Answer:
3,200
Step-by-step explanation:
3 is less than 5 so you round down to 3,200
1) A 22-ft ladder is leaning against a building. If the base of the ladder is 6 ft from the base of the building, what is the angle of elevation of the ladder? (Round your answer to one decimal place.)
2)How high does the ladder reach on the building? (Round your answer to the nearest whole number.)
Answer:
21.9 ft
Step-by-step explanation:
Answer:
Part A)
About 74.2°.
Part B)
About 21 feet.
Step-by-step explanation:
A 22 feet ladder is leaning against a building, where the base of the ladder is six feet from the base of the building.
This is shown in the diagram below (not to scale).
Part A)
We want to determine the angle of elevation of the ladder. That is, we want to find the value of θ.
Since we know the values adjacent to θ and the hypotenuse, we can use the cosine ratio. Recall that:
[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent is 6 and the hypotenuse is 22. Thus:
[tex]\displaystyle \cos \theta = \frac{6}{22} = \frac{3}{11}[/tex]
Take the inverse cosine of both sides:
[tex]\displaystyle \theta = \cos^{-1}\frac{3}{11}[/tex]
Use a calculator. Hence:
[tex]\displaystyle \theta = 74.1733...\approx 74.2^\circ[/tex]
The angle of elevation is approximately 74.2°
Part B)
We want to find how high up the ladder reaches on the building. In other words, we want to find x.
Since x is opposite to θ and we know the adjacent side, we can use the tangent ratio. Recall that:
[tex]\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]
The opposite side is x and the adjacent side is 6. The angle θ is cos⁻¹(3/11) (we use the exact form to prevent rounding errors). Thus:
[tex]\displaystyle \tan \left(\cos^{-1}\frac{3}{11}\right) = \frac{x}{6}[/tex]
Solve for x:
[tex]\displaystyle x = 6 \tan \left(\cos^{-1}\frac{3}{11}\right)[/tex]
Use a calculator. Hence:
[tex]x = 21.1660... \approx 21\text{ feet}[/tex]
The ladder reaches about 21 feet up the building.
in isosceles triangle XYZ, angle X=117°. calculate angleZ
Answer:
31.5
Step-by-step explanation:
Angle Z+ Angle X+ Angle Y=180
As the triangle is isosceles, Z=X, hence Z=63/2=31.5
Which exponential expression is equivalent to (4x^2 y^3)^2
Answer:
[tex] 16 {x}^{4} {y}^{6} [/tex]
Step-by-step explanation:
[tex](4 {x}^{2} {y}^{3} {)}^{2} [/tex]
➡️ [tex] {4}^{2} \times ( {x}^{2} {)}^{2} \times ( {y}^{3} {)}^{2} [/tex]
➡️ [tex] = 16 {x}^{4} {y}^{6} [/tex] ✅
How many different ways can you represent the weight in 1000g?
Jamal and Sean plan to make T-shirts to sell at a fair. Jamal plans to make 6 T-shirts
each day and Sean plans to make 4 T-shirts each day. On which day will Jamal have
made 12 more T-shirts than Sean?
Answer:
Jamal will have made 12 more T-shirts than Sean on the 6th day.
Step-by-step explanation:
1 day for Jamal - 6 T-shirts. 1 day for Sean - 4 T-shirts. 2 day for Jamal - 12 T-shirts. 2 day for Sean - 8 T-shirts. 3 day for Jamal - 18 T-shirts. 3 day for Sean - 12 T-shirts. 4 day for Jamal - 24 T-shirts. 4 day for Sean - 16 T-shirts. 5 day for Jamal - 30 T-shirts. 5 day for Sean - 20 T-shirts. 6 day for Jamal - 36 T-shirts. 6 day for Sean - 24 T-shirts. Number between 24 and 36 = 12.
Both before and after a recent earthquake, surveys were conducted asking voters which of the three candidates they planned on voting for in the upcoming city council election. Has there been a change since the earthquake? Use a level of significance of 0.05. Table shows the results of the survey. Has there been a change in the distribution of voter preferences since the earthquake?
Peter Alan Sui
Before 1838 418 1475
After 1420 329 1140
What is the chi-square test-statistic for this data?
χ2=_____.
Answer:
0.05547
Step-by-step explanation:
Given :
_____Peter __ Alan __ Sui__total
Before 1838 __ 418 ___1475 _3731
After _ 1420 __ 329 ___1140_2889
Total _3258 __ 747 __ 2615 _6620
The expected frequency = (Row total * column total) / N
N = grand total = 6620
Using calculator :
Expected values are :
1836.19 __ 421.006 __ 1473.8
1421.81 ___325.994__ 1141.2
χ² = Σ(Observed - Expected)² / Expected
χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)
χ² = 0.05547
Can someone help with this please
Answer:
x2 1-
Step-by-step explanation:
Answer:
x ≥ 0
Step-by-step explanation:
Domain of a function is the x values of a function
The graph extends from 0 to positive infinity.
Since the point at x=0 is closed, the graph includes 0
help fast pleasee
find the unit rate for Dion and Emily who read faster?
Dion: 36 pages in 3 days
emily: 45 pages in 5 days
36 pages
__________= ? pages per day.
3 days
45 pages
_________=? pages per day.
5 days
deon read _____ pages per day than emily.
Step-by-step explanation:
36 pages in 3 days, 36/3=12 pages per day.
45 pages in 5 days, 45/5=9 pages per day.
Difference is 3 pages per day
Answer:
Deon read 3 more pages per day than Emily.
Please help me with this question
Find the difference between each number:
-11 to -3 is +8
-3 to 5 is +8
The difference is 8
Use the following formula:
Bn = b1 + d(b -1)
Answer: bn = -11 + 8( b-1)
I are these orders pairs a function
х,у
0,9
2,8.
4,7
6,6
8,5
10,4
9514 1404 393
Answer:
yes
Step-by-step explanation:
No x-value is repeated, so these ordered pairs do represent a function.
Devy likes to learn! Could someone please tell me how to answer this question?
If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?
On a coordinate plane, a straight line has a positive slope and goes through (negative 2, negative 1), (0, 0), and (4, 2).
On a coordinate plane, a straight line has a positive slope and goes through (negative 3, negative 3), (0, 0), and (3, 3).
On a coordinate plane, a straight line has a negative slope and goes through (negative 4, 2), (0, 0), and (4, negative 2).
On a coordinate plane, a straight line has a negative slope and goes through (negative 3, 3), (0, 0), (3, negative 3).
Answer:
B
Step-by-step explanation:
Recall that if two functions, f and g, are inverses, then by definition:
[tex]\displaystyle f(g(x)) = g(f(x)) = x[/tex]
Hence, the graph of f(g(x)) should be simply y = x.
Therefore, our answer is B, as both coordinates are equivalent for all three points.
Which of the following options correctly represents the complete factored
form of the polynomial F(x) = x^3- x2 - 4x-6?
A. F(x) - (x - 3)(x + 1 + I)(x+1- I)
B. F(x) = (x - 3)(x+1+I)(x-1-I)
C. F(x) = (x+3)(x + 1)(x - 1)
D. F(x) - (x+3)(x+1+I)(x +1-I )
The completely factored form for the given algebraic expression is f(x) = (x-3)(x+1+i)(x+1-i).
What is a completely factored polynomial?A completely factored polynomial is a polynomial that can no longer be further simplified. A completely factored polynomial can be expressed as a root of its own equation.
Given that:
f(x) = x³ - x² - 4x - 6
To express this as a factored polynomial using the rational:
f(x) = (x-3)(x²+2x+2)
f(x) = (x-3)(x+1+i)(x+1-i)
Learn more about how to completely factor polynomial here:
https://brainly.com/question/11434122
#SPJ1
Which graph represents the equation x2 = 8y? On a coordinate plane, a parabola opens up. It has a vertex at (0, 0), a focus at (0, 8), and a directrix at y = negative 8. On a coordinate plane, a parabola opens up. It has a vertex at (0, 0), a focus at (0, 2), and a directrix at y = negative 2. On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0), a focus at (2, 0), and a directrix at x = negative 2. On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0), a focus at (8, 0), and a directrix at x = negative 8.
Answer:
The parabola x²=8y has,
vertex: (0,0)
focus: (0,2)
directrix: y=-2
so that option is the answer,
btw, the parabola opens up to the top and axis of symmetry is x=0
Answer:
It's A!
Step-by-step explanation:
Got it correct on my test! :)
FIND THE AREA OF THE SHAPE BELOW
PLEASE HELP I HAVE BEEN STUCK ON THIS FOREVERRRR!!
THANK YOU
Answer:
Is answer 22 units sqaure ?
To study the mean respiratory rate of all people in his state, Frank samples the population by dividing the residents by towns and randomly selecting 12 of the towns. He then collects data from all the residents in the selected towns. Which type of sampling is used
Answer:
Cluster Sampling
Step-by-step explanation:
Cluster Sampling involves the random sampling of observation or subjects, which are subsets of a population. Cluster analysis involves the initial division of population subjects into a number of groups called clusters . From the divided groups or clusters , a number of groups is then selected and it's elements sampled randomly. In the scenario above, the divison of the population into towns where each town is a cluster. Then, the selected clusters (12) which are randomly chosen are analysed.
If f(x) = 4x + 3 and g(x) = 22 – 3, then f(g(4)) = ???
Answer:
f(g(4))=79
Step-by-step explanation:
given:
f(x) = 4x + 3
g(x) = 22 – 3
g(x) = 19
the x in parentheses represents x's value. if it is just x then example f(x)=3x would be 3x. if f(x) was f(2)=3x, then x would be 2 and f(2)=3x would be 3*2=6
f(g(4))
first solve g(4)
g(x) = 19
g(4)=19 because there are no x
then substitute
f(g(4))
f(19)
f(19) = 4x + 3
all x become 19
f(19) = 4(19) + 3
=76+3
=79
hope this helps.
Solve each system by graphing.
Answer:
(2,-1)
Step-by-step explanation:
Solved using math.
Answer:
The solution is (2, -1) to show this by graphing do y = -1 by making a straight horizontal line at (0,-1) . And then for the other equation make a line where it starts at (0,4) and passes point (2,-1). Just plot those two points and connect them and you'll have made the line.
Step-by-step explanation:
A tank contains 9,000 L of brine with 18 kg of dissolved salt. Pure water enters the tank at a rate of 90 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.
(a) How much salt is in the tank after t minutes?
(b) How much salt is in the tank after 20 minutes?
Let x(t) denote the amount of salt (in kg) in the tank at time t. The tank starts with 18 kg of salt, so x (0) = 18.
The solution is drained from the tank at a rate of 90 L/min, so that the amount of salt in the tank changes according to the differential equation
dx(t)/dt = - (x(t) kg)/(9000 L) × (90 L/min) = -1/100 x(t) kg/min
or, more succintly,
x' = -1/100 x
This equation is separable as
dx/x = -1/100 dt
Integrating both sides gives
∫ dx/x = -1/100 ∫ dt
ln|x| = -1/100 t + C
x = exp(-1/100 t + C )
x = C exp(-t/100)
(a) Using the initial condition x (0) = 18, we find
18 = C exp(0) ==> C = 18
so that
x(t) = 18 exp(-t/100)
(b) After 20 minutes, we have
x (20) = 18 exp(-20/100) = 18 exp(-1/5) ≈ 14.74
so the tank contains approximately 14.74 kg of salt after this time.
equation that passes 1,3 and slope of 2 in point slope form
Answer:
y-3 = 2(x-1)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y-3 = 2(x-1)
Answer:
3=2x+1
Step-by-step explanation:
Use the equation y=mx+b
where y is the y component, x is the variable and b is the x intercept
Dia is 10 years old. How many years have to add with twice of her age to get 24?
Answer:
4
Step-by-step explanation:
twice her age:
10*2 = 20
24-20 = 4
Answer:
4 i believe that's the answer
what is a 200% increase of 50
Answer:
150
Step-by-step explanation:
Increase = New Number - Original Number.
divide the increase by the original number and multiply the answer by 100.
I hope this helped! :)If the volume of the expanding cube is increasing at the rate 24 cm3 / min , how fast is its surface area increasing when the surface area is 216 cm2 ?
Answer:
16 cm^2/min
Step-by-step explanation:
dV/dt=24
V=a^3, differentiate with respect to t
dV/dt=3a^2*da/dt, a^2*da/dt=8
S=6a^2, 216=6a^2. a=6. da/dt=(8/36)
dS/dt=12*a*da/dt=12*(8/6)=16 cm^2/min
Write the sum using summation notation, assuming the suggested pattern continues. 6, -18, 54, -162, +… Is this sequence arithmetic or geometric? Explain your answer.
Answer:
Hello,
This sequence is geometric with a ratio of -3
the first term is 6
Step-by-step explanation:
[tex]u_1=6\\u_2=-18=6*(-3)=u_1*(-3)\\u_3=54=-18*(-3)=u_2*(-3)=u_1*(-3)^2\\u_4=-162=u_3*(-3)=u_1*(-3)^3\\\\...\\u_{n+1}=u_1*(-3)^n\\\\\displaystyle \sum\limits^\infty _{i=1}u_i = \lim_{n \to \infty} \sum\limits^n _{i=1}u_1*(-3)^{i-1}\\=6*\lim_{n \to \infty} \sum\limits^\infty _{i=1}(-3)^{i-1}\\=6*\frac{1-(-3)^n}{1-(-3)} \\=\dfrac{3}{2} *({1-(-3)^n)\\[/tex]
serie does not converge.
What is the volume of a cone with a height of 6m and a diameter of 12m? Nearest meter.
Answer:
0.0005m^3
Step-by-step explanation:
V=1/3hπr²
h=6m
d=12m
r=12÷2=6m
V=1/3×6×(3.14)×36
V=1/2034.72
V=0.0005m^3
the graph of the parabola y=3(x+5)2-2 has vertex (-5,-2). if this parabola is shifted 1 unit down and 6 units to the right, what is the equation of the new parabola?
Answer:
y = 3(x-1)^2 -3
Step-by-step explanation:
y = 3(x+5)^2 - 2
vertex: (-5, -2)
1 unit down :
-2 - 1 = -3
6 units to the right:
3(x+5-6)^2 -2
3(x-1)^2 - 2
make what's in the parenthesis equal to 0:
(x-1)^2 = 0
x = 1
or
-5 + 6 = 1
new vertex : (1, -3)
equation : y = 3(x-1)^2 -3
Translation involves shifting of points from one position to another. The equation of the new parabola is: [tex]y = 3(x - 1)^2 - 3[/tex]
Given that:
[tex]y = 3(x + 5)^2 - 2[/tex]
[tex](h,k) = (-5,-2)[/tex] --- vertex
The general equation of a parabola is:
[tex]y = a(x - h)^2 + k[/tex]
By comparison:
[tex]a = 3\\ h = -5 \\ k= -2[/tex]
When the vertex is shifted 1 unit down, the rule is:
[tex](x,y) \to (x,y-1)[/tex]
So, we have:
[tex](x,y) \to (-5,-2-1)[/tex]
[tex](x,y) \to (-5,-3)[/tex]
When the vertex is shifted 6 unit right, the rule is:
[tex](x,y) \to (x + 6,y)[/tex]
So, we have:
[tex](h,k) \to (-5 + 6,-3)[/tex]
[tex](h,k) \to (1,-3)[/tex]
This means that:
[tex]h = 1\\ k =-3[/tex]
Recall that:
[tex]a =3[/tex]
Substitute these values in:
[tex]y = a(x - h)^2 + k[/tex]
[tex]y = 3(x - 1)^2 - 3[/tex]
Hence, the equation of the new parabola is: [tex]y = 3(x - 1)^2 - 3[/tex]
Read more about translations at:
https://brainly.com/question/12463306
A triangle is rotated 90° about the origin. Which rule describes the transformation?
(x, y) (-x, -y)
O(x,y) (-y, x)
(x, y) (-), -x)
(x,y) →ly, -x)
Answer:
(x,y) -> (-y,x), second option.
Step-by-step explanation:
Rotation of 90 degrees about the origin:
The rule for a rotation of a point (x,y) 90 degrees about the origin is given by:
(x,y) -> (-y,x)
This is that the question asks, and so, this is the answer, which is the second option.
If 6.45% of the battery life of each mobile phone is used in a day by a typical user, for which mobile phone is 1.6125 hours of battery life used in a day?
The table shows the battery life of four different mobile phones. Mobile Phone Battery Life Phone Battery Life (hours) A 20 B 25 C 10 D 18 If 6.45% of the battery life of each mobile phone is used in a day by a typical user, for which mobile phone is 1.6125 hours of battery life used in a day?
B
Should be the answer
Which best describes the relationship between the lines with equations 2x – 9y = 1 and x + 8y = 6?
A. perpendicular
B. neither perpendicular nor parallel
C. parallel
D. same line
9514 1404 393
Answer:
B. neither perpendicular nor parallel
Step-by-step explanation:
If the lines were perpendicular, the coefficients would be swapped and one negated. (You would have 8x -y = c, or 9x +2y = c in the system.)
If the lines were parallel, the coefficients in the two equations would only differ by a common factor. (Both equations would reduce to 2x -9y = c, or x +8y = c.)
The lines are not the same line (coefficients are different).
So, the only reasonable description is ...
neither perpendicular nor parallel
A ray of light passing from air through an equilateral glass prism undergoes minimum
deviation, when the angle of incidence is 3/4th of the angle of prism. If the speed of light
in air is 3x10^8m/s, calculate the speed of light in the prism?
Answer: 45° and speed of light in prism 2×10⁸m/s
Step-by-step explanation:
The minimum deviation of the equilateral glass prism will form 60° angle.
So angle of incidence = 3/4×60
= 3 ×15
= 45°
Minimum deviation = δmin
= 30
After finding the value of μ using prism law
μ = 1.41
Speed of light will be 2×10⁸m/s
Must click thanks and mark brainliest
pls help! I need the answer quickly! thank you!
Answer:
C) 82/2
Step-by-step explanation:
The area of a square is calculated by multiplying a side by itself
so one side of the square is 9 in
the area of a triangle is calculated by multiplying height and base and that divided by 2
since E is the midpoint, if we draw a line show the height from there
the height would be 9
9*9/2 = 82/2
