In the right triangle shown, \angle B = 60^\circ∠B=60
∘
angle, B, equals, 60, degrees and AB = 12AB=12A, B, equals, 12.
How long is ACACA, C?
Answer exactly, using a radical if needed.
Answers
The length of the side AC for the right triangle is 12√3 and the measure of angle C is equal to 30°.
The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
Considering angle 60 for the right triangle with side AC opposite it we get;
tan 60 = AC/12 {opposite side/adjacent side}
√3 = AC/12
AC = 12 × √3 {cross multiplication}
AC = 12√3
angle C = 180 - (60 + 90) {sum of interior angles of a triangle}
angle C = 180 - 150
angle C = 30°.
Therefore, using the tangent of angles 60 we have the side length AC to be 12√3 and the measure of angle C is 30°.
Question:
In the right triangle shown below, angle B = 60° and side length AB = 12. How long is the side AC, and what is the size of angle C?
Answer exactly, using a radical if needed.
Related Questions
Juanita is booking a 4-night stay at a hotel. The rate is $79 per room plus tax.
If state tax is 6%, city tax is 2%, and municipal tax is 1%, what is her total
lodging cost?
Answers
if it’s $79 per night, then the answer is $344.44
if it’s $79 for all 4 nights, then the answer is $86.11
Final answer:
To determine the total lodging cost for Juanita's 4-night stay, multiply the nightly rate by the number of nights to get the pre-tax cost, calculate the total tax rate and apply it to the pre-tax cost to find the tax amount, and then add this tax to the pre-tax cost for the total cost. The total lodging cost, including taxes, will be $344.44.
Explanation:
Juanita is trying to calculate the total cost of a 4-night stay at a hotel with a nightly rate and additional taxes. To find Juanita's total lodging cost, a multi-step calculation is required. First, calculate the cost before tax by multiplying the nightly rate by the number of nights. Then, calculate the total tax by adding the state, city, and municipal tax rates and applying this sum to the pre-tax cost to get the total tax amount. Finally, add the tax amount to the pre-tax cost to find the total cost of the stay.
The nightly rate is $79 and she is staying for 4 nights, so the initial cost (before tax) is calculated as follows:
79 x 4 = $316
To calculate the total tax, convert the percentages to decimals and sum them up as follows:
State tax (6%) = 0.06
City tax (2%) = 0.02
Municipal tax (1%) = 0.01
Total tax rate = 0.06 + 0.02 + 0.01 = 0.09
Multiply the total tax rate by the pre-tax cost to find the total tax amount:
0.09 x 316 = $28.44
Finally, add the tax amount to the pre-tax cost to get the total lodging cost:
316 + 28.44 = $344.44
The total cost for Juanita's 4-night stay at the hotel, including all taxes, is $344.44.
What is 8+7times15 so what is it tell me now
Answers
Find all values of x in 17/x-12/x-12/(x-1)2
Answers
Answer:
Step-by-step explanation:
To solve
17/x-12/x-12/2(x-1)
5/x-12/2x-2
The LCM of x and 2x-2 is x and 2x-2
5(2x-2)-12x/x(2x-2)
10x-10-12x/x(2x-2)
To collect like in numerator
-2x-10/x(2x-2)
Day 1 2 3 4 5
Temperature (°F) 70 72 68 75 70
The temperature for 5 days is shown in the table. If on the 6th day the temperature was 83°, by how much will this increase the overall median temperature?
A) 1°.
B) 2°.
C) 3°.
D) 4°.
Answers
Answer:
the answer is b 2
Step-by-step explanation:
Final answer:
Adding a sixth temperature of 83°F to the original data set increases the median temperature from 70°F to 71°F, which is an increase of 1°F. Thus, option A is correct.
Explanation:
The question is asking how much the addition of a sixth day's temperature of 83°F will increase the overall median temperature of the previously recorded five days.
First, we need to arrange the temperatures of the first five days in ascending order: 68°, 70°, 70°, 72°, and 75°. The median of these five numbers is 70°F, which is the middle value.
When we add a sixth temperature of 83°F, the new set of temperatures will be 68°, 70°, 70°, 72°, 75°, and 83°.
With an even number of data points, the median is the average of the two middle numbers which are now 70° and 72°F. The average of 70°F and 72°F is 71°F.
Thus, the new median is 71°F, which is a 1°F increase from the original median of 70°F.
Therefore, the correct answer is A) 1°.
Identify the location of the values used to create a box
plot
A= B=
C=
D =
E =
Answers
Answer:A= minimum value
B=lower quartile
C=median
D= upper quartile
E= maxuim value
Step-by-step explanation:
Final answer:
A box plot displays the distribution of data based on a five-number summary: minimum, first quartile, median, third quartile, and maximum. It provides insights into the data's distribution, potential outliers, and comparisons of data sets.
Explanation:
The student's question involves the creation and interpretation of a box plot, which is a standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. To graph a box-and-whisker plot for the given data values, one must first calculate the five-number summary:
Minimum (A): The smallest data value.First quartile (B): The median of the lower half of the data set. This marks the 25th percentile, meaning 25% of the data fall below this value.Median (C): The middle value of the dataset when ordered from least to greatest, which also splits the data into two halves.Third quartile (D): The median of the upper half of the data set. This marks the 75th percentile, so 75% of the data fall below this value.Maximum (E): The largest data value.Once these values are determined, one can create a box plot where the box represents the interquartile range (IQR), stretching from Q1 to Q3, with a line at the median (C). Whiskers extend from the box to the minimum (A) and maximum (E) values. Analyzing the box plot can give insights into the data set, such as the distribution of the data, any potential outliers, and the comparison of different data sets.
A right triangular pyramid has a height of 10 inches and a base area of 41.57 square inches. What is the volume, in cubic inches, of the pyramid?
Answers
The volume of the rectangular pyramid with the given values of height and base area is 138.5 cubic inches.
What is a right triangular pyramid?A right triangular pyramid is simply a triangular pyramid which has an equilateral base, and whose top is directly above the base's centroid.
The volume of right triangular pyramid is expressed as;
V = 1/3 × b² × h
where b is the length of the base and h is the perpendicular height.
Given the data in the question;
Height of the pyramid h = 10in Base area A = 41.57in²First we find the dimension of the base length.
Since area square is A = b².
Hence;
41.57in² = b²
b = √41.57in²
b = 6.447in
Now, we substitute our values into the expression above.
V = 1/3 × b² × h
V = 1/3 × (6.447in)² × 10in
V = 1/3 × 41.563809in² × 10in
V = 138.5in³
Therefore, the volume of the rectangular pyramid with the given values of height and base area is 138.5 cubic inches.
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The graph of which function is decreasing over the interval (–4, ∞)?
Answers
Step-by-step explanation:
ok, logic
all of them are parabolas
1st and 3rd are opening up, so they defenitely increase, so no
decraseing
the vertex hs to be be at x=-4
y=a(x-h)^2+k
h has to be -4
y=a(x+4)^2+k
the answer is 2nd one or f(x)=-(x+4)^2+4
Answer:
B
Step-by-step explanation:
10–{12–[(−9)+(−1)]} answer ASAP please
Answers
Answer:
-12
Step-by-step explanation:
-9+(-1) is -10. 12-(-10) is 22. 10-22= -12
Some people were asked for their favorite numbers.
People's favorite numbers between 1 and 5
X
X
X
X
X
HHHHH
1 2 3 4 5
Favorite number
What is the mean of the numbers?
Answers
Answer:
3 is the mean.Step-by-step explanation:
To find the mean you need to add up all of the given numbers (order does not matter) then divide by that many numbers.
Add all 5 numbers then divide by 5.
1 + 2 + 3 + 4 + 5 = 15
15 / 5 = 3
I hope this helped!
Answer:
3 is mean
Step-by-step explanation:
How many triangles can you construct with two 4-inch sides and an 80 degree angle?
Answers
Answer:
2
Step-by-step explanation:
The 80° angle can be between the two given sides, or opposite one of them. These are the only two possibilities.
Ted and Katie have served up a total of $94 Tata saved six dollars less than four times as much is Katie how much has Katie saved
Answers
Answer:
Katie saved $20.
Step-by-step explanation:
I assume that "served" is a typo for "saved". Also, I assume that Tata and Ted are the same person.
Let the amount Katie saved = k
Then, ted saved $6 less than 4 times k, or 4k - 6.
The total saved by both is k + 4k - 6.
The total saved by both is $94.
k + 4k - 6 = 94
5k - 6 = 94
5k = 100
k = 20
Answer: Katie saved $20.
Final answer:
To determine the amount Katie has saved, two equations were set up based on the given information. The equations were solved simultaneously to find that Katie has saved $20.
Explanation:
Let's denote the amount Katie has saved as K and the amount Tata has saved as T. According to the problem, Tata saved six dollars less than four times as much as Katie, which we can write as T = 4K - 6. Additionally, we know that together they have saved a total of $94, so we can express this as K + T = 94. Substituting the expression for T from the first equation into the second equation, we get K + (4K - 6) = 94. Simplifying this, we get 5K - 6 = 94. By adding 6 to both sides, we obtain 5K = 100, and dividing by 5, we find that K = 20. Therefore, Katie has saved $20.
Find the range of each set of data.
Answers
Answer:
set 1 =11 set 2 =208 Set 2 has the wider spread since the range is bigger
Step-by-step explanation:
range- find the largest number and subtract the smallest number from it
Set 1: 12-1 =11
Set 2: 230-22 =208
how do you solve this?
Answers
Answer:
Step-by-step explanation:
Free Brainiest Fellows
A triangle has 2 angles that each measure 81°.
What kind of triangle is it?
A.
isosceles triangle
B.
equiangular triangle
C.
obtuse triangle
D.
right triangle
Answers
Answer:
Explanation: An isosceles triangle is a triangle in which two of the three sides are the same length, or two of the three angles are the same degree.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
If 2 angles are congruent, then it is an isosceles triangle (ALWAYS)
Describe the difference between an angle with a positive measure and an angle with a negative measure.
Answers
Answer:
negative is rotating counter clockwise and positive is straight
Step-by-step explanation:
positive 180 degresse rotation
Positive angles result from counterclockwise rotation, and negative angles result from clockwise rotation.
What are angles?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.
The difference between the positive and negative angles :-
Angles are sometimes classified based on whether their values are more than or less than 0° into positive and negative angles. The measure of a positive or a negative angle depends on the amount of rotation between the two sides forming the angle. The rotation is measured from the initial side to the terminal side of the angle.
What is a Positive Angle :-
An angle formed by an anti-clock wise or counterclockwise rotation from its initial side is called a positive angle.
12°, 33°, 90°, 180°, 360° are all example of positive angles.
What is a Negative Angle :-
An angle formed by a clockwise rotation from its initial side is called a negative angle.
-9°, -45°, -110°, -280°, -310° are all example of negative angles.
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Which linear equation represents the data given in the table?
Answers
We can find this answer through process of elimination.
From the table of values, we can see that the y-intercept is -3 from the point (0,-3)
We know that the equation for a line is
y = mx+b where b= the y-intercept
and D is the only equation where b = -3
The linear equation represents the data given in the table is option D.
calculation:Here we used the elimination process. From the table of values, we can see that the y-intercept is -3 from the point (0,-3)Now y = mx+b where b= the y-interceptAnd option D represent the only equation where b = -3.Find out more information about the equation here: https://brainly.com/question/2263981?referrer=searchResults
Bobby and his family went to the playground. The slide is 13
feet long. The end of the slide is 7 feet away from the stairs. The
stairs extend 2 feet higher than the end of the slide. How tall are
the stairs?
Answers
Answer:
it would be close to 12 ft im not 100% sure though the measurements are a little off
Step-by-step explanation:
hypotenuse is 13
then you have the adjacent = 7
13^2 = 169
7^2= 49
169-49=120
the square root of 121 is 11 wich is fairly close to 120(doesnt have one because its not exact)
there is two extra feet so 11 +2 is 13 but there was a little less then 11 so i had sid roughly around 12
brainliest, please???
The total height of the stairs can be found by adding the distance from the ground to the end of the slide (7 feet) and the extra height of the stairs (2 feet). This adds up to a total height of 9 feet for the stairs.
Explanation:The subject of the question is Mathematics, and it's suitable for a Middle School level. The problem can be solved using basic addition, and the concept of distance and height.
First, identify the length of the slide, which is 13 feet. Next, you're told that the end of the slide is 7 feet away from the stairs. This distance represents the height from the ground to the end of the slide. Lastly, you're told that the stairs extend 2 feet higher than the end of the slide.
Add these two distances together. So, the total height of the stairs is 7 feet (height to end of slide) plus 2 feet (additional height of stairs) equaling 9 feet.
So, the stairs are 9 feet tall.
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This is the first year Janis is playing softball. She has been practicing her batting. On her last swing the bat made an arc with a radius of 48 inches and swept through 255° of rotation. Assuming the arc is circular, what is the distance the tip of the bat travels in inches in terms of pi? How many feet is this in terms of pi?
Answers
Using the relation between arc length and the radius, the arc length covered by the bat tip for a swing of 255 degrees with a 48-inch radius bat is (85/6)π inches or (85/72)π feet.
Explanation:The subject of the question is based in mathematics, specifically geometry. To solve the question, first, we have to know that the circumference (C) of a given circle is calculated as
2πr
, where 'r' is the radius. Since 255° is a portion of the total circumference (which is considered as 360°), we calculate the fraction of the total circumference covered by 255°, which is 255/360. The arc covered by Janis's bat swing is, therefore,
(255/360)*2πr
. Substituting 'r' with 48 inches, the arc length (As) comes to
(85/6)π inches
. To convert this to feet, divide the result by 12 (since there are 12 inches in one foot), which gives
(85/72)π feet
.
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". Which of the following sentences does not represent a function?
A. Notebooks are sold in a four pack for $20
and a five pack for $25.
B. Shaunette charges $20 for one hour of
babysitting and $40 for two hours.
C. Marcy drove 50 miles in one hour today
and 100 miles in two hours yesterday.
D. Timon chewed six gumballs in two hours
today and six gumballs in three hours
yesterday
Answers
To be a function, each input must correspond to exactly one output. In all cases except for Timon's gumballs, each distinct input yields a distinct output. Therefore, the sentence about Timon's gumballs does not represent a function.
Explanation:In mathematical terms, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let's go through these situations separately:
Notebooks are sold in a four pack for $20 and a five pack for $25. Here, the input, or the number of notebooks, determines the output, or price. No two outputs are the same for any given input. This is a function.Shaunette charges $20 for one hour of babysitting and $40 for two hours. The input (hours) determines the output (price). Similar to the first example, no two outputs are the same for any one input. This is a function.Marcy drove 50 miles in one hour today and 100 miles in two hours yesterday. The input (time) determines the output (distance traveled). There is a unique output for each input. This is a function.Timon chewed six gumballs in two hours today and six gumballs in three hours yesterday. This time, for different inputs (different hours), the output (number of gumballs chewed) is the same. This does not comply with the definition of a function because a function should have a unique output for each input. Therefore, this sentence does not represent a function.Learn more about Functions here:https://brainly.com/question/35114770
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Tickets to a spring concert are $5.00 for students and $8.00 for adults. 250 tickets to the concert were sold for a total of $1550. How many tickets adult tickets and how many student tickets were sold?
Answers
Answer:
100 adult tickets
150 students tickets
Step-by-step explanation:
First, construct an equation that relates the tickets.
For the first equation, 5x represents $5 per ticket for students and 8y represents $8 per ticket for adult, showing the money earned.
For the second equation, x represents student tickets and y represents adult tickets, showing the tickets sold.
[tex]5x+8y=1550\\x+y=250\\[/tex]
Then, you have to cancel out similar factors. I will multiply the second equation by -5 because that is the easiest option for this specific case.
[tex]-5(x+y=250)\\-5x-5y=-1250\\5x+8y=1550\\3y=300\\y=100[/tex]
We have solved for y, which is how many adult tickets were sold. To solve for student tickets, we will solve the second equation.
[tex]x+y=250\\x+100=250\\x=150[/tex]
As a result we have 100 adult tickets and 150 student tickets.
Hope this helps!! <3
Which number best represents the situation. "A plane descends 1, 500ft?
1,500
15
-1,500
-15
Answers
27x+3=6
Whats is x in that problem
Answers
Answer:
x=1/3
Step-by-step explanation:
You have to isolate the variable, so you must first separate the constants from the variable. Add 3 on both sides to cancel out the minus three and to move it to the other side. Now you have 27x=9. It's pretty simple from there just use your calculator and divide 27x/27 and also 9/27. That leaves you with 1/3
To solve for x in the equation 27x+3=6, we subtract 3 from both sides, divide both sides by 27, and get the solution x = 1/9.
Explanation:To solve for x in the equation 27x+3=6, we'll start by isolating the variable x. First, subtract 3 from both sides of the equation to get 27x = 3. Then, divide both sides by 27 to find the value of x.
Subtract 3 from both sides: 27x + 3 - 3 = 6 - 3Simplify: 27x = 3Divide both sides by 27: x = 3 / 27Simplify the fraction: x = 1/9Therefore, the solution to the equation is x = 1/9.
What is the median of this set of numbers?
3, 6, 1, 10, 6, 2, 2, 5
A
5
B
3
C
2
D
4
Answers
Answer:
d. 4
Step-by-step explanation:
Arranging in ascending order
1 , 2 , 2 , 3 , 5 , 6 , 6 , 10
No of data (N) = 8
Position of median
= (N+ 1) / 2 th item
= (8 + 1) / 2 th item
= 9 / 2 th item
= 4.5 th item
Exact median
= (5 + 3 )/2
= 8/2
= 4
0.8342 as a fraction?
Answers
Answer:
4171/5000
Step-by-step explanation:
When diving 4171 by 5000, you get the answer of 0.8342. If you are using a calculator, you can use a button that allows you to convert decimals to fractions and vice versa.
The decimal number 0.8342 as a fraction in the simplest form is 4171/5000.
What is a fraction?In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
In this exercise and scenario, we would convert the given decimal number into a fraction as follows;
0.8342 = 8342/10000
By dividing both the numerator and denominator by 2, we have the following
8342/10000 = 4171/5000
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-48 ÷ [-3 (2 - 4) ] = ?
Answers
Answer:
The answer is -8
Step-by-step explanation:
By the way, is that Lucy Heartfilia? :D
Find the distance between (2, 3) and (–4, 4). If necessary, round to the nearest tenth.
Answers
Answer:
√37
Step-by-step explanation:
Which is the angle of rotational symmetry for the isosceles trapezoid?
Answers
Angle of rotational symmetry for the isosceles trapezoid is 180 degrees .
Given, rotational symmetry for isosceles trapezoid .
The trapezium, also known as the trapezoid is a plane figure with four sides, two of which are of equal length.
If the other two sides are also of same length then the figure is said to be isosceles trapezoid .
There is no symmetry in a trapezoid unless it is an isosceles trapezoid. In that case it has one axis of symmetry that cuts the two bases in half. An 180 degree rotation about this axis produces the same figure. There are no other lines of symmetry.
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A coat is marked down 40% off the original price. If the
original price was S115.00, what is the sale price of the
coat before sales tax?
Answers
Answer:
$69.00
Step-by-step explanation:
Hi there,
In order to solve this problem, I used this formula:
Dollar Markdown = (markdown %)(original price)
You will end up with Markdown = (0.4) (115).
(Be sure to convert the percentage to a decimal value. (ex. 40% = 0.4))
After multiplying, we find that 46 dollars is 40% of the original price.
For the final step, simply subtract the original price by the amount marked down to get $69.00.
Hope this was useful. Cheers.
Please help me with this
Answers
Answer:
a b c and e
Step-by-step explanation:
Answer:
The fist one
Step-by-step explanation:
Sophia wanted to knit a scarf 1 meters long. On Monday, she knit
of the length. On Tuesday, she knit another 45 centimeters.
What fraction of the scarf did she knit altogether?
Answers
She knit 1/4 of the total length of the scarf on monday
Answer:
She knit 7/10 of the scarf altogether
Step-by-step explanation:
Please see the attached file for explanation