Answers
Answer:
7. 46.39 miles
8. 109 cm
9. 18 cm
Step-by-step explanation:
7. Look at the attached picture so you can picture the scenario.
The distance from City A to City B is 85 miles North. Notice that the plane only got to travel 20 miles North because of a cloudbank and redirected 108 degrees NORTH OF EAST, 20 miles towards that direction.
The new path makes a triangle, as shown in the picture.
The angle of the triangle was solved this way.
108° - 90° = 18°
The length of a was solved by getting how many miles the plane didn't travel in its original path.
85 miles - 20 miles = 65 miles.
So now we have our new given:
a = 65 miles
b = 20 miles
c = ?
C = 18°
Using the cosine law we can solve for the c, which is the distance of the plane from City B.
[tex]c^{2}=a^{2}+b^{2}-2abCosC\\\\c^{2}=65^{2}+20^{2}-2(65)(20)Cos18\\\\c^{2}=4225+400-2600(Cos18)\\\\c^{2}=4625-2472.75\\\\\sqrt{c^{2}}=\sqrt{2152.25}\\\\c=46.39miles[/tex]
8. Again look at the attached. So as you can see we make another triangle. We can solve this with the cosine law once again. Just remember that the longer diagonal is opposite the biggest angle.
Given that:
a = 54cm
b = 78 cm
C = 110°
[tex]c^{2}=a^{2}+b^{2}-2abCosC\\\\c^{2}=54^{2}+78^{2}-2(54)(78)Cos110\\\\c^{2}=2916+6084-8424(Cos110)\\\\c^{2}=9000-(-2281.18)\\\\\sqrt{c^{2}}=\sqrt{11881.18}\\\\c=109cm[/tex]
9. Again, the shorter diagonal is facing the smaller angle. But we use the same cosine law to find it, but we use the formula of a, since a is what we are missing.
Given that:
a=?
A = 58°
b = 21cm
c= 15cm
[tex]a^{2}=b^{2}+c^{2}-2bc(CosA)\\\\a^{2}=21^{2}+15^{2}-2(21)(15)(Cos58)\\\\a^{2}=441+225-630(Cos58)\\\\a^{2}=666-333.85\\\\\sqrt{a^{2}}=\sqrt{332.15}\\\\a = 18cm[/tex]
Related Questions
Express the given logarithm in terms of common logarithms. Then approximate its value to four decimal places.
log2 11
Answers
Answer:
3.4594
Step-by-step explanation:
To change the base of a logarithm
• [tex]log_{b}[/tex] x = [tex]\frac{log_{c}x }{log_{c}b }[/tex]
where c represents the new base
Changing the base from 2 to 10
[tex]log_{2}[/tex] 11 = [tex]\frac{log_{10}11 }{log_{10}2 }[/tex] ≈ 3.4594
a school is running a fundraiser. for every $75 worth of wrapping paper sold, the school receives $20. how much wrapping paper must be sold to reach he fundraising goal of $2,500
Answers
Answer:
$9259.26
Step-by-step explanation:
The school receives $20 on $75.
We can calculate the percentage by using the values.
20/75 = 0.27%
The school recieved 0.27% of the payment.
Now we know the target amount and percentage, we can calculate the principal amount here.
Let x dennote the worth on which the school will recieve 2500 dollars. [tex]2500 = x * 0.27\\x = \frac{2500}{0.27}\\ x = 9259.26[/tex]
$9259.26 worth of ribbon has to be sold for the school to get $2500 ..
17400 invested at a rate of 2.5% compounded annually; 8 years
Answers
Answer:
348
Step-by-step explanation:
Which of these numbers is between 7 and 9?
A. √8
B. √79
C. 3√64
Answers
Answer: It has to be A. 8
Step-by-step explanation:
Please help I'm very confused
Answers
30 ≥ g [keyword - "no more than"
4 ≤ i [keyword - "at least"]
which equation can be used to solve for b?
Answers
Answer:
First option
b = (8) * Tan (30)
Step-by-step explanation:
Tan (B) = Oppo. / Adj.
Tan (B) = AC/BC
Tan (30) = b / 8
b = (8) * Tan (30)
Answer
First option
b = (8) * Tan (30)
Find the sum of the measures of the interior angles of each convex polygon decagon
Answers
Answer:
Nvm about those questions the answer is 1440 degrees
Step-by-step explanation:
Question 30
Find the length of the long leg. Leave answer in simplest radical form.
Help plz
Answers
Use SOHCAHTOA. You must use sine or cosine since the hypotenuse is involved, but since you are given both angles, it does not matter which one of them you choose. We'll use sine:
sinx=O/H
sin60=O/14
√3/2=O/14
*Cross multiply*
(14√3)=2O
*Divide both sides by 2*
7√3=O
Hope this helps!!
Answer:
B
Step-by-step explanation:
Since the triangle is right we can use the sine ratio to find TI along with
the exact value of sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{TI}{TR}[/tex] = [tex]\frac{TI}{14}[/tex]
Multiply both sides by 14
TI = 14 × sin60° = 14 ×[tex]\frac{\sqrt{3} }{2}[/tex] = 7[tex]\sqrt{3}[/tex]
Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?
x2(x – 9) – 5(x – 9)
x2(x + 9) – 5(x + 9)
x(x2 + 5) – 9(x2 + 5)
x(x2 – 5) – 9(x2 – 5)
Answers
Answer:
C
Step-by-step explanation:
x(x2 + 5) – 9(x2 + 5)
= x³ + 5x - 9x² - 45
(try to expand one by one of the answer given)
Answer:
x(x2 + 5) – 9(x2 + 5)
Step-by-step explanation:
PLEASE HELP!
The water tank in the diagram is in the shape of an inverted right circular cone. The radius of its base is 16 feet, and its height is 96 feet. What is the height, in feet, of the water in the tank if the amount of water is 25% of the tank’s capacity?
Answers
Answer:
The height of the water is [tex]60.5\ ft[/tex]
Step-by-step explanation:
step 1
Find the volume of the tank
The volume of the inverted right circular cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]r=16\ ft[/tex]
[tex]h=96\ ft[/tex]
substitute
[tex]V=\frac{1}{3}\pi (16)^{2} (96)[/tex]
[tex]V=8,192\pi\ ft^{3}[/tex]
step 2
Find the 25% of the tank’s capacity
[tex]V=(0.25)*8,192\pi=2,048\pi\ ft^{3}[/tex]
step 3
Find the height, of the water in the tank
Let
h ----> the height of the water
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
[tex]\frac{R}{H}=\frac{r}{h}[/tex]
substitute
[tex]\frac{16}{96}=\frac{r}{h}\\ \\r= \frac{h}{6}[/tex]
where
r is the radius of the smaller cone of the figure
h is the height of the smaller cone of the figure
R is the radius of the circular base of tank
H is the height of the tank
we have
[tex]V=2,048\pi\ ft^{3}[/tex] -----> volume of the smaller cone
substitute
[tex]2,048\pi=\frac{1}{3}\pi (\frac{h}{6})^{2}h[/tex]
Simplify
[tex]221,184=h^{3}[/tex]
[tex]h=60.5\ ft[/tex]
The price of a gallon of unleaded gas was $2.83 yesterday. Today, the price rose to $2.88 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answers
The percentage increase from yesterday's gas price to today's price is 1.8%.
Explanation:To find the percentage increase from yesterday's price to today's price, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100.
The difference between $2.88 and $2.83 is $0.05. Dividing $0.05 by $2.83 gives us 0.0176. Multiplying by 100 gives us 1.76%. Rounding to the nearest tenth of a percent, the percentage increase is 1.8%.
kate has 567 cars she put 77 on each table how many cars does she have left
Answers
Answer:
well how many tables are there?
Step-by-step explanation:
Line t intersects the line given by y=4x-2 at the point (4,14) to form a right angle. Which is the equation of line t
Answers
Answer:
y = -1/4 x + 15.
Step-by-step explanation:
y = 4x - 2 has a slope of 4 ( = the coefficient of x).
The line at right angles to it will therefore of a slope of -1/4.
Using the point-slope form of a line the line t which passes through (4, 14) is found as follows:
y - 14 = -1/4(x - 4)
y = -1/4x + 1 + 14
y = -1/4x + 15
plz help god blees if you do it all i will give u BRAINLIEST
Answers
it's the first one !!! so it's A
Steve leaves the beach at 3p.m. and drives along the highway at 55 mph. One hour later, his friend leaves the same beach, and drives along the same highway at 65 mph.
How many hours will it take his friend to catch up to Steve?
10 hours
5.5 hours
8.5 hours
55 hours
Answers
It will take Steve's friend 6.5 hours to catch up to Steve.
The correct answer is:
e) 6.5 hours.
To calculate this, let's first determine the time it takes for Steve's friend to catch up to him after he starts driving.
Steve's speed = 55 mph
Steve's friend's speed = 65 mph
Relative speed = Speed of Steve's friend - Speed of Steve
Relative speed = 65 mph - 55 mph = 10 mph
Now, since Steve's friend starts one hour later, Steve has already traveled for one hour at 55 mph before his friend starts.
Distance traveled by Steve in one hour = Speed × Time
Distance = 55 mph × 1 hour = 55 miles
Now, when Steve's friend starts driving, he needs to catch up this initial distance of 55 miles.
Time = Distance / Relative speed
Time = 55 miles / 10 mph = 5.5 hours
But we must remember that Steve's friend started driving one hour later than Steve. So, we add this one hour to the time calculated above to find the total time it takes for Steve's friend to catch up to Steve.
Total time = 5.5 hours + 1 hour = 6.5 hours
Therefore, it will take Steve's friend 6.5 hours to catch up to Steve.
Steve travels for one hour at 55 mph before his friend starts driving. By then, Steve's friend needs to catch up the initial distance of 55 miles at a relative speed of 10 mph. This gives us a time of 5.5 hours. However, since Steve's friend started one hour later, we add this one hour to the calculated time, resulting in a total time of 6.5 hours. Therefore, the correct answer is 6.5 hours.
Complete question:
Steve leaves the beach at 3p.m. and drives along the highway at 55 mph. One hour later, his friend leaves the same beach, and drives along the same highway at 65 mph.
How many hours will it take his friend to catch up to Steve?
a.10 hours
b.5.5 hours
c.8.5 hours
d.55 hours
e. 6.5 hours.
Factor by grouping: x^3 + 3x^2 - 25x -75 Which of the following is one of the factors?
Answers
Answer:
Final factor is [tex](x + 3)(x+5)(x-5)[/tex].
Step-by-step explanation:
Given expression is [tex]x^3 + 3x^2 - 25x -75[/tex]
Now we need to factor that expression [tex]x^3 + 3x^2 - 25x -75[/tex] by grouping. So let's make group of first two terms and group of last two terms.
[tex]x^3 + 3x^2 - 25x -75[/tex]
[tex]=(x^3 + 3x^2)+( - 25x -75)[/tex]
factor each group
[tex]=x^2(x + 3)-25(x +3)[/tex]
[tex]=(x + 3)(x^2-25)[/tex]
[tex]=(x + 3)(x+5)(x-5)[/tex]
Hence final factor is [tex](x + 3)(x+5)(x-5)[/tex].
I got the Same answer
Daniel looks at the prices of 5 guitars. The prices are $137, $159, $127, $188 and $680. These prices contain one extreme value ($680). Which measure of center should Daniel use to describe the prices?
A. Median
B. Range
C. Mean
D. Mean absolute deviation
Answers
Answer:
A. Median
Step-by-step explanation:
Mean and median both are used to measure the central tendency of a given data while range gives us the spread of the data roughly.
Mean is even affected by a single extreme value in the data while median gives us the central value of data even when there are extreme values.
The given set of five prices has one extreme value which will affect the mean. While median is a better option to measure the central tendency of data.
So Daniel will use median to measure the central tendency to describe the prices..
Step-by-step explanation:
Answer is A. Median by jesse
Find the distance between the points ( - 16, - 9) and ( - 16, - 18).
Answers
notice, the x-coordinate is the same for both points, thus is a vertical line.
Check the picture below.
To find the distance between the points (-16, -9) and (-16, -18), subtract the y-coordinates, which gives us a distance of 9 units.
To find the distance between the points (-16, -9) and (-16, -18), we can use the distance formula for two points in a Cartesian coordinate system. However, because the x-coordinates of the two points are the same, this means that the line connecting these two points is vertical, and we can simply subtract the y-coordinates to find the distance.
The distance formula in a two-dimensional Cartesian coordinate system is:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Since the x-coordinates are identical, the formula simplifies to:
d = |y₂ - y₁|
Applying this to the points given:
d = |-18 - (-9)|
d = |-18 + 9|
d = |-9|
Therefore, the distance is 9 units.
i need help im stuck on this
Answers
Hello There!
Before getting started, we should remember that the top surface and the bottom surface of any cylinder are congruent to each other.
First, we use the formula pi*radius^2 to find the area of a circle since there is always a circle in a cylinder.
Next, we multiply pi*radius^2 * height because a cylinder has a height too.
HOW TO SOLVE
First, we multiply 3.14 which is equal to pi by 25 because the radius is 5 and in the formula we used, it states radius squared so 3.14 multiplied by 25 and then multiplied by the height of our cylinder which equals 6.
Once we multiply, we get a product of 471.
Our final answer is 471.units^3
The graph below is correct for the linear equation y=-3.
True
False
Answers
Answer:
False.
Step-by-step explanation:
The graph that is shown is correct for the equation x= -3. The graph for y= -3 would run vertically, not horizontally.
Answer:
True
Step-by-step explanation:flip it and reverse it its esrever dna ti pilf
What is the 6th term of this sequence? 8,-12,18-27
Answers
Answer:
-60.75
Step-by-step explanation:
-12 / 8 = -3/2
18 / -12 = -3/2
-27 / 18 = -3/2
This is a geometric sequence with a common ratio of -3/2.
an = 8 (-3/2)^(n-1)
The sixth term is:
a₆ = 8 (-3/2)^(6-1)
a₆ = 8 (-3/2)^5
a₆ = -60.75
SOMEONE PLEASE HELP ME ANSWER THIS
Answers
Answer: 84
Step-by-step explanation:
7 x 3 x 4 = 84
It would be 84.
Hope this helps!
Pls tell me if it is inncorrect and i will revise my answer.
7•3•4=84
You ask a friend to think of a
number from four to twelve. What
is the probability that his number
will be 8?
Answers
The answer is 1/9 or about 11%.
Answer:8
Step-by-step explanation: it’s right
There are 20 cups of flour in package of flour, how many muffins can i make from a package of flour if it take 1/4 cup?
Answers
Answer:
80 Muffins.
Step-by-step explanation:
There are 20 cups of flour in package
It takes [tex]\frac{1}{4}[/tex] cup to make one muffin
From a package of 20 cups of flour, you can make:
20 × 1 ÷ [tex]\frac{1}{4}[/tex] = 20 × 4 = 80 muffins
Find the volume of the cone in terms of pi.
Answers
Answer:
how to find pi you have to add a lot of math and for a volume for the cone is V=πr2h 3
Step-by-step explanation:
i had did this all in my head.
In the triangles, and . Which statement correctly compares the angles? Angle G is congruent to angle P. Angle G is smaller than angle P. Angle G is larger than angle P. Angle G is congruent to angle N.
Answers
Answer:
B) Angle G is smaller than angle P.
Step-by-step explanation:
It's logic, the only way the hypotenuse could be shorter is if the angle opposite of it is more acute.
I know that's a mouthful and probably sounds really weird but just trust me.
Would appreciate brainliest, new to brainly! good luck!
The correct option is, (B) Angle G is smaller than angle P.
It's logic, the only way the hypotenuse could be shorter is if the angle opposite of it is more acute.
What is called triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.A triangle is also a polygon.Some real-life examples of triangles include sandwiches, traffic signs, cloth hangers, and a rack in billiards.What is triangle and its types?Triangles are shapes with three sides.There are different names for the types of triangles.A triangle's type depends on the length of its sides and the size of its angles (corners).There are three types of triangle based on the length of the sides: equilateral, isosceles, and scalene.
What is triangle shape?In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices.The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.This property is called angle sum property of triangle.
Learn more about triangle here:
brainly.com/question/1058720
#SPJ2
What is the real part of the complex number 18 - 6i?
• i
• -6i
• 18
•-6
Answers
18 is the real part of the complex number
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
18
Step-by-step explanation:
Given a complex number z = a + bi
where a is the real part the imaginary part is b
Given
18 - 6i then 18 is the real part
Jake is eating dinner at a restaurant. The cost of his meal, including sales tax, is m dollars. After leaving an 18% tip, the amount Jake pays at the restaurant is represented by the following expression in this expression, what does the term 0.18m represent?
m+0.18m
Answers
Answer:
It means meal cost plus the 18% tip
Step-by-step explanation:
Answer:
[tex]0.18m[/tex] represents amount of tip Jake pays to restaurant.
Step-by-step explanation:
We have been given that Jake is eating dinner at a restaurant. The cost of his meal, including sales tax, is m dollars.
Jake left an 18% tip. The amount Jake pays at the restaurant is represented by the following expression in this expression [tex]m+0.18m[/tex].
We know that Jake's total amount will be equal to cost of his meal plus 18% of the cost of meal.
[tex]\text{Total cost of dinner}=m+(\frac{18}{100}\times m)[/tex]
[tex]\text{Total cost of dinner}=m+0.18m[/tex]
Therefore, the term [tex]0.18m[/tex] represents amount of tip Jake pays to restaurant.
The volume of a sphere is 3052.08 units cubed what is its diameter?
Answers
The diameter of the sphere is approximately 19.82 units.
To calculate the diameter of a sphere given its volume, we'll use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3}\pi r^3 \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume of the sphere,
- [tex]\( \pi \)[/tex] is a mathematical constant (approximately equal to 3.14159),
- [tex]\( r \)[/tex] is the radius of the sphere.
Since we have the volume, we rearrange the formula to solve for the radius:
[tex]\[ r = \sqrt[3]{\frac{3V}{4\pi}} \][/tex]
Substituting the given volume [tex]\( V = 3052.08 \)[/tex], and the value of[tex]\( \pi \)[/tex], we can find the radius:
[tex]\[ r = \sqrt[3]{\frac{3 \times 3052.08}{4 \times 3.14159}} \][/tex]
[tex]\[ r \approx \sqrt[3]{\frac{9156.24}{12.56636}} \][/tex]
[tex]\[ r \approx \sqrt[3]{729.128} \][/tex]
[tex]\[ r \approx 9.85 \][/tex]
Now, to find the diameter, we double the radius:
[tex]\[ \text{Diameter} = 2 \times r \][/tex]
[tex]\[ \text{Diameter} = 2 \times 9.85 \][/tex]
[tex]\[ \text{Diameter} \approx 19.82 \][/tex]
So, the diameter of the sphere is approximately 19.82 units.
To recap, we first found the radius of the sphere using the formula for volume, then we doubled the radius to find the diameter.
Complete question:
The volume of a sphere is 3052.08 units cubed what is its diameter?
Winona’s bowling scores for the past nine weeks are 195, 180, 195, 212, 208, 231, 179, 246, and 195. Find the mean, median, and mode. Round to the nearest tenth, if necessary.
Answers
Winona's bowling scores have a mean of 204.6, a median and mode both of 195.
To find the mean, median, and mode of Winona's bowling scores, we follow these steps:
Mean: Add all the scores together and divide by the number of scores.Median: Arrange the scores in ascending order and find the middle score.Mode: Identify the score that occurs most frequently.The bowling scores are 195, 180, 195, 212, 208, 231, 179, 246, and 195.
Mean: (195 + 180 + 195 + 212 + 208 + 231 + 179 + 246 + 195) / 9 = 1841 / 9 = 204.6
The mean score is 204.6.
To find the median, we first arrange the scores in ascending order: 179, 180, 195, 195, 195, 208, 212, 231, 246.
The median, or the middle score, is the fifth one since there are an equal number of scores on either side of it, which is 195.
The mode is the number that appears most often, which is also 195.
Therefore, Winona's mean score is 204.6, the median score is 195, and the mode is 195.