Hello,
I propose this exercise if anyone can answer me.
Let ABC be a right triangle, of hypotenuse BC = a, where [tex]A\widehat{B}C=x[/tex].
Let A' be the symmetric of A with respect to BC.
Determine x so that:
-the area of ​​the triangle AA'C is maximum
Show and justify all the steps (take the picture).

Thank you.

I already did this question once so I'm just gonna include the answer

Answer: The value of KP = 12 units.

Step-by-step explanation:

Since we have given that

KE is a tangent with KE = 18

KPL is a secant with PL = 15

Let KP = x

Since we know that The product of segments of secants is square of the tangents.

Mathematically, it is expressed as ,

[tex]KE^2=KP.KL\\\\18^2=x(x+15)\\\\324=x^2+15x\\\\x^2+15x-324=0\\\\x^2+27x-12x-324=0\\\\x(x+27)-12(x+27)=0\\\\(x+27)(x-12)=0\\\\x=-27,x=12[/tex]

Measure of secant can't be negative.

So, KP = 12

Answer:

  59.0°

Step-by-step explanation:

Many triangle solvers are available for your phone, tablet, or browser. The attachments show the input and output of one of them.

___

You can use the law of cosines to compute the result yourself.

  b^2 = a^2 + c^2 - 2ac·cos(B)

  cos(B) = (a^2 +c^2 -b^2)/(2ac) = (22^2 +18^2 -20^2)/(2·22·18) = 408/792

  B = arccos(408/792) ≈ 58.9924° ≈ 59.0°

Answer:

8. (10/7)x^(0.7) +C

10. (x^-2)/2 -x^-1 +C

Step-by-step explanation:

The integral of x^a is x^(a+1)/(a+1).

8. a = -.3, so the integral is x^0.7/0.7

___

10. This is the difference of two integrals, one with a=-2; the other with a=-3, so ...

the integral is (x^-1)/(-1) -(x^-2)/(-2)

_____

Of course, an arbitrary constant is added to each result to complete the indefinite integral.

Answer:  [tex]\bold{\dfrac{7w^2y^3}{32}}[/tex]

Step-by-step explanation:

[tex]\dfrac{3w^9y^4}{8w^5}\cdot \dfrac{7y^4}{12w^2y^5}\\\\\\\text{Multiply across. ADD exponents when like bases are being multiplied}\\=\dfrac{21w^9y^8}{96w^7y^5}\\\\\\\text{Cancel out common factors. SUBTRACT exponents when dividing}\\=\dfrac{7w^2y^3}{32}[/tex]

See the image for solution

Answer:

It depends on the max amount you can have.

Step-by-step explanation:

For example, if 100 points was the max you'd have 97.6%.

Hope this helps!

Answer:

The area is multiplied by 0.84 (decreased 16%)

Step-by-step explanation:

The length is multiplied by (1 +0.40) = 1.4.

The width is multiplied by (1 -0.40) = 0.6

So, the new area is ...

A = (L·1.4)·(W·0.6) = LW·0.84

The original area was the product of the original length and width, so was LW. This means the new area is 0.84 times the original area.

0.84 = 1 - 0.16

so, another way to describe the change is to say the area decreased 16%.

We want to see how some changes in the measures of a rectangle affect the area of the given rectangle.

We will see that the new area is 0.84 times the original area (meaning that the area decreases by 16%).

We will have.

First, we know that for a rectangle of length L and width W the area is given by:

A = L*W

Now, if we increase the length bt 40%, the new length will be:

L' = L +  (40%/100%)*L = L*1.4

And if the width is decreased by 40%, the new width will be:

W' = W - (40%/100%)*W = W*0.6

The new area is given by:

A' = L'*W' = (L*1.4)*(W*0.6) = (L*W)*(1.4*0.6) = 0.84*(L*W)

Where L*W is the area of the original rectangle, so we can write:

A' = 0.84*A

Meaning that the area decreased, the new area is 0.84 times the original area (we can actually see that the area decreased by 16%).

If you want to learn more, you can read:

https://brainly.com/question/15218510

Answer:

x = 5 and y = 35

OR

x = -4 and y = 8.

Step-by-step explanation:

Equate the right-hand side of the two equations:

x² + 2 x = y = 3 x + 20.

x² + 2 x - 3 x - 20 = 0.

x² - x - 20 = 0.

Quadratic discriminant

Δ = b² - 4 a · c

= (-1)² - 4 × 1 × (-20)

= 81.

There are two roots:

x₁ = (-b + [tex]\sqrt{\Delta}[/tex]) / (2 a)

= (- (-1) + [tex]\sqrt{81}[/tex]) / (2 × 1)

= (1 + 9) / 2

= 10 / 2

= 5

and

x₂ = (-b - [tex]\sqrt{\Delta}[/tex]) / (2 a)

= (1 - 9) / 2

= -4.

Find the value of y in both case.

y₁ = 3 × 5 + 20 = 35.

y₂ = 3 × (-4) + 20 = 8.

The solution to the system of equations is [tex]\( x = 5 \)[/tex] with [tex]\( y = 35 \)[/tex] and [tex]\( x = -4 \)[/tex] with [tex]\( y = 8 \)[/tex].

To solve these equations algebraically, we'll set them equal to each other since they both represent [tex]\( y \)[/tex].

Given equations:

[tex]\[ y = x^2 + 2x \][/tex]

[tex]\[ y = 3x + 20 \][/tex]

Setting them equal to each other:

[tex]\[ x^2 + 2x = 3x + 20 \][/tex]

Now, let's rearrange this equation to solve for \( x \):

[tex]\[ x^2 + 2x = 3x + 20 \[/tex]

[tex]x^2 + 2x - 3x - 20 = 0 \[/tex]

[tex]x^2 - x - 20 = 0[/tex]

This is a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \)[/tex]. We need to factorize or use the quadratic formula to solve for [tex]\( x \)[/tex]. Factoring might work here:

[tex]x^2 - x - 20 = 0[/tex]

[tex](x - 5)(x + 4) = 0[/tex]

Setting each factor equal to zero:

[tex]\[ x - 5 = 0 \] or \( x + 4 = 0 \)[/tex]

Solving for [tex]\( x \)[/tex] in each case:

[tex]\[ x = 5 \] or \( x = -4 \)[/tex]

Now that we have found the potential values of [tex]\( x \)[/tex], let's find the corresponding [tex]\( y \)[/tex] values using either of the original equations. Let's use [tex]\( y = x^2 + 2x \)[/tex]:

For [tex]\( x = 5 \)[/tex]:

[tex]y = 5^2 + 2(5)[/tex]

[tex]y = 25 + 10[/tex]

[tex]y = 35[/tex]

For [tex]\( x = -4 \)[/tex]:

[tex]y = (-4)^2 + 2(-4)[/tex]

[tex]y = 16 - 8[/tex]

[tex]y = 8[/tex]

Therefore, the solution to the system of equations is [tex]\( x = 5 \)[/tex] with [tex]\( y = 35 \)[/tex] and [tex]\( x = -4 \)[/tex] with [tex]\( y = 8 \)[/tex].

Answer:

The base = 4 units and the height = 3 units

Step-by-step explanation:

* Lets remember the rule of the distance between 2 points

- The two points are (x1 , y1) and (x2 , y2)

∴ The distance = √[(x2 - x1)²+(y2 - y1)²]

* The vertices of the triangles are (-3 , 4) , (1 , 4) , (1 , 1)

- If two points have the same y-coordinate

∴ The line joining the to point is horizontal

∴ Its length = x2 - x1

- Because √[(x2 - x1)²+(y2 - y1)²] and y2 = y1

∴ d = √(x2 - x1)² ⇒ cancel power 2 with the radical sign

∴ d = x2 - x1

* Similar you can find the vertical distance

- If two points have the same x-coordinate

∴ The line joining the to point is vertical

- Its length = y2 - y1

∵ The points (-3 , 4) , (1 , 4) have same y-coordinate

∴ This side of the triangle is horizontal

∴ Its length = 1 - -3 = 4

∵ The points (1 , 4) , (1 , 1) have same x-coordinate

∴ This side of the triangle is vertical line

∴ Its length = 4 - 1 = 3

* The two sides of the triangle are ⊥

∴ One of them is the base of the triangle and the other is the height

* The base = 4 units and the height = 3 units

Answer:

200 Boxes of Popcorn

Step-by-step explanation:

To find the total amount of popcorn boxes there are in the store, we need to consider the amount of boxes displayed at the front of the store.

We have:

60 boxes = Cinnamon + Cheese

60 boxes = 15% + 15%

60 = 30% of the total boxes in the store.

Now we know that 60 boxes is equivalent to 30%, we can use this to find the number of kettle corn.

60 + 60 = 120

30% + 30% = 60%

This means that we have 120 Kettle Korn boxes.

We can also use the amount of 60 boxes to find what 10% will be equivalent to.

60 boxes = 30%

So if we divide the number of boxes by 3, we'll get the 10% of the total number of boxes.

60/3 = 30%/3

20 = 10%

So all in all we have:

120 Kettle Korn

60 Cinnamon + Cheese

20 Caramel

120 + 60 + 20 = 200

There are 200 popcorn boxes in the store.

Answer:

  -2 < x < 4/3

Step-by-step explanation:

A graphing calculator can show you the solution. I like to recast the equation as a comparison to zero, since a graphing calculator often can display zeros of a function easily. Here that means ...

  |6x +2| -10 < 0

___

If you want to solve this by hand, you can "unfold" the absolute value to get ...

  -10 < 6x +2 < 10

  -12 < 6x < 8 . . . . . . subtract 2

  -12/6 < x < 8/6 . . . . divide by 6

  -2 < x < 4/3 . . . . . . simplify

This graphs on the number line as a solid line between open circles at -2 and 4/3. On the attached graph, the boundary values are shown as dotted blue lines, and the solution space is shown in blue.

Answer:

Step-by-step explanation:

If we take 1 candy bar and split it between 8 people, each person will get 1/8 of a candy bar. 1/8 for each of those 12 candy bars will give each person 12 × 1/8 = 12/8, or 3/2 = 1 1/2 bars.

You are trying to share 12 candy bars between 8 friends.

Therefore,

12 candy bars ÷ 8 friends = 1.5 bars per person

12 ÷ 8 = 1.5 candy bars

Answer:

  cot(x) = 3

Step-by-step explanation:

The cotangent is the reciprocal of the tangent.

  cot(x) = 1/tan(x) = 1/(1/3) = 3

_____

It is helpful to memorize the relationships between the trig functions: SOH CAH TOA is a mnemonic that relates triangle sides to trig function values. The remaining relationships you need to know are ...

  secant = 1/cosine . . . . . . so cosine = 1/secant

  cosecant = 1/sine . . . . . so sine = 1/cosecant

  cotangent = 1/tangent . . . . . so tangent = 1/cotangent

It is also helpful to realize that ...

  tan = sin/cos

  sin² + cos² = 1 . . . the "Pythagorean" relationship between sine and cosine

  sec² = 1 + tan²

  csc² = 1 + cot²

Over this 10-minute interval, the car's average acceleration is

[tex]\dfrac{30\,\mathrm{mph}-20\,\mathrm{mph}}{10\,\mathrm{min}}=\dfrac{10\,\mathrm{mph}}{\frac16\,\mathrm h}=60\dfrac{\rm mi}{\mathrm h^2}[/tex]

The MVT says that at some point during this 10-minute interval, the car must have had an acceleration of 60 mi/h^2.

The acceleration in this lapse of time is 60 miles per hour squared.

To get this, we need to use the formula:

A = (difference in velocity)/time

The change in velocity is:

30mph - 20mph = 10mph

The time is from 2:00pm to 2:10 pm, so 10 minutes, but we need this in hours so:

10 min = (10/60) hours = 1/6 hours

Then the acceleration is given by:

A = 10mph/(1/6) = 60 m/h²

Learn more about acceleration at:

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The quadratic function y=x^2+10x+25 intersects the x-axis at a single point (x = -5).

A quadratic function intersects the x-axis when the value of y is equal to 0. To find the number of times the function intersects the x-axis, we need to determine the number of solutions for y = 0. The given quadratic function is y = x^2 + 10x + 25. We can solve this equation by factoring or using the quadratic formula.

Factoring: Factoring the quadratic equation, we get (x + 5)(x + 5) = 0.

Since both factors are the same, the function intersects the x-axis at a single point (x = -5).

Quadratic formula: The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a.

Plugging in the values from the given quadratic function, we get x = (-10 ± √(100 - 4(1)(25))) / 2(1).

Simplifying further, we get x = (-10 ± √(100 - 100)) / 2, which reduces to x = -5. This indicates that the quadratic function intersects the x-axis at a single point (x = -5).

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Answer:

  a.  -25

  b.  -52

  c.  54

  d.  8/7 = 1 1/7

Step-by-step explanation:

Evaluate each of the functions for each of the variable values and compute the composite as defined.

a. (f+g)(3) = f(3) + g(3) = 3^2 -5·3 + 8 -3^3 = -25

___

b. (g -f)(4) = g(4) -f(4) = 8 -4^3 -(4^2 -5·4) = 8 -64 -16 +20 = -52

___

c. (f*g)(-1) = f(-1) · g(-1) = ((-1)^2 -5(-1)) · (8 -(-1)^3) = 6·9 = 54

___

d. (g/f)(-2) = (8 -(-2)^3)/((-2)^2 -5(-2)) = (8+8)/(4+10) = 16/14 = 8/7

_____

Comment on approach to the problem

When there are a number of evaluations of the same function with different values of the variable, it can be convenient to let a calculator or spreadsheet do those for you.

Answer:

This is the simplified number for Pi, which is 3.14

Step-by-step explanation:

A kite is a quadrilateral.

So the correct answer is A.

Hope this helps,

Davinia.

Final answer:

A kite is a quadrilateral, which is a shape with four sides, but with unique properties that differentiate it from parallelograms, rectangles, and trapezoids.

Explanation:

A kite in geometry is a quadrilateral. A quadrilateral is a kind of shape with four sides, which might not be as commonly discussed in early education as shapes like squares and triangles. A kite is defined by two pairs of adjacent sides that are equal in length, with one pair longer than the other. Unlike a parallelogram, the sides of a kite do not always have to be parallel to each other. In addition, a kite does not necessarily have right angles as a rectangle does, nor does it have only one pair of parallel sides as a trapezoid does. Therefore, when characterizing a kite, the correct answer is A. quadrilateral.

Answer:

255π (cm³).

Step-by-step explanation:

1. the initial formula for the required volume is V=V1-V2, where V1=π(r1)²h, V2=π(r2)²h;

h=20m=2000cm, r1=0.5*d1, r2=0.5*d2;

d1=1cm., d2=0.7 cm.

2. the final formula of the required volume is

[tex]V=\frac{ \pi*h}{4} (d_1^2-d_2^2);[/tex]

3. if to substitute the values of d1, d2 and h, then

[tex]V=\frac{ \pi*2000}{4} (1-0.49)=500 \pi*0.51=255 \pi \ (cm^3).[/tex]

Answer:

  25 in

Step-by-step explanation:

The diameter is shown to be 10/4 times the height, so the diameter of the smaller solid is ...

  (10/4)×(10 in) = (100/4) in = 25 in

Answer:

25 in.

Step-by-step explanation:

Answer:

60 m/h

Step-by-step explanation:

1. the basic formula is Time=Distance/Speed;

2. total time is time1 (for 84 miles)+time2 (for 130 miles)=time (4 hours);

3. the time for the first 84 mi. is time1=84/S;

4. the time for the rest 130 mi. is time2=130/(S-10);

5. using all the data of items 2-4, it is possible to substitute into the basic formula and resolve an equation:

[tex]\frac{84}{s} +\frac{130}{s-10} =4; \ => \ 2s^2-127s+420=0;[/tex]

[tex]\left[\begin{array}{ccc}s=60\\s=3.5\end{array}[/tex]

note, that the value of speed has one condition: s>10. It means, the only value is true: 60 miles per hour.

The answer is D. 45%

The answer would be 45%

To solve this pretend that 370 is 100

Then put (x) as the value you are looking for

So 100%=370

(x)%=166.5

Then set it up like this:

100%. 370

=

x%. 166.5

Then divide or do cross multiplication and you find out that x is 45%

Hope this helps! :3

Answer:

  73

Step-by-step explanation:

Put the values of the variables where the variables are, then do the arithmetic.

  (2·5)^2 -3·3^2 = 10^2 -3·9 = 100 -27 = 73

___

Or, you can let a calculator or spreadsheet evaluate the function for you.

If [tex]b[/tex] is Ben's age and [tex]i[/tex] is Ishaan's age, then

Rewrite the second equation as

[tex]b-6=6(i-6)\implies b-6=6i-36\implies b+30=6i[/tex]

Substitute [tex]b=4i[/tex] into this equation to solve for [tex]i[/tex]:

[tex]b+30=6i\implies4i+30=6i\implies30=2i\implies i=15[/tex]

Then

[tex]b=4i\implies b=4\cdot15=60[/tex]

So Ben is 60 years old now.

Since f(x) = -3x + 2, the slope of f(x) is greater than the slope of g(x).

Hence, the answer is (D).

The slope of f(x) is greater than the slope of g(x) because the slope of f(x) is 1 option (D) is correct.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have:

g(x) = -2x - 6

f(x) is shown in the graph

The slope of g(x), m = -2

From the graph:

(0, 2) and (-1, 1)

M = (1-2)/(-1) =  1

Thus, the slope of f(x) is greater than the slope of g(x) because the slope of f(x) is 1 option (D) is correct.

Learn more about the slope here:

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The second one is d I’m pretty sure

Answer:

#23, A

#24, D

Hope this helped!!

~A̷l̷i̷s̷h̷e̷a̷♡

1/3

7/12

9/12

1/4

and more

The fraction that is not equivalent to [tex]\( \frac{8}{12} \) is \( \frac{6}{10} \), option D, as it simplifies to \( \frac{3}{5} \), while the others simplify to \( \frac{2}{3} \), which is equivalent to \( \frac{8}{12} \).[/tex]

To find the fraction that is not equivalent to [tex]\( \frac{8}{12} \), we need to simplify each option and compare it with \( \frac{8}{12} \).[/tex]

We simplify each option:

A) [tex]\( \frac{2}{3} \)[/tex]

B) [tex]\( \frac{24}{36} = \frac{2}{3} \) (Equivalent to \( \frac{8}{12} \))[/tex]

C) [tex]\( \frac{4}{6} = \frac{2}{3} \) (Equivalent to \( \frac{8}{12} \))[/tex]

D)[tex]\( \frac{6}{10} = \frac{3}{5} \)[/tex]

So, the fraction that is not equivalent to [tex]\( \frac{8}{12} \) is \( \frac{6}{10} \),[/tex]option D.

Answer:

  4.  maximum: 22; minimum: 1

  5.  maximum: 24; minimum: -6.25

  6.  maximum: 49.7; minimum: 39.625

Step-by-step explanation:

I find a graphing calculator to be "appropriate technology" for answering questions of this sort. For the first and last questions, the extremes are the values of the function at the ends of the intervals specified.

For the second question, the parabola opens upward and the vertex is in the given interval, so the vertex is the minimum. The maximum is found at the end of the interval that is farthest from the vertex.

Answer:

Fiona has 6 quarters

Step-by-step explanation:

If Fiona were to have 1 quarter and 1+6 dimes she would have 8 coins

If she were to have 2 quarters and 2+6 dimes she would have 10 coins

If she were to have 3 quarters and 3+6 dimes she would have 12 coins

If she were to have 4 quarters and 4+6 dimes she would have 14 coins

If she were to have 5 quarters and 5+6 dimes she would have 16 coins

If she were to have 6 quarters and 6+6 dimes she would have 18 coins

Therefore, she has to have 6 quarters in order to have 6 more dimes and a total of 18 coins

I hope this helps, and I'm sorry it took so long for me to write this out