The height of a baseball hit from a bat is modeled by a quadratic function of time, h(t). What does the second coordinate of the vertex of the quadratic function represent?
the minimum height of the baseball
the time at which the baseball hits the ground
the time at which the baseball hits the maximum height
the maximum height of the baseball

The equation x = 7 - 4√3 is a radical expression, and the value of the radical expression is [tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]

The equation is given as:

x = 7 - 4√3

So, we have:

[tex](x + \frac 1x)^2 = (7 - 4\sqrt 3 + \frac{1}{7 - 4\sqrt 3})^2[/tex]

Take the LCM

[tex](x + \frac 1x)^2 = (\frac{49 -56\sqrt3 + 48}{7 - 4\sqrt 3})^2[/tex]

Evaluate the like terms

[tex](x + \frac 1x)^2 = (\frac{97 -56\sqrt3 }{7 - 4\sqrt 3})^2[/tex]

Rationalize

[tex](x + \frac 1x)^2 = (\frac{(97 -56\sqrt3)(7 - 4\sqrt 3) }{49 -48})^2[/tex]

Evaluate the difference

[tex](x + \frac 1x)^2 = ((97 -56\sqrt3)(7 - 4\sqrt 3))^2[/tex]

Expand

[tex](x + \frac 1x)^2 = (679 -388\sqrt 3 -392\sqrt 3 + 672)^2[/tex]

Evaluate the like terms

[tex](x + \frac 1x)^2 = (1351 -780\sqrt 3 )^2[/tex]

Expand

[tex](x + \frac 1x)^2 = 1825201 +1825200 -2107560\sqrt 3[/tex]

[tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]

Hence, the value of the radical expression is [tex](x + \frac 1x)^2 = 3650401 -2107560\sqrt 3[/tex]

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Answer:

Area = 63ft

Step-by-step explanation:

7*9=63

multiply the base and height

157.5 square feet is the area of the roof.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that the roof of a clock tower is a pentagonal pyramid.

a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point

Each side of the base is 7 ft long.

The slant height is 9 ft.

We need to find the  area of the roof.

Area=1/2×7×9×5

=315/2

=157.5

Hence, 157.5 square feet is the area of the roof.

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Number Line:

Closed Circles are used when signs are "≤" or "≥"

Open Circles are used when signs are "<" or ">"

The graph of x > -1 on a number line would be towards the right from -1 with open circle as the sign is ">"

Graph should look like this:

Answer:

12:11

Step-by-step explanation

Answer:

I think it would be 12:11

Step-by-step explanation:

This is because you can't down size the 11

Answer: x=11

Step-by-step explanation:

Set the two equations equal to each other

5x+9 = 6x-2

9=x-2

11=x

x=11

X will need to be 11 in order to make the two equations equal to each other

Answer:

He can print 62 documents

Step-by-step explanation:

500/8=62.5

He can print only 62 documents because he cannot print half a document.

Hope this helps!

If not, I am sorry.

The greasiest possible number of intersections for these graphs is 2 if the Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

As we know the standard form of a quadratic equation is:

[tex]\rm Y = \rm ax^2+bx+c[/tex]

And a linear equation can be written as:

y = mx + d

Equating both the expression:

ax² + bx + c = mx + d

ax² + (b-m)x + c - d = 0

The above equation is an also quadratic equation, and we know that the quadratic equation have maximum two roots.

Thus, the greasiest possible number of intersections for these graphs is 2 if the Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression.

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Question 8 of 25

The amount of water dispensed by a water dispenser is normally distributed,

with a mean of 11.60 ounces and a standard deviation of 0.15 ounces. In

which range will the amount of water dispensed be found 95% of the time

Answer:

s

Answer:

[tex]\overline{TH}[/tex]

Step-by-step explanation:

The diameter of a circle is a line that goes from one side to the other in a circle. It is the longest straight line that can be drawn in a circle. It also goes through the center of a circle.

That is the answer

- Kan Academy Advance

Answer:

a=263.76cm3

b=301.44cm3

c=41.52m3

Answer:

x= 67, y= 113 , z= 67........... ...........

It is TRUE, so shade on the SAME side as (0,0)

Answer:

k=36; y=1.44; x=8

Step-by-step explanation:

a) y= k/square root of x

9=k/square root of 16

9=k/4

9×4= (k/4)×4

therefore k=36

b) Using k...

y=36/25

therefore y=1.44

c) 4.5=36/x

4.5×(x)= (36/x)×(x)

4.5x=36

therefore x=8

Answer:

B. (2, 4)

Explanation:

Given equations:

a) y = x + 2

b) y = 3x – 2

Solve them simultaneously:

x + 2 = 3x – 2

x - 3x = -2 - 2

-2x = -4

x = 2

Then find y = x + 2 = 2 + 2 = 4

Solution: (x, y) = (2, 4)

Answer:

(2,4)

Step-by-step explanation:

substitute the value of y x+2 = 3x-2

solve the value of x  x = 2

substitue the value of x into one of the equations y = 2+2

solve for y value y = 4

The slope of the  line passing through the points (3, 3) and (0, -6) is 3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We need to find the slope of line passing through points (3, 3) and (0, -6)

Plug in the values in formula.

m=-6-3/0-3

m=-9/-3

m=3

Hence, the slope of the  line passing through the points (3, 3) and (0, -6) is 3.

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Answer:

4x(2x-1)

Step-by-step explanation:

Using GCF, you can be able to take out a factor of 4x from 8x^2 and 4x.

Answer:

√10+√15-√14-√21

Explanation:

(√2 * √5) = √10

(√2 * -√7) = -√14

(√3 * √5) = √15

(√3 * -√7) = -√21

Put it all together: √10 + √15 - √14 - √21

Hope this helped :)

The simplified form of the expression  (√2+√3)(√5-√7) is √10-√14+√15-√21

An expression is combination of variables, numbers and operators.

The given expression is (√2+√3)(√5-√7)

√2(√5-√7) + √3(√5-√7)

We have to apply  distributive property

√2.√5 - √2.√7 + √3.√5 -√3.√7

√2×5 -√2×7 +√3×5 -√3×7

√10-√14+√15-√21

Hence, the simplified form of the expression  (√2+√3)(√5-√7) is √10-√14+√15-√21

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Answer:

150

Step-by-step explanation:

The common difference, d, is +3      add +3 to find the next term.

  to find the second term add +3 to the first term

     to find the third term add  2 * +3

        to find the 60th term add  59 * +3 to the first term

                 -27  +   (59*3) = 150

Step-by-step explanation:

We know that,

[tex]\boxed{\sf \sin θ = \dfrac{Opposite \: side}{Hypotenuse}}[/tex]

[tex]\longmapsto \sf \sin 30^{\circ} = \dfrac{x}{12}[/tex]

[tex]\longmapsto \sf \dfrac{1}{2}= \dfrac{x}{12}[/tex]

[tex]\longmapsto \sf \dfrac{1}{2}×12= \dfrac{x}{12}×12[/tex]

[tex]\longmapsto \sf x = 6[/tex]

Answer:

x = 6

Step-by-step explanation:

Hello!

The missing angle is 60°, and is found by subtracting 90° and 30° from 180°.

Using basic triangle theorems of a 30° - 60° - 90° triangle, we know that the leg opposite to 30°, x, is one-half of the hypotenuse.

The value of x is 6.

The leg opposite to 60° is √3 times the leg opposite to 30°.

Answer:

Radius = 3

Circumference = 18.84

Step-by-step explanation:

A = πr²

28.26 = 3.14r²

√9 = √r²

3 = r

C = 2πr

C = (2)(3.14)(3)

C = 18.84

Answer:

0

Step-by-step explanation:

simplfy: 4.5(6.2) = 0

Multiply 4.5 * 6.2

27.9 = 0

and solve

27.9 = 0

I  hope this helps ^^

Answer:

= -27.9

If you mean multiplication,  [tex]4.5\times(-6.2)=-27.9[/tex].

The product is negative because the (-)6.2 is negative.

Step-by-step explanation:

Step-by-step explanation:

I hope this will help you

Answer:

198

Step-by-step explanation:

The correct option is option B.

The common difference between given data is -3/4.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Here, given points;

                            x₁ = 1 , x₂ = 2 and y₁ = -3.75 , y₂ = -4.5

Now,

    d = (y₂ - y₁)/(x₂-x₁)

    d = (-4.5 - (-3.75))/(2 - 1)

     d = -0.75 / 1

     d = - 75/100

      d = -3/4

Thus, The correct option is option B.  The common difference between given data is -3/4.

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Answer:

1st triangle: missing angle is 100

2nd triangle: missing angles are 50

3rd triangle: missing angle is 90, this is also a right triangle. The hypotenuse on this is the side length that reaches from angle 70 to 20. the other sides are legs

Step-by-step explanation:

Answer:

  total: $86.68

Step-by-step explanation:

The value of each change is found by multiplying the base amount by the percentage change. The result is rounded to the nearest cent. Here, we're applying 3 changes. In order to make sure they're rounded properly, we need to apply them in order

__

The discount amount is ...

  discount = bill × 10% = $75.00 × 0.10 = $7.50

The discounted amount is ...

  bill - discount = $75.00 -7.50 = $67.50

__

The tax amount is ...

  tax = discounted bill × tax rate = $67.50 × 0.07 = $4.725 ≈ $4.73

The bill with tax added is ...

  discounted bill + tax = $67.50 +4.73 = $72.23

__

The tip is apparently added to the amount after tax, so the amount of the tip is ...

  tip = taxed bill × 0.20 = $72.23 × 0.20 = $14.446 ≈ $14.45

The bill with tax and tip added is ...

  total bill = $72.23 +14.45 = $86.68

_____

Additional comment

At each stage, the amount can be found by using the multiplying factor (1+p), where p is the percentage change. All three factors applied gives a result of ...

  75×(1-0.10)(1+0.07)(1+0.20) = 75×0.9×1.07×1.2 = 86.67

You will note this differs by a penny from the amount calculated above. That is a consequence of rounding up both the tax and the tip.