Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation h = -8t 2 + 40t, where h represents the height of the ball above the ground and t represents the time in seconds. The maximum value achieved by the function is represented by the vertex. Use factoring to answer the following:

How many seconds does it take the ball to reach its highest point?

What ordered pair represents the highest point that the ball reaches as it travels through the air?

Hint: because parabolas are symmetric, the vertex of a parabola is halfway between the zeroes of the quadratic.

Area of a triangle

1/2×b×h

=1/2×120×95

=60×95

=5700

Answer

5700 ft.

Answer:

5700 ft

Step-by-step explanation:

Answer:

There are 2 sets of numbers that work...

x = 3, y = 5

and

x = 6, y = 2

Step-by-step explanation:

Let x be one number, and let y be the other number.  We have 2 equations...

x + y = 8    (two positive numbers have a sum of 8)

xy = y + 10   (their product is equal to the larger number plus 10)

solve the first equation for y, and substitute that into the second equation...

y = 8 - x

  x(8 - x) = 8 - x + 10

now solve for x...

  8x - x² = 18 - x  

This is a quadratic, so get everything to one side so it's equal to zero...

   -x² + 9x - 18 = 0   (add x and subtract 18 from both sides)

Now solve for x...

     x² - 9x + 18 = 0    (divide both sides by -1)

         (x - 6)(x - 3) = 0    (factor)

so

x - 6 =  0  becomes   x = 6    (add 6 to both sides)

and

x - 3 = 0  becomes x = 3      (add 3 to both sides

If x is 3, then y = 5     (3 + 5 is 8, and 3(5) = 5 + 10, both equations hold up)

If x is 6, then y = 2    (6 + 2 is 8, and 6(2) = 2 + 10, both equation hold up)

Answer:

17

Step-by-step explanation:

Since the number has only 2 factors it must be a prime number

A prime number has 2 factors 1 and itself

Since the difference between the factors is 16 then

17 - 1 = 16 and so the number is 17 with factors 1 and 17

Answer:

14.4

Step-by-step explanation:

AB / BC = AD/CD

AB/6.7 = 13.3 / 6.2

AB = 13.3 * 6.7 / 6.2

AB = 14.4

Answer:

The answer is 14.4 units.(option A)

Step-by-step explanation:

Angles BAC and CAD are equal.

We can solve this by using the proportional relation.

[tex]\frac{AB}{BC} =\frac{AD}{CD}[/tex]

Let AB be = x

So, [tex]\frac{x}{BC} =\frac{AD}{CD}[/tex]

[tex]\frac{x}{6.7} =\frac{13.3}{6.2}[/tex]

[tex]\frac{x}{6.7} =2.145[/tex]

[tex]x=6.7\times2.145[/tex] = 14.37 units

And rounding to nearest tenth, we get 14.4 units.

Answer:

66.67%

Step-by-step explanation:

If there is 1 US open tennis championship and 1 Wimbledon per year, there are a total of 9 US open and 9 wimbledon from 1988 to 1998. So in total there are 18 championships.

Steffi Graf won 5 US open and 7 Wimbledons = 12

Essentially we want to know, 12 is what percent of 18? We can solve this by:

[tex]\frac{12}{18}*100=66.67[/tex]

Hence, 66.67% won

Answer:

 x²  -x + 1   Quotient

Step-by-step explanation:

Given in the question,

the numerator = x^4 + x³ + 7x² - 6x + 8

the denominator = x² + 2x + 8

Dividing :

x^4+x^3+7x^2-6x+8  ("Dividend")

By :

 x2+2x+8    ("Divisor")

                                                                 x²  -x + 1                      Quotient

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

dividend          x² + 2x + 8     | x^4 +   x^3 +  7x² -6x + 8

divisor  *x²                                  x^4 + 2x^3 + 8x²

remainder                                                 -x³   - x²   -6x + 8

divisor  * -x1                                              -x³  -2x² . -8x  

remainder                                                           x²   +2x   +8

divisor  *1                                                            x²   +2x   +8

remainder                                                                          0

B)

(x²  -x + 1)   (x² + 2x + 8)    

= x^4 +   x^3 +  7x² -6x + 8

hence proved 

Answer:

i think it might be fact families

Step-by-step explanation:

this is because they use the 3 same #rrs

Answer: Inverse Operations

Step-by-step explanation:

Answer:

34°

Step-by-step explanation:

The angle made when a tangent and a radius intersect=90°

Therefore angle OQP =90°

The triangle made by the two radii is isosceles ( base angles are equal) hence angle POQ=180-2(62)

=56°

The right triangle  OPQ can hence be solved as follows

angle POQ=56°

angle OQP=90°

angle x=180-(56+90)=34° as all the interior angles of any triangle add up to 180°

Answer:

option (A)

central angle = 0.375 rad

Step-by-step explanation:

Given in the question,

radius of the circle = 8 inches

arc of the circle = 3 inches

To find,

measure of a central angle

Central angles are subtended by an arc between those two points.

Formula to use:

where r = radius

           s = arc length

           θ = angle in radians

Plug in the values in the equation

Answer:

.375 rad

Step-by-step explanation:

Using the equation w=v/r

w=3/8

w=.375

13 quarts of coffee

Answer:

13 quarts

Step-by-step explanation:

1 quart = 32 ounces

mug = 16 ounces = 1/2 quart

26 * 1/2 = 13

It would be answer choice (B) :D

Answer:

See below.

Step-by-step explanation:

Problem  A

I have no tool that will draw this easily but I can direct you to do it.

Problem B

The general formula for the number of  bricks in any pattern (n) is

4n + 1 where n is the pattern number. Try some values.

n =3  

4n + 1

4*3 + 2

13

n = 4 which is the one you just drew

4n + 1

4*4 + 1

16 + 1

17

n = 8

4n + 1

4*8 + 1

32 + 1

33

Problem C

4n + 1 = 49           Formula

4n -1 = 49 - 1         Subtract 1 from both sides

4n = 48                 Divide by 4

4n/4 = 48/4

n = 12                    Answer

Pattern 12 will have 49 bricks

Problem D

The general formula we have been using all along is the answer.

4n + 1

[tex]12 {g}^{2} + 4g - 1[/tex]

Answer:

[tex]12g^2 + 4g - 1[/tex]

Step-by-step explanation:

Hello!

We can add the two polynomials vertically.

The simplified form is  [tex]12g^2 + 4g - 1[/tex].

Answer:

[tex]\boxed{\bold{-5x+8}}[/tex]

Step-by-step explanation:

Combine Similar Elements: [tex]\bold{8x-11x=-3x}[/tex]

[tex]\bold{4\cdot \:2x-3x+6-5\cdot \:2x+2}[/tex]

Multiply: [tex]\bold{4\cdot \:2=8}[/tex]

[tex]\bold{8x-3x+6-10x+2}[/tex]

Group Like Terms

[tex]\bold{8x-3x-10x+6+2}[/tex]

Combine Similar Elements: [tex]\bold{8x-3x-10x=-5x}[/tex]

[tex]\bold{-5x+6+2}[/tex]

Add Numbers: [tex]\bold{6+2=8}[/tex]

[tex]\bold{-5x+8}[/tex]

To simplify the expression, combine like terms resulting in -1[tex]x^2[/tex] - 8x + 8.

To simplify the given algebraic expression, we need to combine like terms. The terms in the expression are: 4[tex]x^2[/tex], 8x, -11x, 6, -5[tex]x^2[/tex], and 2. Combining the [tex]x^2[/tex] terms and the x terms separately, we get:

[tex]4x^2 - 5x^2 = -1x^2[/tex]

8x - 11x - 5x = -8x

Finally, we add the constant terms: 6 + 2 = 8.

Putting it all together, the simplified version of the expression is: -1[tex]x^2[/tex] - 8x + 8.

The equation 4x + y = 7 can be rewritten in slope-intercept form as y = -4x + 7, where -4 is the slope and 7 is the y-intercept. This format makes it easier to graph the line as it directly gives us the slope and y-intercept.

To rewrite the equation 4x + y = 7 in slope-intercept form (y=mx+b), we need to solve for y. This equation can be transformed by subtracting 4x from both sides, resulting in y = -4x + 7. Here, -4 is the slope (m) and 7 is the y-intercept (b).

In comparison, if we look at the given graphic (Figure A1), we see another equation where the slope or 'm' is 3 and the y-intercept 'b' is 9. This slope and y-intercept gives us the equation y = 3x + 9. Thus, it can be seen that y = mx + b format helps to better understand the geometry of a linear equation on a graph, with 'm' indicating the slope and 'b' being the y-intercept.

https://brainly.com/question/29146348

#SPJ3

it would be 25.2 hope this helps

Answer:

X=7

Step-by-step explanation:

X = SQRT(49)

X = 7

Best regards

Answer: $175.50

Step-by-step explanation: Since you are given the formula, your next step is to put your information into it.

I = PRT

I = 450 x .13 x 3

Now to solve for it:

I = $175.50

Hey there!

52.08 ÷ 3 = 17.36

The correct answer is D

Hope this helps you!

God bless ❤️

xXxGolferGirlxXx

Answer:

h > 6000

Step-by-step explanation:

Let h be the height of the Cirrus clouds in the inequality.

h > 6000

This states that  h  is greater than  6000

it is neither, it cannot be raised to a power unless it is 0 or 1 :)

The function is neither an odd function nor an even function

The function is given as:

f(x)=2x^3-x^2

Calculate f(-x)

f(-x)= 2(-x)^3 - (-x)^2

f(-x)= -2x^3 - x^2

Calculate -f(x)

-f(x)= -2x^3 + x^2

From the above computation,

f(x), f(-x) and -f(x) are not equal

Hence, the function is neither an odd function nor an even function

Read more about functions at:

https://brainly.com/question/17059941

Answer: [tex]35\sqrt{x^2y}[/tex]

Step-by-step explanation:

To solve this exercise  you must apply the proccedure shown below:

- Apply multiplication, as following:

[tex]4(5\sqrt{x^2y})+3(5\sqrt{x^2y})=20\sqrt{x^2y}+15\sqrt{x^2y}[/tex]

- As you can see, the index of the radical in the first term is 2 and the index of the radical in the second term is also 2.

- You can observe that the radicands are the same.

- Therefoe, as the index of the first radical is equal to the index of the second radical and the radicands are the same, you can make the addition. Then, you obtain:

[tex]35\sqrt{x^2y}[/tex]

THE ANSWER IS C all the other people are wrong because they don’t even got the answer choices. 7(5sqrt ^2y)

Answer:

The answer is f = 24

Step-by-step explanation:

In order to find this, multiply both sides by 3/2

16 = 2/3f

24 = f

Final answer:

To rewrite 11/35 and 3/10 with a common denominator, find the LCD, which is 70 and it will result in 22/70 and 21/70.

Explanation:

To rewrite the fractions 11/35 and 3/10 so they have a common denominator, we need to find the Least Common Denominator (LCD) for both fractions. The denominators are 35 and 10. Prime factorizing 35, we get 5 and 7. Prime factorizing 10, we get 2 and 5.

The LCD for both will therefore be the product of these prime factors taken at the highest power that appears in each, which is 2 * 5 * 7 = 70. To rewrite the fractions, we multiply the numerator and the denominator of each fraction by any factors needed to reach the LCD.

For 11/35 to have 70 as its denominator, we observe that 35 already has the factor 7 and 5, hence it only needs to be multiplied by 2. So, 11/35 = 11 * 2 / 35 * 2 = 22/70.

For 3/10 to have 70 as its denominator, we see that 10 has the factor 2 and 5, so it needs to be multiplied by 7. Therefore, 3/10 = 3 * 7 / 10 * 7 = 21/70.

Now both fractions have the same denominator of 70, which is 22/70 and 21/70 respectively.

Answer:   A. (3,-2)

Step-by-step explanation:

Solve by Substitution :

// Solve equation [2] for the variable  x  

 [2]    4x = 5y + 22

 [2]    x = 5y/4 + 11/2

// Plug this in for variable  x  in equation [1]

  [1]    2•(5y/4+11/2) + 5y = -4

  [1]    15y/2 = -15

  [1]    15y = -30

// Solve equation [1] for the variable  y  

  [1]    15y = - 30  

  [1]   y = - 2  

// By now we know this much :

   x = 5y/4+11/2

   y = -2

// Use the  y  value to solve for  x  

   x = (5/4)(-2)+11/2 = 3  

Solution :

{x,y} = {3,-2}  

For Those of You With 10 Questions and Are on the Same Topic!

____________________________________________________

1. What is the apparent solution to the system of equations graphed above?

_______________________________________________________

2. A jet ski company charges a flat fee of $26.00 plus $3.25 per hour to rent a jet ski. Another company charges a fee of $24.00 plus $3.50 per hour to rent the same jet ski. Using a graphing calculator, find the number of hours for which the costs are the same. Round your answer to the nearest whole hour.

_______________________________________________________

3. Which graph best represents the solution to the following system?

[tex]\left \{ {{-3x+y < 1} \atop {-x+y\leq 2}} \right.[/tex]

_______________________________________________________

4. A local amusement park charges $21.50 per daily adult ticket and $14.75 per daily child's ticket. A group of 12 people paid $204.00 for tickets. Which system of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased.

_____________________________________________________

5. Which graph best represents the feasibility region for the system shown above?

[tex]\left \{ {{y\geq 2;x\leq 6} \atop {y\leq 3x+2;y\leq -x+10}} \right.[/tex]

____________________________________________________

6. (Graph Shown in Question) [tex]\left \{ {{x\leq 8;y\geq 0} \atop {y\leq 3x+2;y\leq -x+10}} \right.[/tex]

What is the minimum value for P = x - 2y over the feasibility region defined by the constraints shown above?

_______________________________________________________

7. A candy store makes a 13-pound mixture of gummy candy, jelly beans, and hard candy. The cost of gummy candy is $1.00 per pound, jelly beans cost $2.00 per pound, and hard candy costs $2.00 per pound. The mixture calls for three times as many gummy candy pieces as jelly beans. The total cost of the mixture is $20.00. How much of each ingredient did the store use?

______________________________________________________

8. How many solutions does the following system have?

[tex]\left \{ {{2x+3y=1} \atop {-3x-2y=-1}} \right.[/tex]

______________________________________________________

9. Which linear system of equations does the matrix represent?

[-3  5 | 15 ]

[ 2  3 | -10]

______________________________________________________

10. What is the solution to the above system of equations?

[tex]\left \{ {{2x+3y=-4} \atop {4x-5y=22}} \right.[/tex]

______________________________________________________

Should be 10/10. Also, good luck on Part 2 guys!

When x=0, that’s the y-intercept. So in this case the y-intercept would be (0,2)

Answer:

The length of side [tex]x[/tex] is 4.9 cm

Step-by-step explanation:

The first thing we need to do is find the third angle using the angle sum theorem.

The angle sum theorem states that the sum of the interior angles of a triangle is always 180°. A + B + C = 180°

Let's call our missing angle A, so

A + 41° + 62° = 180°

A + 103° = 180°

A = 180° - 103°

A = 77°

Now we can use the rule of sines to find side [tex]x[/tex]:

[tex]\frac{x}{sin(41)} =\frac{14}{sin(77)}[/tex]

[tex]x=\frac{14sin(41)}{sin(77)}[/tex]

[tex]x=9.4[/tex]

We can conclude that the correct answer is 9.4 cm

the answer is 11 trays

Answer:

[tex]\frac{13}{1}[/tex]

[tex]\frac{195}{15}[/tex]

[tex]\frac{130}{10}[/tex]

Step-by-step explanation:

we have the ratio

[tex]\frac{65}{5}[/tex]

step 1

Divide both sides (numerator and denominator) by 5

[tex]\frac{65/5}{5/5}=\frac{13}{1}[/tex]

therefore

[tex]\frac{13}{1}[/tex] is proportional to [tex]\frac{65}{5}[/tex]

step 2

Multiply both sides (numerator and denominator) by 3

[tex]\frac{65*3}{5*3}=\frac{195}{15}[/tex]

therefore

[tex]\frac{195}{15}[/tex] is proportional to [tex]\frac{65}{5}[/tex]

step 3

Multiply both sides (numerator and denominator) by 2

[tex]\frac{65*2}{5*2}=\frac{130}{10}[/tex]

therefore

[tex]\frac{130}{10}[/tex] is proportional to [tex]\frac{65}{5}[/tex]

Answer:

Please see attached graph for further understading of the solution.

To easily solve this problem, we can graph each of the functions and compare them to the original one.

g(x)= 2x-3

An horizontal compression implies a greater slope for the line. This means that the graph of f(x), must reach higher values faster.

Based on the image, the answer is option D