Part B
Assume the statement is true for n=k. Prove that it must be true for n=k+1, therefore proving it true for all natural
numbers, n.
Hint: Since the total number of dots increases by n each time, prove that d (k) + (k+1)=d (k+ 1).

The building is 231.7 m far away.Distance can refer to a physical length or an estimate based on other factors in physics or common use.

Distance is a numerical representation of the space between two objects or locations. |AB| is a symbol for the distance between two points A and B.

Given data;

Speed of sound  = 331 meters per second

Time = 0.7 sec

The distance from the building is;

d=v×t

d=331 m/sec × 0.7 sec

d=231.7 m

Hence the building is 231.7 m far away.

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Answer:

A. $60.25

B. 76 miles

C. 216 miles

Step-by-step explanation:

x is miles

y is total amount spent

For A, 57 miles is the x value. Plug that in to x.

y= 46 + .25(57)

y= 60.25

For B, the total is the y. So plug 65 in for y.

65 = 46 + .25x   Subtract 46 from both sides

19 = .25x             Divide by .25

76 = x

For C, the maximum you can spend is $100. Plug that in for y.

100 = 46 + .25x   Subtract 46 from both sides

54 = .25x             Divide by .25

216 = x

The answer for part a is $60.25, for part b the answer is 76 miles, and for part c the answer is 216 miles.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The equation to represent the cost would be y=46+0.25x

x is the number of miles.

a) What is your cost if you travel 57 miles?

Plug x = 57 in the above equation:

y = 46 + 0.25(57)

y = $60.25

b) If your cost was $65.00, how many miles were you charged for traveling?

Plug y = 65 in the equation:

65 = 46 + 0.25x

x = 76 miles

c) Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?

Plug y = 100 in the equation:

100 = 46 + 0.25x

x = 216 miles

Thus, the answer for part a is $60.25, for part b the answer is 76 miles, and for part c the answer is 216 miles.

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The first term will be 4 and the common ratio will be 2. And the nth term will be given as [tex]\rm a_n = a_{n -1} \cdot 2[/tex].

The complete question is attached below.

Let a be the first term and r be the common ratio. Then the geometric sequences will be

[tex]\rm a_n = a_{n -1} \cdot r[/tex]

The geometric sequence is given below.

4, 8, 16, 32, 64,................

Then the first term will be 4 and the common ratio will be 2.

And the nth term will be given as [tex]\rm a_n = a_{n -1} \cdot 2[/tex].

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Janelle rode the bus to the bus stop, talked with a friend, and then walked home ,  Option D is the correct answer.

The missing graph is attached with the answer.

A graph which shows change in distance with respect to time is called Time- Distance Graph.

It is used to calculate velocity.

As in the graph we it can be seen that , The distance is decreasing at a constant speed ,

then the distance becomes constant with time

and then again decreases but with a lower rate

This means

Janelle rode the bus to the bus stop (distance to time rate is high)

talked with a friend (distance is constant with time)

and then walked home. (distance to time rate is low)

Therefore Option D is the correct answer.

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Answer:

Janelle rode the bus to the bus stop, talked with a friend, and then walked home.

Step-by-step explanation:

Answer:

C) 20cm

Step-by-step explanation:

Perimeter is the distance around the edge of the shape.

8 + 7 + 5 = 20

Answer:

20 is answer

Step-by-step explanation:

as perimeter= sum of all side

= 8 +7+5=2ocm

Answer: Hope this helps you

1/2

Step-by-step explanation:

To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.

8x+2y = 4 ➨ 8x+2*0 = 4

Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:

8x = 4

Now I will divide both sides by 8, which isolates our x.

x = 1/2

The x-int is 1/2.

The complete equation of the ellipse is [tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

The complete question is in the attachment

The given parameters are:

The vertex is represented as (h, k ± a).

So, we have:

h = -5

k + a = 14

k - a = -2

Add the last two equations

2k = 12

Divide by 2

k = 6

Substitute k = 6 in k + a = 14

6 + a = 14

Solve for a

a = 8

The ellipse equation is represented as:

[tex]\frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2} = 1[/tex]

So, we have:

[tex]\frac{(x + 5)^2}{b^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

The ellipse passes through the point (0,6).

So, we have:

[tex]\frac{(0 + 5)^2}{b^2} + \frac{(6 - 6)^2}{8^2} = 1[/tex]

This gives

[tex]\frac{5^2}{b^2} + \frac{0}{8^2} = 1[/tex]

Evaluate the quotient

[tex]\frac{5^2}{b^2} = 1[/tex]

Cross multiply

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

Take the square root of both sides

b = 5

Substitute b = 5 in [tex]\frac{(x + 5)^2}{b^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

[tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

Hence, the complete equation of the ellipse is [tex]\frac{(x + 5)^2}{5^2} + \frac{(y - 6)^2}{8^2} = 1[/tex]

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Answer: [tex]f(x)=-(x-5)^{2}(x+2)[/tex]

Step-by-step explanation:

There is a double root at x=5 and a single root at x=-2, so we know f(x) is of the form [tex]f(x)=a(x-5)^{2}(x+2)[/tex] for some constant a.

To find a, we can substitute the coordinates of the y-intercept, (0, -50).

[tex]-50=a(0-5)^{2}(0+2)\\\\-50=50a\\\\a=-1[/tex]

So, [tex]f(x)=-(x-5)^{2}(x+2)[/tex]

The time taken by a group of 8 people working half the rate of the first group is 7.5 hours.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

A Group of 5 people can do a piece of work in 6hrs.

5 people, at a rate of 1, and the time taken is 6 hours

Work done is 30

8 people, at a rate of 1/2, and the time taken is x hours

8(1/2)x = 30

x = 60/8 = 7.5 hours

Thus, the time taken by a group of 8 people working half the rate of the first group is 7.5 hours.

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The area of the geometry will be 53.1 square feet. Then the correct option is B.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The figure is the combination of the triangle and semicircle.

Then the area will be

Area = area of triangle + area of semicircle

Area of triangle = 1/2 x 8 x 7

Area of triangle = 28 square ft

Area of semicircle = (π / 8)  x 8²

Area of semicircle = 25.13 square ft

Then the area of the geometry will be

Area = 28 + 25.13

Area = 53.1 square feet

Then the correct option is B.

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Answer: the fourth one

Step-by-step explanation:

Answer:

D.) 8x¹²y³

Step-by-step explanation:

When an expression is raised to a power, you have to raise everything in the expression to the power when simplifying. This includes the coefficients and variables. When a variable already raised to a power is raised to another power, the powers are multiplied.

Therefore,

2³ = 8

(x⁴)³ = x⁴*³ = x¹²

(y)³ = y³

Combined, the final answer is 8x¹²y³.

Step-by-step explanation:

please mark me as brainlest

Answer:

8

Step-by-step explanation:

We need to sort your set into Least-to-Greatest order.

4, 5, 5, 6, 10, 11, 12, 13

That is your set in least to greatest order.

Which 2 numbers are in the middle?

They are 6 and 10.

Now, we find the mean of 6 and 10.

(6+10)/2 = 8

8 is your median

Answer:

[tex]\frac{5pi}{6}[/tex]

Step-by-step explanation:

Answer:

[tex]x = \dfrac{\pi}{6}, \dfrac{5 \pi}{6}[/tex]

Step-by-step explanation:

[tex]\begin{aligned}3 \sin x & = \sin x + 1\\\implies 3 \sin x - \sin x & = 1\\2 \sin x & = 1\\\sin x & = \dfrac{1}{2}\\\implies x & = \sin^{-1}\left(\dfrac{1}{2}\right)\\x & = \dfrac{\pi}{6} \pm 2 \pi n, \dfrac{5 \pi}{6}\pm 2 \pi n\end{aligned}[/tex]

Therefore, the value of x in the interval [0, 2π) is:

[tex]x = \dfrac{\pi}{6}, \dfrac{\boxed{5} \pi}{\boxed{6}}[/tex]

Answer:

meight you gotta do better then that

Step-by-step explanation:

a picture is probably necessary

Answer:

the answer for the 2nd question is 1/4

Step-by-step explanation:

i took the test

The percentage by which the cost is increasing will be 75%.

The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.

The percentage of the 8th graders who want to go to the water slides is found from;

In the year 2000, a house was valued at $60 000.

In 2010, the same house was valued at $80 000.

The percentage value is found as;

[tex]\% = \frac{60000}{80000} \times 100 \\\\ \% =75 \%[/tex]

Hence the percentage by which the cost is increasing will be 75%.

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Answer:

y = 2/5 x - 18/5

Step-by-step explanation:

y = mx + b

m = (y2 - y1)/(x2 - x1) = [-2 - (-6)]/[4 - (-6)] = 4/10 = 2/5

y = 2/5 x + b

-6 = (2/5)(-6) + b

-30 = -12 + 5b

5b = -18

b = -18/5

y = 2/5 x - 18/5

Answer:

- 7x + 5y= (-11) -------(1)

-4x + 3y,= (-7) ----------(2)

Multiplying eq 1 with 3 and eq 2 with 5

3( -7x + 5y) = 3(-11)

5(- 4x + 3y) = 5(-7)

-21x + 15y = (-33)

-20x + 15y,= (-35)

Subtracting both the eq.

-x = 2

x = (-2)

Putting this value in eq. 1

- 7x + 5y= (-11)

-7(-2)+ 5y= (-11)

14 + 5y = (-11)

5y = (-11) - 14

5y= (-25)

y = (-5)

Answer: 7x+13

Step-by-step explanation:

7 is being multiplied by some number (x) and then the answer to that is added to 13.

Answer:

1

Step-by-step explanation:

The square root of 1 is 1 so it is a rational number while others are irrational

A percentage is a way to describe a part of a whole. The percentile ranking of Tina's sister is higher than her.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

A.)

The percentile ranking of Tine is,

Tina's Ranking = [1 - (54/300)] × 100% = 82%

Tina's soster Ranking = [1 - (23/175)] × 100% = 86.85%

Hence, the percentile ranking of Tina's sister is higher than her.

B.) It shows that you can succeed in the graduate examination if you exceed this value.

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Answer:

15

Step-by-step explanation:

so if its a 6 faced dice then there is a 3/6 numbers greater than 3. which simplifies to 1/2. 30(1/2)= 15

Answer:

added in the picture

Step-by-step explanation:

added in the picture

do in oder of pemdas....

Answer:

Area = 180 cm^2

Step-by-step explanation:

See attached image.  The width of the rectangle, a , is the hypotenuse of a right triangle with legs 15 and 20.

Use the Pythagorean Theorem: leg^2 +leg^2 = hypotenuse^2

[tex]a^2=15^2+20^2\\\\a^2=225+400\\\\a^2=625\\\\a=\sqrt{625}=15[/tex]

The width, w, is one leg of a right triangle that has hypotenuse 20 and one leg 16.

[tex]w^2+16^2=20^2\\\\w^2+256=400\\\\w^2=144\\\\w=\sqrt{144}=12[/tex]

The rectangle has length 15 cm and width 12 cm so its area is 12 x 15 = 180 cm^2

Answer:

AREA RECTANGLE =300 cm²

Step-by-step explanation:

If 2 of the 3 vertices of a triangle match up with 2 of the 4 vertices of a rectangle,then the area of the triangle will be exactly half of the area of the rectangle

(Or the area of the rectangle  will be exactly double  of the area of the triangle)

  Area right triangle  = ½ × base × height.

A = 1/2(15X20)

A=1/2( 300)

Area triangle =150  

Area of rectangle is DOUBLE as the  area of triangle

AREA RECTANGLE = 300

the correct options are:

Here we have the function:

[tex]F(x) = -\sqrt[3]{x}[/tex]

First, this is a cubic root, so its domain is the set of all real numbers (same for the range). And we know that the cubic root is an increasing function, so if we put a negative sign before it, we will have a decreasing function.

Then the correct options are:

The fourth option is incomplete, so we can't conclude if it is true or not, it would be true if it said:

"The function is a reflection over the x-axis of y = ∛x"

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Answer:

b, c, d

Step-by-step explanation:

Answer:

9=0

Step-by-step explanation:

9=0

The roots of x in the equation -10x² + 12x - 9 = 0 are:

x = (3/5) + (3/5)√(6)i

x = (3/5) - (3/5)√(6)i

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

To find the roots of x in the equation -10x² + 12x - 9 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation in standard form (ax² + bx + c).

In this case, a = -10, b = 12, and c = -9. Substituting these values into the quadratic formula, we get:

x = (-12 ± √(12² - 4(-10)(-9))) / 2(-10)

x = (-12 ± √(144 - 360)) / (-20)

x = (-12 ± √(-216)) / (-20)

Substituting this into the expression for x, we get:

x = (-12 ± 6√(6)i) / (-20)

Simplifying the expression further, we get:

x = (3/5) ± (3/5)√(6)i

Therefore, the roots of x in the equation -10x² + 12x - 9 = 0 are:

x = (3/5) + (3/5)√(6)i

x = (3/5) - (3/5)√(6)i

These roots are complex conjugates of each other.

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The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5).

Let's call the point that divides the line segment point P.

Point P divides the line segment into a ratio of 2:3

The ratio of 2:3 means we are dividing the line segment into 2+3=5 equal parts.

The horizontal distance between the two coordinates is 5.

The vertical distance between the two coordinates is 10.

Dividing both vertical and horizontal distance into five equal parts, we have a horizontal distance of 1 and a vertical distance of 2.

Every time we move one unit to the left from point J and two units up, we are dividing the line segment into five equal parts as shown in the picture.

The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5).

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Answer:

Step-by-step explanation:

The domain is the set of x values, and the range is the set of y values.