To prove that △LMN ~ △XYZ by the SAS similarity theorem, it also needs to be shown that
Answers
For both triangles to be proven to be similar to each other by the SAS similarity theorem, it also needs to be shown that: A. angle N ≅ angle Z.
What is the Side-angle-side Similarity Theorem (SAS)?The side-angle-side similarity theorem (SAS) states that two triangles can be proven to be similar to each other if two pairs of corresponding sides of the two triangles are proportional to each other and one pair of corresponding angles of the two triangles are congruent to each other.
In the image given, we know that in both triangles:
XZ/LN = 6/2 = 3
ZY/NM = 9/3 = 3
Therefore:
XZ/LN = ZY/NM = 3
This means that the two triangles have two pairs of corresponding sides that are proportional to each other.
Thus, we also need to show that both triangles have a pair of congruent included angles before we can prove both triangles are similar to each other.
Thus, what needs to be shown is: A. angle N ≅ angle Z.
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Related Questions
5a3 x 2b2 x 4a2b5/ 3a2 x 5b3
Answers
5a^3 x 2b^2 x 4a^2 x b^5 / 3a^2 x 5b^3 (rewrite)
= 20a^5 x 2b^7 / 3a^2 x 5b^3
= 40a^5 x b^7 / 15a^2 x b^3
= (8/3) x a^3 x b^5
Enter the Correct 4 Digit Code (no spaces)
Answers
The correct 4 Digit Code (no spaces) is 0164 .
In the question ,
the numbers representing the equation are given
to find
the first statement
-C.P-(-K.I)
From the figure we can see that C=2 ,P=7 ,K=5 ,I=4,
hence -C.P-(-K.I) = -2.7-(-5.4) = -14+20 = 6.0 .....(i)
the second statement
E/H + -L/T
From the figure we can see that E=3 ,H=4 ,L=5 ,T=8
hence E/H + -L/T = 3/4 + -5/8 = 3/4 - 5/8 = 1/8 ...(ii)
the third statement
B/W × -N/T
From the figure we can see that B=2 ,W=9 ,N=6 ,T=8
hence B/W × -N/T = 2/9 × -6/8 = -1/6 ...(iii)
the fourth statement
-F/J ÷ -M/V
From the figure we can see that F=3 ,J=5 ,M=6 ,V=8
hence -F/J ÷ -M/V = -3/5 ÷ -6/8 = 4/5 ....(iv)
From equation (i) , (ii) , (iii) and (iv) , we get
-C.P-(-K.I) = 6.0
E/H + -L/T = 1/8
B/W × -N/T = -1/6
-F/J ÷ -M/V = 4/5
the number from the red color lines are 0,1,6,4
hence the code is 0164 .
Therefore , the correct 4 Digit Code (no spaces) is 0164 .
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let x be the hours that Erica babysits. Write an expression to show the total number of hours Erica works each week.
Answers
The expression to represent the number of hours Erica babysits each week is 7x .
In mathematics, an expression that was created using integer variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number) .
However, since they are not produced from integer constants and algebraic operations, transcendental numbers such as such and e are not algebraic. The production of is often done as a geometric expression, but the definition of e requires an infinite number of algebraic operations.A rational expression is one that can be reduced to a rational fraction using the properties of arithmetic operations ( associative properties and commutative properties of addition and multiplication, distributive property and rules for the various operations on the given fractions).Erica works x hours each day and there are 7 days in a week.
Hence Erica works 7x hours in a week
Therefore the expression to represent the number of hours Erica babysits each week is 7x .
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please help i don’t get it and grades are due soon and i need to get this done would be very helpful if you explain it. thank you
Answers
The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points.
What is the separation between A and B?Except for when the points coincide, distances in geometry are always positive. The distance between points A and B is equal to their respective distances. We take two points A(a,b) and B into consideration in order to calculate the formula for the distance between two points in the plane (c,d).
What is a sample of the distance formula?In coordinate geometry, the distance between two given points is calculated using the distance formula. D=(x2x1)2+(y2y1)2 D = (x 2 x 1) 2 + (y 2 y 1) 2 is the formula for calculating the distance between two points (x1,y1) (x 1, y 1) and (x2,y2) (x 2, y 2).
Say, for instance, that you are asked to determine the distance between two points at ( -6,-2 ) and ( -1,10).
First step:
Give x 1, y 1, x 2, and y 2 their respective assignments.
Consider the cases where (x 1, y 1 ) = ( -6,-2)) and (x 2, y 2 ) = ( -1,-10).
x1 = -6
y1 =- 2
x2 = -1
y2 = 10
Second Step:
Replace in the Distance Formula
Now that we know the numbers for x1, y1, x2, and y2, we can enter them into the Distance Formula.
d = √(-6,-2)² + (-1-10)²
= √(8)² + (11)²
= √16+22
= √38.
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Arranging
A. Arrange the set of integers in increasing order.
1. 3,-4, 1, 10, 9,-3
2. 4,-12, 12, -5, 9, 0, -1
3. -6, 63, -45, -7, -50
4. 6,-10, 4, 1, -67, -1
5. -5, 7, 13,-34, -52, 25, 0
Answers
In ascending order the integers are arranged from the left to right of the integer line. The arrangements are shown below.
The arrangement of the set of integers in increasing order is as follows:
-4<-3<1<3<9<10 -12<-5<-1<0<4<9<12 -50<-45<-7<-6<63 -67<-10<-1<1<4<6 -52<-34<-5<0<7<13<25Every positive integer is greater than a negative integer. Zero is less than every positive integer. Zero is greater than every negative integer. The greater the number, the lesser its opposite,i.e., If a and b are two integers such that a>b, then -a<-b.
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The babysitter charges $8 per hour plus $4 for gas to come to the house. If the babysitter earned $36, how many hours did the babysitter work?
Answers
Answer: The answer should be 3 hours
Step-by-step explanation: 8+4=12, divide the sum by 36: 36÷12=3
She had worked 3 hours.
Pleez help me im stuck
Answers
Answer: c
Step-by-step explanation:
A is 190 divided by 125
B is 190 multiplied with 125 (product of the two numbers)
D is the sum of 190 and 125 (addition)
the difference will be found by subtracting the smaller number from the bigger number
Sally’s employer pays for 38% of her annual health insurance premium of $4,350.00. sally pays the remaining balance by having it deducted in equal amounts from her 26 paychecks throughout the calendar year. how much will sally have deducted from each paycheck? a. $63.58 b. $103.73 c. $137.75 d. $207.46 please select the best answer from the choices provided a b c d
Answers
By using percentage, the deductible amount is $103.73 for each paycheck. So, option b is correct.
We are provided by some percentage here. A percentage is a part of a whole that is expressed in hundredths.
Sally paid 38% of her annual health insurance premium of $4,350.00 and left with the 62%.
62% of $4,350.00 is equal to $2697
62/100 x 4,350.00 = 2697
So, the net amount that Sally has to pay is $2697 in equal distribution from her 26 paychecks throughout the calendar year.
Therefore, each paycheck will be deducted as = $2697/26
= $103.73
Hence, $103.73 will be deducted from her paycheck.
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I need to find the slope of (-19, -6), (-19, 20)
Answers
m=20-(-6)/-19-(-19)
m=26/0
m= undefined
The entered points belong to a vertical line. There is no slope.
Equation: x = -19.
7c+36
5c+40
Find x
X
Answers
Answer:
130 degrees
Step-by-step explanation:
When two lines intersect, the opposite angles are equal, therefore, in this example, 7c+36 = 5c+40. We can find c using this equation.
7c+36 = 5c+40
7c-5c = 40-36
2c = 4
c = 4/2 therefore c=2
now that we know c is equal to 2, we can find out both of those angles.
therefore 5c+40 = (5*2)+40 = 10+40= 50
and 7c+36 = (7*2)+36 = 14 +36 = 50
now we know that those two angles add up to 100.
to find the sum of x and the angle opposite to x, subtract 100 from 360
360-100 = 260
since the angle opposite of x is equal to x, x+x = 260
2x=260
x=260/2 = 130
x is 130 degrees
Answer:
x = 130
Step-by-step explanation:
7c + 36 and 5c + 40 are vertically opposite angles and are congruent , so
7c + 36 = 5c + 40 ( subtract 5c from both sides )
2c + 36 = 40 ( subtract 36 from both sides )
2c = 4 ( divide both sides by 2 )
c = 2
Then
7c + 36 = 7(2) + 36 = 14 + 36 = 50
5c + 36 and x are a linear pair and sum to 180° , that is
50 + x = 180 ( subtract 50 from both sides )
x = 130
The diagram shows a 5 cm x 5 cm x 5 cm cube.
A
B
5 cm
AB=
5 cm
ļ
5 cm
Calculate the length of the diagonal AB.
Give your answer correct to 1 decimal place.
+ cm
Submit Answer
Answers
The length of the diagonal AB of the cube is 8.7 cm.
What is the Diagonal of a Cube?A cube's diagonal is a line segment that joins any two of its non-adjacent vertices.Because it has 12 equally spaced edges and is one of the most prevalent forms in our surroundings, the cube is one of the most significant geometric shapes. A cube is a three-dimensional figure, hence it has two different types of diagonals: the face diagonal and the body diagonal.Length of a face diagonal of cube = √2a, where a = Length of each side of a cube.
Length of body diagonal of a cube = √3a, where a = Length of each side of a cube.
Given:
Side length of the cube(a) = 5 cm
We have to find the length of the diagonal AB which is a body diagonal.
Length of Body diagonal(AB) = √3a
Substituting the given value in the formula,
Length of the body diagonal of cube = √3a
⇒ √3a ⇒√3 × 5 = 8.7 cm
Therefore, the length of AB i.e. the body diagonal of the cube is 8.7 cm.
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48. nbc news reported on may 2, 2013, that 1 in 20 children in the united states have a food allergy of some sort. consider selecting a random sample of 25 children and let x be the number in the sample who have a food allergy. then x∼bin(25,.05). a. determine both p(x≤3) and p(x<3). b. determine p(x≥4). c. determine p(1≤x≤3). d. what are e(x) and σx? in a sample of 50 children, what is the probability that none has a food allergy?
Answers
The following are the solutions to the given problems by using binomial probability principle:
P(X ≤ 3) = 0.966 and P(X < 3) = 0.873P(X ≥ 4) = 0.034 and P(1 ≤ X ≤ 3) = 0.689σ(X) = 1.090 and P(X = 0) = 0.0769What is defined as the binomial probability?The probability of precisely x successes on n multiple trials in an experiment with two possible outcomes is referred to as binomial probability (called a binomial experiment).If the success probability on an individual trial is p, therefore the binomial probability is: P(x = x) = nCx * p^x * q^(n-x)p = 0.05q = 1 - 0.05 = 0.95n = sample size = 25 children1.) P(X ≤ 3)
P(X ≤ 3) = p(x = 0) + p(x = 1) + p(x = 2) + p(x = 3)
Use a binomial probability calculator :
P(X ≤ 3) = 0.277 + 0.365 + 0.231 + 0.093
P(X ≤ 3) = 0.966
2.) P(X < 3)
P(X < 3) = p(x = 0) + p(x = 1) + p(x = 2)
Use a binomial probability calculator :
P(X < 3) = 0.277 + 0.365 + 0.231
P(X < 3) = 0.873
3.)P(X ≥ 4)
P(X ≥ 4) = p(x = 4) + p(x = 5) +...+ p(x = 50)
Use a binomial probability calculator :
P(X ≥ 4) = 0.034
4.) P(1 ≤ X ≤ 3)
P(1 ≤ X ≤ 3) = p(x =1) + p(x =2) + p(x =3)
Use a binomial probability calculator :
P(1 ≤ X ≤ 3) = 0.365 + 0.231 + 0.093
P(1 ≤ X ≤ 3)= 0.689
D.) σ(X)
E(X) = np = 25 × 0.05
E(X) = 1.25
σ(X) = √(npq)
σ(X) = √(25 × 0.05 × 0.95)
σ(X) = √1.1875
σ(X) = 1.090
E. Probability for none do have food allergy :
P(X = 0) = ⁵⁰C₀ × 0.05^0 × 0.95^50
P(X = 0) = 0.0769
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Charlie can run 4 miles in 28 minutes. If he runs at a constant pace, how long will it take him to run 3
miles? How long will it take him to run 7 miles?
Answers
It will take 18 minutes to run 3 miles. For 7 miles, it will take him 42 minutes.
What is unitary method?The unitary method is an approach for issue that involves first calculating the value of a single unit, then multiplying that value to find the required value. a single state. This has an identity element in math, in an algebra. Whose inverse is equivalent to its linear algebra, mathematical study of a matrix or operator,
Given Data
Charlie can run 4 miles in 28 minutes.
To run 1 mile,
4 miles = 28 minutes
1 mile - 6 minutes
For 3 miles,
3 miles = 3(6)
3 miles = 18 minutes
It will take 18 minutes to run 3 miles.
For 7 miles,
7 miles = 7(6)
7 miles = 42
For 7 miles, it will take him 42 minutes.
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Hey guys! please respond asap! thanx
Answers
The equation of the line that has a slope of 7 and passes through the point (4, -2) is: y = 7x - 30.
How to Write the Equation of a Line that Passes Across a Point?If we are given a point on a line (x, y), and we know the slope (m) of the line, we can expressed the equation of the line in slope-intercept form as y = mx + b.
Given the following:
Slope of the line, m = 7
A point on the line = (4, -2).
Find the value of b by substituting x = 4, y = -2, and m = 7 into y = mx + b:
-2 = 7(4) + b
-2 = 28 + b
-2 - 28 = 28 + b - 28 [subtraction property of equality]
-30 = b
b = -30
To write the equation of the line, substitute m = 7 and b = -30 into y = mx + b:
y = 7x + (-30)
y = 7x - 30
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An interior designer is planning a room but needs to first figure out the dimensions. The length of the room is 17 inches on the architect’s plan. What is the actual length of the room in feet if the scale of the plan is 1.25 inches to 3 feet?
Answers
If the length of the room is 17 inches one the architect's plan, the actual length of the room in feet if the scale of the plan is 1.25 inches to 3 feet is
40.8 feet
The length of the room on the architect's plan = 17 inches
The scale of the plan = 1.25 inches to 3 feet
That means
The length on the plan/ The actual length = 1.25 inches / 3 feet
Substitute the value of the length on the plan in the equation
17 / The actual length = 1.25/3
The actual length of the room = 17/0.42
= 40.8 feet
Hence, if the length of the room is 17 inches one the architect's plan, the actual length of the room in feet if the scale of the plan is 1.25 inches to 3 feet is 40.8 feet
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Rationalize the denominator Square root 12+Square root 6/Square root 3+1
Answers
Square root 12+Square root 6/Square root 3+1. After Rationalize the denominator we got 4.68.
Given that,
Square root 12+Square root 6/Square root 3+1
We have to Rationalize the denominator.
If the denominator's radical is a square root, multiply by a square root that, when multiplied by the denominator, produces a perfect square beneath the radical.
The square root of a number is the element that, when multiplied by itself, produces the original number. Squares and square roots are examples of special exponents.
[tex]\sqrt{12}+\sqrt{6} /\sqrt{3+1}[/tex]
Square root of [tex]\sqrt{12} is 2\sqrt{3}[/tex]
[tex]2\sqrt{3}+\sqrt{6}/\sqrt{4}[/tex]
Square root of [tex]\sqrt{4} is 2[/tex]
[tex]2\sqrt{3}+\sqrt{6}/2[/tex]
Calculating the terms
3.46+2.44/2
3.46+1.22
4.68
Therefore, After Rationalize the denominator we got 4.68.
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Alice went shopping for shirts. she purchased 4 blue shirts and 5 yellow shirts. what is the ratio of blue shirts to the total number of shirts that she purchased?
Answers
Answer: 4 : 9
Step-by-step explanation:
Total number of blue shirts purchased by Alice = 4
Total number of yellow shirts purchased by Alice = 5
Hence, total number of shirts purchase by her = 4 + 5
= 9
Therefore, Ratio of number of blue shirts to the total number of shirts
[tex]=\frac{Total~number~of~blue~shirts}{Total~number~of~shirts}[/tex]
[tex]=\frac{4}{9}[/tex]
Hence, Ratio = 4 : 9
How do I make a percent for a number that is not 100
Answers
Answer: If you had a fraction, you would have to turn into a decimal, then a percent. You can turn a decimal into a percent by multiplying the decimal by 100 and adding the percent sign. Hopefully this helps!
Answer: Like so:
30 percent of 50...
30/100= 0.30 (percentage)
0.30*50= 15 (discount, deducted amount, etc...)
Subtract answer from original number:
50-15= 35
30% of 50= 15
New amount= 35
A camera has a listed price of 819.95 before tax. If the sales tax rate is 7.25 , find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answers
Answer:
$21.40
Step-by-step explanation:
List price = $19.95
Sales Tax Rate = 7.25%
Total sales tax = 19.95 x 7.25/100 = $ 1.45
Total cost = 19.95 + 1.45 = $21.40
Subtract.
−6/7−(−5/7)
Enter your answer in the box as mixed number in simplest form.
Answers
Step-by-step explanation:
-1/7 is exact form and Slash or / is division . -0.142857, Decimal form and horizontal line is division too . It is the simplest form .
HELP MEH PLS PLS WIL GIVE BRAINLY OR WTV
Answers
Answer:
It would go 3 to the write of x.
Step-by-step explanation:
If B is the 3 spaces to the left of x and T is three spaces to the right of x, x would be in the middle.
In the picture, you have B=2, X= 5
so T goes if X is the midpoint of BT is
X= (B+T)/2
5 x 2= 2+ T
10 = 2+T
therefore, T = 8
Please helppp. 15 pointtts
Answers
Answer:
Y = 60x
Step-by-step explanation:
Find the slope by finding Y2 - Y1/X2 - X1, 1 and 2 being two separate points on the graph. 120-0/2 = 6
please help! will give brainliest!
Answers
Answer:
The correct answer is C. On the vertex of Figure A.
Step-by-step explanation:
Before you can find the answer to the question, you must first know what the center of dilation means in math. The center of dilation is a reference point used to appropriately scale the dilation of a figure. The vertex is the the point opposite to and farthest from the base of a geometrical figure, or the common endpoint of the sides of an angle.
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The temperature drops to -6 in 1 hour. In the next hour it drops to -8. By how much would the temperature have to rise to get to 0?
Answers
NEED ASAP Create a unique table of data for two different linear functions. The table should use the same values of x for both functions. Based on your table, will the graphs of these two functions intersect? Explain your answer.
Answers
A table of data for two different linear functions using the same values of x for both functions is shown below:
From the table, it can be seen that when x = -1, the function y = 2x + 7 has a value of 5 and the function y = -x + 4 has a value of 5.
Therefore, the graph of the two functions will intersect at (1, 5)
An eleven-foot long board must be cut into three pieces so that one piece is 1-foot shorter than half
the length of the longest piece and the other piece is 3 feet shorter than the longest piece. How
long is the shortest piece?
Answers
Answer:
2'
Step-by-step explanation:
An eleven-foot long board must be cut into three pieces so that one piece is 1-foot shorter than half the length of the longest piece and the other piece is 3 feet shorter than the longest piece. How long is the shortest piece?
board 1 = 0.5L - 1
board 2 = L - 3
board 3 = L
so:
(0.5L - 1) + (L - 3) + L = 11'
0.5L - 1 + L - 3 + L = 11'
combine L on left side:
2.5L - 4 = 11
add4 from both sides:
2.5L - 4 + 4 = 11 + 4
2.5L = 15
divide both sides by 2.5:
2.5L/2.5 = 15/2.5
L = 6
Formula for boards are, substitute in L = 6:
board 1 = 0.5L - 1
= 0.5(6) - 1
= 3 - 1
= 2'
board 2 = L - 3
= 6 - 3
3'
board 3 = L
= 6
shortest board is board 1 at 2'
HELP PLS HELPP egrhsdjtkfylkfjhtrgthynbvrshtndgvrehtbgd
Answers
Answer:
126
Step-by-step explanation:
The area of the top triangle is (6)(6)/2 = 18 square meters.
The area of the bottom rectangle is (9)(12)=108 square meters.
Adding these, we get the total area to be 126 square meters.
Given that x: y = 10:9 and x - y = 122, find the value of x + y.
Answers
Answer:
2318
Step-by-step explanation:
[tex] \frac{x}{y} = \frac{10}{9} [/tex][tex]x = \frac{10y}{9} [/tex][tex] \frac{10y}{9} - y = 122[/tex][tex] \frac{10y - 9y}{9} = 122[/tex][tex] \frac{y}{9} = 122[/tex][tex]y = 9 \times 122 = 1098[/tex][tex]x - y = 122 \\ y = 1098 \\ x = 122 + 1098 = 1220[/tex][tex]x + y = 1220 + 1098 = 2318 \\ x + y = 2318[/tex]Write the coordinates of the vertices after a translation 7 units left.
B'=
,
C'=
,
D'=
,
E'=,
please help
Answers
The coordinates of the images of the vertices of the rectangle are B'(x, y) = (- 4, 2), C'(x, y) = (- 4, 7), D'(x, y) = (0, 7) and E'(x, y) = (0, 2).
What are the coordinates of the images of the vertices of a rectangle
Rectangles are defined by the location of its four vertices set on Cartesian plane, whose images must be found by using a transformation known as translation, whose formula is defined below:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Location of the vertex.T(x, y) - Translation vector.P'(x, y) - Location of the image of the vertex.If we know that B(x, y) = (3, 2), C(x, y) = (3, 7), D(x, y) = (7, 7), E(x, y) = (7, 2) and T(x, y) = (- 7, 0), then the images of the vertices are:
B'(x, y) = (3, 2) + (- 7, 0)
B'(x, y) = (- 4, 2)
C'(x, y) = (3, 7) + (- 7, 0)
C'(x, y) = (- 4, 7)
D'(x, y) = (7, 7) + (- 7, 0)
D'(x, y) = (0, 7)
E'(x, y) = (7, 2) + (- 7, 0)
E'(x, y) = (0, 2)
Now we proceed to present the resulting figure.
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The population of a town was 980 in 1970. The population has been growing at a rate of 18% each year. What is the population of the town in the year 1995? Round your answer to the nearest whole number.
Answers
The population of the town in the year 1995 will be 61415.
How to illustrate the information?From the information, the population of a town was 980 in 1970 and the population has been growing at a rate of 18% each year.
Therefore, it should be noted the difference in the number of years will be:
= 1995 - 1970
= 25 years
Therefore, the population of the town in the year 1995 is:
= 980 × (1 + 18%)^25
= 980 × (1.18)^25
= 980 × 66.6686
= 61415
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