Match the figure at the right with the number that represents the sum of the interior angles for that figure.
Answers
To calculate the sum of the internal angles of a polygon you have to use the following formula:
[tex](n-2)\cdot180º[/tex]Where "n" is the number of sides of the polygon.
So you have to subtract 2 to the number of sides of the polygon and then multiply the result by 180º to determine the sum of the interior angles.
1) The first polygon has n=4 sides. To calculate the sum of its interior angles you have to do as follows:
[tex]\begin{gathered} (n-2)\cdot180º \\ (4-2)\cdot180º \\ 2\cdot180º=360º \end{gathered}[/tex]2) The second polygon has n=5 sides. The sum of its interior angles can be calculated as:
[tex]\begin{gathered} (n-2)\cdot180º \\ (5-2)\cdot180º \\ 3\cdot180º=540º \end{gathered}[/tex]3) The third polygon has n=6 sides. You can calculate the sum of its interior angles as:
[tex]\begin{gathered} (n-2)\cdot180º \\ (6-2)\cdot180º \\ 4\cdot180º=720º \end{gathered}[/tex]4) The fourth polygon has n=7 sides, so you can calculate the sum of its interior angles as:
[tex]\begin{gathered} (n-2)\cdot180º \\ (7-2)\cdot180º \\ 5\cdot180º=900º \end{gathered}[/tex]Related Questions
When simplified, |9+ (4-3) – 17| has a value of ______.
Answers
We have the following expression:
[tex]|9+(4-3)-17|[/tex]First, let's solve the operation inside the parenthesis.
[tex]|9+1-17|[/tex]Second, we add and subtract accordingly.
[tex]\lvert-7\rvert[/tex]Third, we apply the absolute value property.
[tex]\lvert-7\rvert=7[/tex]In conclusion, the values is 7
2 Quadrilateral A'B'CD is the result of dilating quadrilateral ABCD about point D by a scale factor of 3 1 ita -4 -3 -2 B Determine whether each claim about the properties of ABCD and A'B'C'D' is true or false. AB and A' B' are on distinct parallel lines. True/false v AD and A'D' are on the same line. True/false v
Answers
Solution
AB and A' B' are on distinct parallel lines. TRUE
Since when we apply the scale factor the new A'B' is on a different line but parallel
AD and A'D' are on the same line. FALSE
The new triangle with the scale factor produce an A'D' line different
Describe the transformation from triangle DEF to triangle D′E′F′ in the figure.Question options:A) Rotation 90° clockwise about the originB) Reflection about the originC) Rotation 90° counterclockwise about the originD) Transformation down 8 units and right 6 units
Answers
The transformation from triangle DEF to triangle D'E'F' is a reflection about the origin.
since,The corrdinates of the traingle DEF is,
point D is (-5,6) , E is (-1,5) , F (-4,2) and The corrdinates of the traingle D'E'F' is,
D' (5,-6) , E' (1,-5) and F' (4,-2).
At an amusement park, the two most popular rollercoasters are the Python and the Vortex. The Python is 212 feet long and the Vortex is 210 feet long. How many times as long is the Python as the Vortex?
Answers
Python is 1.01 times as long as Vortex.
What is division ?
In mathematics, division is the process of dividing a given sum into equal pieces. As an illustration, we could divide a group of 20 people into 4 groups of 5, 5 groups of 4, and so on. The opposite of multiplication is division. When you multiply three groups of four to produce twelve, you get four in each group when you split twelve into three equal groups. The basic objective of splitting is to determine how many equal groups are created or how many people are in each group after a fair distribution.
Here the given ,
length of Python = 212 feet
length of Vortex = 210 feet
Here to find the length we need to divide python length by vortex length
=> [tex]\frac{212}{210}[/tex]
=> 1.01 times.
Therefore Python is 1.01 times as long as Vortex.
To learn more about division
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Zach wanted to prove that the arcs on a railroad crossing symbol did not each equal90°. He drew an inscribed angle A with arc BC as the intercepted arc. Angle Ameasured 35°. Fill in the blank with the measure of the intercepted arc.BmBC =RXR35°A
Answers
The given problem can be exemplified in the following diagram:
In this case the value of angle "x" is 35 degrees, therefore, the measure of arc BC is double this angle, that is:
[tex]\begin{gathered} \text{mBC}=35\times2 \\ mBC=70 \end{gathered}[/tex]ans (alpha particles) at Figure 127 Exercises 12.6. complete the following: Find the intercepts and domain and perform the symmetry test (a) 9x^2 - 16y^2 = 144
Answers
We have that the general equation of the hyperbola is the following:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]where 'a' and '-a' are the x-intercepts.
In this case, we have the following equation:
[tex]9x^2-16y^2=144[/tex]then, we have to divide both sides by 144 to get on the right side 1, thus, we have the following:
[tex]\begin{gathered} (9x^2-16y^2=144)(\frac{1}{144}) \\ \Rightarrow\frac{9}{144}x^2-\frac{16}{144}y^2=1 \\ \Rightarrow\frac{x^2}{16}-\frac{y^2}{9}=1 \end{gathered}[/tex]now, notice that we have that:
[tex]a^2=16[/tex]then, the x-intercepts are:
[tex]\begin{gathered} a^2=16 \\ \Rightarrow a=\pm\sqrt[]{16}=\pm4 \\ a_1=4 \\ \text{and} \\ a_2=-4 \end{gathered}[/tex]therefore, the x-intercepts are 4 and -4.
Now that we know that the intercepts are on those points, we can see that the hyperbola has the following graph:
we can see that the hyperbola is not defined between -4 and 4, therefore, the domain of the hyperbola is:
[tex](-\infty,-4\rbrack\cup\lbrack4,\infty)[/tex]finally, to perform the symmetry test, we have to check first both axis simmetries by changing x to -x and y to -y:
[tex]\begin{gathered} \frac{x^2}{16}-\frac{(-y)^2}{9}=1 \\ \Rightarrow\frac{x^2}{16}-\frac{y^2}{9}=1 \\ then \\ \frac{(-x)^2}{16}-\frac{y^2}{9}=1 \\ \Rightarrow\frac{x^2}{16}-\frac{y^2}{9}=1 \end{gathered}[/tex]since the hyperbola got symmetry about the x-axis and the y-axis, we have that the hyperbola got symmetry about the origin
does the point (2,0) satisfy the equation y=9×
Answers
No, it does not.
[tex]0\ne18[/tex]Write an equation to represent the sum modeled in the following number line. H H H -4 -3 -2 -1 0 1 2 3 4
Answers
The number line shows numbers graded into three parts each such that each point between numbers represent 0.33 units.
This means the red line moving towards the left is a negative because it falls to the left of point 0, where the division between positive and negative numbers take place.
Hence the red line indicates -3.33
The blue line is movin towards the right which means its a positive value. Note that it begins from -3.33 and ends at -1.33. Hence the blue line is a positive value and it covers two units.
The equation that models this number line can be written out as
[tex]x=-3.33+2[/tex]solve the given system of equations2y=x+93x-6y=-15
Answers
Answer:
No solutions
Explanation:
The given system of equations is
2y = x + 9
3x - 6y = -15
To solve the system, we first need to solve the first equation for x, so
2y = x + 9
2y - 9 = x + 9 - 9
2y - 9 = x
Then, replace x = 2y - 9 on the second equation
3x - 6y = -15
3(2y - 9) - 6y = -15
3(2y) + 3(-9) - 6y = -15
6y - 27 - 6y = -15
-27 = -15
Since -27 is not equal to -15, we get that this system of equation doesn't have solutions.
A building has two sizes of apartments, small and regular. The ratio of small apartments to regular apartments is 6 to 18. What percent of apartments in the building are small?
Answers
how many square inches of wrapping paper are needed to wrap a present that is 12 inches wide, 5 inches deep and 12 inches tall
Answers
ok
Area of a rectangular prism: 2(wide x deep) + 2(wide x tall) + 2(tall x deep)
Substitution
Area = 2(12 x 5) + 2(12 x 12) + 2(5 x 12)
Simplification
Area = 2(60) + 2(144) + 2(60)
Area = 120 + 288 + 120
Result
Area = 528 in^2
In which type of composition does a soloist or a small group of instruments interact wi
dance suite
sonata
concerto
chamber music
Answers
Step-by-step explanation:
Hey! The correct answer is Chamber Music.
In triangle EFG, m∠E = 91.6° and m∠F = 30.7°. Determine the measure of the exterior angle to ∠G.
57.7°
60.9°
119.1°
122.3°
Answers
Answer:
122.3
Step-by-step explanation:
91.6 + 30.7 = 122.3
180 - 122.3 = 57.7 (angles in a triangle = 180)
180 - 57.7 = 122.3 (angles on a straight line = 180)
Answer: 122.3
Step-by-step explanation: did the practice test
In right triangle XYZ, the hypotenuse measures 14 inches and one leg measures 10 inches. Find the length of the other leg. Show your work and write your answer in simplest radical form.
Answers
As per given by the question,
There are given that a triangle XYZ, and the hypotenuse of the triangle is 14 in., and one leg is 10 in.
Now,
First draw the triangle XYZ.
Now,
From the triangle XYZ, XZ is hypotenuse of the triangle, XY is the first leg of the triangle, and YZ is second leg of the triangle.
So,
First leg z is 10, then find the value of second leg x.
Then,
To find the value of second leg, here use pythagoras theorem.
So,
From the pythagoras theorem;
[tex]XY^2+YZ^{2^{}^{}}=XZ^2[/tex]Now,
[tex]\begin{gathered} XY^2+YZ^2=XZ^2 \\ 10^2+x^2=14^2 \\ 100+x^2=196 \\ x^2=196-100 \\ x^2=96 \end{gathered}[/tex]Then,
[tex]\begin{gathered} x^2=96 \\ x=\sqrt{96}^{} \\ x=9.79 \end{gathered}[/tex]Hence, the length of the other leg is 9.79.
Which function is nonlinear?Which equation represents a nonlinear function? (Let me know if you can’t read the possible answers for the equation and I will send them)
Answers
Given:
There are 4 equation representations are given.
To find:
The nonlinear equation.
Explanation:
A)
[tex]\begin{gathered} 3x-2y=7 \\ i.e)3x-2y-7=0 \end{gathered}[/tex]Which is of the linear form,
[tex]ax+by+c=0[/tex]B)
[tex]y=\frac{2}{3}x+8[/tex]Which is of the linear form,
[tex]y=mx+c[/tex]C)
Let us consider the two points.
[tex](5,0),(6,2)[/tex]Using the two-point formula,
[tex]\begin{gathered} \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1} \\ \frac{y-0}{2-0}=\frac{x-5}{6-5} \\ \frac{y}{2}=\frac{x-5}{1} \\ y=2x-10 \end{gathered}[/tex]Substituting the first point to verify the linear equation,
[tex]\begin{gathered} -4=2(3)-10 \\ -4=-4 \end{gathered}[/tex]Therefore, the linear equation is satisfied for all 4 points.
Thus, options A, B, and C are linear equation.
So, the nonlinear equation must be given options D.
Final answer:
The correct option is D.
Find the midpoint and distance on points (5,5) and (-1,3)
Answers
Given:
Two points (5, 5) and (-1, 3).
To find the midpoint and distance:
Using the midpoint formula,
[tex]\begin{gathered} m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ =(\frac{5-1}{2},\frac{5+3}{2}) \\ =(\frac{4}{2},\frac{8}{2}) \\ =(2,4) \end{gathered}[/tex]Thus, the mid-point formula is (2, 4).
Using the distance formula,
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2_{}} \\ =\sqrt[]{(-1-5)^2+(3-5)^2} \\ =\sqrt[]{(-6)^2+(-2)^2} \\ =\sqrt[]{36+4} \\ =\sqrt[]{40} \\ =2\sqrt[]{10}\text{ units} \end{gathered}[/tex]Thus, the distance between the two points is,
[tex]2\sqrt[]{10}units[/tex]A property owner paid $960 for the tiles to cover a 800 sq. ft yard. Then he decided to tile an additional 260 sq. ft. How much will be paid for the additional tiles?
Answers
Answer:
$312 will be paid for the addditional tile
Explanation:
Given that the property owner paid $960 for tiles to cover a 800 sq. ft yard
Since he decided to tile an additional 260 sq. ft, to know how much will be paid for the additional tiles, we need to know how much he paid for each of the last set of tiles.
The amount is
960/800 = 1.2
He paid $1.2 per tile.
For 260 sq. ft, he will pay:
$1.2 * 260
= $312
Convert 59°F to degrees Celsius.If necessary, round your answer to the nearest tenth of a degree.Here are the formulas.C= (5/9) (F -32).
Answers
15 ° C
Explanation
to convert form Farenheit to Celcius degree we need to use the formula
[tex]C=\frac{5}{9}(F-32)[/tex]then
Let
F=59
now, replace and evaluate
[tex]\begin{gathered} C=\frac{5}{9}(F-32) \\ C=\frac{5}{9}(59-32) \\ C=\frac{5}{9}(27) \\ C=15 \end{gathered}[/tex]therefore, the answer is
15 ° C
I hope this helps you
x/6 -7 = -4 what value of x makes this equation true
Answers
Answer:
x=18
Explanation:
Given the equation:
[tex]\frac{x}{6}-7=-4[/tex]To solve for x, follow the steps below.
Step 1: Add 7 to both sides of the equation.
[tex]\begin{gathered} \frac{x}{6}-7+7=-4+7 \\ \implies\frac{x}{6}=3 \end{gathered}[/tex]Step 2: Multiply both sides of the equation by 6.
[tex]\begin{gathered} \frac{x}{6}\times6=3\times6 \\ x=18 \end{gathered}[/tex]The value of x that makes the equation true is 18.
I need help answering this question and the solution set
Answers
Let's first try to rewrite the expression to see if we can write it in a fomr more familiar:
[tex]\begin{gathered} x-\sqrt{10-3x}=0, \\ x=\sqrt{10-3x}, \\ x^2=10-3x, \\ x^2+3x-10=0. \end{gathered}[/tex]This is the same equation, but now we recognize a quadratic expression equal to 0. We can use the quadratic formula to find the solutions of this equation:
[tex]x_{1,2}=\frac{-3\pm\sqrt{3^2-4\cdot1\cdot(-10)}}{2\cdot1}[/tex]And solve:
[tex]\begin{gathered} x_{1,2}=\frac{-3\pm\sqrt{9+40}}{2}=\frac{-3\pm7}{2} \\ x_1=\frac{-3+7}{2}=\frac{4}{2}=2 \\ x_2=\frac{-3-7}{2}=\frac{-10}{2}=-5 \end{gathered}[/tex]Thus, the solution set of the equation is x = -5, x = 2
How would you solve this question or similar questions? It is solving for x.
Answers
Given the initial expression
[tex]\sqrt[]{2x+3}=\sqrt[]{2x}+3[/tex]Then,
[tex]\begin{gathered} \sqrt[]{2x+3}=\sqrt[]{2x}+3 \\ \Rightarrow(\sqrt[]{2x+3})^2=(\sqrt[]{2x}+3)^2 \\ \Rightarrow2x+3=2x+6\sqrt[]{2x}+9 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \Rightarrow3=6\sqrt[]{2x}+9 \\ \Rightarrow-6=6\sqrt[]{2x} \\ \Rightarrow\sqrt[]{2x}=-\frac{6}{6}=-1 \\ \Rightarrow\sqrt[]{2x}=-1 \\ \Rightarrow\sqrt[]{2}\sqrt[]{x}=-1 \\ \Rightarrow\sqrt[]{x}=-\frac{1}{\sqrt[]{2}} \end{gathered}[/tex]And sqrt(x)>=0 for any real number.
Therefore, there is no real solution to the equation.
Elisa's school is selling tickets to a choral performance. On the first day of ticket sales the school sold 8 senior citizen tickets and 5 child tickets for a total of $94. The school took in $152 on the second day by selling 4 senior citizen tickets and 10 child tickets. What is the price each of one senior citizen ticket and one child ticket?
Answers
Let's define the next variables:
x: price of one senior ticket
y: the price of one child ticket
On the first day of ticket sales, the school sold 8 senior citizen tickets and 5 child tickets for a total of $94. That is:
8x + 5y = 94 (eq. 1)
The school took in $152 on the second day by selling 4 senior citizen tickets and 10 child tickets. That is:
4x + 10y = 152 (eq. 2)
Multiplying equation 2 by 2, we get:
2(4x + 10y) = 2*152
8x + 20y = 304 (eq. 3)
Subtracting equation 1 to equation 3, we get:
8x + 20y = 304
-
8x + 5y = 94
------------------------
15y = 210
y = 210/15
y = 14
Substituting this result into equation 1:
8x + 5(14) = 94
8x + 70 = 94
8x = 94 - 70
8x = 24
x = 24/8
x = 3
Each senior citizen ticket cost $3 and each child ticket cost $14
a spinner with 10 equally sized slices has four yellow slices, three red slices, and three blue slices. Martina spun the dial 500 times and got the following results. (refer to pic)answer the following. Round your answers to the nearest thousand.a) from Martinas results, compute the experimental probability of landing on red.b) assuming that the spinner is fair, compute the theoretical probability of landing on red.c) assuming that the spinner is fair, choose the statement below that is true. 1. the larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability. 2. the smaller the number spins, the greater the likelihood that the experimental probability will be close to the theoretical probability. 3. the experimental probability will never be close to the theoretical probability, no matter the number of spins.
Answers
Given the experimental results of spinning the spinner:
Yellow: 212
Red: 144
Blue: 144
The sum of times = 500
a) from Martina's results, compute the experimental probability of landing on red.
So, the answer will be probability = 144/500 = 0.288
b) assuming that the spinner is fair, compute the theoretical probability of landing on red.
As shown: the spinner has 10 equally sized slices.
The number of red slices = 3
So, the probability of red = 3/10 = 0.3
c) assuming that the spinner is fair, choose the statement below that is true.
The true statement will be:
1. the larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.
18. Light Bulbs: The mean lifespan of a standard 60 watt incandescent light bulb is 875 hours with a standard deviation of 80 hours. The mean lifespan of a standard 14 watt compact fluorescent light bulb (CFL) is 10,000 hours with a standard deviation of 1,500 hours. These two bulbs put out about the same amount of light. Assume the lifespan’s of both types of bulbs are normally distributed to answer the following questions. (a) I select one incandescent light bulb and put it in my barn. It seems to last forever and I estimate that it has lasted more than 2000 hours. What is the probability of selecting a random incandescent light bulb and having it last 2000 hours or more. Did something unusual happen here? (b) I select one CFL bulb and put it in the bathroom. It doesn’t seem to last very long and I estimate that it has lasted less than 5,000 hours. What is the probability of selecting a random CFL and having it last less than 5,000 hours. Did something unusual happen here? (c) Compare the the lifespan of the middle 99% of all incandescent and CFL light bulbs. (d) Is there much of a chance that I happen to buy an incandescent light bulb that lasts longer than a randomly selected CFL?
Answers
Set
[tex]\begin{gathered} \mu_1=875,\sigma_1=80 \\ \text{and} \\ \mu_2=10000,\sigma=1500 \end{gathered}[/tex]a) The Z-score formula is
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Therefore, in our case, if x=2000
[tex]\Rightarrow Z=\frac{2000-875}{80}=\frac{1125}{80}=14.0625[/tex]Using a Z-score table,
[tex]\begin{gathered} P(z\ge2000)=1-P(z<2000)\approx1-1=0 \\ \Rightarrow P(z\ge2000)=0 \end{gathered}[/tex]A value of 2000 hrs is 14 standard deviations away from the mean. The probability is practically zero.
b) Similarly, set x=5000; then,
[tex]Z=\frac{5000-10000}{1500}=-\frac{5000}{1500}=-3.333\ldots[/tex]Thus, using a z-score table
[tex]P(z\le5000)=0.0004[/tex]The probability is 0.0004=0.04%. It is quite improbable but not an impossible event.
c) According to the empirical rule 99.8% of the data lies within 3 standard deviations; thus,
[tex]\begin{gathered} Incandescent \\ \mu_1\pm3\sigma_1=\lbrack875-240,875+240\rbrack=\lbrack635,1115\rbrack \\ \text{CFL} \\ \mu_2\pm3\sigma_2=\lbrack10000-4500,10000+4500\rbrack=\lbrack5500,14500\rbrack \end{gathered}[/tex]The lifespan of 99% of all incandescent bulbs is between 635 and 1115 hrs, whereas that of all CFL bulbs is between 5500 and 14500 hrs.
d) If we randomly select a CFL, the most probably lifespan is the mean of the distribution, in other words, 10000 hrs.
The probability of an incandescent bulb lasting 10000 hrs is
[tex]\begin{gathered} Z=\frac{10000-875}{80}=114.0625 \\ \Rightarrow P(z\ge10000)=1-P(z<10000)=0 \end{gathered}[/tex]The event is practically impossible.
The local seven-digit telephone numbers in city A have 1,8,0, as the first three digits. How many different telephone numbers are possible in city A?
Answers
ANSWER
10,000
EXPLANATION
Given:
The first-three digits to be 1, 8, 0 out of seven-digit telephone numbers.
Desired outcome:
Total number of possible different telephone numbers
Determine the possibilities of the 4th, 5th, 6th and the 7th digits
The 4th digit has 10 possibilities (i.e: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
The 5th also has 10 possibilities,
likewise the 6th and the 7th digits.
Now, we have:
10 x 10 x 10 x 10 = 10^4 = 10,000
Hence, the number of possible different telephone numbers is 10,000.
The system of equations y= -x - 1 is graphed. what is the solution to the system of equations ?
Answers
We solve as follows:
*First: Given one function, we corroborate and find the second one.
*We have that the first function passes by the points (0, -1) & (1, 0); we find its function:
[tex]m=[/tex]In the figure, LMN is congruent to QRS.What is the value of x and y?
Answers
If they are congruent, then;
3x + 5 = 2x + 10
collect like term
3x - 2x = 10 - 5
x = 5
Similarly,
y + 6 = 2y - 12
collect like term
2y - y = 6 + 12
y = 18
whats the constant proportionality of the table. x 30 24 9 y 10 8 3
Answers
Let:
y = kx
Where:
k = constant proportionality of the table
If x = 30, y = 10:
10 = k30
Solving for k:
k = 10/30 = 1/3
Verify the answer:
If x = 24, y = 8:
y = kx = 1/3*24 =24/3 = 8
Therefore, the constant proportionality of the table is 1/3
10 pointsThe cafeteria manager at a middleschool asked 90 randomly selectedstudents to name their favorite schooldessert. The table below shows theresults of the manager's survey.Favorite School DessertDessertFrequencyCakeTHL THE 1941CookiesTULMAL 18 41Ice Cream MIL MHL MSL 1971CobblerTHEMAFruitPHI HI |||Based on the results of the survey,how many of the school's 1,200students would the manager expoato choose fruit as their favorite schooldessert?A 120C 300B 240D600
Answers
From the table , we can see that:
Cake ------------ -16
cookies - 20
Ice cream - 26
Cobbler - 10
Fruit - 18
Total - 90
Out of 1900 students, the manager is expected to choose fruits as their favourite school desert?
Ice cream - 26/90 x 1900 = 548 .89 = 600 ------- option D
Hello I need help on question number 12 and number 14 if possible please
Answers
N 12
Remember that
In any triangle, the sum of the interior angles must be equal to 180 degrees
so
In the triangle EBF
mso
mm
step 2
we have that
m by form a linear pair
substitute given values
52+mmm