3(x + 1)2 = 108
Create a list of your steps

Answer:

Max

Step-by-step explanation:

the function given that h = -16t³+64t+10

the general function Equation:

h = at²+bt+c

=> t at the highest point is defined by t = -b/2a

= -64/2(-16) = -64/-32 = 2 second

the total times that the ball hits the ground

= 2× 2 seconds = 4 seconds.

so, Max is right

Answer:

Solution given:

Let h=0=when the ball hit the ground,the height=0.

h= -16t^2 + 64t + 10.

0=16t²-64t-10

8t²-32t-5=0

∆=[tex] \frac{32±\sqrt{32²+4*5*8}}{2*8}=\frac{8±\sqrt{74}}{4}[/tex]

taking positive

t1=[tex] \frac{8+\sqrt{74}}{4}=4.15seconds[/tex]

t2=[tex] \frac{8-\sqrt{74}}{4}(t2<O)(neglected)[/tex]

So

t=4.15seconds closer to 4seconds.So

Max is closer.

Answer:

[tex]y=-3(x-5)^2+4[/tex]

Step-by-step explanation:

Hi there!

Given the vertex of a parabola and a point, it's easiest to organize the equation in vertex form:

[tex]y=a(x-h)^2+k[/tex] where the vertex is located at [tex](h,k)[/tex] and a is a numerical value

1) Plug the vertex into the equation

[tex]y=a(x-h)^2+k[/tex]

Plug in the vertex (5,4)

[tex]y=a(x-5)^2+4[/tex]

2) Solve for a

[tex]y=a(x-5)^2+4[/tex]

Plug in the given point (3,-8) and solve for a

[tex]-8=a(3-5)^2+4\\-8=a(-2)^2+4\\-8=4a+4[/tex]

Subtract 4 from both sides

[tex]-8-4=4a+4-4\\-12=4a[/tex]

Divide both sides by 4

[tex]\frac{-12}{4} = \frac{4a}{4} \\-3=a[/tex]

Therefore, a=-3. Plug this back into [tex]y=a(x-5)^2+4[/tex]:

[tex]y=-3(x-5)^2+4[/tex]

I hope this helps!

Answer:

the answer is 55

Step-by-step explanation:

if you have a straight line each side equals 180 degrees so take 60+65 which equals 125 then do 180-125 and you get 55

9514 1404 393

Answer:

  a = 3, b = 12, c = 13

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)/(a^c) = a^(b-c)

  (a^b)^c = a^(bc)

___

You seem to have ...

  [tex]\dfrac{2^5\times8^4}{16}=\dfrac{2^5\times(2^3)^4}{2^4}\qquad (a=3)\\\\=\dfrac{2^5\times2^{3\cdot4}}{2^4}=\dfrac{2^5\times2^{12}}{2^4}\qquad (b=12)\\\\=2^{5+12-4}=2^{13}\qquad(c=13)[/tex]

_____

Additional comment

I find it easy to remember the rules of exponents by remembering that an exponent signifies repeated multiplication. It tells you how many times the base is a factor in the product.

  [tex]2\cdot2\cdot2 = 2^3\qquad\text{2 is a factor 3 times}[/tex]

Multiplication increases the number of times the base is a factor.

  [tex](2\cdot2\cdot2)\times(2\cdot2)=(2\cdot2\cdot2\cdot2\cdot2)\\\\2^3\times2^2=2^{3+2}=2^5[/tex]

Similarly, division cancels factors from numerator and denominator, so decreases the number of times the base is a factor.

  [tex]\dfrac{(2\cdot2\cdot2)}{(2\cdot2)}=2\\\\\dfrac{2^3}{2^2}=2^{3-2}=2^1[/tex]

Answer:

13π m

Step-by-step explanation:

circumference of a circle = 2πr

=2*π*6.5

=13π m

Answer:

13[tex]\pi[/tex] m

Step-by-step explanation:

The formula for circumference is 2r[tex]\pi[/tex], so...

2r[tex]\pi[/tex]

2(6.5)[tex]\pi[/tex]

=13[tex]\pi[/tex]

Answer:

y = 2*x + 4

Step-by-step explanation:

We know that a linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

We know that if this line passes through the points (x₁, y₁) and (x₂, y₂) the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

So, here we know that our line must pass through the points (-2,0) and (0, 4)

Then the slope of this line is:

a = (4 - 0)/(0 - (-2))

a = 4/2 = 2

Then our line is something like:

y = 2*x + b

Now, to find the value of b we can use one of these two points, for example if we use the point (-2, 0), we know that, when x = -2, we must have y = 0.

0 = 2*(-2) + b

0 = -4 + b

4 = b

Then the equation for our line is:

y = 2*x + 4

It is 34.90

Step-by-step explanation:

Your welcome!

Answer:

32

put 12.8% as a decimal which is 0.128 and times it by 250

Answer:

32

Step-by-step explanation:

[tex]\frac{y}{250} :\frac{12.8}{100}[/tex]

y × 100 = 250 × 12.8

100y = 3200

100y ÷ 100 = 3200 ÷ 100

y = 32

Given:

Kiosk is the combination of a cylinder and a cone.

Diameter of cylinder and cone = 5 m

Height of the cylinder = 3 m

Height of the cone = 2 m

To find:

The volume of the kiosk.

Solution:

We know that the radius is half of the diameter. So,

Radius of cylinder and cone = [tex]\dfrac{5}{2}[/tex] m

                                               = [tex]2.5[/tex] m

Volume of the cylinder is:

[tex]V_1=\pi r^2h[/tex]

Where, r is the radius and h is the height of the cylinder.

Putting [tex]\pi =3.14, r=2.5, h=3[/tex] in the above formula, we get

[tex]V_1=(3.14)(2.5)^2(3)[/tex]

[tex]V_1=(3.14)(6.25)(3)[/tex]

[tex]V_1=58.875[/tex]

Volume of a cone is:

[tex]V_2=\dfrac{1}{3}\pi r^2h[/tex]

Where, r is the radius and h is the height of the cone.

Putting [tex]\pi =3.14, r=2.5, h=2[/tex] in the above formula, we get

[tex]V_2=\dfrac{1}{3}(3.14)(2.5)^2(2)[/tex]

[tex]V_2=\dfrac{1}{3}(3.14)(6.25)(2)[/tex]

[tex]V_2\approx 13.083[/tex]

The volume of the kiosk is the sum of volume of cylinder and the volume of cone.

[tex]V=V_1+V_2[/tex]

[tex]V=58.875+13.083[/tex]

[tex]V=71.958[/tex]

[tex]V\approx 72[/tex]

Therefore, the volume of the kiosk is 72 cubic meter.

Answer:

[tex]{ \tt{ - \frac{3}{8} + \frac{1}{6} }} \\ { \bf{l.c.m \: of \: 8 \: and \: 6 = 24}} \\ { \tt{formular = \frac{(l.c.m \times denominator \div numerator)}{l.c.m} }} \ \\ \\ = \frac{(24 \times 8 \div - 3) + (24 \times6 \div 1)}{24} \\ = - \frac{5}{24} [/tex]

Answer:

471 cm

Step-by-step explanation:

here diameter of the circle is 150cm, and we know radius is half of diameter.

therefore r = 150/2

= 75

Now,

according to formula,

Circumference of circle = 2πr

= 2 x 3.14 x 75

= 471 cm

Answer:

3 meters

Step-by-step explanation:

Assuming the window is rectangular

A = l*h

18 = 6*h

Divide each side by 6

18/6 = 6h/6

3 = h

Answer:

a+k ≤ 35

8a+4k ≤ 190

Some possible combinations are 10 adults and 20 kids

5 adults and 29 kids

Step-by-step explanation:

Let k= number of kids

a = number of adults

a+k ≤ 35  since you can have at most 35

8a + 4k ≤ 190 since the most you can spend is 190

Some possible combinations are 10 adults and 20 kids

(10+30 < 35 and 8*10+4*20 = 80+80 =160< 190)

Another possible combination

5 adults and 29 kids

(5+29 < 35  and 5*10 + 4*29 =50+116=166)

Step-by-step explanation:

Angle C: 50 degrees

Angle E: 55 degrees

Angle D: 50 degrees

Angle A: 125 degrees

Angle B: 75 degrees

Answer: y = 1/4x - 1.

Step-by-step explanation: This line has a slope (rise over run) of 1/4, and a y-intercept of -1. Plugging those values into slope-intercept form (y = mx + b) gives you the answer.

Answer:

22.09

Step-by-step explanation:

Given the expression ln(x-2)^2=6

Take exponent of both sides

e^ln(x-2)^2=e^6

(x-2)² = e^6

(x-2)² = 403.43

x - 2 = √403.43

x - 2= 20.09

x = 20.09 + 2

x = 22.09

Hence the value of x is 22.09

Answer:

1.5 hours

Step-by-step explanation:

Total watering hours

4 * 3 = 12

time needed for 8 pipes

12/8 = 1.5 hours

Answer:

y=76+2.5x where y is the amount he earns in a day and x is the number of tshirts sold

y=76+2.5(32)

y=76+80

y=156

he earns 156 dollars if he sold 32 tshirts

Step-by-step explanation:

Answer:

D.

is the correct answer

Answer:

a = 32

b= 27

c = 9

Step-by-step explanation:

a= 5+ b from the second equation

c= b/3 from the third equation

substitute the above equations to the first equation then solve for b your answer will be 27

substitute the value of b in the second equation you will solve for a

perform the same substitution to the third equation you will get the answer for c

Step-by-step explanation:

a-b=5<=>a=5+b (1)

b:c=3<=>b=3c (2)

a+b+c=68<=>5+b+3c+c=68<=>5+3c+3c+c=68

<=>7c=63<=>c=9

Fill in (2), we have b=3c=3.9=27

and in (1), we have a=5+b=5+27=32

So, a=32, b=27, c=9

Answer:

52.37 – 46.37 = y

8y = 48

Step-by-step explanation:

Choose all the equations that are true if y = 6. 52.37 – 46.37 = y 45y =445 8y = 48 3.2 + y = 9 y ÷ 4 = 24

We solve for y in all the equations :

52.37 – 46.37 = y

52.37 – 46.37 = 6 (True)

45y =445

Divide both sides by 45

45y/45 = 445/45

y = 9.888 (False)

8y = 48

y = 48/8

y = 6 (True)

3.2 + y = 9

y = 9 - 3.2

y = 5.8 (false)

y ÷ 4 = 24

y/4 = 24

y = 24 * 4 = 96 ( false)

Answer:

x<=-3

Step-by-step explanation:

2x-5/x-2 <= 1

Multiply both sides by x-2

2x-5<=x-2 (anything times 1 is that number.)

add 5 to both sides

2x<=x-3

subtract x from both sides

x<=-3

Answer:

Step-by-step explanation:

[tex]\frac{2x-5}{x-2} \leq 1\\case ~1. both ~numerator~and~denominator \geq 0\\x\neq 2\\2x-5\leq x-2\\x\leq 3\\so~0\leq x<2U2<x\leq 3\\case~2.\\both~numerator~and~denominator<0\\2x-5\geq x-2\\x>3\\which~is~rejected~as~it~gives~both~2x-5~and ~x-2>0[/tex]

Answer:

Luca

Step-by-step explanation:

Juan 566/734 = 0.7711

Luca 7/9= 0.7777

Luca has a greater percentage

Answer:

[tex]g = 18p[/tex] --- A

[tex]g = 10p[/tex] ---- B

Step-by-step explanation:

Given

[tex]Package\ A: 18\ soda[/tex]

[tex]Package\ B: 10\ soda[/tex]

Required

The equation of both packages

The given details represent the number of sodas in each package.

So, the equation of A is:

[tex]g = 18p[/tex]

And the equation of B is:

[tex]g = 10p[/tex]

Answer:

d = 8

Step-by-step explanation:

V=(π)(r)^2(h/3)

83.7=(π)(r)^2(5/3)

Solve for r

r = 3.9

d = (3.99)(2)

d = 7.98

d = 8

Answer:

x = 46

Step-by-step explanation:

Vertical angles are equal so call the angle y

85+53 +y =y+ 92+x

Subtract y from each side

85+53  = 92+x

Combine like terms

138 = 92+x

Subtract 92 from each side

138 -92 = 92+x-92

46 =x