mark and kevin own 1/4 and 1/3 of the books on a shelf, respectively lori owns the rest of the books. if kevin owns 9 more books than mark, how many books does lori own ?

a divides b (a|b), as required and they are positive integers.

Given that a and b are positive integers, and a³ divides b³ (written as a³|b³), we need to show that a divides b (written as a|b).

Since a³|b³, this means that b³ = k * a³ for some integer k. Taking the cube root of both sides, we get:

b = (k * a³)^(1/3)

Now, we know that the cube root of a³ is a, so:

b = a * (k)^(1/3)

Since a and b are positive integers, and the cube root of an integer is either an integer or an irrational number, the only way for b to be an integer is if (k)^(1/3) is an integer. Let's denote this integer as m, so:

b = a * m

This shows that a divides b (a|b), as required.

To know more about positive integers, refer to the link below:

https://brainly.com/question/18380011#

#SPJ11

Equation connecting C and d is C = 5/3 d.

Direct Proportion of two quantities can be defined as that when one of the quantity increases, the other one also increases and vice versa.

(a) Given that,

C is directly proportional to d.

Equation can be written as C = kd, for some constant k.

Also, given,

C=100 when d=60

100 = 60k

k = 100/60 = 10/6 = 5/3

Equation is C = 5/3 d

(b) When d = 45 km

C = 5/3 × 45 = 75

Cost of transporting goods for 45 km is $75.

(c) When C = $120,

120 = 5/3 d

d = 120 × 3/5 = 72 km

Hence the distance is 72 km when the cost of transporting goods is $120.

Hence the equation is C = 5/3 d.

Learn more about Direct Proportion here :

https://brainly.com/question/14664532

#SPJ1

Answer:

Below

Step-by-step explanation:

x=\(\frac{1-20g}{10(1-4g)}\)

Answer:

using BODMAS=(4x-2)=(2x)

10x-10g(2x)=

10x=10+(2x)=

10x=20x

divide both sides by 10

10x/10=20x/10

x=20/10

x=2

Answer:

Step-by-step explanation:

Wee

Answer:it’s c

Step-by-step explanation:

The measure of angle ∠CBD is 65°.

Given that ∠ABC and ∠CBD are adjacent angles, it is known that their measures add up to 90°.

Therefore, we have:

m∠ABC + m∠CBD = 90°

It is also given that m∠ABC = 25°.

By using the substitution property of equality, we can substitute the value of m∠ABC into the equation:

25° + m∠CBD = 90°

Now, to isolate m∠CBD, we can use the subtraction property of equality:

m∠CBD = 90° - 25°

m∠CBD = 65°

Note : The property of equality refers to the fundamental principles or rules that allow us to manipulate equations while preserving their equality.

These properties are based on the concept that if two quantities or expressions are equal, we can perform certain operations on them without changing their equality.

For similar question on angle.

https://brainly.com/question/28262429

#SPJ11

Answer: x = 5/9

Step-by-step explanation:

Answer:

Ryan attempted 90 shots

Step-by-step explanation:

63 is 70% of 90

90 x .7 = 63

Ryan attempted 90 shots and 63 of them are baskets which is 70 percent.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Ryan made 70% of the basketball shots he attempted.

let, 'x' be the number of shots he attempted and 63 of them are baskets.

So, 70% of x is 63, which is,

(70/100)×x = 63.

0.7x = 63.

x = 63/0.7.

x = 90.

So, Ryan attempted 90 shots in total.

learn more about percentages here :

https://brainly.com/question/24159063

#SPJ2

After solving the system of equations using Gaussian elimination we get the values as x = 5 , y = -11 and z=3

Given we have the system of equations as follows:

2x - y + 4z = 33

x + 2y - 3z = -26

-5 x - 3y +5z = 23

Rewrite the system in matrix form and solve it by Gaussian elimination.

[ 2  -1  4     [ 33

 1  2  -3   =  -26

-5  -3  5 ]      23 ]

Now divide row 1 by row 2.

[ 1  -0.5  2        [ 16.5

 1     2   -3    =  -26

-5    -3  5 ]         23 ]

Now R₂ - 1R₁ → R₂

and R₃ + 5R₁ → R₃

[ 1  -0.5  2        [ 16.5

 0   2.5  -5    =  -42.5

 0  -5.5 15 ]       105.5 ]

Divide row 2 by 2.5.

[ 1  -0.5  2        [ 16.5

 0     1   -2    =  -17

 0  -5.5 15 ]       105.5]

R₁+0.5R₂ → R₁

R₃ + 5.5R₂ → R₃

[ 1   0  1          [ 8

 0   1   -2    =  -17

 0    0   4 ]        12 ]

Divide R₃ by 4

[ 1   0  1          [ 8

 0   1   -2    =  -17

 0    0   1 ]         3 ]

Therefore, R₁-1R₃→R₁

R₂ + 2R₃ → R₂

[ 1   0  1          [ 5

 0   1   0    =    -11

 0    0   1 ]        3 ]

therefore x = 5, y=-11 and z = 3.

Hence we solved the system of equations using Gaussian elimination.

Learn more about Gaussian elimination here:

brainly.com/question/14529256

#SPJ1

Answer:

Combine like terms4ℎ+3ℎ+ℎ8ℎ

Solution8ℎ

Step-by-step explanation:

The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

To know more about marginal utility related question visit:

https://brainly.com/question/30841513

#SPJ11

Answer:

Try incerting a picture it might help me

Step-by-step explanation:

Answer:

a and d

Step-by-step explanation:

got it right.

Answer:

-1/3

Step-by-step explanation:

Answer:

-1/3

Step-by-step explanation:

to find perpendicular you need to reverse the slope

The quadratic function for this problem is defined as follows:

y = 4(x + 3)² - 2.

The quadratic function of vertex(h,k) is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The vertex is the turning point of the function, hence the coordinates in this problem are given as follows:

(-3,-2).

Hence:

y = a(x + 3)² - 2.

When x = -2, y = 2, hence the leading coefficient a is obtained as follows:

2 = a(-2 + 3)² - 2

a = 4

Hence the equation is given as follows:

y = 4(x + 3)² - 2.

More can be learned about quadratic functions at https://brainly.com/question/31895757

#SPJ1

Answer:

\(4x^2\left(3x-1\right)\)

Key:

• \(a^{b+c}=a^ba^c\)

• Factor out the last leading term standing to solve in the end.

Step-by-step explanation:

\(12x^3-4x^2\\x^3=xx^2\\=12xx^2-4x^2\\=4\cdot \:3xx^2-4\cdot \:1\cdot \:x^2\\=4x^2\left(3x-1\right)\)

Answer:

It is 2 which represents 20,000

Answer:

he answer is 49.

Step-by-step explanation:

To find the missing number in the pattern of perfect squares, we can observe that the given numbers are arranged in increasing order. The missing number should fit the pattern of perfect squares.

The given numbers are: 16, 25, 36, ____, 64, 81.

The pattern suggests that each number is the square of a certain integer. Let's find the missing number by looking at the square root of each given number:

√16 = 4,

√25 = 5,

√36 = 6,

_____,

√64 = 8,

√81 = 9.

From the above calculations, we can see that the missing number is the square of 7, since √49 = 7. Therefore, the missing number in the pattern is 49.

So, the answer is 49.

Answer:

These are the answers for A,B,C only. I am sorry but I can't answer the last one.

Explanation

In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.

To translate the function up and down, you simply add or subtract numbers from the whole function. If you add a positive number (or subtract a negative number), you translate the function up. If you subtract a positive number (or add a negative number), you translate the function down.

So for the given question

For the given question

So for the first one, when the parent function is shifted 4 units to the left, we will have

Then the second translation of Shifting 2 units up

we will have

Thus, we will have our answer as

The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2.

b = 1, ≥

From the diagram, the solution to the inequality is x ≥ 1 and x ≤ -3

Hence:

|x + b| ≥ 2

x + b ≥ 2 or -(x + b) ≥ 2

x ≥ 2 - b or x ≤ -2 - b

2 - b = 1 and -2 - b = -3

b = 1

Hence |x + 1| ≥ 2

The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2. b = 1, ≥

Find out more on inequality at: brainly.com/question/24372553

#SPJ1

Answer:

m≥3

Step-by-step explanation:

Answer:

m≥3

Step-by-step explanation:

Given the following polynomial,

We can factor it as follows;

ANSWER:

Answer:

See below.

Step-by-step explanation:

X-intercepts: (-7, 0) & (-3, 0)

Axis of Symmetry: x = -5

Y-intercept: (0, -21)

Vertex: (-5, 4)

Mrs. Shipley moved at a speed of 12.0266 feet per second which was originally expressed in miles per hour.

The miles per hour multiplied by 1.466667 gives the speed in feet per second.

Mrs. Shipley ran at an average speed of 8.2 miles per hour.

These units must be converted into feet/second.

We know that,

1 miles/hour =  1.466667 feet/second

So, 8.2 miles/hour = 8.2 ×  1.466667 feet/second

∴ 8.2 miles/hour = 12.0266 feet/second

Therefore, Mrs. Shipley ran at a rate of 12.0266 feet per second, which was originally expressed in miles per hour.

Learn more about problems based on unit conversion here:

https://brainly.com/question/141163

#SPJ9

Answer:

u forgot the question...........

The height of Lincoln's face on Mt. Rushmore is approximately 126.56 feet.

To calculate the height of Lincoln's face on Mt. Rushmore, we can use trigonometry and the given angle of elevation.

Let's denote the height of Lincoln's face as 'h'. From the two sightings 800 feet from the base of the mountain, we can form a right triangle.

Using the tangent function, we can set up the following equations:

tan(32°) = h / 800 (for the bottom angle of elevation)

tan(35°) = (h + h) / 800 (for the top angle of elevation, since the distance is the same)

Simplifying these equations, we find:

h ≈ 800 * tan(32°) ≈ 465.03 feet (for the bottom of Lincoln's face)

2h ≈ 800 * tan(35°) ≈ 261.53 feet (for the top of Lincoln's face)

Therefore, the height of Lincoln's face is approximately 465.03 feet, and the total height from the bottom to the top is approximately 261.53 feet.

To learn more about “trigonometry” refer to the https://brainly.com/question/25618616

#SPJ11

Answer:

  (b)  5994 cm²

Step-by-step explanation:

You want to know the area of a triangle with base 6ac² and height 3 cm more, given that a=2 and c=3.

The base of the triangle is ...

  base = 6ac² = 6(2)(3²) = 108 . . . . cm

The height of the triangle is 3 cm more, so is ...

  height = base + 3 = 108 cm +3 cm = 111 cm

The area is half the product of base and height:

  A = 1/2(base)(height)

  A = 1/2(108 cm)(111 cm) = 5994 cm²

The area of the triangle is 5994 cm², matching choice B.

<95141404393>

Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

Answer:

Let's assume that the price before adding the VAT is x.

We know that the VAT rate is 8%, which means that the VAT amount is 8% of x, or 0.08x.

The total price including VAT is the sum of the price before VAT and the VAT amount, so we can write:

Total price = price before VAT + VAT amount

or

2,700 = x + 0.08x

Simplifying this equation, we can combine like terms on the right-hand side to get:

2,700 = 1.08x

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 1.08:

x = 2,700 / 1.08

x = 2,500

Therefore, the price before VAT was added is 2,500.

Reason:

There's a 30% chance they buy the popcorn, which means there's a 70% chance they don't buy it.

100% - 30% = 70%

Then convert the 70% to 0.7

Answer:

0.7 or 70%

Step-by-step explanation:

0.3 * 100 = 30%

100%-30% = 70%

You either buy or not. If 30% you don't then 70% you do.