Angles of Polygons The figure below is a pentagon whose interior angles have the same measure.What is the sum of the measures of these 5 angles?
Answers
Given the number of sides of a pentagon:
Number of sides = 5
Let's find the sum of the measures of the 5 equal angles.
To find the sum of the measures of interior angles of a polygon, apply the formula:
[tex]S=(n-2)*180[/tex]Where:
n is the number of sides = 5
Thus, we have:
[tex]\begin{gathered} S=(5-2)*180 \\ \\ S=(3)*180 \\ \\ S=540^o \end{gathered}[/tex]Therefore, the sum of the interior angles of the pentagon is 540 degrees.
ANSWER:
540°
Related Questions
Given points C(-3,-8) and D(-6.5,-4.5), find the coordinate of the point that is 2/3 of the way from C to D.
Answers
Answer:
(-16/3,-17/3)
Explanation:
Let the point which is 2/3 of the way from C to D = X
It means that point X divides the line segment CD internally in the ratio 2:1.
To determine the coordinate of point X, we use the section formula for internal division of a line segment:
[tex](x,y)=\left\{ \frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right\} [/tex][tex]\begin{gathered} (x_{1,}y_1)=(-3,-8) \\ (x_2,y_2)=(-6.5,-4.5) \\ m\colon n=2\colon1 \end{gathered}[/tex]Substituting these values into the formula above, we have:
[tex]X(x,y)=\left\{ \frac{2(-6.5)+1(-3)}{2+1},\frac{2(-4.5)+1(-8)}{2+1}\right\} [/tex]We then simplify:
[tex]\begin{gathered} X(x,y)=\left\{ \frac{-13-3}{3},\frac{-9-8}{3}\right\} \\ =\left\{ \frac{-16}{3},\frac{-17}{3}\right\} \end{gathered}[/tex]Therefore, the exact coordinate of the point that is 2/3 of the way from C to D is (-16/3,-17/3).
12 is what percent of 18
Answers
We have that
[tex]12\cdot\text{ }\frac{100}{18}=\text{ }\frac{1200}{18}\text{ = 66.6666}[/tex]So the answer is: 66.6666 .
10 × 1/3
make sure the answer is a fraction and that u explain
Answers
multiply the top and bottom ----> 10*1 and 1*3
10/3 would be your answer
1. ¿Qué expresiones a continuación se pueden usar para encontrar el área del prisma rectangular de abajo? ¡ELIJA TODOS LOS QUE SE APLIQUEN! Nota: Puede probarlos todos para asegurarse de que sean iguales. * 15 (5x2x3) + (2x3x3) (5x2) + (5x2) + (5x2) + (5x2) 5x2x2 2 (5x2) + 2 (5x2) + 2 (2x2)
Answers
We need to find the area of the prism given in the following image:
You need to add the surfaces of ALL rectangles in the image (recall that the area of a rectangle is : Base x Height)
So for this prism we have:
FOUR rectangles that measure 5 x 2
and also TWO small squares of area 2 x 2
So we need to select all the formulas they give you that read like the addition of the two above:
(5x2) + (5x2) + (5x2) + (5x2) + (2x2) + (2x2)
It can also be written as:
2 (5x2) + 2 (5x2) + 2 (2x2)
Suppose that you earn $15
Answers
Answer: 800 hours
Step-by-step explanation:
Which is a perfect square?583644
Answers
Solution:
A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer.
Hence,
[tex]36=6^2=6\times6[/tex]Therefore, the perfect square is 36.
simplify the rational expression. 18x3y5 45x5y9
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8y+63x+9
Use the distance formula to find the distance between the points given.(3,4), (4,5)
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Solution:
To find the distance between two points, the formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)=(3,4) \\ (x_2,y_2)=(4,5) \end{gathered}[/tex]Substitute the values of the variables into the formula above
[tex]d=\sqrt{(4-3)^2+(5-4)^2}=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt{2}\text{ units}[/tex]Hence, the answer is
[tex]\sqrt{2}\text{ units}[/tex]Write an equation for the description.Two-thirds a number x plus 6 is 10.
Answers
We have the next description:
- Two-thirds a number x plus 6 is 10.
To represent the description we can use the next equation:
[tex]\frac{2}{3}x+6=10[/tex]PLSSS HELPPPPPthe number of stores opened by a coffee company can be modeled by the exponential function graphed on the grid. Based on the graph, which statement does not appear to be true.
Answers
Let's analyze the statements to see which one is not true.
Statement F. The coffee shop company had opened 400 stores by the end of 1992.
The horizontal axis on the graph (the x-axis) represents the number of years that have passed since 1992, thus the year 1992 is at x=0 on the graph.
The vertical axis (the y-axis) represents the number of stores.
As we can see in the following diagram, the red point represents the number of stores at x=0 (at the year 1992):
it is true that the coffee shop had 400 stores by the end of 1992.
Statement G. The coffee shop opened 100 stores in 1 year.
To see if this is true, we look at x=1, which represents 1 year, and check for the number of stores corresponding to 1 year:
This point is at (1,500) --> After 1 year there were 500 stores.
Since they started with 400 stores, this means that it is true that they opened 100 stores in 1 year.
Statement H. Every year the number of stores the coffee company opened increased by 25%.
We can find if this is true just by looking at the form of the graph. This graph has an exponential curve which means that the growth increases at every step. Thus there is an increase in the coffee shop that they open every year. This statement is true.
Statement J. Since 1992 the coffee shop company has opened 250 stores each year.
As we saw with the previous statement, the number of shops opened every year is not constant, it increases with time. Thus, since they do not open the same amount of shops every year, this option the one that is not true.
Answer: Statement J
A gamer spinner, circle O, is divided into 3 regions as shown. RP is a diameter. what is the area of the shaded sector ROS if RP=8 in a m
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we get that the radius is 4 and the angle is 135° which is radians 3/4 pi
so the area is
[tex]A=\frac{\pi}{2}\cdot4^2-\frac{\pi}{8}\cdot4^2=8\pi-2\pi=6\pi\approx18.85[/tex]laws of exponent : multiplication and power to a power5x3 • 2 x ²
Answers
Multiplication of coefficients and variable
It's given the expression:
[tex]5x^3\cdot2x^2[/tex]can anyone help me?
solve using system of linear equations using elimination
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Answers
The values of the variables are x = 2, y = -2 and z =0
How to solve the system of equations?From the question, the system of equations is given as
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Subtract the second equation from the third
This action will eliminate (y)
So, we have
x + 3y – 2z = -4 - (2x + 3y – 3z = -2)
Evaluate
-x + z = -2
Make x the subject
x = z + 2
Substitute x = z + 2 in x – y - 3z = 4 and x + 3y – 2z = -4
z + 2 – y - 3z = 4
z + 2 + 3y – 2z = -4
Evaluate
-2z - y = 2
-z + 3y = -6
Double -z + 3y = -6
-2z + 6y = -12
Subtract -2z + 6y = -12 from -2z - y = 2 to eliminate z
7y = -14
Divide
y = -2
Substitute y = -2 in -z + 3y = -6
-z + 3(-2) = -6
Evaluate
-z - 6 = -6
Evaluate
z = 0
Recall that x – y - 3z = 4
So, we have
x + 2 - 3(0) = 4
Evaluate
x = 2
Hence, the solution is x = 2, y = -2 and z =0
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Need help with this review question. I need to know how to find the measurements from the cyclic quadrilateral
Answers
Given a quadrilateral ABCD
A cyclic quadrilateral has all its vertices on the circumference of the circle
Also cyclic quadrilateral
has the opposites angles add up to 180°
then
[tex]\angle a+\angle c=180[/tex][tex]\angle b+\angle d=180[/tex]then
Option A
A=90
B=90
C=90
D=90
since A+C= 180
and B+D = 180
measures from Option A could come from a cyclic quadrilateral
Option B
A=80
B=80
C=100
D=100
Since A+C = 80+100 = 180
and B+D = 80 + 100 = 180
measures from Option B could come from a cyclic quadrilateral
Option C
A=70
B=110
C=70
D=110
Since A+C=70+70 = 140
And B+D =110+110=220
measures from Option C could NOT come from a cyclic quadrilateral
Option D
A=60
B=50
C=120
D=130
A+C= 60+120 = 180
B+D= 50+130 = 180
measures from Option D could come from a cyclic quadrilateral
Option E
A=50
B=40
C=120
D=150
A+C=50+120= 170
B+D=40+150 = 190
measures from Option E could NOT come from a cyclic quadrilateral
Then correct options are
Options
A,B and D
shows four types of polygons which type of polygon shown has no pairs of parallel sides
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Accoring to the given figures, the pentagon is the one without parallel sides.
Hence, the answer is Pentagon.Suppose you are completely locked out outside of your house. You remember that you left your bedroom window, which is 12 feet above the ground, unlocked from the inside (meaning you can climb up the window if you have a ladder, which you do!). You go to your garage, grab the 20 ft ladder and place it so that it reaches exactly to your bedroom window. What is the angle of elevation needed to reach your window? How far away will the bottom of the ladder be from your house?
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A diagram of the situation is shown below:
In order to determine the angle of elevation x, use the sine function, as follow:
sin x = opposite side/hypotenuse
the opposite side is the distance from the ground to the wi
Samantha started with $25 in her account. she saves $7 per week. Australia has no money in his account, but adds $15 per week. for how many weeks will Australia have more money in his account than Samantha
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In this problem we can made a function to calculate the total amount for Samantha (S) and total amound of Australia (A) fon any time:
[tex]\begin{gathered} S=25+7t \\ A=0+15t \end{gathered}[/tex]when t is the number of weeks. if we made equal the ecuation we will have the time when they would have the same amound:
[tex]\begin{gathered} S=A \\ 25+7t=15t \end{gathered}[/tex]and we solve for t
[tex]\begin{gathered} 25=15t-7t \\ 25=8t \\ \frac{25}{8}=t \\ 3.125=t \end{gathered}[/tex]This means that in the next full number Australia will have more money than Samantha, so in 4 weeks this is going to happen.
what is 5/8 out of 100
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5/8 of 100 can be obtained by applying the rule of three:
[tex]\begin{gathered} 1\text{ ----- 100} \\ 5/8\text{ ----x} \end{gathered}[/tex]then, x is given by
[tex]\begin{gathered} x=\frac{\frac{5}{8}\cdot100}{1} \\ x=62.5 \end{gathered}[/tex]then, the answer is 62.5.
If a rectangle has a perimeter of 70, a length of x and a width of x-9, find the value of the length of the rectangle040 3113O 22
Answers
The formula for the perimeter of rectangle is,
[tex]P=2(l+w)[/tex]Substitute 70 for P, x for l and (x - 9) for w in the formula to determine the value of x.
[tex]\begin{gathered} 70=2(x+x-9) \\ 35=2x-9 \\ 2x=35+9 \\ x=\frac{44}{2} \\ =22 \end{gathered}[/tex]So value of x is 22.
ill take a pic of it
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The line passes through the points given.
Select any two points from the table, (-4,2) and (-3,5).
The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Hence the slope is:
[tex]\begin{gathered} m=\frac{5-2}{-3-(-4)} \\ m=\frac{3}{1} \\ m=3 \end{gathered}[/tex]The slope is 3.
List the elements in the set
{x 1 x is a negative multiple of 5}
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S={-5,-10,-15,-20,-25......}; these are few negative multiples of 5 as stated in the set builder form of set theory {x :x is a negative multiple of 5}.
What is set?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things.
What is set builder form?Set builder notation is a type of mathematical notation used to describe sets by listing their components or highlighting the requirements that each member of the set must meet. We write sets in the form of in the set-builder notation.
{y | (properties of y)} OR {y : (properties of y)}
Here,
{x :x is a negative multiple of 5}
S={-5,-10,-15,-20,-25.....}
According to the set builder form of set theory, {x:x is a negative multiple of 5} S={-5,-10,-15,-20,-25...}; these are a few negative multiples of 5.
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Classify each set of measures as AAS, ASA, SSA, SAS, or SSS. Then find the indicated length or angle measure (to the nearest tenth).
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Hello there. To solve this question, we'll have to remember some properties about triangles.
Given the triangle:
Notice in this case we have two consecutive angles and a side between them. This is a case of ASA (angle-side-angle).
With respect to the side with measure x, we have two consecutive angles then the side, hence AAS.
To find x, we'll have to apply the law of sines:
[tex]\dfrac{A}{\sin(\alpha)}=\dfrac{B}{\sin(\beta)}=\dfrac{C}{\sin(\gamma)}=2R[/tex]In this case, the angle opposite to x measures 73º and the angle opposite to 4 measures 85º, hence:
[tex]\dfrac{x}{\sin(73^{\circ})}=\dfrac{4}{\sin(85^{\circ})}[/tex]Multiply both sides by a factor of sin(73º)
[tex]x=\dfrac{4\sin(73^{\circ})}{\sin(85^{\circ})}[/tex]Using a calculator, we get the following approximation (rounding to the nearest tenth):
[tex]x\approx3.8[/tex]This is the measure of x we're looking for.
You are redecorating your room and the only thing left to paint is your door. You're onlygoing to paint the side that faces the inside of your room. The door is 6 feet 10 inchestall and 30 inches wide. You need to know the surface area of the side of the door todetermine how much paint to buy. The hardware store sells paint by how much coversa square foot. What is the surface area of the garage door? Round your answer to thenearest square foot. (Hint: 1 square foot = 144 square inches) (gridded response)
Answers
The roblem tells us that a door needs to be painted on only one side that measures 6 ft and 10 in height by 30 in wide.
We need to find the area to be painted in order to buy the appropriate quantity of paint. The answer has to be given in square feet at the end.
We start by recalling that the door is represented by a rectangle, and the area of such is given by the height times the wid
Sonia has $725,000 she wants to save. If the FDIC insurance limit per depositor, per bank, is $250,000, which of these ways of distributing her money between three banks will guarantee that all her money is insured?
$220,000 in Bank A, $230,000 in Bank B, $275,000 in Bank C
$220,000 in Bank A, $250,000 in Bank B, $255,000 in Bank C
$240,000 in Bank A, $230,000 in Bank B, $255,000 in Bank C
$240,000 in Bank A,, $245,000 in Bank B 245,000 in Bank c
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As per the dividing method, there are 3 ways of distributing her money between three banks.
Dividing method:
Division is the process of repeated subtraction.
This method, we start from the number called dividend in the number line and keep subtracting the number called divisor till we reach at 0 that is called remainder, and the number of steps we go on backward counting is the quotient or result of division.
Given,
Sonia has $725,000 she wants to save.
FDIC insurance limit per depositor, per bank, is $250,000
So, here we need to find the ways of distributing her money between three banks will guarantee that all her money is insured.
We know that, he limit is $250,000.
So, we have to divide the total amount within these limit across three bank.
Therefore, the possible ways of dividing the amount is given below:
Way 1:
if $250,000 deposited in bank A,
$250,000 deposited in bank B and
remaining money $175,000 will be deposited in bank C.
Way 2:
if $200,000 deposited in bank A,
$250,000 deposited in bank B,
$225,000 deposited in bank C.
Way 3:
If $225,000 deposited in bank A,
$225,000 deposited in bank B,
and $ 225,000 in bank C.
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Which of the following correctly identifies the vertices that lie on the major axis of the conic section shown below? (x - 2) 3-2*) (y+5) = 1 4 9 O A. (2,-2) and (2,-8) O B. (-5,5) and (-5,-1) O C. (5,5) and (-1,-5) O D. (0,-5) and (4,-5)
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General equation of an ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]where (h,k) is the center, and a and b are some constants.
If b² is greater than a², then the y-axis is the major axis.
In this case, the ellipse is defined by the next equation:
[tex]\frac{(x-2)^2}{4}+\frac{(y+5)^2}{9}=1[/tex]This means that:
[tex]\begin{gathered} b^2=9 \\ b=\sqrt[]{9} \\ b=3 \end{gathered}[/tex]And, h = 2, k = -5
The vertices on the major axis are computed as follows:
(h, k+b) and (h, k-b)
Substituting with h = 2, k = -5, and b = 3, the vertices are:
(2, -5+3) and (2, -5-3)
(2, -2) and (2, -8)
Express the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x).
Answers
Answer:
y = 5u², u=x-6
Explanation:
Given the function:
[tex]y=5(x-6)^2[/tex]We want to express f(x) as a composition of two functions.
Let u = x-6
[tex]\implies y=5u^2[/tex]Therefore, the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x)
[tex]\begin{gathered} y=5u^2\text{ where:} \\ f(u)=5u^2 \\ u=g(x)=x-6 \end{gathered}[/tex](Score for Question 1: ___ of 5 points)1. Wendy wants to find the width, AB, of a river. She walks along the edge of the river 300 ft and markspoint C. Then she walks 80 ft further and marks point D. She turns 90° and walks until her location,point A, and point C are collinear. She marks point E at this location, as shown.AriverAD 80 ft300 ftBE(a) Can Wendy conclude that AABC and AEDC are similar? Why or why not?(b) Suppose DE = 50 ft Calculate the width of the river, AB. Show all your work.Answer
Answers
We know that two triangles are similar if two pairs of corresponding angles are equal.
In this case, we have:
• Angles EDC and ABC are right angles. Then, these angles are equal.
,• Angles DCE and ACB are ,vertical angles,. In other words, they are opposite angles made by two intersecting lines. Vertical angles are ,congruent,, then these angles are equal.
AnswerSince the above condition is fulfilled, triangles ABC and EDC are similar.
Part b)When two triangles are similar, their corresponding sides are in the same ratio.
[tex]\frac{a}{e}=\frac{b}{d}=\frac{c}{c^{\prime}}[/tex]Then, we can write and solve the following equation:
[tex]\begin{gathered} \frac{300ft}{80ft}=\frac{c}{50ft} \\ 3.75=\frac{c}{50ft} \\ \text{ Multiply by 50ft from both sides} \\ 3.75*50ft=\frac{c}{50ft}*50ft \\ 187.5ft=c \end{gathered}[/tex]AnswerThe width of the river is 187.5 feet.
A trapezoid has a height of 16 miles. The lengths of the bases are 20 miles and 35miles. What is the area, in square miles, of the trapezoid?
Answers
Given:
A trapezoid has a height of 16 miles.
The lengths of the bases are 20 miles and 35 miles.
To find:
The area of the trapezoid.
Explanation:
Using the area formula of the trapezoid,
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]On substitution we get,
[tex]\begin{gathered} A=\frac{1}{2}(20+35)\times16 \\ =\frac{1}{2}\times55\times16 \\ =440\text{ square miles} \end{gathered}[/tex]Therefore the area of the trapezoid is 440 square miles.
Final answer:
The area of the trapezoid is 440 square miles.
A package of 5 pairs of insulated socks costs 27.95$. What is the unit price of the pairs of ?
Answers
Answer:
$5.59
Step-by-step explanation:
You want the unit price of a pair of socks, given that 5 pairs cost $27.95.
Unit priceThe unit price is found by dividing the price by the number of units.
$27.95/5 = $5.59
The unit price of a pair of socks is $5.59.
given that the measure of arc AD=(17×+2), measure of arc AC=(7×-10),and measure of angle ABC=(4×+15) find the measure of angle ABC
Answers
In the given figure, angle ABC is formed by a tangent and a secant.
The angle formed by tangent and secant is given by
[tex]m\angle ABC=\frac{1}{2}(m\bar{AD}-m\bar{AC})[/tex]Where mAD and mAC are the intercepted arcs.
For the given case,
[tex]\begin{gathered} m\angle ABC=(4x+15)\degree \\ m\bar{AD}=(17x+2)\degree \\ m\bar{AC}=(7x-10)\degree \end{gathered}[/tex]Let us substitute the given values into the above formula and solve for x
[tex]\begin{gathered} m\angle ABC=\frac{1}{2}(m\bar{AD}-m\bar{AC}) \\ (4x+15)\degree=\frac{1}{2}\lbrack(17x+2)\degree-(7x-10)\degree\rbrack \\ 2\cdot(4x+15)\degree=(17x+2)\degree-(7x-10)\degree \\ 8x+30=17x+2-7x+10 \\ 8x-17x+7x=2+10-30 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}[/tex]The value of x is 9
So, the measure of angle ABC is
[tex]\begin{gathered} m\angle ABC=4x+15 \\ m\angle ABC=4(9)+15 \\ m\angle ABC=36+15 \\ m\angle ABC=51\degree \end{gathered}[/tex]Therefore, the measure of angle ABC is 51°
