Philip shoots an arrow from the top of a hill into the ground. the flight of the arrow can be modeled with the quadratic function y=-5x^2+15x+90, where y represents the vertical height of the arrow, in meters, and x represents the time, in seconds. use factoring to find the positive zero of the function. what does this zero represent? then find the maximum value of the function by completing the square. what does the maximum value represent? explain each step in your answer.

Answer:

<40/41,9/41>

Step-by-step explanation:

According to Algebra Lab, "To find a unit vector with the same direction as a given vector, we divide by the magnitude of the vector."

Magnitude of <40, 9> is 41

Divide that by the vector is

<40/41,9/41>

Answer:

p = 3y

Step-by-step explanation:

Compare like terms in both expressions, that is

- 7p = - 21y ( divide both sides by - 7 )

p = 3y

and as a check

p² = (3y)² = 9y²

The value of p is in terms of y as p = 3y

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Given that if 9y²-21y + 8 is written as p²-7p + 8

⇒ 9y²- 21y + 8 = p²-7p + 8

Comparing similar terms in the two expressions, that is

⇒ - 7p = - 21y

Divide both sides by - 7

⇒ p = 3y

And p² = (3y)²

⇒ p² = (3y)²

⇒ p² = 9y²

⇒ p = 3y

Hence, the value of p is in terms of y as p = 3y

Learn more about the equation here:

brainly.com/question/10413253

#SPJ6

Answer:

There is 5 numbers (not including the sum/25)

The average is add up all the numbers and divide by amount of numbers

25/5=5

The average value is 5

Step-by-step explanation:

Answer:

B y = − 3 ( x + 1 ) ^2 + 8

Step-by-step explanation:

Hope it helps.

We have been given that in triangle RST, angle S is marked as a right angle. Side RT is labeled as 40 centimeters. Side ST is labeled as 30 centimeters. We are asked to find the measure of angle R.

First of all, we will draw a right triangle using our given information as shown in the attachment.    

We can see that RT is hypotenuse and St is opposite side to angle R. We know that sine relates opposite side to hypotenuse of right triangle.

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{sin}(\angle R)=\frac{ST}{RT}[/tex]

[tex]\text{sin}(\angle R)=\frac{30}{40}[/tex]

[tex]\text{sin}(\angle R)=\frac{3}{4}[/tex]

Now, we will use arcsin to solve for angle R as:

[tex]\angle R=\text{sin}^{-1}(\frac{3}{4})[/tex]

[tex]\angle R=48.59037789[/tex]

Upon rounding to nearest hundredth, we will get:

[tex]\angle R\approx 48.59[/tex]

Therefore, the measure of angle R is approximately 48.59 degrees.

Answer:

48.59

Step-by-step explanation:

Just took the test!!

Answer:

20%

Step-by-step explanation:

If you want to buy the car again, it means that they are satisfied. 700/3500=7/35=1/5

1/5=20%.

20% of the people were satisfied.

I think this is the answer + working out

x= Tori's age

y= her grandmother's age

x+y=72

5x=y

5x-y=0

x+y=72

+(5x-y=0)

6x=72

72 divided by 6=

x=12

So Tori is 12...

We substitute 12 for x into the first equation...

12+y=72

Bring 12 to the other side

y=72-12

y=60

Her grandmother is 60 and Tori is 12.

Answer: StartFraction n Over 4 EndFraction minus 9 + 3

n/4-9 +3

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given.

The quotient of a number means the result of the division of 2 numbers.

In this case the numbers are: a number (n) and 4 . n/4

Nine less than that quotient means we have to subtract 9 to the quotient.

n/4-9

Increase by three: we simply have to add 3

n/4-9 +3

Feel free to ask for more if needed or if you did not understand something.

Answer:

n/4-9 +3

Step-by-step explanation:

2020-2021 edge

Answer:

we choose f(x) = π cos(πx)

Step-by-step explanation:

Given the information:

Let analyse all possible answers;

1/ f(x) = -2 sec(x)

when x= 0 we have: f(0) = -2 sec(0) = -2[tex]\frac{1}{cos(o)}[/tex] = -2 wrong

2. f(x) = 7sin(x/4 - 1/29)

when x= 0 we have: f(0) =7sin(0/4 - 1/29) = 7sin(-1/29) = -0.00421 wrong

3. (x) = π cos(πx)

when x= 0 we have: f(0) = πcos(π0) = cos(0) = π0 = 0

when x= 2 we have: f(2) = πcos(π2) = πcos(0) = π

True

4. f(x) = 2π cos(x - π/2)

when x= 0 we have: f(0) = 2π cos(0 - π/2) = 2π cos(-π/2) = 0

when x= 2 we have: f(2) =2π cos(2 - π/2) = 2π0.034 = 0.0697π Wrong

So we choose f(x) = π cos(πx)

Answer:

1,5/5=279,3

Step-by-step explanation:

Answer:

225% increase

Step-by-step explanation:

Since the number went up from 24 to 78 this is an increase

To find out how much

(78- 24)/24 =2.25 * 100% =225% increase

The percent of change from 24 songs to 78 songs is a 225% increase.

To identify the percent of change from 24 songs to 78 songs, follow these steps:

Therefore, the percent of change from 24 songs to 78 songs is a 225% increase.

Answer:

3293 ft to nearest tenth = side

Step-by-step explanation:

To find altitude this is the same in trigonometry as finding the side and we use calculation below in finding the hypotenuse which is same term as side for the angle of depression just to double check that height (altitude is less than slope in calculation).

sin (32) = 0.9271838546

3600/0.9271838546 = 3882.725074

= 3883 ft to nearest tenth. = slope

Then cos (32)x3882.725074 = 3292.737608

= 3293 ft to nearest tenth = side

The plane flying with an angle of depression of 32 degrees to a small fire below has an altitude of 2250 ft.

The situation forms a right angle triangle.

A right angle triangle has one of its angles as 90 degrees. The sides can be found using trigonometric ratios.

Therefore, the horizontal distance from the kurt's plane to the fire is the adjacent side of the right triangle.

The altitude of the plane is the opposite side of the triangle.

Hence,

tan 32 = opposite / adjacent

tan 32° = h / 3600

cross multiply

h = 3600 tan 32°

h = 3600 × 0.6248693519

h = 2249.52966687

h = 2250 ft

Therefore, the approximate altitude of the plane is 2250 ft.

learn more on right triangle here: https://brainly.com/question/27403620

Answer:

9cm3

Step-by-step explanation:

6 x 4 x 3/8=9cm3

Answer:

9 cm³

Step-by-step explanation:

V = l x w x h

= 6 x 4 x 3/8

= 24 x 3/8

= 9 cm³

Answer:

-2034

Step-by-step explanation:

make me brainliest please

Answer:

Each friend gets 0.45 cups of ice cream.

Step-by-step explanation:

Divide 3.6 by 8 and you get 0.45.

the answer is 24in its easy

Answer:

Rational

Step-by-step explanation:

2.2360679.  A rational number is a number that terminate or can be written as a fraction.  In this case, the number can be written as 22,360,679/10,000,000.  

The number 2.2360679 is a rational number because it can be expressed as the fraction 22360679/10000000. Rational numbers can be written as fractions with integer numerators and denominators (where the denominator is not zero) or terminates.

The number 2.2360679 is a rational number. A rational number can be expressed as a fraction, where both numerator and denominator are integers and the denominator is not zero. In this case, 2.2360679 can be written as an approximate fraction rounded to seven decimal places: 22360679/10000000.

On the other hand, an irrational number cannot be expressed as an integer fraction. It continues indefinitely without repeating, such as the number pi. Therefore, 2.2360679 is not an irrational number as it doesn't meet this criterion.

Learn more about Rational here:

https://brainly.com/question/33462926

#SPJ3

Answer:

5 power 2 is the answer

Step-by-step explanation:

Answer:

c

or

P (0.25 less-than-or-equal-to z less-than-or-equal-to 1.25)

Step-by-step explanation:

Answer:

x

y

−

2

2

−

1

0.5

0

0

1

0.5

2

2

Step-by-step explanation:

Answer:

If the value of x increases by 1, the value of y will double.

Step-by-step explanation:

i just took the thingy

Step-by-step explanation:

[tex]300 = 3 \times {10}^{2} \\ 47300 = 4.73 \times {10}^{4} \\ 24 = 2.4 \times {10}^{1} \\ 14565 = 1.4565 \times {10}^{4} \\ 7001 = 7.001 \times {10}^{3} \\ 19050000 = 1.905 \times {10}^{7} \\ [/tex]

Answer:

26% of people from city B work less than 20 hours

Answer:

26%

Step-by-step explanation:

Look at the row for city B, first column is for "less than 20"

Answer:

╱▔▔▔▔▔▔▔▔▔▔▔▏  

┈╱╭▏╮╭┻┻╮╭┻┻╮╭▏  

▕╮╰▏╯┃╭╮┃┃╭╮┃╰▏  

▕╯┈▏┈┗┻┻┛┗┻┻┻╮▏  

▕╭╮▏╮┈┈┈┈┏━━━╯▏

▕╰╯▏╯╰┳┳┳┳┳┳╯╭▏  

▕┈╭▏╭╮┃┗┛┗┛┃┈╰▏  

▕┈╰▏╰╯╰━━━━╯┈┈▏

Step-by-step explanation:

Answer:

10

1 + 100 = 101

101 is between 10 and 11

10.04987

Step-by-step explanation:

Answer:

a) 1/32 = 0.0313

b) 21.2058 cm

c) 19.635 ft2

Step-by-step explanation:

We have a total of 8 different areas in the circle.

a) The yellow area are 2 parts of a total of 8, so the probability is 2/8 = 1/4

The number 4 is one area of a total of 8, so the probability is 1/8

So the probability of landing on a yellow and then a 4 is (1/4)*(1/8) = 1/32 = 0.0313

b) The blue area is 3 parts over 8, so we can solve this using rule of three:

Total circunference -> pi*d = 18pi cm

3/8 of the circunference -> x

x = (3/8) * 18pi = 21.2058 cm

c) The purple sections are 2 parts over 8, so following the same logic as letter b), we have:

Total area -> pi*r^2 = 25pi ft2

2/8 of the area -> x

x = (2/8) * 25pi = 19.635 ft2

Answer: 12

               ^

Answer is |

Answer:

8

Step-by-step explanation:

The side opposite the right angle is called the hypotenuse (13), which is always the longer side.

Both of the smaller sides (5 and the third side) add up to the hypotenuse, in this case they both add up to 13.

You would have to take 5 away from 13 to find the answer.

13 - 5 = 8

Answer:

(2, 3 )

Step-by-step explanation:

Given the 2 equations

3x - 5y = - 9 → (1)

x + 2y = 8 → (2)

Multiplying (2) by - 3 and adding to (1) will eliminate the x- term, that is

- 3x - 6y = - 24 → (3)

Add (1) and (3) term by term to eliminate x

(3x - 3x) + (- 5y - 6y) = (- 9 - 24), that is

- 11y = - 33 ( divide both sides by - 11 )

y = 3

Substitute y = 3 into either of the 2 equations and solve for x

Substituting in (2)

x + 2(3) = 8

x + 6 = 8 ( subtract 6 from both sides )

x = 2

Solution is (2, 3 )

Answer:

Step-by-step explanation:

hello :

here is an solution :

Final answer:

To find two consecutive odd integers where the sum of the smaller integer and twice the larger is 43, we use the equation n + 2(n + 2) = 43, which simplifies to n = 13, identifying the smaller integer as 13.

Explanation:

The student is asking for an equation to solve for two consecutive odd integers such that when the smaller is added to twice the larger, their sum is equal to 43. Let's define the smaller integer as n, and since they are consecutive odd integers, the next integer would be n + 2. The equation that represents this situation is:

n + 2(n + 2) = 43

This equation can be simplified:

n + 2n + 4 = 43

Combining like terms, we get:

3n + 4 = 43

To solve for n, subtract 4 from both sides:

3n = 39

Then, divide by 3:

n = 13

Therefore, the smaller integer is 13.

Answer:

x = 2 and x = -2

Step-by-step explanation:

The quadratic formula of a quadratic of the form ax² + bx + c is:

x = [tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] or x = [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

Here, our equation is: 3x² - 18 = -6. Let's move all the terms to one side:

3x² - 12 = 0

a = 3 and c = -12. Notice that since there's no x term, b = 0.

Plug these into the quadratic formula:

x = [tex]\frac{0+\sqrt{0^2-4*3*(-12)} }{2*3}=\frac{\sqrt{144} }{6}=12/6=2[/tex]  

or

x = [tex]\frac{0-\sqrt{0^2-4*3*(-12)} }{2*3}=\frac{-\sqrt{144} }{6}=-12/6=-2[/tex]

So, x = 2 and x = -2.

Answer: x = -2, x = 2

Step-by-step explanation:

The quadratic formula:

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a} \\\\AND\\\\x = \frac{-b-\sqrt{b^2-4ac} }{2a} \\[/tex]

You can find the variables a, b, and c in the standard form of a quadratic equation:

[tex]f(x)=ax^2 + bx+c[/tex]

Your equation:

[tex]f(x)=3x^2 + 0x -12[/tex]

The variables are:

a = 3

b = 0

c = -12

Substitute those for the variables in the quadratic formula:

[tex]x=\frac{-0+\sqrt{0-(4*3*-12)}}{2(3)} \\\\AND\\\\x=\frac{-0-\sqrt{0-(4*3*-12)}}{2(3)} \\[/tex]

You can simplify this to get:

[tex]x=\frac{-\sqrt{144}}{6} \\[/tex]

(or positive square root of 144.)

The square root of 144 is 12, and 12/6 = 2.

The x-values are -2 and 2.