Answers
Note: This is done in the interior triangle as the angle will be equivalent to the other two angles.
Here's how you solve it:
You have to use the law of cosine for the interior triangle; the law of cosine is: c^2 = a^2 +b^2 - 2ab times cos (C)
Substitute each factor so that the equation now appears as so:
h^2 = 8^2 + 10^2 - 2(8)(10) times cos (80)
This will give you: h = 11.67
Now, you have to apply this to the law of sin which is a over sin(A) = b over sin (B) = c over sin (C). (Lowercase letters are the opposite side of uppercase angles.)
This will then give you:
11.67 over sin (80) = 8 over sin (S) = 10 over sin (T)
sin -1 ((8 times sin (80)) over 11.67) is equal to S
sin -1 ((10 times sin (80)0 over 11.67)) is equal to T
Because you now know the angles of S and T, you need to use the law of sin again.
t over sin (T) = s over sin (S)
t = 10 + x
s = 8 + 18 = 22
Thus, you need to substitute the variables to get this equation:
10 + x over sin (57.54) = 22 over sin (42.45)
x = 22 times sin (57.54) over sin (42.45) and next to this is -10
Thus, getting the answer of x = 17.50
Answer: x = 17.5
Step-by-step explanation:
You're using interior angles
Use the law of cosine: c^2 = a^2 +b^2 - 2ab times cos (C)
h^2 = 8^2 + 10^2 - 2(8)(10) times cos (80) so h = 11.67
11.67 over sin (80) = 8 over sin (S) = 10 over sin (T)
sin -1 ((8 times sin (80)) over 11.67) is equal to S
sin -1 ((10 times sin (80)0 over 11.67)) is equal to T
t over sin (T) = s over sin (S)
t = 10 + x
s = 8 + 18 = 22
10 + x over sin (57.54) = 22 over sin (42.45)
x = 22 times sin (57.54) over sin (42.45) and next to this is -10
the answer of x = 17.50
Hope this helps, have a BLESSED and wonderful day! :-)
-Cutiepatutie <3
Related Questions
What is 50,935 divided by 5?
Answers
The table contains data on the admission price (in dollars) for one-day tickets to 10 theme parks in the United States. Find the interquartile range for this data set. The numbers are 60 60 42 43 25 52 65 43 42 40
Answers
To find the IQR, the data was first sorted and then split into two halves to find Q1 (42) and Q3 (60). The IQR of the theme park ticket prices is the difference between Q3 and Q1, which is 18 dollars.
Explanation:To find the interquartile range (IQR) of the admission price for one-day tickets to 10 theme parks in the United States, first, we need to arrange the data in ascending order: 25, 40, 42, 42, 43, 43, 52, 60, 60, 65. With the data sorted, we find the median (the middle value) to divide the data set into two halves. However, since there are an even number of observations, the median will fall between the two middle numbers. The two middle numbers are the 5th and 6th values, which are 43 and 43, so their average is also 43.
Next, we find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the first half of the data (25, 40, 42, 42, 43), which is 42. Q3 is the median of the second half of the data (43, 52, 60, 60, 65), which is 60. The IQR is then found by subtracting Q1 from Q3, which is 60 - 42 = 18.
Please need help on this
Answers
you are u on online school y
rate 5 stars plz
The letter E would be for stock increasing
Letter D for Stock decreasing
and Letter C for it remaining constant
Hope this helped!!
will give crown to best answer!!!!!!
\Which of these pairs of points defines a line with a slope of -1?
A. (3, 10) and (3, 5) B. (3, 10) and (5, 3) C. (10, 3) and (15, -2) D. (10, 3) and (3, 5)
Answers
Answer:
c
Step-by-step explanation:
if sec theta equals negative 5/3, such that 180° <thata<270° then determine what is tan theta ?
Answers
g={(-9,6),(-6,4),(2,-6),(6,-5)}
h(x)=3x-4
find the following
g^-1(-6)=
h^-1(x)=
(h^-1·h)(3)=
Answers
g^-1(-6) = 2
b) Swap x and y and solve for y.
x = 3y -4
x +4 = 3y
(x +4)/3 = y
Then the inverse function can be written as
h^-1(x) = (x +4)/3
c) You have shown the product of h^-1(x) and h(x). We have to assume that is what you intend.
h^-1(3) = (3 +4)/3 = 7/3
h(3) = 3×3 -4 = 5
(h^-1·h)(3) = h^-1(3)·h(3) = (7/3)·5
(h^-1·h)(3) = 35/3
If you intend (h^-1◦h)(3), that value is 3.
roselia build a cabinet in the shape of a rectangular prism.The cabinet was 30 inches wide, 4 feet tall,and 18 inches deep. What is the Valume of the cabinet in cubic feet
Answers
Here, that vol. is V = (2.5 ft)(1.5 ft)(4 ft) = 15 cubic feet (answer)
Note: volume (not valume).
The cabinet's volume is 15 cubic feet.
The student is asking how to calculate the volume of a cabinet in the shape of a rectangular prism. The cabinet dimensions provided are 30 inches wide, 4 feet (48 inches) tall, and 18 inches deep. To find the volume in cubic feet, we first need to ensure all dimensions are in the same units, so we convert inches to feet by dividing by 12.
Thus, the cabinet dimensions in feet are 2.5 feet wide (30 inches / 12), 4 feet tall, and 1.5 feet deep (18 inches / 12).
The formula to calculate volume is length x width x height:
Volume = width x height x depth
Volume = 2.5 ft x 4 ft x 1.5 ft
Volume = 15 cubic feet
Therefore, the volume of Roselia's cabinet is 15 cubic feet.
Marty is spending money at the average rate of $3 per day. After 14 days he has $68 left.
a) Write the equation to model this situation, where x is the number of days.
b) Use the equation to determine how much money Marty had two weeks ago.
c) Use the equation to determine when Marty will run out of money if he continues to spend at this rate.
Answers
After 14 days = $68 left
a) x = 3
14x = - 68
14x + 68 = 0
b) 14(3) + 68 = $120
c) total money = y
y - 14x = 120
y = 14(3) + 120
y = 172
172 - 3n = 0
3n = 172
n = 57 days and 8 hours
Sorry If I am wrong,but I've tried my best to give you the solution..
a) equation to model this situation can be
14x + 68 = 0
b) so, the money he had before two weeks are
14(3) + 68 = $120
c) equation to determine when Marty will run out of money if he continues to spend at this rate is 57 days and 8 hours.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Given:
Spent per day = $3
After 14 days = $68 left
a) equation to model this situation can be
14x + 68 = 0
b) so, the money he had before two weeks are
14(3) + 68 = $120
c) equation to determine when Marty will run out of money if he continues to spend at this rate.
let the total money be a
a - 14x = 120
a = 14(3) + 120
a = 172
So, if m is the number of days
172 - 3m = 0
3m= 172
m = 57 days and 8 hours
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A random sample (Sample 1) of the cars' average driving speed (km/h) is: 120, 132, 142, 119, 112, 130, 149, 111, 167, 139, 141. A random sample (Sample 2) of the SUVs' average driving speed (km/h) is: 112, 135, 124, 115, 119, 90, 112, 134, 113, 114, 115. What is the median of Sample 1? What is the median of Sample 2?
Answers
sample 2 is 115
please I need help and I dont get it..
Answers
40*3=120 total cakes
120*.15=18 chocolate cakes
A bicycle and a bicycle helmet cost 240 dollars. How much did each cost, if the bicycle cost 5 times as much as the helmet?
Question 8 options:
bike = $200 and helmet = $40
bike = $160 and helmet = $80
bike = $120 and helmet = $60
bike = $100 and helmet = $90
Answers
Let j = 16. What is the value of k in the equation k = 2 × j + 4?
Answers
You put 16 in for j
k = 2 * 16 + 4
Multiply
k = 32 + 4
Add
k = 36
The answer is 36
Hope this helps!
That equals:
-------↓-------
k = 2 × 16 + 4
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Multiplication comes before addition
2 × 16 = 32
32 + 4 = 36
k = 36
Hope this helps :)
Simplify the expression insert
Answers
[tex] \frac{96}{8} =12[/tex]
So, we can rewrite our radical as follows:
[tex] \sqrt{ \frac{96}{8}} = \sqrt{12} [/tex]
Now, we are going to decompose 12 into prime factors:
[tex]12=2^2*3[/tex]
So, we can rewrite our fraction as follows:
[tex] \sqrt{12} = \sqrt{2^2*3} [/tex]
Since 2 has the same exponent as the index of the radical, we can take it out:
[tex]\sqrt{2^2*3}=2 \sqrt{3} [/tex]
We can conclude that the simplified form of the expression is: [tex]2 \sqrt{3}[/tex]
a right triangle has a legs measuring 16 in and 28 in
What is the length of the hypotenuse?
Round your answer to the nearest tenth.
a. 23.0 in.
b. 32.2 in.
c. 44.0 in.
d. 1040.0 in.
URGENT
WILL MARK BRAINLEIST
Answers
To solve this, let's use apply the Pythagorean Theorem.
Formula: [tex]a^2 + b^2 = c^2[/tex]
For a and b, we would plug in the values for the two known legs.
[tex]16^2 + 28^2 = c^2[/tex]
[tex]16^2 = 256 28^2 = 784 256 + 784 = 1,040[/tex]
Now we take the square root of 1,040
[tex] \sqrt{1,040} = 32.2[/tex]
Your answer is 32.2 :)
Need help on this please
Answers
So "C"
Find the total surface area of a triangular pyramid if the perimeter is 30 feet, the slant height is 12 and the base is 43.5ft
Answers
You are reading a book with 120 pages if you want to read the same number of pages each night how many would you have to read each night to finish in 10 days
Answers
[tex]120 / 10 = 12[/tex]
If you want to read the same number of pages each night for 10 days, you will read 12 pages every night.
If you wanted to finish an 120 paged book in 10 days you would have to read 12 pages. You can ether divided 10/12 and you confirm your answer by 10•12.
Can you please answer for 30 points Thanks
Answers
Find m∠2.
90 - 72 = 18
m∠2 = 18°
Now ∠2 + ∠3 must equal 180° because they are on a straight line.
Subtract 18 from 180.
180 - 18 = 162
m∠3 = 162°
Answer:
Step-by-step explanation:
To find angle 3, we need to first find angle 2.
-It is given that it's a square. The full angle is 90°. Angle 2 would be 90-72, which is 18°.
Now that we have angle 2, we can find angle 3 because angle 2 and 3 are linear pairs.
180°-18°
162°
m<3=162°
(08.02)Which of the following graphs best represents the solution to the pair of equations below? y = −x + 6 y = 2x − 3
Answers
To figure this out simply set the equations equal to each like this 2x - 3 = -x + 6
this works because if both of the equations are equal to y then you can simply substitute one them in for y and solve.
To check substitute 3 into the new equation and solve:
2(3) - 3 = -3 + 6
6 - 3 = -3 + 6
3 = 3
Which of the following statements describes this sequence 1, 3, 9, 27
I this is an arithmetic sequence
II The common ratio for this sequence is 3
III the next term in the sequence is 54
IV The sequence can be described by the expression n+3
I and IV
I,II, and III
II
Answers
The given sequence is a geometric sequence with a common ratio of 3. The next term of the sequence is 81, not 54. The sequence cannot be described by the expression n+3 or as an arithmetic sequence.
Explanation:The sequence given is 1, 3, 9, 27, which is a sequence where each term is a multiple of the previous term. This type of sequence is called a geometric sequence. In this particular sequence, it is clear that every term is being multiplied by 3 to obtain the next term. Hence, the common ratio for this sequence is indeed 3 (Statement II).
This sequence is not an arithmetic sequence (Statement I is false) because the difference between successive terms is not constant. Furthermore, the sequence can't be described by the expression n+3 (Statement IV is false) because the sequence doesn't increment by adding 3 to each term; instead, it increments by multiplying the previous term by 3. Lastly, the next term in the sequence is not 54 (Statement III is false). It is 81 because you multiply the previous term (27) by the common ratio (3) to get 81.
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Which expressions result in a rational number?
Answers
C+D
A*B
C*D
A*A
A+B does not give a rational number answer; √3+2√3 = 3√3
C+D is a rational number; √25=5 and √16=4; 5+4=9.
A+D is not a rational number; √3+√16 = √3+4
A*B is a rational number; √3*2√3 = 2√9 = 2*3 = 6
B*D is not a rational number; 2√3*√16 = 2√3*4 = 8√3
C*D is a rational number; √25*√16 = 5*4 = 20
A*A is a rational number; √3*√3 = √9 = 3
Rational numbers are those that can be expressed as a fraction of two integers. Examples of expressions that result in rational numbers include simple calculations or operations that result in whole numbers or decimal numbers that can be written as a fraction.
Explanation:In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator not being zero. If an expression results in such a number, then it is considered a rational number.
Let's consider some examples from the given information:
106 (6-3): This equates to 10^3 which will result in the number 1000, a rational number as it can be expressed as 1000/1. 4.5 × 10⁹: The result of this multiplication also gives a rational number as it can be written in a fraction form. 0.3333: This number is also rational as we can write it as 3333/10000. 0.6: This can be written as 6/10 or 3/5, so it's also a rational number.
However, numbers resulting from certain trigonometric functions like sine and cosine, logarithms, or exponential functions may not always be rational. These functions require pure numbers as inputs and outputs.
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Karina bought a camera with the regular price of $99. It was on sale at a 20% discount. There was a 7% tax on the sale price. How much did Karina spend to buy the camera? PLEASE SHOW YOUR WORK
Answers
Convert 20% to a decimal ⇒ 0.2
99 × 0.2 = 19.8
Subtract 19.8 from 99.
99 - 19.8 = 79.2
Now multiply 79.2 by 7%.
7% ⇒ 0.07
79.2 × 0.07 = 5.544
Add 5.544 to 79.2.
5.544 + 79.2 = 84.744
Round to the hundredths place because it's money :)
84.744 ⇒ 84.74
Karina spent $84.74 to buy the camera.
Mr. carlucci brought 8 3/4 pounds pepperoni for large sandwiches. He cut the pepperoni into 1/12 pound slices. A skateboarder bumped into his table and 2 7/12 pound of the pepperoni fell on the ground and was eaten by 3 dogs. Does mr. carlucci have enough pepperoni left to make 74 sandwiches if he puts one slice on each sandwich? By how much is he over or under the amount of pepperoni he needs?
Answers
First make 8 3/4 into a improper fraction ⇒ 35/4.
35/4 ÷ 1/12 ⇒ 35/4 × 12/1 = 105
Mr. Carlucci has 105 pieces of pepperoni.
Now subtract 2 7/12 from 105.
105 - 2 7/12 ⇒ 105 - 31/12 ⇒ 1260/12 = 31/12
1260/12 = 31/12 = 1229/12
1229/12 = ~102
Mr. Carlucci has enough pepperoni to make 74 sandwiches. He is over the amount of pepperoni he needs by 28 slices.
A square has a perimeter of 760 feet, what is the length of each side?
Answers
-4 sides
- All sides are equal
760/4=
190.
Each side has a length of 190 feet
Hope this helps :D!!
Someone pleas help me!!!!!! An irrational number cannot be written as a ______ of two integers.
a) difference b) ratio
Answers
Take Pi for example, it is irrational because it cannot be written as a fraction
If a number cannot be expressed as a fraction, it is irrational
Hope this helps!
Answer: Ratio
True or false;
If two planes cross one another, then their intersection is two lines.
Answers
The answer would be true, because if your planes are not parallel, they're eventually going to meet and intersect.
Hope this helps!
Jaden buys a raffle ticket. Each ticket has a 1% chance of being drawn. How likely is it that Jaden's ticket will be drawn? It definitely will be drawn.
It likely won't be drawn.
It likely will be drawn.
It definitely won't be drawn.
Answers
Your answer would be
It likely won't be drawn.
The answer is - It likely won't be drawn. The likelihood of Jaden's ticket being drawn is 1%, so it is unlikely that his ticket will be selected.
The likelihood that Jaden's ticket will be drawn depends on the probability of his ticket being selected. In this case, each ticket has a 1% chance of being drawn, which means there is a 1 in 100 chance that Jaden's ticket will be selected. Therefore, it is likely that Jaden's ticket won't be drawn.
Jaden's raffle ticket has a 1% chance of being drawn, making it much more likely that it won't be drawn than it will. The concept of 'being due to win' is a common fallacy as each draw is an independent event with a constant probability.
Michael does not want to spend more than $21.00 on a new backpack, not including tax. Select all of the following descriptions of prices for backpacks that Michael would buy.
Answers
• 10% of $25 = $2.5 Therefore B would come to $22.5
• 1/4 of $24 = $6
• 50% of $41 = $20.5 Therefore D would be $20.5
Your answers are A, C and D
20% × 25 = 5
25 - 5 = $20.00
b)
10% × 25 = 2.5
25 - 2.5 = $22.5
c)
24 ÷ 4 = $6.00
d)
41 × 50% = 20.5
41 - 20.5 = $20.5
A, C, and D are all prices for backpacks that Michael would buy.
Which angle in the image corresponds to ∠X in the pre-image?
∠L
∠M
∠N
Answers
The angle that corresponds to angle X would be the angle on the opposite figure that is in the same position as angle X.
Your answer is Angle L.
Lizzie played tennis for 2 2/3 hours. Andrew played tennis for 1 1/3 hours. How much longer did Lizzie play tennis than Andrew?
Answers
Lizzie played for 2 hours and 40 minutes
Andrew played for half as long as Lizzie did, so Lizzie played for 1 1/3 hours longer than Andrew did. Hope this helps!
[tex]2 \frac{2}{3} -1 \frac{1}{3} [/tex]
For simpler subtraction, we can convert the mixed numbers into improper fractions:
[tex]\frac{8}{3} -\frac{4}{3} = \frac{4}{3}= 1\frac{1}{3} [/tex]
Lizzie played tennis [tex]1\frac{1}{3}[/tex] hours, or 1 hour and 20 minutes, longer than Andrew.