In ΔSTU, s = 210 cm, ∠S=115° and ∠T=23°. Find the area of ΔSTU, to the nearest square centimeter.
Answers
The area of ΔSTU is approximately 6358 cm², to the nearest square centimeter.
How did we find the area of triangle STU?We can find the area of ΔSTU using the given side and angles by applying the formula:
Area = (1/2)ab x sin(C)
Where a and b are the lengths of two sides of the triangle and C is the angle between them.
We have one side, s, which is 210 cm. We also have two angles, ∠S = 115° and ∠T = 23°. We can find the third angle, ∠U, by using the fact that the sum of angles in a triangle is 180°:
∠U = 180° - ∠S - ∠T
∠U = 180° - 115° - 23°
∠U = 42°
Now, we have ∠S = 115°, ∠T = 23°, and ∠U = 42°. We can use the Law of Sines to find the other two sides of the triangle. Let side t be opposite ∠T and side u be opposite ∠U. Then:
s / sin(S) = t / sin(T) = u / sin(U)
We can now find t and u using the known values:
t / sin(23°) = 210 / sin(115°) = 90.5
S = 1/2 x 90.5 x 210 x sin 42°
=6358 cm²
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Related Questions
Define radius .A the distance from the center of a circle to any point on the circumference .B. the longest distance from one side of a circle to another .C. the center of a circle .D. none of the above
Answers
Answer:
option A
Explanation:
option B is wrong. radius is a line segment extending from the centre of a circle to the circumference.option C is wrong. radius is not the centre of the circle.Answer:
A
Step-by-step explanation:
Radius: the distance from the center of a circle to any point on the circumference
Diameter: the longest distance from one side of a circle to another.
Center: the center of the circle
Anao Savings and Loan is paying 6% interest compounded quarterly. Find the future value of ₱1,000, deposited at the beginning of every 3 months, for 5 years.
Answers
$1346.86
1) Having these data, we can write out the following:
6% interest compounded quarterly
Present Value: 1,000
5 years
2) Let's plug into the formula below:
\(\begin{gathered} F=P(1+\frac{r}{n})nt \\ F=1000(1+\frac{0.06}{4})^{4\cdot5} \\ F=1346.8555\approx1346.86 \end{gathered}\)Notice the rate is given in the decimal form. N stands for the number of periods that it is compounded.
3) Hence, the future value is: $1346.86 approximately
2x - y=5
x + 3y = 7
What is the value of the system determinant?
5
7
6
Answers
Answer:
A=7
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
The prime factorization of ___ is 2⁴×5.
Answers
Answer:
the prime factorization of 80 is 2⁴×5
Step-by-step explanation:
Answer:
80 is the answer
Step-by-step explanation:
2^4=16
16*5=80
Hope I helped you! :-)
Which of the following sets of data does not contain an outlier?
59, 60, 61, 67, 65
16, 17, 20, 19, 48
-1, 2, 1, 0, 5, 16
95, 99, 97, 94, 60
Answers
An outlier is a number that stands out from the rest, is very different from the rest. Therefore, the first choice is the correct answer as all the numbers are within the same range.
SHOW WORK: h(x)= -4x+4, what is x when h(x)=-20 ? *
Answers
Hope this helps
Answer:
x=6
Step-by-step explanation:
h(x)=-20 is the same as saying y=-20, so you would substitute h(x) with -20 and solve the equation from there.
\(-20=-4x+4\)
\(-4\) \(-4\)
---------------------
\(\frac{-24}{-4} =\frac{-4x}{-4}\)
\(6=x\)
HELP ME HELP ME HELP ME HELP HELP MEEEE
Answers
Answer:
Infinatly many solutions
Step-by-step explanation:
mark me brainlyest
Answer:
i would say a or b but probably b
Step-by-step explanation:
Higher Order Thinking Mrs. Dryson
divided her collection of 52 glass
bears
into equal groups. She had 1 bear
left over. How many groups did
Mrs. Dryson
make? How many bears
are in
each group?
Answers
To ensure that there is an equal number of glass bears in each group, Mrs. Dryson constructed a total of 17 groups, which can be calculated using arithmetic operations.
What is arithmetic operations?
The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.
As given in the question,
Mrs. Dryson divided her collection of 52 glass bears into equal groups and She had one bear left over
The steps listed below can be used to calculate the total amount of Mrs. Dryson's products:
Step 1: Arithmetic operations can be utilized to calculate Mrs. Dryson's overall output.
Step 2: Keep in mind that there are 52 glass bears in all, and after separating them into equal groups, she was left with just one bear.
Step 3 - The total bear population to divide into groups of an equal number is calculated as follows:
= 52 - 1 = 51
Step 4: The number that is divided by 51 such that the result is an integer is 3.
Step 5 - As a result, Mrs. Dryson created a total of the following groups:
= 51/3 = 17.
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1. Find the volume of the cylinder. Round to the
nearest hundredths.
5 CM
0.75 CM
Answers
Answer:
Rounded to the nearest hundredths, the volume of the cylinder is approximately 58.91 cm^3.
Step-by-step explanation:
To find the volume of a cylinder, you need to know its radius (r) and height (h). In this case, the radius is given as 5 cm and the height is 0.75 cm.
The formula for the volume of a cylinder is:
V = π * r^2 * h
where π is a mathematical constant approximately equal to 3.14159.
Let's substitute the given values into the formula:
V = π * (5 cm)^2 * 0.75 cm
V ≈ 3.14159 * (25 cm^2) * 0.75 cm
V ≈ 58.909 cm^3
Solve the equation x2 = 5.
Answers
±√5
Step-by-step explanation:x² = 5
x = ±√5
The solution to the equation \(x^2=5\) is \(x = \pm \sqrt{5}\).
How to evaluate and solve the given equation?In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.
Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical equation:
\(x^2=5\)
By taking the square root of both sides of the equation, we have:
\(x = \pm \sqrt{5}\).
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Identify the range of the function shown in the graph.
Answers
Answer:
Identify the range of the function shown in the graph.
Answer:
range=(10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10)
A staircase handrail is made from congruent parallelograms. In parallelogram PQRS, PQ=17.5, ST=18, and angle QRS=110°. Find each measure.
Answers
Answer:
m∠QRS = m∠QPS = 110°
m∠PQR= m∠RSP = 70°
PQ = SR = 17.5
PS = QR = 26.04 (nearest hundredth)
ST = TQ = 18
QS = 36
PT = TR = 12.97 (nearest hundredth)
PR = 25.93 (nearest hundredth)
Step-by-step explanation:
In a congruent parallelogram, opposite sides are congruent
⇒ PQ = SR = 17.5
⇒ PS = QR
In a congruent parallelogram opposite angles are congruent
⇒ m∠QRS = m∠QPS = 110°
Given:
Sum of interior angles of a quadrilateral = 360°m∠PQR = m∠RSP⇒ 2(m∠PQR) + 2(110) = 360
⇒ m∠PQR= m∠RSP = 70°
ST = TQ = 18
⇒ QS = 18 + 18 = 36
Using cosine rule to find PS:
QS² = PQ² + PS² - 2(PQ)(PS)cos(∠QPS)
⇒ 36² = 17.5² + PS² - 2(17.5)(PS)cos(110)
⇒ 1296 = 306.25 + PS² - 35(PS)cos(110)
⇒ PS² - 35cos(110)(PS) - 989.75 = 0
⇒ PS = 26.03923874 only (as measure > 0)
Using cosine rule to find PR:
PR² = SR² + PS² - 2(SR)(PS)cos(70)
⇒ PR² = 17.5² + 26.04² - 2(17.5)(26.04)cos(70)
⇒ PR² = 672.5839084
⇒ PR = 25.93422273
PT = TR = PR ÷ 2 = 25.93422273 ÷ 2 = 12.96711136
If each of these runners travels the indicated number of spaces in the same amount of time, at which numbered spot will all of the runners be next to one another?
Answers
The numbered spot at which all the runners will be next to one another is spot 19.
What is the LCM?Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.
Starting with the runner on the outside track, the provided parameters are;
The runner covered n₁ = 5 places on the outside track, which is the number of spaces.
Next, the inner runner will traverse n₂ spaces, which equals one space.
The following inner runner will cover n₃ = 3 spaces.
The subsequent runner will traverse n₄ = 2 spaces.
The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.
LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.
Time = 30/ = 6
Consequently, when the first runner has covered 30 places, we have;
Six time units have been expended.
The runner comes to a stop at position 30- (30 -19) = Position 19.
First runner's new destination is Spot 19.
The distance covered simultaneously by runner 2 is 6 x 1 = 6.
The distance covered by two runners running simultaneously equals six spaces.
Second runner's new position: 6 spaces plus spot 13 equals spot 19.
The combined distance covered by the three runners is 6 x 3 = 18.
The distance runner 3 covers 18 spaces simultaneously.
Third runner's new position: 18 spaces + Spot 1 = 19 spaces
Runner 4 covers a distance of 6 x 2 = 12 at the same time.
Distance runner 4 journeys equals 12 spaces
Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.
Therefore, all the runners will be next to one another is spot 19.
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find the sum.
Please please please help me!!
Answers
Answer/ explanation:
3a + 4
a + b
Which is the equation of the given line?
x = 4
y = 3
y=−2x
y = x
Number graph that ranges from negative five to five on the x and y axes. A line passes through the labeled points (four, three) and (four, negative two).
Answers
Since the x-coordinates are equal, hence the equation of the line will be x =4
Equation of a lineThe equation of a line in slope-intercept form is expressed as:
y = mx + b
where
m is the slope
b is the intercept
From the given coordinate points (four, three) and (four, negative two), we can see that the x-coordinates are equal, hence the equation of the line will be x =4
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How many pounds will $42.50 get you? Write just the number.
Answers
Answer: 31.07
Step-by-step explanation:
Answer:
20 ish shkgbksdjvbsdkgbh
Please HElp now no fake answers
Answers
Answer:
5.0 and 5.1
Step-by-step explanation:
√26 = 5.099019514 , it's from the calculator
Answer:
the square root of 26 must lie between 5 and 6
Step-by-step explanation:
5.099019514
Write in ordinary form
3.6
×
10
−
1
Answers
10/1 = 10
so 3.6 x 10 = 36
:)
help and you get all my points
If one quart of paint will cover 22 square feet, how many whole quarts will Mr. Chen need to buy?
Answers
Answer:
8x10=80
4x8=32, 32 divided by 2 = 16
80+16= 96sq.ft
96 divided by 22 = 4.36
the answer is 5 whole quarts
Area of the figure
= (area of rectangle) + (area of triangle)
= (8 × 10) + (½ × 4 × 8)
= 80 + 16
= 96ft²
Quarts of paint needed
= 96/22
= 48/11
= 4.36
Mr. Chen will have to buy 5 quarts of paint.
Which table shows a proportional relationship between x and y?
Answers
From the given tables, Tables 2 and 3 will show the proportional relationship between x and y.
What is Proportionality:Two ratios or two fractions are comparable according to the equation of proportion. In other words, when two ratios are equal, they are said to be proportionate.
Let x and y be proportional relation
=> x ∝ y
=> x = ky
=> x/y = k [ where 'k' proportionality constant ]
Here we have
Table 1
x 2 3 4 5
y 7 9 11 13
=> \(\frac{x}{y} = \frac{3}{7} = \frac{3}{9}\) [ which is not true ]
Hence,
Table 1 not shows any proportional relationship between x and y
Table 2
x 3 7.5 15 25
y 1 2.5 4 6
=> \(\frac{x}{y} = \frac{3}{1} = \frac{7.5}{2.5} = 3\) [ which is true ]
Hence, Table 2, shows a proportional relationship between x and y
Table 3
x 1 2 7 8
y 0.5 1 3.5 4
=> \(\frac{x}{y} = \frac{1}{0.5} = \frac{2}{1} = 2\) [ Which is true ]
Hence, Table 3 shows a proportional relationship between x and y
Table 4
x 3 6 8 10
y 12 15 18 20
=> \(\frac{x}{y} = \frac{3}{12} = \frac{6}{15}\) [ Which is not true ]
Hence, Table 4 not shows a proportional relationship between x and y
Therefore,
From the given tables, Tables 2 and 3 will show the proportional relationship between x and y.
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Some members of the Ruiz family are getting tickets for Fireworks Night at the ballpark. Tickets cost $5 each. 17 of the tickets they get are for children and 13 are for adults. How much will the tickets cost in all?
Answers
Answer:
$150
Step-by-step explanation:
The price does not change for children and adults. They bought 30 tickets total since 17 + 13 = 30. 30*5 = 150. So they spent $150.
Which number from the replacement set {6, 12, 24} is a solution for the equation 3x + 12 = 36 − x?
Answers
Answer:
X=6
Step-by-step explanation:
3x+12=36-X
(3X6) +12=36-6
18+12=30
30=30
TRUE
An inverted conical tank starts the day with 250 ft^3 of crayon wax in it. As the factory commences work, the tank is filled with an additional 40 ft^3 of wax per minute. The height of the wax is modeled by H(V)=3 piV/25. A. Write a function , V(t) to model the volume of wax in the tank after t minutes. B. Find an expression for the composition (HoV)(t) C. The composition in B (above) can be described as the ________ of the wax in terms of _______
Answers
Answer:
A. V(t) = 40t + 250 B. (HoV)(t) = 24πt/5 + 30π C. The composition in B (above) can be described as the height of the wax in terms of time.
Step-by-step explanation:
A. Let the rate of change of volume V with respect to time be dV/dt = 40 ft³/min
Solving this, V = 40t + C. At the start of the day, that is t = 0, V = 250 ft³
Substituting these values, we have
250 ft³ = 40(0) + C
C = 250 ft³
So, V(t) = 40t + 250
B. Since H(V) = 3πV/25
(HoV)(t) = 3π(40t + 250)/25
= 24πt/5 + 30π
C. The composition in B (above) can be described as the height of the wax in terms of time.
the research director at NASA must choose five experiments for the next space shuttle. Twelve experiments are proposed. in how many ways can this decision be made if order does not matter.. how many ways can this be arranged?
Answers
Answer:
95040Step-by-step explanation:
This is the combination of 5 experiments out of 12
Formula to find the combination:
P(n,r) = n!/(n-r)!P(12,5) = 12!/(12-5)! = 12!/7! = 12*11*10*9*8 = 95040So this can be arranged in 95040 ways
7. What is the value of x? Round answer to the nearest tenth (one decimal
place) if needed.
Can you please show work thank you for your time
Answers
Answer:
x= 20,1 degrees
Step-by-step explanation:
The sum of the inner angles of a triangle is 180 degrees
So it must be
3x-11+6x-10+x = 180
added up the terms with x
10x -11-10 = 180
added up the terms without x
10x - 21 = 180
added up (21) in the two members of the equation
10x-21+21 = 180+21
10x = 201
divide the two members by 10
x = 20,1 degrees
\(57=\frac{5}{8}z+7\)
Answers
\(57=\cfrac{5}{8}z+7\implies 57=\cfrac{5z}{8}+7\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{8}}{8(57)=8\left( \cfrac{5z}{8}+7 \right)} \\\\\\ 456=5z+56\implies 400=5z\implies \cfrac{400}{5}=z\implies 80=z\)
a parallelogram which has a line of symmetry is a rectangle
true or false
Answers
Explanation:
If a parallelogram has a line of symmetry through each pair of opposite sides, then we have a rectangle.
But if a parallelogram has a line of symmetry through each pair of opposite vertices, then we have a rhombus.
A square is a combination of both cases above.
The statement "A parallelogram which has a line of symmetry is a rectangle" is sometimes true. Overall its false because it implies that all parallelograms with this property are automatically a rectangle.
Which fraction has the same value as 55.555555555555%?
Answers
Answer:
111111/200000
Step-by-step explanation:
55.5555 is just 555555/1000000 and that simplified is 111111/200000
Katie is making chocolate candies for her classmates' Valentine's Day gifts. She melts 12.8 ounces of chocolate and divides it among 40 candy molds. If Katie divided the melted chocolate evenly, how much would each candy weigh?
Answers
Answer:
0.32 ounces of chocolate per mold
Step-by-step explanation:
Answer:
the correct answer is 3.125
Step-by-step explanation:
What multiplication expression is equal to 3/5÷1/4 out of 3/5×1/4 or 5/3×1/4 or 3/5×1/4 or 3/5×4/1
Answers
Answer:
it would be 3/5*4/1
Step-by-step explanation:
To divide you multiply the first number by the reciprocal of the second number. Check and you'll see that the answer is the same. Hope this helps!
Answer:
The answer is 3/5 x 4/1
Step-by-step explanation: