The sum of money that can be divided between two parts = Rs 200
Adding three times the smaller part to half of the larger part then its will always be less than Rs 200
Let The smaller part = Rs S
The larger part = Rs L
The sum of parts = Rs 200
Larger + Smaller = Rs 200
L+S=200---------------(1)
And, Adding three times the smaller part to half of the larger part then the result will always be less than Rs 200
(3S+1/2× L)-200 = 0
3S+ L/2=200
6S+L=400 --------(2)
Solving eq 1 and eq 2
(6S+L)-(L+S)=400 - 200
(6S-S )+(L-L )=200
5S+0=200
S = 200/4
∴Smaller = S=Rs40
Now, Plug the value of S into eq 1
L+S = Rs 200
L+40 = Rs 200
L = 200 - 40
L = Rs 160
Larger = L= Rs160
Hence, the larger part is Rs 160 and the smaller part is Rs 40
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A parking lot is 80 feet wide by 120 feet long. If the length and width are increased by the same length, what polynomial represents the area of the new lot? What is the new area of the increase is 25 feet?
The polynomial that represents the area of the new lot is x² +200x +9600 and the new area of the increase is 25 feet is 15225 ft²
What is Polynomial?A polynomial is an expression made up of variables (also known as indeterminates) and coefficients that only employs the addition, subtraction, multiplication, and non-negative integer exponents of the variables.
A single variable, x, is used as the only variable in the indeterminate polynomial x² - 4x + 7. Polynomials are used in many areas of science and mathematics.
They are employed in calculus and numerical analysis to approximate other functions, as well as in the definition of polynomial functions, which are used in a variety of fields, from basic chemistry and physics to economics and social science.
Simple word problems to sophisticated scientific conundrums can all be represented using polynomial equations.
Polynomials are used to create algebraic varieties in higher mathematics.
Area = Length x Breadth
Area =(80 + x)x(120 + x) = x² +200x + 9600
Area = (80 + 25)x(120 + 25) = 105x145
Area = 15225 ft²
Therefore, the new area of the plot is 15225 ft²
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Which point lies on the y axis graph i ready
The points that lie on the y-axis of the graph have a x-coordinate of zero.
Hence the format of the point is of:
(0,y).
How to define the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
For the x-coordinate, we have that:
If it is positive, the point is x units right of the origin.If it is negative, the point is x units left of the origin.On the y-axis, the point does not move horizontally, just vertically, hence the points that lie on the y-axis of the graph have a x-coordinate of zero, and the format of the point is given as follows:
(0,y).
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The constant of proportioality between the number of children (c) on a field trip and the number of teachers (t) on the trip is 14/3
The constant of proportionality is known to be the ratio of two proportional values that is said to be in a constant value.
What is constant of proportionality?This means that for every 3 teachers present on the trip, there will be 14 children. This proportion can be represented by the equation c= (14/3)t, where c represents the number of children and t represents the number of teachers. This proportionality can be used to predict the number of children on a trip based on the number of teachers, or vice versa. For example, if there are 9 teachers on a trip, we can use the equation to predict that there will be (14/3) * 9 = 42 children on the trip. This proportionality also implies that as the number of teachers increases, the number of children will also increase in the same proportion. It is represented as a number, often represented by the letter "k", that represents the ratio between the two variables. In a proportion, the two variables are related in a fixed ratio, meaning that if one variable increases, the other variable will also increase in the same proportion. For example, if there is a constant of proportionality of 2 between the number of apples (a) and the number of oranges (o), it means that for every 2 apples there are, there will be 1 orange.To learn more about proportionality refer to:
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Company A has 18 machines that each produce t toy cars per hour. Company B has 15 machines that each produce 75 more toy cars per hour than each of Company A’s machines. In order for the companies to produce an equal number of toy cars, how many toy cars does each machine at Company A need to produce per hour?
Write an equation that can be used to solve the problem.
Part B
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Fill in the blank question.
Company A’s machines each produce
toy cars per hour.
Company B’s machines each produce
toy cars per hour.
The system of equations is solved and the number of toy cars of each machine of Company A should produce to have equal number of toy cars is t = 375 toys
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of toy cars produced by Company A be A
Let the number of toy cars produced by Company B be B
The number of machines for A = 18 machines
The number of machines for B = 15 machines
The number of toy cars produced by A = t cars
The number of toy cars produced by B = 75 + t
And ,
The total number of toy cars of A = 18 x t
The total number of toy cars of B = 15 ( 75 + t )
So , in order for both the company's to have the same toys is
18t = 15 ( 75 + t )
On simplifying the equation , we get
18t = 1125 + 15t
Subtracting 15t on both sides of the equation , we get
3t = 1125
Divide by 3 on both sides of the equation , we get
t = 375 toys
Hence , the equations is A = 18t and B = 15 ( 75 + t )
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Select True or False for each statement. True False The equation y=3x−5 represents a function. True – The equation , y equals 3 x minus 5, represents a function. False – The equation , y equals 3 x minus 5, represents a function. A function can only be represented by a straight line on the coordinate plane. True – A function can only be represented by a straight line on the coordinate plane. False – A function can only be represented by a straight line on the coordinate plane.
The statement "The equation y = 3x - 5 represents a function." is; TRUE
The statement "A function can only be represented by a straight line on the coordinate plane." is; FALSE
How to represent Linear Functions?A linear function is one that is formed when a variable y varies directly with a variable x. That is, when y increases, x also increases and the opposite is also true.
The equation y = 3x - 5 represents a function. This statement is said to be true because every value of x gives a different value of y and as such we can say it maps different elements to different images.
A function can only be represented by a straight line on the coordinate plane. This statement is false because a function can also be represented by a circle, ellipse, parabola, etc.
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Solve for c.
a−b+c‾‾‾‾‾‾‾‾‾√=3
A. c=3−a+b
B. c=9−a‾√+b‾√
C. c=3−a‾√+b‾√
D. c=9−a+b
Answer:
The correc answer is Option A.
if f(x) = 4x^3+24x^2+41x+15 and x+3 is a factor of f(x) then find all of the zeros of f(x) algebraically
All of the zeros of f(x) algebraically are; x = -3, x = -1/2, x = -5/2
How to find the zeros of the polynomial?The zeros of a polynomial p(x) are defined as all the x-values that make the polynomial equal to zero.
The polynomial is;
f(x) = 4x³ + 24x² + 41x + 15
To find the x-intercept, we will equate the polynomial to zero to get;
4x³ + 24x² + 41x + 15 = 0
Since (x + 3) is a factor, then we can factorize the polynomial as;
(x + 3)(4x² + 12x + 5) = 0
Rewriting the quadratic term gives;
(x + 3)(4x² + 2x + 10x + 5) = 0
(x + 3)(2x(2x + 1) + 5(2x + 1)) = 0
Thus, the factors are expressed as;
(x + 3)(2x + 1)(2x + 5) = 0
Thus, the zeros are;
x + 3 = 0
x = -3
2x + 1 = 0
x = -1/2
2x + 5 = 0
x = -5/2
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Use your formula to determine the height of a trapezoid with an area of
24 cubic centimeters and base lengths of 9 cm and 7 cm
Formula: 1/2(a+b)h
The height of a trapezoid is 3cm
How to use the formula for area to determine the height of a trapezoid?The formula for the area of a trapezoid is:
A = 1/2(base1 + base2) × height
Where base1 and base2 are the lengths of the parallel sides of the trapezoid, and height is the distance between the bases.
That is:
A = 1/2(a+b)h
To determine the height of a trapezoid using the formula substituting the given values and solve for h. That is:
A = 1/2(a+b)h
where A = 24 cubic centimeters, a = 9 cm and b = 7cm
24 = 1/2(9+7)h
24 = 1/2(16)h
24 = 8h
8h = 24
h = 24/8
h = 3 cm
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Please Help Me!!!!! Sorry about the small picture!
Answer:
1:12, then 1 :11
wait unless its like in the same thing
wait sorry im confused
if its that then i think it would be 2:12
Step-by-step explanation:
sorry not too sure!!!
Greta is looking for a new fishing pole for an upcoming trip to the Grand Canyon. She found the model she likes at a local sporting goods store. The price of the pole is $59,50 with a sales tax of 6%. However, she can purchase the pole on a website for $62.50 with no sales tax added on to the price. What is the difference in price between the store and the website? Which is more expensive?
To find the total cost of the pole at the store including sales tax, we need to multiply the price of the pole by the sales tax rate (expressed as a decimal).
$59.50 x 0.06 = $3.57
So the total cost of the pole at the store is $59.50 + $3.57 = $63.07.
To find the difference in price between the store and the website, we can subtract the website price from the store price:
$63.07 - $62.50 = $0.57
So the pole is $0.57 more expensive at the store than on the website.
How much interest will you pay over the life of a $220,000 30-year loan at 8 percent with monthly payments of $1,614.28?
The total interest that will be paid over the life is $5,28,000. The solution has been obtained using arithmetic operations.
What are arithmetic operations?
For all the real numbers, there are four basic mathematical operations which are:
1. Addition(‘+’) wherein the sum of the numbers is obtained.
2. Subtraction(‘-’) wherein the difference of the numbers is obtained.
3. Multiplication(‘×’) wherein the product of the numbers is obtained.
4. Division(‘÷’) wherein the quotient of the numbers is obtained.
We are given 30 year loan amounting $220,000 at interest rate of 8 percent with monthly payments of $1,614.28.
The annual interest comes out to be
8% of $220,000 = $17,600
The total interest = $17,600 * 30 = $5,28,000
Hence, the total interest that will be paid over the life is $5,28,000.
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Label each item as factor by grouping or factor using substitution.
To factor a trinomial of the form
ax 2 + bx + c, find a factor pair of ac
that has the sum of b. Rewrite bx as a
sum of those factors. Then factor out
the GCF from the two groups of terms
to write the original trinomial as the
product of two binomials.
Answer:
To factor a trinomial of the form ax^2 + bx + c, you can use the following steps:
Step-by-step explanation:
To factor a trinomial of the form ax^2 + bx + c, you can use the following steps:
Find a factor pair of ac that has the sum of b. For example, if a = 2, b = -7, and c = -21, then the factor pair for -42 (2 * -21) that has the sum of -7 is (-7, -6).
Rewrite bx as a sum of those factors. In the example, -7x = -7x + (-6x).
Factor out the GCF (greatest common factor) from the two groups of terms. In the example, (2x - 7)(x - 6) = 2x(x - 6) - 7(x - 6) = 2x^2 - 14x + 12x - 42 = 2x^2 - 2x - 42.
Write the original trinomial as the product of two binomials. In the example, the trinomial 2x^2 + -7x + -21 can be factored as (2x - 7)(x - 6)
So the final factorization is (2x - 7)(x - 6)
16x² + y² - 128x - 20y + 292 = 0
Find the focal radius of the ellipse and the points at which the two foci sit.
The focal radius of the ellipse of which the two foci seat are:
(-8 + 6√3, 10) (-8 - 6√3, 10).How to solve for the focal radiusAn ellipse can be represented in the standard form as (x/a)² + (y/b)² = 1, where (a,b) is the center of the ellipse and a and b are the semi-major and semi-minor axes respectively.
Given the equation of the ellipse:
16x² + y² - 128x - 20y + 292 = 0
To put it in the standard form, we have to complete the square and then divide both sides by the constant on the right-hand side.
First, we complete the square by adding and subtracting (128/2)² and (20/2)² respectively:
16x² - 128x + (128/2)² + y² - 20y + (20/2)² = 292 + (128/2)² + (20/2)²
Then, we divide both sides by 292:
(16x² - 128x + (128/2)²)/292 + (y² - 20y + (20/2)²)/292 = 1
On simplifying we get:
(4x - 8)²/144 + (y - 10)²/36 = 1
Now we have the standard form of the equation of the ellipse and we can find the semi-major and semi-minor axis and the center of the ellipse.
The semi-major axis is equal to the square root of the coefficient of x squared (144) and the semi-minor axis is equal to the square root of the coefficient of y squared (36).
The center of the ellipse is (-8, 10) and the semi-major and semi-minor axis are 12, 6 respectively.
The focal radius is the distance between the center and the focus. The focal radius is equal to the square root of the semi-major axis squared minus the semi-minor axis squared.
Focal radius = √(a² - b²) = √(144-36) = √108 = 6√3
The two foci of the ellipse sit on the x-axis, symmetric about the center of the ellipse. The foci are located at (-8 ± 6√3, 10).
Therefore, the two foci of the ellipse are at (-8 + 6√3, 10) and (-8 - 6√3, 10).
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Someone baked 2 types of pie.
He served 1/2 of the blueberry pie. And he also served 1/4 of the Apple pie, If each pie had 8 pieces to start, what fraction in eights of the Apple did he served?
The fraction in eights of the Apple pie that the person baked, is 2 / 8 of the apple pie.
How to find the fraction ?The number of pieces that the apple pie had was 8 pieces to start. This means that if the baker served 1 / 4 of this, you can find the fractions in eights by multiplying the fraction served by the number of pieces :
= Fraction served x Number of pieces
= 1 / 4 x 8
= 8 / 4
= 2 pieces
The fraction in eights of the Apple that was served was :
= Number of pieces served / Number of total pieces
= 2 / 8
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Do you know what 20% of 60 is?
Answer:1
Step-by-step explanation:
0
a and b are parallel. Find the missing angles.
Step-by-step explanation:
....................
Answer:
Step-by-step explanation:
top=125 degrees
second from the top= 55 degrees
3rd=35 degrees
4th=55 degrees
5th=125 degrees
$4700 accumulating to $5994.76, compounded monthly for 5 years. What is the interest rate %
48.76%
Step-by-step explanation:Compound interest describes interest on the principal plus interest.
Compound Interest Formula
The formula to find compound interest is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]. In the formula:
A is the total amount, P is the principal, r is the rate as a decimal, n is how often interest is compounded,t is time.We can plug in our information to find the rate.
Solving For Interest Rate
First, let's rewrite the equation with our information. Note that for simplicity I will write rounded values for each step, but in reality, no rounding should be done until the last step.
[tex]5994.76 = 4700(1+\frac{r}{12})^{12*5}[/tex]Then, simplify the exponent and divide both sides by 4700.
[tex]1.275=(1+\frac{r}{12} )^{60}[/tex]Take the 60th root of both sides.
[tex]1.004=(1+\frac{r}{12} )[/tex]Subtract 1 from both sides.
[tex]0.004063=\frac{r}{12}[/tex]Finally, multiply both sides by 12.
r = 0.04876This means that the rate is 0.04876. We can multiply this by 100 to get the rate as a percentage. The interest rate is 48.76%.
Solve for t
18,000=9000(1.003)^12t
Answer:
t=1.92938456
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
2. Write an inequality statement whose solution is an empty set.
3. Write an inequality statement whose solution is some but not all real numbers. Graph the solution on a number line.
4. Write an inequality statement whose solution is all real numbers. Graph the solution on a number line.
5. Write an inequality statement whose solution is exactly one number. Graph the solution on a number line.
The inequality statements are 1 < 0, x > 0, x = x and x = 5
How to determine the inequality statementsAn empty set
An empty set is a set with no elements.
An inequality statement with no solutions results in an empty set.
One example of an inequality statement with no solutions is 1 < 0.
Some solution but not all real numbers
An inequality statement whose solution is some but not all real numbers is x > 0.
The solution set is the set of all positive real numbers, excluding 0.
The number line is represented as follows
|------------------------------------| 0 |----------------------------- |
All real numbers
A statement whose solution is all real numbers is x = x
The solution set is the set of all real numbers
The number line is represented as follows
|--------------------------- | ... | -2 | -1 | 0 | 1 | 2 | ... |
Exactly one number
A statement whose solution is exactly one number is x = 5.
The solution set is the set containing only the number 5
The number line is represented as follows
|--------------------------- | ... | 4 | ... |
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Let f(x)-3x+5, h(x)-4x-2 and g(x)=x^2. Write an expression for each function.
a. f+g
b. f-g
Answer:
a. f+g = -3x+5 + x^2
b. f-g = -3x+5 - x^2
Step-by-step explanation:
g(x) = x^2
I'll assume the other two equations were meant to be:
f(x) = -3x+5, and h(x) = -4x-2
a. f+g = -3x+5 + x^2
b. f-g = -3x+5 - x^2
The table shows some ordered pairs that belong to quadratic function h. What is the range of h?
Answer:
The range of a function is the set of all possible outputs (or y-values) of the function. To find the range of h, we can look at the y-values in the table.
The y-values for h(x) are: -27, -13, -3, 3, 5, 3, -3
The range of h is the set of all these y-values. We can see that the lowest y-value is -27 and the highest y-value is 5. So, the range of h is {-27,-13,-3,3,5}
Therefore, the range of h is from -27 to 5.
if m< is 28 degrees, what is m< DAC
We can write the measurement of ∠DAC as -
∠DAC = ∠ADB - ∠DCA
What is a triangle?A triangle is a polygon with three edges and three vertices.
Given is a triangle ABC.
The external angle is the sum of two interior opposite angles.
We can write -
∠ADB = ∠DAC + ∠DCA
So, we can write -
∠DAC = ∠ADB - ∠DCA
Therefore, we can write the measurement of ∠DAC as -
∠DAC = ∠ADB - ∠DCA.
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Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0.
The equation of the plane passing P (1,2,1) and orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is -3x-2y-z+8=0.
Equation of plane passing through (x1,y1,z1) is given by
A(x-x1)+B(y-y1)+C(z-z1)=0
where, A, B, and C are direction ratios
In the question, it is given that the plane passes through (1,2,1)
So, the equation of the plane will be in the form,
A(x-1)+B(y-2)+C(z-1)=0
It is also given that the plane is perpendicular to give 2 planes.
So, their normal to the plane would be perpendicular to the normal of both planes.
So, the required normal is a cross-product of the normals of planes
x-y-z-10=0 and x-2y+z-2=0
i.e,
-3i-2j-k=0
so, the direction ratios,
A=-3, B=-2, C=-1
putting the direction ratios in the previous equation of the plane,
-3(x-1)-2(y-2)-1(z-1)=0
-3x+3-2y+4-z+1=0
-3x-2y-z+8=0
is the required equation of the plane
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On a certain hot summer's day, 560 people used the public swimming pool. The daily prices are $1. 50 for children and $2. 00 for adults. The receipts for admission totaled $991. 0. How many children and how many adults swam at the public pool that day?
If the daily prices are $1.50 for children and $2.00 for adults , then the number of adults swam at public pool is 302 and number of children who swam at public pool is 258 .
let the number of children swam at swimming pool be = c ;
let the number of adults swam at swimming pool be = a ;
the total number of person who used the swimming pool is = 560 ;
the equation is ⇒ c + a = 560 ...equation(1) ;
the price for 1 child is $1.50 and price for 1 adult is = $2 ;
the total money collected can be written as :
= (price of children tickets)×(number of children that swam)+(price of adults tickets)×(number of adults that swam) ;
⇒ 1.5c + 2(560 - c) = 991 ;
⇒ 1.5c + 1120 - 2c = 991 ;
⇒ -0.5c = 991 - 1120 ;
⇒ -0.5c = -129 ;
⇒ c = 129/0.5 = 258 ;
So , adults (a) = 560 - 258 = 302 ;
Therefore , the number of adults are 302 and number of children are 258 .
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Prove the Pythagorean Theorem with Similar Triangles using a two-column proof.
Answer:
u
Step-by-step explanation
The equation, 3(3x - 10) = 5(x +10) shows the relationship between the perimeter of an equilateral triangle and the perimeter of a regular pentagon.What is the perimeter of the pentagon?
The equation, 3(3x - 10) = 5(x +10) shows the relationship between the perimeter of an equilateral triangle and the perimeter of a regular pentagon.What is the perimeter of the pentagon?
100
20
50
150
in the given figure,AB is parallel to CD and angle EAB =50°,angle ECD =100°,find angle AEC
If AB is parallel to CD and angle EAB =50°,angle ECD =100° then Angle AEC is 112∘
Since AB∥CD
∴∠CAB+∠DCA=180 ∘ (Co-interior angles)
The inside angles total 180 degrees and are known as co-interior angles. It indicates that two internal angles that are on the same side of the transversal have a sum that is additional.
∴22 ∘ +∠DCA=180 ∘
⇒∠DCA=180 ∘ −22 ∘ =158 ∘
Also, ∠ECD+∠DCA+∠y=360 ∘ (Angles about a point)
Angles around a point refer to the total number of angles that can be combined to produce a complete turn. A point's surrounding angles add up to 360°. The angles circling a point add up to 360° since they have completed a full turn and are identical in magnitude.
⇒90 ∘ +158 ∘ +∠y=360 ∘
⇒∠y=360 ∘ −(90 ∘ +158 ∘ )
⇒∠AEC=y=360 ∘ −248 ∘ =112∘
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X/4 = 20
please help
Answer:
x = 80
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Note that x is being divided by 4. To isolate x, do the opposite. Multiply 4 to both sides of the equation:
[tex]\frac{x}{4} = 20\\(\frac{x}{4} ) * 4 = (20) * 4\\x = 20 * 4\\x = 80[/tex]
x = 80 is your answer.
~
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In an experiment with a bag of marbles, P(green) = three fourths. Interpret the likelihood of choosing a green marble.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
The probability of picking a green marble is 3/4 or 0.75. This means it is likely the event would occur. Therefore, option A is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, an experiment with a bag of marbles, P(green)=3/4.
Probability is used to determine how likely it is that a random event would happen. The probability that a random event occurs lie between 0 and 1. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability of picking a green marble is 3/4 or 0.75. 0.75 is more than 0.5. This means it is likely the event would occur.
Therefore, option A is the correct answer.
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то 13.) Solve the right triangle. Round answers to the nearest tenth. To receive full credit you must show all work. R S 57° 15 T RT = RS= m/T=
Answer:
RT = 17.9
RS = 9.7
m<T = 33°
Step-by-step explanation:
sin R = opp/hyp
sin R = ST/RT
sin 57° = 15/RT
RT = 15/sin 57°
RT = 17.9
cos R = adj/hyp
cos R = RS/RT
cos 57° = RS/17.88544939
RS = 17.88544939 × cos 57°
RS = 9.7
m<R + m<S + m<T = 180°
57° + 90° + m<T = 180°
m<T = 33°