An amusement park ride consists of four circular cars. The ride rotates at a rate of 0.25 revolution per second. In addition, each car rotates 0.5 revolution per second. If Jane is positioned at point P when the ride begins, what coordinates describe her position after 31 seconds?

Answer:

A. 70>5g+61

Step-by-step explanation:

$5 per gigabyte means $5g

$61 + 5g

he keeps his budget lower than $70 so,

5g + 61 < 70

Given statement 'Extended ratios can be used to compare three or more quantities.' is True.

We know that an extended ratios are ratios that compare more than two quantities.

If we're comparing values x, y and z, then we would express this using the extended ratio x : y : z.

For example, suppose a triangle has side lengths of 15, 45, and 10.

The extended ratio that compares the side lengths of the triangle is:

15 : 45 : 10

We can simplify this ratio by factoring each of 15, 45, and 10 and cancelling out any factors that are common to all three quantities.

(5 × 3) : (5 × 9) : (5 × 2)

5 is a common factor of all three quantities, so cancel it out.

3 : 9 : 2

Therefore, given statement 'Extended ratios can be used to compare three or more quantities.' is True.

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Answer:

The Fibonacci sequence is defined by , for all , when and . In other words, to get the next term in the sequence, add the two previous terms. The notation that we will use to represent the Fibonacci sequence is as follows: f1=1,f2=1,f3=2,f4=3,f5=5,f6=8,f7=13,f8=21,f9=34,f10=55,f11=89,f12=144,…

Answer:

Ava had a greater percentage of change because her allowance increased by 150%, while Joey's only increased by 133%

Step-by-step explanation:

To find the percentage of change, you'll divide.

For Ava:

18 ÷ 12 = 1.5

This means her percentage of change is 150%

For Joey:

24 ÷ 18 = 1.33333... (Round to 1.33)

This means his percentage of change is 133%

150% > 133%, so Ava has the greater percentage of change.

[tex]\frac{6}{7} \times(\frac{-3}{13} )+\frac{3}{13}-\frac{( \frac{3}{13} \times8)}{7}[/tex]

By simplifying answer is [tex]\frac{-3}{13}[/tex] in decimals -0.230769

Here, we have done addition, subtraction, multiplication and division.

[tex]\frac{6}{7} \times(\frac{-3}{13} )+\frac{3}{13}-\frac{( \frac{3}{13} \times8)}{7}\\[/tex]

First, We will do Multiplication

Adding a number to itself as many times as the value of the other number is equivalent to multiplying two numbers by their sum.

[tex]\frac{-18}{91} +\frac{3}{13}-\frac{\frac{24}{13} }{7}[/tex]

Now, We will do the division

Basically, dividing is the act of dividing anything into equal sections or groups.

[tex]\frac{-18}{91} +\frac{3}{13}-\frac{24 }{91}[/tex]

Now, We will do the subtraction and Addition

When objects are collected together, addition, a mathematical operation, describes how many total items there are in the collection.

The reverse of adding in mathematics is called subtraction. When a specific number of objects from a group are removed, subtraction is used to determine how many objects are still present in the group.

[tex]\frac{3}{13}-\frac{6 }{13}\\\frac{-3}{13} \\[/tex]

Therefore, the simplified answer is  [tex]\frac{-3}{13}[/tex] in decimals -0.230769.

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By SSS (Side, side, side) congruency;

⇒ ΔA B C ≅ ΔX Y Z .

Given that;

The vertices of ΔA B C are;

A (3, -1) , B (3, 7) and C (7, 7)

The vertices of  ΔX Y Z  are;

X (-7, 0), Y (-7, 4), Z (1, 4)

We have to prove that ΔA B C ≅ ΔX Y Z .

What is congruency in triangle?

If all three corresponding sides are equal and all the three corresponding angles are equal in measure, then Two triangles are said to be congruent.

Now,

The vertices of ΔA B C are;

A (3, -1) , B (3, 7) and C (7, 7)

The vertices of  ΔX Y Z  are;

X (-7, 0), Y (-7, 4), and Z (1, 4)

To prove ΔA B C ≅ ΔX Y Z we use distance formula and prove all sides are equal.

In ΔA B C;

Distance between A and B;

[tex]D_{AB} = \sqrt{(3-3)^2 + (7 -(-1))^2} = \sqrt{64} = 8[/tex]

Distance between B and C;

[tex]D_{BC} = \sqrt{(7-3)^2 + (7 -7)^2} = \sqrt{16} = 4[/tex]

Distance between C and A;

[tex]D_{CA} = \sqrt{(7-3)^2 + (7 -(-1))^2} = \sqrt{80}[/tex]

In ΔX Y Z;

Distance between X and Y;

[tex]D_{XY} = \sqrt{(-7-(-7))^2 + (4 -0)^2} = \sqrt{16} = 4[/tex]

Distance between Y and Z;

[tex]D_{YZ} = \sqrt{(-7-1)^2 + (4 -4)^2} = \sqrt{64}= 8[/tex]

Distance between Z and X;

Clearly, Distance between sides of  ΔA B C and  ΔX Y Z are;

[tex]D_{AB} = D_{YZ} \\\\D_{BC} = D_{XY}\\\\D_{CA} = D_{XZ}[/tex]

Hence, By SSS congruency;

⇒ ΔA B C ≅ ΔX Y Z .

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Answer:

3 because you always know your answer by the smalest number which has a digit of 3

Step-by-step explanation:

Answer: 1000 ft

Step-by-step explanation:

Its pretty simple, 250 ft per hour, if they go for 4 hours theyll be at 1000 feet i guess

Answer:

1000 ft

Step-by-step explanation:

you multiple 250 by 4 and the is the change in elevation

Answer:

0.6 centimeter

Step-by-step explanation:

The picture below should help you see the tenth place, or where we are rounding to! Since, the number after the tenth place is above 4, we are going to round the tenth place up :)

0.5835 cen. → 0.6 cen.

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

The graph of the equation is showing that we are walking towards our home. If the equation d = 4 - (1/15)t represents your distance from home d for each minute you walk t .

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope

We have given d = 4 - (1/15)t

We will use the graph tool and determine the coordinates

(see the attached image)

When t = 0, d = 4                     (y-intercept)

This provide the info that at the time t = 0 the house was four units away.

When t = 60 min,  d = 0           (x-intercept)

This provide the info that he was already at home at the time t = 60 minutes.

Thus, this slope proves that he was walking towards the house.

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5:9 is degrees Celsius and the second element is its equivalent in degrees Fahrenheit.

What does a temperature in Fahrenheit mean?

F = (9/5)C+32

F = C x 9/5 + 32

C = (F - 32) x 5/9

The above equations could easily be derived by the following relationships:

Freezing Point = 0C or 32F and Boiling Point = 100C or 212F

Range from freezing point to boiling point = 100C or 180F,

i.e. C : F = 100:180 = 5:9

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If Ana owns a lot that contains 27 acres and is 972' wide and if she buys an adjacent lot that has the same depth but is only 648' wide then the total acres of land she will own is c.45

First of all, we convert the acres into square feet.

As 1 acre = 43560 square feet

27 × 43560 = 1176120 square feet

Dividing it with 972' to find the depth of the lot she already owns:

1176120 / 972 = 1210 depth

As the adjacent lot has the same depth, therefore;

1210 × 648 = 784080 square feet

Converting square feet into acres by division;

784080 / 43560 = 18 acres

Now we can calculate the total acres of land she will own by addition;

total acres = 27 acres + 18 acres

total acres = 45 acres

Therefore, the total acres of land she will own is calculated to be 45.

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The change in price of the inline skates for the month  of July is $153, August is $141 and September is $129 and using the mathematical operations we conclude that we cannot buy the inline skates after savings in the month of August

As per the question statement, we are supposed to find the change in  price of the inline skates when price of the inline skates for the month of June is $165.

Using mathematical operations,

Price In July =165+(-12)=153 dollars

Price In August =165+2(-12)=165-24=141 dollars

Price In September =165+3(-12)=165-36=129 dollars

Also in the second part of question asks that whether we will be able to buy the skates in the month of August if we save $[tex]35[/tex] in June, $[tex]55[/tex] in July,  $[tex]45[/tex] in August and $[tex]18[/tex] in September.

Price of Skates in August = $141

Using mathematical operations,

Total savings tlll August =35+55+45=135$dollars

As the savings is less than the price of Skates in August, we CANNOT buy the inline skates in the month of August.

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ΔACD ≅ ΔBCE so DC = EC therefore the triangle will isosceles triangle.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

In the given figure

AC = CB , DA = EB and ∠A = ∠B

So,

ΔACD ≅ ΔBCE

Now corresponding sides of a congruent triangle are the same.

So,

DC = EC therefore the triangle will isosceles triangle.

Hence "ΔACD ≅ ΔBCE so DC = EC, therefore, the triangle will isosceles triangle".

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The difference between 6 and 2 is 4

The difference between 10 and 6 is 4

The difference between 14 and 10 is 4

for each number  we just add 4 to the previous number.

14+4 = 18

18+4 =22

22+4 =26

The next 3 numbers in the pattern are 18, 22, 26.

In an Arithmetic Sequence the difference between one term and the another could be a constant. In other words, we just include the same value each time infinitely. An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term.

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Answer:

[tex] {7}^{ \frac{1}{4} } = \sqrt[4]{7} [/tex]

The correct answer is A.

Using proportions, it is found that:

a) You would find 36 kg of carbon is a 300 kg piece of marvel.

b) 40% of marble is Calcium.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For this problem, the ratio 10:3:12 of calcium, carbon and oxygen means that:

Hence for item a, the amount is given as follows:

300 x 3/25 = 36.

You would find 36 kg of carbon is a 300 kg piece of marvel.

For item b, the percentage is found as follows:

10/25 = 40%.

40% of marble is Calcium.

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Answer:

Step-by-step explanation:Given f(x)=x-5

f(-1)= -1-5

    = -6

f(0)=0-5

   = -5

f(1)=1-5

  = -4

f(2)=2-5

   = -3

f(5)=5-5  

    =0

f(8)=8-5

    = 3

The actual distance between Los Angeles and San Francisco is 19,83,824 feet.

Given that, the distance between San Diego and San Francisco is 2,683,824 feet away and Los Angeles is about 700,000 feet closer to San Francisco than San Diego.

Distance is the total movement of an object without any regard for direction. We can define distance as how much ground an object has covered despite its starting or ending point.

The actual distance between Los Angeles and San Francisco = The distance between San Diego and San Francisco - The difference in distance.

= 2,683,824-700,000

= 19,83,824

Therefore, the actual distance between Los Angeles and San Francisco is 19,83,824 feet.

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The number of shirts produced by each company to have the same cost are 5 shirts.

We have that:

For Company A:

Fixed cost will be = $ 20

Cost per shirt = $ 5

For company B:

Fixed cost will be = $ 10

Cost per shirt = $ 7

Let the number of shirts be x.

Equation for cost for company A:

Cost = 20 + 5 x

Equation for cost for company B:

Cost = 10 + 7 x

Now, put both the companies cost equal, we get that:

10 + 7 x = 20 + 5 x

7 x - 5 x = 20 - 10

2 x = 10

x = 10 / 2

x = 5

Therefore, the number of shirts produced by each company to have the same cost are 5 shirts.

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Answer:

1. Sides of ∠4 are DC and DG

2. Vertex of ∠2 = Point D

3. Another name for ∠3 = ∠EDG

4. ∠5 is an acute angle

5. ∠CDE is a straight angle

6. m ∠CDF = m∠5 + m∠1 = 42 + 117 = 159°

7. m ∠FDE = 17°

Step-by-step explanation:

For # 7 note that since DG is perpendicular to DF, m ∠GDF = 90°

m ∠GDF = m ∠3 + m ∠FDE
Since m ∠3 = 73°, m∠FDE = 90 - 73 = 17°

Answer:

Question:

Sunil has 40 counters. 9 of Sunil's counters are red. (c) What fraction of Sunil's counters are not red?

Answer: 0.775 or 77.5%

Step-by-step explanation:

Based on the given conditions, formulate: (40 - 9) / 40

Calculate the sum or difference: 31/40

= 31/40 = 77.5% or 0.775

The constant of variation in y = (12) x is (12)

y = kx            (Where k is the constant)

Here,

⇒ y = (12) x

So, k = (12)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

To multiply radicals with different indices, we need to find a common denominator, which is the lowest common multiple (LCM) between the roots. Once we obtain the LCM, we can multiply each root and exponent in the radicand to obtain the LCM, and rewrite as one radical

When we multiply two radicals with the same type of root (both square roots, both cube roots, and so on), we simply multiply the radicands (the expressions under the radical signs) and put the product under a radical sign

Answer:

-291.462

Step-by-step explanation:

My mom is a teacher lol and I have a calculator haha

Answer:

[tex]x \leq \dfrac{13}{4}[/tex]

Step-by-step explanation:

Given inequality:

[tex]2x-6(x-3)\geq 5[/tex]

Expand -6(x - 3):

[tex]\implies 2x-6(x)-6(-3)\geq 5[/tex]

[tex]\implies 2x-6x+18\geq 5[/tex]

Combine like terms  2x - 6x = -4x:

[tex]\implies -4x+18\geq 5[/tex]

Subtract 18 from both sides:

[tex]\implies -4x+18-18\geq 5-18[/tex]

[tex]\implies -4x\geq -13[/tex]

Divide both sides by -1, remembering to reverse the inequality:

[tex]\implies\dfrac{ -4x}{-1}\geq \dfrac{-13}{-1}[/tex]

[tex]\implies 4x\leq 13[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4x}{4}\leq \dfrac{13}{4}[/tex]

[tex]\implies x \leq \dfrac{13}{4}[/tex]

The cube with he greater side length is: cube B.

Volume of a cube = a³

Surface area of a cube = 6a²

Therefore:

Volume of cube A = 125 in.³

125 = a³

√125 = a

a = 5 in.

Side length of Cube A = 5 in.

Surface area of Cube B = 121 in.²

121 = 6a²

√(121/6) = a

√(121/6) = a

10.7 = a

a = 10.7

Side length of cube B = 10.7 in.

Therefore, the cube with he greater side length is: cube B.

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Answer:

12:1

Step-by-step explanation:

Answer:

2:1

Step-by-step explanation: