Use cross products to solve the proportion:

5/m = 15/9

progress prior to 1980. if n is an integer greater than two (n > 2)

Final answer:

Fermat's Last Theorem is an extension of the Pythagorean Theorem, with the latter being a special case where n=2 in the general form of equations proposed by Fermat.

Explanation:

The familiar theorem that Fermat's Last Theorem is an extension of is the Pythagorean Theorem. The Pythagorean Theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²), can be seen as the case n=2 in a series of equations of the form a⁴ + b⁴ ≠ c⁴ for any integer value of n greater than 2, which is what Fermat's Last Theorem addresses. The conviction behind mathematical postulates, as well as the certainty and consistency of mathematical proofs, contribute to the trust we place in mathematical theorems, just as repeated verification confirms theories in physics when the correct postulates are chosen.

Answer:

r=25.6

Step-by-step explanation:

[tex]p=-4.8\\q=3.2\\\\r=-3.2p+q^2\\r=-3.2(-4.8)+(3.2)^2\\r=15.36+10.24\\r=25.6[/tex]

Answer:

See the picture below for the graph.

To solve the given system of equations, we have to find the intersecting point of the two lines.

As shown in the picture below, the intersecting point is (3, -1).

Therefore, x = 3 and y = -1.

Answer:

Step-by-step explanation:

y = -x + 2

2x - y = 7

I think you would benefit from graphing these equations yourself and then identifying the coordinates of their intersection.  To help you get started out:

Line 1:  Here the slope is -1 and the y-intercept is 2.  Plot a dark dot at (0, 2).  Now, starting with your pencil point on that dot, move 1 unit to the right and from this new location move 1 unit down.  Plot another dark dot there.  Now draw a line through these two dots.

Line 2:  2x - y = 7 when solved for y is   y = 2x - 7, which has a slope of 2 and y-intercept of -7.  Plot a dot at (0, -7).  From that point, move 1 unit to the right and from this new location move 7 units down.  Plot another dot there.  Draw a line thru these two dots.

Identify the coordinates of the point of intersection of these two lines.  For your reference I will find the solution using elimination by addition and subtraction.  Rewrite 2x - y = 7 as y = 2x - 7:

y = 2x - 7

y = -x   +2

--------------     SUBTRACT the second equation from the first, obtaining:

0  = 3x - 9.  Then 3x = 9 and x = 3.  Subbing 3 for x in y = 2x - 7, we get y = 2(3) - 7, or y = -1.

The two lines intersect at the point (3, -1).

Answer:

Answer D

Step-by-step explanation:

We'd need more information to answer this question, namely, the unit price for organic apples.  Without this info there is nothing to compare.  Answer D

Steepness of a line is measured by its slope. For the considered case: Option D: We need more information to answer this question.

A straight line of the form [tex]y = mx + c[/tex] has its slope as 'm'

It is constant for a line. The more the slope is, the steeper the line is.

Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have negative slope. Horizontal line has 0 slope and vertical line has infinite slope, as it is now at maximum steepness.

For the given case, we're not given the price of organic apples. If we assume that the price of organic apples is given by [tex]y = Ax[/tex] [tex]y = Px[/tex]

Then, if A > 2.75, then graph of organic apples is steeper, else if A < 2.75, then the graph of pears is steeper.

Otherwise, if A = 2.75 (which means price of pears = price of organic appples), then both are of same steepness.

Since we don't know A's value here, thus:

For the considered case: Option D: We need more information to answer this question.

Learn more about slope of a straight line here:

https://brainly.com/question/2503591

Answer:

so they dont get cramps or chairly horses

Step-by-step explanation:

Answer:

Here's the reasons why it's important to stretch before and after a workout. When it comes to pre-workout stretching, stretching before a workout helps your body to become more pliable, which decreases your risk for injury. ... The main muscles groups used during the session are the ones that need to stretch. And sometimes for example middle splits you might need to repair your hips to fake one because you didn't stretch to open the muscles up first not force them

Step-by-step explanation:

I hope you understood it. Good Luck

Please mark me brainliest please!!

Formula used: cos(x) = [tex]\frac{adjacent}{hypotenuse}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: D. AE and BD intersect at point C.

Answer: A AND B

Step-by-step explanation:

The answer is: Area 38.5

The insurance company's payment is $1,680.00 and Bill's share of the charge is $670.00.

To calculate the insurance company's payment, we first need to determine the amount after the deductible is applied. Since the bill was $2,350.00 and the deductible is $250, we subtract the deductible from the bill: $2,350.00 - $250 = $2,100.00. The insurance company covers 80% of this amount, so we multiply $2,100.00 by 80%: $2,100.00 x 80% = $1,680.00. Therefore, the insurance company's payment is $1,680.00.

Bill's share of the charge is calculated by subtracting the insurance company's payment from the total bill: $2,350.00 - $1,680.00 = $670.00. Therefore, Bill's share of the charge is $670.00.

https://brainly.com/question/37317228

#SPJ3

recall that an absolute value expression is in effect a piece-wise with a ± version.

[tex]\bf |x-1| > 2\implies \begin{cases} +(x-1)>2\implies x-1>2\\\\ ~\hfill x>3\\ \cline{1-1} -(x-1)>2\implies x-1\stackrel{\downarrow }{<}-2\\\\ ~\hfill x<-1 \end{cases}[/tex]

Check the picture below.

Answer:

Step-by-step explanation:

[tex]x< -1\ or\ x>3\\\\\dfrac{-1+3}{2}=\dfrac{2}{2}=1\\\\x<-1\ or\ x>3\qquad\text{subtract 1 from all sides}\\\\x-1<-2\ or\ x-1>2\to|x-1|>2[/tex]

Answer: the value of y is 1. If needed, the value of x is 4.

Step-by-step explanation:

See paper attached. (: I went ahead and solved for x too, just in case.

Answer:

0.525 %

Step-by-step explanation:

there is a total of 80 students and 42 received a A or B so 42/80 = 0.525

Hope this helps!

Answer:

64 in² (Answer B)

Step-by-step explanation:

Note that this rhombus is made up of a large upper triangle and a large lower triangle.  Each of these two triangles has base 2(8 in) (or 16 in) and height 4 in.

The area-of-a-triangle formula is

A = (1/2)(base)(height), which here is

A = (1/2)(16 in)(4 in) = 32 in².

Now double that, because we have an upper triangle of area 32 in² and a lower triangle of the same area 32 in².  So the total area of the rhombus is 64 in²

Answer:

to the full amount

Step-by-step explanation:

Answer:

125 packages of chips.

Step-by-step explanation:

A vending machine sells chips at $0.55

And candy at $0.75

Last month, the vending machine yielded $170.00 with the sale of 260 items.

Let x be the number of chips sold and y be the number of candies sold.

$0.55x + $0.75y = $170.00

x + y = 260

Solving the above simultaneous equations by substitution;

x = 260 - y

Then,

0.55(260 - y) + 0.75y = 170

143 - 0.55y + 0.75y = 170

0.2y = 170 - 143 = 27

y = [tex]\frac{27}{0.2}[/tex] = 135

x = 260 - 135 = 125

So there were 125 packages of chips sold.

She would be multiplying. If you send me the answers I can give you a better explained answer?

The answers are:

Part a: The money in the account is growing.

Part b: The rate of growth is 3%

Part c: The value 250 represents the starting amount of money.

To solve the problem, first, we must remember the structure of the exponential growth or decay function:

[tex]P(t)=StartAmount*(rate)^{t}[/tex]

Where,

- Start Amount, is the starting value or amount

- Rate, is the rate of growth or decay, we must consider the following conditions:

If the rate is greater than 1, the rate is a growth rate.

If the rate is lower than 1, the rate is a decay rate.

- t, is the time elapsed.

Therefore, we are given the following function:

[tex]f(x)=250(1.03)^{x}[/tex]

From the function we can see that:

- Since the rate is 1.03 and it's greater than 1, the money in the account is growing.

- From the function we already know that the rate of growth is equal to 1.03

The rate is calculated by the following formula:

[tex]Rate=1+percent(growth)[/tex]

- The value 250 represents the starting amount of money.

Hence, the answers are:

Part a: The money in the account is growing.

Part b: The rate of growth is 3%

Part c: The value 250 represents the starting amount of money.

Have a nice day!

The exponent represents

An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

Given

The exponential function [tex]\rm f(x)=250(1.03)^x[/tex]

where x is the number of years.

Part A: The money in the account growing or decaying.

If the power increases the value of the function increases.Since the x can never be negative so it is growing.

Part B: The rate of growth or decay.

The rate of growth is the base of the exponent.

Since the base is 1.03, then the rate will be 1.03.

Part C: The value 250 represents.

250 represents the principal value that was invested initially.

A. The x can never be negative so it is growing.

B. The base is 1.03, then the rate will be 1.03.

C. 250 represents the principal value that was invested initially.

More about the exponent link is given below.

https://brainly.com/question/5497425

Answer:

The answer is ± 5i

Answer:

A bar graph

Step-by-step explanation:

A bar chart will give you the visual understanding of your data.It will clearly show the book with most number of pages and compare the books according to the number of pages.You can formart using different colors for each bar.

Answer:

yeeeeeeeeeeeeeeeees

Answer:

Step-by-step explanation:

6(4*2-5)-5(2)

= 6(8-5)-10

= 6(3)-10

= 18-10

= 8

Answer:

Part a) The paint needed will be [tex]24\ pints[/tex]

Part b) The weight of the life sized statue  is [tex]896\ lb[/tex]

Step-by-step explanation:

step 1

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z----> the scale factor

x----> surface area of the life sized statue

y----> surface area of the smaller statue

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=4[/tex]

substitute

[tex]4^{2}=\frac{x}{y}[/tex]

[tex]x=16y[/tex]

The surface area of the life sized statue  is 16 times the surface area of the smaller statue

therefore

The paint needed will be

[tex]16(1.5)=24\ pints[/tex]

step 2

Find the weight of the life sized statue

we know that

If two figures are similar, then the ratio of its weights (or volumes) is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> weight of the life sized statue

y----> weight of the smaller statue

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=4[/tex]

[tex]y=14\ lb[/tex]

substitute

[tex]4^{3}=\frac{x}{14}[/tex]

[tex]x=64(14)=896\ lb[/tex]

The life-size statue will need 96 pints of paint since its volume is 64 times larger than the smaller statue.

Step 1: Determine the volume ratio between the life-size statue and the smaller statue.

Since the dimensions of the life-size statue are four times those of the smaller statue, the volume ratio is [tex]\(4^3 = 64\)[/tex]. This means the life-size statue will have 64 times the volume of the smaller statue.

Step 2: Calculate the amount of paint needed for the life-size statue.

If 1.5 pints of paint are needed for the smaller statue, then the life-size statue will require [tex]\(1.5 \times 64 = 96\)[/tex] pints of paint.

Step 3: Write the final answer.

Therefore, 96 pints of paint will be needed to paint the life-sized statue.

Answer:

A

Step-by-step explanation:

segment cd is the only line that passes through and meets at a right angle

Answer:

A; The graph has a slope of 6.

Step-by-step explanation:

A; True

B; The y value changes with the x

C; Has a steady slope of 6

D; You cant tell if this is a parabola

Answer:

Step-by-step explanation:

Remember that the slope represents the constant ratio of variation. In other words, is the number that variates the relation between variable.

So, the given table represents a proportional relationship, because you can observe that x-variable changes one unit, while y-variable changes 6 units. In other words, while y-variable changes 6 units, x-variable changes 1 unit, that's a proportional relationship, and its ratio is

[tex]m=\frac{y}{x}=\frac{6}{1}=6[/tex]

This means the proportional relationship has a slope of 6.

Therefore, the right answer is the first choice.

Remember that proportional relationships are represented by a straight line, where the slope is the constant of variation.

[tex]255.35 \div 5 = 51.07 [/tex]

[tex]51.07 \times 2 = 102.14[/tex]

Answer:

102.14

Step-by-step explanation:

Answer:

4-3y and 2−4x

Step-by-step explanation:

Use the distributive property to multiply 1/3  by 12−9y.

1/3⋅12+1/3 (−9)y

Multiply 1/3  and 12 to get 12/3.

12/3+1/3 (−9)y

Divide 12 by 3 to get 4.

4+1/3 (−9)y

Multiply 1/3  and −9 to get (−9)/3.

4+(−9)/3 y

Divide −9 by 3 to get −3.

4−3y

Use the distributive property to multiply 1/4  by −16x+8.

1/4 (−16)x+1/4⋅8

Multiply 1/4  and −16 to get (−16)/4.

(−16)/4 x+1/4⋅8

Divide −16 by 4 to get −4.

−4x+1/4⋅8

Multiply 1/4  and 8 to get 8/4.

−4x+8/4

Divide 8 by 4 to get 2.

−4x+2  

The expressions 1/3(12-9y) and 1/4(-16x+8) are simplified by distributing the fractions over each term inside the parentheses, resulting in the simplified forms 4 - 3y and -4x + 2, respectively.

To solve the two separate algebraic expressions given, we'll perform operations step by step.

Solution for 1/3(12-9y):

Solution for 1/4(-16x+8):

Note that these are not equations with equals signs, so we cannot 'solve for y or x' in the traditional sense; we merely simplified the expressions.

For this case we must find the inverse of the following function:

[tex]f (x) = (x-6) ^ 2 + 7[/tex]

For this we follow the steps below:

Replace f (x) with y:

[tex]y = (x-6) ^ 2 + 7[/tex]

We exchange the variables:

[tex]x = (y-6) ^ 2 + 7[/tex]

We solve the equation for "y", that is, we clear "y":

[tex](y-6) ^ 2 + 7 = x[/tex]

We subtract 7 on both sides of the equation:

[tex](y-6) ^ 2 = x-7[/tex]

We apply square root on both sides of the equation to eliminate the exponent:

[tex]y-6 = \sqrt {x-7}[/tex]

We add 6 to both sides of the equation:

[tex]y = \pm \sqrt {x-7} +6[/tex]

We change y by [tex]f ^ {- 1} (x):[/tex]

[tex]f ^ {- 1} (x) = \pm \sqrt {x-7} +6[/tex]

Answer;

[tex]f ^ {- 1} (x) = \pm \sqrt {x-7} +6[/tex]

If it is a inverse function.

Answer:

3x3 in.

Why did you need to know that?

Well, anyway...hope it helped anyway...

Step-by-step explanation: