As per the congruency theorem, the two triangles are congruent.
Congruency theorem:
Congruency theorem states that "if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other."
Given,
Here we need to prove that congruency theorem can be used to prove that △wut ≅ △vtu.
Let us consider triangles WUT and VTU.
And in these triangles:
=> WU≅VT
And in those one, ∠T≅∠U,
Therefore, m∠T = m∠U = 90°
Here the side TU is common.
Now, we have to note that triangles WUT and VTU are right triangles, because m∠T = m∠U = 90°.
Then the side TU is common leg and sides WU and VT are hypotenuses.
Therefore, the HL theorem states: if the hypotenuse (WU) and one leg (TU) of a right triangle (ΔWUT) are congruent to the hypotenuse (VT) and one leg (TU) of another right triangle (ΔVTU), then the triangles are congruent.
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Answer: HL
Step-by-step explanation:
In slope intercept form, write the equation for each line.
Answer:
A: y = -0.4x -5
B: y = -1x +7
C: y = 1.25x +7
D: y = 3x -5
Step-by-step explanation:
See the attached worksheet. Finding the equations for the graph lines is reasonabvly straightforward, but the number of lines quadruples the space required. We'll find equations of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0). The worksheet notes the 4 steps needed:
1. mark any two points on the graph for each line.
2. Find the slope for each line by calculating the Rise/Run
3. Find the y-intercepts from the graph.
4. Assemoble the slopes and intercepts into the four equations.
Use a spreasheet to keep organized, and nbe patient. Check the equations using a free online graphing utility (e.g., DESMOS).
Use the ALEKS calculator to approximate √68.
Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
1\
\
How do I do this right here
X to the power of 3 - 5X
Answer:
it's so simple like very simple
Step-by-step explanation:
you just have to do
5x-3=2
x=2
A tennis ball is dropped from a certain height. Its height in feet is given by
h=-16t²+36 where t represents the time in seconds after launch. How long is
the ball in the air?
The amount of time the tennis ball will be in the air after launch is √2 seconds.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
The height of the tennis ball is given by the function h = - 16t² + 36, where t represents time in seconds.
Now, The amount of time the tennis ball will be in the air can be determined by the time when it hits the ground and at that time height of the ball should be zero.
Therefore, The time in the air is,
0 = - 16t² + 36.
16t² = 36.
t² = 2.
t = + √2 seconds, as time can not be negative.
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Pls help will make brain crown thing
Answer:
10,5 should be changed
Step-by-step explanation:
hope this helps
what is the circumference of a circle with a diameter of 58 inches
Answer:
58π or about 182.12
Step-by-step explanation:
In order to find circumference with diameter, you need to use the formula:
C = πd
Multiply the diameter (58) by pi, and since pi is an irrational number, let's use 3.14.
3.14(58) = 182.12
58π would be the answer as well if you don't multiply pi.
Given various values of the linear functions f (x) and g(x in the table, determine the y-intercept of (f − g)(x).
x −6 −4 −1 3 4
f (x) 20 14 5 −7 −10
g(x) −36 −26 −11 9 14
(0, 4)
(0, −4)
(0, 8)
(0, −8)
The y-intercept of (f − g)(x) is 8. Therefore, option C is the correct answer.
Given various values of the linear functions f (x) and g(x) in the table.
What is a y-intercept?An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.
For the function f(x)
Here, (-6, 20) and (-4, 14)
Slope =(14-20)/(-4+6)
= -3
Substitute, m=-3 and (x, y)=(-6, 20) in y=mx+c, we get
20=-3(-6)+c
c=2
Substitute, m=-3 and c=2 in y=mx+c, we get
f(x)=-3x+2 --------(I)
For the function g(x)
Here, (-6, -36) and (-4, -26)
Slope =(-26+36)/(-4+6)
= 10/2 =5
Substitute, m=5 and (x, y)=(-6, -36) in y=mx+c, we get
-36=5(-6)+c
c=-6
Substitute, m=5 and c=-6 in y=mx+c, we get
g(x)=5x-6 --------(II)
Now, (f − g)(x)=-3x+2-(5x-6)
= -3x+2-5x+6
= -8x+8
Here, y-intercept is 8
The y-intercept of (f − g)(x) is 8. Therefore, option C is the correct answer.
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Use the original price and the markdown to find the retail price.
Original price: $110; Markdown: 30%
Answer:
Step-by-step explanation:
regergergr
Please help:
In the figure, solve for x and y
Answer:y=124
x=67
Step-by-step explanation:
y=180-56
y=124
x=67
the perpendicular line equation given y=7x-2 and passes through -4,6
The equation of the perpendicular line is y = -1/7(x + 4) + 6
How to determine the perpendicular line equation?From the question, we have the following parameters that can be used in our computation:
y = 7x - 2
Also, from the question;
We have the following points
The point is given as
Point = (-4, 6) i.e. (x, y) = (-4, 6)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 7
This means that the slope is 7
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -1/7
The equation of the line is then calculated as
y = m(x - x₁) +y₁
Where
m = -1/7
(x₁, y₁) = (-4, 6)
So, we have
y = -1/7(x + 4) + 6
Hence, the line has an equation of y = -10/3x + 1
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Jovan is tired of measuring all the angles and sides to determine
if two triangles are similar. "There must be an easier way," he
thinks. "What if I know that all of the angles are congruent?
Does that mean that the triangles are similar?"
Answer:
yes congruent means identical of the same
Step-by-step explanation:
hope this helps
Answer: The answer is here
Step-by-step explanation:
If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar. Thus, if ∠A = ∠X and AB/XY = AC/XZ then ΔABC ~ΔXYZ.
If the measures of the corresponding sides of two triangles are proportional then the triangles are similar. Likewise if the measures of two sides in one triangle are proportional to the corresponding sides in another triangle and the including angles are congruent then the triangles are similar.
can someone help me thanks!
m=10d is the equation of line of the given graph.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
In the given graph,
the line shows the Arias savings account.
Arias savings account over time.
As the line is passing through the origin it forms a linear equation.
From the graph we can see for 1 month it is 10 dollars
2 months has 20 dollars
m=10d
Hence, m=10d is the equation of line of the given graph.
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ther are a total of 60 gils and boys in a math class there are 4 times as many boys as girls in the class how many grls and boys are in the class
The number of boys in the class = 48 boys
The number of girls in the class = 12 girls
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 boys in the class be = x
Let the number of girls in the class be = y
Now , the total number of students in the class = 60
So , the equation , will be
x + y = 60 be equation (1)
Now , the number of boys = 4 times the number of girls
So , the equation will be
x = 4y be equation (2)
Substitute the value of equation (2) in equation (1) , we get
4y + y = 60
On simplifying the equation , we get
5y = 60
Divide by 5 on both sides of the equation , we get
y = 12
So , the value of y is 12
Substitute , the value of y in equation (2) , we get
x = 4y
x = 4 x 12
x = 48
Therefore , the number of boys is 48 and the number of girls is 12
Hence , The number of boys in the class = 48 boys
The number of girls in the class = 12 girls
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suppose 48 out of every 120 people like baseball and of the people who like baseball three out of five play baseball if you ask 500 people how may would you expect to play baseball?
120 people out 500 people would play baseball.
What is fraction ?
The number of parts that make up a whole is all that a fraction informs us. With a slash between the two numbers, you can see if the numbers are fractions. The denominator is the lowest number, and the numerator is the highest. 1/2 is a fraction, for instance.
According to question
People who like baseball = 48/120
= 2/5
People who play baseball = 3/5 * 2/5
= 6/25
so, if there are 500 people,
then
500 * 6/25 = 120
hence, 120 People will play baseball.
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Jayden has two jobs. One week his paycheck was the same for both jobs. As a server he eared $9. 64 per hour plus $82. 35 in tips Working at a jewelry store he earned $14. 86 per hour plus $17. 10 in sales
bonuses.
Part A
Select the equation that can be used to determine the number of hours, h, that Jayden worked the week his paycheck was the same
for both jobs.
O 24. 5h
= 99. 45
0 91 99
= 31. 96h
0 82. 35h + 9. 64
0 9. 64h + 82. 35
17. 10h + 14. 86
14. 86h + 17. 10
Part B
BE
The total amount of money that Jayden made when both paychecks were the same is $
The equation that can be used to determine the number of hours, h, that Jayden worked the week his paycheck was the same is 65.25 = 5.22h and total amount of money that Jayden made when both paychecks were the same is $202.85.
Given :
Jayden has two jobs. One week his paycheck was the same for both jobs. As a server he eared $9. 64 per hour plus $82. 35 in tips Working at a jewelry store he earned $14. 86 per hour plus $17. 10 in sales
A )
Let h be the number of hours
9.64 * h + 82.35 = 14.86 * h + 17.10
82.35 - 17.10 = 14.86h - 9.64h
65.25 = 5.22h
B )
The total amount of money :
= 9.64 * 12.5 + 82.35
= 120.5 + 82.35
= $202.85
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Please help! Fin, the measures of the numbered angLes 1 and 4!
Applying the properties of a rhombus, the measures of the numbered angles are:
m<1 = 58°
m<2 = 90°
m<3 = 32°
m<4 = 58°
What are the Properties of a Rhombus?Some properties of a rhombus include:
Angles that are opposite each other are congruent/equal.Diagonals intersect each other at right angles.Diagonals bisect each angle in a rhombus.Adjacent angles are supplementary.Given the rhombus in the image above, the numbered angles are:
m<3 = 32° [opposite angles are equal]
m<2 = right angle = 90°
m<1 = 180 - 90 - 32 = 58°
m<1 = m<4
m<4 = 58°
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X | 0 | 1 2 3
y|-2| 0 [?][ ]
Answer: 2, 4
Step-by-step explanation:
Assuming this is a linear relationship, [tex]y[/tex] increases by 2 whenever [tex]x[/tex] increases by 1.
So, the blanks in the table are [tex]0+2=2[/tex] and [tex]2+2=4[/tex], respectively.
STEM AND LEAF
What is the median number of minutes students read?
U
44°
T
V
R
25°
S
mTQ= type your answer...
type your answer.
mTQ=
mQR =
mTS =
mSQR
mRQT =
=
mTS=
mQR=
Answer:
Step-by-step explanation:
TQ = 44 + 25 = 69°
QR = 180 - 25 = 155°
TS = 180 -(44 + 25) = 180 - 69 = 111°
SQR = 180 + 155 = 335°
RQT = 180 + 44 = 224°
Solve each system by elimination: 3x-7y=6 2x+7y=4
Answer:
Your answer is [tex]x=2[/tex] and [tex]y = 0[/tex]
Step-by-step explanation:
(attached)
Answer:
(2,0)
x=2, y=0
Step-by-step explanation:
(-2)3x-7y=6(-2)
(3)2x+7y=4(3)
-6x+14y=-12
6x+21y=12
-6x+14y=-12+6x+21y=12
35y=0
y=0
sub into one of the original equations
2x+7(0)=4
2x=4
x=2
What is the value of x?
Use picture below:
please help, I'm literally bEgGiNg-
The value of x is 135°
What is Exterior Angle Theorem?
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle.
An exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles.
Linear pair of angles are,
∠1 + ∠2 = 180°
where, ∠1 is exterior angle
and, ∠2 is interior angle
Given ,
One angle is = 90°
Then other two angle will be = 45° and 45°
Now, According to Exterior angle property,
x + 45 = 180
x = 180 - 45
x = 135°
Hence, the value of x is 135°
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PLEASE HELP!!! I NEED HELP ASAP
Answer:
y = 6x
Explanation:
This question is asking you to write a linear equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
The y-intercept (where the line crosses the y-axis) is visibly 0. As for the slope, you can take two points, I'll use (0,0) and (0.1,0.6) to calculate it.
Slope = y - y/x- x
Slope = (0.6 - 0)/(0.1 - 0) = 0.6/0.1 = 6
Plug in 0 for b and 6 for m and you have an equation.
y = 6x + 0
y = 6x
Answer: y = 6x
Step-by-step explanation: To find the equation you use the form y=mx+b, m is the slope meaning the rise of the function over the run of the function. This function rises 0.6 in terms of y in the time it takes to move or “run” over 0.1 in terms of x. so it would be 6/10 divided by 1/10. which leaves you with 6. b stands for the y-intercept which in this case it crosses the y-axis at zero so it would be zero. so putting it together you would have y=6x
GEOMETRY HELP NEEDED
Answer:
this is easy get a protractor
Step-by-step explanation:
Suppose that the probability of snow is 0.58. What is the probability that is will NOT snow?
The probability that it will NOT snow is 0.42
How to determine the probability that it will NOT snow?From the question, we have the following parameters that can be used in our computation:
Probability of snow = 0.58
The probability that it will NOT snow is the complement of the probability that it will snow
This is represented as
Probability that it will NOT snow = 1 - probability that it will snow
Substitute the known values in the above equation, so, we have the following representation
Probability that it will NOT snow = 1 - 0.58
Evaluate
Probability that it will NOT snow = 0.42
Hence, the value is 0.42
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> S.18 Solve percent word problems YAB
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At the sewing store, Tessa bought a bag of mixed buttons. She got 19 large buttons and 31
small buttons. What percentage of the buttons were large?
Write your answer using a percent sign (%).
You
The percentage of large buttons Tessa bought is 38%
How to determine the percentage of large bottoms?You should know that percentage deals with the proportion of the large buttons when divided by 100
The given parameters are
Recall that she bought mixed buttons on the shop
19 large buttons
31 small buttons
Then total number of buttons is 19+31=50 mixed buttons
Then percentage of large buttons is
(19/50)*100
Simplify the fractions to have
=38%
In conclusion, Tessa bought 38% of large buttons
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find the value of the unknowns
chapter matrices. with full explanations and working.
The unknowns in the given matrix total must have the values w = -5, z = 15, and y = 1.
Given,
To determine the value of the unknowns in the matrix,
What is the matrix?A matrix is a rectangular array made up of numbers that are arranged in rows and columns. The figures are known as matrix elements or entries. Matrices are widely utilized in engineering, physics, economics, and statistics, as well as many other.
Here,
From the above matrix,
Equation formed,
2z -18 = 12
z = 15
2w + 6 = 16,
w = 5,
10 - 6 = 4y
y = 1
Thus, The unknowns in the given matrix total must have the values w = -5, z = 15, and y = 1.
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A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 164 pounds requires 205
milligrams of medicine. What is the weight of a patient who requires 173.75 milligrams of medicine?
pounds
The amount of medicine required for a patient whose weight is 173.75 pounds will be equal to 217.18 milligrams.
What is the ratio?The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is. A ratio divides two quantities to compare them.
As per the data given in the question,
Weight of patient = 164 pounds
Medicine for 164 pounds weight = 205 milligrams
Weight of another patient = 173.75 pounds
Let the amount of medicine required is x.
So,
164 pounds = 205 milligrams and,
173.75 pounds = x milligrams
Perform Cross-multiplication,
164x = 205 × 173.75
x = 35618.75/164
x = 217.18 milligrams.
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6th Grade Math Inequalitys
Find the slope of the line write your answer in simplest form -4,1 1,-2