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The measure of angle n is 81 degrees
Here, we want to find the measure of the missing angle labeled n
Firstly, we need to know the measure of the total interior angle of the polygon
The polygon has 6 sides
Mathematically, the sum of the interior angles of a polygon can be calculated using the equation;
[tex]\begin{gathered} 180(n-2) \\ \\ \text{Here, n = 6} \\ \\ 180(6-2) \\ \\ 180(4)\text{ = 720 } \end{gathered}[/tex]So, when we add all the angles, the total measure should be 720
Thus, we have;
[tex]\begin{gathered} n\text{ + 156 + 122 + 143 + 108 + 110 = 720} \\ \\ n\text{ + 639 = 720} \\ \\ n\text{ = 720-639} \\ \\ n\text{ = 81} \end{gathered}[/tex]Related Questions
use the graph below to find the point of intersection for the functions .
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The equations are in the slope-intercept form:
y= mx+b
Where:
m= slope ( rise / run )
b= y-intercept (where the line crosses the y axis)
Graph:
Both functions intersect at the point (-1,3)
Assume lines that look tangent, are tangent.Find the value of x.(The ones that are crossed out don’t need answered)
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Take into account that for secant and tangent lines related to circles, use the following formula:
x = 1/2·(larger arc - smaller arc)
Then, you have, for the first circle:
larger arc = 360° - 124° = 236°
smaller arc = 124°
x = 1/2·(236° - 124°)
x = 1/2·(112°)
x = 56°
For the second circle, the value of x is the same that the given arc:
x = 124°
For the fourth circle:
larger arc = 171°
smaler arc = 67°
x = 1/2·(171° - 67°)
x = 1/2·(104°)
x = 52°
For the fifth circle:
x = 1/2·(101° + 39°)
x = 70°
3/5t+ 7 = -8 What is t
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The equation to solve is:
[tex]\frac{3}{5t}+7=-8[/tex]We take "7" to the right hand side:
[tex]\begin{gathered} \frac{3}{5t}+7=-8 \\ \frac{3}{5t}=-8-7 \\ \frac{3}{5t}=-15 \end{gathered}[/tex]Now, we cross multiply:
[tex]\begin{gathered} 3=5t\times-15 \\ 3=-75t \end{gathered}[/tex]Now we divide by -75 to solve for t:
[tex]\begin{gathered} 3=-75t \\ t=-\frac{3}{75} \end{gathered}[/tex]CoursesStandard Normal DistributionCatalog and Study ToolsRental OptionsMasoStandard Devletion 10College Success TipsCareer Success Tips0 Help5000-500001 Give Feedback-2.0-1.00:00.00001.02.0P(Z > 2.00)P(Z > -1.00) =p(Z < 0.50) =p(z < 1.75) -Grade It NowSave & ContinueContinue without saving
Answers
From z table:
For P(Z > 2.00)
[tex]P(Z>2.00)=1-P(Z<2.00)=1-0.9772=0.0228[/tex]Answer: 0.0228
For P(Z > -1.00)
[tex]P(Z>-1.00)=1-P(Z<-1.00)=1-\text{0}.1587=0.8413[/tex]Answer: 0.8413
For p(Z < 0.50)
[tex]P(Z<0.50)=0.6915[/tex]Answer: 0.6915
For p(z < 1.75)
[tex]P(Z<1.75)=0.9599[/tex]Answer: 0.9599
Can someone walk me through this? I know it’s familiar but I can’t recall how to do it.
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18 dimes and 6 quarters
1) Let's recall that 1 dime = $0.10 and a quarter is $0.25
2) We can solve this by writing a Linear System of Equations:
[tex]\begin{gathered} x+y=24 \\ 0.1x+0.25y=3.3 \end{gathered}[/tex]Note that the second equation relates the quantities in dollars, 330 cents is the same as $3.30.
2.2) So now let's solve it using the Elimination Method multiplying one of those equations by -0.1:
[tex]\begin{gathered} 0.1x+0.25y=3.3 \\ -0.1x-0.1y=-2.4 \\ ---------------- \\ 0.15y=0.9 \end{gathered}[/tex]Let's divide both sides by 0.15:
[tex]\begin{gathered} \frac{0.15y}{0.15}=\frac{0.9}{0.15} \\ y=6 \end{gathered}[/tex]So we have 6 coins of quarters, now let's plug into the original equation x+y=24 to get the number of dimes:
[tex]\begin{gathered} x+6=24 \\ x+6-6=24-6 \\ x=18 \end{gathered}[/tex]3) Hence, there are 18 dimes and 6 quarters
Pay Cut Todd works for a computer firm, and last year he earned a salary of $120,000. Recently, Todd was required to take a 15% pay cut. Find Todd's salary after the pay cut.
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Given:
The salary of Todd last year, C=$120,000.
The percentage rate of pay cut, R=15%.
Todd's salary after the pay cut can be calculated as,
T=C x (100-R)/100
T=120000 x (100-15)/100
T=120000 x 85/100
T=102000
Therefore, Todd's salary after the pay cut is $102000.
Which values are solutions to the inequality below? √x≤=4 check all that apply: A. 20 B. 12 C. 2 D. 5 E. -1. F. NO SOLUTIONS.
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we can replace the value of X for each option and check the inequality
A.20
[tex]\begin{gathered} \sqrt[]{20}\le4 \\ 4.47\le4 \end{gathered}[/tex]the inequality is wrong because 4.47 is greater than 4
B.12
[tex]\begin{gathered} \sqrt[]{12}\le4 \\ 3.46\le4 \end{gathered}[/tex]The inequality is right because 3.46 is less than 4
C.2
[tex]\begin{gathered} \sqrt[]{2}\le4 \\ 1.41\le4 \end{gathered}[/tex]The inequality is right because 1.41 is less than 4
D.5
[tex]\begin{gathered} \sqrt[]{5}\le4 \\ 2.23\le4 \end{gathered}[/tex]inequality is right because 2.23 is less than 4
E. -1
[tex]\sqrt[]{-1}\le4[/tex]we can calculate the root of a negative number then the option is wrong
which of the following sets of numbers could not represent the the sides of a right triangle?{57, 76, 94}{39, 52, 65}{54, 72, 90}{9, 40, 41}
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Answer:
{57, 76, 94}
Explanation:
For the set of numbers to represent the the sides of a right triangle, the square of the longest side must be equal to the sum of the square of other two sides
For the first option:
{57, 76, 94}
Longest side = 94
Square of the longest side = 94^2 = 8836
Sum of the square of other two sides = 57^2 + 76^2
Sum of the square of other two sides = 9025
Since both values are bot equal hence teh set of number {57, 76, 94} does not represent the sides of a right triangle.
P varies jointly with Q and R,and P=6 when Q=3 and R=12.Find P Q=4 and R=16
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Answer:
10.67
Explanation:
We're told that P varies jointly as Q and R, this can be represented as shown below;
[tex]\begin{gathered} P\propto QR \\ P=\text{kQR} \end{gathered}[/tex]where k = constant of proportionality
Given P = 6, Q = 3 and R = 12, let's go ahead and solve for k;
[tex]k=\frac{P}{QR}=\frac{6}{3\times12}=\frac{6}{36}=\frac{1}{6}[/tex]Knowing k = 1/6, let's solve for P when Q = 4 and R = 16;
[tex]P=\frac{1}{6}\times4\times16=\frac{64}{6}=10.67[/tex]what is the equation fir the graph below1. y=2/5x+42. y= -2/5x+43. y= 4/1x-2/54. y= -5/2x+4
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y = -2/5 x + 4 (option 2)
Explanation:Equation of line: y = mx + b
m = slope, b = y-intercept
Slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]Using points (5, 2) and (0, 4)
[tex]\begin{gathered} x_1=5,y_1=2,x_2=0,y_2\text{ = }4 \\ \text{slope = }\frac{4-2}{0-5}=\text{ }\frac{2}{-5} \\ \text{slope = -2/5} \end{gathered}[/tex]The y -intercept is point the line crosses the y axis. The point is at y = 4
b = 4
The equation of the line becomes:
y = -2/5 x + 4 (option 2)
9. A zoo has two water tanks that are leaking. One tank contains 100 gal of water and is leaking at a constant rate of 4 gal/h. The second tank contains 60 gal of water and is leaking at a constant rate of 2 gal/h. When will the tanks have the same amount of water?
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we can write an equation for each statement
One tank contains 100 gal of water and is leaking at a constant rate of 4 gal/h
[tex]y=100-4h[/tex]
where y are the total gallons and H the hours elapsed
he second tank contains 60 gal of water and is leaking at a constant rate of 2 gal/h.
[tex]y=60-2h[/tex]
where y are the total gallons and H the hours elapsed
When will the tanks have the same amount of water?
we must replace one equation in the other to find the time that its measure is equal,so
[tex]100-4h=60-2h[/tex]now solve h
[tex]\begin{gathered} 100-60=4h-2h \\ 40=2h \\ \frac{40}{2}=h \\ \\ h=20 \end{gathered}[/tex]the two tanks will have the same volume when 20 hours have passed
Evaluate the factorial expression.10!/7!
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To evaluate the expression we need to remember that:
[tex]n!=n(n-1)![/tex]Then we have:
[tex]\frac{10!}{7!}=\frac{10\cdot9!}{7!}=\frac{10\cdot9\cdot8!}{7!}=\frac{10\cdot9\cdot8\cdot7!}{7!}=10\cdot9\cdot8=720[/tex]Therefore:
[tex]\frac{10!}{7!}=720[/tex]Find the value of f(-6).yy = f(x)108642-10-8-6-422468.10-2-4-6-8
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The given graph is a downward parabola.
The roots of the equation is -2 and -8, and the vertex is (-5,7).
The general root form of parabola will be,
a(x-(-2))(x-(-8))=a(x+2)(x+8).
The value of a can be determined from the coordinate of vertex,
[tex]\begin{gathered} y=a(x+2)(x+8) \\ 7=a(-5+2)(-5+8) \\ 7=a\times(-3)(3) \\ a=\frac{-7}{9} \end{gathered}[/tex]Thus, the required quadratic is,
[tex]f(x)=\frac{-7}{9}(x+2)(x+8)[/tex]The value of f(-6) can be determined as,
[tex]\begin{gathered} f(-6)=\frac{-7}{9}(-6+2)(-6+8) \\ =6.22 \end{gathered}[/tex]Thus, the requried value of f(-6) is 6.22.
It’s two-parter question I would like the answer and how to solve
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Answer:
x > 10 ; D
Step-by-step explanation:
Solve for y:x/y = h-k
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We have to solve for y:
[tex]\begin{gathered} \frac{x}{y}=h-k \\ x=(h-k)\cdot y \\ \frac{x}{h-k}=y \\ y=\frac{x}{h-k} \end{gathered}[/tex]Answer: y = x / (h-k)
Solve the equation by factoring: x2 - 5x - 14 a. X = -2 or 7 b. X = 2 and - 7 c. x = -2 or -7 d. X = 2 or 7
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We need to solve the quadratic equation:
x^2 - 5 x - 14 = 0 by factoring.
So we look for a pair of factors whose product is -14 and when combined render - 5. So we find the pair "-7 and 2"
Their product = (-7) * 2 = -14
combining them we get: -7 + 2 = -5
So we used them to split the middle term in the equation:
x^2 - 5 x - 14 = 0
x^2 - 7 x + 2 x - 14 = 0
Factor by grouping:
x ( x - 7) + 2 x - 14 = 0
x (x - 7) + 2 (x - 7) = 0
(x - 7) (x + 2 ) = 0
Then for this product to render zero, (x - 7) must be zero (so x = 7)
or (x + 2) is zero (and therefore x = -2)
Then we look for the answers x = -2 or x = 7
This coincides with answer (a) in your list.
Wendy is a kickboxing instructor who will be teaching classes at a local gym. To get certified as an instructor, she spent a total of $100. Wendy will be earning a base salary of $70 per month from the gym, plus an additional $3 for every class she teaches. If Wendy teaches a certain number of classes during her first month as an instructor, she will earn back the amount she spent on certification. How much will Wendy's expenses and earnings be?
Write a system of equations, graph them, and type the solution.
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Wendy's expenses and earnings be will becomes $100 once she completed 10 classes.
What is meant by the term system of equations?System of equations, also known as simultaneous equations, Two or even more equations to just be solved together in algebra. The number of equations should then equal the number of uncertainties for a system to produce a unique solution.The information regarding the teaching classes at a local gym by kickboxing instructor is given-
Total amount spent = $100.
Basic salary of Wendy = $70.
Additional salary = $3 for each class.
Let 'x' be the number of classes during first month.
The, the equation forms as;
100 = 70 + 3x (equation)
Simplifying,
x = 30/3
x = 10 (solution)
The graph is shown.
Wendy's expenses and earnings be will becomes $100 once she completed 10 classes.
To know more about the system of equations, here
https://brainly.com/question/25976025
#SPJ1
For an unknown parent function f(x), write a function g(x) that is:-vertically stretched by a factor of 2,- shifted up 5 units, and - shifted right 4 units. Explain how your function accomplishes these transformations.
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Given the parent function to be:
[tex]f(x)[/tex]Write the function g(x), when the parent function is
1. vertically stretched by a factor of 2 - Multiply the parent function by 2
[tex]g(x)=2f(x)[/tex]2. Shifted up 5 units - Add 5 units outside of the parent function
[tex]g(x)=2f(x)+5[/tex]3. Shifted right 4 units - Subtract 4 from within the parent function
[tex]g(x)=2f(x-4)+5[/tex]Therefore, the transformation of the parent function f(x) to g(x) is
[tex]g(x)=2f(x-4)+5[/tex]x+4y=4 I know how to solve it. But how. how do you plot it on a graph?
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In order to plot it, we start by solving for y:
[tex]\Rightarrow4y=4-x\Rightarrow y=1-\frac{x}{4}[/tex]After this we simply replace values for x and we will get values for y inordered pairs, the
evaluate the expression x² + y²/10when x = 6 and y =8
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The given expression is
[tex]\frac{x^2+y^2}{10}[/tex]Let's replace x = 6 and y = 8.
[tex]\frac{6^2+8^2}{10}=\frac{36+64}{10}=\frac{100}{10}=10[/tex]Hence, the evaluation gives 10.solve the following equation for f .
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f = 3U/2
Explanation:[tex]U\text{ = }\frac{2}{3}f[/tex]cross multiply:
[tex]\begin{gathered} U\text{ = }\frac{2f}{3} \\ 3(U)\text{ = 2f} \end{gathered}[/tex]Divide both sides by 2:
[tex]\begin{gathered} \frac{3U\text{ }}{2}\text{= }\frac{\text{2f}}{2} \\ f\text{ = }\frac{3U\text{ }}{2} \end{gathered}[/tex]The bird population of an island is declining at the rate of 2.2% per year the population was 3500 in the year 2016 which answer is the best prediction of the population in year 2022
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ANSWER:
3063
STEP-BY-STEP EXPLANATION:
The first thing is to create an equation that models the situation with the data of the statement:
[tex]\begin{gathered} y=A\cdot(1-r)^x \\ \\ \text{ Where y is the best population prediction, A is the initial amount, r is the rate of decline, and x is the elapsed time.} \\ \\ \text{ We replacing:} \\ \\ y=3500(1-2.2\%)^x \\ \\ y=3500(1-0.022)^x=3500(0.978)^x \end{gathered}[/tex]We evaluate when x = 6, since the time elapsed between 2016 - 2022 is 6 years and we would be left with the following:
[tex]\begin{gathered} y=3500\cdot\left(0.978\right)^6 \\ \\ y=3062.676\approx3063 \end{gathered}[/tex]The best prediction of the population in the year 2022 is 3063
find the constant rate of change and interpret its meaning
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The constat rate is given by the slope of the line. By definition, the slope of the line is defined as follows:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]Where (X1,Y1) and (X2,Y2) are given points on the line. In our case, for example, we can take the points:
(X2,Y2) =(4,50)
(X1,Y1)=(2,70)
Replacing the previous data in the equation of the slope we obtain:
[tex]rate=m\text{ = }\frac{Y2-Y1}{X2-X1}=\frac{50-70}{4-2}=\frac{-20}{2}\text{ =-10 ft/s}[/tex]Then, we can conclude that the constant rate is
-10 ft /s : a descent of 10 ft per second.
Can you help me please I just paid 100 dollar for the tutor version and I can’t find one tutor
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The Solution.
Given the function below:
[tex]f(x)=\frac{1}{x+9}\text{ and the interval \lbrack{}10,10+h\rbrack}[/tex]The average rate of change in the given interval is
[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]In this case,
[tex]a=10,b=10+h[/tex]So,
[tex]f(a)=f(10)=\frac{1}{10+9}=\frac{1}{19}[/tex][tex]f(b)=f(10+h)=\frac{1}{10+h+9}=\frac{1}{19+h}[/tex]Substituting in the formula, we have
[tex]\text{Average rate of change =}\frac{\frac{1}{19+h}-\frac{1}{19}}{10+h-10}[/tex][tex]\begin{gathered} \text{Average rate of change =}\frac{\frac{19-(19+h)}{19(19+h)}}{h}=\frac{-h}{19h(19+h)}=\frac{-1}{19(19+h)} \\ \end{gathered}[/tex]So, the correct answer is
[tex]\frac{-1}{19(19+h)}[/tex]8What is the slope of the line that passes through the points (-2, 5) and (3, 4) in the standard (x,y) plane?
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Answer
Slope = -(1/5) = -0.20
Explanation
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (-2, 5) and (3, 4)
[tex]\text{Slope = }\frac{4-5}{3-(-2)}=\frac{-1}{3+2}=\frac{-1}{5}[/tex]Hope this Helps!!!
1,898,130,000,000,000,000,000,000,000 in scientific notation (round to two digts after the decimal
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in scientific notation is
[tex]1.89\times10^{27}[/tex]Solve for x and y:x – 3y = -83x + 2y = 31Select one:a. (-11,-1)b.(11,-1)c. (5,8)d. (7,5)
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We have two unknowns (x and y) and 2 equations.
We will clear one unknown in the first equation and then replace it in the second.
Then, we can solve for the other variable and solve backwards.
The first equation is:
[tex]\begin{gathered} x-3y=-8 \\ x=3y-8 \end{gathered}[/tex]We replace the value of x in the second equation:
[tex]\begin{gathered} 3x+2y=31 \\ 3(3y-8)+2y=31 \\ 9y-24+2y=31 \\ 11y=31+24 \\ 11y=55 \\ y=\frac{55}{11} \\ y=5 \end{gathered}[/tex]Then, with y=5, we can calculate the value of x:
[tex]x=3y-8=3\cdot5-8=15-8=7[/tex]The solution (x,y) is (7,5). The answer is Option D.
Don’t know how to do this some help would be nice pls and thanks
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Looking at the graph, f(2) means that the function is evaluated at x = 2.
Using this information, we need to identify the corresponding y-value on the graph, just like the image below:
We conclude that f(2) = -5
Which of the following is a trinomial with a constant term? A. 4x5 + 2x - 2x2 B. 5x2 - 4 + x C. x2 - 6 D. -3 + 4x4
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Step 1: What is a trinomial expression?
A trinomial is an algebraic expression composed of three terms and is normally of the form
[tex]ax^2\text{ + bx + c}[/tex]Where c is the constant term
A constant term is a term without x
Step 2:
From the options, it only options A and B that are trinomial.
[tex]Option\text{ B has a constant term }-4,\text{ because it is also a trinomial}[/tex]Step 3:
Final answer
[tex]\begin{gathered} Option\text{ B} \\ 5x^2\text{ - 4 + x} \end{gathered}[/tex]If EF = 2x - 12 FG = 3x - 15. and EG = 23, find the values of x. EF, and FG. The drawing is not to scale. x =3, EF = 8, FG = 15 Ox=10, EF = 32, FG = 45 O x =3, EF = -6, FG = -6 x =10, EF = 8, FG = 15
Answers
We have the next information
EF=2x-12
FG=3x-15
EG=23
With the information above we can have the next equation in order to find x
2x-12+3x-15=23
Then we sum similar terms
5x-27=23
then we isolate the x
5x=23+27
5x=50
x=10
then we substitute the value of x for each segment
EF=2x-12=2(10)-12=20-12=8
FG=3x-15=3(10)-15=30-15=15