Answers
The equation of the line is y = -2x + c
What is an equation ?
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.
Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another.
To find the slope, use the two points (4.5,0) and (0,9) and substitute these in the slope formula:
m = [tex]\frac{(y_{2} - y_{1})}{(x_{2} - x_{1} )}[/tex]
= (9 - 0) / (0 - 4.5)
= -2
The equation of the line is
y = mx + c
y = -2x + c
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Related Questions
(b) if the coupons are different, how many ways are there to distribute the coupons so that at least one woman receives a coupon?
Answers
By probability ,181753 are ways are there to distribute the coupons so that at least one woman receives a coupon.
What does the math term "probability" mean?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
Statistics describes the examination of events subject to probability.
Number of ways such that the coupons are distributed such that at least one woman receives a coupon is computed as:
= Total number of ways to select 10 people from the 20 people - Total number of ways to select 10 men from the 15 men
= ( 20 10 ) - ( 15 10 ) = 184756 - 3003
= 181753
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The complete question is -
10 coupons are given to 20 shoppers in a store. Each shopper can receive at most one coupon. 5 of the shoppers are women and 15 of the shoppers are men.
(a) If the coupons are identical, how many ways are there to distribute the coupons so that at least one woman receives a coupon?
By probability ,181753 are ways are there to distribute the coupons so that at least one woman receives a coupon.
What does the math term "probability" mean?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
Statistics describes the examination of events subject to probability.
Number of ways such that the coupons are distributed such that at least one woman receives a coupon is computed as:
= Total number of ways to select 10 people from the 20 people - Total number of ways to select 10 men from the 15 men
= ( 20 10 ) - ( 15 10 ) = 184756 - 3003
= 181753
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Pls plss help me on this !!
Answers
Answer:
C) is 20
Step-by-step explanation:
3 inches x 5= 15
so we do the same with 4 minutes
4 minutes x 5= 20
For linear function f.f(2)= 0 and f(4)=-6.
Write function f in slope-intercept
How do you find the slope of the line when you have 2 points?
Answers
Hence, when [tex]m=-3,b=6[/tex], so the equation of slope is [tex]y=-3x+6[/tex].
What is the slope of line?
The slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] can be easily determined by finding the difference between the coordinates of the points.
The slope is usually represented by the letter [tex]m[/tex].
Here given that,
The linear function [tex]f(2)= 0[/tex] and [tex]f(4)=-6[/tex].
Let the linear function is
[tex]y=mx+b[/tex]
[tex]x=2,y=0[/tex]
Then
[tex]0=m(2)+b\\\\2m+b=0[/tex] .......[tex](1)[/tex]
And for
[tex]f(4)=-6\\x=4,y=-6[/tex]
[tex]-6=m(4)+b\\\\4m+b=-6[/tex] ......[tex](2)[/tex]
Solving equation [tex](1)[/tex] and [tex](2)[/tex], we get
In equation [tex](1)[/tex]
[tex]b=-2m[/tex] ........[tex](*)[/tex]
Substitute [tex]b=-2m[/tex] in equation [tex](2)[/tex]
[tex]4m-2m=-6\\\\2m=-6\\\\m==\frac{6}{2}\\\\m=-3[/tex]
Put [tex]m=-3[/tex] in [tex](*)[/tex] equation
[tex]b=2m\\\\b=-2(-3)\\\\b=6[/tex]
Hence, when [tex]m=-3,b=6[/tex], so the equation of slope is [tex]y=-3x+6[/tex].
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The area of a triangle is 474. Two of the side lengths are 87 and 19 and the included angle is acute. Find the measure of the included angle, to the nearest tenth of a degree.
Answers
Answer:
Let $x$ be the measure of the included angle. We can use the formula for the area of a triangle to find an equation in terms of $x$.
The area of a triangle is given by $\frac{1}{2}bh$, where $b$ is the length of the base and $h$ is the length of the altitude from the base to the opposite vertex. In this case, the base is 87 and the altitude is the length of the line segment from the vertex opposite the included angle to the base, which we can find using the Law of Sines:
$$\frac{h}{\sin x} = \frac{19}{\sin(180^\circ-x)}$$
$$h = \frac{19\sin x}{\sin(180^\circ-x)}$$
Substituting this expression for $h$ into the formula for the area of the triangle, we get
$$\frac{1}{2}bh = \frac{1}{2} \cdot 87 \cdot \frac{19\sin x}{\sin(180^\circ-x)} = 474$$
Solving this equation for $x$ is somewhat difficult, but we can use a calculator or computer to approximate the value of $x$. Using a calculator, we find that $x \approx 31.4^\circ$. Rounding to the nearest tenth of a degree, the measure of the included angle is $\boxed{31.4^\circ}$.
Step-by-step explanation:
Waterworks is a company that manufactures and sells paddleboards. Its profit P, in hundreds of dollars earned, is a function of the number of paddleboards sold x, measured in thousands. Profit is modeled by the function [tex]p(x)=-3x^{3}+45x^{2} -132x[/tex]. What do the zeros of the function tell you about the number of paddleboards that Waterworks should produce?
In order to make a profit, Waterworks must produce more than ___ and fewer than ____ paddleboards.
Answers
Waterworks must produce more than 4 and fewer than 11 paddleboards.
What do you mean by polynomial?
A polynomial is defined as an expression consisting of variables, constants, and exponents combined by mathematical operations such as addition, subtraction, multiplication, and division (not division by a variable). Based on the number of terms in the expression, it is classified as monomial, binomial, and trinomial.
It is given that Waterworks is a company that manufactures and sells paddleboards. Its profit P, in hundreds of dollars earned, is a function of the number of paddleboards sold x, measured in thousands. Profit is modeled by the function
[tex]p(x) = -3x^{3}+45x^{2} -132x[/tex]
zeroes of the p(x) will show the quantity at which profit = 0 i.e. breakeven
Let p(x) = 0
[tex]-3x^{3} +45x^{2} -132x =0[/tex]
-3x ([tex]x^{2} -15x+44[/tex]) = 0
-3x ([tex]x^{2} -11x-4x+44[/tex] ) = 0
-3x (x(x-11) - 4(x-11)) = 0
-3x (x-11) (x-4) = 0
-3x = 0 or x-11 = 0 or x-4=0
x = 0,11,4
So,profit is obtained when 4<x<11.
Therefore, Waterworks must produce more than 4 and fewer than 11 paddleboards.
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Write whether each is an example of commutative, associative, or distributive properties.
Answers
15. commulative
16. distributive, distributing the 3 to the 'a' and 'b' within the parentheses.
17. distributive, distributing the w to the variables inside of the parentheses.
Simplify 2/3(6x-1/9)-x+3/6
Answers
Answer:
Step-by-step explanation:
3x+23/54
A group of 10 students took tests in math, English, and chemistry.
The scatter plots compare the students’ scores on the tests
Complete the sentences to describe the data.
The math and English scores show
a positive correlation
a negative correlation
no correlation
The math and chemistry scores show
a positive correlation
a negative correlation
no correlation
Answers
The correlation of the scatterplots are defined as;
The math and English scores show; A positive correlation.
The math and chemistry scores show; A negative correlation
What is the correlation of the scatterplot?In correlation in statistics, it could either be positive correlation, negative correlation or no correlation at all.
A positive correlation is defined as a relationship between two variables that tend to move in the same direction. Thus, a positive correlation exists in the event that one variable tends to decrease while the other variable decreases, or one variable tends to increase while the other variable increases.
A negative correlation is defined as a relationship between two variables whereby one variable increases while the other decreases, and vice versa.
No correlation means there is no relationship between the two variables.
Now, for scatterplot of the math and English scores shown, we see that majority of the english scores increase as the maths scores increase and as sch it is a positive correlation.
Meanwhile, for the math and chemistry scores shown, majority of the maths score decreases with an increase in the chemistry score and as such this is a negative correlation.
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For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
A bag contains three blue marbles, five red marbles, and four green marbles.
Part A: What is the probability of selecting three marbles where one is blue and two are green?
Part B: What is the probability of selecting one blue marble and then selecting three red marbles?
Part C: In your own words, write a short paragraph that explains your work for Parts A and B.
Answers
a) The probability of selecting three marbles where one is blue and two are green is of: 0.0818 = 8.18%.
b) The probability of selecting one blue marble and then selecting three red marbles is of: 0.0152 = 1.52%.
c) The probabilities were obtained dividing the number of desired outcomes by the number of total outcomes, and all the possible combinations were considered.
How to obtain the probabilities?The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.
The outcomes with one blue and two green are given as follows:
Blue (3/12 probability) then two green, with 4/11 and 3/10 probabilities.Green then blue then green.Green, green then blue.Hence a multiplication for 3 is used for the probability, as follows:
p = 3 x 3/12 x 4/11 x 3/10 = 0.0818 = 8.18%.
For blue then three red, the outcomes are given as follows:
Blue (3/12 probability).Red: 5/11.Red: 4/10.Red: 3/9.Thus the probability is of:
p = 3/12 x 5/11 x 4/10 x 3/9 = 0.0152 = 1.52%.
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a graphic is printed on a circular banner that has a diameter of 4 feet. the same graphic undergoes a dilation with a scale factor of 1/6 to be printed on circular stickers. the diameter of the dilated graphic is _[blank]_ inches.
Answers
The required diameter of the dilated graphic is 8 inches.
Explain scale factor.
Scale factor is the ratio of comparing sides on two comparative figures. In math, scale factor is utilized to decide how often bigger or more modest one item or figure is to another.
According to question:We have,
diameter of circular banner = 4 feet
scale factor = 1/6
Then, the diameter of circular sticker = 4(1/6) = 4/6 feet.
In inches, we know
1 foot = 12 inches
4/6 feet = 12(4/6) = 8 inches
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Currently my bank balance is R2 000. What will the new balance be if I withdraw R600 from the account in each of the next 3 months?
Answers
Answer:
R200
Step-by-step explanation:
R200
A taxi ride costs $4, plus an additional $3 per mile. Graph the line relating taxi ride costs to distance (in miles).
Answers
The required equation of line in slope intercept form is
y = 3x + 4
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Let the taxi is driven x miles and the total cost is $y
A taxi ride costs $4, plus an additional $3 per mile
Total cost = 4 + 3x
By the problem,
y = 4 + 3x
This is the required equation of line which represents the above situation.
The graph has been attached here.
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If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).
Answers
The point of intersection of f(x) and [tex]f^{-1}[/tex](x) is (3, 3)
What is a function?"It defines a relation between input and output values."
"In function, for each input there is exactly one output."
What is inverse function?"The inverse function of x = f(m) is m =[tex]f^{-1}[/tex] , where x, m are real values"
For given question,
A function f(x) and its inverse function [tex]f^{-1}(x)[/tex], are both plotted on the same coordinate plane.
We know that the inverse function [tex]f^{-1}(x)[/tex] is the mirror image of the function f(x.)
This means, both the functions must be symmetric about the line y = x.
The curve of inverse function [tex]f^{-1} (x)[/tex] would cross the Y-axis at (0, 2), changes direction at (-1, -1) and crosses the X-axis at (-2, 0)
And both the functions intersect each other only on y = x
The point which satisfy the line y = x is (3, 3)
Therefore, the point of intersection of f(x) and[tex]f^{-1} (x)[/tex] is (3, 3)
The complete question is : If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?
On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).
A.(0, –2)
B.(1, –1)
C.(2, 0)
D.(3, 3)
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If an antelope eats 7kg of vegetation in 2 days how many killograms of vegetation does it eat per day
Answers
Antelope eats 3.5kg of vegetation per day .
What are fractions?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given :
antelope eats 7kg of vegetation in 2 days
Thus , vegetation eated per day = 7 / 2 = 3.5 kg
Hence , antelope eats 3.5kg of vegetation per day .
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10mm
5mm
13mm
Trapezium
Answers
The area of the trapezium will be = 90[tex]mm^{2}[/tex]
According to the figure of the trapezium =
Let us consider the length of base a = 5mm
length of base b = 13mm
height h of the trapezium = 10mm
According to the formula of the area of trapezium
= (1/2) x h x (a + b)
= (1/2) x 10 x (13 + 5)
= 5 x 18
= 90[tex]mm^{2}[/tex]
Therefore, the area of the trapezium will be = 90[tex]mm^{2}[/tex]
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The complete question here could be- Find the area of the trapezium given base a= 5mm, base b= 13mm and height h= 10mm
--7x-7y= 28
2x - 7y = 1
please solve this systems of eqautions
Answers
After solving the equation the linear equation is x = 27/5 , y = 7/5.
What do you mean by linear equation?
Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line.
A linear equation is an algebraic equation in which each term has exponent 1, and the graph of this equation is always a straight line. For this reason, it is called a "linear equation".
Given system of equation:
7x - 7y = 28 ..........(1)
2x - 7y = 1 .............(2)
Solve this system of linear equation. Find the value of 7y from equation (1) and substitute in equation(2)
7x - 7y = 28
7x - 28 =7y .............(3)
Substitute this value in equation (2)
2x - (7x - 28) = 1
2x - 7x + 28 = 1
-5x + 28 = 1
5x = 28 - 1
5x = 27
x = 27/5
Substitute this value in equation (3)
7y = 7(27/5) - 28
7y = 189/5 - 28
7y = 49/5
y = 7/5
Therefore, x = 27/5 , y = 7/5
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s 1}} 10of 0.9. E Juliet is incorrect because 90 is 1}} 10of 9.
Answers
For the given operation Julia is incorrect because the product of 10 and 0.9 will be 9.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that the expression is,10of 0.9, and its simplification is obtained as 90.
We have to find out why Juliet is incorrect.
Juliet is incorrect because when any decimal value is multiplied by 10 the obtained value is increased by its one's place,
=10 × 0.9
=9
Thus, for the given operation Julia is incorrect because the product of 10 and 0.9 will be 9.
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Ninth grade math and I need help.
Answers
Answer:
Step-by-step explanation: By using the verticle line test, because the line has passed more than one point, it is NOT A FUNCTION.
A standard television screen has a 4:3 aspect ratio between the width and the height of the viewable screen. What would be the height of Television that is 16 inches wide?
Answers
The standard height of the television is 12 inches.
What are ratios?
By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other.
The given ratio is 4:3. Let us take a variable 'x' such that 4x=16 and 3x=height.
We find x from 4x=16
x=4
Now putting the value of x in 3x, we get 12 inches.
Therefore, the height of the television is 12 inches.
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The standard height of the television is 12 inches.
The aspect ratio of a screen is the ratio of the width to the height. In the case of a television screen with a 4:3 aspect ratio, the width is 4 units and the height is 3 units.
If we let "h" represent the height of the television screen, we can set up the following equation:
4:3 = 16:h
To solve for "h", we can cross-multiply to get:
4h = 48
Dividing both sides by 4, we get:
h = 12
So the height of a television screen that is 16 inches wide and has a 4:3 aspect ratio is 12 inches.
what is aspect ratio?
The aspect ratio of a screen is the ratio of the width to the height of the viewable area of the screen. It is usually expressed as two numbers separated by a colon, such as 16:9 or 4:3.
Aspect ratios are used in a variety of applications, including television screens, computer monitors, and movie theaters. Different aspect ratios are used for different types of content, and some screens can be adjusted to display content in different aspect ratios.
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Write the expression that completes the equation to represent the
result of transforming y = |x| with the steps listed below.
1: Shift the function 5 units to the left.
2: Shift the function 4 units down.
Answers
y = | x + 5 | - 4
You subtract 4 outside the abs val to move the graph down.
You add 5 inside the abs val to move the graph left. (Inside translations are the opposite of what you'd expect.)
Hello please perform indicated operation with steps please
Answers
Answer:
x^3-2x^2+6x+1
Step-by-step explanation:
x^3+2x-1-2x^2-4x+2
collect like terms
x^3-2x^2+2x+4x-1+2
x^3-2x^2+6x+1
The length (L) of a rectangle of fixed area varies inversely as the width (W). If the
length of the rectangle is 6 feet when the width is 12 feet, find the length of the
rectangle when the width is 4 feet.
Answers
Answer:
Length of the rectangle is 18 ft when its width is 4ft
Step-by-step explanation:
Let us assume that the length is represented by l.
Let us assume that the width is represented by w.
As given
The length of the rectangle varies inversely with its width.
Thus
L x 1/w
l=k/w
Where k is the constant of proportionality .
As given
If the
length of the rectangle is 6 feet when the width is 12 feet,
l=6, w=12
putting the values in l = k/w
6 = k/12
k = 12 x 6
k=72
As given
width is 4ft
k= 72, w = 4
Putting the values in, L = k/w
L= 72/4
L=18 ft
Therefore the length of the rectangle is 18 ft when its width is 4ft
Hope this helps You
what is the equation in slope intersept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y=2/5x +2
Answers
The line that goes through the point (2,-2) and is perpendicular to the line shown by y=2/5x +2 will have the slope intercept equation 5x+3y=6.
What is equation of line?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
Here,
Slope of the line given=2/5
Slope of the line perpendicular=-5/2
coordinates=(2,-2)
y=mx+b
-2=-5/2*2+b
b=3
y=-5/2x+3
3y=-5x+6
5x+3y=6
The equation in slope intercept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y=2/5x +2 will be 5x+3y=6.
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What are the domain and range of this graph? f(x)=x^5+x^2
Answers
Therefore ,the domain and range of this graph f(x)=x^5+x^2
Domain : (-∞,∞), {x|x ∈ R} Range:(-∞,∞), {y|y ∈} R
what is domain?A function's domain is the set of possible values that can be entered. This set reflects the values of x in a function like f. (x). Its range refers to the set of possible values that a function can accept. These are the values that are returned by the function when we enter an x value.
Here,
The domain is all values of x that make the expression defined.
Interval Notation:
(−∞,0)∪(0,∞)
=>(-∞,∞)
The Range is all values of y that make the expression defined.
Interval Notation:
(−∞,0)∪(0,∞)
=>(-∞,∞)
Therefore ,the domain and range of this graph f(x)=x^5+x^2 Domain : (-∞,∞), {x|x ∈ R} Range:(-∞,∞), {y|y ∈} R
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An step by step explanation of all of them would be great .
Btw I did 1 to 5 and they all worked
Answers
Solution of x is 1± 5√2 for the given quadratic equation.
What is quadratic equation?
Quadratics are often outlined as a polynomial equation of a second degree, which means that it contains a minimum of 1 term that's square. it's conjointly known as quadratic equations.
Main body;
11)
x² = 2x +48
The given is an quadratic equation:
solution of this can be found out using quadratic formula:
x =(-b ±[tex]\sqrt{b^{2} -4ac}[/tex])/2a
for this ,
x² -2x -48 = 0
a = 1
b= -2
c = -48
x =( 2±√ (4- 4*1*-48))/2
x = (2±√200)/2
x = 1± 5√2
Hence solution of x is 1± 5√2.
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Find the area of $\triangle ABC$ with vertices $A\left(2,\ -2\right)$ , $B\left(4,\ -2\right)$ , and $C\left(6,\ -11\right)$ .
The area of $\triangle ABC$ is
square units.
Answers
The area of the triangle from the vertices is 27 square units
How to determine the area of the triangle?From the question, we have the following parameters that can be used in our computation:
$A\left(2,\ -2\right)$ , $B\left(4,\ -2\right)$ , and $C\left(6,\ -11\right)$ .
Represent the vertices properly
So, we have
A = (2, -2)
B = (4, -2)
C = (6, -11)
The area of the triangle is calculated using
Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|
Substitute the known values in the above equation, so, we have the following representation
Area = 0.5 * |2 * (-2 + 11) + 4 * (-2 + 11) + 6 * (-2 + 2)|
Evaluate the sum of products
Area = 0.5 * |54|
Remove the absolute bracket
Area = 0.5 * 54
Evaluate
Area = 27
Hence, the area of ABC with vertices is 27 square units
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solve for x. Express your answer as a proper or improper fraction in simplest terms,
-1/2= 4/9x+5/6
x=
Answers
Answer: x=-3
Step-by-step explanation:
PLEASE HELP The definition states that a glide reflection is the composition of a translation and a reflection. Explain why these can occur in either order. (1 pt)
Answers
In particular, despite the language overlap, a glide reflection is not a reflection and a (ordinary) reflection is not a glide reflection.
There are many intriguing accounts of what occurs when you mix two of them together. Here are a few instances:
Each isometry may be classified as belonging to one of the five classes listed below.
a consideration,an interpretationthe rotationa reflection of a glide,The map of identity.The identity is the combination of two reflections along the same line.
Translation is the combination of two reflections in dissimilar but related directions. Rotation is the result of two reflections in non-parallel lines.
A gliding reflection is made up of a reflection over a line plus a translation along a non-perpendicular line (and not a reflection).
A reflection is made up of a translation along a perpendicular line and a reflection across a line (and not a glide reflection).
There are fascinating things to say about what occurs when you combine two isometries dependent on the types of the isometries that you combine, but it does not change the fact that the five types are all distinct from one another. I could go on, but I think you get the point now.
Learn more about Glide reflection from the link below
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THE DIFFERENCE OF TWO NUMBERS IS 10 IF THE GREATER NUMBER IS 32, FIND THE SMALLER ONE. (STEP BY STEP)
Answers
Answer:
22
Step-by-step explanation:
we can set this up and make the unknown number X
32-x=10
Subtract 32 from both sides
32-x=10
-32. -32
-x= -22
Divide both sides by -1
-x=-22
/-1. /-1
x=22
Hopes this helps
11-14 are confusing can anyone help and tell me how to get the written answer
Answers
Answer:
11) KF = DB
12) DC=YZ
13) <C = <W
14) <S and <K
Step-by-step explanation:
11) For this question, we want to try and use SSS to prove the triangles are congruent. SSS stands for side-side-side postulate, so all sides have to be equivalent. We already have ED = FB as given, and DF = DF due to reflexive property. From this information, we already have two sides. Additional information that would be needed to figure out the third side is KF = DB, as it's the only side we are missing.
12) For this question, we want to use SAS postulate, which stands for side-angle-side. We already have one side congruent, which is BC=YX. We have one angle congruent which is <C = <Y. With this information, we have one side and one angle. This means that we need to find another side that is congruent. The side that we need to find here is DC=YZ, as it will help us prove the triangles are congruent with SAS.
13) For this question, we want to use AAS, which stands for angle-angle-side. We already have one angle congruent, which is <CDE = WDE. We have one side congruent as well, which is DE = DE due to reflexive property. With this given information, we have one angle and one side. We only need one more angle before the other angle to figure this out. The angles that are needed are <C = <W.
14) For this question, we want to use ASA, which stands for angle-side-angle. The one angle we have already is <KTM = <UTS, which is because of vertical angles are congruent. The one side that we have is ST=TK. With this, we have one angle and one side. We just need one more angle to prove this, which would be <S and <K.
Remember, for triangle congruency postulates, they have to be in order. They cannot just be out of order. For example, in question 14, we have to find the measures in order. First we need an angle, side, and then another angle. The first angle is <S and <K, then the side we have is ST=TK, and then our last angle, <KTM = <UTS.