what is the area of the regular 15-gon with radius 12mm?
The regular pentagon can divide into 5 congruent isosceles triangles
The equal sides of each triangle have length r and vertex angle of measure 72 degrees
Then we will use the sine rule of the area to find the area of each triangle, then multiply it by 5 to get the area of the pentagon
Since the radius is 7mm, then
r = 7
[tex]A=5\times\frac{1}{2}\times r\times r\times sin72[/tex]Substitute r by 7
[tex]\begin{gathered} A=5\times\frac{1}{2}\times7\times7\times sin72 \\ \\ A=116.5044232\text{ mm}^2 \end{gathered}[/tex]Round it to the nearest whole number
A = 117 mm^2
The area of the pentagon is 117 mm^2
1(c). What is a better deal? Explain. Deal 1: 2 mediums 14'' (round) pizza for $14 total Deal 2: 1 large 20'' (round) pizza for $13 total
To get the better deal of the two, we need to find the cost per area of pizza for each deal and compare.
Deal 1: 2 medium 14'' (round) pizza for $14 total
The area of a circle is calculated as
[tex]A=\pi r^2[/tex]where r is the radius.
The area of the pizza is calculated to be:
[tex]\begin{gathered} r=14 \\ \therefore \\ A_1=\pi\times14^2=196\pi \end{gathered}[/tex]Hence, the total area for the two pizzas will be:
[tex]\Rightarrow196\pi\times2=392\pi[/tex]The cost per square inch of pizza is, therefore, calculated to be:
[tex]\Rightarrow\frac{14}{392\pi}=0.011[/tex]The pizza costs $0.011 per square inch.
Deal 2: 1 large 20'' (round) pizza for $13 total
The area of the pizza is calculated to be:
[tex]\begin{gathered} r=20 \\ \therefore \\ A_2=\pi\times20^2=400\pi \end{gathered}[/tex]Hence, the cost per square inch of pizza is calculated to be:
[tex]\Rightarrow\frac{13}{400\pi}=0.010[/tex]The pizza costs $0.010 per square inch.
CONCLUSION:
The better deal will be the deal with the lesser cost per square inch. As can be seen from the calculation, both deals are about the same price per square inch if approximated. However, without approximation, Deal 2 has a slightly lesser cost per square inch.
Therefore, DEAL 2 IS THE BETTER DEAL.
у A 5 8 106 С C m2l= m22= m23= mZ4= m25= needing quadrilaterals area
Angles in a quadrilaterals
The sum of all interior angles in a quadrilateral is 360°
Angle 5 is congruent with angle of 106°
Thus measure of 5 = 106°
These two angles add up to 212°. The remaining to reach 360° is:
360° - 212° = 148°
Angles 1, 2, 3, and 4 are congruent, thus the measure of each one of them is 148/4=37°. Thus
measure of 1 = measure of 2 = measure of 3 = measure of 4 = 37°
find the area of the composite figures by either adding and subtracting regions
Explanation:
This figure is a rectangle and a quarter of a circle. We can find their areas and add them to find the total area of the figure.
The area of the rectangle is:
[tex]A_{\text{rectangle}}=17cm\times10\operatorname{cm}=170\operatorname{cm}^2[/tex]The area of a circle is:
[tex]A_{\text{circle}}=\pi\cdot r^2[/tex]Where r is the radius of the circle. In this case we have a quarter of a circle, so its area is a quarter of the area of the circle:
[tex]A_{1/4\text{circle}}=\frac{A_{\text{circle}}}{4}=\frac{\pi\cdot r^2}{4}[/tex]The radius of this circle is 8cm:
[tex]A_{1/4\text{circle}}=\frac{\pi\cdot8^2}{4}=\frac{\pi\cdot64}{4}=\pi\cdot16\approx50.27\operatorname{cm}^2[/tex]The total area of the figure is:
[tex]A_{\text{figure}}=A_{\text{rectangle}}+A_{1/4\text{circle}}=170\operatorname{cm}+50.27\operatorname{cm}=220.27\operatorname{cm}^2[/tex]Answer:
The area is 220.27 cm²
Which of the following is not a valid way of starting the process of factoring60x² +84x +49?Choose the inappropriate beginning below.O A. (x )(60)OB. (2x (30%)O C. (6x X10x)OD. (2x (5x )
Given the equation:
60x^2 + 84x + 49
We are to determine among the options which is not a process of factorizing.
In factorizing, you get factors of the given numbers of the equation that when they are being multiplied or added, they give the numbers in the equation.
So, looking at the options, the only option that does not satisfies the requirement for starting a factorization process is B, which is (2x (30%)
Therefore, the inappropriate process of starting factorization among the option is option B which is (2x (30%).
Andre and Elena are each saving money, Andre starts with 100 dollars in his savings account and adds 5 dollars per week, Elena starts with 10 dollars in her savings account and adds 20 dollars each week.After 4 weeks who has more money in their savings account?? Explain how you know.After how many weeks will Elena and Andre have the same amount of money in their savings account? How do you know?
We can model each savings account balance in function of time as a linear function.
Andre starts with $100 and he adds $5 per week. If t is the number of weeks, we can write this as:
[tex]A(t)=100+5\cdot t[/tex]In the same way, as Elena starts with $10 and saves $20 each week, we can write her balance as:
[tex]E(t)=10+20\cdot t[/tex]We can evaluate their savings after 4 weeks (t=4) as:
[tex]\begin{gathered} A(4)=100+5\cdot4=100+20=120 \\ E(4)=10+20\cdot4=10+80=90 \end{gathered}[/tex]After 4 weeks, Andre will have $120 and Elena will have $90.
We can calculate at which week their savings will be the same by writing A(t)=E(t) and calculating for t:
[tex]\begin{gathered} A(t)=E(t) \\ 100+5t=10+20t \\ 5t-20t=10-100 \\ -15t=-90 \\ t=\frac{-90}{-15} \\ t=6 \end{gathered}[/tex]In 6 weeks, their savings will be the same. We know it beca
find the inverse function of g(x)= x-1÷x+5
1. replace g(x) with y:
[tex]y=\frac{x-1}{x+5}[/tex]2.Replace every x with a y and replace every y with an x
[tex]x=\frac{y-1}{y+5}[/tex]3. Solve for y:
[tex]\begin{gathered} (y+5)x=y-1 \\ yx+5x=y-1 \\ yx-y=-1-5x \\ y(x-1)=-1-5x \\ y=\frac{-1-5x}{x-1} \end{gathered}[/tex]4. Replace y with g−1(x) g− 1 ( x ):
[tex]g(x)^{-1}=\frac{-5x-1}{x-1}[/tex]PLS HELP ASAP
Clara and Toby are telemarketers.
Yesterday, Clara reached 4 people in 10 phone calls, while Toby reached 3 people in 8 phone calls.
If they continue at those rates, who will reach more people in 40 phone calls?
Use the drop-down menu to show your answer.
A tutoring service charges an initial consultation fee of $50 plus $25 for each tutoringsession.A. Write an equation that determines the total cost of tutoring services (y) based on thenumber of tutoring sessions (x).B. If a student decides to purchase 8 tutoring sessions, what will be his total cost?c. If a student had a total cost of $200, how many tutoring sessions did he attend?EditVioInsertFormatThols Table
A. y = 50 + 25x
B. number of session (x) = 8
Substitute x= 8 in the equation y= 50 + 25x
y = 50 + 25( 8 )= 50 + 200 = $250
The total cost for 8 tutoring sessions is $250
C. y = $200
x= ?
y = 50 + 25x
200 = 50 + 25x
200 - 50 = 25x
150 = 25x
Dividing through by 25
x = 150/25 =6
He attended 6 tutoring sessions
describe the center and spread of the data using the more appropriate status either the mean median range interquartile range or standard division
Help me due is tomorrow
Step-by-step explanation:
5.3g+9=2.3g+15
5.3g-2.3g=15-9
3g=6
3g/3=6/3
g=2
B,5.3(2)+9=2.3(2)+15
10.6+9=4.6+15
19.6=19.6
g = 2
Step-by-step explanation:5.3g + 9 = 2.3g + 15
Subtract 9 from both sides.
5.3g + 9 - 9 = 2.3g + 15 - 9
5.3g = 2.3g + 6
Subtract 2.3g from both sides
5.3g - 2.3g = 2.3g - 2.3g + 6
3g = 6
Divide both sides by 3
g = 2
To check if the value of g is correct, substitute the value of g in the equation above and remember that the both sides should be equal because of the equal sign (=) in the equation.
5.3g + 9 = 2.3g + 15
5.3(2) + 9 = 2.3(2) + 15
10.6 + 9 = 4.6 + 15
19.6 = 19.6
Find the zeros of the following logarithmic function: f(x) = 2logx - 6.
A pendulum swings through an angle of 14° each second. If the pendulum is 14 cm in length and the complete swing from right to left last two seconds what area is covered by each complete swing?
Answer;
[tex]\text{Area = 47.90 cm}^2[/tex]Explanation;
Firstly, we need a diagrammatic representation to get what is described in the question.
We have this as follows;
Now, from what we have here, the total angle swept by the pendulum moving from left to right is 28 degrees
To get the area, we simply need to find the area of the sector formed by the by pendulum
Mathematically, we have the area of a sector calculated as follows;
[tex]A\text{ = }\frac{\theta}{360}\times\pi\times R^2[/tex]theta is the angle made by the pendulum in one complete swing which is 28 degrees
pi is 22/7
R is the length of the pendulum which is 14 cm
Substituting these values in the formula above, we have it that;
[tex]\begin{gathered} A=\frac{28}{360}\times\frac{22}{7}\times14^2 \\ \\ A=47.90cm^2 \end{gathered}[/tex]The diamond method for factoring: Fill in the missing value
Consider a quadratic expression, let "m" and "n" represent the factors.
The diamond method of factoring is the following:
On the left of the diamond, there is one of the factors, for example, "m", of the right of the diamond you will find the other factor "n".
On the top of the diamond, you will find the product of both factors, on the bottom of the diamond you will find the sum of the factors.
Looking at the given diamond, you know the result of the product and the sum of both factors:
[tex]m*n=-15[/tex][tex]m+n=14[/tex]Using these expressions, you can find both factors.
- First, write the second expression for one of the variables, for example, for "n"
[tex]\begin{gathered} m+n=14 \\ m=14-n \end{gathered}[/tex]- Second, replace the expression obtained on the second equation:
[tex]\begin{gathered} m*n=-15 \\ (14-n)n=-15 \end{gathered}[/tex]Distribute the multiplication
[tex]14n-n^2=-15[/tex]Zero the expression and order the terms from greatest to least:
[tex]\begin{gathered} 14n-n^2+15=-15+15 \\ 14n-n^2+15=0 \\ -n^2+14n+15=0 \end{gathered}[/tex]- Third, use the quadratic expression to determine the possible values of n:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Where
a is the coefficient of the quadratic term
b is the coefficient of the x-term
c is the constant
For the quadratic expression obtained, where "n" represents the x-variable.
[tex]-n^2+14n+15=0[/tex]The coefficients are:
a= -1
b=14
c=15
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ n=\frac{-14\pm\sqrt{14^2-4*(-1)*15}}{2*(-1)} \\ n=\frac{-14\pm\sqrt{196+60}}{-2} \\ n=\frac{-14\pm\sqrt{256}}{-2} \\ n=\frac{-14\pm16}{-2} \end{gathered}[/tex]Solve the sum and difference separately to determine both possible values for "n"
→Sum:
[tex]\begin{gathered} n=\frac{-14+16}{-2} \\ n=\frac{2}{-2} \\ n=-1 \end{gathered}[/tex]→Difference:
[tex]\begin{gathered} n=\frac{-14-16}{-2} \\ n=\frac{-30}{-2} \\ n=15 \end{gathered}[/tex]- Finally, determine the possible value/s of m:
For n=-1
[tex]\begin{gathered} m+n=14 \\ m+(-1)=14 \\ m-1=14 \\ m=14+1 \\ m=15 \end{gathered}[/tex]For n=15
[tex]\begin{gathered} m+n=14 \\ m+15=14 \\ m=14-15 \\ m=-1 \end{gathered}[/tex]So, the factors are -1 and 15 and the diamond is:
determine whether the given by binomial is a factor of the polynomial p(x) . If so, find the remaining factors of p(x).
The given binomial is a factor of the polynomial p(x) with remaining factors of (x + 1)(x - 1).
What is termed as the factors of polynomial?Factorisation is the process of determining the factors of a given value as well as mathematical expression. Factors are integers which are multiplied together to create the original number.For the given question.
The polynomial is given as; x³ + 2x² -x - 2.
The binomial is given as; (x +2).
The, to get the remainder, divide the polynomial with the binomial.
= (x³ + 2x² - x - 2)/ (x +2)
Taking x² common from the first two terms of the numerator and (-1) from the last two terms.
= x²(x + 2) - (x + 2)/ (x +2)
Taking (x + 2) common from two terms.
= (x + 2)(x² - 1)/(x + 2)
Cancel (x + 2) from both.
= (x² - 1)
Now use the identity to open the square.
(a² + b² ) = (a + b) (a - b)
= (x + 1)(x - 1).
Thus, the given binomial is a factor of the polynomial p(x) with remaining factors of (x + 1)(x - 1).
To know more about the factors of polynomial, here
https://brainly.com/question/28920058
#SPJ13
The correct question is-
Determine whether the given binomial is a factor of the polynomial p(x).
If so, find the remaining factors of p(x).
p(x) = x³ + 2x² -x - 2 ; (x +2)
Answer:
a
Step-by-step explanation:
Please see attached picture of problem I need help with.
Step 1
List the elements of D
[tex]D=\lbrace2,.........\rbrace[/tex]List the elements of E
[tex]E=\lbrace........,8\rbrace[/tex]Find
[tex]D\cap E[/tex][tex]D\cap E=(1,8]--(\text{what is common\rparen}[/tex]Find
[tex]D\cup E[/tex][tex]\begin{gathered} D\cup E=(1,\infty)\cup(-\infty,8]--(Listing\text{ all elements in D and E\rparen} \\ D\cup E=(-\infty,\infty) \end{gathered}[/tex]Answers;
[tex]\begin{gathered} \begin{equation*} D\cap E=(1,8] \end{equation*} \\ \begin{equation*} D\cup E=(-\infty,\infty) \end{equation*} \end{gathered}[/tex]During a game, 65% of the pitches Tina threw were strikes. She threw 120 2 poi total pitches during the game. How many throws were strikes? * a) 92 O b) 65 c) 78 d) 44
You are given the equation 12 = 3x + 4 with no solution set. Part A: Determine two values that make the equation false. Part B: Explain why your integer solutions are false. Show all work.
[tex]12=3x+4 \\ \\ 8=3x \\ \\ x=8/3[/tex]
So, two integer values are 1 and 2 since they are not the solution to the equation.
need help finding the exact value of sec pi/3
Solution:
Given:
[tex]sec(\frac{\pi}{3})[/tex]To find the exact value,
Step 1: Apply the trigonometri identieties.
From the trigonometric identities,
[tex]sec\text{ }\theta\text{ =}\frac{1}{cos\theta}[/tex]This implies that
[tex]sec(\frac{\pi}{3})=\frac{1}{\cos(\frac{\pi}{3})}[/tex]Step 2: Evaluate the exact value.
[tex]\begin{gathered} since \\ \cos(\frac{\pi}{3})=\frac{1}{2}, \\ we\text{ have} \\ sec(\frac{\pi}{3})=\frac{1}{\cos(\pi\/3)}=\frac{1}{\frac{1}{2}}=2 \end{gathered}[/tex]Hence, te exact value of
[tex]sec(\frac{\pi}{3})[/tex]is evaluated to be 2
What is the equation of the line that passes through points (1,-19) and (-2,-7)?
This problem is about linear equations. We need to find the equation of the line w
2064 is divisible by 2, 4 and 8 true or false
I need help question 10 b and c
Part b.
In this case, we have the following function:
[tex]y=5(2.4)^x[/tex]First, we need to solve for x. Then, by applying natural logarithm to both sides, we have
[tex]\log y=\log (5(2.4^x))[/tex]By the properties of the logarithm, it yields
[tex]\log y=\log 5+x\log 2.4[/tex]By moving log5 to the left hand side, we have
[tex]\begin{gathered} \log y-\log 5=x\log 2.4 \\ \text{which is equivalent to} \\ \log (\frac{y}{5})=x\log 2.4 \end{gathered}[/tex]By moving log2.4 to the left hand side, we obtain
[tex]\begin{gathered} \frac{\log\frac{y}{5}}{\log2.4}=x \\ or\text{ equivalently,} \\ x=\frac{\log\frac{y}{5}}{\log2.4} \end{gathered}[/tex]Therfore, the answer is
[tex]f^{-1}(y)=\frac{\log\frac{y}{5}}{\log2.4}[/tex]Part C.
In this case, the given function is
[tex]y=\log _{10}(\frac{x}{17})[/tex]and we need to solve x. Then, by raising both side to the power 10, we have
[tex]\begin{gathered} 10^y=10^{\log _{10}(\frac{x}{17})} \\ \text{which gives} \\ 10^y=\frac{x}{17} \end{gathered}[/tex]By moving 17 to the left hand side, we get
[tex]\begin{gathered} 17\times10^y=x \\ or\text{ equivalently,} \\ x=17\times10^y \end{gathered}[/tex]Therefore, the answer is
[tex]f^{-1}(y)=17\times10^y[/tex]what do I do to compute the exact average of the fractions, in decimal form?
Average is computed as follows:
[tex]\begin{gathered} \text{Avg=}\frac{\text{ sum of terms}}{\text{ number of terms}} \\ \text{Avg}=\frac{5+0.2+2}{3} \\ \text{Avg}=\frac{7.2}{3} \\ Avg=2.4 \end{gathered}[/tex]Please help me with this problem just wanted to be sure that I am correct in order to help my son to under stand the break down of this problem. I believe that the answer is -3 but I am not sure please help?Solve for x.14x−1/2(4x+6)=3(x−4)−18 Enter your answer in the box.x =
SOLUTION
We want to solve for x in the equation
[tex]14x-\frac{1}{2}\mleft(4x+6\mright)=3\mleft(x-4\mright)-18[/tex]First we expand the brackets in both sides of the equation, this becomes
[tex]\begin{gathered} 14x-\frac{1}{2}(4x+6)=3(x-4)-18 \\ 14x-2x-3=3x-12-18 \end{gathered}[/tex]Note that the minus sign multiplies the items in the brackets too
Now, we collect like terms we have
[tex]\begin{gathered} 14x-2x-3x=-12-18+3 \\ 9x=-27 \\ \text{divide both sides by 9, we have } \\ \frac{9x}{9}=\frac{-27}{9} \\ x=-3 \end{gathered}[/tex]Hence x = -3
can you help with this question please
We need to give the steps for proving the corresponding angles theorem for parallel lines crossed by a transverse line.
Westart with the
p || q as Given info
Next we use that
< 1 = <7 due to internal alternate angles among parallel lines
< 7 = <5 due to angles opposed by vertex
<1 = <5 due to transitive property <1 = <7 = <5
10 ftA4 ftThe following are the dimension of four rectangles. Which rectangle has the same area as the triangle above?a 1.6 ft by 25 ftC. 3.5 ft by 4 ftb. 5 ft by 16 ftd. 0.4 ft by 50 ft
step 1: Find the area of the triangle
The area of the triangle given is:
[tex]\begin{gathered} \text{Area = }\frac{1}{2}\times base\times height \\ =\frac{1}{2}\times4\times10 \\ =20ft^2 \end{gathered}[/tex]step 2: Find the dimension of rectangles that will give the same area as the triangle
The area of a rectangle is given by:
[tex]\text{Area}=\text{ length x width}[/tex][tex]\begin{gathered} \text{ option a: }1.6ftx25ft=40ft^2 \\ \text{option b: 5 ft x 16 ft =}80ft^2 \\ \text{option c: }3.5ftx4ft=14ft^2 \\ \text{option d: }0.4\text{ ft x 50 ft=}20ft^2 \end{gathered}[/tex]Therefore, the dimension of the rectangle with the same area as the triangle is
[tex]0.4\text{ ft}\times50\text{ ft}[/tex]OptionD is correct
8. Factor ()=63−252++60 completely given that x=3 is a zero of p(x). Use only the techniques from the lecture on 3.3 (synthetic division). Other methods will receive a score of zero. Be sure to show all your work (including the synthetic division).
Factor the polynomial
[tex]\begin{gathered} p(x)=6x^3-25x^2+x+60 \\ \text{Given that, }x=3\text{ is a zero} \end{gathered}[/tex]Using the synthetic division method to factorize the polynomial completely,
The resulting coefficients from the table are 6, -7, -20, 0
Thus the quotient is
[tex]6x^2-7x-20[/tex]Factorizing the quotient completely,
[tex]\begin{gathered} 6x^2-7x-20 \\ =6x^2-15x+8x-20 \\ =3x(2x-5)+4(2x-5) \\ =(3x+4)(2x-5) \end{gathered}[/tex]Therefore, the other two zeros of the polynomial are:
[tex]\begin{gathered} (3x+4)(2x-5)=0 \\ 3x+4=0 \\ x=-\frac{4}{3} \\ 2x-5=0 \\ x=\frac{5}{2} \\ \\ Therefore,t\text{he factors of the polynomial are:} \\ (x-3)(3x+4)(2x-5) \end{gathered}[/tex]how would u decide if 3/5 or 59% is greater?
SOLUTION
Step 1 : One of the easiest ways to determine which one of the quantities is greater is by expressing the quantities as a decimal.
[tex]\begin{gathered} \frac{3}{5}\text{ = 0.6} \\ \\ 59\text{ \% = 0.59} \end{gathered}[/tex]Step 2: From the two quantities expressed as decimals, we can see that :
[tex]\frac{3}{5}\text{ is greater.}[/tex]CONCLUSION :
[tex]\frac{3}{5}\text{ is greater.}[/tex]A. What is the common ratio of the pattern?B. Write the explicit formula for the pattern?C. If the pattern continued how many stars would be in the 11th set?
Given:
The sequence of number of stars is 2,4,8,16
a) To find the common ratio of the pattern.
[tex]\begin{gathered} \text{Common ratio=}\frac{2nd\text{ term}}{1st\text{ term}} \\ r=\frac{4}{2} \\ r=2 \end{gathered}[/tex]Hence the common ratio is 2.
b) To find the explicit formula for the pattern.
The general for a geometric progression sequence is,
[tex]a_n=a_1(r)^{n-1}_{}_{}[/tex]Hence, the formula for the above pattern will be,
[tex]a_n=2(2)^{n-1}[/tex]c) To find the number of stars in 11th set.
Substitute n=11 in the explicit formula of the pattern.
[tex]\begin{gathered} a_{11}=2(2)^{11-1} \\ a_{11}=2(2)^{10} \\ a_{11}=2(1024) \\ a_{11}=2048 \end{gathered}[/tex]Hence, the number of stars in 11th set will be 2048.
what is the geometric sequence of 2 4
an = ar^ (n- 1)
for n = 3 (3rd term)
r = common ratio = 4/ 2 = 2
a3 = 2 (2) ^ (3-1)
a3 = 2 (2)^2
a3 = 2 (4)
a3 = 8
n= 4 (4th term)
a4 = 2 (2)^(4-1)
a4 = 2 (2)^3
a4 = 2 (8)
a4 = 16
2, 4 , 8 , 16
