Write and solve an inequality.

Bobby hopes that he will someday be more than 72 inches tall. He is currently 59 inches tall. How many more inches, x, does Bobby need to grow to reach his desired height?

Answers

Answer 1

Answer: We can write an inequality to show how many more inches Bobby needs to grow to reach his desired height by using the following information:

Bobby hopes that he will someday be more than 72 inches tall.

He is currently 59 inches tall.

We can use the inequality x + 59 > 72, where x is the number of inches Bobby needs to grow to reach his desired height.

This inequality represents the total height (x + 59) being greater than the desired height (72).

To solve this inequality, we can subtract 59 from both sides:

x > 72 - 59

x > 13

So, Bobby needs to grow 13 inches or more to reach his desired height.

Step-by-step explanation:


Related Questions

solve the equation

(x + 2)(x + 6) = 0

Answers

Answer:

The zeroes of the equation are -2 and -6.

Step-by-step explanation:

(x + 2)(x + 6) = 0

=> x = -2, -6

Hope it helps.

Find the equation of the line that passes through (1,3) and is perpendicular to y=2x+3. Leave your answer in the form ax+by=c Where a, b and c are integers.

Answers

Answer:

2y+x=7

Step-by-step explanation:

The equation of a line is in the form:

[tex]y = mx + c[/tex]

where m is the gradient and c is the y-intercept.

In the equation y=2x+3 the gradient is 2, so to find the perpendicular gradient, it is the negative reciprocal, or in other words, flip the number upside down and make it negative:

[tex]2 = \frac{2}{1} [/tex]

[tex] \frac{2}{1} \: flipped \: upside \: down = \frac{1}{2} [/tex]

[tex] make \: \frac{1}{2} \: negative = - \frac{1}{2} [/tex]

So the gradient for the point (1, 3) is -1/2

Using y=mx+c to find c (the y-intercept) where y=1, m=-1/2, x=1, substitute these values in:

[tex]y = mx + c[/tex]

[tex]3 = - \frac{1}{2} (1) + c[/tex]

[tex]3 = - \frac{1}{2} + c[/tex]

[tex]3 + \frac{1}{2} = c[/tex]

[tex]c = \frac{7}{2} [/tex]

So the equation is:

[tex]y = - \frac{1}{2} x + \frac{7}{2} [/tex]

We need to write this in the form ax+by=c, so multiply everything by 2 to get rid of the fractions on the right:

[tex]2y = - x + 7[/tex]

Bring x to the left side by adding it:

[tex]2y + x = 7[/tex]

This is now in the form ax+by=c

(01.04 MC)
Which radical function has a domain of (x € R|x≤-3) and range of y€R|y24}?

Answers

The domain and range of the the function are given below -

Domain → [-5, 10)

Range → [-3, 3)

What is a function?A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes.

Given is a graph of the function.

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes. So, we can write the domain as -

Domain → [-5, 10)

Range → [-3, 3)

Therefore, the domain and range of the the function are given below -

Domain → [-5, 10)

Range → [-3, 3)

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Write the equation of the line that passes at the point (-8,5) with the slope m=-1 in slope-intercept form.

Answers

Answer:

y = -x - 3

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Given that the point (-8,5) lies on the line and the slope of the line is m=-1, we can use the point-slope form of a linear equation to write the equation of the line.

The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

So substituting the given point (-8,5) and slope m=-1 into the point-slope form, we get:

y - 5 = -1(x + 8)

Simplifying, we get:

y = -x - 3

This equation is the slope-intercept form of the line that passes through the point (-8,5) and has a slope of -1.

The average cost of making rx televisions per week is
C(x) = x² - 40x+500 dollars per television.
a How many televisions should be made per week to
minimise the average cost?
b
<
Find the minimum average cost.
How many televisions are made per week if the average
cost is $200 per television?

Answers

Answer:

Step-by-step explanation:

a. To minimize the average cost, we need to find the value of x that minimizes the cost function C(x) = x² - 40x + 500.

This is the same as finding the minimum value of the parabola represented by the function. The vertex of the parabola is the point at which the parabola reaches its minimum or maximum value. The vertex form of a parabola is given by C(x) = a(x - h)² + k, where (h, k) is the vertex.

By comparing the given function with the vertex form of a parabola, we can find the vertex:

C(x) = x² - 40x + 500

= a(x - h)² + k

= (x - h)² + k

The x-coordinate of the vertex h = 40/2 = 20

So the minimum average cost occurs when 20 televisions are made per week.

b. To find the minimum average cost, we need to substitute the value of x = 20 into the cost function:

C(x) = x² - 40x + 500

= 20² - 40*20 + 500

= 400 - 800 + 500

= 100

So the minimum average cost is $100 per television.

If the average cost is $200 per television, we can set C(x) = 200 and solve for x:

200 = x² - 40x + 500

0 = x² - 40x + 300

This is a quadratic equation that can be solved by factoring or by using the quadratic formula.

we can factor it as

0 = (x-50)(x-6)

x = 50 or x = 6

The number of televisions made per week if the average cost is $200 per television is 50 or 6. Since 50 is much higher than 20, the minimum average cost, it is not physically possible to make 50 televisions with the average cost of $200 per television. So the answer is 6 televisions per week.

A cyclist travels 2 miles in 10 minutes and then a further 8 miles in 30 minutes without stopping. Calculate the cyclist's average speed in mph.

Answers

The cyclist's average speed is

14.93

mph.

Total

distance

covered is=2+8=10

Total time =10+30=40

=40/60 min

=.0.67 hours.

Convert miles per min to miles per hour,

average speed= 10 miles/0.67 hours,

=14.93 mph.

The average speed is =4.93 mph

The total distance covered is 2 + 8 = 10 miles. The total time taken is 10 minutes + 30 minutes = 40 minutes. To convert minutes to hours, divide the time in minutes by 60. So, the total time taken in hours is 40 minutes / 60 = 0.67 hours. To convert miles per minute to miles per hour, multiply the speed in miles per minute by 60. So, the average speed in miles per hour is

10 miles / 0.67 hours = 14.93 mph

The average speed is =14.93 mph

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Pls help me solve this!! It’s due today!!

Answers

f(x) and g(x) are inverses using composition

How to use composition to prove that f(x) and g(x) are inverses?

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

To confirm the inverse relationship using composition.

For valid inverse f(g(x)) must be equal to g(f(x))

f(x) = ∛(x) + 13; g(x) = (x - 13)³:

f(g(x)) = f((x - 13)³)

f(g(x)) = ∛((x - 13)³) + 13

f(g(x)) = x - 13 + 13

f(g(x)) = x

g(f(x)) = g(∛(x) + 13)

g(f(x)) =  (∛(x) + 13 - 13)³

g(f(x)) =  (∛(x))³
g(f(x)) =  x

Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse

f(x) = x³ + 1; g(x) = ∛(x - 1):

f(x) = x³ + 1; g(x) = ∛(x - 1)

f(g(x)) = f(∛(x - 1))

f(g(x)) =  (∛(x - 1))³ + 1

f(g(x)) =  x - 1 + 1

f(g(x)) =  x

g(f(x)) = g(x³ + 1)

g(f(x)) = ∛((x³ + 1) - 1)

g(f(x)) = ∛(x³)

g(f(x)) = x

Since f(g(x)) = g(f(x)) then f(x) and g(x) are inverse

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5s+7s fatorise this answer

Answers

Answer:

s(5+7)

Step-by-step explanation:

Since 's' is the Highest Common Factor that will go outside the brackets.

Answer:

[tex]s(5+7).[/tex]

Step-by-step explanation:

1. Write the expression.

[tex]5s+7s[/tex]

2. Find a common term between the 2 elements.

As you can tell, a common term between "5s" and "7s" is variable "s". Hence, we may factorize using that variable.

3. Divide by "s" ans express as a factor.

[tex]s(\frac{5s+7s}{s} )\\\\s(\frac{5s}{s} +\frac{7s}{s} )\\ \\s(5+7)[/tex]

4. Conclude.

Final answer: [tex]s(5+7)[/tex].

log10 2=P,then the value of log10 5 is

Answers

The value of log10 5 as required to be determined using the given information is; 0.3979 + P..

What is the value of log10 5 as required?

It follows from the task content that; the value of log10 5 is to be determined based on the given information.

Since the given expression is; log10 2 = P;

The expression which can be inferred from the equation above is;

10^P = 2..............(i)

However, let; log10 5 = x

Therefore; 10^x = 5..........(ii)

By dividing the equation (ii) by (i); we have that;

10^(x - P) = 2.5

Therefore, from the converse of logarithmic law;

x - P = log10 2.5

x = P + log10 2.5

where, log10 2.5 = 0.3979

x = 0.3979 + P

Ultimately, the value of log10 5 as required is; 0.3979 + P.

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Use the FOIL method to find the product below.
(x+5)(x²-3x)
O A. x³ + 2x²-15
OB. x³+2x2-15x
OC. x³ +5x2-15x
OD. x³ + 5x2-15
SUBM

Answers

The FOIL method to find the product (x + 5)(x² - 3x) is x³ + 2x² - 15

How to use the foil method?

You should note the following about FOIL method

It stands for "First, Outer, Inner, Last"

It is the sum of:

· multiplying the First terms,

· multiplying the Outer terms,

· multiplying the Inner terms, and

· multiplying the Last terms

That is  (a+b)(c+d) = ac + ad + bc + bd

Use FOIL (First, Outside, Inside, Last)

The give expression is

x(x²) = x³

x(-3x) = -3x²

5(x²) = 5x²

5(-3x) = -15x

Combine like terms:

x³ - 3x² + 5x² - 15x

x³ + 2x² - 15

Therefore the FOIL method is x³ + 2x² - 15

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Pls help. I think it's only one answer, but I need help just to make sure two more of the answers are not part of it, since the question says to choose all possible answers. Pls help quickly, I'll mark you Brainliest if it is correct.

Answers

Answer:

-5 and -3

Step-by-step explanation:

-2x + 1 > 6

[tex]-2(-\frac{5}{2}) + 1 > 6\\6 > 6[/tex]

Not an answer

-2(-5) + 1 > 6

11 > 6

An answer

-2(-2) + 1 > 6

5 > 6

Not an answer

[tex]-2(-\frac{3}{2}) + 1 > 6\\4 > 6[/tex]

Not an answer

-2(0) + 1 > 6

1 > 6

Not an answer

-2(-3) + 1 > 6

7 > 6

An answer

HELP MEEEEEEEEEEEEEE

Answers

Answer:

B

Step-by-step explanation:

after 0 it's 1 and 4 is after 5

The table shows the costs of playing several carnival games. You have $20 and play each game twice. How much money do you have left?

Ring Toss : $1.50
Balloon Pop : $1.5
Basketball : $2.50

Answers

Answer:

$9 left

Step-by-step explanation:

1.50 x 2 = $3

1.50 x 2 = $3

2.50 x 2 = $5

5 + 3 + 3 = $11

$20 - $11 = $9

Answer:

9

Step-by-step explanation:

1.50+1.50+3

1.50+1.50+3

2.50+2.50= 5

5 + 3 + 3 = 11

20 - 11 = 9

cylinder has a volume of 2,034.72 cubic millimeters and a radius of 6 mm, whats the height?​

Answers

Answer:

2,260.80 cubic millimeters

Step-by-step explanation:

The figure is made up of a cylinder and a sphere which has been cut in half. The radius of each half sphere is 6 mm. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth. A cylinder and 2 half spheres. All have a radius of 6 millimeters. The cylinder has a height of 12 millimeters. Recall the formulas V = B h and V = four-thirds pi r cubed 527.52 cubic millimeters 1,431.84 cubic millimeters 2,034.72 cubic millimeters 2,260.80 cubic millimeters

ayudaaa a resolver esto plis​

Answers

The value of x in degrees will be 6° and 11° using properties of parallel lines.

What Qualities Characterize Parallel Lines?

They are typically equal-distance, parallel straight lines. The lines here are parallel. They never come together no matter how far you extend them in any one way.

Pairs of equal-sized angles that are both obtuse or acute and are generated on the same side of the transversal are known as corresponding angles. Each pair of comparable angles on the same side of the crossing transversal is equal to the other.

The alternative angle theorem states that alternate interior angles or alternate exterior angles that come from cutting two parallel lines are congruent.

In the above figure,

8x + 7 = 55

8x  = 55 - 7

x = 6

Measure of the angle will be 8 × 6 + 7 = 49

In 11)

10x + 10 = 9x + 21 (by using first corresponding angles and then alternate angles)

⇒x = 11

The value of x in degrees will be = 11° using properties of parallel lines.

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Find the length of the midsegment of each trapezoid.

Answers

Answer:

D

Step-by-step explanation:

the midsegment of a trapezoid is half the sum of the parallel sides, that is

midsegment = [tex]\frac{WT+VU}{2}[/tex] = [tex]\frac{17.5+6.1}{2}[/tex] = [tex]\frac{23.6}{2}[/tex] = 11.8

what is the difference between f(9) and f(x)=9

Answers

Answer:

Step-by-step explanation:

The f(9) means that the value of x would be 9 in any given equations or functions.

For example:

[tex]f(x) = 2x^{2} + 5\\f(9) = 2(9)^{2} + 5\\f(9) = 2(81) + 5\\f(9) = 162 + 5\\f(9) = 167[/tex]

On the other hand, f(x) = 9 means that the value of a certain function is simply equal to 9.

How many square feet of outdoor carpet will we need for this hole?

Answers

The area of a outdoor carpet is 42 square feet.

What is area?

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

In the given figure, the outdoor carpet consist two triangles and one rectangle.

Here, rectangle measures length=11 ft and width = 3 ft, small triangle has base= 2 ft and height =3 ft and large triangle has base= 4ft and height =3 ft.

So, area of rectangle is 11×3 = 33 square ft

Area of small triangle = 1/2 ×Base×Height

= 0.5×2×3

= 3 square feet

Area of large triangle = 1/2 × 4×3

= 6 square feet

Total area = 33+3+6

= 42 square feet

Therefore, the area of a outdoor carpet is 42 square feet.

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How can we use linear functions in real life

Answers

Answer:

Step-by-step explanation:

Linear functions can be used in many real-world applications such as:

Economics: Linear functions can be used to model the relationship between the price of a product and the quantity of the product that will be sold.

Engineering: Linear functions can be used to model the relationship between force and displacement in elastic materials.

Sciences: Linear functions can be used to model the relationship between the concentration of a substance in a solution and the time it takes for that substance to be consumed or produced.

Business and Finance: Linear functions can be used to model the relationship between the cost of a product and the number of products produced.

Graphing: Linear functions can be used to graph the relationship between different variables.

Transportation: Linear functions can be used to model the relationship between the distance traveled and the time it takes to travel that distance at a constant speed.

Construction: Linear functions can be used to model the relationship between the height of a building and the number of floors in the building.

Weather forecasting: Linear functions can be used to model the relationship between temperature and time of the day.

Answer:

I'm going to provide a real life case for this answer. I own and manage an online soccer jersey store and the process behind it is quite simple:

1. Receive order

2. Buy jerseys from supplier

3. Resell at an slighly higher price

4. Pay taxes + shipping

Now, say that "x" is the amount of jerseys my store sells in a month. I can use functions to create an expression that tells me what is the total net revenue I get from selling "x" amount of jerseys a month.

For example, say that the jerseys cost $50 and you sell them for 60$. You also need to pay the shipping for each jersey (say it is $5 per jersey). Then, we can form a function like this:

[tex]y=60x-50x-5x[/tex]

As you can tell, the money that comes back to the seller ($60 dollars per jersey) is expressed as a possitive coefficient for variable "x" (number of sold jerseys). And, all the other costs, which is money that you spend in order to sell the jerseys, are expressed with a negative coefficient meaning that they are not net revenue, it isn't profit. Now, to see how much money you can make by selling 2 jerseys, simplify the function and substitute variable "x" (number of sold jerseys) by 1:

[tex]y=60x-55x\\ \\y=5x[/tex]

Say "y" is the net revenue:

[tex]y=5(2)\\ \\y=10[/tex]

You can also use functions to determine things such as, how many jerseys do I need to sell in order to make $750 of net revenue? In that case you do the following:

[tex](750)=5x\\\\x=\frac{750}{5} \\ \\x=150[/tex]

From this analysis, you can conclude that you need to sell 150 jerseys ij order to amke a net revenue of $750.

In conclusion, linear functions can be used to see how a variable value (normally called "x") can affect in the results in multiple daily situations: how many miles can your car run with a full tank, how much time do I need to work so I can buy a product, how much money I can spend in something so I can have saving of "x" amount at the end of the year, etc...

Some students collected the data below. They will graph the data. What is the y-intercept? Your answer should be an ordered pair ( , )

Answers

Answer:

(0, 28)

Step-by-step explanation:

Overview

To answer the question given, we have to find the point on the line that goes through the points given in the table when the x-axis represents the month of the year (1 is Jan, 2 is Feb, etc.) and the y-axis represents the average temperature for that month.

Method 1

I've attached a graph of the line for reference.

When we look at the graph of the line that goes through the points given in the table, we can determine that its y-intercept is (0, 28).

Method 2

To determine the y-intercept of the line without actually graphing it, we can construct an equation using the given points.

We know that the line's slope is defined as [tex]\dfrac{\textrm{rise}}{\textrm{run}}[/tex].

Using that information, we can solve for the line's slope by using any two of the given points. I will use the points for January (1, 42) and February (2, 56).

[tex]\textrm{slope} = \dfrac{56-42}{2-1} = \dfrac{14}{1} = 14[/tex]

Then, we can plug this value into the point-slope form equation

[tex]y - b = m(x - a)[/tex]

along with one of the given points [tex](a,b)[/tex] -- I'll use January (1, 42):

[tex]y-42=14(x-1)[/tex]

Next, to solve for the y-coordinate of the line's y-intercept, we can plug 0 into the equation for x and solve for y.

[tex]y - 42 = 14(0 - 1)[/tex]

[tex]y - 42 = 14(-1)[/tex]

[tex]y - 42 = -14[/tex]

[tex]y = -14 + 42[/tex]

[tex]y = 28[/tex]

Finally, we can plug the solved y-coordinate and 0 for the x-value (because we solved for when y when x = 0) into the format of a Cartesian coordinate:

(0, 28)

I just need this question left pls help

Answers

By using the fact that the sum of the interior angles must be 180°, we wil see that:

x = 110°.

How to find the value of x?

First, remember that the sum of the interior angles of a triangle is alway equal to 180°.

We also can see that the interior angle that is adjacent to x can be written as:

a = 180° - x

Then the sum of the interior angles will give:

30° + 80° + (180° - x) = 180°

30° + 80° - x = 0

110° - x = 0

110° = x

That is the value of x.

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2. Kasie lives in Seattle. She can see her house from the observation deck of the Seattle Space Needle. The
observation deck is 520 feet above the ground and the angle of depression from the deck to her house
is 70. What is the direct distance from the base of the Space Needle to Kasie's house? Round your
answer to the nearest foot.

Answers

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

What is angle of depression?

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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Please help me with this question.

Answers

The solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

What is initial value problem?In multivariable calculus, an initial value problem is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.

Given is the initial value problem -

y''' + 10y'' + 25y' = 0

We can write the -

[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]

The given differential equation can be solved and written as -

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)

Therefore, the solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

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What is the equation of the midline of the sinusoidal function?

Answers

Answer:

y = -3

Step-by-step explanation:

The midline of a sinusoidal function is y = a where "a" is halfway between the minimum and maximum y-values of the function.

From inspection of the given graph:

Maximum y-value = 1Minimum y-value = -7

Therefore, the y-value that is halfway between the minimum and maximum points is:

[tex]\implies y=\dfrac{y_2+y_1}{2}=\dfrac{-7+1}{2}=\dfrac{-6}{2}=-3[/tex]

Therefore, the equation of the midline of the given sinusoidal function is:

y = -3

Test the convergence of the series ∑∧∞ 4.7.10…(3n+1) /1.2.3….n

Answers

The convergence of the series ∑∧∞ 4.7.10…(3n+1) /1.2.3….n is π =3+. 1. 10. +. 4. 102. +. 1. 103. +. 5. 104. +. 9. 105. +. 2. 106

What is the convergence of  a series?

You should understand that any series that is not convergent is said to be divergent or to diverge

The reciprocals of the positive integers produce a divergent series

This can be written as π =3+. 1. 10. +. 4. 102. +. 1. 103. +. 5. 104. +. 9. 105. +. 2. 106 .... For x ∈ R, the (infinite) geometric series ∑n≥0 xn converges if |x| < 1 and ...

This is to say that the convergence series is the reciprocal of the series.

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Which expression is equivalent to 3 square root 27c7 • 3 square root 250c2, if c≠0

Answers

Answer:3 square root 27c7 • 3 square root 250c2 can be simplified by applying the property of square roots, (√a * √b) = √(ab) .

So, 3 square root 27c7 • 3 square root 250c2 = √(27c7 * 250c2) = √(27250c7c2) = √(675c7*c2) = √(675c9) = √(675) * √(c9) = 15c3

Therefore, 3 square root 27c7 • 3 square root 250c2 = 15c3 is the equivalent expression.

Step-by-step explanation:

Borrowed 600$ from the bank. Interest is $14.25 for 90 days. What is interest rate?

Answers

Answer:

0.01 %

Step-by-step explanation:

The interest rate is the percentage of the principal (the amount borrowed) that is charged as interest over a certain period of time.

To find the interest rate, we can use the formula:

Interest Rate = Interest / Principal x Number of days / 365

We know that the principal is 600$, the interest is 14.25$ and the number of days is 90

so we can substitute the values into the formula:

Interest Rate = 14.25 / 600 x 90 / 365

Interest Rate = 0.02375 * 90 / 365

Interest Rate = 0.0104

Rounded to the nearest thousandth, the interest rate is 0.010 or 0.01 %

The cork in a wine bottle should not exceed 8.77KPa of normal stress. If the shear stress induced by the friction of its perimeter with the bottle is 4.98KPa, which is the maximum allowed ratio between the cork length H and the cork radius R?

Answers

The maximum allowed ratio for the cord such that the maximum allowable normal stress is 8.77 kilopascals is equal to 2.081.

How to determine the maximum allowed ratio of a cork in a wine bottle

Let assume that the cork is made of a ductile material, in this case we find that the normal stress (σ), in kilopascals, and shear stress (τ), in kilopascals, are described below:

Normal stress

σ = F / A

Shear stress

τ = (3 · V) / (2 · A')

Where:

V - Shear force, in kilonewtons.F - Normal force, in kilonewtons. A - Transversal area, in square meters. A' - Transversal shear area, in square meters.

Let assume that cork is at static equilibrium and at inminent motion, then the shear and normal forces are, respectively:

F = P

V = P / 2

And the transversal areas are introduced below:

A = π · R²

A' = 2 · R · H

Where:

R - Radius of the cork, in meters.H - Height of the cork, in meters.

If we know that σ = 8.77 kPa and τ = 4.98 kPa, then the maximum allowed ratio between the cork height and the cork radius is:

8.77 = P / (π · R²)

8.77 = [1 / (π · R)] · (P / R)

4.98 = 1.5 · (0.5 · P) / (2 · R · H)

4.98 = [0.75 / (2 · H)] · (P / R)

Then, we eliminate P / R of the two equations:

8.77π · R = 13.24 · H

H / R = 8.77π / 13.24

H / R = 2.081

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Please help me with this question.

Answers

i) The absolute change of the CPI from 2009 to 2014 is given as follows: 22,199.

ii) The absolute change of the Tuition from 2009 to 2014 is given as follows: $26.5.

iii) The relative change of the CPI from 2009 to 2014 is given as follows: 10.35%.

iv) The relative change of the Tuition from 2009 to 2014 is given as follows: 26.59%.

Tuition has increased more in this time period.

How to obtain the changes?

The absolute change between two amounts is given by the absolute value of the difference of these two amounts.

Hence for the CPI from 2009 to 2014 is given as follows:

236736 - 214537 = 22,199

For the Tuition, it is given as follows:

126.15 - 99.65 = $26.5.

The relative change is given by the absolute change divided by the initial value and multiplied by 100%, hence:

CPI = 22199/214537 x 100% = 10.35%.Tuition: 26.5/99.65 x 100% = 26.59%.

Due to the higher relative change, the Tuition increased more in this time period.

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Given the figure below, find the values of x and z.
92°
(10x + 32)°

Answers

Since Z and 92 both have vertical angles, they are equal. Subtract from 180 to determine the measure of the other angle, which is 88 degrees since it forms a straight line with the 92-degree angle. Solve the expression by setting the value at 88.

What is meant by vertical angle?The intersection of two straight lines produces a pair of vertical angles, which are not next to one another. Vertical angles that are across from one another form the corners of the "X" formed by two straight lines.The fact that they are located across from one another gives them the name "vertically opposite angles." Whenever two angles are vertically opposed, they are equal. Additionally, a vertical angle and the angle to it are supplementary angles because they add up to 180 degrees. For instance, if two lines cross and form an angle with a given value (X=45°), then the opposing angle also has a value of 45°. The angle measure of vertical angles is constant, making them congruent.

∠AOB + ∠BOC = 180°

92°+( 10x  +  32 )° = 180°

10x + 32° = 180 - 92

10x + 32° = 88

10x = 88 - 32

10x = 56

x = 56 ÷ 10

x = 5.6°

Hence, the value of X is 5.6 and Z is 92.

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