A pilot flies 720 miles from dallas, texas, to his first destination. after dropping off his cargo, he flies southeast 290 miles to his second destination. if the angle formed by his trip is 125°, what is the distance he will fly from the second destination back to dallas? 490 miles 918 miles 1,010 miles 842,026 miles
Answer:
B) 918 miles
Step-by-step explanation:
Here with I have attached the figure of the story.
Here we need to find side c, which represents distance from the second destination back to Dallas.
We have to use the cosine formula to find the missing side.
If we are given two sides and one included angle, we can use the cosine formula and find the missing side.
a = 720, b = 290 and ∠C =125°
[tex]c^2 = a^2 + b^2 - 2ab cos C[/tex]
Now plug in the given values and simplify.
[tex]c^2 = {720}^2 + 290^2 - 2*720*290 cos 125[/tex]
[tex]c^2 = 518400 + 84100 - 417600 cos125[/tex]
[tex]c^2 = 602500 - (-239,525.5)\\c^2 = 602500 + 239,525.5\\c^2 = 842025.5[/tex]
Taking the square root on both sides, we get
c = 917.6
Which is equivalent to 918 miles (rounded off to the nearest whole number)
A dentist had some fish in a fish tank. The dentist added 43 more fish to the fish tank. Now there are 66 fish in the fish tank. How many fish were in the fish tank before the dentist added more?
___fish
Answer:
The dentist had 23 fish before she added 43
Step-by-step explanation:
Ken, Justin, and Tiff have read a total of 90
books from the library. Justin read 3 times
as many books as Ken and Tiff read 2
times as many as Justin. How many books
did Justin read?
PLEASE HELP
Three times the number of blue marbles exceeds twice the number of red marbles by 18 also five times the number of blue marbles is two less than six times the number of red marbles how much of each are there
Robby and Tony both took a 25 question test. Robby completed 25 questions and Tony completed 14 questions. Can we conclude that Robby will make a higher grade than Tony? Explain why or why not. -
If ΔMNO ≅ ΔPQR, which of the following can you conclude as being true? I'LL MARK BRAINLIEST !!!!
Answer:
NO=QR
Step-by-step explanation:
The roof of a factory rises vertically 7 ft through a horizontal run of 42 ft. What is the pitch of the roof?
Final answer:
The pitch of the roof, which rises vertically 7 ft through a horizontal run of 42 ft, is 2. This means the roof rises 2 inches for every 12 inches of horizontal run.
Explanation:
The question asks about calculating the pitch of a roof with a vertical rise of 7 ft and a horizontal run of 42 ft. The pitch of a roof is generally expressed as the amount of vertical rise per 12 inches of horizontal run. To find the pitch, we first need to calculate the rise per 12 inches of horizontal run.
Given:
Rise = 7 ft
Run = 42 ft
To find how much the roof rises for every 12 inches of run, we use the formula:
Pitch = (Rise / Run) × 12
Plugging in the given values:
Pitch = (7 / 42) × 12 = 2
Thus, the pitch of the roof is 2, meaning the roof rises 2 inches for every foot (12 inches) of horizontal run.
need an answer quick. If a circle with a diameter of 124 m is inscribed in a square, what is the probability that a point picked at random in the square is in the shaded region? Round to the nearest thousandth.
A.
0.013
B.
0.032
C.
0.215
D.
0.785
Answer: C. 0.215
Step-by-step explanation:
Given: A circle with a diameter of 124 m is inscribed in a square .
Thus side of square =124 m
Now, area of square=[tex](side)^2=(124)^2=15,376\ m^2[/tex]
Radius of circle=[tex]\frac{d}{2}=\frac{124}{2}=62\ m[/tex]
Area of circle=[tex]\pi\ r^2=3.14\times(62)^2=3.14\times3.14=12,070.16\ m^2[/tex]
Now, Area of shaded region= Area of square-Area of circle
Area of shaded region=[tex]15,376-12,070.16=3,305.84\ m^2[/tex]
Probability that a point picked at random in the square is in the shaded region
[tex]=\frac{\text{area of shaded region}}{\text{area of square}}=\frac{3305.84}{15376}=0.215[/tex]
How many solutions exist for the given equation? 3(x+10)+6=3(x+12)
Which dot plot has the smallest mode.
Segment AB has endpoints A(–4, 6) and B(1, 4). After a dilation, centered at the origin, the image of A is (–6, 9). Without measuring the distance, explain how you could find the image of B
The image of point B is B'(1.5,6).and this can be determined by finding the dilation factor and then multiplying point B by the dilation factor.
Given :
Segment AB has endpoints A(–4, 6) and B(1, 4).After a dilation, centered at the origin, the image of A is (–6, 9).In order to determine the image of point B, first, determine the dilation factor. let 'x' be the dilation factor, then:
[tex]-4\times x = -6[/tex]
[tex]x = \dfrac{3}{2}[/tex]
Now, after dilation the point B becomes:
[tex]\rm B(1,4)\to B'(1\times \dfrac{3}{2},4\times \dfrac{3}{2})[/tex]
Simplify the above expression.
[tex]\rm B'\left(\dfrac{3}{2},6\right) = B'(1.5,6)[/tex]
The image of point B is B'(1.5,6).
For more information, refer to the link given below:
https://brainly.com/question/19347268
The first pentagon is dilated to form the second pentagon. Drag and drop the answer to correctly complete the statement. The scale factor is . A pentagon with a side length of 4. An arrow points to a larger pentagon with a side length of 5
A 0.8 B 1.25 C 4 D 5
Answer:
1.25
Step-by-step explanation:
Julie spends 3/4 hour studying on Monday and 1/6 hour studying on Tuesday. How many hours does Julie study on the two days? (A 1/3 hour (B 2/5 hour (C 5/6 hour (D 11/12 hour (HELP ASAP 20 POINTS)
Carlo wants to join gym.the total gym offers three options for the membership. Option1:pay as you go.pay only $6 each time You work out. Option2: Regular Deal. Pay $50 a month and $2 each time you workout.
Devin is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 10 cm and the height of the pyramid is 11 cm. To get the wax for the candle, Devin melts cubes of wax that are each 3 cm by 3 cm by 3 cm. What is the minimum number of wax cubes Devin will need in need in order to make the candle? Show your work. Please explain.
A boat is 122 meters from the base of a lighthouse that is 34 meters above sea level. What is the angle of elevation from the boat to the top of the lighthouse? Round to the nearest degree. °
Answer: 16
Step-by-step explanation:
FOURTH TIME POSTING! EXTRA POINTS!
Complete each function. ( y = -x )
Find two consecutive even integers such that the smaller added to three times the larger gives a sum of 54
If point P is at the center of the circle, and the length of equals 12 inches, which is the length of AP?
a)4.5 inches
b)6 inches
c)9 inches
d)12 inches
If you work 52 weeks/year and 40 hours/week, how many hours would you work in one year? quizlrt
Final answer:
To find the total hours worked in a year, multiply the number of hours worked per week by the number of weeks in a year.
Explanation:
To calculate the total hours worked in a year:
Hours worked per week = 40 hours
Weeks worked per year = 52 weeks
Total hours worked in a year = 40 hours/week x 52 weeks = 2080 hours
30 POINTS + BRAINLIEST!
The answer is 15.87.
A florist sold 15 arrangements in its first month of business. The number of arrangements sold doubled each month.
What was the total number of arrangements the florist sold during the first 9 months?
Answer:
total number of arrangements the florist sold during the first 9 months = 7665 arragements
Explanation:
Florist start a business.
In his 1st month Florist sold 15 arrangement.
He grow his business, he sold twice arrangements as compare to the previous month.
First month = 15
Second month = 2*15 = 30
Third month = 2*30 = 60
15, 30, 60 .....
we need to find the total number of arrangements in first nine months
This sequence is geometric series.
A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term, i.e.,
r = [tex] \frac{30}{15} = \frac{60}{30} = 2 [/tex]
Sum of Terms in a Geometric Progression ([tex] S_{n} [/tex])= [tex] \frac{a_{1} (r^{n} -1)}{r-1} [/tex]
where [tex] a_{1} [/tex] is first term = 15
n is the number of terms = 9
r is common ratio = 2
[tex] S_{9} =\frac{15(2^{9}-1)}{2-1} [/tex]
[tex] S_{9} =\frac{15*(512-1)}{1} [/tex]
[tex] S_{9} = 7665 [/tex]
total number of arrangements the florist sold during the first 9 months = 7665.
Answer:7665
Step-by-step explanation:
What is the product? Zx(x-4)
The product of Zx (x-4) is:
Zx2 - 4Zx
Explanation and Solution:
Multiply Zx to each term of the expression inside the parenthesis
Zx multiplied by x is equal to Zx2
Zx multiplied by -4 is equal to -4Zx,
Combining all the product, we have Zx2 - 4Zx as the answer.
PS. The x2 there is X squared
What is the value of x in the figure?
Enter your answer in the box.
x =
Answer:
The value of x in the given figure is, [tex]34^{\circ}[/tex]
Step-by-step explanation:
Complementary angle states that the two angles sum up to 90 degree.
From the given figure
[tex]x^{\circ}[/tex] and [tex]56^{\circ}[/tex] are complementary angles.
by definition of complementary angles;
[tex]x^{\circ} +56^{\circ} = 90^{\circ}[/tex]
Subtract [tex]56^{\circ}[/tex] from both sides we get;
[tex]x^{\circ} = 90^{\circ} -56^{\circ}[/tex]
Simplify:
[tex]x = 34^{\circ}[/tex]
therefore, the value of x in the given figure is, [tex]34^{\circ}[/tex]
ILL GIVE BRAINLIEST IF YOU HELP
Find the hypotenuse of a right triangle with legs measuring 4 and 5 ft. 6.40
ANSWER a=4, b=5, so 42 + 52 = c2 and 16 + 25 = c2, so 41 = c2, then the square root of 41 =c
CAN SOMEONE EXPLAIN HOW TO GET THIS??!!
Answer:
4^2 + 5^2 = X^2
16 + 25 = X^2
41 = x^2
X = sqrt(41)
x = 6.40
hypotenuse = 6.40
Step-by-step explanation:
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a fund drive announces that it has raised 4376 which is 20% of its goal. How much more must be raised?
Tickets to a school play cost $3 for students and $8 for adults. On opening night, $1000 was collected and 150 tickets sold. How many of each kind of ticket were sold? Write a system of equations and use substitution to solve.
To solve this problem, set up a system of equations representing the number of student and adult tickets sold. Solve the system using substitution to find the numbers of each type of ticket sold.
Explanation:To solve this problem, we can set up a system of equations to represent the number of student tickets and adult tickets sold.
Let x be the number of student tickets sold and y be the number of adult tickets sold.
We know that the total number of tickets sold is 150, so we have the equation:
x + y = 150
We also know that the total amount collected is $1000, so we have the equation:
3x + 8y = 1000
We can solve this system of equations using substitution.
From the first equation, we can solve for x in terms of y as:
x = 150 - y
Substituting this into the second equation, we have:
3(150 - y) + 8y = 1000
Simplifying, we get:
450 - 3y + 8y = 1000
Combining like terms, we get:
5y = 550
Dividing both sides by 5, we get:
y = 110
Substituting this value back into the first equation, we have:
x + 110 = 150
Simplifying, we get:
x = 40
Therefore, 40 student tickets and 110 adult tickets were sold.
Which of these sentences is always true with a parallelogram?
A.) all sides are congruent
B.) all angles are congruent
C.) the diagonals are congruent
D.) opposite angles are congruent
Answer:
Opposite angles are congruent
Step-by-step explanation:
The parallelogram has parallel opposite sides and also the opposite sides are congruent. Few other properties of parallelogram are -
It has two pairs of parallel opposite sides. Its diagonals bisect each other.It has two pairs of equal opposite angles. It has two pairs of equal and parallel opposite sides.So, the answer is D.) opposite angles are congruent.
Answer:
D. Opposite angles are congruent.
Step-by-step explanation:
plato
If a couple has three children, let x represent the number of girls. what is the probability that the couple does not have boys for all three children?