The height y of a jumping frog can be modeled by y = -16x^2+ 4x, where x is the time in
seconds) since the frog jumped from the ground. Find the roots of the equation when y = 0
Explain what the roots mean in this situation.

Step-by-step explanation:

We find,

[tex](x+2y)^7[/tex]

To find, the binomial expansion of of [tex](x+2y)^7[/tex] = ?

We know that,

[tex](x+y)^{n} =^nC_0x^n+^nC_1x^{n-1}y+nC_2x^{n-2}y^2+nC_3x^{n-3}y^3+...+^nC_ny^n[/tex]

∴ [tex](x+2y)^7[/tex]

Here, n = 7, x = x and y = 2y

[tex](x+2y)^7[/tex]= [tex]^7C_0x^7+^7C_1x^{7-1}(2y)+^7C_2x^{7-2}(2y)^2+^7C_3x^{7-3}(2y)^3+^7C_4x^{7-4}(2y)^4+^7C_5x^{7-5}(2y)^5+^7C_6x(2y)^6+(2y)^7[/tex][tex]=x^7+7x^{6(2y)+21x^{5}4y^2+35x^{4}8y^3+^35x^{3}16y^4+21x^{2}32y^5+7x64y^6+128y^7[/tex]

[tex]=x^7+14x^{6}y+84x^{5}y^2+280x^{4}y^3+560x^{3}y^4+672x^{2}y^5+448xy^6+128y^7[/tex]

∴ The binomial expansion of of [tex](x+2y)^7[/tex]

[tex]=x^7+14x^{6}y+84x^{5}y^2+280x^{4}y^3+560x^{3}y^4+672x^{2}y^5+448xy^6+128y^7[/tex]

Thus, the required "option 4)"  is correct.

Answer:

D. x7 + 14x6y + 84x5y2 + 280x4y3 + 560x3y4 + 672x2y5 + 448xy6 + 128y7

Step-by-step explanation:

Without knowing the function itself, it's impossible to definitively say which of the values (-6,-2,4,7) is an output. Any of these numbers could potentially be an output depending on the function.

In the context of this question, an output of a function refers to the result you get after substituting an input (or value from the domain) into the function. For example, if we have a function f(x) = x+2, and we input the value 3 (from our domain), our output (or range) will be 5. Unless we know the actual function, it's difficult to determine which of the listed values (-6,-2,4,7) is an output because any of these could potentially be an output depending on the function. Thus, without additional context, the statement 'Which value is an output of the function?' cannot be definitively answered.

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The output of a function is -6.

The output of a function is the value that the function produces when a certain input is given. In the table above, the function is f(x). We are given that x can be any of the values -6, -2, 4, or 7. We want to know which of the values -6, -2, 4, 7, or 12 is an output of the function.

To find out, we can look at the table. We see that the only value in the table that is an output of the function is -6. This is because when we plug in x = -6 into the function, we get f(x) = -6.

Therefore, the answer is -6.

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Answer:

Scalene triangle

Step-by-step explanation:

It is a scalene triangle because none of the sides are equal .equilateral triangle have the three sides equal. isosceles triangle have only two equal sides

Answer:

YES

Step-by-step explanation:

Answer:

49.5

Step-by-step explanation: 11x9=99/2

Hey there!

First off, I’m going to assume that the 2 in the second term is an exponent. If it isn’t, let me know and I’ll fix the answer.

Anyways, let’s start by plugging the values for the variables into the equation.

36(3)-8(-6)^2

Square -6

108-8(36)

Multiply.

108-288

Subtract.

-180

Your answer is -180.

Hope this helps!

Answer:

One triangle

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Verify the length sides of triangle

Applying the triangle inequality theorem

1) 3+5 > 6 ---> is true

2) 3+6 > 5 ---> is true

3) 5+6> 3----> is true

therefore

One triangle can be drawn with the given lengths

With side lengths of 3 inches, 5 inches, and 6 inches, only one triangle can be drawn as these dimensions meet the triangle inequality theorem, allowing for the creation of one unique triangle.

The question is about determining if a triangle can be constructed with given side lengths. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the third side. In this case, the side lengths are 3 inches, 5 inches, and 6 inches.

Adding the lengths of the two shorter sides, 3 inches + 5 inches = 8 inches, which is greater than the length of the longest side, 6 inches. This means a triangle with these side lengths can be drawn. However, it is important to note that the lengths provided can only create one unique triangle, since the lengths are fixed and there can't be another triangle with different angles with the same side lengths.

Therefore, with side lengths of 3 inches, 5 inches, and 6 inches, exactly one triangle can be drawn.

Answer:

E

Step-by-step explanation:

Given the system of two equations:

[tex]\left\{\begin{array}{l}\dfrac{2}{3}x-\dfrac{1}{2}y=1\\ \\-\dfrac{4}{3}x+y=-3\end{array}\right.[/tex]

Multiply the first equation by 6 and the second equation by 3 to eliminate fractions:

[tex]\left\{\begin{array}{l}4}x-3y=6\\ \\-4x+3y=-9\end{array}\right.[/tex]

Add these two equations:

[tex]4x-3y-4x+3y=6-9\\ \\0=-3[/tex]

You get false equality [tex](0\neq -9)[/tex], so the system of two equations has no solution (two equations represent parallel lines)

Answer:

2108

Step-by-step explanation:

Divide 67,456 by 32, using long division.

1) How many times 32 go into 67? (2 times, with a remainder of 3)

2) Bring down the 4.

3) How many times does 32 go into 34? (1 time, with a remainder of 2)

4) Bring down the 5

5) How many times does 32 go into 25? (0 times, so write 0)

6) Bring down the 6.

7) How many times does 32 go into 256? ( 8 times, no remainder)

8) Your answer is 2108

Answer: 8%

Step-by-step explanation: 370 * 8% = 29.60

Answer: 8% sales tax rate

Step-by-step explanation:

First, you need to find what percentage 29.60 is from 370, so you divide 29.60 by 370 and you get 0.08 then you multiply that by 100 to get your answer in percent. 100 multiplied by 0.08 would be 8%.

Answer:

18.19

Step-by-step explanation:

$20-15%=$17

$17+7%=18.19

Lin's father pays $18.19 for the meal after the 15% discount and 7% sales tax.

To find out what Lin's father pays for the meal after the discount and sales tax, we need to follow these steps:

Let's apply these steps to the given information:

Step 1: Discount amount = $20 x 15% = $3

Step 2: Discounted price = $20 - $3 = $17

Step 3: Sales tax amount = $17 x 7% = $1.19

Step 4: Total amount paid = $17 + $1.19 = $18.19

Therefore, Lin's father pays $18.19 for the meal after the discount and sales tax.

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Answer:

Step-by-step explanation:

Since 8^2+15^2 = 289 and 17^2 = 289 then 8^2+15^2 = 17^2

8^2+15^2 = 17^2 Then according to the reciprocal of the Pythagorean theorem

it’s a right triangle

Answer: 19 and 31

Step-by-step explanation: Make the first number x, the second number y.

The sum of x and y is 50: x+y=50

x is 43 less than 2y: x=2y-43

replace x in equation x+y=50 with x=2y-43: 2y-43+y=50

combine like terms: 3y-43=50

add 43 to both sides: 3y=93

divide both sides by 3: y=31

replace y in equation x+y=50 with y=31: x+31=50

subtract 43 31 from both sides: x=19

the solution to the question is the first number is 19, the second number is 31

The two numbers that sum up to 50 with one being 43 less than twice the other, we set up a system of equations, solve for one variable, and then substitute it back into the other equation, resulting in the numbers 19 and 31.

The question asks us to find two numbers whose sum is 50 and where the first number is 43 less than twice the second number. To solve this, we can create a system of equations to represent the given conditions. Let the first number be x and the second number be y.

According to the question, the sum of the two numbers is 50, which gives us our first equation:

x + y = 50 (Equation 1)

The first number x is 43 less than twice the second number y. This provides the second equation:

x = 2y - 43 (Equation 2)

We now have a simple system of two linear equations:

x + y = 50

x = 2y - 43

We can substitute the second equation into the first to solve for y:

(2y - 43) + y = 50

3y - 43 = 50

Add 43 to both sides:

3y = 93

Divide both sides by 3:

y = 31

We can now substitute y = 31 back into Equation 2 to find x:

x = 2(31) - 43

x = 62 - 43

x = 19

Therefore, the two numbers are 19 and 31.

[tex]y = 48.28(1.06)^t[/tex] is the model giving the annual price p (in dollars) of a ticket t in years after 2000 is found

Solution:

Given that,

In 2000, the average price of a football ticket for a Minnesota Vikings game was $48.28

During the next 20 years, the price increased an average of 6% each year

The increasing function is given by:

[tex]y = a(1+r)^t[/tex]

Where,

y is the value after t years

t is the number of years

a is the initial value

r is rate of increase in decimal

From given,

a = 48.28

[tex]r = 6 \% = \frac{6}{100} = 0.06[/tex]

Substituting the values we get,

[tex]y = 48.28(1+0.06)^t\\\\y = 48.28(1.06)^t[/tex]

Thus the model giving the annual price p (in dollars) of a ticket t in years after 2000 is found

Answer:

A, D, E

Step-by-step explanation:

Answer:

[tex]y=3x[/tex]

Step-by-step explanation:

Let

x ----> the number of kids in a group

y ----> the total number of caramel chews Erica gives to that group

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

Find the value of the constant of proportionality k

take a ordered pair from the data in the table and determine the value of k

For x=2, y=6 ----> [tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{6}{2}=3\ caramels/kid[/tex]

therefore

[tex]y=3x[/tex]

Answer:

y=(x+1)(x-1)(x+8)

Step-by-step explanation:

When creating a factor with a known zero, use (x-ZERO)

For instance: a zero of -1 would be reprsented as (x+1)

x + (-4) = 10.

We can use the positive - negative rule.

x + (-4) = 10.

x - 4 = 10.

x = 10 + 4

x = 14.

Answer:

x= - 3.5

y= - 6.5

Step-by-step explanation:

-3x+y = 4 equation 1

-9x + 5y = -1 equation 2

and

equation 1 can be written as

y = 4+ 3x

so put this in equation 2

-9x + 5 ( 4+ 3x) = -1

-9x +20 +15x = -1

6x = -21

X= -21 ÷ 6

X = - 3.5

so put this value of x in equation 1 to find value of y

-3 ( -3.5) + y = 4

10.5 + y = 4

y = 4 - 10.5

Y = - 6.5

Answer:

x= - 3.5

y= - 6.5-

Answer:

20

Step-by-step explanation:

-4/-0.2

When dividing numbers with the same sign, the result is always positive. In this case, -4 divided by -0.2 is equal to 20.

When dividing numbers with the same sign, the result is always positive. In this case, -4 divided by -0.2 is equal to 20.

Answer: x = -6, and y = -6  (-6, -6)

Step-by-step explanation: What we have here is a pair of simultaneous equations. Since we have been instructed to solve by substitution, we shall begin with the one which has one of the variables as having a coefficient of 1. We shall start with equation 2 which is,

y = 2x + 6

Having taken note of this, we can now go on to the other equation and substitute for the value of y.

Hence, from equation 1,

4x - 4y = 0 (substitute for the value of y)

4x - 4(2x + 6) = 0

4x - 8x - 24 = 0

-4x -24 = 0

Add 24 to both sides of the equation

-4x = 24

Divide both sides of the equation by -4

x = -6

Having calculated the value of x, we can now go on to substitute for the value of x in equation 2.

Therefore,

y = 2x + 6

y = 2(-6) + 6

y = -12 + 6

y = -6.

So, x = -6 and y = -6

6 3/11 that well be the answer

Answer:6 3/5

Step-by-step explanation: 10 2/5 - 3 4/5 = 33

5

= 63

5

= 6.6

Answer:

Quotient =(3x²-5x-1)  and reminder = 1

Step-by-step explanation:

[tex]\frac{9x^3-18x^2+2x+2}{3x-1}[/tex]

3x-1)9x³-18x²+2x+2(3x²-5x-1

      9x³-3x²

    ------------------------

          -15x²+2x+2

          -15x²+5x

           ------------------

                  -3x+2

                   -3x+1

                    --------

                         1

Therefore 9x³-18x²+2x+2=(3x²-5x-1)(3x-1)+1

Quotient =(3x²-5x-1)  and reminder = 1

Answer:

120.6

Step-by-step explanation:

Since we know that 67 percent of coins are quarters.

Total coins = 180

67% of 180= 180 * 67/100

120.6.

So he has about 120.6 quarters.

Answer:

126 quarters

Step-by-step explanation:

67% ≈ 70%

70% = 70/100

70% = 7/10

180 * 7/10 = 126 quarters

Answer:

4

Step-by-step explanation:

Answer:

She spend $32,640 on cruises.

Step-by-step explanation:

Given:

Shane spends 48% of her income on cruises.

If she makes $68,000 per year.

Now, to find the money she spend on cruises.

Shane makes income per year = $68,000.

Percent Shane spends of her income on cruises = 48%.

Now, to get the income she spends on cruises:

48% of $68,000.

[tex]=\frac{48}{100} \times 68000[/tex]

[tex]=0.48\times 68000[/tex]

[tex]=\$32,640.[/tex]

Therefore, she spend $32,640 on cruises.

Answer:

4/7

Step-by-step explanation:

1/6-8/6=-7/6

-[1/6-8/6]=7/6

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

(2/3)/(7/6)=(2/3)(6/7)=12/21=4/7

Answer:

59

Step-by-step explanation:

77+(-18)=59

Check:

59-77=(-18)

Hoped this helped !

Cheers, Z.

Answer:

59

Step-by-step explanation:

59-77=-18

77+-18=59