Is the pythagorean theorem only for right triangles

Answer:

1st line

Step-by-step explanation:

Should be z=11-3x-2y, then solve from there.

Answer:

Step-by-step explanation:

if you can pick the same card 3 times the probability of winning is

[tex](\frac{5}{10})^{3} = \frac{1}{8}[/tex]

but if you remove each card after you've picked them it's :

[tex]\frac{5}{10}.\frac{4}{9}.\frac{3}{8}= \frac{60}{720}[/tex]

notice if you remove an odd card every time you pick one of them you are also removing one of the overall cards

and if you subtract these two you get : [tex]\frac{1}{8} - \frac{60}{720} =0.0417[/tex]

which is like 4 percent

Answer:

I think the answer is 23

Answer:

  the resulting error is about 0.754 in²

Step-by-step explanation:

  A(r) -A(r0) ≈ dA/dr·(r -r0)

The area of a circle is given by ...

  A(r) = πr²

so the derivative is

  dA/dr = 2πr

and the area error is ...

  dA/dr·(r -r0) = 2π(12 in)(0.01 in) = 0.24π in² ≈ 0.754 in²

Answer:

Step-by-step explanation:

Based on the answer selections, it appears we need to find the radius and circumference of the sphere. We can start with the volume formula in terms of the radius:

  V = (4/3)πr³

  36π = (4/3)πr³

  (36π)(3/(4π)) = r³ = 27 . . . . . . mm³

  r = ∛27 = 3 . . . . mm³

Then the circumference is ...

  C = 2πr = 2π(3 mm) = 6π mm

The radius is 3 mm; the circumference is 6π mm.

Answer:

a and b is the answer

Step-by-step explanation:

Explanation:

Polygons are classified by ...

The number of coordinate pairs will define the number of vertices.

The differences between "adjacent" coordinate pairs can be used to find side lengths and relationships (angles, parallel, perpendicular).

_____

If the differences between adjacent coordinate pairs are ...

  (∆x, ∆y) = (x2 -x1, y2 -y1)

then the slope of the line joining those coordinates is ∆y/∆x. (This may be "undefined" if ∆x = 0.) Two line segments with the same slope are parallel. Two line segments with slopes that have a product of -1 are perpendicular. (Two segments with slopes of 0 and "undefined" are also perpendicular.)

It can be useful on occasion to know that the angle (α) a line segment makes with the x-axis can be found from ...

  α = arctan(slope)

The length of a line segment (d) can be found from the Pythagorean theorem:

  d = √((∆x)² +(∆y)²)

Answer:

2/3

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

To solve this simplest form, you'd need to divide 2 from numerator into denominator.

4/2=2

6/2=3

2/3, which is our answer.

I hope this helps!

The total number of votes would be: 7752 total votes.

Here's how you solve it!

For every 3 yes there was 5 no's.

You would but that into a fraction so it would be 3/5

Then you take the number of no votes and multiply.

3/5 x 4845

Then you would get 2907.

4845+ 2907= 7752

4845= no votes

2907= yes votes

7752= total votes

Hope this helps! :3

Answer:

C. is your answer

Step-by-step explanation:

In order to determine the line of symmetry, it would help to put this standard form parabola into vertex form, which is

[tex]y=a(x-h)^2+k[/tex],

where x = h is the equation of the line of symmetry.

To get this into vertex form we will complete the square.  The first couple of steps I will combine into 1.  We will set the quadratic equal to zero, then move the constant over to the other side:

[tex]88x^2-264x=-300[/tex]

The next rule is that the leading coefficient HAS to be a positive 1.  Ours is a positive 88, so we have to factor it out:

[tex]88(x^2-3x)=300[/tex]

Now we can perform the process of completing the square.  The rule is to take half the linear term, square it, and add it to both sides.  Our linear term is 3.  Half of 3 is 3/2, and 3/2 squared is 9/2.  We will add 9/2 inside the parenthesis on the left, but don't forget about that 88 sitting out front which refuses to be ignored.  It serves as a multiplier into the parenthesis.  What we actually added in, then, was 88(9/2) which is 198:

[tex]88(x^2-3x+\frac{9}{4})=-300+198[/tex]

The purpose of completing the square is to give us a perfect square binomial which serves as the axis of symmetry of the parabola and also gives us the h coordinate of the vertex.  We will state that binomial and at the same time do the addition on the right:

[tex]88(x-\frac{3}{2})^2=-102[/tex]

Now we can move the constant back over and set it back equal to y:

[tex]y=88(x-\frac{3}{2})^2+102[/tex]

From that form you can see that the equation of the line of symmetry is x = 1.5.  The coordinates of the vertex are (1.5, 102).  If we move 1 unit to the left of the vertex, or 1 unit to the right of the vertex, we will be at the same height.

C then is your answer.

The solution is : C. is the answer.

C. The trajectory of the airplane is symmetric about the line x = 1.5 km, which indicates that the height of the airplane when it moves a horizontal distance of 0.5 km is the same as the height of the airplane when it moves a horizontal distance of 2.5 km.

The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.

here, we have,

In order to determine the line of symmetry, it would help to put this standard form parabola into vertex form, which is

y = a (x-h)^2 + k

,where x = h is the equation of the line of symmetry.

To get this into vertex form we will complete the square.  The first couple of steps I will combine into 1.  We will set the quadratic equal to zero, then move the constant over to the other side:

88x^2 - 264x = -300

The next rule is that the leading coefficient HAS to be a positive 1.  Ours is a positive 88, so we have to factor it out:

88( x^2 - 3x) = 300

Now we can perform the process of completing the square.  The rule is to take half the linear term, square it, and add it to both sides.  Our linear term is 3.  Half of 3 is 3/2, and 3/2 squared is 9/2.  We will add 9/2 inside the parenthesis on the left, but don't forget about that 88 sitting out front which refuses to be ignored.  It serves as a multiplier into the parenthesis.  What we actually added in, then, was 88(9/2) which is 198:

88( x^2 - 3x + 9/4 ) = -300 + 198

The purpose of completing the square is to give us a perfect square binomial which serves as the axis of symmetry of the parabola and also gives us the h coordinate of the vertex.  We will state that binomial and at the same time do the addition on the right:

88( x - 3/2)^2 = -102

Now we can move the constant back over and set it back equal to y:

y = 88( x - 3/2)^2 + 102

From that form you can see that the equation of the line of symmetry is x = 1.5.  The coordinates of the vertex are (1.5, 102).  If we move 1 unit to the left of the vertex, or 1 unit to the right of the vertex, we will be at the same height.

C then is the answer.

learn more on parabola:

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Answer:

m<DEB = 62°

Step-by-step explanation:

From the figure we can see a circle with center O.

To find the measure of <DOB

From the figure we get,

m<DOC = 44° and m<COB = 80°

We know that, m<DEB = m<DOB/2

m<DOB = m<DOC +m<COB

 =  44 + 80

 = 124

To find the measure of <DEB

m<DOB = 124

Therefore  m<DEB =  m<DOB/2

 = 124/2 = 62°

Answer: 236 degrees

Step-by-step explanation: Add the two angles that are given. 44+80=124. The angle DOB is 124 degrees. The angle DEB is the rest of the circle. There are 360 degrees in a circle. So subtext 360 from 124.

360 - 124 = 236

DEB = 236 degrees.

Step-by-step explanation:

f(x) = x² − 6x + 9

f(½) = (½)² − 6(½) + 9

f(½) = ¼ − 3 + 9

f(½) = 6¼

The value is 6¼, or as an improper fraction, 25/4.

Answer:   The correct answer is:   " 6 [tex]\frac{1}{4}[/tex] " ;  

_______________________________________________                  

                                 or;  write as:   " 6.25 " .

______________________________________________

     " f([tex]\frac{1}{2})[/tex] =  6 [tex]\frac{1}{4}[/tex] " ;

                                             =  6.26 " .

______________________________________________

Step-by-step explanation:

______________________________________________

Given the function:

______________________________________________

      " f(x)  =  x² − 6x + 9 " ;

______________________________________________

What is:   " f([tex]\frac{1}{2}[/tex]) " ?

______________________________________________

Plug in "([tex]\frac{1}{2}[/tex])"  for all values of "x" in the equation;  

                →  to solve for:  " f([tex]\frac{1}{2}[/tex]) " ;   as follows:

______________________________________________

→     " f([tex]\frac{1}{2}[/tex]) " ;  

     =  ([tex]\frac{1}{2}[/tex])² −  6*([tex]\frac{1}{2}[/tex]) + 9  ;

    =   ([tex]\frac{1^{2} }{2^{2}}[/tex])  −  ([tex]\frac{6*1}{2}[/tex]) + 9 ;

     =        ([tex]\frac{1}{4}[/tex]) −  ([tex]\frac{6}{2}[/tex])   +  9    ;

     =       ([tex]\frac{1}{4}[/tex])  −  3    +  9    ;

Note:   " - 3 + 9 "  =  9 + (-3)  =  9 −  3 =  " 6 " ;  

So:  Rewrite as:

______________________________________________

      →  " ([tex]\frac{1}{4}[/tex]) + 6 "  ;

______________________________________________    

      →   which equals:  " 6 [tex]\frac{1}{4}[/tex] " ;  

_______________________________________________                  

                         or;  write as:  " 6.25 " .

_______________________________________________

Hope this answer —and lengthy explanation — is helpful to you!

       Wishing you the best in your academic endeavors

                 — and within the "Brainly" community!

_______________________________________________

Answer:

So the probability that the city won't receive rain on none of these days is [tex]\frac{2}{15}[/tex]

Step-by-step explanation:

From the question we know that the probability of rain on June 1 is [tex]\frac{1}{2}[/tex], on July 1 is [tex]\frac{1}{5}[/tex] and in August 1 is [tex]\frac{2}{3}[/tex], So the probability of no rain at any of these days is calculate as:

For June 1:

[tex]P(no-rain)=1-\frac{1}{2} =\frac{1}{2}[/tex]

For July 1:

[tex]P(no-rain)=1-\frac{1}{5} =\frac{4}{5}[/tex]

For August 1:

[tex]P(no-rain)=1-\frac{2}{3} =\frac{1}{3}[/tex]  

So the probability that the city won't receive rain on none of these days is the multiplication of the probabilities of no rain for every one of these days. Then:

[tex]P=\frac{1}{2} *\frac{4}{5} *\frac{1}{3} =\frac{4}{30}[/tex]

Simplified the value of P, we obtain: [tex]P=\frac{2}{15}[/tex]

Answer:

They are both the same at 3/4 of an hour

Step-by-step explanation:

We have a system of equations here.  The first one is for Friday:

3A + 5B = 6, which says that 3 people at the number of hours for plan A plus 5 people at the number of hours for plan B equals 6 hours total.

The second equation is for Saturday:

9A + 7B = 12, which says that 9 people at the number of hours for plan A plus 7 people at th number of hours for plan B equals 12 hours total.

We can solve this easily using the addition/elimination method.  Begin by multipying the first equation through by a -3 to eliminate the A's.  That gives you a new first equation of:

  -9A  -  15B  =  -18

  9A  +    7B  =  12

You can see that the A's are eliminated, and adding what remains leaves us with

-8B = -6 so

B = 3/4 hour

Now we can sub that back in for B in either one of our original equations to solve for A.  I changed the 3/4 to .75 for ease of multiplying:

9A + 7(.75) = 12 and

9A + 5.25 = 12 and

9A = 6.75 so

A = .75 which is also 3/4 of an hour

Explanation:

Any function that has a derivative that changes sign will have an extreme value (maximum or minimum). If the derivative never changes sign, the function will not have any extreme values.

__

Logarithmic, exponential, and certain trigonometric, hyperbolic, and rational functions are monotonic, having a derivative that does not change sign. Odd-degree polynomials may also have this characteristic, though not necessarily. These functions will not have maximum or minimum values.

__

Certain other trigonometric, hyperbolic, and rational functions, as well as any even-degree polynomial function will have extreme values (maximum or minimum). Some of those extremes may be local, and some may be global. In the case of trig functions, they may be periodic.

Composite functions involving ones with extreme values may also have extreme values.

Answer:

30 Inches

Step-by-step explanation:

Please refer to the image we have attached to this.

The frame is ABCD and The diagonal is AC, which is 50 inches long and making an angle of  36.87° from the bottom of the frame.

We are asked the height of the frame which is h in this image. We are going to use the trigonometric ratios in order to find the same.

[tex]\sin \theta = \frac{opposite}{Hypotenuse}[/tex]

[tex]\sin 36.87[/tex]° = [tex]\frac{h}{50}[/tex]

[tex]0.60=\frac{h}{50}[/tex]

[tex]h=0.60 \times 50[/tex]

[tex]h=30[/tex]

hence height of the frame is 30 inches

Answer:

This is because √-1 is i, which is an extension of real numbers called complex numbers.

Step-by-step explanation:

A real number is one that can be expressed in decimal form.Real numbers are those that appear on the number line.In mathematics, √-1 is i which is an extension of real numbers to represent complex numbers.

Answer:

there is no number than can be multiplied by itself it give a negative answer.

Step-by-step explanation:

Eg. 1 X 1 = 1

     -1 X -1 = 1

B

3+5=8

8-2=6

6-1=5

Answer 5

Answer:

The correct option is C.

Step-by-step explanation:

We need to find the problem that could be solved with the expression 3(5-2)-1.

The solution of given expression is

[tex]3(5-2)-1=8[/tex]

1. Ralph's problem

His 5 toy cars, he gave two to his sister = 5 - 2

After that he found one more toy car = 5-2+1

Then, he decided to go to the store and triple his number of cars, therefore the total number of toys = 3(5-2+1) =12

2. Stephanie's problem

Stephanie had 3 apples. Then, she found 5 more = 3+5

but immediately ate 2 of them = 3+5-2

Several minutes later, she ate 1 more, therefore the total number of apples = 3+5-2-1 = 5

3. Orlando' problem

Orlando had 5 action figures but decided to give 2 of them to his younger brother = 5-2

His parents were so impressed with his kindness that thy tripled the action figures he had left = 3(5-2)

Since he got so many new action figures, then he gave 1 more to his brother, therefore the total number of action figures = 3(5-2)-1 = 8

Orlando' problem could be solved with the expression 3(5-2)-1. Therefore the correct option is C.

Answer:

The answer is 0.067.

Step-by-step explanation:

Let the entire sample size be = s

Now there are 2 laptops in sample size, hence these can be chosen in one way only.

The required probability that both selected setups are for laptop computers can be found as:

[tex]p(two laptops)=\frac{s(two laptops)}{s}[/tex]

= [tex]\frac{1}{15}[/tex] or 0.067.

So, the probability is 0.067.

The probability of both selected setups being for laptop computers is 2/15.

The probability of both selected setups being for laptop computers can be calculated as the ratio of favorable outcomes to total outcomes. Out of the six computers, two have been selected to be laptops. The first laptop can be any of the two laptops, and the second laptop can be any of the remaining one laptop. Therefore, the probability of both selected setups being for laptop computers is 2/15.

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Answer:

C is correct as well as D.

Step-by-step explanation:

The rhombus also shares the common traits that the picture shows

Answer:

so  equation for the temperature in terms of t is D = 5 sin [tex]\pi[/tex] / 12 (t) + 45

Step-by-step explanation:

Given data

temperature = 45 degrees

high temperature = 50 degrees

low temperature = 40 degrees

to find out

an equation for the temperature in terms of t

solution

first we find the amplitude i.e.

Amplitude (A) = ( high temperature - low temperature )  / 2

Amplitude (A) = (50 - 40)  / 2

Amplitude (A)  = 5

here we know in a day 24 hours so

2[tex]\pi[/tex] /K = 24

K = [tex]\pi[/tex] / 12

so we have temperature equation is

temperature D = amplitude sinK (t) + avg temperature midnight

D = 5 sin [tex]\pi[/tex] / 12 (t) + 45

so  equation for the temperature in terms of t is D = 5 sin [tex]\pi[/tex] / 12 (t) + 45

The temperature over a day can be modeled as a sinusoidal function. The equation for the temperature, D, in terms of t is: D = 5cos((pi/12)t) + 45.

The temperature over a day can be modeled as a sinusoidal (sine or cosine) function. To find an equation for the temperature, we can use the cosine function because it starts at its maximum value at t = 0, which corresponds to midnight. The equation for the temperature, D, in terms of t is:

D = 5cos((pi/12)t) + 45

Here, t represents the number of hours since midnight, and D represents the temperature in degrees. The amplitude of the sinusoidal function is 5, which represents the difference between the high and low temperatures. The cosine function is scaled and shifted to match the given data: it is multiplied by 5 to match the amplitude, and 45 is added to shift the function vertically so that it starts at 45 degrees at t = 0.

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Answer:

Step-by-step explanation:

Both x and y are inscribed angles.  The value of an inscribed angle is half the measure of its intercepted arc.  This means that x has a value of 33°, and y has a value of 48°.  That means that, according to the triangle angle sum theorem, the third angle has to equal 180 - 33 - 48 = 99°.

This angle is vertical with angle z, so angle z also equals 99°

Answer:

  a)  t = 2 seconds

  b)  6.05 meters

Step-by-step explanation:

I prefer a graph for questions like this, but I have attached a table, too. Here, the table is created using a graphing calculator to evaluate the function. A spreadsheet can do this nicely, too.

The maximum height occurs at t=0.9 seconds, and the ball hits the ground at a time that is slightly more than double that, 2.0 seconds.

The maximum height is 6.05 meters.

Answer:

radius = 2.05 units

Step-by-step explanation:

The volume of a sphere is given by the formula: [tex]V=\frac{4}{3} \pi r^3[/tex]. In this formula:

Since we are given the volume of the sphere (36 units^3), we just need to solve for r in the equation for the volume of a sphere.

Substitute 36 for V into the formula and solve for r.

[tex]36=\frac{4}{3} \pi r^3[/tex]

Divide both sides by [tex]\frac{4}{3}[/tex]. To do this, multiply 36 by the reciprocal of [tex]\frac{4}{3}[/tex].

Simplify and rewrite the equation.

[tex]27=\pi r^3[/tex]

Now divide both sides of the equation by pi ([tex]\pi[/tex]).

Rewrite the equation.

[tex]8.59436692696=r^3[/tex]

To isolate and solve for r, cube root both sides of the equation.

The radius of this sphere is 2.04835218977 units. If your question wants this rounded to the nearest:

I'll just give the answer rounded to the nearest hundredth as that seems the most popular.

Answer:

Before they deleted my answer, I was correct. remember to correctly round if you have a different but similar question.  

Step-by-step explanation:

The number of ways to distribute five identical fruits into three bowls is solved using the stars and bars technique in combinatorics, resulting in 21 different ways.

The student is asking about the number of ways to distribute five identical fruits into three bowls, where bowls can be left empty.

This problem is a classic example of a combinatorial problem in mathematics, often approached using the stars and bars method.

The stars and bars technique is a way to solve problems related to distributing indistinguishable items into distinguishable groups.

To solve this, think of the five identical fruits as stars (*) and the separations between bowls as bars (|).

We need to place two bars to create three sections (bowls) among the five stars.

The question then becomes: In how many ways can we arrange five stars and two bars?

This is equivalent to choosing two places for bars out of seven possible positions (five stars plus two bars).

The number of ways we can choose two positions out of seven for the bars is given by the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of items and k is the number of items to choose.

In this case, C(7, 2) = 7! / (2!5!) = 21 ways.

Therefore, there are 21 different ways to distribute five identical fruits into three bowls.

Answer:

graph 1

Step-by-step explanation:

Let's look at graph 1:

The first vertex (the left hand top corner) has a degree 3 because there are 3 line segments coming from it.

Let's check to see if the other vertices have degree 3.

The second vertex (the middle top) has degree 3 because again it has 3 line segments coming from it.

The third vertex (the top right) has degree 3 because it has 3 line segments coming from it.

The fourth vertex (the bottom left) has degree 3 because it has 3 line segments coming from it.

The fifth vertex (the middle bottom) has degree 3 because it has 3 line segments coming from it.

The last vertex (the bottom right) has degree 3 because it has 3 line segments coming from it.

Let's look at graph 2:

The first vertex (top left) has degree 1 because it has one line segment coming from it.

The second vertex( middle top) has degree 2 because it has 2 line segments coming from it.

Graph 2 doesn't have the same degree per vertex.

Looking at graph 3:

The first vertex (top left) has degree 1 while the second (top middle) has degree 2.

Graph 3 doesn't have the same degree per vertex.

Looking at graph 4:

The top left has degree 1.  Looking at one of the middle vertices there, they have degree 4 each because they have 4 line segments coming from it. So graph 4 doesn't have the same degree per vertex.

The answer is only graph 1.

Answer:

y = 10x - 3

Step-by-step explanation:

We have the point (0, -3), which is the y-intercept. In slope-intercept form,

y = mx + b,

that is the b.

Now we find the slope between the other 2 points:

[tex]\frac{18-8}{3-2}=10[/tex]

So m = 10.  Therefore, the equation is

y = 10x - 3

Answer:

B

Step-by-step explanation:

This is the difference of perfect squares, which follows a pattern of

(A+B)(A-B)

We have 64, which is 8-squared,

we have A squared, which is A squared ( :/ )

we have 81, which is 9-squared, and

we have B-squared, which is B squared.

We can factor this then following the pattern into:

(8A+9B)(8A-9B)

Choice B only matches one of our binomials.

Answer:

B. 8A + 9B.

Step-by-step explanation:

The general form is

a^2 - b^2 = (a - b)(a + b) so here we have:

a = square root of 64A^2 = 8A and b = square root of 81B^2 = 9B and therefore:

64A^2 - 81B^2

= (8A - 9B)(8A + 9B).

Final answer:

The mathematical system of inequalities for Keitaro's walking and running routine must satisfy his target of covering at least 36 miles and not more than 90 miles in a month, given his pace.

Explanation:

Keitaro's exercise routine is defined by a system of inequalities that reflect the minimum and maximum distances he wants to cover each month by walking and running. Given his walking pace of 3 miles per hour and his running pace of 6 miles per hour, we can set up two inequalities to represent walking hours w and running hours r. The first inequality would ensure that when multiplied by their respective paces, the total distance is at least 36 miles. The second inequality ensures that the sum of distances does not exceed 90 miles:

3w + 6r ≥ 36 (for the minimum distance)

3w + 6r ≤ 90 (for the maximum distance)

Keitaro needs to allocate his walking and running hours such that these inequalities are satisfied to meet his monthly exercise goals.

Answer:

Step-by-step explanation:

Divide 1 7/10 by 3/5 to see if the quotient is greater than 2.  If it's not, you can't get 2 scarves out of it.  If it is, then you can get 2 scarves out of it and have whatever the remainder is as left-over.  Before we divide, let's change that 1 7/10 into an improper fraction since it will be easier to work with.

1 7/10 = 17/10

Now we can divide:

[tex]\frac{\frac{17}{10} }{\frac{3}{5} }[/tex]

The rule for dividing fractions is that you bring up the lower fraction and flip it to multiply, so that looks like this:

[tex]\frac{17}{10}[/tex]×[tex]\frac{5}{3}[/tex]

To simplify before we multiply, we can reduce between the 5 and the 10 and have smaller numbers to deal with:

[tex]\frac{17}{2}[/tex]×[tex]\frac{1}{3}[/tex]

The product there is [tex]\frac{17}{6}=2\frac{5}{6}[/tex]

So the answer you want from your choices is

"Yes, because the quotient of Fraction 1 and 7 over 10 [division sign]Fraction 3 over 5 is 2 and 5 over 6", third choice

Answer:

Yes, because the quotient of Fraction 1 and 7/10 [division sign]Fraction 3/5  is 2 and 5/6", third choice

Step-by-step explanation:

Divide 1 7/10 by 3/5 to see if the quotient is greater than 2.  If it's not, you can't get 2 scarves out of it.  If it is, then you can get 2 scarves out of it and have whatever the remainder is as left-over.  Before we divide, let's change that 1 7/10 into an improper fraction since it will be easier to work with.

1 7/10 = 17/10

Now we can divide:

The rule for dividing fractions is that you bring up the lower fraction and flip it to multiply, so that looks like this:

×

To simplify before we multiply, we can reduce between the 5 and the 10 and have smaller numbers to deal with:

×

The product there is  

So the answer you want from your choices is

"Yes, because the quotient of Fraction 1 and 7 over 10 [division sign]Fraction 3 over 5 is 2 and 5 over 6", third choice

[tex](x-(-2))(x-(-3))(x-(3-6i)(x-(3+6i))=\\(x+2)(x+3)(x-3+6i)(x-3-6i)=\\(x^2+3x+2x+6)((x-3)^2+36)=\\(x^2+5x+6)(x^2-6x+9+36)=\\(x^2+5x+6)(x^2-6x+45)=\\x^4-6x^3+45x^2+5x^3-30x^2+225x+6x^2-36x+270=\\x^4-x^3+21x^2+189x+270[/tex]

Answer:

[tex]\large\boxed{Q5.\ x=45\sqrt2}\\\boxed{Q6.\ x=8\sqrt2,\ y=4\sqrt6}[/tex]

Step-by-step explanation:

Q5.

x it's a diagonal of a square.

The formula of a length of diagonal of a square:

[tex]d=a\sqrt2[/tex]

a - side of a square

We have a = 45.

Substitute:

[tex]x=45\sqrt2[/tex]

Q6.

Look at the first picture.

In a triangle 45° - 45° - 90°, all sides are in ratio 1 : 1 : √2.

In a triangle 30° - 60° - 90°, all sidea are in ratio 1 : √3 : 2.

Look at the second picture.

from the triangle 45° - 45° - 90°

[tex]a\sqrt2=8[/tex]        multiply both sides by √√2  (use √a · √a = a)

[tex]2a=8\sqrt2[/tex]      divide both sides by 2

[tex]a=4\sqrt2[/tex]

from the triangle 30° - 60° - 90°

[tex]x=2a\to x=2(4\sqrt2)=8\sqrt2[/tex]

[tex]y=a\sqrt3\to y=(4\sqrt2)(\sqrt3)=4\sqrt6[/tex]

Answer:

6. [tex]\displaystyle 4\sqrt{6} = y \\ 4\sqrt{2} = x[/tex]

5. [tex]\displaystyle 45\sqrt{2} = x[/tex]

Step-by-step explanation:

30°-60°-90° Triangles

Hypotenuse → 2x

Short Leg → x

Long Leg → x√3

45°-45°-90° Triangles

Hypotenuse → x√2

Two identical legs → x

6. You solve the shorter triangle first:

[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ \\ x^2 + x^2 = 8^2 \\ \\ \frac{2x^2}{2} = \frac{64}{2} → \sqrt{x^2} = \sqrt{32} \\ \\ 4\sqrt{2} = x[/tex]

Now that we know our x-value, we can solve the larger triangle:

[tex]\displaystyle 4\sqrt{6} = 4\sqrt{2}\sqrt{3} \\ \\ 4\sqrt{6} = y[/tex]

5. This exercise is EXTREMELY SIMPLE since two congruent isosceles right triangles form that square, so all you have to do, according to the rules for 45°-45°-90° triangles, is attach [tex]\displaystyle \sqrt{2}[/tex]to 45, giving you [tex]\displaystyle 45\sqrt{2}.[/tex]

I am joyous to assist you anytime.