A ball is launched from a 48.314-meter tall platform. The equation
=
for the ball's height h at time t seconds after launch is h (t) =
-4.9t² +2.45t + 48.314, where his in meters. When does the
object strike the ground?

Answer:

x=0

Step-by-step explanation:

[tex]16^{x^2}=8^0\\\\16^{x^2}=1\\\\x^2\ln(16)=0\\\\x^2=0\\\\x=0[/tex]

The reason why the cousin's procedure for getting the x and y intercepts work is because they represent the definition of those points on a graph.

The x-intercept of a graph or function simply refers to the point at which the graph crosses the graph crosses the x-axis or the point at which y = 0. In a similar manner, the y-intercept simply refers to the point at which the graph crosses the y-axis or simply the point at which x = 0.

Now, we are given the equation of the line as;

5x + 4y = 14

The general form of equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Rewriting the equation of the line in slope intercept form is;

y = -⁵/₄x + ⁷/₂

Now, the reason why we plug in 0 for x to get the y-intercept is because when x = 0, that is only where we can get the y-intercept as the corresponding value of x will be traced to 0.

Similarly,  the reason why we plug in 0 for y to get the x-intercept is because when y = 0, that is only where we can get the x-intercept as the corresponding value of y will be traced to 0.

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Answer:

width = 10 yds

Step-by-step explanation:

perimeter = 2L + 2W

74 = 2(27) + 2W

74 = 54 + 2W

subtract 54 from both sides of the equation:

2W = 20

divide both sides by 2:

W = 10

The width of the yard whose length is 27 yards and perimeter is 74 yards is evaluated to be 10 yards

For a rectangle with length and width L and W units, we get:

Perimeter of the rectangle = [tex]2(L + W) \: \rm units[/tex]

For this case, let we assume that:

The width of the considered rectangular field = W yards

Then, as we're provided that:

Putting these in the formula for perimeter of a rectangle, we get;

[tex]Perimeter = 2( L + W)\\74 = 2(27 + W)\\\\\text{Dividing both the sides by 2}\\\\\dfrac{74}{2} = \dfrac{2(27+W)}{2}\\\\37 = 27 + W\\\\\text{Subtracting 27 from both the sides}\\\\37 - 27 = W\\W = 10 \: \rm yards[/tex]

Thus, the width of the yard whose length is 27 yards and perimeter is 74 yards is evaluated to be 10 yards

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Answer:

The answer is D

Step-by-step explanation:

V= 5,000(1.035)*

Answer:

a) ≈ 0.1

b) ≈ 0.2

c) ≈ 0.9

Step-by-step explanation:

GIVEN :-

TO FIND :-

FACTS TO KNOW BEFORE SOLVING :-

SOLUTION :-

a) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{0.1}{0.995}[/tex] ≈ 0.1

b) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{-0.158}{-0.987} = 0.16 (appx)[/tex] ≈ 0.2

c) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{0.631}{0.776} = 0.81 (appx)[/tex] ≈ 0.9

Answer:

C

Step-by-step explanation:

The sum of the angles is 90

2x + x = 90

3x = 90

x = 30

the angle ABC is 2x, so it means that is the double of x, so it is 60 degrees

The result of the product of the given complex numbers as required to be determined is; Choice C; -5 + 14i.

It follows from the task content that the result of the product of the given complex numbers is to be determined.

On this note, since the required product to be evaluated is; (–4 + i) (2 – 3i).

We can therefore multiply as follows;

-8 + 12i + 2i - 3i².

However, it is noteworthy to know that; i² = -1.

Hence, we have that;

-8 + 14i + 3

= -5 + 14i

On this note, it follows that the result of the product of complex numbers as required is; -5 + 14i.

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The area of a shape is the amount of space, the shape can occupy. The equation to calculate the value of x is: [tex](e)\ x^2 + 11x -42= 0[/tex]

The space on the border is given as:

[tex]Top = 2[/tex]

[tex]Others = 3[/tex]

So, the dimension of the sheet of paper is:

[tex]Length = x + 2 + 3[/tex]

[tex]Length = x + 5[/tex]

[tex]Width = x + 3 + 3[/tex]

[tex]Width = x + 6[/tex]

The area of the sheet is then calculated as follows:

[tex]Area= Length \times Width[/tex]

[tex]Area= (x + 5) \times (x + 6)[/tex]

Open brackets

[tex]Area= x^2 + 5x + 6x + 30[/tex]

[tex]Area= x^2 + 11x + 30[/tex]

From the question, we understand that the area of the sheet is [tex]72cm^2[/tex]

So, the equation becomes

[tex]x^2 + 11x + 30 = 72[/tex]

Subtract 72 from both sides

[tex]x^2 + 11x + 30 -72= 0[/tex]

[tex]x^2 + 11x -42= 0[/tex]

Hence,

[tex](e)\ x^2 + 11x -42= 0[/tex] can be used to calculate the value of x

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According to the question the angle between right angle triangle hence the   M∠1 = [tex]90^{0}[/tex] .

90 degrees or a straight angle is always one angle. The hypotenuse is the side that has an angle of 90° on it. Always, the hypotenuse is the longest side. The remaining two inner angles add up to a total of 90°.

Right triangles are triangles with one of the internal angles at a right angle of 90 degrees. Since a triangle's three interior angles sum up to 180 degrees, a right triangle's three interior angles must always add up to 90 degrees since one of them is always 90 degrees (they are complementary).

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Question: If the dimensions of the following cylinder are doubled, what factor will the surface area change by?

8

6

4

2

Answer: i think it is 8 but i will update it if not i am on the test

If the dimensions of the cylinder are doubled, then by 4 factor the surface area changed

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

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.

The radius of cylinder is r=8 inches

Height is 0.5 feet.

Surface area of cylinder=2πr(r+h)

We know that 0.5feet=6 inches

Suface area of original cylinder=2πr(r+h)

=2×π×8(8+6)

=224π

Now the dimensions are doubled ,so r=16 inches , h=12 inches

Suface area of changed cylinder=2πr(r+h)

=2π×16(16+12)

=32π×(28)

=896π

=4(224π)

Hence by 4 factor the surface area is changed.

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Answer:

-3

Step-by-step explanation:

i hope this helps

Given:

The function is:

[tex]y=x+2[/tex]

To find:

The inverse of the given function.

[tex]y=x+2[/tex]

Solution:

We have,

[tex]y=x+2[/tex]

Step 1: Interchange x and y.

[tex]x=y+2[/tex]

Step 2: Solve to y.

[tex]x-2=y[/tex]

[tex]y=x-2[/tex]

Therefore, the inverse of the given function is [tex]y=x-2[/tex].

Answer:

Shift down 15 units

Step-by-step explanation:

the number on the right is the one that determines where the line intersects through the y axis

Answer:

No because 9.307 is less than due the facts that the seven in 9.307 is in the thousandth while the seven in 9.37 is in the hundredths

Answer: in explanation

Step-by-step explanation

Sandi can perform  1/9 of the task in a day

Eva can perform 1/5 of the task in a day

Working together, they can perform

                                                            1/9 + 1/5 of the task per day

                                                            = 5/45 + 9/45 = 14/45 of the task in a day

or                                                             45/14 days in the task = 3.2 days

So

          It would take about 3.2 days to complete the task working togethe

Answer:

Step-by-step explanation:

Formula

t = 1.06 * p

Givens

p = 8.5

Solution

t = 1.06 * 8.5

t = 9.01

Answer: 125y³

To rise a product to a power, rise each factor to that power:

(5y)³ = 5³y³ = 125y³

Answer:

transmission   absorption

Step-by-step explanation:

This is because the sound of the foot striking the floor is being transmitted through the air. The sun's light is absorbed when it strikes the sidewalk.

What is absorption and transmission?

Absorption is the process or action by which one thing absorbs or is absorbed by another.

The act of sending something, such as a cold or a message, or the component of a machine that transfers power from the engine to the moving parts is known as transmission.

Because of the air pressure, people can hear when their foot strikes the ground. In a similar manner, when sunlight strikes a sidewalk, it warms up as a result of absorbing the heat.

Therefore, the first statement is transmission and second statement is absorption.

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Answer:

? = -1/2    dark gray box = - 1

y = -1/2 x - 1       or

y = -0.5x - 1

Step-by-step explanation:

The place to start is at 0.

When x = 0 then y = - 1

That means that the second box (the dark gray one) is - 1

So far what you know about the equation is

y = ?x - 1

We need to check two more points.

x =  4

y =  - 3

- 3 = ? 4 - 1             Add 1 to both sides

-3 +1 = ?4 - 1 + 1     Combine   The -1 and + 1 Cancel

-2 = ?4                   Divide by 4

-2/4 = ?

?  = -1/2 or - 0.5

Now we need 1 more point to check the result

Let x = 2. Do we get - 2 for y

y = -1/2 * 2 - 1

y = -1 - 1

y = - 2       just as it should

Answer: Let n be the number of members in the Science Club.

On the first day, the total cost for transportation plus the cost of tickets is 60 + (15n) dollars.

On the second day, the total cost for transportation plus the cost of tickets is 95 + (12n) dollars.

So, the total cost for both days is (60 + 15n) + (95 + 12n) = 155 + 27n dollars.

The expression to represent the total cost for two days for the n members of the club is 155 + 27n dollars.

This equation represents the total cost for the transportation, planetarium and geology museum for 2 days for the n members in the club.

It should be noted that this is the monetary representation and it might vary depending on other factors, such as group discounts.

Step-by-step explanation:

Answer:

(n x 27)+155

Step-by-step explanation:

15 +12 = 27

Each member pays $27 for the tickets so we multiply it by the number of members.

95 + 60 = 155

The members pay $155 in total for transportation.

Answer:

A cute

Step-by-step explanation:

1. The length of the altitude is 15 units.

2. The perimeter of trapezoid ABCD is 132 units.

An altitude is the vertical height of a given object from the sea level. This is majorly a height reached by an object to the sea level as a reference.

The perimeter of a trapezoid is the sum of all its sides.

From the question;

1. To determine AE,

DE = (DG - EF)/ 2

     = (22 - 6)/ 2          (since AB = EF = 6)

     = 8

DE = 8 units

The altitude AE can be determined by applying the Pythagorean theorem to triangle ADE. So that;

/hyp/^2 = /opp/^2 + /adj/^2

AD^2 = DE^" + AE^2

17^2 = 8^2 + AE^2

289 = 64 + AE^2

AE^2 = 225

AE = 15

Thus the length of the altitude is 15 units.

2. To determine the perimeter of the trapezoid, we have;

AE = (AD - EF)/ 2

     = (58 - 16)/ 2           (since BC = EF = 16)

     = 21

AE = 21 units

So that from triangle ABE, applying the Pythagorean theorem to determine the value of AB, we have;

/hyp/^2 = /opp/^2 + /adj/^2

AB^2 = BE^2 + AE^2

         = 20^2 + 21^2

AB = 841^1/2

AB = 29

Perimeter of the trapezoid = 29 + 16 + 29 + 58

                       = 132 units

Thus, the perimeter of the trapezoid is 132 units.

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Therefore , the solution of the problem of expression comes out to be

9.12 x 10 ^-2.

An algebraic expression must be checked via replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is comparable to 6, since 6 + 6 equal 12. If we know the values of the variables, we can replace them with those values and evaluate the expression.

Here,

Given : 0.0912 in scientific notation

=> 9.12 /100

By using scientific notation

=> 9.12 × 10^-2

=> 9.12 x 10 ^-2

So, we get 9.12 x 10 ^-2 as the scientific notation for the given expression

Therefore , the solution of the problem of expression comes out to be

9.12 x 10 ^-2.

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Answer:

( a + 2 ) ( x - y )

Step-by-step explanation:

2 ( x - y ) - a ( y - x )

= 2 ( x - y ) + a ( x - y )

= ( 2 + a ) ( x - y )

= ( a + 2 ) ( x - y )

Hence factorised.

Answer:

Step-by-step explanation:

We know that:

So the value of the expression is:

Answer:

75°

Step-by-step explanation:

Recall the common trigonometric angles:

  [tex]\sin 30^{\circ}=\dfrac{1}{2}[/tex]

  [tex]\tan 45^{\circ}=1[/tex]

Arcsin is the inverse of sin.

Arctan is the inverse of tan.

[tex]\implies \arcsin \left(\dfrac{1}{2}\right)=30^{\circ}[/tex]

[tex]\implies \arctan (1) = 45^{\circ}[/tex]

Therefore:

[tex]\implies \arcsin \left(\dfrac{1}{2}\right)+\arctan (1) = 30^{\circ}+ 45^{\circ}=75^{\circ}[/tex]

Step-by-step explanation:

please refer to the 3 pages of sketch for details