1. What is the cross section formed by cutting a cylinder perpendicular to its base?
2. What is the cross section formed by cutting a cone parallel to its base?
3. What is Cavalier's Principle? Can you think of an example applying it to everyday life?



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The Ratio of the boy's allowance to his sister's is 5 : 4.

The new Ratio is 1 : 10000.

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Option D is the correct answer.

From the graph, we can conclude that,

1. The two lines are continuous lines and not broken lines. So, the inequality sign should be either ≤ or ≥.

2. The points on the lines of the shaded region are also included in the solution.

The only option that matches with the above conditions is option D. So, option D is the correct answer.

Let us verify it.

Now, let us consider a point that is inside the shaded region and also on any one line.

Let us take (0, 2).

Plug in 0 for x and 2 for y in each of the options and check which inequality holds true.

Considering the inequalities,

y ≥ 3x - 2

x + 2y ≤ 4

Solving we get,

2 ≥ 3(0) - 2

2 ≥ -2

x + 2y ≤ 4

0 + 2(2) ≤ 4

4 ≤ 4

Here, both inequalities are correct.

So, option D is the correct answer.

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The complete question is =

Which system of linear inequalities is graphed?

A. y < 3x-2

x + 2y ≥ 4

B. y < 3x - 2

x + 2y > 4

C. y > 3x - 2

x + 2y < 4

D. y ≥ 3x - 2

x + 2y ≤ 4

Answer:

cost of 1 pound each=$10.50

Step-by-step explanation:

Let t = cost per pound of turkey

Let h = cost per pound of ham

4t + 2h = 30

t = h - 1.5

substitute h-1.5 in place of t in 1st equation

4(h-1.5) + 2h = 30

4h - 6 + 2h = 30

6h - 6 = 30

6h = 36

h = 6

t = h-1.5 = 4.5

1 pound of turkey costs $4.50

1 pound of ham costs    $6.00

                                ----------

Step-by-step explanation:

\( {(x - 3)}^{ - 1} \\ = - (x - 3) \times (1) \\ = - (x - 3)\)

Answer:

6 mph

Step-by-step explanation:

60 minutes in an hour, so that would be 20×3. So in one hour, 2×3=6, she will run 6 miles

Answer:

6 miles per hour

Step-by-step explanation:

Hey there! I'm happy to help!

Let's call this number n. We can now set up the following equation.

0.4n+n=196

We combine like terms.

1.4n=196

Divide both sides by 1.4

n=140.

Have a wonderful day! :D

Answer:

c = 3 because 4 times 3 = 12

Answer:

12= 3+3+3+3 or 12= 3x4

9514 1404 393

Answer:

  (c)  1/(36·a^4·b^10)

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)/(a^c) = a^(b-c)

  (a^b)^c = a^(bc)

  a^-1 = 1/a

__

  \(\left(\dfrac{(2a^{-3}b^4)^2}{(3a^5b)^{-2}}\right)^{-1}=\dfrac{(3a^5b)^{-2}}{(2a^{-3}b^4)^2}=\dfrac{3^{-2}a^{-10}b^{-2}}{2^2a^{-6}b^8}=\dfrac{1}{3^22^2}a^{-10-(-6)}b^{-2-8}\\\\=\boxed{\dfrac{1}{36a^4b^{10}}}\)

it would be option D

Answer:

c. 42 1/12

Step-by-step explanation:

sorry if it's wrong. this was an educated guess

Using the coordinates of the vertices of a polygon (-3, 1), (-3, 3), (-1, 5), (2, 4), and (2, 1) the perimeter of the polygon is 16.0 units

The perimeter is calculated by summing the sides

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

(-3, 1) and (-3, 3) =√{(-3 - -3)² + (3 - 1)²} = 2

(-3, 3) and (-1, 5) = √{(-1 - -3)² + (5 - 3)²} = 2√2

(-1, 5) and (2, 4) = √{(2 - -1)² + (4 - 5)²} = √10

(2, 4) and (2, 1) = √{(2 - 2)² + (1 - 4)²} = 3

(2, 1) and (-3, 1) = √{(-3 - 2)² + (1 - 1)²} = 5

The perimeter = 2 + 2√2 + √10 + 3 + 5

The perimeter = 15.9907

The perimeter = 16.0 units

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Answer: 144 square centimeters

Step-by-step explanation:

An area of a triangle is determined by this formula: Area = Length * Height/2. Since 12 x 24 = 288, divide 288 by 2 and you will have 144

Conclusion:

it's 144 square centimeters

In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.

To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).

The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.

Given data:

Cost of a 30-second commercial in 2021 = $5.6 million

CPI in 2021 = 271.4

CPI in 1967 = 33.4

To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:

Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)

Cost in 1967 = ($5.6 million) * (33.4 / 271.4)

Cost in 1967 ≈ $0.689 million

To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:

Cost in 1967 ≈ $68,900

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As per the perimeter the length of the shorter side is 10.5 feet and the length of the longer side is 73.5 feet.

The perimeter of a rectangle is the sum of the lengths of all its sides. If we know the perimeter of a rectangle and some information about the relationship between its sides, we can use that information to find the lengths of the sides.

Let's call the length of the shorter side "x".

The other side is seven times as long, so it is 7x.

The perimeter of the rectangle is 168 feet, so we have

=> 2x + 14x = 168.

Simplifying the equation, we have

=> 16x = 168.

Dividing both sides of the equation by 16, we find

=> x = 10.5.

So, the length of the shorter side is 10.5 feet and the length of the longer side is

=> 7x = 7 * 10.5 = 73.5 feet.

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Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

Step-by-step explanation:

substitute the angle of sine with a variable and differentiate

Answer: -20

Step-by-step explanation: i hope its right

A sequence of instructions that solves a problem is called an algorithm.

Answer:

from the graph we can see that

for 2 gallones - it can travell 70 miles

4 gallones - 140 miles

we will take the first case

2 gallones - 70 miles

17 gallones - ? miles

cross multiply

\( \frac{17 \times 70}{2} \)

= 595 miles

Answer:

Mochi

Step-by-step explanation:

Mochi

Each week theres a increase of 4 in Mochi's weight. So you will add 4 twice to get to the 5th week.

4th week : 17

5th week : 21

Kappa

In 4 weeks Kappa weighed 14, which is less that Mochi at the pace Kappa is going at.

on the 3rd week Kappa weighed 11

and 2nd week Kappa weighed 5

and 1st week Kappa weighed 3

Looking at the graph, we can give a rough estimate on the 5th week it's going to be 16 or 17 either way making Mochi heavier.

ADC & BCD are congruent triangles (by SAS postulate). Since triangle ADC & BCD are congruent according to the SAS postulate, we may utilize CPCTC to determine that section AC is equal to segment BD.

In arithmetic progression, the triangles 3: 4: 5 are the only ones with edges. Pythagorean triple-based triangles are Herodian, which means they have integer areas and sides.

The easiest approach I've found to know for sure if an aspect is 90 degrees is to use the 3:4:5 triangle. According to this rule, a triangle is said to be a right triangle if one of its sides is 3 and the other is 4.

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Answer:

7. 14

15. 30

28. 56

32. 64

18 36

x 2x

1/2y. y

2x. 4x

x+3 2x+9

Step-by-step explanation:

each out is double the in

Determining the highest point of value for a particular solution relies heavily on the type of problem which needs to be resolved.

Evaluate equations or functions: If you possess an equation or function that symbolizes the desired answer, it is prudent to study it intensely in order to pinpoint its maximum value. For instance, taking the derivative of the equation and establishing zero as an equalizer will allow you to determine any critical points. Shortly afterward, evaluating those points alongside endpoints within its domain verifies what its maximum value is.

Optimization strategies: In cases where a particular quantity must be maximized amidst constraints, such as linear programming or quadratic programming techniques, it is useful to implement optimization strategies to resolve these kinds of problems conveniently and effectively.

Experimentation via simulation: In instances where mathematical analyses prove too difficult given the complexity involved, it becomes necessary to use simulation or experimentation techniques to investigate potential solutions thoroughly. It involves improvising input parameters while watching output meticulously with an eye to spotting the corresponding maximum value.

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Answer:

200 tiles

Step-by-step explanation:

First convert meters to centimeters:

2 m = 200 cm and 4 m = 400 cm

Get the area of the floor:

Area 1: 200 x 400 = 80,000 cm

Get the area of the tile:

Area 2: 20 x 20 = 400 cm

Then, we divide area of the floor by area of the tile:

x = Area 1 / Area 2

x = 80,000/400

x = 200 tiles

The circles are similar because you can translate circle 1 using the transformation rule (x + 10, y) and then dilate it using a scale factor of 2/5.

First analyze the centers, the original center is at (-3, 5) and the new center is at (7, 5)

The change is in the x-value, the change is:

7 - (-3) = 10

So there is a translation of 10 units to the right,

And the original radius is R = 10, the new one is R' = 4

if the scale factor of the dilation is k we can write:

10*k = 4

k = 4/10 = 2/5

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Answer:

18 cm

Step-by-step:

The formula for the volume of a triangular prism is given by:

V_triangular_prism = (1/2) * base * height * length

where the base is the area of the base triangle, height is the perpendicular distance between the two parallel base planes, and length is the distance between the two triangular faces.

We are given that the base area of the triangular prism is 36 cm² and the volume is 432 cm³. Using these values, we can solve for the height:

432 = (1/2) * 36 * height * length

height * length = 24

Since we want to find the base side length of a rectangular prism that has the same volume, we can use the formula for the volume of a rectangular prism:

V_rectangular_prism = length * width * height

We know that the volume of the rectangular prism is also 432 cm³, so we can substitute this value and the value we found for the height * length product:

432 = length * width * height

432 = length * width * (24/length)

432 = 24 * width

width = 18

Therefore, the base side length of the rectangular prism needs to be 18 cm.

Hope this helps!

Answer:

\(\boxed{22n^8-16n^7-140n^4+112n^3-98}\)

Step-by-step explanation:

\((7n^4-14 - 5n^3) (7-8n^3 + 11n^4)\)

According to the distributive property, each term multiplies each of the terms in the other equation. Therefore, we can do the following:

\(\begin{aligned}\Rightarrow &7n^4 (7-8n^3 + 11n^4)= 49n^4-56n^3 n^4+77n^4n^4 \\&=49n^4-56n^7+77n^8 \end{aligned}\)

\(\begin{aligned}\Rightarrow &-14 (7-8n^3 + 11n^4)\\& = -98+112n^3-154n^4 \end{aligned}\)

\(\begin{aligned}\Rightarrow &-5n^4 (7-8n^3 + 11n^4)= -35n^4+40n^3n^4-55n^4n^4 \\&=-35n^4+40n^7-55n^8 \end{aligned}\)

Next, we combine all the terms of the plynomial equation:

\(49n^4-56^7+77n^8-98+112n^3-154n^4-35n^4+40n^7-55n^8\)

common factor:

\(22n^8-16n^7-140n^4+112n^3-98\)

By this, we have solved the exercise.

\(\text{-B$\mathfrak{randon}$VN}\)

Solving the equation for x, we have:

So the value of x is 6.

Answer:

The first is 1:6 and the second one is 4

Step-by-step explanation:

Answer:

if we want to find the maximum or minimum of a function, there are some methods, like see where the derivate is equal to zero and such.

Now, if we have a constraint, for example x> 4

This obviously changes the domain of the possible points where we can find the extremum.

But particularly, we can check at x  = 4 and see it there is a maximum.

if the constraint is x > 4, then then we may found a upper/lower bound.

if the constraint is x ≥ 4, then we may find a maximum/minimum.

Now, when we work with more complex situations, like find the maximum value of f(x) while we have the constraint g(x) = x^4 + x^3 + x^2 = 5

Then the domain will be equal to the intersection of the domains of both functions:

This means, the only possible values that we can input in f(x) to search the extremes, are the values of x such that x^4 + x^3 + x^2 = 5, so this relation defines our new domain (remember that f(x) also may have problems in some values of x, this is why we take the intersection of the domains of f(x) and g(x))

This means that constraints can limit a lot the domain of our functions.

Lee's TV costs $4.05 to operate for a month of 30 days.

To calculate the cost of operating Lee's TV for a month, we need to find out the total number of kilowatt-hours (kWh) of electricity consumed by the TV during that time.

First, let's find out how many watts Lee's TV consumes in a day:

250 watts/hour x 3 hours/day = 750 watts/day

To convert this to kilowatts, we divide by 1000:

750 watts/day ÷ 1000 = 0.75 kilowatts/day

Now, we can calculate the total number of kilowatt-hours consumed by the TV in a month:

0.75 kilowatts/day x 30 days = 22.5 kilowatt-hours

Finally, we can calculate the cost of operating the TV for a month:

22.5 kilowatt-hours x 18 cents/kilowatt-hour = $4.05

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