What is X? −2(x−6)= x+5

Answer:

The equation that describes the path of the water balloon is:

[tex]y =-\frac{1}{10}\cdot (x-10)^{2}+15[/tex]

Step-by-step explanation:

The motion of the water balloon is represented by quadratic functions. Tommy launches a water balloon from [tex]A(x,y) = (0\,ft, 5\,ft)[/tex] and hits Arnold at [tex]B(x,y) = (20\,ft, 5\,ft)[/tex]. Given the property of symmetry of quadratic function, water ballon reaches its maximum at [tex]C(x,y) = (10\,ft,15\,ft)[/tex], which corresponds to the vertex of the standard equation of the parabola, whose form is:

[tex]y = a\cdot (x-h)^{2}+k[/tex] (Eq. 1)

Where:

[tex]a[/tex] - Vertex parameter, measured in [tex]\frac{1}{ft}[/tex].

[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the vertex, measured in feet.

[tex]x[/tex], [tex]y[/tex] - Horizontal and vertical location of the ball, measured in feet.

If we know that [tex]x = 0\,ft[/tex], [tex]y = 5\,ft[/tex], [tex]h = 10\,ft[/tex] and [tex]k = 15\,ft[/tex], the vertex parameter is:

[tex]5\,ft = a\cdot (0\,ft-10\,ft)^{2}+15\,ft[/tex]

[tex]a = \frac{5\,ft-15\,ft}{(0\,ft-10\,ft)^{2}}[/tex]

[tex]a = - \frac{1}{10}\,\frac{1}{ft}[/tex]

The equation that describes the path of the water balloon is:

[tex]y =-\frac{1}{10}\cdot (x-10)^{2}+15[/tex]

Answer:

3.98 seconds

Step-by-step explanation:

The given relationship between height, in feet, and the time, in seconds, is

[tex]h(t)=-10t^2+40[/tex]

[tex]\Rightarrow t^2=\frac{40-h(t)}{10}[/tex]

[tex]\Rightarrow t= \pm\sqrt{4-0.1h(t)}\cdots(i)[/tex]

Let at time [tex]t_1[/tex], the ball was at the goalie, so, [tex]h(t_1)=0[/tex], and at the time [tex]t_2[/tex], the ball was intercepted, so, [tex]h(t_2)=11[/tex].

Now, the time to reach the player after the goalie kicks the ball

[tex]\Delta t=t_2-t_1[/tex]

By using equation (i)

[tex]\Delta t=(\pm\sqrt{4-0.1h(t_2)})-\left(\pm\sqrt{4-0.1h(t_1)}\right)\cdots(ii)[/tex]

Now, at the highest point, the slope of the graph must be zero.

So, [tex]\frac {dh(t)}{dt}=0[/tex]

[tex]\Rightarrow -20t=0[/tex]

[tex]\Rightarrow t=0[/tex]

As at the highest point, the time is zero, to before reaching the highest point ( when kikes by the goalie, [tex]t_1[/tex]) take the time with the negative sign and after the highest point (when the ball intercepted, [tex]t_2[/tex]) take the positive sign.

So, from equation (ii) become.

[tex]\Delta t=\sqrt{4-0.1\times 11}-\left(-\sqrt{4-0.1\times 0} \right)[/tex]

[tex]=\sqrt{3.9}-(-\sqrt 4)[/tex]

[tex]=1.98+2[/tex]

= 3.98 seconds

Hence, the time to reach the ball to the player after the goalie kicks the ball is 3.98 seconds.

Answer:

4/6

Step-by-step explanation:

( 0, -4 ) is the vertex of the parabola

Answer:

y = 120

Step-by-step explanation:

If y = 32 when x = 8, then y is 4 times the number of x. If x = 30, then (4)30 = 120.

Answer:

B

Step-by-step explanation:

the line is perpendicular to y=1/2x-3

so its gradient, m, would be -2 (m¹m²= -1)

sub the coordinates and the gradient into this equation to find the equation of line in slope intercept form

y-y¹ = m(x-x¹)

The equation of the line  in slope-intercept form that passes through (-2,2) and is perpendicular to the graph of y= 1/2x-3 is; y = -2x - 2

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Where x₁ - x coordinate, y₁ - y coordinate, m - slope

Point (-2,2)

Then the equation of a line perpendicular to the graph of y= 1/2x-3.

its gradient, m, would be; -2 (m¹m²= -1)

Now Write the equation as;

y-y₁ = m(x-x₁)

y - 2= -2(x + 2)

y = -2x - 2

Hence, the equation of the line  in slope-intercept form that passes through (-2,2) and is perpendicular to the graph of y= 1/2x-3 is; y = -2x - 2

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Answer:

4x (9+2)

Step-by-step explanation:

36x+8x

36 and 8 can be divided by 4 and they both have an x

[tex]36x + 8x = 4x(9 + 2)[/tex]

[tex]44x = 36x + 8 x[/tex]

[tex]44x = 44x[/tex]

The Answer is

[tex] \green {\boxed{4x(9+2)}}[/tex]

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A,B,C

Step-by-step explanation:

Answer:

A, B and C

Step-by-step explanation:

Answer:

ok I did it two ways and got different answers

Step-by-step explanation:

addition

42^2 +69^2= x^2

1,764 +4,761=x^2

1,764 + 4,761= 6,525

Square root of 6,525 is 80.77 or 15/29

subtracting

4,761 -1,764= 2,997

Square root of 2,997 is 54.74 or 9/37

hope one of these are right, good luck

Answer:

b

Step-by-step explanation:

Answer:

3,000 is your answer.

Step-by-step explanation:

3

When rounding off to the nearest whole number all you do is look at the first decimal and see if it is bigger than 5 which in this case it isn't so, the 3 stays the same and that would be your answer. If it was bigger than 5 then your whole number changes to 4.

Answer:

Ok... hmmmmm

So im going to assume that this is an adding fractions question so for a half batch it would be 1 1/4 + 2 2/4 which is 3 3/4 cups and for a double batch it would be 15 cups because 10 + 5 is 15.

The first blank probably is 3 3/4

The second blank probably is 15

<3 I already answered this on the other question but I want points so tysm.

Answer:

x=9, hope I helped :P

Answer:

Would it be 25 that’s what I got

Step-by-step explanation:

Answer:

x=2 y=3

Step-by-step explanation:

3x=6

2y=6

x=2

y=3

Answer:

t>28

Step-by-step explanation:

Answer:

$24

Step-by-step explanation:

James

Allowance per week = $6

He spends = $4

Balance = $6 - $4 = $2

Mike

Allowance per week = $7

He spends = $3

Balance = $7 - $3 = $4

Their mother's birthday is in 4 weeks

how much money can they save together in that time to buy her present?

James savings per week × 4 weeks

= $2 × 4

= $8

Mike's savings per week × 4 weeks

= $4 × 4

= $16

Total amount James and Mike can save together = $8 + $16

= $24

i gotchu: (-8,0) (0,-4) (4,-6)

Answer:

(-8,0) (0,-4) (4,-6)

Step-by-step explanation:

Answer:

9 degrees

Step-by-step explanation:

The temperatire was -3 and then rose by 12, -3 + 12 = 9

Answer:

slope is easy it is rise over run.

Step-by-step explanation:

rise/run

rise means up

run means move sideways.

Answer: what do you mean by slope?

Step-by-step explanation:

the game that you have to control a ball and you have power-ups and you have to stay on platforms and you have to avoid the red rectangles?

Answer:

y=1/2x-1

Step-by-step explanation:

0,-1

2,0

0--1 si 1

2-0 is 2

1/2

Answer:

(2, 4, 3)

Step-by-step explanation:

Range = Y

Answer:

The exponent of the simplified power is 3

Step-by-step explanation:

Given:

6 × 6 × 6 × 6 × 6 × 6 × 6 / 6 × 6 × 6 × 6

Dividing common factors ( cancel out 4 6's in the Numerator and Denominator

= 6 × 6 × 6 / 1

= 6^3 /1

= 6^3

The exponent of the simplified power is 3

Answer:

The exponent of the simplified power is 3

Step-by-step explanation:

If we perform the vertical line test, we can see that every line touches the graph once. This means that the graph is a graph of a function.

Answer choice b is correct.

Answer:

1) r >-5       2) x >9

Step-by-step explanation:

Answer:

there are teo solutions that can be written as tge difference of square have.

There are two possible solutions for the quadratic equation that can be written as the difference of squares.

A quadratic equation is of the form -

y = f(x) = ax² + bx + c

Given is a quadratic equation that can be written as the difference of squares.

A quadratic equation that can be written as the difference of squares is of the form -

(x² - a²)

For the roots, we can write the equation as -

(x² - a²) = 0

x² = a²

x  = ± a

Therefore, there are two possible solutions for the quadratic equation that can be written as the difference of squares.

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Answer:

247

Step-by-step explanation:

Answer: 247

Step-by-step explanation: 247