Guided Practice


You drop a handball from a height of 100 centimeters. Each curved path has 64% of the height of the previous path.

Write a rule for the sequence using centimeters. The initial height is when n = 1.

What height will the ball reach at the top of the sixth path?


A.
an=100 · (0.64)n−1a subscript n baseline equals 100 times left parenthesis 0.64 right parenthesis superscript n minus 1 baseline; about 10.74 cm


B.
an=0.64 · (100)n−1a subscript n baseline equals 0.64 times left parenthesis 100 right parenthesis superscript n minus 1 baseline; about 0.11 cm


C.
an=1 · (0.64)n−1a subscript n baseline equals 1 times left parenthesis 0.64 right parenthesis superscript n minus 1 baseline; 6,400,000,000 cm

Answers

Answer 1

Answer:

The correct choice is (A)

Answer 2

Answer:  

A.

an=100 · (0.64)n−1a subscript n baseline equals 100 times left parenthesis 0.64 right parenthesis superscript n minus 1 baseline; about 10.74 cm

Step-by-step explanation:  I got it off of the internet

Step 1 of 1

In geometric sequence, the ratio between two consecutive terms is constant. This ration is called the common ratio.

Consider the following sequence:

Thus the common ratio of the sequence is .

...............................................................................................................................................

You drop a handball from a height of 1 meter. Each curved path has 64% of the height of the previous path.   A. A(n)= 100*(0.64)^n-1

Guided PracticeYou Drop A Handball From A Height Of 100 Centimeters. Each Curved Path Has 64% Of The

Related Questions

Ryan rented a truck for one day. There was a base fee of $16.99, and there was an additional charge of 74 cents for each mile driven. Ryan had to pay $133.17 when he returned the truck. For how many miles did he drive the truck?

Answers

Answer:

157 miles

Step-by-step explanation:

total cost = flat fee + cost per mile * miles

133.17 = 16.99 + .74 * m

Subtract 16.99 from each side

116.18 = .74m

Divide each side by .74

116.18 / .74 = .74m/.74

157 = m

Mr. James asked his students that which of the following equations can be formed using the expression x = 5:
a)2 x + 3 = 13
b)3x + 2 = 13
c)x –5 =
1d)4x –9 = 21

Answers

Answer:

[tex]2x + 3 = 13 \\ 2 \times 5 + 3 = 15 \\ 10 + 13 = 15 \\ 23 = 15 \\ 23 - 15 = 8 \\ \\ 3x + 2 = 13 \\ 3 \times 5 + 2 = 13 \\ 15 + 2 = 13 \\ 17 - 13 \\ = 4 \\ \\ x - 5 = 0 \\ 5 - 5 = 0 \\ 0 = 0 \\ \\ 4x - 9 = 21 \\ 4 \times 5 - 9 = 21 \\ 20 - 9 = 21 \\ 21 - 11 \\ = 10[/tex]

PERE
Given: ZABC is a right angle and ZDEF is a right angle.
Prove: All right angles are congruent by showing that ZABC = ZDEF.
What are the missing reasons in the steps of the proof?
ZABC, ZDEF are
right angles
M2ABC = 90°
m2DEF = 90°
m2ABC = m_DEF
ZABC = ZDEF
Given
A
B
A:
B:
C:
Intro

Answers

Answers:

A) Definition of right anglesB) SubstitutionC) Definition of congruence

=========================================

Explanation:

A) The term "right angle" is another way of saying "90 degree angle". This is a definition. Think of a definition in a dictionary. B) The substitution property allows us to replace one thing for another, as long as the two things are equal. The transitive property works as a similar idea.C) If two angles have the same measure, then they are congruent. This is the definition of congruence (or one form of it).

In this exercise we have to use the knowledge of angles, in this way we can say that:

A) Right angles

B) Substitution

C) Congruence

So punctuating some necessary definitions we have that:

A) This alternative is a right angle, that is, an angle that has 90 degrees.

B) The substitution property allows us to replace one thing for another, as long as the two things are equal.

C) IIn this alternative, we are dealing with congruent angles, that is, angles that have the same measure, normally less than 90 degrees.

See more about angles at brainly.com/question/15767203

Which expression is equivalent to 2(a+2b)-a-2b
o 3a+2b
o 3a-2b
o a-2b

Answers

Answer:

a -2b

Step-by-step explanation:

2(a+2b)-a-2b

Distribute

2a+4b -a-2b

Combine like terms

a -2b

Kasey has three pieces of wood that measure 9 inches, 12 inches, and 21 inches. Can she make a right triangle
with the three pieces of wood (without cutting or overlapping)?

Answers

Answer: No

Step-by-step explanation:

Add 2 sides together. If the sum of greater than the length of the 3rd side for all 3 options it can form a right triangle if it doesn’t than it can’t:

9 + 12 = 21 which is not greater than the 3rd side length of 21 so this cannot form a right triangle.

The answer would be (no)

The cars of a circular Ferris wheel at an amusement park are equally spaced about the wheel's circumference. They are numbered consecutively beginning with 1. The cars numbered 14 and 30 lie on opposite ends of a diameter. How many cars are on the Ferris wheel?

Answers

Answer:

32 cars

Step-by-step explanation:

we know that 14 and 30 lie on opposite sides of the ferris wheel, so we need to calculate how many cars are inbetween car number 14 and carn number 30. since each car is numbered starting from 1, we know that the cars do not skip any numbers. after counting, we know that there are 16 cars inbetween car number 14 and car number 30. since there are 2 sides of a circle we have to double our number by 2. so 16×2 is 32

Math step-by-step:

30-14=16

16×2=32

You have 80$ panted cost 29$ And shirts cost 12$. Mom told you to buy one pair of pants and use the rest of the money to buy shirts. Use this information to write and solve and inequality how many shirts can you buy

Answers

Answer: 4 Shirts

Step-by-step explanation:

Given

Person has [tex]\$80[/tex]

Pant costs [tex]\$29[/tex] and shirt costs [tex]\$12[/tex]

Suppose [tex]x\ \text{and}\ y[/tex] as number of pant and shirts

Spent money must be equal or less than the total money. The inequality becomes

[tex]\Rightarrow 80\geq29x+12y[/tex]

For 1 pair of pants that is, 1 pants

[tex]\Rightarrow 80\geq 29+12y\\\Rightarrow 51\geq 12y\\\Rightarrow 4.25\geq y[/tex]

That is maximum number of shirts that can be bought are 4.

Is the relationship shown by the data linear? If so, model the data with an equation. x y –7 5 –5 9 –3 13 –1 17

Answers

Given:

The table of values is:

x :     -7          -5         -3           -1

y :      5           9         13          17

To find:

Whether the given data is linear and then find the equation.

Solution:

The given data is linear if the slope and rate of change is constant.

Slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using the slope formula. we get

[tex]\dfrac{9-5}{-5-(-7)}=2[/tex]

[tex]\dfrac{13-9}{-3-(-5)}=2[/tex]

[tex]\dfrac{17-13}{-1-(-3)}=2[/tex]

Since the rate of change is constant, i.e., 2, therefore the given data is linear.

The slope of a linear equation is 2 and it passes through the point (-7,5). So, the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-5=2(x-(-7))[/tex]

[tex]y-5=2(x+7)[/tex]

[tex]y-5=2x+14[/tex]

Adding 5 on both sides, we get

[tex]y-5+5=2x+14+5[/tex]

[tex]y=2x+19[/tex]

Therefore, the equation for the given data is [tex]y=2x+19[/tex].

The speed of a toy car is 20 m/s. The time taken for a trip is 200seconds. Find the
distance covered in meter

Answers

Distance = time/ speed

Distance = 200 seconds / 20 m/s

Distance = 10 meters

Answer:

Distance:

[tex]{ \tt{distance = speed \times time}} \\ { \tt{ = 20 \times 200}} \\ { \tt{ = 4000 \: metres}}[/tex]

Can someone help me with this math homework please!

Answers

Answer:

X1 = 2 Y1 = -5

Step-by-step explanation:

math simple slope

In Owen's class, there are 15 girls and 12 boys. Write the ratio of boys to girls.

Answers

Answer:

4       :  5

Step-by-step explanation:

boys : girls

12          15

Divide each by 3

12/3 :  15/3

4       :  5

Answer: 4:5

Step-by-step explanation:

To simplify the ratio 12:15, divide both numbers by the GCF of the 2 numbers (3). This gives you the simplified ratio, 4:5.

i need help plz!!!!!!!!!!!!

Answers

Answer:

54 and 36

Step-by-step explanation:

84

45% of 120 students chose the amusement park , then

45% of 120 = 0.45 × 120 = 54

54 students chose the amusement park

85

45% of 180 = 0.45 × 180 = 81

25% of 180 = 0.25 × 180 = 45

81 - 45 = 36

36 more students chose the amusement park than the water park

Answer:

54, 36

Step-by-step explanation:

84

45% of 120 students chose the amusement park

45% of 120 = 0.45×120=54

54 students chose the amusement park

85

45% of 180 = 0.45 × 180 = 81

25% of 180 = 0.25 × 180 = 45

81 - 45 = 36

36 students chose the amusement park than the water park

Now measure the lengths of the sides of polygon ABCD and tbe lengths of the sides of the translated images. Record the measurements in the table.

Answers

Answer:

3.16, 3.16, 3.16

3.16, 3.16, 3.16

1.41, 1.41, 1.41

3.16, 3.16, 3.16

Step-by-step explanation:

Answer:

Length Length  Length

3.16         3.16   3.16

3.16 3.16   3.16

1.41   1.41   1.41

3.16  3.16  3.16

Step-by-step explanation:

If ABCD is dilated by a factor of 2, the
coordinate of A' would be:

Answers

Answer: -5, -1

Step-by-step explanation:

Let 0 be an acute angle of a right triangle. Evaluate the other five trigonometric functions of 0.

Answers

Answer:

sin θ = (√119)/12

tan θ = (√119)/5

csc θ = 12/(√119)

cot θ = 5/(√119)

Five trigonometric functions of θ are

sinθ = [tex]\frac{\sqrt{119} }{12}[/tex]cosθ = [tex]\frac{5}{12}[/tex]tanθ = [tex]\frac{\sqrt{119} }{5}[/tex]cosecθ = [tex]\frac{12}{\sqrt{119} }[/tex]secθ = [tex]\frac{12}{5}[/tex]cotθ = [tex]\frac{5}{\sqrt{119} }[/tex]

What is trigonometric functions?

"The trigonometric functions of θ are functions of an angle. sine, cosine, and tangent are familiar trigonometric functions. The trigonometric functions relates the angles of a triangle to the length of its side."

Let θ be an acute angle of a right angle triangle

What is acute angle?

"An acute angle ("acute" meaning "small") is an angle smaller than a right angle. The range of an acute angle is between 0 and 90 degrees."

What is right angled triangle?

"A right angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle).

What is hypotenuse?

"The side opposite the right angle is called the 'hypotenuse'. The hypotenuse is always the longest side. The sum of the other two interior angles is equal to 90°."

What is opposite side?

"An 'opposite' side is the one across from a given angle."

What is adjacent side?

"An 'adjacent' side is next to a given angle. We use special words to describe the sides of right triangles."

we have,

cosθ = [tex]\frac{5}{12}[/tex]

secθ = [tex]\frac{12}{5}[/tex]

Hypotenuse side = 12

Adjacent side = 5

Opposite side = [tex]\sqrt{hyp^{2}-adj^{2} }[/tex]= [tex]\sqrt{12^{2}-5^{2} }[/tex] = [tex]\sqrt{119}[/tex]

sinθ = [tex]\frac{opp}{hyp}[/tex] = [tex]\frac{\sqrt{119} }{12}[/tex]

tanθ = [tex]\frac{opp}{adj}[/tex] = [tex]\frac{\sqrt{119} }{5}[/tex]

cosecθ = [tex]\frac{hyp}{opp}[/tex] = [tex]\frac{12}{\sqrt{119} }[/tex]

cotθ  = [tex]\frac{adj}{opp}[/tex] = [tex]\frac{5}{\sqrt{119} }[/tex]

Learn more about trigonometric functions, acute angle and right angle triangle here

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#SPJ2

Please help me find this box guys I’m struggling

Answers

Answer:

(0,-9)

Step-by-step explanation:

To find the y-intercept, substitute x=0

y=(0)^2+4(0)-9

=-9

Here's a tip to help you find the y-intercept faster, it is usually the constant of the graph equation

Answer:

see explanation

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

The equation of the axis of symmetry which is also the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = x² + 4x - 9 ← is in standard form

with a = 1, b = 4 , then

x = - [tex]\frac{4}{2}[/tex] = - 2

x = - 2 is the equation of the axis of symmetry

Substitute x = - 2 into the equation for corresponding y- coordinate of vertex

y = (- 2)² + 4(- 2) - 9 = 4 - 8 - 9 = - 13

vertex = (- 2, - 13 )

To find the y- intercept let x = 0 and solve for y

y = 0² + 4(0) - 9 = 0 + 0 - 9 = - 9

y- intercept = (0, - 9)

From the standard form of the parabola

• If a > 0 then vertex is a minimum

• If a < 0 then vertex is a maximum

Here a = 1 , that is > 0

vertex (- 2, - 13 ) is a minimum

Find the surface area and the volume of the prism.
10
26
18

Answers

Volume: 1320
Surface Area: 2160

Enter the equation of the line in slope-intercept form.
Slope is 4, and (5,2) is on the line.
The equation of the line is y =

Answers

Answer:

y = 4x -18

Step-by-step explanation:

y-2 = 4(x-5)

y = 4x -20+2

y = 4x -18

Answer:

y = 4x-18

Step-by-step explanation:

Slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = 4x+b

Substitute the point in the equation and solve for b

2 = 4(5)+b

2 = 20+b

2-20 = b

-18 =b

y = 4x-18

if triangle 3 shows a 100 degree rotation of triangle 1 about point p what is the degree of intersection of lines m and n?

Answers

The given transformations are rigid transformations, such that

the image and the preimage have the same dimensions.

Correct responses:

The degree of the intersection of lines m and n is; 50°

This image also shows two A. reflection about lines m and then line n.

How can the angle between the lines be determined, and what is a reflection?

Given;

The images of triangle 1 are; Triangle 2, and triangle 3

Taking the image of line m as line m, we have;

Required:

The degree of the intersection of lines m and n

Solution:

Triangle 2 is the reflection of triangle 1 across line m, and

triangle 3 is the reflection of triangle 2 across line n

The distance of triangles 1 and 2 from line m are equal

The distance of triangle 2 and 3 from line n are equal.

Whereby the degree of rotation of triangle 1 to triangle 2, θ₁ is

equal to the degree of rotation of triangle 2 to triangle 3, θ₂,

we have;

θ₁ = θ₂

100° = θ₁ + θ₂ = 2·θ₁

θ₁ = θ₂ = 100° ÷ 2 = 50°

The angle of rotation of line m to line n = Rotation of triangle 1 to triangle 2 = θ₁ = 50°

The degree of the intersection of lines m and n = 50°

The transformation to give triangle 2 from triangle 1 is a reflection about line m.

Similarly, the transformation that gives triangle 3 from triangle 2 is a reflection about line n.

Therefore;

The image also shows two A. Reflections about line m and then line n.

Learn more about rigid transformations here:

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An automobile manufacturing plant produced vehicles today: were sedans, were trucks, and were motorcycles. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles. What is the probability that two motorcycles will be selected

Answers

Answer:

120 / 561

Step-by-step explanation:

An automobile manufacturing plant produced 34 vehicles today: 16 were motorcycles, 9 were trucks, and 9 were vans. Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles.What is the probability that two motorcycles will be selected

16/34 X 15 X 33

A biased 3-coloured spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times. If you spin this spinner 1000 times, how many times do you expect it to land on Red?

Answers

Answer:

83 spins

Step-by-step explanation:

Number of red spins = n

Number of orange spins = 8n

Number of yellow spins = 3n

Total number of trials = 240

Total number of spins :

(n + 8n + 3n) = 240

12n = 240

n = 240 / 12

n = 20

Number of red spins = 20

(1000/240) * n

4.1666666 * 20

= 83.333

= 83 spins

Solve for x. 4/3 = 24/x
Help me please!!

Answers

Answer: x=18
First cross multiply 4/3=24/x to get 4x= 3*24
Then simplify: 4x=72; x=18

PLS HELP!!! The problem is in the photo attached

Answers

Answer:

The answer is C!

Step-by-step explanation:

Answer:

D

NOTE: the answer "C" is NOT correct... see the image the green is "C" the purple is "D"

Step-by-step explanation:

plzzz helppp i need to pass this classs

Answers


D. X=130 but im not sure if this is correct

Answer:

C

Step-by-step explanation:

x + 40 + 100 + x=360. (sum of angles at a point)

2x+140=360

2x=360-140

2x=220

x=220/2

x=110⁰

Given: `bar(DE)` and `bar(DF)` are midsegments of `Delta` ABC as shown. Prove: A midsegment of `Delta`ABC is half the length of the side of `Delta`ABC to which it is parallel. Match each statement to its corresponding reason. Scroll down to see all the choices. Drag the items on the left to the correct location on the right.

Answers

Answer:

here

Step-by-step explanation:

Someone, PLEASE HELP! ):

Answers

Answer:

i dont see anything

Step-by-step explanation:

Polygon has 18 sides!!

Find the distance between the two points rounding to the nearest tenth (if necessary). ( − 8 , 6 ) and ( − 6 , 0 )

Answers

Answer:

[tex]\sqrt{40\\}[/tex], [tex]2\sqrt{10}[/tex], or 6.3 (rounded).

Step-by-step explanation:

Use the distance formula, [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} \\x_1 is -8, y_1 is 6, x_2 is -6, y_2 is 0.[/tex]

Find the value of x in the isosceles triangle shown below.
2
2
5
8

Answers

Answer:

[tex]\sqrt{41}[/tex]

Step-by-step explanation:

think of this triangle being made up of 2 triangles with the lengths of 5, 4, and x.

x being the hypotenuse, 5 being one of the legs, and 4 being one of the legs. (8/2).

pythagorean theorem:

a^2 + b^2 = c^2

5^2 + 4^2 = x^2

25 + 16 = x^2

41 = x^2

x = sqrt 41

CANNNN SOMEONEEEEE HELPPPP MEEE OUTTTTT !!!!!

Answers

Answer:

sin X = 21/ 29

Step-by-step explanation:

Since this is a right triangle

sin X = opp side/ hypotenuse

sin X = 21/ 29

Answer:

[tex]\boxed{\sf sinX =\frac{21}{29}}[/tex]

Step-by-step explanation:

We need to find out the value of sinX using the given triangle . Here we can see that the sides of the triangle are 21 , 29 and 20.

We know that the ratio of sine is perpendicular to hypontenuse .

[tex]\sf\longrightarrow sin\theta =\dfrac{ perpendicular}{hypontenuse}[/tex]

Here we can see that the side opposite to angle X is 21 , therefore the perpendicular of the triangle is 21. And the side opposite to 90° angle is 29 . So it's the hypontenuse . On using the ratio of sine ,

[tex]\sf\longrightarrow sinX =\dfrac{ p}{h}=\dfrac{ZY}{ZX}[/tex]

Substitute the respective values ,

[tex]\sf\longrightarrow \boxed{\blue{\sf sin\ X =\dfrac{21}{29}}}[/tex]

Hence the required answer is 21/29 .

53. A right triangle has a hypotenuse measuring 15 inches and one leg measuring 9 inches What is the length, in inches, of the other leg of the triangle?

A. 3
B.6
C. 10
D. 12 ​

Answers

Answer:

D

Step-by-step explanation:

Pythagorean

[tex]x^{2} + 9^{2} = 15^{2}[/tex] (x>0)

=> [tex]x=\sqrt{15^{2}-9^{2} }[/tex] [tex]=12[/tex]

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