The height H of a skydiver t seconds after jumping. Let T be the independent variable, and assume the skydiver jumps from a height of 12,500 feet and lands after 300 seconds of flight

Answer:

360

Step-by-step explanation:

f varies directly as g

f = kg  where k is the constant of variation

f varies inversely as h

f = kg/h

We know g = 198 when  h = –11 and f = –6.  Substituting in

-6 = k*198/(-11)

-6 =k*(-18)

Dividing each side by -18

-6/-18 = k*-18/-18

1/3 =k

Our equation is

f = 1/3 g/h

Letting  f = 12 and h = 10

12 = 1/3 g/10

Multiply each side by 10

12*10 =1/3 g/10*10

120 = 1/3 g

Multiply each side by 3

120*3 =1/3 g *3

360 =g

Answer:

5(1248 lb/horse + t lb) ≤ 8000 lb

Step-by-step explanation:

One way to do this is to find the average weight of the 5 horses:

It is:

6,240 lb

---------------- = 1248 lb/horse

  5 horses

and to this, for each horse, we must add t lbs tack.

Thus, 5(1248 lb/horse + t lb) ≤ 8000 lb

would be an appropriate inequality.

Please note that your question mentions "the following inequalities;" that means you are expected to share them!  Please do so next time.  Thanks.

Answer:

Addition of two vectors Will make an resultant vector or a third vectors

Step-by-step explanation:

When two vectors represents in both magnitude and direction as two sides of triangle then resultant will represent as both as third side of triangle but in opposite order

Answer:

x=35

Step-by-step explanation:

The angles are alternate interior angles.  Alternate interior angles are equal if the lines are parallel.

3x+16 = 5x-54

Subtract 3x from each side

3x -3x+16 = 5x-3x-54

16 = 2x-54

Add 54 to each side

16+54 = 2x-54+54

70 = 2x

Divide each side by 2

70/2 = 2x/2

35 =x

After distributing the -1, you will find

y+7= -x-6

Finally, isolate y to find your answer in the linear form of

y= -x-13

3 hours equals 195.

5 hours equals 325

9 hours equals 585

10 hours equals 650

To find this I multiplied the hours by 65 pages.

Hope this helps :)

Answer:30

Step-by-step explanation: V=1/3 Bh, 9x10=90 divide that by 3 for 30

The volume of a triangular pyramid that is 10 inches tall and has a base area of 9 square inches is 30 cubics in.

Take a triangle. This is a base.

Now take 3 triangles such that each of them is connected to the one-one side of the first triangle and when they're taken together, they form a closed object, called a triangular pyramid.

The volume of a triangular pyramid that is 10 inches tall and has a base area of 9 square inches

The volume of a triangular pyramid

V = 1/3 x B x h,

V = 1/3 x 9 x 10

V = 3 x 10

V = 30

Hence, the volume will be 30 cubics in.

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Answer:

Step-by-step explanation:

Answer:

The correct answer option is B. [tex]1[/tex], [tex]\frac{1}{2}[/tex], [tex]\frac{1}{4}[/tex].

Step-by-step explanation:

We are given the following geometric sequence and we are to find its 8th term:

[tex]16, 8, 4, 2,...[/tex]  

Here [tex]a_1=16[/tex] and common ratio [tex](r) = \frac{2}{4}=0.5[/tex].

The formula we will use to find the next three terms is:  

nth term = [tex]a_1 \times r^{(n-1)}[/tex]  

5th term = [tex]16 \times 0.5^{(5-1)} = 1[/tex]

6th term = [tex]16 \times 0.5^{(6-1)}[/tex] = [tex]\frac{1}{2}[/tex]

7th term = [tex]16 \times 0.5^{(7-1)}[/tex] = [tex]\frac{1}{4}[/tex]

14+38=52

52-38= 14

Answer: 38 and 14.

I think this is the answer.

33 and 19

33+19=52

33-19=14

Answer:

10 pairs of earrings and 5 necklaces (the maximum profit will be $250)

Step-by-step explanation:

Let x be the number of earrings and y be the number of necklaces Lisa makes.

1.  Lisa only has enough materials to make 15 total jewelry items per week, then

[tex]x+y\le 15.[/tex]

2.  It takes half an hour to make a pair of earrings, so it takes her [tex]\dfrac{1}{2}x[/tex] hours to make x earrings. It takes her 1 hour to make a necklace, so it takes her y hours to make y necklaces. Lisa only has 10 hours a week to make jewelry, thus

[tex]\dfrac{x}{2}+y\le 10[/tex]

3. Lisa makes a profit of $15 on each pair of earrings and $20 on each necklace. In total her profit is

[tex]P=15x+20y.[/tex]

You have to find the maximum value of the function [tex]P=15x+20y[/tex] with respect to inequalities

[tex]x+y\le 15\\ \\\dfrac{x}{2}+y\le 10[/tex]

Draw the solution set on the coordinate plane (see attached diagram). The maximum value of the efunction P is at point (10,5) and is

[tex]P=15\cdot 10+20\cdot 5=150+100=\$250[/tex]

Answer:48 red marbles

Step-by-step explanation:

144÷24= 6

6*5= 30 white

6*11= 66 black

6*8= 48 red

Answer:  The number of red marbles in the jar is 48.

Step-by-step explanation:  Given that the number of white, black and red marbles in a jar are in the ratio 5 : 11 : 18. And the total number of marbles in the jar is 144.

We are to find the number of red marbles in the jar.

Let, 5x, 11x and 8x be the number of white, black and red marbles in the jar.

Then, according to the given information, we have

[tex]5x+11x+8x=144\\\\\Rightarrow 24x=144\\\\\Rightarrow x=6.[/tex]

Therefore, the number of red marbles will be

[tex]8x=8\times6=48.[/tex]

Thus, there are 48 red marbles in the jar.

Answer:

70/9

Step-by-step explanation:

multiply the parenthesis

add the constant together then divide

Answer:

70 / 9

Step-by-step explanation:

9(X - 9) = -11

9X - 81 = -11

      9X = -11 + 81

      9X = 70

        X = 70 / 9

Answer:

C) 50,653

Step-by-step explanation:

y = 1000(3.7)^x

After 3 hours   x=3

y = 1000(3.7)^3

y = 1000(50.653)

y =50653

Answer: OPTION C

Step-by-step explanation:

You know that in the function [tex]y = 1000(3.7^x)[/tex] the variable "y" is the number of bacterias in a petri dish  and the variable "x" is the number of hours.

Then, to answer the question "How many bacteria will there be after 3 hours?", you need to substitute [tex]x=3[/tex] into the function.

Therefore, the number of baterias after 3 hours will be:

[tex]y = 1000(3.7^3)[/tex]

[tex]y = 1000(50.653)[/tex]

[tex]y = 50,653[/tex]

This matches with the option C.

Answer:

A

Step-by-step explanation:

If the corresponding parts of the triangles are congruent then the triangles are congruent.

Here there are 2 corresponding congruent angles, that is 51° and 80°

The non- included corresponding sides are congruent both 10

Then by AAS postulate the triangles are congruent- True

Answer:

True

Step-by-step explanation:

A pex

Answer:

C. (5, -2)

Step-by-step explanation:

Midpoint:

x = (x1+x2)/2 = (16-6)/2 = 10/2 = 5

y = (y1+y2)/2 = (5 - 9)/2 = -4/2 = -2

Answer

Midpoint (5, -2)

The midpoint of the graphed line segment is (5, -2)

The correct option is C) (5, -2).

The midpoint formula is expressed as;

Midpoint = ( ( x₁+x₂ )/2, ( y₁+y₂ )/2 )

From the graph:

Point 1 (16, 5)

x₁ = 16

y₁ = 5

Point 2 (-6,-9)

x₂ = -6

y₂ = -9

Plug the coordinates into the above formula and solve for the midpoint:

Midpoint = ( ( x₁+x₂ )/2, ( y₁+y₂ )/2 )

Midpoint = ( ( 16+(-6) )/2, ( 5+(-9) )/2 )

Midpoint = ( ( 16 - 6 )/2, ( 5 - 9 )/2 )

Midpoint = ( 10/2, -4/2 )

Midpoint = ( 5, -2 )

Therefore, the midpoint is (5, -2).

Option C) (5, -2) is the correct answer.

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Answer:

Yes

Step-by-step explanation:

Try the points and see:

(x, y) = (-1, 3) . . . . x + y = -1 + 3 = 2 . . . . yes

(x, y) = (3, -1) . . . . x + y = 3 + (-1) = 2 . . . yes

The remaining points lie on the line connecting these points, so they, too will be on the graph of that line.

Answer:

3.6 hours

Step-by-step explanation:

Blake can do work in hours = 9

Blake can do a part of work in 1 hour = [tex]\frac{1}{9}[/tex]

Ned can paint the same room in six hours.

Ned can do a part of work in 1 hour = [tex]\frac{1}{6}[/tex]

They can do a part of work together in 1 hour =  [tex]\frac{1}{9}+\frac{1}{6}[/tex]

                                                                           =  [tex]\frac{5}{18}[/tex]  

Now they can do [tex]\frac{5}{18}[/tex]  part of work in hour = 1

So, they can do whole work in hours =  [tex]\frac{1}{\frac{5}{18}}[/tex]

                                                             =  [tex]3.6[/tex]

Hence it will take 3.6 hours to paint the room if they work together.

Answer:

1) 45 minutes or 0.75 hours

2) 45 minutes or 0.75 hours

Step-by-step explanation:

We are given the graph that shows Miriam's bike ride.

The x-axis represents the time (in minutes) and the y-axis represents the distance traveled in miles.

1) How many hours did Miriam stop to rest?

The graphs stays the same from 45 minutes to 90 minutes, where he took the rest. No distance covered in that time.

Rest time = 90 minutes - 45 minutes = 45 minutes

He took rest for 45 minutes.

In hours, it is 45/60 = 0.75 hours

2) How many hours did it take Miriam to bike the initial 8 miles.

Look at the graph, the graph reached 8 miles when the time was 45 minutes.

It took 45 minutest to reach 8 miles initially.

In hours, it is 45/60 = 0.75 hours

Answer: Second Option

{x| x< -3 ∪ x > 3}

Step-by-step explanation:

To solve the inequality

[tex]| x | >3[/tex] there are two cases:

Case 1.   [tex]x>0[/tex]

[tex]x > 3[/tex]

Case2. [tex]x<0[/tex]

[tex]-x > 3[/tex]

[tex]x < -3[/tex]

The final solution is the union of the solution of each case

This is:

[tex]x < -3[/tex] or [tex]x > 3[/tex]

{x| x< -3 ∪ x > 3}

The solution is X=0.4

The answer is the first one

Answer:

The cost of one pack of paper was $0.90 and the cost of one box of pens was $2.00

Step-by-step explanation:

Let

x----> the cost of one pack of paper

y---> the cost of one box of pens

we know that

10x+12y=33 ----> equation A

15x+7y=27.50 ---> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (0.9,2)

see the attached figure

Therefore

The cost of one pack of paper was $0.90

The cost of one box of pens was $2.00

Answer:

pens = $2

paper = .9

Step-by-step explanation:

p = price of a pack of paper

n =  price of a box of pens

10p + 12n = 33

15p + 7n = 27.50

Multiply the first equation by 3

3(10p + 12n )= 33*3

30p +36n = 99

Multiply the second equation by -2

-2(15p + 7n) = 27.50*-2

-30p -14n = -55

Add the 2 modified equations together

30p +36n = 99

-30p -14n = -55

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

    22n = 44

Divide each side by 22

22n/22 = 44/22

n =2

Each box of pens is $2

Now we can find the price of the paper

10p + 12n = 33

10p +12(2) = 33

10p +24 =33

Subtract 24 from each side

10p+24-24=33-24

10p = 9

Divide by 10

10p/10 =9/10

p = .9

The rate of change of the function can be determined by finding the slope of the function at different points in the table.

The rate of change of a function can be determined by finding the slope of the function at different points. In this case, we can use the values provided in the table to find the rate of change. The rate of change is equal to the difference in the y-values divided by the difference in the x-values.

Let's take the first two points in the table as an example. The first point is (12/5, 5) and the second point is (5, 25/2). The difference in the y-values is 25/2 - 5 = 15/2, and the difference in the x-values is 5 - 12/5 = 23/5. Therefore, the rate of change is (15/2) / (23/5) = 15/2 * 5/23 = 75/46. So, the rate of change of the function for these two points is 75/46.

[tex] \sqrt{0.81} = (0.9)[/tex]

Answer:

the correct answer is .9

.9 times .9 is .81

blackpink dun dunna dun dun dun dunna

I would say option A best proves it is a parallelogram.

Answer:

The equation [tex]y=x^2+1[/tex] will be a parabola when it is graphed

Answer:

It's a parabola

Step-by-step explanation:

The equation seems to a parabolic function. The parabola is defined as:

[tex]y=Ax^2+b[/tex]

where b is a displacement, we can notice that in our case A=1 and b=1

so it is a parabola with a vertical displacement of one unit.

The answer is 96 you’re welcome

For this case we must simplify the following expression:

[tex](3 ^ {-2}) ^ 4[/tex]

By definition of power properties we have to:[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

So, rewriting the expression we have:

[tex](\frac {1} {3 ^ 2}) ^ 4 = \frac {1 ^ 4} {(3 ^ 2) ^ 4} = \frac {1} {(3 ^ 2) ^ 4}[/tex]

By definition of power properties we have:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So:

[tex]\frac {1} {(3 ^ 2) ^ 4} = \frac {1} {3 ^ 8}[/tex]

Answer:

Option D

Final answer:

The Ishango bone, found in the Congo with scratches believed to represent counting, shows evidence of prehistoric mathematical activity 20,000 years ago. It suggests early numerical understanding and supports the theory that Stone Age humans engaged in proto-mathematics.

Explanation:

The Ishango bone is a significant archaeological find believed by many archaeologists to be evidence of prehistoric mathematical activity. Found 20,000 years ago in what is now the Democratic Republic of Congo, the bone has a series of noticeable scratches that many scholars interpret as a form of counting. The precise nature of these markings is still the subject of debate, but the prevailing theory is that they were used for arithmetic operations, such as keeping track of numbers or simple calculations.

The archaeological context of the Ishango bone, being from the Stone Age, highlights the early presence of numerical comprehension, which could suggest that the humans of that era had some sense of numbers and possibly even a form of proto-mathematics. This idea is reinforced not just by the Ishango bone, but also by the evidence from various archaeological sites across Africa, where other mathematical tools and representations, such as carved stones with depictions of animal figures, which date back tens of thousands of years, have been found.

The discovery of the Ishango bone adds to a growing body of evidence that early humans had the ability to count and perform simple mathematical operations long before the establishment of formal systems of writing or the development of modern number systems. Such artifacts are invaluable for understanding the cognitive abilities of our early ancestors and the origins of mathematical practices.

ANSWER

1. No solution

2. 4 and 6

3. 81

EXPLANATION

1. The given quadratic equation is

[tex] {x}^{2} + 1 = 0[/tex]

This implies that:

[tex] {x}^{2} = - 1[/tex]

There is no real number whose square is negative one.

This quadratic equation has no solution.

2. The given quadratic equation is

[tex] {x}^{2} - 10x + 24 = 0[/tex]

We split the middle term with -6,-4 because their product is 24 and their sum is -10

[tex]{x}^{2} - 6x - 4x+ 24 = 0[/tex]

We factor by grouping

[tex]{x}(x - 6)- 4(x - 6)= 0[/tex]

[tex](x - 6)(x - 4)= 0[/tex]

We have x=4 and x=6.

3. The given quadratic equation is

[tex] {x}^{2} - 18x = 7[/tex]

We the square of half the coefficient of x to both sides of the equation.

[tex]( - \frac{18}{2} )^{2} = ( { - 9)}^{2} = 81[/tex]

The correct choice is C.