Find the missing part.

An equation in terms of r which models the situation described is : 100r² = 10r² + 90r - 337.50

First investment :

Luke:

Total amount had = $100

Amount invested = $10

Amount left = $100 - $10 = $90

Return = r times the amount invested = (10 × r) = 10r

Owen:

Total amount had = $100

Amount invested = $100

Return = r times the amount invested = (100 × r) = 100r

Second investment :

Luke :

Amount invested = Return on first + amount left = 10r + 90

Return is r times the amount invested :

Return on second investment = (10r + 90) × r = (10r² + 90r)

Total amount earned after both investment = 10r² + 90r

Owen :

Amount invested = Return on first = 100r

Return is r times the amount invested :

Return on second investment = (100r × r) = 100r²

Total amount earned after both investment = 100r²

Owen made 337.50 more than Luke ; This means that :

Total earned by Owen = Total earned by Luke + 337.50

100r² = 10r² + 90r + 337.50

Hence, the equation in terms of r is : 100r² = 10r² + 90r - 337.50

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Answer:

I'm assuming the chessboard is square so 49cm square.

Step-by-step explanation:

Area of a square= side × side

7×7=49

Have a nice day.

The area of the chessboard is 49 square inches, and which side length is 7 inches.

To find the area of the chessboard, we need to calculate the product of its length and width.

In this case, since the chessboard is a square, the length, and width are equal.

Given that the side length of the chessboard is 7 inches, we can calculate the area as follows:

Area of the chessboard = side length x side length

Area of the chessboard = 7 inches x 7 inches

Area of the chessboard = 49 square inches

Therefore, the area of the chessboard is 49 square inches.

Learn more about the area of the square here:

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Answer:

a. 6

Step-by-step explanation:

AB +BC =AC

2x-2+2x+10=32

4x+8=32

4x=32-8

4x=24

x=24/4

x=6

Answer:

B) (0,2)

Step-by-step explanation:

We substitute the values of x and y into this inequality:

2 ≥ 2(0)-1

2 ≥ 0-1

2 ≥ -1

This is true, so this is the correct point

hope this helps have a good day

Answer:

there it is

Step-by-step explanation:

Answer:

Jeff is moving faster.

Step-by-step explanation:

To compare two speeds, first we make them in one unit.

We know that,

1 km/h = 0.2777 m/s

7 km/h = 1.94 m/s

Jeff can run at a speed of 7 km/h i.e. 1.94 m/s while Cameron can run with a speed of 10 m/min or 0.167 m/s.

On comparing 1.94 m/s and 0.167 m/s, we found that Jeff is moving with more speed.

So, Jeff is faster.

Answer:

x=30

Step-by-step explanation:

Hi there!

For A to be parallel to B, 5x would be equal to 3x+60. (If they were parallel, these two angles would be alternate exterior angles, which are equal.)

[tex]5x=3x+60[/tex]

Subtract 3x from both sides

[tex]5x-3x=3x+60-3x\\2x=60[/tex]

Divide both sides by 2

[tex]x=30[/tex]

I hope this helps!

Answer:

5n² + 8bnv² + 3b²v^4

Step-by-step explanation:

(n+bv²) (5n+3bv²)

5n² + 3bnv² + 5bnv² + 3b²v^4

5n² + 8bnv² + 3b²v^4

Answer:

AC is greater than BC

Step-by-step explanation:

First, we know that the angle of a straight line is 180°, so angle B as a whole is equal to 180 degrees. Therefore, angle YBC + angle ABC = 180 degrees. As angle YBC is a right angle, signified by the small square on the angle, it is 90 degrees. Therefore,

90 degrees + angle ABC = 180 degrees

subtract 90 degrees from both sides to isolate angle ABC

angle ABC = 90 degrees

Therefore, as angle ABC is equal to 90 degrees, and a right angle is 90 degrees, triangle ABC has a right angle, making it a right triangle.

In a right triangle, using the Pythagorean Theorem, the square of the side opposite the right angle is equal to the sum of the squares of the other side. Since side AC is opposite the right angle, we can say that

AC² = AB² + BC²

As the length of a side has to be greater than 0, we can say that

AC² = AB² + BC²

AB² > 0

AC² > BC²

square root both sides

AC > BC

Therefore, AC is greater than BC

Answer:

see explanation

Step-by-step explanation:

Angles on the circumference subtended on the same arc are equal

Angle at the centre is twice the angle at the circumference subtended on the same arc.

Then

∠ BAC = ∠ BDC = 29°

∠ BOC = 2 × ∠ BDC = 2 × 29° = 58°

Answer:

3x-14=180

3x=194

x= 64 2/3

4(x-9)=180

4x-36=180

4x=216

x=54

Hope This Helps!!!

Step-by-step explanation:

(3x-14)°=180°

3x-14=180

3x=180+14

3x=194

x=64.6

[4(x-9)]°=180°

4x-36=180

4x=180+36

4x=216

x=54

Answer:

your y-intercept is 5 and your slope is 1 hope this helps with translating into the form you want

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

3/4 x 2/3

= 1/2

Answer:

22,999 feets

Step-by-step explanation:

Given the solution diagram attached,

The altitude, h of the plane can be solved using trigonometry :

Using :

Sin θ = opposite / hypotenus

Opposite = h

Hypotenus = 47440

Sin 29 = h / 47440

h = 47440 * sin29

h = 22999.368

h = 22,999 feets

Answer:

$11.76

Step-by-step explanation:

2.94×4=$11.76

Answer: x = 82°

Step-by-step explanation:

The angle on the other side of 108° can be calculated as 180° - 108° = 72°

All angles within a triangle add up to 180°, so the x-value can be found as:

x = 180° - 72° - 26° = 82°

Answer:

1). 6x - 14    2). y = 1x + 1       3). y = -4x + 22     4).y = -7/2x + 51/2

Step-by-step explanation:

1). y2 - y1 / x2 - x1      4 - (-2) / 3-2         = 6

y = 6x + b           4 = 6(3) + b      4 = 18 + b        -14 = b

y = 6x - 14

2). 2 - (-2) / 1 - (-3)      = 1

y = 1x + b        2 = 1(1) + b     2 = 1 + b    1 = b

y = 1x + 1

3).  2 - 6 / 5 - 4      = -4

y = -4x + b      6 = -4(4) + b      6 = -16 + b       22 = b

y = -4x + 22

4). 1 - 8 / 7 - 5      = -7/2

y = -7/2x + 51/2

Step-by-step explanation:

[tex]\longrightarrow \tt { SI = \dfrac{PRT}{100} } \\ [/tex]

[tex]\longrightarrow \tt { 250 = \dfrac{P \times 12\cfrac{1}{2} \times 4}{100} } \\ [/tex]

[tex]\longrightarrow \tt { 250 = \dfrac{P \times \cfrac{25}{2} \times 4}{100} } \\ [/tex]

[tex]\longrightarrow \tt { 250 = \dfrac{P \times 25 \times 2}{100} } \\ [/tex]

[tex]\longrightarrow \tt { 250 = \dfrac{P \times 50}{100} } \\ [/tex]

[tex]\longrightarrow \tt { 250 \times 100 = P \times 50} \\ [/tex]

[tex]\longrightarrow \tt { 25000 = P \times 50} \\ [/tex]

[tex]\longrightarrow \tt { \dfrac{25000}{50} = P } \\ [/tex]

[tex]\longrightarrow \underline{\boxed{ \green{ \tt { \$ \; 500 = P }}}} \\ [/tex]

Therefore principal is $500.

Let the total number of balls be x.

→ Red balls + Blue balls + Yellow balls = Total number of balls

[tex]\longrightarrow \tt{ \dfrac{2}{7}x + \dfrac{3}{5}x + 36 = x} \\ [/tex]

[tex]\longrightarrow \tt{ \dfrac{10x + 21x + 1260}{35} = x} \\ [/tex]

[tex]\longrightarrow \tt{ \dfrac{31x + 1260}{35} = x} \\ [/tex]

[tex]\longrightarrow \tt{ 31x + 1260= 35x} \\ [/tex]

[tex]\longrightarrow \tt{ 1260= 35x-31x} \\ [/tex]

[tex]\longrightarrow \tt{ 1260= 4x} \\ [/tex]

[tex]\longrightarrow \tt{ \dfrac{1260 }{4}= x} \\ [/tex]

[tex]\longrightarrow \underline{\boxed{ \tt { 315 = x }}} \\ [/tex]

Total number of balls is 315.

A/Q,

3/5 of the balls are blue.

[tex]\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}x} \\ [/tex]

[tex]\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}(315)} \\ [/tex]

[tex]\longrightarrow \tt{ Balls_{(Blue)} = 3(63)} \\ [/tex]

[tex]\longrightarrow \underline{\boxed{ \green {\tt { Balls_{(Blue)} = 189 }}}} \\ [/tex]

Answer:

The smallest number is 10

Step-by-step explanation:

x+y=24---equation 1

x-y=¹/6×24=>x-y=4---equation 2

Add both equations

2x=28

x=14

put x=14 into equation 1

14+y=24

y=24-14=10

Answer:

O D

Step-by-step explanation:

f+g(x)

3x+10+2x-4

3x +2x+6

Answer:

hello!

where are you from ?

Step-by-step explanation:

option 4 is correct ...there is no constant ratio.

Answer:

a)

x=4, y=-2

b)

x=2, y=2

c)

x=0, y=0

d)

x=1, y=1

e)

x=3, y=3

f)

x=4, y=4

Step-by-step explanation:

a) (x,-2) = (4,y)

x=4

y=-2

b) (3x, 4) = (6, 2y)

3x=6 => x=2

2y=4 => y=2

c) (2x-1, y + 2) = (-1,2)

2x-1 =-1 => x=0

y+2 = 2 => y=0

d) (2x + 4, y + 5) = (3x + 3,6)

2x+4 = 3x+3 => x=1

y+5 = 6 => y=1

e) (x + y,y + 3) = (6, 2y)

x+y = 6 => x+3 = 6 => x=3

y+3 = 2y => y=3

f) (x + y, x - y) - (8,0)​

x+y = 8 => 2x=8 => x=4

x-y = 0 => x=y => y=4

Answer:

£624

Step-by-step explanation:

Surface area of a box = 2(length*width + length*height + width*height)

Length = 60 cm

Width = 50 cm

Height = 20 cm

Surface area of a box = 2(length*width + length*height + width*height)

= 2(60*50 + 60*20 + 50*20)

= 2(3000 + 1200 + 1000)

= 2(5,200)

= 10,400 cm²

Surface area of a box = 10,400 cm²

The paint costs = £0.06 per cm²

Total cost of painting the box = 10,400 cm² × £0.06

= £624

Step-by-step explanation:

Question 13 :-

Question 14 :-

Answer:

13.) -56cd²

14.) n-⁴

Step-by-step explanation:

Question 13 :- -4c³• 7d² • 2c-²

Calculate the products.

Multiplying the terms with the same base by adding their exponents.

Calculate the exponents.

Question 14 :- n-⁴w⁰

Any non - zero expression raised to the power 0 equals 1.

Any expression multiplied by 1 remains the same.

Answer:

Step-by-step explanation:

Answer:

Every year, the population is increasing by a certain amount. This type of continuous growth is increasing at an increasing rate. Exponential growth.

Step-by-step explanation:

Let's say the population of Atlanta was 100,000 in year 0. At the end of year 1, it would have grown 3%. 100,000 * 103% = 103,000.

103% because if it were 3%, the population would be shrinking.

at the end of year 2, you take the ending amount of year 1, 103,000*103%=106,090.

Exponential growth is everywhere in the world, population sizes, production, intelligence. The formula f(x)=a(1+r)^x :

f(x): the amount in x years.

a: The starting population.

r: The yearly growth rate.

x: How many years.

If you are given months, convert from years to months.

For example: Detroit is expected to grow 1.1% each year until the year 2029. This means that 8 years would have passed, 2029-2021. You take the starting population, which is roughly 675,000 as of now and input into the exponential formula equation.

f(8)=675,000(1+.011)^8 = 736,738 (Population of Detroit in the year 2029).

.011 because 1.1% is converted to decimal form.

Answer:

V₂ = V₁

Step-by-step explanation:

Let the height of the rectangular prism = h

Let s represent the side length of the base of the square prism, we have;

The volume of the prism, [tex]V_{prism}[/tex] = s²·h

The volume of the square pyramid, [tex]V_{pyramid}[/tex] = (1/3)·s²·h

∴ V₁ = The area not taken up by the square pyramid = [tex]V_{prism}[/tex] - [tex]V_{pyramid}[/tex]

∴ V₁ = s²·h - (1/3)·s²·h = (2/3)·s²·h

Similarly, for the cylinder, we have;

Let h represent the height of the cylinder

Let r represent the radius of the base of the cone, we have;

Therefore;

The volume of the cylinder, [tex]V_{cylinder}[/tex] = π·r²·h

The volume of the cone, [tex]V_{cone}[/tex] = (1/3)·π·r²·h

∴ V₂ = π·r²·h - (1/3)·π·r²·h = (2/3)·π·r²·h

V₂ = (2/3)·π·r²·h

[tex]V_{cone}[/tex] = [tex]V_{pyramid}[/tex]

Therefore;

(1/3)·π·r²·h = (1/3)·s²·h

∴ π·r² = s²

Therefore, V₂ = (2/3)·π·r²·h = V₂ = (2/3)·s²·h = V₁

V₂ = V₁.