Find the surface area of the prism. 8 4 14

Graph is in attached image.

The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.

Quadratic functions are polynomials of grade 2 of the form y = a · t² + b · t + c, where t and y are the time and the height of the ball, in seconds and feet, respectively. To determine the value of the three coefficients we need to know three different points of the form (t, y).

If we know that (t₁, y₁) = (0 s, 0 ft), (t₂, y₂) = (1 s, 16 ft) and (t₃, y₃) = (3 s, 0 ft), then the quadratic function is:

a · 0² + b · 0 + c = 0     (1)

a · 1² + b · 1 + c = 16      (2)

a · 3² + b · 3 + c = 0      (3)

The solution to this system is a = - 8, b = 24, c = 0.

The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.

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Answer:

  (c)  5.00×10^-5 kg

Step-by-step explanation:

The mass and energy are related by Einstein's formula E = mc².

__

Solving for mass in kg, we find it to be ...

  m = E/c² . . . . . . . . where E is in joules, and c is in meters/second

  m = (4.50×10^12 J)/(3×10^8 m/s)² = 5.00×10^-5 kg

The lost mass was about 5.00×10^-5 kg.

Answer:

5.00×10^−5 kg

Step-by-step explanation:

I took the test and it was correct! PLEASE LIKE  and have a wonderful day!

Force (F) = WSin(angle)

F = 2000×Sin(10)

Therefore, F = 347lb.

Answer:

area = 28.27

circumference = 18.85

Step-by-step explanation:

Using the formulas for area,

A = πr^2

d = 2r

Solving for area,

A = 1/4 πd^2 = 1/4 × π × 6^2 ≈ 28.27yd²

Using the formulas for circumference,

C = 2 πr

d = 2r

Solving for circumference,

C = πd = π × 6 ≈ 18.85yd

[tex](2,3) \longrightarrow (2+1, 3-3)=\boxed{(3,0)}\\(-4,5) \longrightarrow (-4+1, 5-3)=\boxed{(-3, 2)}\\(-3,4) \longrightarrow (-3+1, 4-3)=\boxed{(-2, 1)}[/tex]

The lower bound for the profit is $2425.

When a number of rounded off to the nearest $10, it means that the value of the number in the units place, if greater than 5 becomes zero and one is added to the $10 number. If the number is less than 5, there is no change in the $10 number and the units number becomes 0

The possible values of the average profit are 2425, 2426, 2427, 2428, 2429, 2430. 2431. 2432, 2433, 2434  

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Answer:

C

Step-by-step explanation:

Two negatives cancel out and turn into a positive.

In the expression 11 - ( -3 5/8 ) there are two negative signs. If the parenthesis are removed, the two negative signs cancel out and turn into a positive and we are left with 11 +3 5/8

So the answer is C

Answer:

6x² + 7x-20

A. (3x-4)(2x + 5)

The perimeter and area of the square are 16√5 mm and 80 mm²

Perimeter of a square = 4L

where

Therefore,

Perimeter of a square = 4 × 4√5

Perimeter of a square = 16√5 mm

Area of a square = l²

Area of a square = (4√5)²

Area of a square = 16 × 5

Area of a square = 80 mm²

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[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=250 \end{cases}\implies 250=2\pi r\implies \cfrac{250}{2\pi }=r\implies \stackrel{cm}{39.79}\approx r[/tex]

By solving a quadratic equation we will see that the egg will hit the ground after 1.58 seconds.

Here we know that the initial height of the egg is 40ft, so the equation for the height will be:

[tex]h(t) = -16*t^2 + 40[/tex]

The egg will hit the ground when h(t) = 0, so we need to solve the quadratic equation:

[tex]h(t) = -16*t^2 + 40 = 0\\\\16t^2 = 40\\\\t^2 = 40/16\\\\t = \sqrt{40/16} = 1.58[/tex]

This means that the egg will hit the ground after 1.58 seconds.

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Step-by-step explanation:

12 . The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations..

The height and the base area of both the design must be equal. Then the correct option is A.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers.

Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder.

The figure shows both designs.

The volume of the cylinder will be given as

V = πr² h

If the volume of the oblique cylinder and right cylinder is the same.

Then the height of both the designs must be equal and the base area of both the design must be equal.

Then the correct option is A.

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Answer:

D

Step-by-step explanation:

did the test on edmentum

No, the cone and the cylinder can't have congruent heights and bases.

The volume of a cylinder of radius R and height H is:

V = pi*R^2*H

And for a cone of radius R and height H is:

V = pi*R^2*H/3

So, for the same dimensions R and H, the cone has 1/3 of the volume of the cylinder.

Here, the cylinder has a volume of 120cm³ and the cone a volume of 360cm³, so the cone has 3 times the volume of the cylinder.

This means that the measures must be different, so the cone and the cylinder can't have congruent heights and bases.

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Answer:

D

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{4}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2x = 4[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

x = 2[tex]\sqrt{2}[/tex]

Answer:

I think 10 is the answer it's not sure.

Answer:

The number that belongs in the green box is equal to 909.

General Formulas and Concepts:
Algebra I

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2[/tex]

Step-by-step explanation:

Step 1: Define

Identify given variables.

a = 30

b = 3

c = x

Step 2: Find x

Let's solve for the general equation that allows us to find the hypotenuse:

Now that we have the formula to solve for the hypotenuse, let's figure out what x is equal to:

∴ the hypotenuse length x is equal to √909 and the number under the square root, our answer, is equal to 909.

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Topic: Trigonometry

The kind of annuity does Lila own is: variable immediate annuity.

Variable immediate annuity can be defined as the type of annuity that vary or fluctuate based on the type of investment you choose or pick.

In this type of annuity the payment you will receive will not be fixed  reason being that payments that will made to you will always increase or decrease.

Therefore the kind of annuity does Lila own is: variable immediate annuity.

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Answer:

B

Step-by-step explanation:

The y-intercept is 8

The slope is -2x

Therefore the slope-intercept is y = -2x + 8

The rationalization the denominator of the fraction  (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].

Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]

Then the conjugate of the denominator is given by b - c

Thus, rationalizing the fraction will give us

[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]

The given expression is

[tex]\dfrac{6}{4+\sqrt(5)}\\\\[/tex]

By rationalizing the denominator of the fraction

[tex]\dfrac{6}{4+\sqrt(5)}\times \dfrac{4-\sqrt(5)}{4-\sqrt(5)} \\\\\\\dfrac{6(4-\sqrt(5))}{4^2-(5)}\\\\\\\dfrac{6(4-\sqrt(5))}{11}[/tex]

Thus, the rationalization the denominator of the fraction  (6)/(4+\sqrt(5)) is [tex]\dfrac{6(4-\sqrt(5))}{11}[/tex].

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Answer:

Step-by-step explanation:

In trigonometry, secant in a right triangle, is the reciprocal of the cosine of an angle symbol: sec while cosine is in a right triangle, is the ratio of the length of the side adjacent to an acute angle to the length of the hypotenuse.

The cosine of an angle is the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse of the triangle. The cosine of ∠A will be abbreviated as cos ∠A

The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .

Answer:

Step-by-step explanation:

Suppose a right triangle ABC in which

BC=3 units and AC=5 unit and angle B=90 degree

Let x be the missing angle of right triangle

We know that

Hence, there is no difference between using cosine ratio to solve for a missing angle in a right triangle versus using the secant ratio.

Answer:

5x2-2x+1 The highest exponent is the 2 so this is a 2nd degree trinomial.

Step-by-step explanation: Also pls answer by question

A point that is exterior to an angle is found on the acute side of the angle which is true.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

We know that the sum of the exterior angle and interior angle is equal to 180 degrees.

"If one of the exterior angles is an acute angle, then the corresponding interior angle is an obtuse angle."

A point that is exterior to an angle is found on the acute side of the angle which is true.

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The volume of the given rectangular prism.

[tex]\huge\boxed{Formula: lwh}[/tex]

To find the the volume we'll have to multiply the height, width and length.

[tex]V=\: 13×7×5 [/tex]

[tex]\large\boxed{V= \:455\: {cm}^{3}}[/tex]

Therefore, the volume of the given rectangular prism is 455 cubic centimeters.

Answer:

d

Step-by-step explanation:

the y- intercept is the point on the y- axis where the graph crosses

the graph crosses the y- axis at point (0, - 9 )

then y- intercept = (0, - 9 )

Answer:

Step-by-step explanation:

#a

pattern 0 will include 4 reds in square

Because it's independent of pattern no

#b

Figure 1 has 4+4=8

Figure 2=4+8+2=14

Figure 3=4+12+3=19

The pattern n rule is

So for 13th n

#c

attached

#d

Already given in c

Answer:

He multiplied the denominators incorrectly

Step-by-step explanation:

we know that

The volume of a rectangular prism is given by the formula

V=LWH

we have

L=3/4 ft

W=5/1 ft

H=1/2

substitute

V=(3/4)(5/1)(1/2)= 3x5x1=    15

                           ₋₋₋₋₋₋₋₋    ₋₋₋₋ ft³

                           4x1x2=    8

therefore

He multiplied the denominators incorrectly