Six times the cube of a number

The equation that models the path of the ball is y =  -0.05·x² + 5·x.

Given,

The distance where the football landed from where it was kicked = 100 feet

The maximum height that the football reached =  125 feet

We have to write an equation that models the path of the ball while it was in the air.

The path may be parabola.

So, equation is like:

y = a·(x - h)² + k

Where;

(h, k) = The coordinate of the vertex (which is the coordinates of the highest point reached by the ball)

Therefore, taking the x-coordinate of the highest point reached by the ball as midpoint of the horizontal distance moved by the ball, we have;

The x-coordinate of the midpoint of the horizontal distance moved by the ball = (50, 0)

We have;

The coordinate of the highest point reached by the ball = (50, 125)

Therefore;

(h, k) = (50, 125)

Substituting the above values in the equation of the parabola gives;

y = a·(x - 50)² + 125

At x = 100, y = 0, which gives;

0 = a·(100 - 50)² + 125 = a·2500 + 125

0 = a·2500 + 125

a = -125/2500 = -0.05

Therefore, we have;

y = a·(x - h)² + k = y = -0.05 × (x - 50)² + 125 = -0.05·x² + 5·x - 125 + 125

y  = -0.05·x² + 5·x - 125 + 125 = -0.05·x² + 5·x

y =  -0.05·x² + 5·x

The equation that models the path of the ball is y =  -0.05·x² + 5·x.

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Answer:

(3+9)/(5-2)x5 = 20

Step-by-step explanation:

It's a rather tedious type of task, because there's no simple way to solve them, except kind of by brute force or by trial and error. Here we can start by noticing x5 at the end, so if we can force everything before to be 4 it's gonna be dandy:

can we add brackets to 3+9/5-2 to be equal to 4 (because 20 / 5)?

fortunately, 3+9 is 4 times more than 5-2, so (3+9)/(5-2) = 4

so (3+9)/(5-2)x5=20 is a correct solution

The correct sequence of the steps required to construct the bisector of [tex] \angle{A}[/tex] is presented as follows;

The game given steps and their number of appearance in the question photo are;

1. Label the intersection of the arcs in the interior of the angle as point D.

2. Without changing the opening of the compass, place the point of the compass at point C and draw another arc in the interior of the angle

3. Place the point of the compass on point B and draw an arc in the interior of the angle

4. Use the straight edge to draw [tex] \overrightarrow{AD}[/tex]

5. Place the point of the compass at point A and draw an arc that intersects the sides of [tex] \angle{A}[/tex]. Label the points of intersection as points B and C.

The correct order of the steps required to construct the bisector of [tex] \angle{A}[/tex] is as follows;

Step 5 → Step 3 → Step 2 → Step 1 → Step 4

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Using trigonometric relations, we can see that the length of the wire is  1,454.5 ft.

We can think of this as a right triangle, such that the height of the tower is one of the legs, and the wire is the hypotenuse.

In this case, we know that the angle between the tower and the wire measures 55.4°, and the height is the adjacent cathetus to this angle.

Then we can use the relation:

cos(a) = (adjacent cathetus)/(hypotenuse)

Where:

a = 55.4°

adjacent cathetus = 600ft

hypotenuse = L = length of the wire.

Replacing that we get:

cos(55.4°) = 600ft/L

L = 600ft/cos(55.4°) = 1,454.5 ft

We conclude that the length of the wire is 1,454.5 ft.

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-120... I would be easier if you used a scientific calculator

Answer:   24

Step-by-step explanation:

[Solve brackets first]

[tex](-7--9)\\-7+9 = 2[/tex]

[Perform the multiplication]

[tex]8[/tex] x [tex]2 = 16[/tex]

[Finally do the Addition]

[tex]16 + 8 = 24[/tex]

General Rule:

Brackets Indices Division Multiplication Addition Subtraction

[tex]Negative + Negative = Positive \\Negative + Positive = Negative[/tex]

The area of a Dragon's kite with the given dimensions is 6 square feet.

Given that, team Dragon's kite is 4 feet long and 3 feet across.

We need to find how much fabric it takes to make their kite.

The area of a kite can be defined as the amount of space enclosed or encompassed by a kite in a two-dimensional plane. Like a square, and a rhombus, a kite does not have all four sides equal.

The area of a kite is half the product of the lengths of its diagonals. The formula to determine the area of a kite is Area = ½ × d1 × d2. Here d1 and d2 are long and short diagonals of a kite.

Now, the area of Dragon's kite = 1/2 × 4 × 3=6 square feet.

Therefore, the area of a Dragon's kite with the given dimensions is 6 square feet.

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Answer:

The height is 5.

Step-by-step explanation:

Find this answer here in this link!

This is the correct answer

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We have proved that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length by using a vector.

A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature. A quantity or phenomenon that just exhibits magnitude and no specific direction is referred to as a scalar. (Weight is the force produced by the acceleration of gravity acting on a mass.) Scalars include things like velocity, mass, electrical resistance, and hard disk storage space.

In the triangle ABC, D is the midpoint of AB, and E is the midpoint of AC.

Now, using the triangle rule for triangle ADE,

AE+AD = ED

And for triangle ABC,

CA+AB = CB

2AE+2AD = CB [as AD = 1/2AB and AE=1/2AC]

=> 2(AE+AD) = CB

=> 2ED = CB

=> ED = CB/2

We can write two vectors equal to each other with only difference in magnitude only when they are parallel, i.e., the angle between ED  and CB is 0.

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It will take the object 1/5 hour to travel 2 1/5 mi

The given parameters are

Speed = 9 4/5 mi/h

Distance = 2 1/5 mi

The time is calculated as

Time = Distance/Speed

So, we have

Time = (2 1/5)/(9 4/5)

Approximate the factors

Time = (2)/(10)

Evaluate

Time = 1/5

Hence, it will take the object 1/5 hour to travel 2 1/5 mi

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We get that the absolute inequality will be | x + 16 | < 8.

We are given two inequalities:

x < - 8 and  x > 24

We need to write one inequality by combining both the inequalities.

We know that:

x < - 8 means that x can have any value less than - 8

x ∈ ( - ∞ ,  - 8 )

Also, x > 24 means that:

x ∈ ( 24 , ∞ )

So, combining these, we get that:

x = ( - ∞ ,  - 8 ) U ( 24 , ∞ )

Inequality will be:

| x + 16 | < 8

Therefore, we get that the absolute inequality will be | x + 16 | < 8.

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Answer:

(0,-5)

(2,1)

5,3

Step-by-step explanation:

Answer:

(l) y=2x-2

(ll) y=4x+1

(lll) y=5x+13

(lV) y=-3x-6

(V) y=-5x-17

(Vl) y=(2/3)x-3

Answer:

56

Step-by-step explanation:

(1+2*3)^2+7

(1+6)^2+7

7^2+7

49+7

56

Answer:

Step-by-step explanation:

Using PEMDAS, first find the product of the parentheses. 2*3=6. 1+6=7. 7² is 49. 49+7=56.

Answer: 1.29 x 104 lbs.

Step-by-step explanation:

4.23 x 103 lbs. and 8.7 x 103 lbs.

4.23 x 103 + 8.7 x 103 =

4.23 x 10^3 + 8.7 x 10^3 =

(4.23+8.7) x 10^3 =

(4.23+8.70) x 10^3 =

(12.93) x 10^3 =

1.293 x 10 x 10^3 =

1.293 x 10^1 x 10^3 =

1.293 x 10^(1+3) =

1.293 x 10^4 =

1.293 x 10^4 = 1.29 x 104 lbs.

The total weights of the two animals in scientific notation is

13.32 x 10² lbs

What is scientific notation ?

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

According to the given question,

First animal weight 4.23 x 103 lbs

Second animal weigh 8.7 x 103 lbs

adding both the animal weights

= 4.23 x 103 + 8.7 x 103

= (4.23 + 8.7 ) x 103

= 12.93 x 103

= 1331.79 lbs

converting into scientific notation

= 13.3179 x 10² lbs  (rounding off)

≈ 13.32 x 10² lbs

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According to the statement if One x-intercept for a parabola is at the point (-4,0)  of the equation the other x-intercept for the parabola is (2, 0).

A parabola is an U-shaped mirror-symmetrical planar curve. It matches a variety of seemingly dissimilar mathematical formulations, all of which identify the same curves. A point and a line are two ways to describe a parabola.

Apollonius, who discovered numerous features of conic sections, is credited with the name "parabola." It signifies "application," referring to the "application of regions" notion, which, as Apollonius demonstrated, has a connection with this curve. Pappus is responsible for the focus-directrix attribute of the parabola as well as other conic sections.

given equation:  y=X² -2x+8

on solving the equation:

y==X² -2x+8

X² + 4x -2x -8

x(x - 4) -2(x - 4)

-1(x-2)(x+4)

According to the statement if One x-intercept for a parabola is at the point (-4,0)  of the equation the other x-intercept for the parabola is (2, 0).

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After the rotation of the point, we get the point as (5, 2)

We are given a point:

C (2, -5)

We first need to rotate it 180°.

When rotating a point 180 degrees counterclockwise about the origin our point A(x, y) becomes A'(-x, -y). So all we do is make both x and y negative.

So, we get the point as:

( - 2 , 5 )

Now, we need to rotate it 270°

The algebraic rule for a figure that is rotated 270° clockwise about the origin is (y, -x).

So, we get the point as:

(5, 2)

Therefore, after the rotation of the point, we get the point as (5, 2)

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Answer:

5,4

Step-by-step explanation:

The equation of the line is [tex]5y+4x-35=0[/tex]

Given,

Point is (5,3)

Slope m=-4/5

so formula of  equation of line is

[tex](y-y_{1})=m(x-x_{1})[/tex]

[tex](y-3)=-4/5(x-5)[/tex]

[tex]5y-15=-4x+20\\5y+4x-15-20=0\\5y+4x-35=0[/tex]

A line's equation can be formed using the slope of the line and a point on the line. To better understand the formation of a line equation, let us learn more about the slope of the line and the required point on the line. The slope of a line is its inclination with respect to the positive x-axis, and it is expressed as a numeric integer, fraction, or the tangent of the angle it makes with respect to the positive x-axis. The term "point" refers to a coordinate system point with the x and y coordinates.

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Answer:

1) 4

2) 16

Step-by-step explanation:

It can be concluded that only 2 birds of species A make alarm calls and 10 do not. For species B, there are no alarm calls.

Now,

Hence, It can be concluded that only 2 birds of species A make alarm calls and 10 do not. For species B, there are no alarm calls.

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Answer:

6 yards

Step-by-step explanation:

Answer:

[tex]5\frac{3}{4}[/tex]

Step-by-step explanation:

bottom is below, so we use a negative number

[tex]bottom = -3\frac{1}{2}\\top = 2\frac{1}{4}\\distance = top - bottom = 2\frac{1}{4} - (-3\frac{1}{2}) = 2\frac{1}{4} + 3\frac{1}{2} = 5\frac{3}{4}[/tex]

The distance from the given point to the given line is d = 13/5 units.    

Given:

To find:

So,

Let us define line L as follows:

Choose A as the fixed point on line L with the coordinates ( m, k ).

The line L now gives the coordinates of any point (x, y):

That was accomplished by subtracting the coordinates (x,y) from (m,k).

The dot product of constants (a, b) to vector coordinates between points (x,y) to (m,k):

For the above expression to be true, the dot product of two orthogonal vectors must be zero.

As a result, vector (a, b) is always perpendicular to every vector pointing in the direction of line L.

The vector is:

It could be the line connecting the points (x_1, y_1) and (m, k).

The magnitude of the scalar projection of v onto a gives the distance d from the point P 1: (x_1, y_1) to the line L because the latter is the duration of the side of a right triangle with two vertices being P_1 and (m, k), and the other vertex lying on L.

So:

In which point A (m,k) is on the line;

Then,

Given a point P (-2,3) and a line L, the equation is 3x - 4y + 5 = 0.

Where.

Now, calculate:                  

Therefore, the distance from the given point to the given line is d = 13/5 units.    

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The correct question is given below:
Use scalar projection to show that the distance from a point P1(x1,y1) to the line ax+by+c=0 is |ax1+by1+c|/underfoot(a^2 +b^2)

Use this formula to find the distance from the point (-2,3) to the line 3x-4y+5=0

Answer: A=-1/12

Step-by-step explanation:

[tex]\displaystyle\\\frac{1}{2}+(-\frac{5}{6} )+\frac{1}{4}=\\\\\frac{1*6-5*2+1*3}{12} =\\\\ \frac{6-10+3}{12}= \\\\\frac{-1}{12}= \\\\-\frac{1}{12}[/tex]

Answer: 97°

Step-by-step explanation:

∠XWY = 153°

∠2 = 56°

∠1 = ?

∠XWY-∠2=∠1

153°-56°=?

? = 97°

Answer:

23

Step-by-step explanation:

38/13 = 3

69/3 = 23

As we first choose a cluster of the store before surveying all of the customers present in the store, they employed cluster sampling in this instance.

A population is divided into several clusters that are representative of homogeneous traits and have an equal chance of being included in the sample using the sampling technique known as cluster sampling.

Cluster sampling using a single stage: As the name implies, sampling only happens once.

Two-stage cluster sampling: In this case, a small number of individuals are chosen from each group by means of systematic or simple random sampling rather than the entire cluster.

Multiple stage cluster sampling: Compared to two stage sample, multiple stage cluster sampling goes one or more steps beyond. Complex clusters must be formed in order to conduct effective research across several geographies, and this can only be done by employing the multiple-stage sampling technique.

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One and one fifth pounds of chicken will be needed for a single serving.

Adapting recipes to fit the requirements of various contexts is common. Changing the amount of individual servings a recipe yields is the most frequent cause for recipe modifications. A typical recipe, for instance, might be written to make 25 pieces. The recipe must be properly altered if a circumstance develops when 60 servings of the item are required.

Changes in portion sizes (which may entail adjusting the recipe's batch size) and improved use of the preparation tools available are two additional reasons to modify recipes (for example, you need to divide a recipe to make two half batches due to a lack of oven space).

4 servings requires 4 and 4/5th pounds = 4+4/5= 24/5 pounds

1 serving will require = 24/5 pounds / 4 = 6/5 = (1+1/5) pounds

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Answer: 1 1/5

Step-by-step explanation: I took the test

The width of the rectangular mat is 7/10 units.

We know that the area of rectangle is A = length × width

For given question,

Let w be the width of the rectangular mat and l be the length of the rectangular mat.

The length of the mat is 5/6.

⇒ l = 5/6

A rectangular mat has an area of 7/12.

⇒ A = l × w

⇒ 7/12 = 5/6 × w

⇒ w = 7/12 × 6/5

⇒ w = 7/10

Therefore, the width of the rectangular mat is 7/10 units.

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Answer:

Step-by-step explanation:

Write an expression for the perimeter of a rectangle with a length of

(3x² + x + 2) and a width of (-x² – 5x + 1).

P = 2 × (L + W)

2 × [(3x² + x + 2) + (-x² – 5x + 1)] =

if you want the result:

4x²−8x+6