What is the length of BC, rounded to the nearest tenth?
A. 13.0 units
B. 28.8 units
C. 31.2 units
D. 33.8 units
Answers
Answer:
Option C. [tex]BC=31.2\ units[/tex]
Step-by-step explanation:
step 1
In the right triangle ABD find the length side AB
Applying the Pythagoras Theorem
[tex]AB^{2}=5^{2}+12^{2}[/tex]
[tex]AB^{2}=169[/tex]
[tex]AB=13\ units[/tex]
step 2
In the right triangle ABD
we know that
[tex]m<ABD=m<BCD[/tex]
[tex]sin(<ABD)=\frac{5}{13}[/tex] -------> equation A
step 3
In the right triangle ABC
[tex]sin(<BCD)=\frac{13}{5+DC}[/tex] ------> equation B
Remember that
[tex]m<ABD=m<BCD[/tex]
so equate equation A and equation B solve for DC
[tex]\frac{5}{13}=\frac{13}{5+DC}[/tex]
[tex]5(5+DC)=13*13[/tex]
[tex]25+5DC=169[/tex]
[tex]5DC=169-25[/tex]
[tex]5DC=144[/tex]
[tex]DC=144/5=28.8\ units[/tex]
step 4
In the right triangle BDC find the length side BC
Applying the Pythagoras Theorem
[tex]BC^{2}=28.8^{2}+12^{2}[/tex]
[tex]BC^{2}=973.44[/tex]
[tex]BC=31.2\ units[/tex]
Related Questions
What is the smallest angle of rotational symmetry that maps a regular nonagon (9 sides) onto itself?
___°
Answers
The smallest angle of rotational symmetry that maps a regular nonagon onto itself is 40 degrees. This is calculated by dividing the total 360 degrees of the nonagon by its number of sides, which is 9.
Explanation:The smallest angle of rotational symmetry that maps a regular nonagon onto itself is obtained calculating the total 360 degrees of the nonagon divided by the total number of sides, which is 9.
Here is the step-by-step calculation: 360 degrees / 9 sides = 40 degrees
Therefore, the smallest angle of rotational symmetry for a regular nonagon is 40 degrees.
Learn more about Rotational Symmetry here:https://brainly.com/question/1597409
#SPJ12
Which of the following expressions is equivalent to 6m - 10?
2(3m + 5)
-2(5 - 3m)
2(3m - 10)
Answers
Test each answer to find out which one's correct.
2(3m + 5)
6m + 10
-2(5 - 3m)
-10 + 6m
6m - 10
2(3m - 10)
6m - 20
The correct answer is -2(5 - 3m).
Subtract. Your answer should be a polynomial in standard form. (-9g^4+3g^2h+1) -(6g^4-3g^2h+h)
Answers
The length of a rectangle is 3 meters less than 3 times the width. the perimeter is 42 meters. find the width.
Answers
Let length = 3x - 3
Let perimeter = 42
42 = 2x + 2(3x - 3)
42 = 2x + 6x - 6
42 = 8x - 6
42 + 6 = 8x
48 = 8x
48/8 = x
6 = x
The width is 6 meters.
The width of the rectangle will be 6 meters.
What is mean by Perimeter ?
The perimeter of any quadrilateral is the sum of all sides of a
quadrilateral .
Given that;
The length of a rectangle is 3 meters less than 3 times the width.
The perimeter of a rectangle = 42 meters.
Now,
Let the width of a rectangle = x meter
Then, By condition The length of a rectangle is 3 meters less than 3 times the width.
We get;
The length of the rectangle = ( 3x - 3 ) meters
Since,
The perimeter of a rectangle = 2 ( Length + Width )
Here, The perimeter of a rectangle = 42 meters.
Now, After substitute all the values we get;
The perimeter of a rectangle = 2 ( Length + Width )
The perimeter of a rectangle = 2 ( 3x - 3 + x)
42 = 2 ( 4x - 3)
42 = 2 (4x - 3)
Solve for x as,
Divide by 2;
21 = 4x - 3
Add 3 both side;
21 + 3 = 4x - 3 + 3
24 = 4x
Divide by 4, we get;
x = 24/4
x = 6
Thus, The width of a rectangle = 6 meters.
Therefore, The width of the rectangle will be 6 meters.
Learn more about the perimeter visit:
https://brainly.com/question/443376
#SPJ2
Find a formula for the number of patrons as a function of profit.
Answers
Let us make patrons the independent variable, the two points are: (1314, 11333) and (1544, 13518).
m = (13518-11333)/(1544-1314)
m = 9.5
profit = 9.5 patrons (you pick the variable names)
For 1 more patron substitute 1:
profit = 9.5 (1)
profit = 9.5
Isolate "patrons" and you get the function based on profit:
patrons = profit/9.5
The break even point is for 0 < profit.
0 < profit = 9.5 patrons
0 < 9.5 patrons
0 < patron
The perimeter of a rectangular pig pen is 310 ft. The length is 15 ft greater than the width. Find the width
Answers
280/4=70
Juan is saving money for a new car. He has already saved $200 and plans to save $25 per week. This situation can be represented by the function f(x) = 200 + 25x, where x is the number of weeks. How much money has Juan saved after 8 weeks?
$200
$400
$600
$800
Answers
400 is the correct answer. I am too lazy to put an explanation, but trust me it's not 800, I just got it wrong.
Write an equation, in the slope intercept form, of the line with an x-intercept at (3 , 0) and a y-intercept at (0 , -5).
Answers
Hello : let A(3,0) B(0,-5)
the slope is : (YB - YA)/(XB -XA)
(-5-0)/(0-3) = 5/3
y = (5/3)x - 5
3. Solve. 5 < x - 2 < 11
A. 5 < x < 11
B. 7 < x < 13
C. 7 < x < 11
D. 5 < x < 16
Answers
5 + 2 < x < 11 + 2
Simplify
Answer: B) 7 < x < 13 or the second option.
Sam made $198 last week cutting grass. He worked for 18 hours. How much did he make per hour? He thinks he made $12 per hour. True False
Answers
divide:
198/18 = 11
he made $11 per hour
so it's False, he did not make $12 per hour
Which of the following will result in a rational answer?
A. multiplying pie by a fraction
B. adding the square root of a non perfect square to a whole number
C. adding the square root of a perfect square to pie
D. multiplying a fraction by a repeating decimal.
P.S. I asked a question 2 before this one, no one has answered it can someone do that?
Answers
B. adding the square root of a non perfect square to a whole number
P.S
Non-perfect square roots as rational numbers
(any fraction) * (any decimal) = rational answer
For example: (3/5) * 0.11111(1)= rational
PS: any fraction is a rational number if a nominator is an integer and a denominator is a natural number
In his free time, Gary spends 8 hours per week on the Internet and 10 hours per week playing video games. If Gary has five hours of free time per day, approximately what percent of his free time is spent on the Internet and playing video games?
Answers
assuming our week has 7 days and he even does this on Saturday ad Sunday,
freetimetotal in 1 week=freetime per day times 7=5*7=35
so percent free time spent on video games and internet=(videogames+internet)/totaltimeperweek=(8+10)/35=18/35≈0.514≈51%
the answer is A. 51%
also, regarding how much he's playing:
Answer:
He spent a total of 22.85+28.57 = 51.42 % of his free time o internet and videogames.
Step-by-step explanation:
If Gary has 5 hours of free time per day, he has 5*7=35 hours of free time per week.
Now, in the case of internet:
[tex]\frac{35h}{8h}= \frac{100}{x}[/tex]
[tex]x= \frac{8*100}{35}[/tex]
x= 22.85% spent on internet.
In the case of videogames:
[tex]\frac{35h}{10h}= \frac{100}{x}[/tex]
[tex]x= \frac{10*100}{35}[/tex]
x= 28.57% spent on internet.
The banner over the finish line of a running race is 400. Centimeters long and 85 centimeters high. What is the area over the banner?
Answers
Information for the park trails is displayed at the entrance to the park office.
How long is Trail B?
Show your work and round your answer to the nearest foot.
Answers
Since we know Trail E is 1700, we're looking for the patch of trail A that is the adjacent. So if we put 42 into a tan calculator we get about 0.9.
So that means that 1,700 / adjacent = 0.9.
So we can also say
1,700/0.9 = adjacent
or, 1,700/0.9 = 1888.89
Now, we have the little patch of trail A in the smaller right triangle. We want to find the patch of trail A in the larger right triangle.
So just do 5,000 - 1,888.89
You get 3111.11
So if we know that's that, and we're looking for the hypotenuse, or Trail B, we can use cosine, because that's adjacent / hypotenuse.
So 42 in a cosine calculator is 0.74 ish.
So 3111.11 / hypotenuse = 0.74
Or 3111.11 / 0.74 = hypotenuse
Or 3111.11 / 0.74 = 4204
So Trail C should be 4204 feet long.
SOMEONE PLEASE HELP ME ASAP!!!!!!!
Below is a data set consisting of 33 whole-number observations. Its five-number summary is:
(16,20,22,30,46).
What is the range of the data?
A. 6
B. 16
C. 24
D. 30
Below is a data set consisting of 33 whole-number observations. Its five-number summary is:
(16,20,22,30,46).
How many observations are strictly less than 20?
A wide variety of oak trees grow in the United States, In one study, a sample, of acorns was collected from different locations, and their volumes, in cm^3, were recorded. In the table are the summary statistics for these data:
Statistic | Value
N | 38
Mean | 3.0
Median | 1.8
St.Dev. | 2.6
Minimum | 0.3
Maximum | 10.5
1st Quartile | 1.1
3rd Quartile | 4.3
Describe a procedure that uses some or all of these summary statistics to determine whether outliers are present in the data.
Show the work using the procedure from the previous question to determine if there are outliers in these data.
Answers
To determine the number of observations below 24 in the given data set with a five-number summary, we find 25% of 33, yielding 8 observations.
To find the number of observations strictly less than 24, we need to understand the structure of the five-number summary: minimum (12), Q1 (24), median (38), Q3 (51), and maximum (69).
Since Q1 (24) represents the 25th percentile, it indicates that 25% of the observations lie below 24. Therefore, the number of observations strictly less than 24 is 25% of the total number of observations.
Given that there are 33 unique observations, we calculate 25% of 33 as:
[tex]\[ \text{Number of observations} = \frac{25}{100} \times 33 = 8.25 \][/tex]
As we can't have a fraction of an observation, we round down to the nearest whole number. Therefore, there are 8 observations strictly less than 24.
Hence, 8 observations are strictly less than 24 in the given data set.
This calculation involves understanding the position of Q1 in the data set and applying the concept of percentiles to determine the number of observations below a certain value.
The question probable maybe:
Given a data set consisting of 33 unique whole number observations, its five-number summary is: 12, 24, 38, 51, 69
How many observations are strictly less than 24 ?
1. The range of the data is 30.
2. The number of observations strictly less than 20 is the count of observations is 16.
3. Based on the IQR method, there are no outliers in the data.
Let's address each question one by one:
1. Range of the data:
The range of the data is the difference between the maximum and minimum values in the dataset. From the five-number summary given, we have:
Maximum = 46
Minimum = 16
So, the range is:
[tex]\[ \text{Range} = \text{Maximum} - \text{Minimum} = 46 - 16 = 30 \][/tex]
Therefore, the range of the data is 30. Hence, the correct answer is D. 30.
2. Observations strictly less than 20:
From the five-number summary, we know that 20 is the second quartile (median) of the dataset. Observations strictly less than 20 would fall in the first quartile. Therefore, we need to find the number of observations below the first quartile.
Given:
First Quartile = 16
Observations strictly less than 20 = Number of observations below the first quartile.
So, the number of observations strictly less than 20 is the count of observations below the first quartile, which is 16.
Now, for the third question:
To determine if outliers are present in the data, we can use the Interquartile Range (IQR) method.
The Interquartile Range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1).
[tex]\[ \text{IQR} = Q3 - Q1 \][/tex]
Any data point that falls below [tex]\( Q1 - 1.5 \times \text{IQR} \) or above \( Q3 + 1.5 \times \text{IQR} \)[/tex] is considered an outlier.
Given:
Q1 = 1.1
Q3 = 4.3
[tex]\[ \text{IQR} = Q3 - Q1 = 4.3 - 1.1 = 3.2 \][/tex]
Therefore, the lower bound for outliers is [tex]\( 1.1 - 1.5 \times 3.2 = -3.7 \)[/tex] (which is not relevant in this context), and the upper bound for outliers is [tex]\( 4.3 + 1.5 \times 3.2 = 9.9 \).[/tex]
Looking at the summary statistics:
- The minimum value is 0.3, which is within the range.
- The maximum value is 10.5, which is also within the range.
Hence, based on the IQR method, there are no outliers in the data.
Please help with the tennis court one.
Answers
We also have two sides of length '2w+6' which are the horizontal sides.
So we have these four sides
side1 = w
side2 = 2w+6
side3 = w
side4 = 2w+6
Let's add up those four sides to get
Perimeter = (side1)+(side2)+(side3)+(side4)
Perimeter = (w)+(2w+6)+(w)+(2w+6)
Perimeter = w+2w+6+w+2w+6
Perimeter = 6w+12
------------------------
Since the perimeter is given to be 228, and we found the perimeter expression to be 6w+12, this must mean that the two are equal
So, 6w+12 = 228
Let's solve for w
6w+12 = 228
6w+12-12 = 228-12
6w = 216
6w/6 = 216/6
w = 36
------------------------
Now that we know that w = 36, we can find the dimensions of this rectangle
The vertical sides are simply w, so the vertical sides are 36 feet each. I simply replaced w with 36.
The horizontal sides are a bit more complicated. The expression we have is 2w+6 or 2*w+6. Let's replace w with 36 and use PEMDAS to evaluate
2*w+6 = 2*36+6 = 78
------------------------------------------
------------------------------------------
Answers are...
Length = 78 feet
Width = 36 feet
(the length is the horizontal component, the width is the vertical)
Answer:
Length = 78 feet
Width = 36 feet
Step-by-step explanation:
A garage charged $248 in parts and $30 per hour in labor for work on a car. How many did the garage spend working on the car if the total bill was $572? Use a two step equation to model the scenario and then solve the question
Answers
Labor payment = $572 - $248 = $324
From here you can count how many hours the labor did too. It would be: $324/ (30$/hour) = 10.8 hours
Add 11.25 and 0.03.
3 is repeating.
Answers
11.25
+0.0333333
________
11.28333333333
For 0.03 (3 repeating), we can write that as 1/30. For 0.003 (3 repeating), it's 1/300. Therefore, we have 11.28+0.003=11.28 + 1/300
Find the sample standard deviation. round to the nearest tenth. 15 42 53 7 9 12 14 28 47
Answers
Dominick’s unpaid credit card balance was $2103.24. His APR is 14.4%.
What is his new balance after he makes one new transaction for $280?
Answers
First we need to calculate the finance charge in order to find the new balance
Finance charge=2,103.24×(0.144÷12 months)
=25.24
New balance
2,103.24+25.24+280
=2,408.48
Hope it helps!
Based on the information given the new balance is $2,408.48.
New balanceFirst step is to calculate the finance charge
Finance charge=2,103.24×(0.144÷12 months)
Finance charge=2,103.24×0.012
Finance charge=25.24
Second step is to calculate the New balance
New balance=2,103.24+25.24+280
New balance=$2,408.48
Inconclusion the new balance is $2,408.48.
Learn more about new balance here:https://brainly.com/question/25610363
Check my answer?
Students observed that their teacher's desk plant looked wilted on Monday morning compared to how it looked at the end of the day on Friday. Some students hypothesized that a warmer room temperature over the weekend caused the plant to wilt. Other students hypothesized that the lack of light caused the plant to wilt. Both hypotheses are valuable because they
A.) are reasonable and testable ---- (My answer)
B.) compare independent variables
C.) compare light and temperature
D.) are the only possible explanations.
Answers
If mRV = mVU, what is mVU?
Answers
Answer:
Answer: C
Step-by-step explanation:
Edge 2021
A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 4 and tangent to the y-axis at 4. Which of the following is an equation of the circle?
a
(x − 4)2 + (y − 4)2 = 16
b
x2 + y2 = 16
c
(x + 4)2 + (y + 4)2 = 16
d
x2 + y2 = 4
e
(x − 4)2 + (y − 4)2 = 4
Answers
The equation of the circle is: is (x - 4)² + (y - 4)² = 16 Option A
How the equation of the circle was derivedTo find the equation of a circle tangent to the x-axis at (4, 0) and tangent to the y-axis at (0, 4)
Let's use the general form of the equation for a circle:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle, and r is the radius.
The center of the circle is (4, 4) because it's tangent to both the x-axis and y-axis at 4.
The radius can be found by the distance from the center to the point (4, 0) (which is on the x-axis):
r = √((4 - 4)² + (0 - 4)²) = √(0 + 16) = √16 = 4
So the equation of the circle is:
(x - 4)² + (y - 4)² = 4²
(x - 4)² + (y - 4)²= 16
The correct option is: a) (x - 4)² + (y - 4)² = 16
Learn more about circle here
https://brainly.com/question/24375372
#SPJ3
Temperatures in the Gobi desert reach -40 F in the winter and 90 F in the summer. Find the range of the temperatures
Answers
add the 2 numbers together
40 + 90 = 130 degree range
solve y=x^2+2 for x.
Answers
x= √(2-y) is the solution to the problem
Write the decimal 3.59 as a mixed number in simplest form.
Answers
Why does a low range indicate precision in a measurement tool?
Answers
CHECK TWO ANSWERS PLS!!
Answers
For the second one, sin(x) (including any x value)has a range of [-1, 1] so 2sinx would have a range from [-2, 2] and the range for 2sinx-2 would be
[-4, -2] with the minimum being -4. For g(x), squaring something makes it positive, meaning that the minimum of (x-3)^2 would be 0. 0-1 would be -1. For h(x), the lowest is clearly -6, and -6 is lower than both -1 and -4, mking h(x) the smallest
A clothing store offers a shirt in 5 colors, in long or short sleeves, with a choice of three different collars. How many ways can the shirt be designed? a. 20 c. 30 b. 25 d. 50
Answers
5 colors
2 lengths of sleaves
3 colors
5*2*3=30
answer is 30
C is answer
Answer:
30
Step-by-step explanation:
please help me ASAP
What is the length of segment NS?
1 unit
2 units
4 units
6 units
Answers
Answer:
Option C. 4 units
Step-by-step explanation:
As we know median of a triangle intersect each other at a point in the ratio of 2.01.
Therefore, in Δ QNL,
[tex]\frac{NS}{SR}[/tex] = [tex]\frac{2}{1}[/tex]
[tex]\frac{(7x-3)}{(5x-3)}[/tex] = [tex]\frac{2}{1}[/tex]
By cross multiplication
(7x - 3) = 2(5x -3)
7x - 3 = 10x - 6
6 - 3 = 10x - 7x
3 = 3x
x = 1
Now length of NS
= (7x - 3)
= (7 × 1 - 3)
= (7 - 3)
= 4 units
Option C. 4 units is the answer.