What catapulted object hit the ground first?

Catapult A:
h(x)= -16x^2+64x+17

Catapult B:
time- 0,0.5,1.0,1.5,2.0,2.5,3.0,3.5
height- 28,48,60,64,60,48,28,0

Answers:

Object from Catapult B

They reached the ground at the same time

Object from catapult A

It went up but then never came down

Answer:

About 6400

Step-by-step explanation:

Round all values: 316 --> 320, 4.03 --> 4, 0.198 --> 0.2

Expression: 320*4/0.2

Multiply: 320*4 = 1280, 1280/0.2

Divide: 2180/0.2 = 6400

316 times 4.03 equals 1273.48 then divide the product by 0.198 and you should get 6431.71717 and could round to 6432. sorry if this is wrong but have a wonderful day

±1/2. The equation [tex]4x^{2} =1[/tex] has two possible solutions +1/2 and -1/2.

The problem is a quadratic equations and it can be solved using the equation [tex]x=-b±\frac{\sqrt{b^{2} -4ac} }{2a}[/tex].

Ordering the quadratic equation given in the problem, we obtain [tex]4x^{2} -1=0[/tex] where a = 4, b = 0, and c = -1

Substituting the values

[tex]x=±\frac{\sqrt{-4(4)(-1)} }{2(4)}=±\frac{\sqrt{16}}{8} =±\frac{4}{8} \\x=±\frac{1}{2}[/tex]

The answer is:

The correct option is the second option,

[tex]4x^{2}=+-\frac{1}{2}[/tex]

We are given the expression:

[tex]4x^{2}[/tex]

Now, solving we have:

Applying square root to both sides of the equation in order to isolate x:

[tex]4x^{2}=1\\\\\sqrt{4x^{2} } =+-\sqrt{1}\\\\2x=+-1\\\\x=+-\frac{1}{2}[/tex]

Hence, the correct option is the second option,

[tex]4x^{2}=+-\frac{1}{2}[/tex]

Have a nice day!

Answer:

FE = 14.4

Step-by-step explanation:

Cos = Adj / Hypo.

So

Cos (F) = FE / DF

Cos (26) = FE / 16

FE = Cos (26) * 16

FE = 0.8988 * 16

FE = 14.4

18.3.................

Answer:

1st pic: Answer is 3

2nd pic: Answer is 5

3rd pic: Answer 4

Step-by-step explanation:

Final result :

 (x + 5) • (x + 4)

 ———————

         2        

Step by step solution :

Step  1  :

           x2 - 16

Simplify   ———————

           2x + 6

Step  2  :

Pulling out like terms :

2.1     Pull out like factors :

  2x + 6  =   2 • (x + 3)

Trying to factor as a Difference of Squares :

2.2      Factoring:  x2 - 16

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 16 is the square of 4

Check :  x2  is the square of  x1

Factorization is :       (x + 4)  •  (x - 4)

Polynomial Long Division :

2.3    Polynomial Long Division

Dividing :  x + 4

                             ("Dividend")

By         :    x + 3    ("Divisor")

dividend     x  +  4

- divisor  * x0     x  +  3

remainder         1

Quotient :  1  

Remainder :  1  

Equation at the end of step  2  :

 (((x2)+8x)+15) (x+4)•(x-4)

 ——————————————•———————————

     (x-4)        2•(x+3)  

Step  3  :

           x2 + 8x + 15

Simplify   ————————————

              x - 4    

Trying to factor by splitting the middle term

3.1     Factoring  x2 + 8x + 15

The first term is,  x2  its coefficient is  1 .

The middle term is,  +8x  its coefficient is  8 .

The last term, "the constant", is  +15

Step-1 : Multiply the coefficient of the first term by the constant   1 • 15 = 15

Step-2 : Find two factors of  15  whose sum equals the coefficient of the middle term, which is   8 .

     -15    +    -1    =    -16

     -5    +    -3    =    -8

     -3    +    -5    =    -8

     -1    +    -15    =    -16

     1    +    15    =    16

     3    +    5    =    8    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  3  and  5

                    x2 + 3x + 5x + 15

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x+3)

             Add up the last 2 terms, pulling out common factors :

                   5 • (x+3)

Step-5 : Add up the four terms of step 4 :

                   (x+5)  •  (x+3)

            Which is the desired factorization

Equation at the end of step  3  :

 (x + 5) • (x + 3)   (x + 4) • (x - 4)

 ————————————————— • —————————————————

       x - 4            2 • (x + 3)  

Step  4  :

Canceling Out :

4.1    Cancel out  (x+3)  which appears on both sides of the fraction line.

Canceling Out :

4.2    Cancel out  (x-4)  which appears on both sides of the fraction line.

Final result :

 (x + 5) • (x + 4)

 ——————---

         2        

Answer:

[tex]cos(C) =\frac{40}{41}\\\\cos(C)=0.976[/tex]

Step-by-step explanation:

To find the [tex]cos (C)[/tex] we must use the cosine theorem.

The cosine theorem says that:

[tex]c^2 = a^2 +b^2 -2abcos(C)[/tex]

In this case:

[tex]c=AB = 9[/tex]

[tex]b=CA = 41[/tex]

[tex]a=BC = 40[/tex]

So

[tex]9^2 = 40^2 +41^2 -2(40)*(41)cos(C)[/tex]

[tex]9^2- 40^2- 41^2 =-2(40)*(41)cos(C)[/tex]

[tex]cos(C) = -\frac{9^2- 40^2- 41^2}{2(40)*(41)}[/tex]

[tex]cos(C) =\frac{40}{41}\\\\cos(C)=0.976[/tex]

Answer:

C I got this question right on my test that I just finished.

Step-by-step explanation:

Also I just wanted to say that I am praying for all those with the virus and we are all in this together #WorldUnited :):):):)

For this case we have the following equation:

[tex]\frac {1} {4} (8-4p) + 2p = 12[/tex]

We apply distributive property to the terms within parentheses.

[tex]\frac {8} {4} - \frac {4p} {4} + 2p = 12\\2-p + 2p = 12\\2 + p = 12[/tex]

Subtracting 2 on both sides of the equation:

[tex]p = 12-2\\p = 10[/tex]

ANswer:

[tex]p = 10[/tex]

Answer:

p = 10

Step-by-step explanation:

1\4(8 - 4p) + 2p = 12

8 - 4p/4 + 2p = 12

8 - 4p + 8p/4 = 12

8 + 4p = 12 × 4

4p = 48 - 8

4p = 40

p = 40/4

p = 10

Thus, the value of p is 10

Final answer:

To find the number of sliders and chicken wings in the combination meal, set up a system of equations and solve. There are 2 sliders and 10 chicken wings in the combination meal.

Explanation:

In order to find the number of sliders and chicken wings in the combination meal, we can set up a system of equations. Let's assume that the number of sliders is 's' and the number of chicken wings is 'c'. We know that each slider has 250 calories and each chicken wing has 60 calories. The total number of sliders and chicken wings in the combination meal is 12, so we have the equation s + c = 12.

We also know that the total number of calories in the combination meal is 1100. Since each slider has 250 calories and each chicken wing has 60 calories, we can write the equation 250s + 60c = 1100.

Now we can solve this system of equations to find the values of 's' and 'c'.

Multiplying the first equation by 60, we get 60s + 60c = 720. Subtracting this equation from the second equation, we get 250s - 60s = 1100 - 720, which simplifies to 190s = 380. Dividing both sides by 190, we find that s = 2.

Substituting this value back into the first equation, we have 2 + c = 12. Solving for 'c', we find that c = 10.

Therefore, there are 2 sliders and 10 chicken wings in the combination meal.

Answer:

Step-by-step explanation:

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Njxjdh

Ndjdjjf

Mjd

490x9 this is because he traveled 490 miles everyday for 9 days

+1292 then he travels an extra 1292 miles so you add it on

The answers are:

- The quantity that represents the initial number of bacteria is 64.

- The quantity that represents the rate at which the number of bacteria is increasing is (1+0.12) or 1.12 which means the growth rate percentage for the bacteria is 0.12 or (0.12*100), it will be 12%.

To solve the problem, and complete the statements, we need to remember the form of the exponential growth.

The exponential growth formula is given by the following formula:

[tex]P(t)=StartAmount(1+PercentageRate)^{t}[/tex]

Where,

Start Amount, is the starting population or amount.

(1+Percentage Rate), is the increasing rate

Percentage Rate, is the growth rate percentage.

t, is the time elapsed.

Now, we are given the following expression:

[tex]P(3)=64(1.12)^{3}[/tex]

Which can be rewrited as:

[tex]P(3)=64(1+0.12)^{3}[/tex]

So, we have that:

- The quantity that represents the initial number of bacteria is 64.

- The quantity that represents the rate at which the number of bacteria is increasing is (1+0.12) or 1.12 which means the growth rate percentage for the bacteria is 0.12 or (0.12*100), it will be 12%.

Have a nice day!

Answer:

b

Step-by-step explanation:

Answer:

The distance between the center and the foci is √13 ≅ 3.6 units

Step-by-step explanation:

* Lets revise the equation of the ellipse

- The standard form of the equation of an ellipse with center

  (0 ,  0) and major axis parallel to the x-axis is

x²/a² + y²/b² = 1

# a  >  b

- The length of the major axis is 2a

- The coordinates of the vertices are  (± a , 0)

- The length of the minor axis is 2b

- The coordinates of the co-vertices are (0 , ± b)

- The coordinates of the foci are  (± c , 0), where c² =  a² −  b²

* Lets solve the problem

∵ The equation is x²/49 + y²/36 = 1

∴ a² = 49

∴ b² = 36

∵ The coordinates of the foci are (± c  , 0)

∵  c² = a² − b²

∴ c² = 49 - 36 = 13 ⇒ take square root for both sides

∴ c = ± √13

∴ The foci are (√13 , 0) and (-√13 , 0)

∵ The center is (0 , 0)

∴ The distance between the center and the foci is c - 0 = c or

   0 - (-c) = c

∴ The distance between the center and the foci = √13 - 0 = √13 units

* The distance between the center and the foci is √13 ≅ 3.6 units

The distance of the foci from the center of the ellipse given by the equation [tex]x^{2/49} + y^{2/36}[/tex] = 1 is approximately 3.61 units.

To find the distance of the foci from the center of the ellipse given by the equation  [tex]x^{2/49} + y^{2/36}[/tex] = 1, we use the formula for the focal distance in an ellipse: c = √(a² - b²).

Here, a² is the larger denominator, which is 49, and b² is the smaller denominator, which is 36. Therefore:

Now, calculate the focal distance:

c = √(a² - b²) = √(49 - 36) = √(13) ≈ 3.61

Thus, the foci are approximately 3.61 units away from the center of the ellipse.

Answer:

answer is B...2 1/2

Step-by-step explanation:

4(t+1)=6t-1

4t+4=6t -1

4t-6t+4=6t-6t-1

-2t+4=-1

-2t+4-4=-1-4

-2t=-5

Divide by -2 for -2t and -5

-2t/-2=-5/-2

t=5/2= 2 1/2

Answer is b) 2 1/2

the correct answer is b.33

Answer:

b

Step-by-step explanation:

Answer:

171 sq units.

Step-by-step explanation:

Since you don't specify you want a the side surface area only, we'll calculate both.

First, the base...

We have a square with a side of 9 units.

Area of the base is then 9 x 9 = 81 sq units.

For the sides, we have 4 triangles with a base of 9 and a height of 5 units.

The area of a triangle is calculated with A = (b * h)/2

So, each of the sides of the pyramid has an area of:

A = (9 * 5) / 2 = 22.5 sq units

There are four sides, so total lateral area: 4 * 22.5 = 90 sq units.

Total area: 81 + 90 = 171 sq units.

Answer:

5.5360

Step-by-step explanation:

I added

5+0.5= 5.5

5.5+0.03=5.53

5.53+0.006=

5.5360

Here, the given equation is,

x^2+y^2+px+6y-3=0

By copairing it with x^2+y^2+2gx+2fy+c=0, we get,

2g=p or, g=p/2

2f=6 or, f=3

c=-3

now the radius is,

r^2=g^2+f^2-c

or, 4^2=(p/2)^2 +3^2 -(-3)

or, 16= p^2/4 +9+3

or, 16-9-3=p^2/4

or p^2/4=4

or, p^2=4×4

or p^2=4^2

or p=4

therefore the rewuired value of p is 4.

Answer:

Possible values are 4 and -4.

Step-by-step explanation:

First complete the square on the x and y terms:

x^2 + y^2 + px + 6y - 3 = 0

(x + 0.5p)^2 - 0.25p^2 + (y + 3)^2 - 9 - 3 = 0

(x + 0.5p)^2 + (y + 3)^2 = 12 + 0.25p^2

This is the standard form of the equation of the circle where the right side = radius^2 so we can write:

12 + 0.25p^2 = 4^2

0.25p^2 = 16 - 12 = 4

Taking square roots:-

0.5p = +/- 2

p = 2 / 0.5 , -2 / 0.5

p = 4, -4.

Answer:

To calculate the mean, simply add all of your numbers together. Next, divide the sum by however many numbers you added. The result is your mean or average score.

Step-by-step explanation:

This is the correct answer to this question.

Hope this helps!!!

Kyle.

Answer:

I'm guessing you mean Statistics so here is the best answer i can find The branch of mathematics that deals with the collection, organization, analysis, and interpretation of numerical data. Statistics is especially useful in drawing general conclusions about a set of data from a sample of the data.

Step-by-step explanation:

Answer:

x=5, Now you just have to insert x into the equation for DG

Step-by-step explanation:

2x+4=4x-6

-2x     -2x

 4=2x-6

+6     +6

 10=2x

÷2   ÷2

5=x

The correct option is C.

Carlos can make 4 different burgers by choosing between beef or turkey and wheat or white roll.

To calculate the number of different burgers Carlos can make, we'll use the fundamental principle of counting.

Step 1: Determine the number of options for the type of burger. Carlos can choose either beef or turkey, so there are 2 options.

Step 2: Determine the number of options for the type of roll. Carlos can choose either wheat or white, so there are 2 options.

Step 3: Multiply the number of options for each step together to find the total number of combinations.

Number of burger options × Number of roll options = Total combinations

2 options for type of burger × 2 options for type of roll = 4 total combinations

So, Carlos can make 4 different burgers.

Answer: C. 4

The complete question is here:

Carlos can choose from a beef or turkey burger and from a wheat or a white roll. How many different burgers can he make?

A. 8

B. 3

C. 4

D. 2

Answer:

always increasing

Step-by-step explanation:

When you look at the graph from left to right on the x-axis the y-axis is always increasing in value.

The graph in question is a line graph, used to show correlations between two variables on a horizontal and vertical axis. Other graph types include bar graphs, for comparing different categories of data, and pie charts, for representing parts of a whole. The third exam vs final exam graph demonstrates a good model of linearity with little deviation.

The description best fitting the graph in this instance is that of a line graph. Line graphs are used to show the correlation between two variables, one on the horizontal axis and one on the vertical axis. They are most appropriate when trying to communicate trends, such as increases, decreases, or consistency over a period of time.

Another type of graph is a bar graph, which is most effective when comparing different categories of data. For example, comparing the amount of rainfall each month can be appropriately represented using a bar graph. Finally, a pie chart displays proportional relationships in the data and is best used when representing parts of a whole, such as voters' preferences in an election.

Referring back to the graph about the third and final exams, it could be said that the line of best fit models the data well, where there appears to be little deviation from the line. By analyzing the graphs carefully, it is possible to draw meaningful conclusions and compare data accurately.

https://brainly.com/question/32550800

#SPJ3

the sum of all interior angles in a polygon is

180(n - 2)

n = number of sides in the polygon

this polygon has 5 sides, so is a PENTAgon, so the sum of all its sides is

180(5 - 2) => 180(3) =>  540

so then

[tex]\bf 90+148+(3x+10)+(x)+112=540\implies 360+4x=540 \\\\\\ 4x=180\implies x=\cfrac{180}{4}\implies x=45[/tex]

Answer:

L=10 cm

Step-by-step explanation:

Surface area of cube = 600

6L^2=600

L^2=600/6

L^2=100

L=

[tex] \sqrt{100} [/tex]

L=10 cm

Answer:

Step-by-step explanation:

If you're given a line, determine its slope.

Any parallel line you construct must have the same slope as does the given line.

Any perpendicular line you construct must have a slope which is the negative reciprocal of the slope of the given line.

Parallel lines have the same slope.

And perpendicular lines have negative reciprocal slopes. Ex. 2/3 x and -3/2x

Answer:

C; 117,147

Step-by-step explanation:

Its 3(n-1)

Just multiply the first term by 3, 12 times.

Answer: 177,147

Step-by-step explanation: this is because a1 is 1 then a2 is 3 then a3 is 9 then a4 is 27 and so on. This means that you start at 3 to the 0th power and multiply 3 as you go on

Answer:

28.26

Step-by-step explanation:

π r² = A

A = (3.14) (3²)

A = 3.14 · 9 = 28.26

Hello There!

WHAT WE KNOW

Pi = 3.14

R = 3

HOW TO SOLVE

A = 3.14*9

Answer 28.26

Answer: A) Measurement Data

Step-by-step explanation:

you're recording time

Answer:

$3.66

Step-by-step explanation:

5 minus 1.34 equals 3.66.

You just have to subtract the bill and the change like this: 5-1.34= 3.66$

Answer:

the answer is a. y=2x+4

Answer: A y = 2x + 4

for USATestprep

Answer:

The answer is 525

Answer:

Option B. 525 students.

Step-by-step explanation:

The school enrollment for Oakwood Elementary is shown in the graph.

The given graph is representing a linear function. So we will form the function first to calculate the enrollment in 2012.

Equation of the given line in the graph will be in the form of y = mx + c

where m is the slope and c = y- intercept

y-intercept = 300

this line passes through two ordered pairs (0, 300) and (1, 325)

Now the slope m = [tex]\frac{y-y'}{x-x'}[/tex]

m = [tex]\frac{325-300}{1-0}=25[/tex]

Therefore, equation representing the situation will be y = 25x + 300

Now we will put the value of x = year 2012 - year 2003 = 9 years

y = 25×9 + 300

y = 225 + 300

y = 525

Option B. 525 is the correct option.