11. A surveyor at point S discovers that the angle between peaks A and B is 3 times as large as the angle
between peaks B and C. The surveyor knows that ZASC is a right angle. Find mzASs and m2BSC.
Answers
The measures of the angles between the peaks are;
m∠BSC = 22.5°
m∠ASB = 67.5°
The reason for arriving at the above angles is as follows:
The known values are;
The location of the surveyor = Point S
The angle between peaks A and B = m∠ASB = 3 times as large as the angle between peaks B and C = 3 × m∠BSC
The measure of angle m∠ASC = A right angle = 90°
Required:
To find m∠ASB and m∠BSC
From the given diagram, we have;
m∠ASC = 90°
m∠ASC = m∠ASB + m∠BSC (angle addition postulate)
m∠ASB = 3 × m∠BSC
∴ m∠ASC = 3 × m∠BSC + m∠BSC = 4 × m∠BSC
m∠ASC = 4 × m∠BSC = 90°
m∠BSC = 90°/4 = 22.5°
m∠BSC = 22.5°
m∠ASB = 3 × m∠BSC
∴ m∠ASB = 3 × 22.5° = 67.5°
m∠ASB = 67.5°
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Related Questions
Martina has 240 meters of fencing and wishes to form three sides of a rectangular field. The fourth side borders a river and will not need fencing.
As shown below, one of the sides has length x (in meters).
x
Side along river
(a) Find a function that gives the area Ax of the field (in square meters) in terms of x.
=Ax
(b) What side length x gives the maximum area that the field can have?
Side lengthx:meters
(c) What is the maximum area that the field can have?
Maximum area:square meters
Answers
Answer:
Step-by-step explanation:
Answering a comes from simplification, and answering b and c are done all in one step: completing the square on the quadratic that results from a.
(a) If Martina has 240 m of fencing and is only utilizing one side for the length and 2 sides for the width, the perimeter formula is
240 = x + 2w where x is a length and w is the width. Solving this for w in terms of x:
240 - x = 2w so
[tex]w=120-.5x[/tex] The area for a rectangle is L * W, so our area using the lengths we have is
A(x) = x(120 - .5x) and we simplify:
A(x) = 120x - .5x² That's the answer to a.
Now for b and c, we will complete the square on this to get the vertex.
Begin by factoring out the -.5:
[tex]A(x)=-.5(x^2-240x)[/tex] Now we take half the linear term, square it and add it both inside the parenthesis and outside the parenthesis. Our linear term is 240. Half of 240 is 120, and 120 squared is 14400:
[tex]A(x)=-.5(x^2-240x+14400)+7200[/tex] (The 7200 comes from multiplying the 14400 times the -.5; -.5 times 14400 is -7200 so to balance things out, we have to add 7200).
The perfect square binomial that results from this is
A(x) = -.5(x - 120)² + 7200. From this we determine that our vertex is
(120, 7200). The 120 is the value of x, the length we are asked to find in b; the 7200 is the max area we are asked to find in c.
The required solutions are,,
(a) area = 240x - 2x²
(b) the side adjacent to the rivers gives the maximum length of the field.
(c) the maximum area could be 6400-meter square.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
length of the field is x,
The perimeter of the field, = 240
x + x + width = 240
width = 240 - 2x
now,
(a)
area of the field,
= length * width,
= x(240-2x)
= 240x - 2x²
Similarly,
(b) the side adjacent to the rivers gives the maximum area of the field.
(c) the maximum area could be 6400-meter square.
Thus, the required solutions are mentioned above.
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prove that tan² theta + cot² theta = sec² theta cosec² theta- 2
Answers
Step-by-step explanation:
Tan² theta = sec² theta - 1
Cot² theta = cosec² theta - 1
Tan²+Cot² = sec²-1+cosec²-1
= sec²+cosec²-2
Please find attached herewith the solution of your question.
If you have any doubt, please comment.
A scientist is studying the growth and development of an epidemic virus with a growth rate of 9% per month that has infected 3,124 people. If this rate continues, what will be the number of infected people in another 9 months? Round your answer to the nearest whole number.
Answers
Answer:
About 6,785 people will be infected about nine months.
Step-by-step explanation:
We can write an exponential function to represent the situation. The standard exponential function is given by:
[tex]\displaystyle f(x) = a(r)^x[/tex]
Where a is the initial value, r is the rate, and x, in this case, is the time that has passed in months.
3,124 people have already been infected. Thus, our initial value a = 3124.
And an additional 9% will be infected per month. Therefore, our rate r will be 1 + 9% or 1.09.
Hence, our function is:
[tex]\displaystyle f(x) = 3124(1.09)^x[/tex]
Then after nine months, the total amount of infected people will be f(9):
[tex]\displaystyle f(9) = 3124(1.09)^{(9)}[/tex]
Use a calculator:
[tex]\displaystyle f(9) \approx 6785[/tex]
About 6,785 people will be infected about nine months.
Answer:
7,022
Step-by-step explanation:
14. The data below show the average ages and number of volunteer hours for five randomly chosen persons. Given the equation of the regression line is y' = 9.309x - 167.012, predict the number of hours a person will volunteer if her age is 27.5 years. Age, x Volunteer Hours, y 24.9 66.5 25.6 70.0 26.1 74.8 27.3 89.6 27.0 82.6
Answers
The Predicted time a person will serve is "88.9855 months". A complete solution is provided below.
Given equation is,
→ [tex]\hat{y}=9.309x - 167.012[/tex]
Her age,
→ x = 27.5 years
By substituting the value of "x" in the given equation, we get the predicted time,
hence,
→ [tex]\hat{y}=9.309\times 27.5 - 167.012[/tex]
[tex]= 255.9975- 167.012[/tex]
[tex]=88.9855 \ months[/tex]
Thus the above is the right answer
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what is this expression in simplest form? x^2+x-2/x^3-x^2+2x-2
Answers
The Required expression is (x+2) / (x^2+2).
x^2+x-2/x^3-x^2+2x-2
The process in mathematics to operate and interpret the function to make function simple or more understandable called simplify and the process is called simplification.
= (x^2+x-2) / (x^3-x^2+2x-2)
= (x-1)(x+2) / (x^2+2)(x-1)
=(x+2) / (x^2+2)
Thus, The Required expression is (x+2) / (x^2+2).
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Answer: see photo#2
Step-by-step explanation:
Digits to write five hundred seven billion,six hundred forty million,seven hundred forty-two thousand,seventy two
Answers
write each equation explicitly in terms of x. then indicate whether the equation is a function.
y^2-x^2+1=50
Answers
Answer:
Hello,
Step-by-step explanation:
[tex]y^2-x^2+1=50\\y^2=x^2+49\\2\ functions \ :\\\\y=\sqrt{x^2+49} \\\\or\\\\y=-\sqrt{x^2+49} \\[/tex]
Using function concepts, it is found that:
The explicit equation in terms of x is given by: [tex]y = \pm \sqrt{x^2 + 49}[/tex]The equation is not a function, as there are multiple outputs for a single input.----------------------
The expression is given by:
[tex]y^2 - x^2 + 1 = 50[/tex]
In terms of x, the equation is given by:
[tex]y^2 = 50 + x^2 - 1[/tex]
[tex]y^2 = x^2 + 49[/tex]
[tex]y = \pm \sqrt{x^2 + 49}[/tex]
----------------------
An equation is a function if for each value of the input, there is only one output.Testing the input x = 0:
[tex]y = \pm \sqrt{0^2 + 49}[/tex]
[tex]y = \pm \sqrt{49}[/tex]
[tex]y = \pm 7[/tex]
Two output values for one input, thus, it is not a function.
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use green theroem to find integral of x^2ydx-xy^2dy
Answers
Answer:
complementary angles 25
Alexa has saved
2/7
of the cost of her trip to the Caribbean. Estimate how much money she
has left to save.
A.3/4 of the cost
B.1/2 of the cost
C.1 1/4 of the cost
D.1/4 of the cost
Answers
Answer:
A 3/4
Step-by-step explanation:
Set up equation to find the percentage 2/7 equals:
Variable x = percentage
2/7 = x/100
Cross multiply:
2 × 100 = 7 × x
200 = 7x
Divide:
28.57142... = x
About 30% (I rounded to 30% because it is a nice number to use when all other numbers end in 5 or 0)
If Alexa has about 30% saved, she will need to save about 70% more. Find the solution that is closest to 70%.
A is 3/4 which comes out to 75%. So far, this sounds like the best answer. Let's check the others just in case.
B is 1/2, or 50% which isn't as close as A was to 70%.
C is 1 1/4 which means 125% needs to be saved. This would mean Alexa is in debt and hasn't saved any money which is not the case.
D is 1/4, or 25%. The trick here is that she's saved about 30% so 25% is closest, but we are looking for how much more she needs to save.
class 8 question please answer
(sin x - sin y) (sin x + sin y)
Answers
Step-by-step explanation:
[tex](\sin{x} - \sin{y})(\sin{x} + \sin{y}) = \sin^2{x} + \sin{x}\sin{y} - \sin{x}\sin{y} - \sin^2{y}[/tex]
[tex]= \sin^2{x} - \sin^2{y}[/tex]
find the difference between the product of 2.5 and 7.5 and the sum of2.75 and 9.55
Answers
Answer:
6.45
Step-by-step explanation:
The answer=2.5*7.5-(2.75+9.55)=18.75-(12.3)=6.45
A diamond ring was reduced from $999.99 to S789.99. Find the percent reduction in the price. Round the answer to the nearest tenth of a percent, if
necessary.
The reduction in price is?
Answers
Answer:
21%
Step-by-step explanation:
Percentage reduction is (999.99-789.99)/(999.99)=21%
What is the formula for the volume of a pyramid?
V = πr2h
V = 3/4πr2h
V = 1/3πr2h
V = 1/3Bh
Answers
(g o f)(6)
A. Find f(6)
B. Substitute the value you found in part A into g(x) to find g(f(6))
Answers
Step-by-step explanation:
A. gof=g(f(x))
= g(f(6))
=6×6
36
The table and the Circle Chart shown display the percentage of dogs in seven different groups of dog breeds in a dog competition.
How does the Circle Graph misrepresent the data in the table?
A. The percentages do not add up to 100.
B. The size of the section representing the Non-Sporting group is smaller than the section that represents Herding group.
C. The number of regions in the graph is not correct for the data.
D. One of the breeds in the table is not represented in the Circle Chart.
Answers
Answer:
a
Step-by-step explanation:
Answer:
Incorrect, it's actually B.
Step-by-step explanation:
Look at the Non-Sporting Group and Herding Group. The sizes of the slices are different (NSG being smaller than HG)
Complete the equation describing how x
and y are related.
Х у
y = [? ]x +
07
1 9
2 11
3 13
4 15
5 17
Enter the answer that
belongs in [?]
Answers
Answer:
Hello,
Answer 2
Step-by-step explanation:
7=2*0+7
9=2*1+7
11=2*2+7
13=2*3+7
15=2*4+7
17=2*5+7
y=2*x+7
An other way:
[tex]points\ ( 0,7)\ and\ (1,9)\\\\\Delta\ y=9-7=2\\\Delta\ x=1-0=1\\\\\\y-7=(x-0)*2\\\\y=2x+7\\[/tex]
The complete equation is [tex]y = 2x+7[/tex].
What is equation?An equation is a condition on a variable such that two expressions in the variable should have equal value.
What is substitution?Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.
According to the question.
We have a table which shows the relation between x and y.
Let the missing term be a and b.
The the given equation becomes
[tex]y = ax + b[/tex]
For finding the value of a and b.
Substitute x = 0 and y = 7 in equation y = ax + b.
[tex]\implies 7 = a(0) + b\\\implies b = 7[/tex]
Again, substitute x = 1 and y = 9 in the equation y = ax+ b
[tex]\implies 9 = a(1) +b\\\implies 9 = a + 7\\\implies a = 2[/tex]
substitute the value of a and b in the equation y = ax + b.
[tex]\implies y = 2x+ 7[/tex]
Therefore, the complete equation is [tex]y = 2x+7[/tex].
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Solve 3-(2x-5)<-4(x+2)
Answers
Answer:
Step-by-step explanation:
3-(2x-5)=-4(x+2)
We simplify the equation to the form, which is simple to understand
3-(2x-5)=-4(x+2)
Remove unnecessary parentheses
3-2x+5=-4*(x+2)
Reorder the terms in parentheses
3-2x+5=+(-4x-8)
Remove unnecessary parentheses
+3-2x+5=-4x-8
We move all terms containing x to the left and all other terms to the right.
-2x+4x=-8-3-5
We simplify left and right side of the equation.
+2x=-16
We divide both sides of the equation by 2 to get x.
x=-8
Answer:
x < - 8
Step-by-step explanation:
Given
3 - (2x - 5) < - 4(x + 2) ← distribute parenthesis on both sides
3 - 2x + 5 < - 4x - 8
- 2x + 8 < - 4x - 8 ( add 4x to both sides )
2x + 8 < - 8 ( subtract 8 from both sides )
2x < - 16 ( divide both sides by 2 )
x < - 8
HELPPPPP ASP PLZZZZZ
Answers
Answer:
[tex](f-g)(x)[/tex]
[tex]f(x)-g(x)[/tex]
[tex]x^{2} -6x-27-x+9[/tex]
[tex]x^{2} -7x-18[/tex]
----------------------
[tex](f*g)(x)[/tex]
[tex]=f(x)g(x)[/tex]
[tex](x^{2} -6x-27)(x-9)[/tex]
[tex]=x^{3} -15x^{2}+27x+243[/tex]
----------------------
[tex]\frac{f}{g} (x)[/tex]
[tex]\frac{x^{2} -6x-27}{x-9}[/tex]
[tex]\frac{(x-9)(x+3)}{x-9}[/tex]
[tex]x+3[/tex]
-----------------------
[tex](f+g)(x)[/tex]
[tex]f(x)+g(x)[/tex]
[tex]=x^{2} -6x-27+x-9[/tex]
[tex]=x^{2} -5x-36[/tex]
------------------------
OAmalOHopeO
------------------------
evaluate the ratio 2.8×10^9:0.4×10^7 in standard form
Answers
please mark this answer as brainlist
find the missing side. round your answer to the nearest tenth. PLEASE HURRY
Answers
Answer:
5.4
Step-by-step explanation:
cos(theta) = B/H
cos(75)=x/21, x=5.4
Can someone please help me with this math problem
Answers
We have [tex]f\left(f^{-1}(x)\right) = x[/tex] for inverse functions [tex]f(x)[/tex] and [tex]f^{-1}(x)[/tex]. Then if [tex]f(x) = 2x+5[/tex], we have
[tex]f\left(f^{-1}(x)\right) = 2f^{-1}(x) + 5 = x \implies f^{-1}(x) = \dfrac{x-5}2[/tex]
Then
[tex]f^{-1}(8) = \dfrac{8-5}2 = \boxed{\dfrac32}[/tex]
• What is the constant term in the expression 3x + 11?
Answers
Answer:
11
Step-by-step explanation:
A constant term in an expression or equation contains no variables. In other words, it’s just number on its own. For example: f (x) = 2x2 + 3 (the constant term is 3). Other examples of constant terms: 5, -99, 1.2 and pi (π = 3.14…).
Answer: Constant = 11
Concept:
In an algebraic expression, there are three main kinds of terms:
Constants: an individual numberVariable: the unknown valueCoefficient: the number before a variableIf you are still confused, you may refer to the attachment below for a graphical explanation.
Solve:
Given expression: 3x + 11
As we know, the constant is defined as an individual number. Thus, as we can see from the given expression, 11 is the only number that is isolated and being an individual.
Hope this helps!! :)
Please let me know if you have any questions
Function: y = x^2+ 5x - 7
Vertex:(
Solutions:(
and
Answers
Answer:
Vertex: [tex](-\frac{5}{2} , -\frac{53}{4})[/tex]
Solutions: (0,-7), (1, -1), (2, 7)
I hope this helps!
Find a fraction equivalent to 2/3 that has a denominator of 6. Then add the fraction to 1/6. What is the sum?
THIS IS FROM SAXON MATH
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Answers
5/6
Step-by-step explanation:
2/3 is equal to 4/6 and if you add 1/6 + 4/6 you get 5/6
Answer:
Step-by-step explanation:
4/6 is equivalent to 2/3 (Times by two).
Since we now have a fraction with the denominator of 6, we can add 1/6 easily.
4/6 + 1/6 = 5/6
The sum is 5/6
(07.03. 07.04 MC)
Part A: The area of a square is (4x2 + 20x + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show
your work (5 points)
Part B: The area of a rectangle is (4x2 - 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work
(5 points)
Answers
Answer:
A) 4x^2+20x+25=(2x)^2+2*(2x)*5+5^2=(2x+5)^2
Area=(side)^2, side=sqrt(area)=sqrt((2x+5)^2)=2x+5
B) 4x^2-9y^2=(2x-3y)(2x+3y), these are the dimensions of the rectangle
A) The length of each side of the square is (2x + 5).
B) The dimensions of the rectangle are (2x - 3y) and (2x + 3y).
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that,
Part A: The area of a square is [tex](4x^2 + 20x + 25)[/tex] square units.
Part B: The area of a rectangle is [tex](4x^2 - 9y^2)[/tex] square units.
A) Now the length of each side of the square is calculated by factoring the area expression completely,
[tex](4x^2 + 20x + 25)[/tex]
[tex]4x^2 + (10 + 10)x + 25[/tex]
[tex]4x^2 + 10x + 10x + 25[/tex]
[tex]2x (x + 5) + 5(2x + 5)[/tex]
[tex](2x + 5) (2x+5)[/tex]
Hence the length of each side of the square is (2x + 5).
B) the dimensions of the rectangle are calculated by factoring the area expression completely,
[tex](4x^2 - 9y^2)[/tex]
[tex](2x)^2 - (3y)^2[/tex]
[tex](2x - 3y) (2x + 3y)[/tex]
Therefore, the dimensions of the rectangle are (2x - 3y) and (2x + 3y).
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Choose Yes or No to tell if each statement is true.
3
.
072
>
3
.
2
Choose...
728
.
307
>
729
.
07
Choose...
12
.
040
=
12
.
04
Choose...
531
.
135
<
531
.
315
Choose...
Answers
Answer:
1. No 2. No 3. Yes 4. Yes
Step-by-step explanation:
Compare the value of each digit from the leftmost digit.
Select the correct answer.
Select the function that defines the given sequence.
-8, -20, -50, –125, 625,...
ОА
- 1)
f(n) = -8-()
n-
OB.
- 1)
= -8.(29)
OC f(1) = -8
f(n) = f(n − 1), for n = 2, 3, 4, ...
OD. (1) = 8
f(n) = - . 1(n − 1), for n = 2, 3, 4, ...
Answers
Answer:
Option C
Step-by-step explanation:
f(1) = -8
f(2) = -5/2×-8 = -20
f(3) = -5/2×-20 = -125
.
.
.
So option C is the answer
Answer:
C. a1 = -8
an = an-1 * 5/2 for n >1
Step-by-step explanation:
-8, -20, -50, –125, 625,...
We need to find the common ratio
Take the second term and divide by the first term
-20/-8 = 5/2
Take the third term and divide by the second term
-50/-20 = 5/2
The common ratio is 5/2
A geometric sequence is
an = a1 * r^(n-1)
an = -8 *(5/2)^(n-1)
We can also write a recursive formula
a1 = -8
an = an-1 * 5/2 for n >1
6. Order these fractions from least to
greatest:
2/3
7/12
3/4
Answers
2/3 = 8/12
7/12 = 7/12
3/4 = 9/12
7/12 < 8/12 < 9/12
So, 7/12 < 2/3 < 3/4
Help pls and thank you :)
Answers
Answer: B
[tex]tan(N)=\frac{opposite}{adjacent}=\frac{n}{r}[/tex]
Help ive been stuck on this forever
Answers
Answer:
3480
Step-by-step explanation:
It always help if you make clear how the state assesses taxes. Usually it is done the way I will do it, but it is no guarantee.
First 3000 = 3000 * 2/100 = 60.00
The next 2000 (excess over 3000) = 2000 * 3/100 = 60
The next 12000 (excess over 5000) = 12000 * 5/100 = 600
The next step would be excess over 12000 = 48000 * 5.75/100 = 2760
That's the way most taxes for federal taxes and state taxes work. What you have to know is this: does the question use the term excess anywhere? Or do your notes. If you are accustomed to the word then this is the way the question is done.
So the total taxes = 60 + 60 + 600 + 2760 = 3480
