The path of a projectile launched from a 20-ft-tall tower is modeled by the equation y = -5x2 + 40x + 20. What is the maximum height, in meters
reached by the projectile?

Answer:

B) 1.4

Step-by-step explanation:

The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.

sin(B)=opp/hyp

The maximum length of the seesaw is 1.4 meters

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let h represent the length of the seesaw, hence using trigonometric ratio:

sin(45) = 1 / h

h = 1.4 meters

The maximum length of the seesaw is 1.4 meters

Find out more on Trigonometric ratio at: https://brainly.com/question/1201366

Answer:

Part 1;

(0, 0)

Part 2;

(0, 2.5)

Step-by-step explanation:

Part 1

The given system of inequalities is presented as follows;

f(x) < x + 4; f(x) > -x - 3; and f(x) < 5

We check each of the points as follows;

The point (0, 0) in the inequality f(x) < x + 4, gives;

f(0) < 0 + 4

f(0) = 0 < (is less than) 0 + 4 = 4

Therefore, (0, 0) is a solution of the inequality f(x) < x + 4

The point (0, 0) in the inequality f(x) > -x - 3, gives;

f(0) < -0 - 3

f(0) = 0 > (is larger than) -0 - 3 = -3

Therefore, (0, 0) is a solution of the inequality f(x) > -x - 3

The point (0, 0) in the inequality f(x) < 5, gives;

f(0) < 5

f(0) = 0 < (is less than) 5

Therefore, (0, 0) is a solution of the inequality f(x) < 5

The point (-6, 0) in the inequality f(x) > -x - 3, gives;

f(-6) = -6 - 3 = 3

The point (-6, 0) with y = 0 < (is less than) f(-6) = 3, therefore (-6, 0) is not a solution to (not included in the graph of) the inequality f(x) > -x - 3 and therefore to the system of inequalities because at x = -6, the values of f(x) > -x - 3 are larger than 3

The point (-3, 4) in the inequality f(x) < x + 4, gives;

f(-3) = -3 + 4 = 1

The point (-3, 4) with y = 4 < (is larger than) f(-2) = 1, therefore (-3, 4) is not a solution to (not included in the graph of) the inequality f(x) < x + 4  and therefore to the system of inequalities because at x = -3, the values of f(x) < x + 4 are less than 1

The point (4, 6) is not a solution to (not included in the graph of) the inequality f(x) < 5  and therefore to the system of inequalities because f(x) is larger than 5 for all x

Therefore, the point which is part of the solution set of the system of inequalities is (0, 0)

Part 2

The given system of inequalities are, f(x) ≥ 2·x + 2; f(x) ≤ -4·x + 3; and f(x) ≤ 6·x + 5

Plotting the given system of inequalities on MS Excel the point which is part of the solution is given by points which are within the triangular intersection area of the three inequalities, with coordinates, (1/6, 7/3), (-3/4, 1/2), and (-1/5, 19/5)

Therefore, the points, (0, 0), (-2.5, 0) are not solutions because, the y-value of the solution area are all higher than the line y = 0

The point (0. 6.5) is not a solution because the points in the triangular solution area all have x-values lesser than x = 6.5

The point which is part of the solution by examination is the point (0, 2.5) which is a point between the lines y = 19/5 = 3.8, y = 1/2, x = -3/4, and x = 1/6.

Answer:

augmented

Step-by-step explanation:

In the field of linear algebra, the augmented matrix is defined as the matrix that is [tex]\text{obtained by appending}[/tex] the given columns of any two given matrices, that is usually for the [tex]\text{purpose of performing the same elementary row operations on each of the given matrices. }[/tex]

Here, each row forms an equation having a constant and the column have the  coefficients for the single variable.

Thus an augmented matrix is obtained from a system of linear equation in matrix.

Answer:

Step-by-step explanation:

Jazmine they are asking about the absolute value signs,   see how that first one has a negative 6 for the solution?  well the absolute value of the other side of that equal sign will never be a negative 6  ,  see now?  so that first answer has no solution  :)

Answer:

Value of x:

[tex]{ \tt{(13x + 9) + (5x + 9) = 180 \degree}} \\ { \tt{18x + 18 = 180 }} \\ { \tt{18x = 162}} \\ { \tt{x = 9}} \\ [/tex]

Angle m‹6:

[tex]{ \boxed{ \tt{m \angle6 = (5x + 9) \degree}}} \\ { \tt{m \angle6 = (5 \times 9) + 9}} \\ { \tt{m \angle6 = 54 \degree}}[/tex]

Answer:

B. 54 degrees

Step-by-step explanation:

Set up an equation that equals 180 degrees because a line is 180 degrees:

(13x+9)+(5x+9)=180

Solve for x:

x=9

Substitute 9 in 5x+9:

5(9)+9

Solve.

54

Since angle 6 is complementary, it is the same as the 7th angle.

So the answer is B, 54 degrees.

Hope this helps!

Step-by-step explanation:

316 days when you get the idea the most important thing is that the people who are looking for the right reasons why you

Answer:

[tex]y = 5x + 3[/tex]

Step-by-step explanation:

Given

[tex]y = 3x - 2[/tex]

[tex]10(x + \frac{3}{5}) = 2y[/tex]

Required

The second equation in slope intercept form

We have:

[tex]10(x + \frac{3}{5}) = 2y[/tex]

Divide both sides by 2

[tex]5(x + \frac{3}{5}) = y[/tex]

Open bracket

[tex]5x + 3 = y[/tex]

Rewrite as:

[tex]y = 5x + 3[/tex]

Hence, the equation in slope intercept form is: [tex]y = 5x + 3[/tex]

Answer: I agree with the other person

Step-by-step explanation:

Answer:

Step-by-step explanation:

If a point (x, y) is translated by 4 units horizontally right and 1 unit upwards, coordinates of the image point will be,

(x, y) → (x + 4. y + 1)

Therefore, vertices of the image triangle ABC will be,

A(2, 2) → A'(2+4, 2+1)

           → A'(6, 3)

B(5, -1) → B'(5+4, -1+1)

           → B'(9, 0)

C(1, -2) → C'(1+4, -2+1)

           → C'(5, -1)

Then reflected across y-axis.

Rule for the reflection across y-axis will be,

(x, y) → (-x, y)

A'(6, 3) → A"(-6, 3)

B'(9, 0) → B"(-9, 0)

C'(5, -1) → C"(-5, -1)

Answer:

A"(-6, 3)

B"(-9, 0)

C"(-5, -1)

Step-by-step explanation:

Answer:

C. 4

Step-by-step explanation:

Use the slope formula y2-y1 / x2-x1

6+2/3-1

8/2

4

So, the answer is C. 4.

Step-by-step explanation:

To Find :-

Solution :-

Using Distance Formula ,

> d = √{ ( 2-3)² + (0-1)² + (-1-4)² }

> d = √{ (-1)² + (-1)² + (-5)² }

> d = √{ 1 + 1 + 25 }

> d = √26 .

Using midpoint formula ,

> m = ( 2+3/2 , 0+1/2 , -1+4/3 )

> m = ( 5/2 , 1/2 , -3/3 )

> m = ( 2.5 , 0.5 , -1 )

Answer:

sei lá, pergunta pra tua mãe

Answer:

in scientific notation, the expression can be written as 6.237 x 10⁶

Step-by-step explanation:

Given;

6.3×10 to the second power times 9.9×10 to the 3rd power

Using scientific notation, it can be interpreted as;

[tex](6.3 \times 10^2) \times (9.9 \times 10^3)[/tex]

This can be simplified as;

[tex](6.3 \times 10^2) \times (9.9 \times 10^3) = (6.3\times 9.9)\times 10^{2+3}\\\\= 62.37\times 10^5 = 6.237\times 10^6[/tex]

Therefore, in scientific notation, the expression can be written as 6.237 x 10⁶

Answer:

I would say 5 kg because you get more kg with a little bit more money added

Hi there!

[tex]\large\boxed{A. \text{ } 7}[/tex]

The following trapezoidal theorem states that:

Middle segment = average of top and bottom side

Thus:

M = 1/2(b1 + b2)

21 - x = 1/2(17 + 11)

Solve:

21 - x = 1/2(28)

21 - x = 14

Subtract 21 from both sides:

-x = 14 - 21

-x = -7

Multiply both sides by -1:

x = 7

Answer:

= 1728km2

Step-by-step explanation:

From the formula A = PRT/100%

Where; A is final

P is initial

T is time taken

R is the rate

Therefore A = 3600 × (6/100) × 8

= 1728km2

═══════ღ❦ღ══╮

[tex]\boxed{ \sf{Answer}} [/tex]

↦ First find the value of x

[tex]27x = 45263514282 \\ x = \frac{45263514282}{27} \\ x = 1676426454.89[/tex]

↦ Now, find the value of 200x

[tex]x = 1676426454.89 \\ 200x = 200 \times 1676426454.89 \\ 200x = 335285290978[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Given that,

→ 27x = 45263514282

Then we have,

To find the required value of 200x.

Before that,

find the required value of x.

→ 27x = 45263514282

→ x = 45263514282/27

→ [x = 1676426454.89]

Now we can,

Solve for the value of 200x.

→ 200x

→ 200 × (x)

→ 200 × (1676426454.89)

→ 335285290978

Hence, 200x is 335285290978.

Answer:

1/64 is 0.015625 in decimals

Answer: The slope is 2 -Please mark brainliest

1. Find the X and Y values of each point

X1: 1

X2: -1

Y1: 3

Y2: -1

2. Subtract X1 from X2 and Y1 from Y2

Y: -1-3=-4

X: -1-1=-2

3. Divide the X value by the Y value

-4/-2=2

The slope of the line shown on the coordinate plane is 2.

Answer:

2

Step-by-step explanation:

(X1,Y1)=(1,3)

(X2,y2)=(-1,-1)

slope(m)=y2-y1/x2-x1

= -1-3/-1-1

= -4/-2

= 2

Answer:

Step-by-step explanation:

1,008/1.8=10,080/18

18)10080(560

     90

    -

   ----------

      108

      108

     -

   ------------

           0

 ---------------

Step-by-step explanation:

If the volume of a cubical room is 2700 cm³ .

l³=2700

l=3 (100)⅓

Answer: $268.75

Step-by-step explanation:

First, find the amount he earned from his sales:

1500(0.0125) = $18.75

Next, add that to his monthly salary:

$250 + $18.75 = $268.75

Answer:

8050 m²

Step-by-step explanation:

We can divide the diagram up into two components: a rectangle with a width of 60 m and a height of 80 m, and a triangle with a base of 130 m (190 - 60) and a height of 50 m (80 - 30).

The area of the rectangle:

A = lw

A = 60 m (80 m)

A = 4800 m²

The area of the triangle:

A = 1/2 b*h

A = 1/2 (130 m) (50 m)

A = 1/2 (6500 m²)

A = 3250 m²

Now, we can add the areas of the two separate components:

A = 4800 m² + 3250 m²

A = 8050 m²

Answer:

x ≈ 60.6°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{IJ}{HI}[/tex] = [tex]\frac{3.9}{2.2}[/tex] , then

x = [tex]tan^{-1}[/tex] ([tex]\frac{3.9}{2.2}[/tex] ) ≈ 60.6° ( to the nearest tenth )

Answer:

2:5

Step-by-step explanation:

10:25 = 10/25 = 2/5 = 2:5

Answer:

2:5

Step-by-step explanation:

divide both of them by 5

10 divided by 5 is 2

25 divided by 5 is 5

Answer:

4w-8

Step-by-step explanation:

4(w-2)

(4*w)-(4*2)

4w-8

Answer:

4w-8

Step-by-step explanation:

4(w - 2)

Distribute

4*w - 4*2

4w-8

Answer:

$21

Step-by-step explanation:

Find the cost of the wristband that took an hour and a half to make:

2(1.5) + 7

= 10

Find the cost of the one that took 2 hours to make:

2(2) + 7

= 11

Add together the prices:

10 + 11

= 21

So, it will cost $21

Answer:

the function is the solution is done using the operation

Answer:

[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}[/tex]

Step-by-step explanation:

Given

[tex]y=c_1e^x +c_2e^{-x[/tex]

[tex]y(1) = 0[/tex]

[tex]y'(1) =e[/tex]

Required

The solution

Differentiate [tex]y=c_1e^x +c_2e^{-x[/tex]

[tex]y' = c_1e^x - c_2e^{-x}[/tex]

Next, we solve for c1 and c2

[tex]y(1) = 0[/tex] implies that; x = 1 and y = 0

So, we have:

[tex]y=c_1e^x +c_2e^{-x[/tex]

[tex]0 = c_1 * e^1 + c_2 * e^{-1}[/tex]

[tex]0 = c_1 e + \frac{1}{e}c_2[/tex] --- (1)

[tex]y'(1) =e[/tex] implies that: x = 1 and y' = e

So, we have:

[tex]y' = c_1e^x - c_2e^{-x}[/tex]

[tex]e = c_1 * e^1 - c_2 * e^{-1}[/tex]

[tex]e = c_1 e - \frac{1}{e}c_2[/tex] --- (2)

Add (1) and (2)

[tex]0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2[/tex]

[tex]e = 2c_1e[/tex]

Divide both sided by e

[tex]1 = 2c_1[/tex]

Divide both sides by 2

[tex]c_1 = \frac{1}{2}[/tex]

Substitute [tex]c_1 = \frac{1}{2}[/tex] in [tex]0 = c_1 e + \frac{1}{e}c_2[/tex]

[tex]0 = \frac{1}{2} e+ \frac{1}{e}c_2[/tex]

Rewrite as:

[tex]\frac{1}{e}c_2 = -\frac{1}{2} e[/tex]

Multiply both sides by e

[tex]c_2 = -\frac{1}{2} e^2[/tex]

So, we have:

[tex]y=c_1e^x +c_2e^{-x[/tex]

[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}[/tex]

[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}[/tex]