Answer:
720
Explanation:
the general formula to find the sum of interior angles of any polygon is:
180*(n−2)
where n is the number of side of the polygon.
Since hexagon has 6 sides, then the sum of interior angles is 180(6−2)=180×4=720
The angles in the hexagon
we can use the formula degrees = (# of sides – 2) * 180. Then degrees = (6 – 2) * 180 = 720 degrees. Each angle is 720/6 = 120 degrees.
$870 is invested in an account earning 2.9% interest (APR),
compounded continuously. Write a function showing the
value of the account after t years, where the annual growth
rate can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also,
determine the percentage of growth per year (APY), to the
nearest hundredth of a percent.
Answer:
Step-by-step explanation:
[tex]\text{Continuous compounding is}\\ \\ A=Pe^{rt}\\ \\ V=870e^{0.029t}\\ \\ \text{The yearly growth rate is}\\ \\ e^0.029\approx 1.0294\\ \\ \text{Which is a growth of }2.94\% [/tex]
The U.S. Senate has 100 members. After a certain election, there were 20 more Democrats than Republicans, with no other parties represented. How many members of each party were there in the Senate?
On Aaron’s farm, 1/10 of the animals are cows, ⅖ of the animals are chickens,
and ¼ of the remaining animals are pigs. If there are 40 animals on Aaron’s farm,
how many pigs are on Aaron’s farm?
Answer:
There are 5 pigs on Aaron's farm
Step-by-step explanation:
1. Start with 40 animals
2. 1/10 of the animals are cows, so divide 40 by 10 and you will find that 4 of the animals are cows
3. 2/5 of the animals are chickens, so multiple 40 by 2 to get 80 and then divide 80 by 5 and you will find that 16 of the animals are chickens
4. Subtract the 4 cows and 16 chickens from the 40 total animals and you find there are 20 more animals that are neither cows nor chickens
5. Of the 20 remaining animals, 1/4 are pigs, so divide 20 by 4 and you will find that there are 5 pigs
Answer:
There are 5 pigs on Aaron's farm
Hope this helps! good luck :)
In ΔABC , angle C is a right angle.
Which statement must be true?
A.sin A = cos B
B.sin A = tan B
C.sin B = tan A
D.sin B = cos B
Answer: Choice A. sin(A) = cos(B)
============================================================
Explanation:
The rule is that sin(A) = cos(B) if and only if A+B = 90.
Note how
sin(A) = opposite/hypotenuse = BC/ABcos(B) = adjacent/hypotenuse = BC/ABSince both result in the same fraction BC/AB, this helps us see why sin(A) = cos(B). Similarly, we can find that cos(A) = sin(B).
In the diagram below, the angles A and B are complementary, meaning they add to 90 degrees. So this trick only applies to right triangles.
The side lengths can be anything you want, as long as you're dealing with a right triangle.
A boy 1.5 m tall is standing 12 m away from a church building which has a tower on top of its roof. The top of the cross on the tower is 14.6 m away from the boy’s head (eyes). If the boy has to raise his eyes through an angle of 31° in order to see the top of the roof, calculate,Correct to the nearest degree, the angle through which the boy must raise his eyes to see the top of the cross on the tower.
Correct to one decimal place, the height of the top of the cross from ground.
Correct to one decimal place the height of the church building.
Answer:
1. [tex]35^{o}[/tex]
2. 9.8 m
3. 8.7 m.
Step-by-step explanation:
1. Let the angle be represented by θ, so that:
Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
= [tex]\frac{12}{14.6}[/tex]
Cos θ = 0.82192
θ = [tex]Cos^{-1}[/tex] 0.8219
= [tex]34.73^{o}[/tex]
θ = [tex]35^{o}[/tex]
The angle through which the boy must raise his eyes to see the top of the cross on the tower is [tex]35^{o}[/tex].
2. Let the height from the boy's head to the top of the cross be represented by y, so that:
Sin [tex]34.73^{o}[/tex] = [tex]\frac{y}{14.6}[/tex]
y = Sin [tex]34.73^{o}[/tex] x 14.6
= 0.5697 x 14.6
y = 8.32 m
The height of the top of the cross from the ground = 1.5 + 8.32
= 9.82 m
The height of the top of the cross from the ground is 9.8 m.
3. Let the height from the boy's head to the top of the building be represented by x, so that:
Tan 31 = [tex]\frac{opposite}{adjacent}[/tex]
= [tex]\frac{x}{12}[/tex]
x = Tan 31 x 12
= 0.6009 x 12
x = 7.21
The height of the church building = 1.5 + 7.21
= 8.71
The height of the church building is 8.7 m.
The sketch to the question is attached to this answer.
when solving a system of equations by elimination, there are multiple correct ways you can start. which of the following is NOT a correct first step to solve this system?
(picture included)
Answer: the 2nd one
Step-by-step explanation: you didn’t multiply the -7 by 5, therefore being wrong
A plane is going to fly 300 miles at a planned speed of 530 mph. The flight will have an average headwind of w miles per hour the entire time, meaning the plane is flying directly against the wind. The time
Tin hours of the flight is a function of the speed of the headwind w, in mph, and can be modeled by
300
T(W) =
530-W
At what value of w does the graph have a vertical asymptote ? Explain what this asymptote means in this situation.
Answer:
Step-by-step explanation:
T(100) represents that the plane flies against the wind at 110mph for 0.714 hours
What is an approximation?An approximation is anything that is similar to but not identical to something else. Rounding can be used to approximate a number.
Given that a plane is going to fly 300 miles at a planned speed of 530 mph. The equation is T(W) = ( 300 ) / ( 530 -W).
The value of approximation will be calculated as
T(W) = ( 300 ) / ( 530 -W).
T(110) = ( 300 ) / ( 530 - 110)
T(110) = (300 ) / ( 420)
T(110) = 0.714
T(100) represents that the plane flies against the wind at 110mph for 0.714 hours.
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Need help!!! Wil mary brainlyest!
Answer:
-17/5/11/10
=-17/5*10/11=-34/11=
[tex]3 \: \div1 \div 11[/tex]
Hope it helps
Answer:
Easy. The answer is -3 1/11
Step-by-step explanation:
-17/5/11/10
-170/55
-3 1/11
What is the area of a circle that has a radius of 5 meters
Answer:
Step-by-step explanation:
area of circle = pi* r^2
Area = (3.14)*(5)^2
area= 78.5 m^2
Step-by-step answer:
The formula for the area of a circle is pi•r², so substitute 5 in for r.
pi•5²
Now, simplify the equation. Use PEMDAS.
There are no Parentheses, so we move on to Exponents.
pi•25
Now, we move to Multiplication.
P.S. If you are using 3.14 for pi, your answer is 78.5; otherwise, your answer is below.
78.53981634
Plzzzzz give me Brainliest!!!!!
Estimate if this angle is acute or obtuse.
Answer:
obtuse
Step-by-step explanation:
because they angle is over 90 degrees
What is 4 1/3 + 4 3/4 simplest form?
Answer:
109/12
Step-by-step explanation:
4 1/3 = 13/3
4 3/4 = 19/4
13/3 = 52/12
4 3/4 = 57/12
52/12 + 57/12 = 109/12
109 and 12 have no common factors
Jada has read 7/10 of a book. The book has 80 pages. How many more pages does she need to read before she is done with the book?
Answer:
24 More Pages
Step-by-step explanation:
7/10=0.7=70%
70% of 80 = 56
80 - 56 = 24
24 More Pages
Answer: 24 pages
Step-by-step explanation:
7 x
10 80
560=10x
÷10 ÷10
56=x
56 pages already read
80-56=24
24 pages left
simplify the expression 5t + (3r+2r) + 3t +4r
Rendi akan membuat kartu anggota taman bacaannya berbentuk setengah lingkaran. Jika
diameternya adalah 7 cm dan banyak kartu yang akan dibuat adalah sebanyak 500 lembar
maka tentukan luas karton yang dibutuhkan.
Find the value of y when
2x. + 6y = 1
Fast please!!!???
please help me find area
Answer:
whats the quetsion
Step-by-step explanation:
ded
The length of a rectangle is shown below:
On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis, two points A and B are shown. The point A is on ordered pair 1, 2, and the point B is on ordered pair negative 2, 2. A straight line joins the points A and B.
If the area of the rectangle to be drawn is 12 square units, where should points C and D be located, if they lie vertically below the line that connects B and A, to make this rectangle? (5 points)
Group of answer choices
C(−2, −4), D(1, −4)
C(−2, −1), D(1, −1)
C(−2, −5), D(1, −5)
C(−2, −2), D(1, −2)
Answer:
b
Step-by-step explanation:
7-2 Practice Questions
Due 02/20/211
X 72PS-11
Question Help
Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all
possible sums from the 36 possible combinations when rolling two number cubes. How many times
should Tamara expect the sum of the two cubes be equal to 9 if she rolls the two number cubes
216 times?
Click the icon to view the possible sums.
The sum should be equal to 9 about
time(s).
Enter your answer in the answer box and then click Check Answer
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Answer:
24
Step-by-step explanation:
There are 36 possible outcomes when rolling 2 dice. The sums range from 2 to 12. There are 4 ways of rolling a 9: 3, 6; 4, 5; 5, 4; 6, 3.
p(sum of 9) = 4/36 = 1/9
1/9 of the rolls are expected to have a sum of 9.
1/9 * 216 = 24
Robert has 5 pizzas at his birthday party, and each pizza is cut into 5 slices. His guest take 2 pieces from each pizza what equation would represent the amount of pizza that is left?
Answer:
15 slices of pizza are left
Step-by-step explanation:15 slices of pizza are left bc 5 pizzas with 5 slices equal 25 slices and 2 slices are taken away from each pizza, and there are 5 pizzas that is 10 slices eaten and 25-10=15. Its so easy
PLZ HELP ME WITH THIS NEED THE ANSWER NOW PLSSSSSSSSS THIS IS 7TH GRADE AMTH
Answer:
Just by the looks at it P has the greater slope I think but graph it to make sure cause I might be wrong.
Answer:
Function 2
Step-by-step explanation:
Use the following figures to find the value of x.
(any help would be appreciated)
Answer:
x=9
Step-by-step explanation:
the two sides are equivalent so set equal to each other
x-6=1/3x
3x-18=x
3x-x=18
2x=18
x=9
Review the graph. On a coordinate plane, a function starts at (negative StartFraction pi Over 2 EndFraction, negative 1), has an inflection point at (0, 0), and curves up to (StartFraction pi Over 2 EndFraction, 1). What is the inverse of the trigonometric function in the graph?
Answer:
A
Step-by-step explanation:
make two equations for each:
exactly one solution
no solutions
infinitely many solutions
Answer:
Two equations with exactly one solution
y=x
y=-x
Two equations with no solutions
y=x
y=x+1
Two equations with infinitely many solutions
x+y+1
2x+2y=2
Step-by-step explanation:
Let's use linear equations. The slope intercept form is
y=mx+b
m is the slope and b is the y intercept.
To make the equations have one solution, the two equations must represent lines that do not have the same slope, so that they intersect. We must choose different slopes, but any y intercepts will do. Example: Choose the slopes to be 1 and -1 and choose both y intercepts to be 0
y=x
y=-x
For there to be no solutions, all we need are the same slopes and different y intercepts, so that the lines are parallel and at different heights. Let's choose the slopes to be 1 and the y intercepts to be 0 and 1.
y=x
y=x+1
To get infinitely many solutions all we need is for the lines to be parallel with the same y intercept, so that they lie on top of each other. We could use
y=x
y=x
but your teacher probably wants something different. So, lets use another form of a linear equation, the so-called standard form.
ax+by=c
if you solve this for y, you get
y=-(a/b)x+(c/b)
This is in the y=mx+b form we used before, except that now the slope is -(a/b) and the y intercept is (c/b). So, we will get the same slope if the ratio of a to b is the same for both equations and the ratio of c to b is the same for both equations. In other words, simply choose a standard form equation and then get another by multiplying through by any number. In general
ax+by=c
and
kax+kby=kc
will do the trick. Here is an example.
x+y+1
2x+2y=2
help me with this fast and explain it for brainiest :)
So i think it would be 1/2 (OR .5), or possibly 2 depending on what its asking.
Every number in X can be multiplied by 2 to receive y, or the numbers in y.
The linear equation would be x*2=y, making the linear function 2, UNLESS you want to take Y and DIVIDE it by 2, making it 1/2, linear equasion would be y*.5=x, or y/.5=2 OR y*1/2=x.
Hope this helps, I'm so sorry if its wrong, I'm not too good at linear functions, I'm pretty sure its 1/2.
Find the VOLUME of the right circular cone:
26 m
10 m
The Springfield Middle School sixth-grade teachers of history, science, and art are listed in the table.
Sixth Grade Teachers
History
Science
Art
Mr. Nelson
Ms. Porter
Mr. Rosenberger
Ms. Hogan
Mr. Grist
Ms. Patel
Ms. Miller
Ms. O’Reilly
Ms. George
Mr. Springer
Ms. Trufant
Ms. Callahan
Ms. Daniels
Mr. Pollard
Ms. Cartwright
Ms. Davis
Mr. Bergeron
Mr. Cooper
Mr. Chin
Mr. Dawson
Ms. Sarno
How many combinations of one history, one science teacher, and one art teacher include Mr. Bergeron?
13
36
252
288
Answer:
Step-by-step explanation:
The Springfield Middle School sixth-grade teachers of history, science, and art are listed in the table. How many combinations of one history, one science teacher, and one art teacher
let say number of history. teacher = H
number of science teacher = S
number of Art teacher = A
Acombinations of one history, one science teacher, and one art teacher = H * S * A
The combinations of one history, one science teacher, and one art teacher include Mr. Bergeron is (H x S x A).
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
We have,
The Springfield Middle School sixth-grade teachers of history, science, and art are listed in the table.
The number of history teacher = H
and, the number of science teacher = S
and, the number of Art teacher = A
So, the combinations of one history, one science teacher, and one art teacher
= H x S x A
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The height of a tree when planted is 1.1 m.
One year later, the height of the tree is 2.4 m.
Calculate the percentage
increase in the height of the tree
over the year, correct to 1 d.p.
Answer:
118.2
Step-by-step explanation:
1.1m is 100%
2.4m×100=240
240/1.1= 218.(18)
218.(18)%-100%=118.(18)=118.2
The marked price of washing machine is $500.00 and the rate of discount is 15%. Find the selling price.
How do you solve the attached?
Answer:
it dont show
maybe try again
Minimize the objective function P = 45x + 48y for the given constraints.
X20
y 20
5x + y = 16
x + 3y 26
Answer:
Following are the solution to the given equation:
Step-by-step explanation:
The graph file and correct question are defined in the attachment please find it.
According to the linear programming principle, we predict, that towards the intersections of the constraint points in the viability area, and its optimal solution exists. The sketch shows the points that are (0,16), (3,1), and (6,0).
by putting each point value into the objective function:
[tex]\to P(0,16) = 768\\\\\to P(3,1) = 183\\\\\to P(6,0) = 270[/tex]
Thus, the objective of the function is reduced with a value of 183 at (3,1).