An aircraft is timetabled to travel from A to B. Due to bad weather it flies from A to C then from C to B, where AC and CB make angles of 27° and 66° respectively with AB. If |AC| = 220 km, calculate |AB|.
Answer:
|AB| = 240 km
Step-by-step explanation:
Finding ∠C :
⇒ 27° + 66° + ∠C = 180°
⇒ ∠C = 180° - 93°
⇒ ∠C = 87°
Applying the Law of Sines :
⇒ sin 66° / 220 = sin 87° / AB
⇒ 0.913545458 / 220 = 0.998629535 / AB
⇒ AB = 220/0.913545458 x 0.998629535
⇒ AB = 240.819981 x 0.998629535
⇒ AB = 240.489946
⇒ |AB| = 240 km (nearest whole kilometer)
Answer:
|AB| = 240 km (nearest km)
Step-by-step explanation:
Draw a sketch with the given information (attached).
Calculate the missing angle (shown in red on the attached diagram).
Given:
∠CAB = 27°∠CBA = 66°The interior angles of a triangle sum to 180°
⇒ ∠ACB + ∠CAB + ∠CBA = 180°
⇒ ∠ACB + 27° + 66° = 180°
⇒ ∠ACB = 180° - 27° - 66°
⇒ ∠ACB = 87°
Use Sine Rule for sides to calculate |AB|:
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
[tex]\implies \sf \dfrac{|AB|}{\sin ACB}=\dfrac{|AC|}{\sin CBA}[/tex]
[tex]\implies \sf \dfrac{|AB|}{\sin (87^{\circ})}=\dfrac{220}{\sin (66^{\circ})}[/tex]
[tex]\implies \sf |AB|=\dfrac{220\:\sin (87^{\circ})}{\sin (66^{\circ})}[/tex]
[tex]\implies \sf |AB|=240.4899459...[/tex]
[tex]\implies \sf |AB|=240\:km\:(nearest\:km)[/tex]
1. Kyle put $300 of his birthday money in the bank. The bank offers an annual interest rate of 4%, compounded twice a
year. How much money will Kyle have after three years?
Answer:
300(1 + 0.04/2)3(2) = $337.85
Step-by-step explanation:
Let g(x)= - |x+2|+2 What is the parent function of g(x)?
Here's the link to the answer:
https://riverside.rocks/index.php
Using the Data Set {125, 6, 133, 129, 125}, find the standard deviation:
the backyard is 20 inches long and 37 inches wide. What is the area of the backyard.
- - - - - - -- - - - - - - - - - - - - -- -
[tex]\diamond\large\textsf{\textbf{\underline{Given\:question:-}}}[/tex]
The backyard is 20 inches long and 37 inches wide. What is the area of the backyard?
[tex]\diamond\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
We are given the backyard's length (20 inches long) and the backyard's width (37 inches wide).
We are asked to find the area of the backyard, which can be found using the following formula:-
[tex]\boxed{\bold{A_{(rectangle)}=LW}}[/tex]
Where:-
A=Area of rectangleL=Length (20 inches)W=Width (37 inches)
Substitute the values:-
[tex]\boxed{\bold{A=20*37}}[/tex]
On simplification,
✳︎ [tex]\boxed{\bold{A=740\:in^2}}[/tex], which is our final answer.
Good luck with your studies.- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - -
Answer: 37·20=740
Step-by-step explanation:
a pentagon with sides 3 4 5 6 and 7 has area 48m. find the perimeter of a similar pentagon whose area is 27m
PLS RESPOND I WILL GIVE BRAINLIEST
Answer & step-by-step explanation:
See the image attached below:
Which set of numbers best describes the possible values of x in the equation below?
[x-1)=Lx]
all integer values of x
O all real number values of x
O only negative values of x
O only noninteger values of x
Answer:
Only noninteger values of x
Step-by-step explanation:
did this already
Only non integer values of x best describes the possible values of x in the equation [x-1]=[x]
What is Number system?A number system is defined as a system of writing to express numbers.
When x is an integer, the equation simplifies to [x-1] = [x], which means that the greatest integer less than or equal to (x-1) is equal to the greatest integer less than or equal to x.
This is only possible if x-1 and x are consecutive integers, so x must be an integer value of n + 1/2 for some integer n.
For non-integer values of x, we have x-1 < [x] < x, which means that [x] is equal to the greatest integer less than or equal to x-1.
So, the equation becomes x-1 < [x] < x, which simplifies to x-1 < x - {x} <= x, where {x} is the fractional part of x.
Therefore, we have x-1 < x - {x} and x - {x} <= x, which gives 1 < {x} and {x} <= 0, which is not possible.
Hence, the only values of x that satisfy the equation are non-integer values of x.
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NEED HELP ASAP 10 POINTS
Drag the values to order them from least to greatest with the least at the top 6pi-6, pi^3, and 99
Answer:
the square root of 99
6pi-6
pi^3
Step-by-step explanation:
The square root of 99 is approximately 9.9.
6pi-6 is approximately 12.8
pi^3 is approximately 12.8
Nadia is buying sweater for $17.69 and a pair of pants for $24.35. if Nadia pays with a $50 bill, how much change will she receive
Joey is putting all of his trophies onto 7 shelves. If he places 7 trophies on each shelf but still has 4 trophies left over, how many
trophies does he have?
OA. 53
OB. 35
OC. 18
OD. 49
Answer:
53
Step-by-step explanation:
7 * 7 = 49 + 4 = 53
Answer:
A. 53
Step-by-step explanation:
Find number of trophies on shelves:
7 shelves x 7 trophies each = 49 trophies on shelves
Find total number of trophies:
49 trophies on shelves + 4 leftover = 53 trophies overall
So the answer is A. 53
You pick a card at random.
6
7
8
9
What is P(less than 7)?
Write your answer as a fraction or
whole number.
Obisa has a radio which uses 18-volt batteries. Each battery has 1.5 volts. How many batteries does he need to use his radio?
Answer:
I believe he would need 12 batteries
Pleas help ppppppp pls
Step-by-step explanation:
option A is correct answer
An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.
Answer:
Length = 15.14, width = 7.14 and height = 2.43 inches.
( correct to the nearest hundredth).
Step-by-step explanation:
Let the lengths of the squares cut out be x inches.
Then the width of the box will be 12 - 2x and the length will be
20 - 2x inches.
The height of the box is x inches.
Volume V = x(20-2x)(12-2x)
To find the value of x when V is a maximum we find the derivative and equate it to zero.
V = x( 240 - 64x + 4x^2)
V = 4x^3 - 64x^2 + 240x
dV/dx = 12x^2 - 128x + 240 = 0
4(3x^2 - 32x + 60) = 0
This won't factor so we use the formula:
x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6
= 8.24, 2.43.
So one of these gives a maximum Volume.
The second derivative
d^2V/dx^2 = 24x - 128
When x = 8.24, this = 69.6 (positive) so this gives a minimum.
x = 2.43 gives a negative value ( -49.7) so this is the maximum
So the dimensions are:-
length = 20 - 2(2.43) = 15.14
width = 12 - 2(2.43) = 7.14
height = 2.43.
On his third math quiz of the semester, Cooper answered 28 questions correctly and got 7 wrong. What is the ratio of the number of questions he got right on the quiz to the total number of questions?
Step-by-step explanation:
Given that Cooper answered 28 questions correctly and 7 incorrect answers, If the total number of questions is x,
let total number of questions be X,therefore X = 28+7
= 35
ratio of right answered questions to the total questions, R isR =
[tex] \frac{28}{35} [/tex]
=
[tex] \frac{4}{5} [/tex]
therefore, the ratio is 4:5
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = -8 - 1/2x
Step-by-step explanation:
1. Are the side lengths congruent?
2. Are the opposite sides parallel?
3. Are the adjacent sides perpendicular?
4. The most specific name for this quadrilateral is:
Answer:
opposite sides are congruentopposite sides are paralleladjacent sides are not perpendicularthe figure is a parallelogramStep-by-step explanation:
An easy way to determine the nature of the quadrilateral is to look at the lengths and midpoints of the diagonals. Adding and subtracting the coordinates of one end point from the other can tell what you need to know.
The diagonals of a parallelogram are mutual bisectors. The diagonals of a rhombus are perpendicular. The diagonals of a rectangle are congruent.
__
diagonal ACThe difference of end points of diagonal AC is ...
C -A = (7, 2) -(-6, 1) = (13, 1)
The sum of the end points of diagonal AC is ...
C +A = (7, 2) +(-6, 1) = (1, 3)
diagonal BDThe difference of end points of diagonal BD is ...
B -D = (0, 7) -(1, -4) = (-1, 11)
The sum of end points of diagonal BD is ...
B +D = (0, 7) +(1, -4) = (1, 3)
comparison of diagonalsmidpoints
The two diagonals have the same end point sum, (1, 3), meaning their midpoints are coincident. The figure is a parallelogram.
lengths
The lengths of the diagonals will be the same if the sum of squares of the coordinates of the end-point differences are the same.
Σ(C -A)² = 13² +1² = 170
Σ(B -D)² = (-1)² +11² = 122 ≠ 170 . . . . . not a rectangle
perpendicularity
The diagonals will be perpendicular if the "dot product" of the end-point differences is zero.
x1·x2 +y1·y2 = 13(-1) +1(11) = -2 ≠ 0 . . . . not a rhombus
The most specific name for this quadrilateral is parallelogram.
_____
Opposite sides of a parallelogram are congruent and parallel.
Adjacent sides of a rectangle are perpendicular. This is not a rectangle, so adjacent sides are not perpendicular.
A parallelogram that is not a rectangle or rhombus is described most specifically as a parallelogram.
4. (x + 4)2 + (y – 5)2 = 25
Center:
Radius:
Answer:
Center = (-4, 5)
Radius = 5
Step-by-step explanation:
Equation of a Circle :
(x - h)² + (y - k)² = r²(h, k) = coordinates of the centerr = radiusFinding the center :
h = -(4) = -4k = 5Center = (-4, 5)Finding the radius :
r² = 25r = √25radius = 5What are practical situations of geometric series.
Answer:
One of the practical situation of geometric series is : A ball bouncing is an example of a finite geometric sequence. Each time the ball bounces it’s height gets cut down by half. If the ball’s first height is 4 feet, the next time it bounces it’s highest bounce will be at 2 feet, then 1, then 6 inches and so on, until the ball stops bouncing
Answer:
Geometric series are seen in practical situations, most notably in those involving geometric growth or decay. If a series of numbers are formed by percentages, then it can result in a geometric sequence. Ex. compound interest (see below).
Step-by-step explanation:
A geometric series is the result of adding the terms of a geometric sequence. These sequences have a common ratio, r, which is used to find missing terms. The common ratio is found with [tex]r=\frac{a_n}{a_{n-1}}[/tex]. For example, [tex]a_1(r)=a_2, \mbox{ and } a_2(r)=a_3... \mbox{ etc.}[/tex]
Geometric sequences can be used to model practical situations, and such situation could involve geometric growth or decay.
A geometric sequence can be used to model compound interest. An example of this is [tex]A = P (1 + \frac{r}{100})^n[/tex] where the common ratio, r, of the series is equal to 1 + r/100 in the compound interest formula above.
Which statements describe the graph of 2 and StartFraction 8 over 9 EndFraction greater-than-or-equal-to x on a number line? Select three options. There is an open circle on 2 and StartFraction 8 over 9 EndFraction. The graph contains the point 0 There is a closed circle on 2 and StartFraction 8 over 9 EndFraction. The arrow points to the left. The arrow points to the right.
Inequalities help us to compare two unequal expressions. The options that are correct about the given statement are B, C, and D.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The points that are correct about the given inequality 2(8/9)≥x are:
The graph contains the point 0There is a closed circle on 2 and StartFraction 8 over 9 EndFraction.The arrow points to the left.Hence, the options that are correct about the given statement are B, C, and D.
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Hannah earns $4.50 each hour walking dogs. How much money will Hannah earn after 8
hours
Answer:
36 dollars
Step-by-step explanation:
4.50 times 8 = 36 dollars
What is the range of this data set? {5, 12, 15, 11, 15, 7, 15, 10, 13}
8
10
12
15
Answer:
B) 10
Step-by-step explanation:
The range of a data set is found by subtracting the smallest term given in the set from the largest term given in the set. First, set the terms in order from least to greatest:
5 , 7 , 10 , 11 , 12 , 13 , 15 , 15, 15 ,
Subtract the greatest (15) with the least (5): 15 - 5 = 10
B) 10 is your answer.
~
Answer:
The answer is b) 10
Step-by-step explanation:
i took the test
d. Your doctor tells you you are in the 30th percentile for blood pressure among US adults. What is your systolic BP? Round to 2 decimal places.
Using the normal distribution, it is found that your systolic blood pressure is of 110.45.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Researching the problem on the internet, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 122, \sigma = 22[/tex].
The 30th percentile is X when Z = -0.525, hence your BP is given as follows.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.525 = \frac{X - 122}{22}[/tex]
X - 122 = -0.525 x 22
X = 110.45.
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What is the area of the triangle in the coordinate plane?
36 units²
38 units²
66 units²
72 units²
Answer:
36 units
Step-by-step explanation:
area of right angle triangle =1/2* b*h.
by counting the square,b=8 units and h=9 units
therefore,area 1/2* 8units * 9units
1/2*72units^2
36units^3
Out of 270 students in 6th grade, only 60% are going on the field trip. How many students are NOT going on the field trip
Step-by-step explanation: answer: 108
270
[tex]270 \times \frac{60}{100} [/tex]
[tex]27 \times 6 = 162[/tex]
270=60%
60% =162
40% = not going
270 students - 60% 162= 108
→108 students are not going
Answer:
270 students - 60% 162= 108
Step-by-step explanation:
Between which x-values and y-values does the cluster lie
Answer:
See below ~
Step-by-step explanation:
x-values :
Lowest : 2Highest : 10Lies between 2 and 10y-values :
Lowest = 4Highest = 11Lies between 4 and 11Answer:B
Step-by-step explanation: The cluster is the 5 points in the bottom right corner or; between x-values 8 and 10 and y-values 4 and 6.
Let A = {1, 2, 3} and R be the following relation on A;
R = {(1, 1), (1, 2), (1, 3), (3, 1), (2, 3)}
Answer:
The relation is reflexive as
(1,1),(2,2),(3,3)∈R
(2,1)∈R will not imply (1,2)∈R,
hence R is not symmetric
(2,1),(1,3)∈R doesn't imply (2,3)∈R, hence R is not transitive
Step-by-step explanation:
hope this helps if not let me know have a blessed day
PLEASE HELP!!
Suppose Lamar places
$4500 in an account that
pays 9% interest
compounded each year.
Assume that no withdrawals
are made from the account.
Follow the instructions
below.
Do not do any
rounding.
(a) Find the amount in the
account at the end of 1 year.
$__
(b) Find the amount in the
account at the end of 2
years.
$__
Answer:
A) $4,905 B) $5,310
Step-by-step explanation:
To get the answer, just simply add the amount by the percentage.
4,500 + 9% = A
For 2 years, just do 9 x 2 = 18 because it's 2 years
4,500 + 18% = B
Look at this equation.
6x - 4= -4(X-5)
What value of x makes the equation true?
Answer:
Step-by-step explanation:
Equation 6x - 4= -4(X-5) Remove the brackets
Solution
6x - 4 = -4x + 20 Add 4x to both sides
6x + 4x -4 = -4x+4x + 20 Combine
10x - 4 = 20 Add 4 to both sides
10x - 4 + 4 = 20 + 4 Combine
10x = 24 Divide by 10
10x/10 = 24/10
x = 2.4
Answer: x = 2.4
A rideshare service charges a flat fee of $6.00, plus $1.50 for every mile driven. Let t represent the total cost of the ride, and m represent the number of miles driven. Determine the dependent and independent variables, write an equation to represent this relationship, and then complete the table to show the total cost for riding 3 to 10 miles.
Answer:
The independent variable is m, while the dependent variable is t.
Step-by-step explanation:
What is the independent variable?An independent variable is a variable that does not rely on another variable to change its outcome. In this case, the variable 'm' does not rely on the ride's total cost.
What is the dependent variable?The dependent variable is a variable that depends on another variable to give its amount. In this case, 't' is the dependent variable, because it depends on how many miles were driven, in order to provide the correct answer.
Write an equation representing this relationship:t = $6 + ($1.50 x m)
Complete the table to show the total cost for riding 3 to 10 miles:3 miles: t = $6 + ($1.50 x m) or $10.50 = $6 + ($1.50 x 3)
4 miles: t = $6 + ($1.50 x m) or $12 = $6 + ($1.50 x 4)
5 miles: t = $6 + ($1.50 x m) or $13.50 = $6 + ($1.50 x 5)
6 miles: t = $6 + ($1.50 x m) or $15 = $6 + ($1.50 x 6)
7 miles: t = $6 + ($1.50 x m) or $16.50 = $6 + ($1.50 x 7)
8 miles: t = $6 + ($1.50 x m) or $18 = $6 + ($1.50 x 8)
9 miles: t = $6 + ($1.50 x m) or $19.50 = $6 + ($1.50 x 9)
10 miles: t = $6 + ($1.50 x m) or $21 = $6 + ($1.50 x 10)
