2x³ - x² - 6x-1/x-1

There is no catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance.

From the graph,

x axis represents the arm length of the catapult and the y axis represents the distance.

The point at which the catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance is the intersecting point of the both line

The coordinates of the intersecting point = (-30, 90)

Here arm length represents -30, but the arm length cannot be a negative value

Therefore, there is no arm length that gives equal distance

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Answer:

There is no catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance.

Step-by-step explanation:

The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be r=0.0.7 m and h=0.08 m.

The maximum volume of  right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be 2640.4 m³.

How to find volume of Right Circular Cylinder?

Right cylinders are cylinders with axes that are perpendicular to the bases.

Volume of a Right Circular Cylinder= πr²h  

where,

r = radius of the base

h = height of right circular cylinder

Maximum volume of right circular cylinder that can be inscribed in a sphere will be,    

                  [tex]\pi r^{2} h-\frac{\pi }{4} h^{3}\\\\= \frac{4\pi r^{3} }{3\sqrt{3} }[/tex]

given that, radius=70cm=0.0.7 m

so,

       [tex]Maximum\ volume=\frac{4\pi r^{3} }{3\sqrt{3} } \\\\= \frac{4\pi (70)^{3} }{3\sqrt{3} }\\\\=2640.4\pi \ m^{3}[/tex]

Using volume of right circular cylinder,

                [tex]h=\frac{2r}{\sqrt{3} }\\\\ h = \frac{2(0.07)}{\sqrt{3} }\\\\h= 0.08\ m[/tex]

Hence, The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be r=0.0.7 m and h=0.08 m.

The maximum volume of  right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be 2640.4 m³.

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The rule of translation will be; Horizontal shift by 3 units right and vertical shift by 2 units down (x, y) → (x + 3, y -2)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

For the shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

Given that Trapezoid 1 with vertices

A(-4, 3), B(1, 3), C(0, 0), D(-3, 0)

Trapezoid 2 with vertices are;

A'(-1, 1), B'(4, 1), C'(3, -2), D'(0, -2)

It can be observed by comparison that the x-values have increased by 3 units and the y-values have decreased by 2 units

So the rule of translation will be; Horizontal shift by 3 units right and vertical shift by 2 units down (x, y) → (x + 3, y -2)

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Using the percentage method, we know that the original price of the TV set was $400.

Percentages are just fractions with a denominator of 100.

To show that a number is a percentage, we place the percent sign (%) next to it.

For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

So, we know that the percentage is always out of 100.

Then we automatically know that:

100% - 15% = 85%

We know:
85% = $340

15% = ?

Now, calculate the reduced price as follows:
85/340 = 15/x

85x = 15(340)

85x = 5,100

x = 5100/85

x = $60

Original price of the TV set:

Sold cost + Reduced cost

$340 + $60

$400

Therefore, using the percentage method, we know that the original price of the TV set was $400.

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The value of v in the triangle is 15 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

The exterior angle theorem is used to find the value of v.

Therefore,

31 + 4v + 44 = 9v

31 + 44 = 9v - 4v

75 = 5v

divide both sides by 5

v = 75 / 5

v = 15

Therefore,

v = 15

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Answer:

Step-by-step explanation:

You want to identify the true statements about the function f(x) = |x+3|.

A graph of the function is attached. It shows the function is decreasing to the left of x = -3, increasing to the right of that point, and has an x-intercept at x = -3. The function is positive everywhere.

The true descriptions are ...

Answer:X+(X+10)+(2X)

Step-by-step explanation:

Lets say X is the amount of children tickets sold.

So she sold some kid tickets and we get an X

So X

and then she sold ten more than X tickets to adults

So now we have

X+(X+10)

And then she sold twice as many senior tickets than kids tickets

so now we have

X+(X+10)+(2X)

hope that helped at all!

Answer:

2.5x103

Step-by-step explanation:

The probability of getting exactly 0 heads is, 0.031.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

A fair coin is tossed 5 times.

So, the the total number of possibilities are,

[tex]2^5= 32[/tex]

We have to find the probability of getting exactly 0 heads.

The only possible set of flips that yields 0 heads is {T, T, T, T, T}.

So,

The probability is, [tex]\frac{1}{32}=0.03125[/tex]

Probability ≈ 0.031

Hence, the probability of getting exactly 0 heads is, 0.031.

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Answer:3

Step-by-step explanation:3

As describes in geometry the area of the rectangle = 288cm

what is geometry ?

The area of mathematics known as geometry is concerned with the characteristics of the surrounding space as well as the shapes of individual objects and their spatial relationships.

solution

radius of semicircle = 12

diameter will be = 24 and this is the length of rectangle s given in the question

area of the rectangle  = l*b

                                     = 24*12

area of the rectangle = 288cm

Hence the area of the rectangle = 288cm

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When the car is acquired for $22600 and depreciates at an 11.5% rate, it will take 6.7 years for its worth to reach $5200.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Here,

Cost of car=$22600

Rate of depreciation=11.5%

After n years, value of car=$5200

Annual depreciation expense=22600*11.5%

=$2599

Value of the Car = Purchase cost - (Annual depreciation expenses * n)

5200=22600-(2599*n)

2599n=22600-5200

2599n=17400

n=6.695

n=6.7 years

The number of years until the value of the car is 5200 dollars at depreciation rate of 11.5% when purchased at 22600 dollars will be 6.7 years.

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Answer:

The slope is -0.5, which indicates a negative correlation.

Step-by-step explanation:

y = mx + b

Is a slope-intercept form of the equation.

The y represents the distance of the line from the y-axis. (if u were to graph the problem)

M represents the slope of the line.

An the value of b is equal to y when x = 0

The equation that was given is y = 4.0 - 0.5x, which wasn't written the normal way, like  y = mx + b, they just switched the spots from y = mx + b, to y = b + mx.

So the slope is the 0.5. (which is also -0.5)

Trust me, I took a test and it had this answer, and I got it right.

Answer:

B- -0.5

Step-by-step explanation:

-.05 is a negative correlation

Negative Correlation definition- Is a  situation or an event where two variables move in the opposite direction

(Plus I also Took the test and got it right)

Using simple mathematical operations, we know that we sold a total (D) of 50 units of orange juice.

A mathematical function known as an operation converts zero or more input values into a precisely defined output value.

The quantity of operands affects the operation's arity.

The order of operations refers to the rules that define the sequence in which we should perform the operations necessary to solve an equation.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are collectively referred to as PEMDAS.

So, we begin the week with 30 units of orange juice.

We purchase more than 50 units of orange juice.

Total: 30 + 50 = 80 units

Our ending inventory was 30 units.

Units of orange juice sold: 80 - 30 = 50 units

Therefore, using simple mathematical operations, we know that we sold a total (D) of 50 units of orange juice.

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Complete question:

You begin the week with 30 units of orange juice. You purchase 50 units. Your ending inventory for the week is 30 units. How many units did you sell?

a) 5

b) 15

c) 49

d) 50

The equation (y = mx + b) of this graph is equal to the equation for this arithmetic sequence aₙ =  a₁ + (n - 1)d

Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:

aₙ =  a₁ + (n - 1)d

Where:

For the 10th term, the equation for the arithmetic sequence is given by;

a₁₀ =  a₁ + (n - 1)d

15 =  a₁ + (10 - 1)d

15 =  a₁ + 9d

For the 14th term, the equation for the arithmetic sequence is given by;

a₁₄ =  a₁ + (n - 1)d

35 =  a₁ + (14 - 1)d

35 =  a₁ + 13d

Next, we would determine the common difference as follows;

a + 9d = 15

a + 13d = 35

-4d = -20

Common difference, d = -20/-4

Common difference, d = 5.

For the first term of this arithmetic sequence, we have;

a + 9d = 15

a + 9(5) = 15

a = 15 - 45

First term, a = -30

Finally, we would write an equation for the nth term of an arithmetic sequence as follows;

aₙ =  a₁ + (n - 1)d

aₙ =  -30 + (n - 1)5

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Answer:

0.40

Step-by-step explanation:

.04 x 10 = .40

Answer: $0.40

Step-by-step explanation: The sales tax will be 4% of the selling price

The end price will be 10.40

Answer:

8.9

Step-by-step explanation:

Answer:

0.34

Step-by-step explanation:

[tex] {0.5 }^{2} + {0.3}^{2} \\ 0.25 + 0.09 \\ = 0.34[/tex]

(I'm not sure if this is what you meant)

hana is 4 year older than her brother. 2 years ago, her brother’s age was ¾ of her age then brother age will be 19 years

The concept of age describes how old a person is at a particular point in time. It is defined as the measure of the time elapsed from date of live birth to a specific point in time, usually the date of collection of the data

Hana is 4 years older then her brother

let x be brother present age

and x+4 be the hana present age

2 year ago

hana was x+2

and brother was x-2

according to the question

x-2= 3/4 * ( x+2)

x= 14

after 5 years he will be 19 years

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The co-ordinates of the point P that divides the line segment AB in the ratio 3:2 are (3,0)

What is Line Geometry?

A line is an endlessly long object with no breadth, depth, or curve in geometry. Lines are thus one-dimensional objects, even if they can exist in two, three, or higher dimensions. In ordinary language, the term line can also refer to a line segment with two points denoting its endpoints.

Solution:

To find the co-ordinates of point P we wil use section formula

(x,y) = (m*x2 + n*x1 / m+n), (m*y2 + n*y1 / m+n)

(x,y) = (3*3 + 2*3)/5 , (3*2 + 2*(-3))/5

(x,y) = 15/5 , 0/5

(x,y) = 3,0

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By using the concept of complex number, it can be calculated that

There is only one complex number which satisfies  |z – 1| = |z + 1| = |z – i|  

What is a complex number?

Any number of the form a+ib where, a and b are real numbers and           i = [tex]\sqrt{-1}[/tex] are called complex number.

Let z = x + iy

[tex]|z - 1|^2 = |z + 1|^2 = |z - i|^2[/tex]

[tex]|x + iy - 1|^2 = |x+iy + 1|^2 = |x+iy - i|^2\\(x-1)^2+y^2 = (x+1)^2+y^2 = x^2+(y -1)^2[/tex]

So the point (x, y) is equidistant from (1, 0), (-1, 0) and (0, 1)

(0, 0) is the only point which is equidistant from (1, 0), (-1, 0) and (0, 1)

z = 0 is the only complex number which satisfies  |z – 1| = |z + 1| = |z – i|

There is only one complex number which satisfies  |z – 1| = |z + 1| = |z – i|  

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Answer:

628 m

Step-by-step explanation:

We need to find the circumference, C, of the circle.

C = πd

C = 3.14 × 100 m

C = 314 m

Walking around the circular path twice is twice the length of the circumference.

distance = 2C = 2 × 314 m = 628 m

the surface integral. s (x + y + z) ds, s is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v is 10[tex]\sqrt{14}[/tex]

The surface element is

dS = || ∂r/∂u  x  ∂r/dv || du dv

where

r (u, v) = x (u, v) i + y (u, v) j + z (u, v) k

r (u, v) = (u + v) i + (u - v) j + (1 + 2u + v) k

is the vector parameterization for the surface S.

The normal vector to the surface is

∂r/∂u  x  ∂r/dv

… = (i + j + 2 k)  x  (i - j + k)

… = 3 i + j - 2 k

and has norm

|| ∂r/∂u  x  ∂r/dv || = √(3² + 1² + (-2)²) = √(14)

Now compute the integral:

∫∫ (x + y + z) dS = √(14) ∫₀¹ ∫₀² ((u + v) + (u - v) + (1 + 2u + v)) du dv

… = √(14) ∫₀¹ ∫₀² (3u + v + 1) du dv

… = √(14) ∫₀¹ (3/2 u² + uv + u) |₀² dv

… = √(14) ∫₀¹ (8 + 2v) dv

… = √(14) (8v + 2v²) |₀¹

… = 10 √(14)

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From the given average the number of students are more in the afternoon quiz as compare to the morning quiz .

As given in the question,

Combined average score of the two classes = 84.

Average score of students in the morning quiz = 80

Let 'x' be the number of students in the morning quiz

80 = ( Sum of all number of students in the morning quiz) / x

⇒  Sum of all number of students in the morning quiz = 80x __(1)

Average score of students in the afternoon quiz = 86

Let 'y' be the number of students in the afternoon quiz

86 = ( Sum of all number of students in the afternoon quiz) / y

⇒  Sum of all number of students in the afternoon quiz = 86y __(2)

Average score of combined classes = ( 80x + 86y ) / (x + y)

⇒ 84 = ( 80x + 86y ) / (x + y)

⇒ 84x + 84y = 80x + 86y

⇒4x = 2y

⇒ y = 2x

Number of students in the afternoon are double  the number of students in the morning.

Therefore, from the given averages afternoon class has more number of students than morning class

The complete question is :

Professor Liu gave the same quiz to the students in her morning class and in her afternoon class. The average (arithmetic mean) score for the two classes combined was 84. Which class had more students?(1) The average score for the students in the morning class was 80

(2) the average score for the students in the afternoon class was 86

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Answer:

9 + 4i

Step-by-step explanation:

5 + 4 + 9i - 5i

=> 9 + 4i

Answer:

900

Step-by-step explanation:

l = 2w + 5

2(2w + 5) + 2w = 130

4w + 10 + 2w = 130

6w + 10 = 130

6w = 120

w = 20

l = 2(20) + 5

l = 40 + 5

l = 45

130 = 2(45) + 2(20)

130 = 90 + 40

130 = 130

A = l × w

A = 45 × 20

A = 900

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The centroid appears to be in the middle of the base and one-third of the way up the triangle, at (1.5, e^1).

The center of the object is represented by the centroid. The centroid of a triangle is the location where the triangle's three medians cross. The intersection of all three medians is another definition of it. The median is a line that connects the middle of a side to the opposite vertex of a triangle. The region bounded by the curves is a triangle with the tip at (0, e^0) and the base at (3, 0). The centroid appears to be in the middle of the base and one-third of the way up the triangle, at (1.5, e^1).

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Total number of straight lines are 45 and it can be found out using combination.

What is combination?

A combination could be a choice of things from a collection that has distinct members, such the order of choice doesn't matter.

Main body:

Total points = 10

we need to find no three lie on the same straight line.

so , to find we can select 2 lines out of 10 and assume packing them together so  no 3 points lie on a line .

selection of 2 points out of 10.

C(10,2) = ¹⁰C₂

           = 10!/2!8!

           = 10*9/2

           = 45 lines.

Hence ,Total number of straight lines are 45 .

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