(a) A convex, 11-sided polygon can have at most how many obtuse interior angles? (b) A convex, 11-sided polygon can have at most how many acute interior angles?
Please provide an explanation!

Answers

Answer 1

A) All 11 interior angles may be obtuse.
B) At most 3 interior angles may be acute.

Explanation:
A) To find the sum of the angles of a polygon, we use (n-2)(180), where n is the number of sides. We would then have (11-2)(180)=9(180)=1620. If the polygon is regular, we divide this by the number of sides; 1620/11 = 147.23. Thus all 11 angles would be obtuse in a regular 11-sided figure.

B) All interior angles of a polygon have an exterior angle that is supplementary to it. If the interior angles are acute, that means the exterior angles are obtuse. Likewise, if the interior angles are obtuse, the exterior angles would have to be acute.

The sum of the exterior angles of any polygon is 360. This means there can be no more than 3 obtuse exterior angles; since obtuse means greater than 90, if there were 4 obtuse angles, 4 angles greater than 90, the sum would be more than 360. If there can be no more than 3 obtuse exterior angles, then there can be no more than 3 acute interior angles.

Related Questions

Please explain how you worked the problem to find x!

1/x +1/(x+4) =1/5

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[tex]\frac{1}{x} +\frac{1}{x+4}[/tex] (by taking the common factor for the two elements of the equation
[tex]\frac{1]{x} *\frac{x+4}{x+4} +\frac{1}{x+4}*\frac{x}{x}=\frac{x+4}{x*(x+4)}+\frac{x}{x*(x+4)}[/tex] now we can add both of the equation as the denominators have the same value.
[tex]\frac{x+4+x}{x*(x+4)}=\frac{2x+4}{x^{2}+4x} = \frac{1}{5}[/tex] by multiplying both sides by [tex]5*(x^{2}+4x)[/tex]
[tex] 5*(2x+4)=x^{2} +4x[/tex]
[tex] 10x+20=x^{2}+4x[/tex] by subtracting both sides by (10x+20)
[tex] x^{2} -6x -20 = 0[/tex] (by using the quadratic formula)
we will find two answers for this equation
x={[tex]\frac{-6- \sqrt{116}}{-2}[/tex] and [tex] \frac{-6+\sqrt{116}}{-2}[/tex]

if tyrone works 40 hours per week and has no other sources of income what is his total monthly cash inflow

Answers

[tex]18 \times 40 = 720[/tex]

[tex]720 \times 4 = 2880[/tex]

[tex]2880 - 1800 = 1080[/tex]

~~

Answer : B

~~

I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

how many time does 2 go into 19

Answers

Hello There @Diamondinthesky123 (Cute Username)

When you state the question, "How many times does 2 go into 19", I assume your talking about Long Division. (Not so long in this case)

In this case, we would divide 19 by 2, resulting in 9 with a remainder of 1.
Thats It! :)

I hope I helped, Have a great Day!

Thank you,
Darian D.

Final answer:

In basic division, 2 goes into 19 a total of 9 times with 1 leftover. This demonstrates division and the concept of remainders in mathematics.

Explanation:

The student is asking about basic division in mathematics, specifically how many times 2 goes into 19. To find this, we divide 19 by 2.

Doing the division, we get:

19 divided by 2 equals 9 with a remainder of 1.

Therefore, 2 goes into 19 9 times with 1 left over.

It's worth noting that there's also a mathematics technique called estimation that might be considered here. If we estimate to the nearest whole number, 2 would go into 19 approximately 9 times since 2 times 9 is 18, which is very close to 19.

Analyze the following budget, with an income of $750, to determine how much can be spent on food for the month. Month________ Budgeted Amount Food $___ Personal Items $20 Cell Phone $75 Entertainment $85 Car Expenses – Gas, Insurance $260 College Savings $250 a. No more than $70 can be spent on food. b. No more than $75 can be spent on food. c. No more than $80 can be spent on food. d. No more than $60 can be spent on food.

Answers

The answer is D
Hope it helps

A monthly of $60 can be spent for food after all the expenses and savings

are sorted.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The numerical form of the given information can be formed as,

$(750 - 20 - 75 - 85 - 260 - 25).

= $60.

So, With an income of $750 and all the expenses including saving for for college worth of $250 the amount that can be spent on food is $60.

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What is the factored form of x2 - 4x - 5 ?

Answers

(X-5)(x+1)

Two factors of five that subtract to four

Use the data to create a scatter plot. Year 0 1 2 3 4 Population 3 4 6 11 15 Use the point tool to plot the points from the table in the coordinate grid to create a scatter plot.

Answers

In order to create the scatter plot in your point tool, mark the points one by one on the coordinate grid. The first point will be (0,3). This means for location 0 on x-axis the value on y axis is 3. First point goes there. The second point is (1, 4). Move one unit on the x-axis and 4 units on y-axis. Second point goes there. Do this process for all the points to complete the scatter plot. I used Microsoft excel to create the scatter plot. Your plot will be similar to the plot shown below.

Enter the values in the first two columns of MS excel. Then go on the insert tab and click insert scatter plot. A scatter plot will be made as shown below in the attached picture.

The same plot can be made by hand by simply inserting the correct points on the graph. From the scatter plot we can observe that a positive correlation occurs in the given variables. A straight line can be used to approximate the trend of the data.

Answer:

Refer the attached figure.

Step-by-step explanation:

Given : Data of population

To find : Use the data to create a scatter plot?

Solution :

Data :

Year(x) Population(y)

0 3

1 4

2 6

3 11

4 15

A Scatter Plot has points that show the relationship between two sets of data.

With the help of scatter plot graph,

We plot the points of the data.

Refer the attached figure below.

What is the constant term in the expression 4x3y + 8x2 + 6x + 5?

Answers

Answer:

Step-by-step explanation:

The constant term is the one with no variables in it: +5.

Answer:

i took the test and its 5.

Find the values of a b and c for which the quadratic equation ax^2+bx+c=0 has the solutions -3 and 1

Answers

It may be easier to start from

.. a(x +3)(x -1) = 0
.. a(x^2 +2x -3) = 0

The quadratic
.. ax^2 +bx +c = 0 will have solutions -3 and 1 for ...

.. a ≠ 0
.. b = 2a
.. c = -3a

1) Which two lines are parallel?

I. 5y = -3x-5
II. 5y = -1 - 3x
III. 3y - 2x = -1

a. I. and II.
b. I. and III.
c. II. and III.
d. No two of the lines are parallel.

2) Which do lines are parallel?

I. 3y = -2x - 3
II. 3y = 1 - 2x
III. 4y - 3x = -1

a. I. and II.
c. II. and III.
b. I. and III.
d. No two of the lines are parallel.

Answers

1)a

2)a
hope this helps

2x+5y=-6 , wht is the x intercept, what is the y intercept

Answers

Final answer:

The x-intercept is (-3,0) and the y-intercept is (0,-6/5).

Explanation:

The x-intercept is the point where the line crosses the x-axis. To find the x-intercept, we set y=0 and solve for x. In the equation 2x+5y=-6, we substitute 0 for y and solve for x:

2x + 5(0) = -6

2x = -6

x = -3

So, the x-intercept is the point (-3,0).

The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we set x=0 and solve for y. In the equation 2x+5y=-6, we substitute 0 for x and solve for y:

2(0) + 5y = -6

5y = -6

y = -6/5

So, the y-intercept is the point (0,-6/5).

what term has to be added to x^2-3x to be a trinomial 3/2 9/4 6 9

Answers

Your question is probably what should be added to the given expression to make it a perfect square.

The given expression is:

[tex] x^{2} -3x[/tex]

The formula of [tex] (a-b)^{2} [/tex] is [tex] a^{2} -2ab+ b^{2} [/tex]

Re-writing the given expression:

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

So, we have the square of first term and twice the product of first and second term. What is missing is the square of second term.

So, the complete expression for perfect square will be:

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

Therefore, 9/4 should be added to the given expression to make it a perfect square.

Answer: The correct option is (B) [tex]\dfrac{9}{4}.[/tex]

Step-by-step explanation: We are given to find the term that has to be added to [tex]x^2-3x[/tex] to be a perfect trinomial.

Let, c denote the term to be added.

Then,

[tex]x^2-3x+c\\\\=x^2-2\times x\times \dfrac{3}{2}+c\\\\\\=x^2-2\times x\times \dfrac{3}{2}+\dfrac{9}{4}+c-\dfrac{9}{4}\\\\\\=\left(x-\dfrac{3}{2}\right)+c-\dfrac{9}{4}.[/tex]

Therefore, the given expression will be a perfect trinomial if

[tex]c-\dfrac{9}{4}=0\\\\\\\Rightarrow c=\dfrac{9}{4}.[/tex]

Thus, the required term to be added is [tex]\dfrac{9}{4}.[/tex]

Option (B) is CORRECT,

A triangle has sides with lengths of 6 millimeters, 8 millimeters, and 10 millimeters. Is it a right triangle?

Answers

If it is a right triangle, then a^2 + b^2 = c^2
6^2 + 8^2 = 100^2
36 + 64 = 100
100 = 100

Yes, the triangle is a right triangle.

Hope this helps =)

The sides 6 mm, 8 mm and 10 mm forms a right angles triangle.

We have,

The sides of the triangle are of lengths 6 mm, 8 mm and 10 mm.

The longest side length is 10 mm.

Now, the sum of squares of the smaller sides is given as:

6² + 8² = 36 + 64 = 100 = 10²

As, the sum of squares of the smaller sides is equal to the square of the longer side.

So, by the Pythagorean Theorem, the sides form a right triangle.

Learn more about Pythagoras theorem here:

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The sum of two numbers is 44. One number is 3 times as large as the other. What are the numbers?

Answers

let one of the number be x

one number = x
the other number = 3x

Given that the sum of these two number is 44.
x + 3x = 44
4x = 44
x = 44 ÷ 4
x = 11

x = 11
3x = 11 x 3 = 33

The two numbers are 11 and 33

Set up 2 variables:
x = larger number
y = smaller number

Set up equations:
[tex]x + y = 44[/tex]
[tex]3y = x[/tex]

Solve by substituting. I will use the x already given to us (in second equation) to substitute in 1st equation (x = 3y):
[tex]3y + y = 44[/tex]
[tex]4y = 44[/tex]
[tex]y = 11[/tex]

Plug it back into 2nd equation to solve for x:
[tex]3y = x[/tex]
[tex]3(11) = x = 33[/tex]

So, our two values are: x = 33 and y = 11.

We can check, x + y = 33 + 11 does equal 44 and 33 times is 3 times larger than 11. So, the initial criteria work out and we are right.

A cylinder has a radius of 4x+2 and a height of 5x+4. Which polynomial in standard form best describes the total volume of the cylinder. Use the formula V=pir^2h for the volume of a cylinder.

Answers

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=4x+2\\ h=5x+4 \end{cases}\implies V=\pi (4x+2)^2(5x+4) \\\\\\ V=\pi [(4x+2)(4x+2)](5x+4)\\\\\\ V=\pi \stackrel{FOIL}{(16x^2+16x+4)}(5x+4) \\\\\\ V=\pi[ (80x^3+80x^2+20x)+(64x^2+64x+16)] \\\\\\ V=80\pi x^3+144\pi x^2+84\pi x+16\pi [/tex]

is possible to have a shape with different dimensions while having the same volume?

Answers

Yes, they could be different and still have the same volume

yes,

a cuboid with dimensions 2, 4, 8 has volume = 64 unit^3

a cube with side 4 has volume = 64 unit^3

so, they have different shapes but same volume

Answer and how you get then answer

Answers

Percent Change = ((new value)/(old value) -1) * 100%
= (480/540 -1)*100%
≈ -11.11%

The number of calories in a child's meal was reduced about 11%.

$8000 invested at an APR of 6% for 10 years.
If interest is compounded annually, what is the amount of money after 10 years?

Answers

The formula in finding the maturity value is the following:

A = P (1 + r) ^t

Where A = Maturity value

P = principal amount

r = Annual percentage rate

t = time in years

Substituting the given amount to the formula:

A = $8,000 (1 + 6%) ^10

= $8,000 (1.7908)

= $14,326.40

Therefore, the amount of $8,000 after 10 years compounded annually at 6% is $14,326.40

How do I solve this equation for n? (6x2n)÷8=15

Answers

multiply 8 on both sides so we have no division so 8 multiplied by 15 = 120
now we know (6x2n) = 120
so if we re-write this you can make it 6x(2n) = 120
Now we divide by 6 on both sides that gives us (2n) = 20
divide by two and you have your answer

hope this helps

To solve the equation (6x2n)÷8=15 for n, you must perform algebraic operations to isolate n. This involves multiplying by 8, then dividing by 6x, and finally by 2, to arrive at n = 20 / x.

To solve the equation (6x2n)÷8=15 for n, we need to follow several steps. This involves manipulating the equation using algebraic operations until we isolate the variable n on one side. Here is the step-by-step process:

Multiply both sides of the equation by 8 to get rid of the fraction: 6x2n = 15 × 8.Simplify the right side: 6x2n = 120.Divide both sides by 6x to isolate n: 2n = 120 / 6x.Further simplify the right side to get n on its own: n = (120 / 6x) / 2.Complete the calculation based on the values of x that are given: n = 20 / x.

If x is known, you can substitute the value of x into the equation to find the value of n. If x is not given, then this is the simplified form of the equation in terms of n and x.

Charlie reads quickly. He reads 1 and 3 seventh pages every 2 third minutes. Charlie reads at a constant rate. How many pages does charlie read per minute?

Answers

The unit rate would be 1 3/7 ÷ 2/3 10/7 ÷ 2/3 10/7 · 3/2 separate by division, rearrange and multiply 15/7

Charlies reads 15/7, or 2 1/7, page per minute.

Hope this helps a bit.

Which terms accurately classify this triangle? Choose exactly two answers that are correct. A. right B. acute C. isosceles D. scalene

Answers

The answer is (C isosceles) hope it helps and have a great day!

Which of the following is a monomial?
A. 2xyz2
B. 2x + yz
C. 2 + xyz
D. 2x − yz

Answers

A monomial has one term, even if it has multiple variables.
So your answer would be A. 2xyz2. Hope it helps! :)

5 plus 500% of 10 is the same as 110% of what number?

Answers

5+10×500%=5+50=55
55÷110%=50
so 5 plus 500% of 10 is the same as 110% of 50

15% of the toddlers in a preschool class drink water with their lunch. How many toddlers
are in the class if 3 toddlers drink water with their lunch?
(a) Draw a model for the situation (if you prefer to use a 100-grid model or ratio table
model, that’s fine too!) and label the “part,” “whole,” and “percent.”

Answers

15/100 = 3/x

15x = 300
x = 300/15
x = 20 kids

If the sum of four consecutive odd integers is 208, what is the smallest of the four integers?

Answers

The least of these numbers is 20.

A candy maker buys a bar of chocolate weighing 162 ounces. About how many pounds does the bar weigh?

Answers

For this case, the first thing you should keep in mind is the following conversion:
1 pound = 16 ounces
Applying the comversion we have:
(162) * (1/16) = 10,125 pounds
Therefore, the weight of the chocolate bar in pounds is 10,125
Answer:
the bar does weigh 10,125 pounds

Assume that the weights of all packages of a certain brand of cookies are normally distributed with a mean of 32 ounces and a standard deviation of 0.3 ounce. find the probability that the mean weight, x¯, of a random sample of 20 packages of this brand of cookies will be between 31.8 and 31.9 ounces.

Answers

That probability is about 6.7%.

116=0.0625. Which calculation is NOT a way to find 1516?

Answers

we have that
1/16=0.0625

we know that
Multiply (0.0625) by 15 is a way to find (15/16)--------> 0.0625*15=0.9375
so
any operation that results in any other value is not a way to find (15/16)

Answer: 16 divided by 15

Step-by-step explanation:

I got it right.

Let u = (1,0,2) , v = (0,-1,2) and w = (2,1,0). Compute

(i) the area of the parallelogram bounded by u and v (5)

(ii) the equation of the plane parallel to v and w pass through the tip of u

Answers

Answers:

(i) 3
(ii) [tex]-2x + 4y + 2z = 2[/tex]

Explanation:

(i) The area of the parallelogram bounded by vectors u and v is given by:

[tex]\text{Area} = \left \| u \times v \right \|[/tex]

Note that if [tex]u = (u_1, u_2, u_3) = (1, 0, 2), v = (v_1, v_2, v_3) = (0, -1, 2) [/tex],

[tex]u \times v \\ = \left(u_2v_3-u_3v_2, u_3v_1-u_1v_3, u_1v_2-u_2v_1\right) \\ = \left((0)(2)-(2)(-1), (2)(0)-(1)(2), (1)(-1)-(0)(0)\right) \\ \boxed{u \times v = \left(2, -2, -1 \right)}[/tex]

Thus, the area of the parallelogram formed by vectors u and v is calculated as

[tex]\text{Area} = \left \| u \times v \right \| \\ = \left \| \left(2, -2, -1 \right) \right \| \\ = \sqrt{(2)^2 + (-2)^2 + (1)^2} \\ \boxed{\text{Area} = 3}[/tex]

Hence, the area of the parallelogram is 3.

(ii) To obtain the equation of the plane, we must get its normal vector and a point in the plane.

As calculated in (i), the normal vector to the plane is [tex]v \times w[/tex] because the plane is parallel to vectors v and w. Note that if [tex]v = (v_1, v_2, v_3) = (0, -1, 2), w = (w_1, w_2, w_3) = (2, 1, 0)[/tex],

[tex]v \times w \\ = \left(v_2w_3-v_3w_2, v_3w_1-v_1w_3, v_1w_2-v_2w_1\right) \\ = \left((-2)(0)-(2)(1), (2)(2)-(0)(0), (0)(1)-(-1)(2)\right) \\ \boxed{v \times w = \left(-2, 4, 2 \right)}[/tex]

Thus, a normal vector to the plane is [tex]\left(-2, 4, 2 \right)[/tex].

To get a point in the plane, note that vector u can be represented by any pairs of points. So, we can take (0, 0, 0) to be the starting point of vector u. Since [tex]u = (1, 0, 2)[/tex], the tip of vector u is [tex](0 + 1, 0, 0 + 2) = (1, 0, 2)[/tex]. Because the plane passes thru the tip of vector u, a point in the plane has coordinates [tex] (1, 0, 2)[/tex].

So for any point [tex](x, y, z)[/tex] in the plane, the equation is given by

[tex]n \cdot (x - 1, y - 0, z - 2) = 0[/tex]

Where n is the normal vector to the plane.

Since [tex]n = \left(-2, 4, 2 \right)[/tex], the equation becomes

[tex]\left(-2, 4, 2 \right) \cdot (x - 1, y - 0, z - 2) = 0 \\ \left(-2, 4, 2 \right) \cdot (x - 1, y, z - 2) = 0 \\ -2(x - 1) + 4y + 2(z - 2) = 0 \\ -2x + 2 + 4y + 2z - 4 = 0 \\ -2x + 4y + 2z - 2 = 0 \\ \boxed{-2x + 4y + 2z = 2 }[/tex]

Melissa had a balance of $104 in her checking account at the beginning of the month. She made one additional deposi of $216 and wrote checks $78 , $119 , and $105. What was the balance in her checking account at end of the month

Answers

Do you deposit or cash the checks?

Answer:

She only had $18 left

Step-by-step explanation:

solve the proportion
[tex] \frac{3}{4} = \frac{x}{6} [/tex]

Answers

To solve a problem like this, you can use a method called cross-multiplying. This is when you multiply the denominator of the first fraction by the numerator of the other and then multiply the two remaining numbers.

[tex] \frac{3}{4} = \frac{x}{6} [/tex] Multiply 3 by 6 and multiply 4 by x.
4x = 18 Divide by 4.
x = [tex] \frac{18}{4} [/tex] Simplify!
x = [tex] \frac{9}{2} [/tex]

You can check this by comparing the fractions with [tex] \frac{9}{2} [/tex] in the place of x.

[tex] \frac{3}{4} = \frac{ \frac{9}{2} }{6} [/tex] Divide [tex] \frac{9}{2} [/tex] by 6 ( [tex] \frac{9}{2} [/tex] times [tex] \frac{1}{6} [/tex]).
[tex] \frac{3}{4} = \frac{9}{12} [/tex] Simplify!
[tex] \frac{3}{4} = \frac{3}{4} [/tex]

The fractions are equal, so x = [tex] \frac{9}{2} [/tex] .

Other Questions

ancient belief systems were heavily rooted in the understanding of?A. natureB. other peopleC. loveD. wealth Which statement is true of universities in the late middle ages?A. They contributed to social change because people of all classes studied there.B. They contributed to religious tolerance because they provided a secular education.C. They contributed to good government because they trained court administrators.D. They contributed to modern literature because they taught in the vernacular. according to this graph most of immigrants to Europe come from Which of the following summarizes the role of the hypothalamus? A. It connects the endocrine and nervous systems and controls the pituitary gland. B. It controls the rate at which cells burn fuels from food to produce energy.C. It produces glucagon and insulin to control glucose levels in the blood. D.It releases adrenaline as a response to fear, stress, and excitement. 2. On which date does the Antarctic Circle have 24 hours of daylight? (1 point)June 21March 21September 21December 213. When energy is transferred to air, what happens to the particles of air? (1 point)They move slower.They move faster.They cool down.none of the above Enrique is analyzing the poem She Walks in Beauty by Lord Byron. Read the poem Enrique is analyzing. She Walks in Beauty by Lord Byron (George Gordon) She walks in beauty, like the night Of cloudless climes and starry skies; And all thats best of dark and bright Meet in her aspect and her eyes; Thus mellowed to that tender light Which heaven to gaudy day denies. One shade the more, one ray the less, Had half impaired the nameless grace Which waves in every raven tress, Or softly lightens oer her face; Where thoughts serenely sweet express, How pure, how dear their dwelling-place. And on that cheek, and oer that brow, So soft, so calm, yet eloquent, The smiles that win, the tints that glow, But tell of days in goodness spent, A mind at peace with all below, A heart whose love is innocent! Enrique is analyzing the poem for alliteration that emphasizes the differences in natural light at different times. Which pair of lines should Enrique mention in his analysis? A. She walks in beauty, like the night / Of cloudless climes and starry skies; B. Thus mellowed to that tender light / Which heaven to gaudy day denies. C. Where thoughts serenely sweet express, / How pure, how dear their dwelling-place. D. And on that cheek, and oer that brow, / So soft, so calm, yet eloquent, Two numbers are in the ratio of 2 to 3. If the smaller number is 18, the larger number is _____. 21 27 36 54 Light with a frequency of 7.18 1014 hz lies in the violet region of the visible spectrum. what is the wavelength of this frequency of light? answer in units of nm. 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(a) A convex, 11-sided polygon can have at most how many obtuse interior angles? (b) A convex, 11-sided polygon can have at most how many acute interior angles?Please provide an explanation!

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(a) A convex, 11-sided polygon can have at most how many obtuse interior angles? (b) A convex, 11-sided polygon can have at most how many acute interior angles?
Please provide an explanation!