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The function H(t) = −16t2 + 48t + 12 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 10 + 15.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds. Part A: Create a table using integers 0 through 3 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points) Part B: Explain what the solution from Part A means in the context of the problem. (4 points)

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Given two functions: h(t)=-16t^2+48t+12 and g(t)=10+15.2t
A] The table of both functions from 0 to 3 will be:
h(t)=-16t^2+48t+12
t           0           1            2          3
h(t)       12         44          44        12

g(t)=10+15.2t

t          0        1            2             3
g(t)     10      25.2       40.4        55.6

the point in which h(t)=g(t) will be given by:
-16t^2+48t+12=10+15.2t
forming quadratic equation we get:
-16t^2+32.8t+12=0
solving the above quadratic equation using the formula we get:
t=-0.32 or t=2.4
therefore we conclude that they only met once, at point t=2.4 sec
therefore they met between points t=-0.32 and t=2.4

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The sum of two consecutive even integers is 234. what is the larger integer?

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The sum of two consecutive even integers is 234. what is the larger integer?

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The sum of 4 consecutive integers is 130. what is the third number in the sequence?

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Answer:

The third number in the sequence 31, 32, 33, 34 is 33

Step-by-step explanation:

let first number be the smallest number be x.

Consecutive numbers are those numbers that follow each other in order and they should have a difference of 1 between every two numbers.

Then, the four consecutive integers are x , (x+1), (x+2) , (x+3)

Given: the sum of 4 consecutive integers is 130.

From the given condition we have,

x+(x+1)+(x+2)+(x+3)=130

Like terms states that contain the same variables raised to the same power.

Combine like terms we get,

4x+6=130

Subtract 6 from both the sides, we get

4x+6-6=130-6

Simplify we get,

4x=124

Divide both sides by 4;  frac{4x}{4}= frac{124}{4}

On simplify we get, the value of x i.e, x=31

the sequence we have, 31, 32, 33, 34,

therefore, the third number in the sequence is, 33.

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The ages of Edna,Ellie,and Elsa are consecutive integers. The sum of their ages is 120. What are their ages?

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The ages of Edna,Ellie,and Elsa are consecutive integers. The sum of their ages is 120. What are their ages?

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Find three consecutive integers such twice the greatest integer is 2 less than 3 times the least integer

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127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to
120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:
n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.
You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

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Two consecutive even integers have a sum of 346. Find the smailler of these two numbers

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Two consecutive even integers have a sum of 346. Find the smailler of these two numbers

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A number is chosen at random from the first twenty integers. Find the probability that the number is a multiple of 3. 3/10 3/5 6

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127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to
120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:
n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.
You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

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The sum of three consecutive positive integers is a perfect cube. find the least possible value of the smallest number, assuming that the middle number ends in at least 5 zeros.

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127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to
120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:
n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.
You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

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Find two consecutive integers such that their product is 11 more than 2 times their sum

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127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to
120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:
n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.
You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

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The sum of four consecutive integers are 198. What’s the fourth number in this sequence?

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Answer:

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

So, AD=AB=44.8 cm

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC=  x+y=84.8 …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z

H^2=P^2+B^2

(44.8)^2=x^2+z^2  ………[2]

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z

H^2=P^2+B^2

(72)^2=y^2+z^2 …………[3]

Subtract [2] and [3]

(72)^2-(44.8)^2=y^2+z^2-x^2-z^2

5184-2007.04=(x+y)(x-y)

3176.96=(84.8)(x-y)

37.464=x-y ……….[4]

Add equation [1] and [4], to get values of x and y

x+y+x-y=84.8+37.464

2x=122.264

x=61.132

Substitute x in [1]

x+y=84.8

61.132+y=84.8

y=23.668

Substitute value of x in equation [2], to get z

(44.8)^2=x^2+z^2

(44.8)^2=(23.668)^2+z^2

2007.04-560.174224=z^2

z=sqrt{1446.865776}

z=38.06

We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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The sum of 5 consecutive integers is 265. What is the fifth number in this sequence?

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Answer:

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

So, AD=AB=44.8 cm

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC=  x+y=84.8 …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z

H^2=P^2+B^2

(44.8)^2=x^2+z^2  ………[2]

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z

H^2=P^2+B^2

(72)^2=y^2+z^2 …………[3]

Subtract [2] and [3]

(72)^2-(44.8)^2=y^2+z^2-x^2-z^2

5184-2007.04=(x+y)(x-y)

3176.96=(84.8)(x-y)

37.464=x-y ……….[4]

Add equation [1] and [4], to get values of x and y

x+y+x-y=84.8+37.464

2x=122.264

x=61.132

Substitute x in [1]

x+y=84.8

61.132+y=84.8

y=23.668

Substitute value of x in equation [2], to get z

(44.8)^2=x^2+z^2

(44.8)^2=(23.668)^2+z^2

2007.04-560.174224=z^2

z=sqrt{1446.865776}

z=38.06

We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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How many positive integers satisfy 127=7 (mod n)? n=1 is allowed.

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Answer:

3 positive real root and 1 negative real root and no complex root.

Step-by-step explanation:

Here, the given function,

f(x) = -3x^4 + 5x^3 - x^2 + 8x + 4

Since, the coefficient of variables are,

-3,   5,    -1,    8,    4,

The sign of variables goes from Negative(-3) to positive (5) , positive(5) to negative(-1) and negative (-1) to positive (8),

So, the total changes in sign = 3,

By the Descartes’s rule of sign,

Hence, the number of real positive roots = 3,

Also,

f(-x) = -3x^4 - 5x^3 - x^2 - 8x + 4

Since, the coefficient of variables are,

-3,   -5,   -1,    -8,   4

The sign of varibles goes to negative (-8) to positive (4),

So, the total changes in sign = 1,

Hence, the number of real negative roots = 1,

Now, the degree of the function f(x) is 4,

Thus, the highest number of roots of f(x) is 4,

So, it does not have any complex root.

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PLEASE HELP!! {The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those intergerscan have?}

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Number of cans donated the first week = 132
Number of cans donated the second week = 146
Number of cans donated the third week = c, where c is some positive number

Add up the three values (132, 146, and c) to get 132+146+c. I’m choosing not to simplify because each answer choice hasn’t simplified either.

The expression of 132+146+c represents the total amount of cans donated for weeks 1 through 3. We want “at least 325 cans”, so that means the expression is 325 or larger. That translates to this inequality

132+146+c ge 325

The “greater than or equal to” sign indicates we want that sum to be 325 or larger.

Now we solve for c

132+146+c ge 325
278+c ge 325
278+c-278 ge 325-278
c ge 47

So the amount of cans donated for week three needs to be 47 or larger. If you collect exactly 47 cans for week three, then you meet the goal of 325 total cans. If you collect more than 47 cans for week three, then you exceed the goal of 325 total cans.

————————————

In summary we have the inequality 
132+146+c ge 325
which solves to
c ge 47

Meaning that the answer is choice D

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Without actually calculating the logarithm, determine what two integers the value of log(1.37×109) falls between.

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Sample Response: To determine the degree of the product of the given trinomials, you would multiply the term with the highest degree of each trinomial together. Both trinomials are degree 2, and when you multiply x2 by x2, you add the exponents to get x4. Thus, the degree of the product is 4. If the product is degree 4, and there is only one variable, the maximum number of terms is 5. There can be an x4 term, an x3 term, an x2 term, an x term, and a constant term.

What did you include in your response? Check all that apply.

The degree of the product of the trinomials is 4 because the degree of each trinomial is 2.

The maximum number of terms in the product of the trinomials is 5.

There can be an x4 term, an x3 term, an x2 term, an x term, and a constant term.

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The sum of three consecutive even integers is 90. Find the three even integers?

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The sum of three consecutive even integers is 90. Find the three even integers?

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Two consecutive positive integers have a product of 600. What is the smaller of the two numbers?

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Two consecutive positive integers have a product of 600. What is the smaller of the two numbers?

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The sum of two consecutive even integers is 234. What is the larger integer? A. 114 B. 116 C. 118 D. 124

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Answer:  First option is correct.

Step-by-step explanation:

Since we have given that

If two sides of a triangle are not equal,

According to Relationship between the angle and side , we know that the angle opposite the shortest side is the larger angle,

And,

The angle opposite the longest side is the shortest angle

So, First option is correct.

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Of these integers, -65, -42, 65, and 90, which two are farthest apart on the number line? A) -65 and -42 B) -65 and 65 C) -65 and 90 D) -42 and 65

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Posted in Mathematics

C) negative sixty-five and ninety


Related Questions

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Solve linear equation

The opposite of subtraction is addition, so I’ll undo the –3 by adding 3 to both sides, and then adding down: Then the solution is x = –2. You can use the Mathway widget below to practice solving a linear equation by adding or subtracting. Try the entered exercise, or type in your own exercise.

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Write 98/12 as a mixed number in simplest form

98/12 as a mixed number in simplest form is 8 1/6
To find simplest form you can divide the numerator by the denominator of the fraction. When I divided 98 by 12 I got 8.16666667. Move the decimal point twice to the right and take away the 8 for now so that you can form a new number. Now divide 100 by 16.666667. This would be 5.99999988 on a calculator. You can round your answer up to 6. Since 16.666667 is around 1/6 of 100 you can use that fraction in your answer. When we add 8 and 1/6 we should get 8 1/6.
There is a way to check if we have the right fraction.
Multiply your whole number by the denominator of the fraction and then add the numerator to the product. Finally put your remaining sum over the denominator. 8 x 6 = 48 + 1 = 49
49/6 = 98/12

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What is 65% as a decimal?

Answer: 0.65

Step-by-step explanation: To write a percent as a decimal, first remember that a percent is a ratio that compares a number to 100. We can think of 65% as the ratio 82 to 100 or 82 divided by 100. Remember that dividing by 100 moves the decimal point 2 places to the left.

65% → .65 or 0.65

Therefore, 65% can be written as the decimal 0.65.

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