Answers
90-7 =83 degrees
height = 3 miles
divide 3 by the cos of 83 degrees
3/cos(83) = 24.6165
rounded to nearest mile = 25 miles
Related Questions
An isosceles trapezoid has bases of 4 and 10. If the base angle is 45°, find the area.
A: 42 sq. units
B: 21√2 sq. units
C: 21 sq. units
Answers
DC, the larger one (=10)
From A & B draw the altitude AA' & BB'. You notice that ABA'B' is a rectangle and A'B' = 4,. You conclude that DA' = B'C = 3 .
Now let's calculate the altitude AA'.
The right triangle ADA' is also an isosceles right triangle:
( angle DA'A=90, angle ADA' = 45 and angle DAA' =45) , then
DA' = AA' (altitude) = 3 units. Now we can calculate the area of the trapezoid:
Area = (B+b).H/2
Area = (4+10)x3/2 = 14x3/2 = 42/2 = 21 sq.unit
Answer:
21 sq. units
Step-by-step explanation:
what is the vaule of 3.85+0.004+0.117 ?
Answers
How can x2 = x2 + 2x + 9 be set up as a system of equations?
Answers
Final answer:
To set up x^2 = x^2 + 2x + 9 as a system of equations, we would have x^2 = x^2 + 2x + 9 and x = -4.5.
Explanation:
To set up x2 = x2 + 2x + 9 as a system of equations, we can separate it into two separate equations:
Equation 1: x2 = x2 + 2x + 9
Equation 2: 0 = 2x + 9
By rearranging Equation 2, we can rewrite it as:
x = -4.5
Therefore, the system of equations for x2 = x2 + 2x + 9 is: x2 = x2 + 2x + 9 and x = -4.5.
you invest 2,600 in an account that pays an interest rate of 8.5% compounded continuously. Calculate the balance of your account after 5 years
Answers
A=p e^rt
A future value?
P present value 2600
R interest rate 0.085
T time 5years
E constant
A=2,600×e^(0.085×5)
A=3,976.94
Given the point (5, 6) and the slope of 5, find y when x = 21.
Answers
6=5(5)+b
6=25+b
-19=b
y=5x-19
y=5(21)-19
y=105-19
y=86
Final answer: y=86
The standard form of the equation of a parabola is x=y^2+6y+1. What is the vertex form of the equation?
A. X=(y+3)^2-8
B. X=(y+3)^2-5
C. X=(y+6)^2-35
Answers
What you want to do is get the quadratic (y^2+6y+1) into it's root factor form, in other words, the quantity of (y+what) squared will equal y^2+6y+1. Well it's not a perfect square so we'll have to play around with it a little.
In the format ay^2 + by + c, completing the square first requires finding out what value would do that: c = (b/2)^2 = (6/2)^2 = 3^2 = 9
So we need y^2+6y+1 to have the last number (c) to equal 9 to have (y+b/2)^2, or (y+3)^2
How do we get 9 down to the 1 that we have for c?? 9-1=8, so just subtract 8.
That means that y^2+6y+1 is the same as (y^2+6y+9)-8, and y^2+6y+9 = (y+3)^2, so now we have: y^2+6y+1 = (y+3)^2-8, which is answer [A]
a gas-filled balloon rises 40 feet in the 1st minute, 60 feet in the 2nd minute, and 80 feet in the 3rd minute, how many feet will the balloon rise during the 15th minute?
Answers
so
[tex]g_1=40[/tex] ft , means that in the 1st minute, the balloon rose 40 feet
[tex]g_2=60[/tex] ft, means : in the 2nd minute the balloon rose 60 feet
[tex]g_3=80[/tex]
we notice that each minute, the balloon rises a multiple of 20, feet:
[tex]g_1=40=2*20[/tex]
[tex]g_2=60=3*20[/tex]
[tex]g_3=80=4*20[/tex]
so it is clear that [tex]g_n=(n+1)*20[/tex]
during the 15th minute the balloon rises [tex]g_1_5=16*20=320[/tex](feet)
Answer: 320
Which of the relations given by the following sets of ordered pairs is a function?
Select one:
a. {
(2,4),(2,6),(2,8),(2,10),(2,12)
(2,4),(2,6),(2,8),(2,10),(2,12)
}
b. {
(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)
(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)
}
c. {
(0,3),(−6,8),(−3,5),(0,−3),(7,11)
(0,3),(−6,8),(−3,5),(0,−3),(7,11)
}
d. {
(8,1),(−4,1),(3,5),(0,4),(−1,2)
(8,1),(−4,1),(3,5),(0,4),(−1,2)
}
Answers
ur answer would be D....because ur x values (8,-4,3,0,-1) are all different
Since no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The relation might be put up as a table of ordered pairs. The next step is to determine if each element in the domain matches precisely one element in the range.
A function is a collection of ordered pairs where no two ordered pairs are the same in terms of x-coordinate. A function is defined by an equation that yields such a collection of paired objects.
The relations given by the following sets of ordered pairs is a function is,
d. {(8,1),(−4,1),(3,5),(0,4),(−1,2)(8,1),(−4,1),(3,5),(0,4),(−1,2)}
Thus, no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.
Learn more about the function here:
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Benny bought 5 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 43 cards left. How many cards did Benny start with?
Answers
One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 12$ and $a^5 b^5 = 7776$. what is the value of $a$ in this ordered pair?
Answers
To find the value of a in the ordered pair (a,b), we can solve the given equations. Substituting ab^4 with 12 in the second equation, we get a^5 (12)^5 = 7776. Solving for a gives a = 0.03125^(1/5) = 0.5.
Explanation:To find the value of a in the ordered pair (a,b), we can solve the given equations.
From the first equation, ab^4 = 12, we can substitute ab^4 with 12 in the second equation:
a^5 b^5 = 7776
This gives us:
a^5 (12)^5 = 7776
12^5 = 12 * 12 * 12 * 12 * 12 = 248,832
Dividing both sides of the equation by (12^5) gives:
a^5 = 7776 / (12^5) = 7776 / 248,832 = 0.03125
Taking the fifth root of both sides gives:
a = 0.03125^(1/5) = 0.5
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The cost of painting a circular traffic sign is $3.50 per square foot. How much, to the nearest dollar, will it cost to paint the sign if its diameter measures 36 INCHES.
Answers
area of a circle = pi x r^2
using 3.14 for pi
radius = 36/2 =18
area = 3.14 x 18^2 = 1017.36 square inches
1 sq ft = 144"
1017.36/144 = 7.065 sq ft
7.065*3.50 = $24.73 to the nearest dollar = $25
Find the area of the triangle with the given measurements. round the solution to the nearest hundredth if necessary. b = 107°, a = 10 cm, c = 22 cm
Answers
Answer:
105.19 cm²
Step-by-step explanation:
The applicable area formula is ...
area = (1/2)ac·sin(B) = (1/2)(10)(22)sin(107°) ≈ 105.19 cm²
How to convert decimal to binary by hand?
Answers
10 : 2 = 5 | 0
5 : 2 = 2 | 1
2 : 2 = 1 | 0
1 : 2 = 0 | 1
↑
Finally: 10 ( decimal ) = 1010 ( binary )
the price of 9-volt batteries is increasing according to the function below, where t is years after January 1, 1980. During what year will the price reach $4? use formula P(t)=1.1*e^0.047t A.)2007 B.)2005 C.)2003 D.)2009
Answers
40/11=e^(0.047t) take the natural log of both sides
ln(40/11)=0.047t divide both sides by 0.047
t=ln(40/11)/0.047
t≈24.5
1980+24.5
2007.5
So during 2007 the price will reach $4.
Answer:
The option A.) 2007 is correct
Step-by-step explanation:
The formula which is to be used is given :
[tex]P(t) = 1.1\cdot e^{0.047t}[/tex]
where P(t) is the function of time t and t is the time in years after January 1 , 1980
Now, we need to find the year when the price will reach $4
So, substituting P(t) = 4 and finding the value of t from the given equation.
[tex]\implies 4=1.1\cdot e^{0.047t}\\\\\implies 3.64=e^{0.047t}\\\\\text{Taking natural log ln on both the sides}\\\\\implies \ln 3.64=\ln e^{0.047t}\\\\\implies 1.29=0.047\cdot t\\\\\implies t = 27.49[/tex]
So, t = 27.49 which is approximately equals to 27.5 years
So, 27.5 years after January 1, 1980 is the year 2007
Hence, The price will reach $4 in the year 2007
Therefore, The option A.) 2007 is correct
Let f(x) = 16x5 − 48x4 − 8x3 and g(x) = 8x2. Find f of x over g of x.
Answers
2x^3-6x^2-x
It is given in the question that
[tex]f(x) = 16x^5 -48x^4-8x^3 \ and \ g(x) = 8x^2[/tex]
And we have to find the value of
[tex]\frac{f(x)}{g(x)}[/tex]
Substituting the values of two functions, we will get
[tex]=\frac{16x^5 -48x^4 -8x^3}{8x^2}[/tex]
8x^3 is common in the numerator, and on taking it out, we will get
[tex]= \frac{8x^3(2x^2 -6x-1)}{8x^2} = x(2x^2 -6x-1)[/tex]
And that's the required answer .
Can someone help me with this one real quick ? Thanks a lot! Please explain and show your work :)
Answers
You were given the proof.
b. Corresponding angles are congruent.
Since angles 1 and 2 are corresponding, then if one is 130, then the other one is also 130.
c. Vertical angles are congruent.
Angles 2 and 3 are vertical, meaning they'll also be congruent.
d. Transitive Property of Equality.
If angles 2 and 3 are vertical, then if 2 is 130, then 3 is also 130.
Find the equation of the line specified.
The slope is 3, and it passes through ( -4, -7).
a.
y = 6x + 5
c.
y = 3x - 7
b.
y = 3x + 5
d.
y = 3x - 19
Please select the best answer from the choices provided
A
B
C
D
Answers
B. y = 3x + 5
Answer:
B
Step-by-step explanation:
Edge 2021
what is the greatest integer that satisfies the inequality 3x-4≤8 ?
A.4
B.5
C.6
D.7
Answers
3x ≤ 12
x ≤ 4
answer
A.4
For example, answer choice "A.)";
3(4) -4 <_ 8
We plugged in 4 for x.
Let's see if A.) is correct.
3(4) -4 <_ 8
12 - 4 <_ 8
8 <_ 8
This is the GREATEST possible integer, as the question asks for what the highest possible number would match the inequality.
Your correct answer choice is "A.)"
I hope this helps!
Write an equation for each translation of y=lxl
7 units up
Answers
[tex]\bf % template detailing \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]
with that template in mind.. .let's see
[tex]\bf y=|x|\implies \begin{array}{lllcll} y=&1|&1x&+0|+&0\\ &\uparrow&\uparrow &\uparrow &\uparrow \\ &A&B&C&D \end{array}[/tex]
7 units up, meaning D = 7
Evaluate the limit lim h → 0 (−5 + h)2 − 25 h
Answers
(-5 + 0)^2 -25(0) = 25 -0 = 25
What is the slope of the line on the graph below?
A. -1/2
B. 1/2
C. 1
D. 2
Answers
---------------------------------------------------------------------
---------------------------------------------------------------------
Work Shown:
Pick any two points on the line. I'm going to pick (0,1) and (1,3)
Label these two points as (x1,y1) and (x2,y2).
So,
(x1,y1) = (0,1) meaning that x1 = 0 and y1 = 1
(x2,y2) = (1,3) meaning that x2 = 1 and y2 = 3
Now use the slope formula
m = (y2 - y1)/(x2 - x1)
m = (3-1)/(1-0)
m = 2/1
m = 2
Going from (0,1) to (1,3) we move 2 units up and 1 unit to the right.
The "2 units up" is the "rise"
The "1 unit to the right" is the "run"
Slope = rise/run = (change in y)/(change in x)
Answer:
d on edge
Step-by-step explanation:
Find the product of 543.1187 and 100
Answers
-x+3+5(2x-6)+9(3x+11) will you answer with work shown and answer
Answers
[tex]#-x + 3 + 5(2x - 6) + 9(3x + 11)# #-x + 3 + 10x - 30 + 27x + 99# Put the common terms together #-x + 10x + 27x + 3 + 99# #36x + 72#[/tex]
What is the value of
x/3y, when x = 18 and y = 3?
Answers
x=18 and y=3
[tex]\frac{18}{(3)(3)}=\frac{18}{9}=2[/tex]
this has been asked at least 3 times so far today
18/3*3 = 18/9 = 2
answer is 2
HELPPPPPP make sure your right !:)
Answers
Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account. What rate of interest did she earn? Use the formula A= Pe^rt, where A is the ending amount, P is the principal (initial amount), r is the interest rate, and t is time.
Answers
okay, what you want to do is plug in the numbers you already have, to get the number you don't have(r).
First, you plug in the numbers.
1. P= $2000
A=$2543
t= 4(years)
r=?
2543=2000^r(4)
Secondly, you want to solve the equation.
Answer:
Rate of interest = 6%
Step-by-step explanation:
Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account.
Use the formula,
[tex]A=Pe^{rt}[/tex]
[tex]P\rightarrow \$2000[/tex]
[tex]r\rightarrow ?[/tex]
[tex]A\rightarrow \$2543[/tex]
[tex]t\rightarrow 4\text{ years}[/tex]
Substitute the value into formula and solve r
[tex]2543=2000e^{4r}[/tex]
[tex]e^{4r}=1.2715[/tex]
Apply ln both sides
[tex]4r\ln(e)=\ln(1.2715)[/tex]
[tex]r=0.06[/tex]
Rate of interest = 6%
Hence, The rate of interest is 6%
What can you say about the function that generated the following table of values
Answers
best answer is b = it has exactly 1 x intercept
Answer:
B.
Step-by-step explanation:
We know that for x-intercept the graph crosses x-axis i.e the value of y = 0.
As in the table, the value of y is changing from negative to positive, so it will obtain the value y = 0 for some vale of x.
Therefore, this function will have only one x-intercept.
Hence, option A, C, D are discarded and option B is correct.
Find the equation of the perpendicular line passing through the midpoint of the line segment connecting (−1, 7) and (2, 3). incorrect: your answer is incorrect.
Answers
A stick 42 inches long is broken into two pieces, so that one piece is twice as long as the other one. How long are the two pieces ?
Answers
Let the shorter piece be x inches.
Thus, the longer piece is 2x.
2x + x = 42
3x = 42
x = 14
Therefore, the length of the two pieces are 14 inches and 28 inches.
The answer is 14 inches and 28 inches:
Total length of stick = 42 inches.
Let the shorter piece be x inches.
Thus, the longer piece is 2x.
2x + x = 42
3x = 42
x = 14
Therefore, the length of the two pieces are 14 inches and 28 inches.
Simplify 5(6x - (6 - 7y + 7x) + 6y)
-80x + 87y - 91
-5x + 65y - 30
-82x + 73y - 54
-60x + 9y - 17
None of the above
Answers
= 5(6x - 6 + 7y - 7x + 6y)
= 5(-x + 13y -6)
= -5x +65y -30
Hence, the answer is B.