A model rocket is launched from the top of a building. The height (in meters) of the
rocket above the ground is given by f (t) = -4t² + 16+ + 12 where t is the time (in
seconds) since the rocket was launched.

Answer:

[tex](f + g)(x) = 7 - 6x[/tex] --- (1)

[tex](f - g)(x) = 6x - 1[/tex] -- (2)

[tex](f . g)(x) =4(5^x)[/tex] ---- (3)

[tex](f / g)(x) = \frac{4}{5^x}[/tex] ----- (4)

[tex](f + g)(x) = -7x-7[/tex] --- (5)

[tex](f - g)(x) = 9x+ 9[/tex] --- (6)

[tex](f . g)(x) = (-8)(x+1)^2[/tex] --- (7)

[tex](f / g)(x) = -\frac{1}{8}[/tex] ----- (8)

[tex]F(t) = \frac{9}{5}t^2 + 32[/tex] ---- (9)

[tex]T(t) = (t - 2)^2 - 4[/tex] --- (10)

Step-by-step explanation:

Given

[tex]f(x) = 3[/tex]

[tex]g(x) = 4 - 6x[/tex]

Solving (1): (f + g)(x)

[tex](f + g)(x) = f(x) + g(x)[/tex]

So, we have:

[tex](f + g)(x) = 3 + 4 - 6x[/tex]

[tex](f + g)(x) = 7 - 6x[/tex]

Solving (2): (f - g)(x)

[tex](f - g)(x) =f(x) - g(x)[/tex]

So, we have:

[tex](f - g)(x) =3 - (4 - 6x)[/tex]

[tex](f - g)(x) =3 - 4 + 6x[/tex]

[tex](f - g)(x) =-1 + 6x[/tex]

[tex](f - g)(x) = 6x - 1[/tex]

Given

[tex]f(x) = 4[/tex]

[tex]g(x) = 5^x[/tex]

Solving (3): (f . g)(x)

[tex](f . g)(x) =f(x) * g(x)[/tex]

So, we have:

[tex](f . g)(x) =4 * 5^x[/tex]

[tex](f . g)(x) =4(5^x)[/tex]

Solving (4): (f / g)(x)

[tex](f / g)(x) = \frac{f(x)}{g(x)}[/tex]

So, we have:

[tex](f / g)(x) = \frac{4}{5^x}[/tex]

Given

f(x) = x + 1

g(x) = -8 - 8x

Solving (5): (f + g)(x)

[tex](f + g)(x) = f(x) + g(x)[/tex]

So, we have:

[tex](f + g)(x) = x + 1 -8-8x[/tex]

Collect Like Terms

[tex](f + g)(x) = x -8x+ 1 -8[/tex]

[tex](f + g)(x) = -7x-7[/tex]

Solving (6): (f - g)(x)

[tex](f - g)(x) = f(x) - g(x)[/tex]

So, we have:

[tex](f - g)(x) = x + 1 -( -8-8x)[/tex]

[tex](f - g)(x) = x + 1 +8+8x[/tex]

Collect Like Terms

[tex](f - g)(x) = x +8x+ 1 +8[/tex]

[tex](f - g)(x) = 9x+ 9[/tex]

Solving (7): (f . g)(x)

[tex](f . g)(x) = f(x) . g(x)[/tex]

So, we have:

[tex](f . g)(x) = (x+1) . (-8 - 8x)[/tex]

Factorize

[tex](f . g)(x) = (x+1) .(-8) (1 + x)[/tex]

Rewrite as:

[tex](f . g)(x) = (x+1) .(-8) (x+1)[/tex]

[tex](f . g)(x) = (-8)(x+1) (x+1)[/tex]

[tex](f . g)(x) = (-8)(x+1)^2[/tex]

Solving (8): (f / g)(x)

[tex](f / g)(x) = \frac{f(x)}{g(x)}[/tex]

So, we have:

[tex](f / g)(x) = \frac{(x+1)}{(-8-8x)}[/tex]

Factorize

[tex](f / g)(x) = \frac{(x+1)}{-8(1+x)}[/tex]

[tex](f / g)(x) = \frac{1}{-8}[/tex]

[tex](f / g)(x) = -\frac{1}{8}[/tex]

Solving (9):

From the question, we have that:

[tex]F(c) = \frac{9}{5}c + 32[/tex]

[tex]C(t) = t^2[/tex]

Required

Determine function F in terms of c

The implication of this question is to solve for [tex]F(c(t))[/tex]

If [tex]F(c) = \frac{9}{5}c + 32[/tex] and [tex]C(t) = t^2[/tex],

Then

[tex]F(c(t)) = \frac{9}{5}*t^2 + 32[/tex]

[tex]F(c(t)) = \frac{9}{5}t^2 + 32[/tex]

This can be rewritten as:

[tex]F(t) = \frac{9}{5}t^2 + 32[/tex]

Solving (10):

[tex]T(h) = h^2 - 4[/tex]

[tex]h(t) = t - 2[/tex]

Required

Find [tex]T(h(t))[/tex]

If [tex]T(h) = h^2 - 4[/tex]  and   [tex]h(t) = t - 2[/tex], then

[tex]T(h(t)) = (t - 2)^2 - 4[/tex]

This is gotten by substituting t -2 for h

The solution can be rewritten as:

[tex]T(t) = (t - 2)^2 - 4[/tex]

Answer: B

Step-by-step explanation:

Answer: 8/27

Step-by-step explanation:

Just evaluate the equation.

Do it in this order: Parenthesis, Exponents, Multiply/Divide, Add/Subtract.

So:

16/81 = 16/81

16/81 To the Power of 3/4 = 0.2^0.75 = 8/27

Answer:

x = 280/17 = 16.471

Step-by-step explanation:

Two triangles are congruent if two pairs of corresponding angles and included sides are congruent.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

In order to prove △ABC ≅ △DBC by SAS. Then the additional information must be given will be

SAS: Two triangles are congruent if two pairs of corresponding sides and included angles are congruent.

More about the triangle link is given below.

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image ????? please attach image and try again

Answer:

x = 30

Step-by-step explanation:

The interior angles of a triangle must always add up to 180.

2x + 2x + 3x - 30 = 180

Add 30 to both sides to seperate variables.

2x + 2x + 3x = 210

Combine like terms.

7x = 210

Divide by 7 to isolate x.

x = 30

Step-by-step explanation:

answer A should be correct

Answer:

go to jesus

Step-by-step explanation:

put both hands together and pray we know your struggling

Answer: Yes. Dominic is correct

Step-by-step explanation:

We are informed that Two fifth of the students wrote a report. This also means that (2/5 × 100) = 40% = 0.4 wrote a report and 0.6 of the students gave a presentation.

From the decimals gotten, we can see that 0.6 is more than 0.4. Therefore, more students gave a presentation. This implies that Dominic is correct.

Answer:93

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

By the rule of opposite angles, we can determine that x=120 because:

AB is parallel to CD

120 degree angle (let's call it Y) is on AB

X (we can see that it is obtuse) is on CD

So, Y is congruent to X, vice versa, so x=120

hope this helps! :)

ibrahim

Answer:

8.5

Step-by-step explanation:

X^2 = 9^2 - 3^2

x^2 = 81 - 9

x^2 = 72

x = √72

x = 8.485

9514 1404 393

Answer:

  (13.06, 16.41)

Step-by-step explanation:

Any point not on a perpendicular bisector of the line between towns will be closer to one town than the other. So, the intersection of perpendicular bisectors will be the equidistant from all towns. That point is the circumcenter of the circle circumscribing the triangle with the towns as its vertices. This can be found as the intersection of two perpendicular bisectors of the segments between the towns.

The midpoint of AB is ...

  (A +B)/2 = ((15, 3) +(25, 10))/2 = (40, 13)/2 = (20, 6.5)

The midpoint of AC is ...

  (A +C)/2 = ((15, 3) +(0, 20))/2 = (15, 23)/2 = (7.5, 11.5)

__

The differences between points are ...

  B -A = (25, 10) -(15, 3) = (10, 7)

  C -A = (0, 20) -(15, 3) = (-15, 17)

Then the perpendicular bisector equations can be written as ...

  bisector of AB  ⇒  10(x -20) +7(y -6.5) = 0

     10x +7x -245.5 = 0

  bisector of AC  ⇒  -15(x -7.5) +17(y -11.5) = 0

     -15x +17y -83 = 0

These have coefficients that aren't particularly nice, so a method similar to Cramer's Rule is suitable for solving this pair of equations. Using the "cross multiplication method", we have ...

  x = (7(-83) -17(-245.5))/(10(17) -(-15)(7)) = 3592.5/275 = 13 7/110 ≈ 13.06

  y = (-245.5(-15) -(-83)(10))/275 = 4512.5/275 = 16 9/22 ≈ 16.41

The point as far as possible from each town within the boundary of the island has coordinates (13.06, 16.41).

_____

Further detail regarding the solution

Here, we have written the equation for the perpendicular bisector this way. The difference in coordinates between points R and S can be called ...

  R -S = (∆x, ∆y)

The midpoint of segment RS can be called ...

  (R +S)/2 = (h, k)

Then the line that is a perpendicular bisector of RS can be written as ...

  ∆x(x -h) +∆y(y -k) = 0

This is the form that is used above.

__

The "cross multiplication method" for solving a pair of general-form linear equations ...

  ax +by +c = 0

  dx +ey +g = 0

will give the solution as ...

  1/(ae -db) = x/(bg -ec) = y/(cd -ga)

If you write the coefficients in two rows of four, the pattern of products and differences is easy to see.

  [tex]\left[\begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}\right][/tex]

Answer:

A

Step-by-step explanation:

That's the only one that makes sense

Answer:

It's either A or C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

4800

Step-by-step explanation:

A day consist of 24 hours. Half of 24 is 12. 4 x 13 = 12 so 1600 x 3 = 4800.

Answer:

b

Step-by-step explanation:

Answer:

14 cars, 42 vans

Step-by-step explanation:

can divide the total by 4, since the number of cars is just 3x the number of vans

x+3x=56

4x=56

56/4

14 cars times 3 plus the original 14

There are 14 cars times 3 plus the original 14.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given Between 7 and 8 o'clock, there were 56 vehicles in the zoo parking lot. There were 3 times as many vans as cars.

Then it can divide the total by 4, since the number of cars is just 3x the number of vans.

x+3x=56

4x=56

56/4

Therefore, there are 14 cars times 3 plus the original 14.

Learn more about the unitary method here;

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Answer:

1/5th

Step-by-step explanation:

trust me. ik how to do slopes

Answer:

B. 135

Step-by-step explanation:

According to corresponding angles answer is b

135 is congruent to angle 1 and angle 1 is congruent to angle 5

so if angle 1 is 135 then angle 5 is 135

Brainliest please

Hope this helps

Answer:

d.

Step-by-step explanation:

straight angle = 180 degress

135+45=180

Answer:

$2271.54

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Compounded Interest Formula: [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

Step-by-step explanation:

Step 1: Define

P = 800.00

r = 0.11

n = 1

t = 10

Step 2: Find A

Answer:

it's 8x

hope i could help :)

The value is less than 1 and the impact of the negative exponent is that it moves the decimal point to the left

Standard form can be defined as a mathematical way of writing large or too small numbers in a defined manner.

Given the standard form;

8.5 × 10–3

The negative exponent (-3) indicates an addition of three zeros ruled out from the start.

It could be written as;

0. 0085

This is 0. 9915 less than the value of 1

The impact of the negative value is that it moves the decimal point to the left.

Thus, the value is less than 1 and the impact of the negative exponent is that it moves the decimal point to the left

Learn more about standard form here:

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Answer:

Wheres the question then i'll help

Step-by-step explanation:

Step-by-step explanation:

15:30

Divide by 5

3:6

1:2

Answer:

3:4

Step-by-step explanation:

speed of cycle=15 km pers

speed of scooter=30 km per s

Now,

Ratio of speed= distance travelled ÷time taken

= (15+30)÷60 (1 hour=60 min)

= 45÷60

= 3÷4

= 3:4

:: The answer is 3:4.

The midpoint of the line segment CD whose coordinates (-2,-4) and D (6,2) will be (2, -1).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoint of the segment CD is given as C(-2, -4) and D(6, 2). Then the mid-point of the line segment CD will be

(x, y) = [(-2 + 6) / 2, (-4 + 2) / 2]

(x, y) = (4/2, -2/2)

(x, y) = (2, -1)

The midpoint of the line segment CD whose coordinates (-2,-4) and D (6,2) will be (2, -1).

More about the Mid-point link is given below.

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Answer: O f)= (x+ 6)(x + 6)

Hope this helps :)