Answers
.. x +150 +(2x -50) +(x +40) +80 +(x +20) = 720
.. 5x +240 = 720 . . . . . . . . simplify
.. 5x = 480 . . . . . . . . . . . . . subtract 240
.. x = 96 . . . . . . . . . . . . . . . .divide by 5
The angles (clockwise from lower left) are
.. 96°
.. 150°
.. 142°
.. 136°
.. 80°
.. 116°
Related Questions
A board is leaning against a vertical wall, The board makes a 62 degree angle with the ground and touches the wall at a point that is 45 in, above the ground. What is the length of the board, rounded to the nearest inch?
Answers
Angle B = 90°
Side a = 45
The length of the board is side b
Use the Law of Sines to find side b.
b / sin(B) = a / sin(A)
b / sin(90°) = 45 / sin(62°)
b = (sin(90°) x 45) / sin(62°)
b = 50.966
Rounded to the nearest inch is 51 inches.
Hope this helps!
Answer:
Option C. 51 in.
Step-by-step explanation:
In the given right angle triangle height is given as 45 in. above the ground.
Length of the board is making an angle of 62°with the ground.
Therefore by sine rule
sin 62° = height / hypotenuse
sin 62° = 45/h
0.8829 = 45/h
h = 45/0.8829 = 50.96 ≈ 51 in.
Therefore option C. 51 in. is the answer.
the yearly changes in the population of a town for four consecutive years were, respectively, 25% increase, 25% increase, 25% decrease, and 25% decrease. what is the net present decrease over the four years, rounded to the nearest percent?
Answers
To see what is going on in this problem, we should write an equation. Let's start by using P to represent the total population.
P x 1.25 x 12.5 x 0.75 x 0.75 = 0.8789
For the increases, we multiplied by 1.25. For the decreases, we multiplied by 0.75.
The final result is the P gets multiplied by 0.8789. In other words it is made smaller by 12.11%. 100% - 87.89% = 12.11%
A tree on a hillside casts a shadow c = 230 ft down the hill. if the angle of inclination of the hillside is b = 19° to the horizontal and the angle of elevation of the sun is a = 49°, find the height of the tree. (round your answer to the nearest foot.)
Answers
let x be the distance from point A to when y intersects the horizonal.
x/230=cos 19
x=230 cos 19=217.5
y/x=tan 19
y=xtan19
y=217.5 tan 19=74.88
(h+y)/x=tan 49
h+y=xtan 49=217.5tan49=250.205
hence
h=250.205-74.88=175.325 ft
the answer is:
height of the tree ~ 175 ft
Which statements are always true regarding the diagram? Check all that apply.
CAN SOMEONE PLEASE ANSWEERRRRRR
m∠3 + m∠4 = 180°
m∠2 + m∠4 + m∠6 = 180°
m∠2 + m∠4 = m∠5
m∠1 + m∠2 = 90°
m∠4 + m∠6 = m∠2
m∠2 + m∠6 = m∠5
Answers
As these 2 angles make up a straight line, the sum of the magnitude of angles is 180° so this is true
m∠2 + m∠4 + m∠6 = 180°
these 3 angles are the interior angles of a triangle. the sum of all the interior angles of a triangle sum up to 180° so this is true.
m∠2 + m∠4 = m∠5
for this statement, use the previously stated concepts
m∠2 + m∠4 + m∠6 = 180°
m∠5 + m∠6 = 180°
since both equations are equal lets put them into one equation
m∠2 + m∠4 + m∠6 =m∠5 + m∠6
since m∠6 is common for both sides lets cancel it out which leaves us with
m∠2 + m∠4 = m∠5
therefore this statement is true
m∠1 + m∠2 = 90°
sum of the angles making up a straight line is 180 °, therefore this is incorrect
m∠4 + m∠6 = m∠2
lets use the following equation
m∠2 + m∠4 + m∠6 = 180°
if m∠6 + m∠4 = m∠2
then using this we substitute in the previous equation
m∠2 + ∠m∠2 = 180°
m∠2 = 90°
so this angle should be a right angle, but in the diagram its not a right angle therefore this is incorrect
m∠2 + m∠6 = m∠5
since
m∠5 + m∠6 = 180°
m∠2 + m∠4 + m∠6 = 180°
then putting both the equations in one as they are both equal
m∠2 + m∠4 + m∠6 = m∠5 + m∠6
this shows that
m∠2 + m∠4 = m∠5
then m∠4 should be equal to m∠6
but judging from the sides opposite to the angles m∠4 and m∠6 the sides aren't equal so these angles too cannot be equal so this statement is wrong.
m∠2 + m∠4 + m∠6 = 180°m∠2 + m∠4 = m∠5
In Emily's physics class, she had to solve the equation 9 = 12at2 + ut for u. Each step of her work is shown below.
Use the drop-down menus to explain each step.
Answers
Answer:
[tex]u=(9-\frac{1}{2}at^{2})/t[/tex]
Step-by-step explanation:
we have
[tex]9=\frac{1}{2}at^{2}+ut[/tex]
Solve for u
That means-------> isolate the variable u
step 1
Subtract [tex]\frac{1}{2}at^{2}[/tex] both sides
[tex]9-\frac{1}{2}at^{2}=ut[/tex]
step 2
Divide by [tex]t[/tex] both sides
[tex]u=(9-\frac{1}{2}at^{2})/t[/tex]
In Step 1, Emily subtracts (1/2)at² from both sides to isolate 'u.' In Step 2, she divides both sides by 't' to solve for 'u,' simplification of the equation further.
The equation is 9 = (1/2)at² + ut
Step 1 . 9 - (1/2)at² = ut
In this step, Emily subtracts (1/2)at² from both sides of the equation.
The purpose of this is to isolate the term containing 'u' on the right side of the equation.
Starting with the original equation, Emily recognizes that the term (1/2)at² is added to ut, and she wants to get rid of it from the right side.
To do that, she subtracts (1/2)at² from both sides to keep the equation balanced.
So, she ends up with 9 - (1/2)at² on the left side and ut on the right side.
This is a crucial step because it isolates the term ut, making it easier to solve for 'u' in the next step.
Step 2. [9 - (1/2)at²] / t = u
In this step, Emily divides both sides of the equation by 't' to solve for 'u.' The purpose is to isolate 'u' on the right side of the equation.
Starting with the equation from Step 1 (9 - (1/2)at² = ut), Emily recognizes that she wants to isolate 'u' by itself.
To do that, she divides both sides of the equation by 't.'
This division cancels out 't' on the right side, leaving 'u' alone.
Therefore, simplification of the equation ends up with [9 - (1/2)at²] / t on the left side and 'u' on the right side, this step allows her to find the value of 'u' using the given values of 'a,' 't,' and '9.'
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A model ship is built to a scale of 1 cm: 4 m. The length of the model is 40 cm. What is the length of the actual ship? a. 160 m c. 40 m b. 50 m d. 15 m Please select the best answer from the choices provided A B C D
Answers
You can get this answer by multiplying the scale by the length of the model
..................................................................... 70.6 m × 14 m =
Answers
For this case we are in the presence of a multiplication where each number represents a unit.
The unit for each number in this case is meters.
Therefore, the result will be expressed in meters squared.
Multiplying we have:
70.6 m × 14 m = 988.4 m ^ 2
Answer:
70.6 m × 14 m = 988.4 m ^ 2
The vertex form of a function is g(x) = (x – 3)2 + 9. How does the graph of g(x) compare to the graph of the function
f(x) = x2?
A.g(x) is shifted 3 units left and 9 units up.
B.g(x) is shifted 3 units right and 9 units up.
C.g(x) is shifted 9 units left and 3 units down.
D.g(x) is shifted 9 units right and 3 units down.
Answers
and The + 9 moves the graph upwards 9 units
Its B
For this case we have that the main function is given by:
[tex]f (x) = x ^ 2[/tex]
First, we apply the horizontal transformation. To do this, we evaluate the function for x-3, that is, we move the graph 3 units to the right.
[tex]f (x-3) = (x-3) ^ 2[/tex]
We apply the vertical transformation. To do this, add to the function 9 units, that is, we move the graph 9 units up.
[tex]f (x-3) +9 = (x-3) ^ 2 + 9[/tex]
We have then:
[tex]g (x) = (x-3) ^ 2 + 9[/tex]
Answer:
B.g (x) is shifted 3 units right and 9 units up.
Let f(x) = 5x + 6 and g(x) = -7x - 4.
Find f(x) + g(x)
Answers
5x + 6 - 7x - 4
-2x + 2
This is the term in a polynomial without a variable
Answers
A term in a polynomial without a variable is known as a constant. It is the term that does not change its value.
Explanation:The term in a polynomial without a variable is often referred to as the constant term. In a polynomial expression, variables are raised to various powers and multiplied by coefficients. However, the constant term is a unique element within the polynomial because it does not involve any variables. It is a number on its own and typically represents the y-intercept of the polynomial graph when plotted on a Cartesian plane.
For example, in the polynomial expression "[tex]3x^2 + 5x - 7,"[/tex] the constant term is "-7." This term contributes a fixed value to the overall expression, regardless of the value of the variable "x." It's a crucial component in polynomial mathematics, as it affects the position of the polynomial graph on the vertical axis. Understanding the constant term is essential for polynomial evaluation, graphing, and solving equations involving these expressions. In essence, the constant term is the base value around which the polynomial varies as the variable changes.
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helpppppppppppppppppppppppppppp
Answers
We then have to rewrite:
x*x ^ 2 = 64
Rewriting:
x ^ 3- 64 = 0
x = 4
Answer:
x = 4
option 2
Divide the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of x.
(4x^2 - 10x -24) / (2x + 3)
Answers
Answer:
2x-8
Step-by-step explanation:
What is the first step in solving the problem 3/4 + 1/8?
Answers
One of the ways, for example, is a simple addition of fractions.
We have then:
Step 1:
Cross product
3/4 + 1/8 = ((3 * 8) + (1 * 4)) / (4 * 8)
Step 2:
Rewrite
((3 * 8) + (1 * 4)) / (4 * 8) = (24 + 4) / (32) = 28/32
Step 3:
simplify
28/32 = 14/16 = 7/8
Answer:
Step 1:
Cross product
3/4 + 1/8 = ((3 * 8) + (1 * 4)) / (4 * 8)
HELLPPPP ASAP
Identify the type of function represented by f(x)=(1/2) x (3)^x
A. Decreasing linear
B. Exponential decay
C. Exponential growth
D. Increasing linear
Answers
Answer:
The correct option is (C) Exponential growth.
Step-by-step explanation:
The simplest exponential function is: f(x) = [tex]a^{x}[/tex], a>0, a≠1
If the x is positive then graph of exponential is increasing and if the x is negative then graph of exponential is decreasing.
In given function [tex]f(x)=\frac{1}{2}\times(3)^x[/tex]
x is positive so, it is graph of exponential growth.
Hence, the correct option is (C) Exponential growth.
Answer:C
Step-by-step explanation:
BIG BRAIN
Which polynomial is in standard form
Answers
Answer:
Last option is correct.
Step-by-step explanation:
We are given with some polynomials.
We have to tell which one is in standard form of polynomial.
In Standard Form of a polynomial , Terms are arranged in decreasing or descending order of degree of the terms.
Polynomial 1.
1 + 2x - 8x² + 6x³
In this Terms are arranged in Increasing order of degree of terms.
This is not in Standard form.
Polynomial 2.
2x² + 6x³ - 9x + 12
In this polynomial first two terms are arranged in Increasing order of degree while last two arranged in decreasing order of degree.
This is not in Standard form.
Polynomial 3.
6x³ + 5x - 3x² + 2
In this Terms are arranged in jumbled order of degree
This is not in Standard form.
Polynomial 4.
2x³ + 4x² - 7x + 5
In this Terms are arranged in Decreasing order of degree of terms.
This is in Standard form.
Therefore, Last option is correct.
simplify 4x+2 - x^2 +x-12 / x-3
a) 3x-2
b)3x+4
c)5x-4
d)5x+4
Answers
Answer:
3x-2
Step-by-step explanation:
on edge
What is the value of x in the equation 3x – y = 18, when y = 27?
Answers
To find the value of x in the equation 3x - y = 18 when y = 27, substitute 27 for y and solve the resulting equation. The value of x is found to be 15.
The student has asked for the value of x in the equation 3x - y = 18, given that y = 27. To solve for x, we simply substitute 27 for y in the equation and solve for x:
3x - 27 = 18
3x = 18 + 27 (Add 27 to both sides)
3x = 45
x = 45 / 3 (Divide both sides by 3)
x = 15
The value of x is 15 when y = 27.
WILL GIVE BRAINLIEST-Let f(x)=x2−3x−4 .
What is the average rate of change from x = 7 to x = 10?
Enter your answer in the box.
Answers
The average rate of change on that interval is 14.
Answer:
14
Step-by-step explanation:
14
What is the effect on the volume of a rectangular prism if the width is doubled and the hight is reduced to half of the original height?
A) the volume is doubled.
B) the volume is halved.
C) the volume is tripled.
D) the volume is unchanged.
Answers
Find the area of the trapezoid. Leave your answer in simplest radical form.
Answers
A=[(18-4)+18]*4√3/2=32*2√3=64√3
A=64√3
7 is greater than or equal to w, and - 1 is less than w
Answers
Hope this helps!
_____a function is the same as moving a function ... im not totally sure
Answers
A recipe for lemon cranberry pound cake calls for 80 milliliters of lemon juice and 240 milliliters of plain yogurt. How many liters of lemon juice and yogurt are needed to make 11 cakes?
Answers
1 liter------------> is equal to 1000 ml
if for one cake--------------> are required 80 milliliters of lemon juice
for 11 cakes--------------> X
X=11*80---------> 880 ml
if for one cake--------------> are required 240 milliliters of plain yogurt
for 11 cakes--------------> X
X=11*240---------> 2640 ml
liters of lemon juice needed to make 11 cakes
880 ml/1000------> 0.88 lt
liters of yogurt needed to make 11 cakes
2640 ml/1000--------> 2.64 lt
the answer is
are needed 0.88 lt of lemon juice and 2.64 lt of yogurt to make 11 cakes
Answer: 3 liters 520 milliliters
Step-by-step explanation:
Total liquid amount:
80 ml + 240 ml = 320 milliliters
Total amount for 11 cakes:
320 milliliters × 11 = 3,520 milliliters
Total amount for 11 cakes conversion:
3,520 milliliters ÷ 1,000 = 3 remainder 520 = 3 liters 520 milliliters
Refer to Explorations in Literature for a complete version of this passage.
Which quotations from “Here Is New York” develop the author’s viewpoint that commuters do not truly experience New York City?
Select each correct answer.
A "About 400,000 men and women come charging on to the Island each week-day morning, out of the mouths of tubes and tunnels."
B "Second, there is the New York of the commuter—the city that is devoured by locusts each day and spat out each night."
C "The commuter dies with tremendous mileage to his credit, but he is no rover."
D "Or they may work in a midtown office and may let a whole year swing round without sighting Governors Island from the sea wall."
Answers
C "The commuter dies with tremendous mileage to his credit, but he is no rover."
D "Or they may work in a midtown office and may let a whole year swing round without sighting Governors Island from the sea wall."
Final answer:
The quotations that develop the author's viewpoint about commuters not truly experiencing New York City are highlighted.
Explanation:
The quotations from “Here Is New York” that develop the author’s viewpoint that commuters do not truly experience New York City are:
“Second, there is the New York of the commuter—the city that is devoured by locusts each day and spat out each night.”
“The commuter dies with tremendous mileage to his credit, but he is no rover.”
“Or they may work in a midtown office and may let a whole year swing round without sighting Governors Island from the seawall.”
These quotes highlight the idea that commuters only see a limited and narrow part of the city, and they do not take the time to truly explore and experience all that New York has to offer.
your boss is impressed with your work and gives you a 3% raise.if the inflation rate is 3% you are
A) making more money in today's dollars
B) making about the same amount in today's dollars
C) making less money in today's dollars
D) seeing no change in your paycheck
Answers
Answer: The answer is (B) making about the same amount in today's dollars.
Step-by-step explanation: Given that our boss is impressed with our work and give us a 3% raise.
We are to select the correct statement if there is an inflation of 3%.
Since the raise of 3% and inflation rate of 3% occur simultaneously, so there will not be much change in the amount of money we are making in dollars.
Thus, (B) is the correct option.
A party size bag of tortilla normally coast 3.80. the supermarket has them on sale today for 2.25. what is the percentage of the discount
Answers
.. = (2.25/3.80 -1)*100%
.. = (0.5921 -1)*100%
.. = -0.4079*100%
.. = -40.79%
The discount is about 41% from the regular price.
What is the area of a sector with a central angle of 10pi/7 radians and a radius of 18.4 m? Enter your answer as a decimal.
Answers
.. = (1/2)*(18.4 m)^2*(10π/7)
.. = 759.73 m^2
Delia work for 45 minutes on her oil panting she took a brake a 10:35 am what time did delia starting working
Answers
⇒ count back 45 minutes from 10.35am
45 mins before 10.35am = 9.50am
Kiki works in a furniture store. Her base salary is $150 per day, plus 8 percent commission on her sales. She sells several high-priced items. table What is the total amount she earned over these three days?
Answers
Answer:
614
Step-by-step explanation:
614 can also look like this ^!$ if you hold down caps.
Kiki works in a furniture store. Her base salary is $150 per day, plus 8 percent commission on her sales. She sells several high-priced items.
What is the total amount she earned over these three days?
$ 614
Got it correct.
Hope it helps
PLEASE HELP ME!! 25 points
Anna has a 10-foot long ladder that she is going to rest against a vertical wall along the bottom of a window-sill that is 8.5 feet above the ground. The safety code recommends that the angle the ladder makes with the ground be no greater than 65°. Will the ladder be safe resting on the window sill?
please help with too -->Draw a diagram, and show work to support your answer.
Answers
sin x=opposite/hypotenuse
opposite=8.5 ft
hypotenuse=10 ft
thus
sin x=8.5/10
sin x=0.85
x=arcsin 0.85
x=58.21°
Since 58.21°<65° the we conclude that the ladder is very safe.