How would you get the answer??

In a convex polygon, all interior angles are less than or equal to 180. So pentagons are polygons of five sides. We need to draw two different pentagons with the previous characteristics and measures of the internal angles. Therefore, we will choose to type of pentagons.

Every pentagon can be divided up into three triangles, either a regular or irregular one and each triangle adds up to 180 degrees. Therefore, the angles in every pentagon must add up to 540 degrees.

1. Drawing of the first convex pentagon (Regular Pentagon).

A polygon is regular when all angles are equal and all sides are equal. The regular pentagon is a 5-sided polygon. This is shown in Figure 1. Note that all angles are equal to 108°.

1.1. Sum of the interior angles of the first convex pentagon.

According to Figure 1, the sum of its interior angles is as follows:

[tex]\alpha=5 \times 108^{\circ}=540^{\circ}[/tex]

As we said, the angles in every pentagon must add up to 540 degrees. If the pentagon is regular each internal angle measures 108°. In fact, in a Regular Polygon with N sides, each angle is:

[tex]\frac{(N-2)180{^\circ}}{N} \\ \\ Since \ N=5 \\ \\ \\ \frac{(5-2)180{^\circ}}{5}= 108^{\circ}[/tex]

2. Drawing of the second convex pentagon (Irregular Pentagon)

This is a type of polygon that does not have all sides equal and all angles equal. In Figure 2 is shown this pentagon. Note that there are five sides and all angles are not equal.

2.1 Sum of the interior angles of the second convex pentagon.

According to Figure 2, the sum of its interior angles is given by:

 [tex]\beta=81^{\circ}+139^{\circ}+139^{\circ}+94^{\circ}+87^{\circ}=540^{\circ}[/tex]

As we said, no matter if the pentagon is irregular, the angles in every pentagon must add up to 540 degrees.

Answer with explanation:

A Polygon is said to be convex, if all the diagonals of the polygon lies in the interior of the polygon.

→Sum of interior angle of polygon =(n-2)×180°, where n is the number of sides of the polygon.-----(1)

→A pentagon is said to be convex, if it has 5 sides and all the Diagonals of pentagon lies in the interior.

Sum of interior Angles of Triangle =(3-2)×180°=180°

Sum of interior angles of Quadrilateral = (4-2)×180°=2×180°=360°

Sum of Interior angles of Polygon =(5-2)×180°=3×180°=540°

Used the formula (1) in all the three cases.

The congruence theorem that can be used to prove △MLQ ≅ △NPQ is the SAS (Side-Angle-Side) congruence theorem.

To prove that triangles MLQ and NPQ are congruent, we can use the SAS (Side-Angle-Side) congruence theorem. The given information MQ = NQ indicates that the sides MQ and NQ are congruent. Since Q is the midpoint of LP, we can conclude that the side LQ is congruent to side PQ. Lastly, the fact that LM ≅ PN means that the side LM is congruent to side PN. Therefore, we have congruent corresponding sides and an included congruent angle, allowing us to use the SAS congruence theorem. So, △MLQ ≅ △NPQ.

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Answer:

He should place it in Bank A

For bank A Total amount = $1240

For bank bA= $1196.68

Step-by-step explanation:

For bank A with simple interest rate of 4%

Interest = PRT/100

Interest =( 1000*4*6)/100

Interest=$240

Total amount = principal + interest

Total amount = $1000+$240

Total amount = $1240

For Bank B with compound interest rate of 3%

A = p(1+r/n)^(nt)

A = 1000(1+(0.03/6))^(6*6)

A = 1000*1.19668

A= $1196.68

Answer:

(x+2)(x+4)

Step-by-step explanation:

Answer:

Sum = (n -2) * 180

Step-by-step explanation:

Step 1 : The formula for calculating the sum of the interior angles = (n - 2) × 180, where "n" is the number of sides of a regular polygon.

Step 2: Here we are given the sum of the interior angles is 180 degrees. Therefore, the given figure must be triangle.

true transformation is a dilation

Yes it is true!! Dilation is a transformation because each point of the object is moved- like tracing- a perfectly strait line! The strait line is drawn from a point called the center of dilation!

Have a great day! :)

Answer:

The intervals where the function is increasing are [tex](-\infty,0)[/tex] and [tex](1,2)[/tex]

Step-by-step explanation:

We are required to find the intervals in which the function is increasing.

From the figure, we see that,

The graph is going up towards the origin to reach the point (0,0).

Then, it is going down in the interval (0,1).

Then, it is again going up to reach the point (2,0).

Finally, it is going downwards towards infinity.

Thus, we see that,

The intervals where the function is increasing are [tex](-\infty,0)[/tex] and [tex](1,2)[/tex]

Answer:(−∞, 0) and(1,2)

Step-by-step explanation:

Answer: The answer is actually 6.

Step-by-step explanation:

The value of x is 6, rounded to the nearest whole number.

To solve for x given the conditions:

1. Define the variables based on the problem:

  - Length of the rectangle [tex](\( L \)) = \( x + 2 \)[/tex]

  - Width of the rectangle [tex](\( W \)) = \( 2x - 5 \)[/tex]

2. Write the equation for the area of the rectangle:

  - Area [tex](\( A \)) = \( L \times W \)[/tex]

  - Given that the area is 56 cm², we have:

[tex]\[ (x + 2)(2x - 5) = 56 \][/tex]

3. Expand the equation:

[tex]\[ (x + 2)(2x - 5) = 2x^2 - 5x + 4x - 10 = 2x^2 - x - 10 \][/tex]

4. Set up the equation:

[tex]\[ 2x^2 - x - 10 = 56 \][/tex]

5. Move all terms to one side of the equation to set it to zero:

[tex]\[ 2x^2 - x - 10 - 56 = 0 \] \[ 2x^2 - x - 66 = 0 \][/tex]

6. Solve the quadratic equation using the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\\ where \( a = 2 \), \( b = -1 \), and \( c = -66 \).[/tex]

7. Calculate the discriminant:

[tex]\[ \Delta = b^2 - 4ac = (-1)^2 - 4(2)(-66) = 1 + 528 = 529 \][/tex]

8. Calculate the roots:

[tex]\[ x = \frac{-(-1) \pm \sqrt{529}}{2(2)} = \frac{1 \pm 23}{4} \][/tex]

So, the solutions are:

[tex]\[ x = \frac{1 + 23}{4} = \frac{24}{4} = 6 \][/tex]

and

[tex]\[ x = \frac{1 - 23}{4} = \frac{-22}{4} = -5.5 \][/tex]

Since x must be a positive value in the context of this problem, we have: x = 6

9. Verify the solution:

Length L = x + 2 = 6 + 2 = 8 cm

Width W = 2x - 5 = 2(6) - 5 = 12 - 5 = 7  cm

Area = [tex]\( 8 \times 7 = 56 \)[/tex] cm², which matches the given area.

Therefore, ( x = 6).

The sum of a number X and 4 divided by three is (X+4)/3

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol can also be used to indicate the logical syntax's order of operations and other features.

Given that  sum of a number X and 4 divided by 3

That makes the expression as;

Sum = x + 4

Then

(X+4) over 3

Therefore, the expression would be (X+4)/3

To know more about an expression follow;

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Answer:

Your answer is D :)

Step-by-step explanation:

No explanation :) <3

Answer:

The answer is 72 degrees

Step-by-step explanation:

The picture that Helpmetnx showed does work. But they made a mistake and assumed that the diagonal is a angle bisector, and it's not.

1. rectangle ABCD, BD & AC are the diagonals. ∠ABD =36 degrees

2. ∠ABD= ∠BDC = 36 - alternate interior angles

3. ∠DBC = 90 - 36 = 54. ∠DBC =∠ADB = ∠BCA = 54

4. Now we know that the triangle formed between the two diagonals is a isosceles triangle because of base angle theorem.

5. 180 - 54*2 = 72 degrees

I hope this helps!

Answer: ASA

hope that helps have a nice day

Perimeter is 30 units

Semi-perimeter is 15 units

The Area is 39.7 square units

Answer:

We know: 0 Celsius = 32 Fahrenheit.

We can convert the Celsius to Fahrenheit using this formula:

[tex](C\times9/5)+32[/tex]

a. 35° C

= [tex](35\times9/5)+32=95[/tex] degrees Fahrenheit

b. 500° C

= [tex](500\times9/5)+32=932[/tex] degrees Fahrenheit

c. 10° C

= [tex](10\times9/5)+32=50[/tex] degrees Fahrenheit

d. 55° C

= [tex](55\times9/5)+32=131[/tex] degrees Fahrenheit

a. 35°C to Fahrenheit: 95°F

b. 500°C to Fahrenheit: 932°F

c. 10°C to Fahrenheit: 50°F

d. 55°C to Fahrenheit: 131°F

1. Formula:

To convert Celsius to Fahrenheit, you can use the formula:

[tex]\[ F = \frac{9}{5}C + 32 \][/tex]

2. Calculations:

a. For 35°C:

[tex]\[ F = \frac{9}{5} \times 35 + 32[/tex]

= 95°F    

b. For 500°C:

[tex]\[ F = \frac{9}{5} \times 500 + 32[/tex]

= 932°F

c. For 10°C:

[tex]\[ F = \frac{9}{5} \times 10 + 32[/tex]

= 50°F

d. For 55°C:

[tex]\[ F = \frac{9}{5} \times 55 + 32[/tex]

= 131°F

Both Oscar and Kim are correct and do have enough money to purchase the book.

Using Oscars way:

Multiply the original price by the discount 28.50 x 0.30 = 8.55

Take that amount and subtract it from the price 28.50 - 8.55 = 19.95

Then multiply the discounted price by the sales tax rate 19.95 x 0.10 = 1.995 = 2.00

Add the sales tax amount to get the final cost 19.95 + 2.00 = 21.95 total cost

Kim's way:

Subtracting the discount percent from 100 percent ypu get 70 percent, so multiplying the price by 70 percent will get you the sale price 28.50 x 0.70 = 19.95

Multiplying the sale price by 110 percent calculates the tax amount plus the price together to get the final cost 19.95 x 1.10 = 21945 = 21.95 total cost

Both Oscar and Kim are correct and do have enough money to purchase the book.

All the given expressions are binomials except the expression in (i) which is a trinomial.

What are binomials in expressions?

Binomials can be defined as the expression that contains two variables that are different in terms.

ii.) 5x³* 2x²- 10x⁴+3x⁵+ 3x * (-2)x⁴

= 10x⁵-10x⁴+3x⁵-6x⁵

= 7x⁵+10x⁴ (this is an example of a binominal)

iii.) (t+2)²- 4t = t²+ 4t+4-4t = t²+4(binomial)

iv.) 5(a-1)-10(a-1)+100(a-1)

= 5a-5-10a+10+100a-100

= 95a - 95 (binomials)

v.) (2πr-πr²)r-(2πr-πr²)2r

= 2πr²-πr³-4πr²+2πr³

= -2πr²+πr³(binomials)

Answer:

Step-by-step explanation:

The given equation is:

[tex]f(x)=x^2+12x+32[/tex]

Simplifying the above expression, we have

[tex]f(x)=x^2+4x+8x+32[/tex]

[tex]f(x)=x(x+4)+8(x+4)[/tex]

[tex]f(x)=(x+4)(x+8)[/tex]

Thus, zeroes of the given function will be:

[tex]f(x)=0[/tex]

[tex](x+4)(x+8)=0[/tex]

[tex]x=-4 and x=-8[/tex]

Therefore the zeroes of the given function are [tex]x=-4 and x=-8[/tex].