If sinx = 0.6 and AB = 12 , what is the area of ΔABC ?
a. 9.6 units²
b. 28.8 units²
c. 31.2 units²
d. 34.6 units²
e. 42.3 units²
Answers
If sinx =0.6 and AB =12, then area of triangle ABC is equal to 96 units².
As given in the question,
In triangle ABC,
AB = Perpendicular side
BC = Base
AC = Hypotenuse
sinx = 0.6
AB = 12
sinx = AB / AC
⇒0.6 = 12/AC
⇒AC = 12 /0.6
⇒ AC = 20
Using Pythagoras theorem,
AB² + BC² = AC²
⇒ BC² = 20² -12²
⇒BC = 16
Area of ΔABC = (1/2)× AB×BC
= (1/2)×12×16
= 96 units²
Therefore, if sinx =0.6 and AB =12, then area of triangle ABC is equal to 96 units².
The complete question is:
If sin x = 0.6 and AB = 12 as shown in the diagram , what is the area of ΔABC ?
a. 96 units²
b. 28.8 units²
c. 31.2 units²
d. 34.6 units²
e. 42.3 units²
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Related Questions
Find an expression which represents the difference when (3x+1)(3x+1) is subtracted from (-9x+1)(−9x+1) in simplest terms.
Answers
Answer:
(3/+1)= 9
Step-by-step explanation:
in simplest terms
Answer:
Step-by-step explanation:
-12x
The figure above shows a graph of a line that goes through the origin. What is the value of (k)/(h) ? (A) 4 (B) 3 (C) (4)/(3) (D) -(4)/(3) (E) "-4"
Answers
The value of (k)/(h) from the graph of a line that goes through the origin is 4.
What is a graph of a line?A line graph joins distinct data points that generally show quantitative values across an interval. Line graphs have two axes:
The x-axis (horizontal), andThe y-axis (vertical), which are visually expressed as (x,y).From the image attached below, the value of (h,k) as translated on the graph in the negative x and y axis shows that:
(h,k) = (-1,-4) in terms of (x,y) respectively.However, we are to determine the value of (k)/(h):
i.e.
(k)/(h) = -4/-1
(k)/(h) = 4
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Express 80 as the product of its prime factors
Write the prime factors in ascending order.
Answers
Answer:
Give brainliest - the crown thingy.
2*2*2*2*5
Or
2^4 * 5
The * is the symbol on my keyboard for the multiplication symbol.
Step-by-step explanation:
The current value of a baseball card is 80 times its original value v (in dollars). The baseball card is worth $36. Write and solve an equation to find the original value of the baseball card.
Answers
The original value of the baseball in discuss according to the task content is; $0.45.
What is the original value of the baseball card?It follows from the word phrase given that; the current value of a baseball card is 80 times its original value v (in dollars) where the current value is; $36.
Therefore, we have; 36 = 80 × v
Divide both sides by 80;
Hence; v = 36/80 = $0.45.
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b. Without calculating, use the pattern to predict the sum of the squares of the first ten terms of the Fibonacci sequence.
Answers
Answer:23
Step-by-step explanation:
because you add the two
Write the specified type of proof.
Flow proof of Corollary 4.1
Answers
The Corollary 4.1 states that , the acute angles of a right triangles are complementary.
What is Corollary ?A corollary can be defined as a theorem that follows a direct result of an another theorem. With an original theorem, a corollary can be used as a reason to proof it. There are two main corollaries which follow directly from the Triangle Angle-Sum theorem. These are defined below :
Corollary 4.1
It states that the " acute angles of the right triangle are always complementary".
Abbreviation : Acute ∠s of rt. Δ are comp.
Corollary 4.2
It states that, "there is at most only one right angle or an obtuse angle in triangle".
Flow Proof of Corollary 4.1Given : a triangle ABC, right angled at A
To Prove: ∠B and ∠C are complimentary
Proof :
step 1 : ∠A = 90°
step 2: According to angle-sum theorem
∠A + ∠B + ∠C = 180
step 3: 90 + ∠B + ∠C = 180
step 4: ∠B + ∠C = 180 - 90
step 5: ∠B + ∠C = 90
Thus, Corollary 4.1 is proved.
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Question 12
Write an equation of a line that passes through (8,5) and (11, 14).
Answers
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{11}~,~\stackrel{y_2}{14})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{11}-\underset{x_1}{8}}} \implies \cfrac{14 -5}{11 -8} \implies \cfrac{ 9 }{ 3 }\implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{3}(x-\stackrel{x_1}{8}) \\\\\\ y-5=3x-24\implies y=3x-19[/tex]
Answer:
So to write this as an equation follow the steps:
1.First you take y delta divided by x delta. This means that you but in the coordinates, take them minus eachother then divided by eachother. Let me show you with maths for better understanding:
Now you have k in y=kx+m ( the equation has different letters depening on where you are from but I think you understand).
So know we just use simple algebra bu putting in the coordinates in the equation. So for this example im going to use the coordinates x= 8 and y=5
so we get:
Find the missing term of each geometric sequence. It could be the geometric mean or its opposite. 2/5,||| 8/45
Answers
The missing item in the given geometric sequence is: [tex]\frac{4}{15}[/tex].
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: [tex]\frac{2}{5}[/tex], ___, [tex]\frac{8}{45}[/tex]
Here, Let b = missing term of the geometric sequence.
By using the concept of geometric mean, we can find the missing term; geometric mean is used to find the mean, i.e., the middle term between two terms.
GM = [tex]\sqrt{(term_1)(term_2)}[/tex]
Here, b = [tex]\sqrt{\frac{2}{5}\times\frac{8}{45}}[/tex]
=> b = [tex]\sqrt{\frac{16}{25\times9}}[/tex]
=> b = [tex]\frac{4}{5\times3}=\frac{4}{15}[/tex]
Hence, The missing item in the given geometric sequence is: [tex]\frac{4}{15}[/tex].
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How do u write and graph an inequality for
{x | x< 7}
Answers
The inequality expression x < 7 is equivalent to the given inequality expression {x | x < 7}
How to write and graph an inequality for the inequality expression?The inequality expression is given as
{x | x < 7}
When the braces are removed, the inequality expression becomes
x < 7
This means that x < 7 is equivalent to the given inequality expression {x | x < 7}
Next, we represent the inequality expression on a plot
See attachment for the graph of the inequality expression
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In a 3-digit number, the hundreds digit is four more than the units digit, and the tens digit is three less than the sum of the other two digits. If the sum of all three digits in the number is 17, find the free digits. Then find the number
Answers
Step-by-step explanation:
the number is abc
c = units digit
b = tens digit
a = hundreds digit
a = c + 4
b = (a + c) - 3
a + b + c = 17
we use the first equation in the second and get
b = (c + 4 + c) - 3 = 2c + 4 - 3 = 2c + 1
abd we use the first and the second equation more in the third and get
c + 4 + 2c + 1 + c = 17
4c = 12
c = 3
b = 2c + 1 = 2×3 + 1 = 6 + 1 = 7
a = c + 4 = 3 + 4 = 7
so, the number is
773
A particle P moves with constant velocity v. Initially P is at the point with position vector a. t seconds later P is at the point with position vector b. Find v when:
a= 2i + 3j, b= 6i + 13j , t = 2
Answers
Answer:
correct
Step-by-step explanation:
So the acute angle between the vectors is 7.122° (3sf). Explanation: The angle θ between two vectors →A and →B is related to the modulus.
Find the specified term of the following geometric sequences.
A^1 = 2, r= 3 find A^8
A^1 = 0, r = 1/2 find A^8
Answers
Answer:
7374
0.
Step-by-step explanation:
a^r = a1 * r^(n-1)
So, the terms are:
2*(3)^(8-1) = 4374
and
0*(1/2)^-1/2 = 0
You roll 3 dice. What is the probability that the outcome of at least two of the dice will be less than or equal to 4 ? Explain your reasoning.
Answers
6 out of 36 or I in 6 is the probability that the outcome of at least two of the dice will be less than or equal to 4 .
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Probability is the branch of mathematics concerning the occurrence of a random event, and four main types of probability exist: classical, empirical, subjective and axiomatic.There are 36 possible outcomes for rolling two dice.
There are six possible ways that the two dice will land on the same number, so the probability is 6 out of 36 or I in 6.
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Use your ruler and compasses to construct the angle bisector of angle ABC
Answers
Step-by-step explanation:
Step 1: Draw any angle, say ∠ABC. Step 3: Now, taking D and E as centers and with the same radius as taken in the previous step, draw two arcs to intersect each other at F. Step 4: Join B to F and extend it as a ray. This ray BF is the required angle bisector of angle ABC.
Evaluate each expression for x=0 . 13-6.5 x
Answers
After evaluating the expression for x=0, the equation 13-6.5x = 13
⇒ 13-6.5(0)
⇒ 13 - 0
⇒ 13
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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At the farmers market, Joyce buys 2 2/10 pounds of apples. The apples cost $1.25 per pound. She pays for the apples with a $10 bill. What is the change she should receive back?
Group of answer choices
10.00
7.25
7.50
2.25
Answers
Answer: Option 2
2.2 x 1.25 = 2.75
10-2.75=7.25
pls help will mark brainlyiest
Answers
Answer:
B
Step-by-step explanation:
3/5 multiplied by itself 4 times is a fraction exponent so it’s either b or c.
But C is [tex]\frac{3^{4}}{5}[/tex]. 3/5 multiplied 4 times means the bottom has a exponent too so it’s not c.
I need help asap please!
Enter the numerator and denominator of the fraction in simplest form that is equal to the decimal number shown.
0.23=
Answers
Answer:
23/99
Step-by-step explanation:
I took the test and got it right.
Hope this helps!
АB=2x+6
BC=3x-6
AC=?
Answers
Answer:
they cuestion is AC=2x-6
Ms Smith has 10 cubes in her hand. There are 10 students in her class. They each have 10 cubes in their hands. How many cubes do they all have?
answer choices
100
110
90
125
Answers
Answer:
110
Step-by-step explanation:
if each of the 10 students have 10 cubes, that's 100, plus the 10 cubes Ms Smith has is 110
While shopping for books, Dominique spent $38 less than 3 times what Roberto
spent. Write an equation to represent the scenario if Dominique spent $10.
Answers
The equation to represent the scenario is 3y - 38 = 10
How to write an equation to represent the scenario?Represent the given parameters as
x = Dominique
y = Roberto
From the question, we have
Dominique spent $38 less than 3 times what Roberto spent
This means that
x = 3y - 38
Also, Dominique spent $10
So, we have
3y - 38 = 10
Hence, the equation to represent the scenario is 3y - 38 = 10
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please help will give out brainlist
Answers
Because the line PQ is perpendicular to line ST, the slope of line ST is -1
How to determine the slope of ST?The points are given as
P = (1, 4)
Q = (-2, 1)
Start by calculating the slope (m) of ST using
m = (y2 - y1)/(x2 - x1)
This gives
m = (1 - 4)/(-2 - 1)
Evaluate the difference
m = -3/-3
Evaluate the quotient
m = 1
From the question, we have
Line PQ is perpendicular to line ST
This means that
Slope of ST = -1/Slope of PQ
This gives
Slope of ST = -1/1
Evaluate
Slope of ST = -1
Hence, the slope of line ST is -1
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find the measure of the missing angle
Answers
Answer:
47 degrees
Step-by-step explanation:
180 degrees - 90 (right angle) = 90.
90 - 43 = 47
Gimme brainliest <3
Which is the most accurate way to estimate 15% of 43?
Answers
Answer:
Multiply 43 x 15%
Step-by-step explanation:
Answer will be 6.45. To doublecheck yourself multiply 43 x 85% which is 36.55. Add 36.55 to 6.45 = 43
The opposite of the difference between x and 4
Please help!!
Answers
Answer:
It would be the sum of x and 4
Step-by-step explanation:
A telephone tree is used to send messages. the person at the top calls 2 people. each person calls 2 more people. suppose it takes 1 min to call someone. a message is relayed until the bottom row of the tree has 256 people. how long did this take? how do you know? the tree has 8 rows because each time a person calls 2 people, they call two more people.
Answers
Time taken by people in 8rows of given tree with each time a person calls 2 people and it takes 1 min to call someone is 510 minutes.
As given,
Given tree: Person at the top calls 2 people. each person calls 2 more people
Time taken by each person to call someone=1minute
Row wise
First1 +1=2
Second2+2=4
Third4+4=8
Fourth8+8=16
Fifth16+16=32
Sixth32+32=64
Seventh64+64=128
Eighth128+128=256
Total time
2 +4+8+16+32+64 +128 +256=510 minutes
Therefore, time taken by people in 8rows of given tree with each time a person calls 2 people and it takes 1 min to call someone is 510 minutes.
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Please help me out!!
Answers
Gimme brainlliest
If 7/2 meler of wire ris cut from a 2 piece of 10 meter long wire, how much wire is left?
Answers
The wire left is 16 1/2 meters.
How to calculate the fraction?From the information 7/2 wire is cut from piece of wire that is 2 piece of 10 meters.
Therefore, the wire that will be left will be:
= (2 × 10) - 7/2
= 20 - 7/2
= 20 - 3 1/2
= 16 1/2 meter
The wire left is 16 1/2 meters.
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Write an example from daily life that uses each type of real number.
integers
Answers
Most of the numbers we work with on a daily basis are real numbers. These include the cash you have in your wallet, sports statistics and the measures we see in recipes. A fraction can be used to represent each of these numbers (whether we like it or not).
What is real numbers?The value of a continuous quantity that may be used to describe a distance along a line is known as a "real number" in mathematics (or alternatively, a quantity that can be represented as an infinite decimal expansion).In one dimension, real numbers may be used to quantify things like distance, velocity, acceleration, force, momentum, and other physical quantities that can be measured (roughly) physically.Positive and negative numbers, as well as the zero, are real numbers.Since they do not belong to the imaginary number system, they are known as real numbers. For example, the square root of -1 is an imaginary number that cannot be quantified.Most of the numbers we work with on a daily basis are real numbers. These include the cash you have in your wallet, sports statistics and the measures we see in recipes. A fraction can be used to represent each of these numbers (whether we like it or not).
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Suppose a family drives at an average rate of 60 miles an hour on the way to visit relatives and then at rate of 40 miles an hour on the way back. The return trip takes 1 hour longer than the trip there. Let D be the distance in miles the family traveled. How many hours did it take to drive there?
Answers
Answer:
3 hours
Step-by-step explanation:
[tex]speed = \frac{distance}{time} \\ 60 = \frac{d}{t} \\ d = 60t \\ \\ speed = \frac{distance}{time} \\ 40 = \frac{d}{t + 1} \\ d = 40(t + 1)[/tex]
Since;
[tex]d = 60t \: \: \: and\\ d = 40(t + 1) \\ [/tex]
Therefore;
[tex]60t = 40(t + 1) \\ 60t = 40t + 40 \\ 60t - 40t = 40 \\ 20t = 40[/tex]
Divide both sides by 20
[tex] \frac{20t}{20} = \frac{40}{20} \\ t = 2 \: hours[/tex]
Since the return trip took an hour longer to get back home an hour will be added to the time
[tex]t + 1 = 2 + 1 \\ = 3 \: hours[/tex]
