x + 3 + 2)

Now solve for x

6/13 = (3x + 3)/(3x + 4x + 3 + 2)

6/13 = (3x + 3)/(7x + 5)

6(7x + 5) = 13(3x + 3)

42x + 30 = 39x + 39

42x - 39x = 39 - 30

3x = 9

x = 9/3

x = 3

So total number of green counters are

green counters = 3x = 3*3 = 9

So total number of red counters are

red counters = 4x = 4*3 = 12

Answer:

[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]

Step-by-step explanation:

tan(sin⁻¹x + cos⁻¹y)

Use angle sum formula:

[tan(sin⁻¹x) + tan(cos⁻¹y)] / [1 − tan(sin⁻¹x) tan(cos⁻¹y)]

To evaluate these expressions, I suggest drawing right triangles.

For example, let's draw a triangle where x is the side opposite of angle θ, and the hypotenuse is 1.  Therefore:

sin θ = x/1

θ = sin⁻¹x

Using Pythagorean theorem, the adjacent side is √(1−x²).  Therefore:

tan θ = x / √(1−x²)

tan(sin⁻¹x) = x / √(1−x²)

Draw a new triangle.  This time we'll make y the adjacent side to angle θ.

cos θ = y/1

θ = cos⁻¹y

Using Pythagorean theorem, the opposite side is √(1−y²).  Therefore:

tan θ = √(1−y²) / y

tan(cos⁻¹y) = √(1−y²) / y

Substituting:

[x / √(1−x²) + √(1−y²) / y] / [1 − x / √(1−x²) × √(1−y²) / y]

Multiply top and bottom by √(1−x²).

[x + √(1−x²) √(1−y²) / y] / [√(1−x²) − x × √(1−y²) / y]

Multiply top and bottom by y.

[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]

Answer:

D. the slope of f(x) is greater than the slope of g(x)

Step-by-step explanation:

slope of f(x) =rise/run

=y2 -y1 / x2 -x1

slope of f(x)= -1-2/1-0= -3

g(x)= -5x-6

slope of g(x)= -5

-3>-5

D. the slope og f(x) is greater than the slope of g(x)

Step-by-step explanation:

squaring both side

(18√8-8√18)^2=(√n)^2

(18√8)^2+(8√18)^2-(2)(8√18)(18√8)=n

after solving it we will get

3744-3456=n

n=288

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

Explanation:

Simplify the first part of the left side

[tex]18\sqrt{8} = 18\sqrt{4*2}\\\\18\sqrt{8} = 18\sqrt{4}*\sqrt{2}\\\\18\sqrt{8} = 18*2*\sqrt{2}\\\\18\sqrt{8} = 36\sqrt{2}[/tex]

And do the same for the second part of the left side

[tex]8\sqrt{18} = 8\sqrt{9*2}\\\\8\sqrt{18} = 8\sqrt{9}*\sqrt{2}\\\\8\sqrt{18} = 8*3*\sqrt{2}\\\\8\sqrt{18} = 24\sqrt{2}[/tex]

For each simplification, you are trying to factor the stuff under the square root so that you pull out the largest perfect square factor possible.

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

The original equation [tex]18\sqrt{8}-8\sqrt{18} = \sqrt{n}[/tex] turns into [tex]36\sqrt{2}-24\sqrt{2} = \sqrt{n}[/tex]

We have the common factor of [tex]\sqrt{2}[/tex] so we can combine like terms on the left side ending up with [tex]12\sqrt{2}[/tex]

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

So,

[tex]18\sqrt{8}-8\sqrt{18} = \sqrt{n}\\\\36\sqrt{2}-24\sqrt{2} = \sqrt{n}\\\\12\sqrt{2} = \sqrt{n}\\\\\sqrt{n} = 12\sqrt{2}\\\\\left(\sqrt{n}\right)^2 = \left(12\sqrt{2}\right)^2\\\\n = 288[/tex]

Yes it is possible to express [tex]18\sqrt{8}-8\sqrt{18}[/tex] as multiples of the same square root. In this case, we can express the left hand side of the original equation as 12 multiples of [tex]\sqrt{2}[/tex]

Answer:

51 mph

Step-by-step explanation:

→ The first thing we need is a formula which links speed, distance and time so,

Speed = Distance ÷ Time

Speed = mph

Distance = metres/miles

Time = hours

→ Since we want to work out the average speed of the entire journey we need to first work out the total distance and total time. Using the first sentence of the paragraph, it says that the car travels at an average speed of 45 mph for 40 minutes, we can rearrange the formula to work out the distance so,

Speed = Distance ÷ Time

→ Rearrange to get distance as subject

Distance = Speed × Time

→ Substitute in the values

Distance = 45 × 40

→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60

40 ÷ 60 = 0.666666667

→ Substitute in the time value multiplied by the speed

Distance = 45 × 0.666666667 = 30

⇒ 30 metres/miles is overall distance for the first part of the journey

→ Now we have to work out the distance for the second part of the journey. State the distance formula.

Distance = Speed × Time

→ Substitute in the values into the distance formula

Distance = 60 × 25

→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60

25 ÷ 60 = 0.416666667

→ Substitute in the time value multiplied by the speed

Distance = 60 × 0.416666667 = 25

⇒ 25 metres/miles is overall distance for the second part of the journey

→ Now we have to add the distance of both the journeys together

25 + 30 = 55

→ Then we add the times of the journey together

40 minutes + 25 minutes = 65 minutes

→ Convert 65 minutes into hours

65 ÷ 60 = 1.08333 hours

→ Substitute both values into the speed = distance ÷ time formula

Speed = 55 ÷ 1.08333 = 50.76923077

→ The question says to round it to the nearest whole number so,

50.76923077 = 51 mph

Answer:

y=3/4 x+2

Step-by-step explanation:

y=mx+b

take two points from graph

(0,2) and (4,5)

find b when x=0 then y=b=2

find m : y2-y1/x2-x1=5-2/4-0

m=3/4

y=3/4 x +2

Answer:

The value of the car after two years is $14,100.025

Step-by-step explanation:

Here, we want to calculate the value of a car after its second year, given the depreciation percentage.

To get the value of the car year after year at the fixed percentage level, what we do is to set up an exponential equation;

V = I(1-r)^t

where V is the present value

I is the initial value = $25,000

r is the rate = 24.9% = 24.9/100 = 0.249

t is the number of years = 2 in this case

So we substitute these values in the depreciation case and have;

V = 25000(1-0.249)^2

V = 25000(0.751)^2

V = $14,100.025

Explanation:

Here is our take on the proof shown in the problem statement. The missing statements and reasons are shown in bold.

Statements  Reasons

1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given

2. AB ≅ AC and AY ≅ AX  2. definition of isosceles triangle

3. AB = AC and AY = AX  3. definition of congruency

4. AY • AC = AX • AC  4. multiplication property of equality

5. AY • AC = AX • AB  5. substitution property of equality

6. AY • AC/AX = AB  6. division property of equality

7. AC/AX = AB/AY  7. division property of equality

8. Corresponding sides are proportional  8. Definition of proportional

9. △ABC ~ △AYX  9. SAS similarity theorem

_____

The reason given in statements 6 and 7 suggest you need to divide something. For SAS similarity, you need to show corresponding sides are proportional. The missing steps are to get to the point where you can say that.

Answer:

I think its A. ∠A ≅ ∠A; reflexive property

Step-by-step explanation:

Answer:

The diameter is 91.

Step-by-step explanation:

The formula for circumference is 2*pi*radius(you can use circumference = diameter*pi too). Plug 285.74 into it. Divide both sides by 3.14, and you get 2*radius(aka the diameter) = 91

Answer:

91 yards

Step-by-step explanation:

The circumference of a circle can be found using the following formula:

c=π * d

We know that the circumference is 285.74 yards and we are using 3.14 for pi. Substitute 285.74 in for c and 3.14 for pi.

285.74= 3.14 *d

We want to find the diameter. Therefore, we need to get the variable d by itself. d is being multiplied by 3.14 The inverse of multiplication is division. Divide both sides of the equation by 3.14

285.74/3.14= 3.14*d/3.14

285.74/3.14=d

Divide

91=d

d= 91 yards

The diameter of the field is 91 yards.

Answer:

-11/9 is the slope

Step-by-step explanation:

Use the formula and u will find this is the answer, hope this helped!

Y2 - Y1 / X2 - X1

(-9 - 2) / (6 - (-3))

<!> Brainliest is appreciated!

Answer:

-11/9

Step-by-step explanation:

In order to find the slope from 2 points, use the following formula: [tex]m=\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]

Plug in each of the numbers into their corresponding areas. Basically, we are subtracting the y values together and dividing it with the difference of the x values:

[tex]\frac{-9-2}{6-(-3)}[/tex]

The negatives cancel out and become postive, so the denominator will then read to be 6+3:

[tex]\frac{-9-2}{6+3}[/tex]

[tex]-\frac{11}{9}[/tex]

Answer:

[tex]\boxed{x = \frac{21}{8} }[/tex]

Step-by-step explanation:

=> 8x-6 = 15

Adding 6 to both sides

=> 8x = 15+6

=> 8x = 21

Dividing both sides by 8

=> x = 21/8 (In its simplest form)

Answer:

B

Step-by-step explanation:

I can't really see the problem, however I believe B is the only one that shows an infinite number of solutions.

Answer:

B

Step-by-step explanation:

It is too blurry BTW but B is correct

Answer:

10\7

Step-by-step explanation:

7x-4=6

7x=6+4

7x=10

7x\7=10\7

x=10\7

Answer:-13/3

Step-by-step explanation:

Answer:

B. not found in a toy store

Step-by-step explanation:

Given:

T = the set of things found in a toy store.

V = the set of things that cost more than $50.

T∪V = the set of things that found in a toy store or cost more than $50.

T∩V = the set of things that found in a toy store and cost more than $50.

The set T′ is the complement of the set T and it consists of the  set of things that are not found in a toy store.

The correct option is B

Answer:

c.{(3,-2),(-4,7),(7,3),(4,8)}

The inverse relation of the set will be {(3, –2), (–4, 7), (7, 3), (4, 8)}. Then the correct option is C.

Let the function f is given as

y = m(x + a) + c

Then the inverse function of the function f will be given by the swapping of x with y and y with x.

The relation of the set is given below.

{(–2,3), (7,–4), (3,7), (8,4)}

For the inverse relation, the coordinate (a, b) will get swapped as (b, a).

Then the inverse relation of the set will be {(3,–2), (–4,7), (7,3), (4,8)}.

Then the correct option is C.

More about the inverse function is given below.

https://brainly.com/question/2541698

#SPJ5