Given: NM // XZ
We know that side NM is
v to side XZ. If
Prove: AXYZ ~ ANYM
we consider side NY the transversal for these parallel
lines, we create angle pairs. Using the
v. we can state that
ZYXZ is congruent to ZYNM. We know that angle
XYZ is congruent to angle
v by the reflexive
property. Therefore, triangle XYZ is similar to triangle
NYM by the
similarity theorem.
M
Answers
A transversal is a straight line that intersects two parallel lines forming four angles at each point of intersection. Thus the required answers to the given question are:
i. Side NM is parallel to side XZ.
ii. Using the corresponding property
iii. <XYZ is congruent to <NYM
iv. ΔXYZ is similar toΔNYM by SAS theorem
Two or more angles are said to be congruent if and only if they have equal measure. This property can be used to relate equal angles.
While a transversal is a straight line that intersects two parallel lines forming four angles at each point of the intersection.
The required answers to the question are as stated below:
i. Side NM is parallel to side XZ.
ii. The corresponding property
iii. <XYZ is congruent to <NYM
iv. ΔXYZ is similar toΔNYM by SAS theorem
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Answer: For the first box it is parallel, for the second box it is the corresponding angles theorem, the third is NYM, and the last one is AA.
Step-by-step explanation: 1.) Since line NM has an arrow on it's line and XZ has an arrow on it's line, that means that those two line are parallel to each other. 2.) Since both triangle contain the same transversal line (NY) and the corresponding angles theorem states that if a transversal intersects parallel lines, the corresponding angles are congruent. From this we can conclude that this means that the angle <YXZ has is congruent to the angle <YNM. Therefore we use the corresponding angles theorem. 3.) Answer 2 basically answers box number three but since we concluded that Angles of <YXZ and <YNM are both congruent <NYM would be your answer its just flipped. 4.) We use the AA theorem, because the AA theorem states that if an angle or angle(s) of one triangle is congruent to another angle/angle(s) of another triangle, then the triangles are similar (congruent). Therefore we would use the AA theorem.
Hope this helps :)
By the way this is the answer for EDGE in 2023
Related Questions
Tristan has a points card for a movie theater.
He receives 25 rewards points just for signing up.
He earns 8.5 points for each visit to the movie theater.
He needs at least 110 points for a free movie ticket.
Write and solve an inequality which can be used to determine vv, the number of visits Tristan can make to earn his first free movie ticket.
Answers
You would have to visit the movies 10 times to get your first free ticket
Tristan needs to make at least 10 visits to the movie theater to earn his first free movie ticket.
Let v be the number of visits Tristan makes to the movie theater.
He receives 25 rewards points just for signing up, and he earns 8.5 points for each visit. So, the total rewards points he will have is
25+8.5v.
He needs at least 110 points for a free movie ticket. Therefore, we can write the inequality:
25+8.5v≥110
To solve for v, we can subtract 25 from both sides of the inequality and then divide by 8.5:
8.5v≥85
v≥85/8.5
v≥10
So, Tristan needs to make at least 10 visits to the movie theater to earn his first free movie ticket.
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1. Decide if the following is a properly formed syllogism. If you are going to wrap Holly’s gift, you need wrapping paper. If you need wrapping paper, you have to go to the store. Therefore, if you go to the store, then you’re going to wrap Holly’s gift.
A) This is a syllogism.
B) This is not a syllogism.
Answers
This is not a syllogism. Hence option B is correct.
What is a syllogism?A logical structure for a formal argument that includes a major, minor, and conclusion.
This syllogism cannot be concluded without a given statement.
You'll need wrapping paper if you're going to wrap Holly's present. To get wrapping paper, you must visit a store.
Therefore, you will wrap Holly's present if you visit the store. This isn't a syllogism
Hence option B is correct.
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Answer:
This is not a syllogism
Step-by-step explanation:
I took the quiz. :)
Chords AC and BD intersect in circle O as shown in the diagram. Two of the angle measurements are marked. What is mL CED?
Answers
Answer:
By using the formulas of circle and geometry, we find that ∠CED = 65°.
Step-by-step explanation:
We know that the measure of the interior angle is the half sum of the arcs comprising it and its opposite, so
∠CED = 0.5 × (arc AB + arc CD)
See the attached figure with letters to better understand the problem
arc AB = 82° (by central angle)
arc CD = 48° (by central angle)
Substitute the values in the formula above
∠CED = 0.5 × (82° + 48°)
∠CED = 0.5 × 130°
∠CED = 65°
Therefore the answer is ∠CED = 65°
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If n= 1999 ! then [tex]\large \sf\sum\limits_{x = 1}^{1999} log_{n}(x) [/tex] is equal to
a) -1
b) 0
c) 1
d) [tex] \sf \sqrt[1999]{1999} [/tex]
Answers
Answer:
a) 1
Step-by-step explanation:
added in the picture
Solve for x :
[tex] \sf \: \: \: \: \: \: \: \: \: \: \: 29x + x = 30[/tex]
[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
[tex] \tiny \sf bluh... \: \: so \: \: boring[/tex]
Answers
Answer:
x = 1
Step-by-step explanation:
Step 1: Combine like terms.
[tex](29x + x) = (30)[/tex] [tex]30x=30[/tex]Step 2: Divide both sides by 30.
[tex]30x/30=30/30[/tex] [tex]x=1[/tex]Step 3: Check if solution is correct.
[tex]29(1)+(1)=30[/tex] [tex]29+1=30[/tex] [tex]30=30[/tex]Therefore, x = 1.
Solution: X=1
[tex]\searrow[/tex]
Detailed explanation:
Here we need to solve for x. x is our unknown. It's what we should find.
[tex]\searrow[/tex]
Note right up front that we can add the x's. This is a process that is known as "Combining Like Terms". We can combine them by adding, like here.
[tex]\twoheadrightarrow\sf 29x+x=30[/tex]
"x" is the same as 1x.
[tex]\twoheadrightarrow\sf 30x=30[/tex]
We're getting closer to finding the value of the unknown!
Now we know that if we multiply 30 times the unknown, we will get 30.
What will we get if we multiply 1 times the unknown? 1 is what we will obtain upon dividing by 30.
So our unknown, or x, is 1.
Voila! There's our answer!
Cheers! ^-^_____________________________
Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
_____________________________
what is 5xy-x^2t+2xy+3x^2t
Answers
Answer:
x • (2xt + 7y)
Step-by-step explanation:
1. ((5xy-((x2)•t))+2xy)+(3x2•t)
2. Pull out like factors :
2x2t + 7xy = x • (2xt + 7y)
Final result
x • (2xt + 7y)
Answer:
[tex]7xy + {x}^{2} t[/tex]
Step-by-step explanation:
[tex](5xy + 2xy) + ( - 2 {x}^{2} t + 3 {x}^{2}t) [/tex]
If a(x) = 3x + 1 and b (x) = square root of x-4, what is the domain of (b o a)(x)
Answers
( 1, ∞) is the domain of (b o a)(x)
What is Function?
A function is defined as a relation between a set of inputs having one output each.
According to the question,
[tex]a(x) = 3x + 1 \\\\b (x) =\sqrt{x+4}[/tex]
To find the domain of the composite function,
[tex](b o x) (x) = b(a(x))\\\\(b o x) (x) = b(a(3x-1))\\\\(b o x) (x) = \sqrt{3x+ 1 -4} \\\\(b o x) (x) = \sqrt{3x -3}\\\\[/tex]
Therefore,
[tex]3x - 3 \geq 0\\3x \geq 3\\x \geq 1\\\\[/tex]
Hence , [ 1, ∞ ] is is the domain of (b o a)(x).
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Can somebody help me, i would really appreciate it!!
Answers
It will take 5 seconds for the waste to hit the ground.
How many seconds will it take for the waste to hit the ground?We know that the bird releases the waste from a height of 400ft, so the height equation is:
[tex]h(t) = -16t^2 + 400[/tex]
The waste will hit the ground when its height is equal to zero, so we just need to solve the quadratic equation:
[tex]h(t) = 0 = -16t^2 + 400\\\\16t^2 = 400\\\\t^2 = 400/16 = 25\\\\[/tex]
Now we can apply the square root in both sides:
[tex]t = \sqrt{25} = 5[/tex]
It will take 5 seconds for the waste to hit the ground.
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Find the area and perimeter.
The figure shows a triangle. One side is given by 4 x minus 3 units. The second side is given by x plus 9 units. The third side is equal to 8 units. The height from the third side is given by 3 x units.
Hint: The height of a non-right triangle is the length of the segment of a line that is perpendicular to the base and that contains the opposite vertex
Answers
Answer:
Area=12x square units; Perimeter=5x+14 units
Step-by-step explanation:
Recall the formulas for area and perimeter of a triangle:
Area of a triangle is half of the product of a base its corresponding height:
[tex]A=\frac{1}{2}bh[/tex]
Perimeter is the sum of all of the side lengths:
[tex]P=a+b+c[/tex]
In arbitrary triangles ABC, the sides are labeled across from a vertex with a matching lowercase letter. So, in my diagram, side "b" is the bottom with length "8". Side "b" is also the base, so the corresponding height is the perpendicular line segment that connects side "b" with vertex "B", which measures "3x"... 3 times some unknown value.
Side "a" is length "4x-3", and side "c" is length "x+9".
In this situation, where the sides have their specific relationship with "x" and the height is exactly triple "x", solving for x (and thus exact numerical values for the Perimeter and Area) involves trying to relate the two equations, possibly done with Heron's formula for area, or with trigonometry. Ultimately, it involves solving a 4th degree polynomial to get an exact answer, which is not what the question intends, so we'll leave the Area and Perimeter in terms of x (meaning there will still be "x" in our expressions to represent the Area and Perimeter).
Area
[tex]A=\frac{1}{2}bh\\A=\frac{1}{2}(8)(3x)\\A=12x[/tex]
So the Area of the triangle equals 12x square units.
Perimeter
[tex]P=a+b+c\\P=(4x-3)+(8)+(x+9)\\P=5x+14[/tex]
So the Perimeter of the triangle equals 5x+14 units
Define the hypothesis and the conclusion of the following conditional statement.
Conditional Statement: All kids who wear braces will have straight teeth.
Answers
The hypothesis will be that "If a kid wears braces, then the kid will have a straight teeth".
What is hypothesis?It should be noted that a hypothesis means a proposed explanation based on reasoning and evidence.
In this case, the hypothesis will be that "If a kid wears braces, then the kid will have a straight teeth".
The conclusion is that kids who wear braces will have straight teeth.
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A 12 foot ladder leans against a wall so that the base of the ladder is 7 feet from the wall. How high up on the wall will the ladder reach? Round to the nearest hundredth of a foot.
Answers
Reason
Using the Pythagorean theory,
a^2 + b^2 = c^2 (the hypotenuse)
Since we know the diagonal measurement (the hypotenuse) we will call c=12
We know one leg is 7, so we will call b=7
Now we will solve for “a”
Changing the equation to subtract
c^2 - b^2 = a^2
Substitute in our numbers
12^2 - 7^2 = a^2
144-49= a^2
95 = a^2
Take square root of both sides
9.746 = “a” the unknown length
Round to nearest hundredth
9.75
Solve the system of equations.
y = -2x + 5
y = x^2 + 3x +9
a. (-1,7), (-4,13)
b. (-1,-3), (-4,3)
c. (-1,13), (-4, 7)
d. (1,3), (4,13)
Answers
Answer:
A
Step-by-step explanation:
y = - 2x + 5 → (1)
y = x² + 3x + 9 → (2)
substitute y = x² + 3x + 9 into (1)
x² + 3x + 9 = - 2x + 5 ( subtract - 2x + 5 from both sides )
x² + 5x + 4 = 0 ← in standard form
(x + 1)(x + 4) = 0 ← in factored form
equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 4 = 0 ⇒ x = - 4
substitute these values into (1) for corresponding values of y
x = - 1 : y = - 2(- 1) + 5 = 2 + 5 = 7 ⇒ (- 1, 7 )
x = - 4 : y = - 2(- 4) + 5 = 8 + 5 = 13 ⇒ (- 4, 13 )
4. If u = {1,2,3,....10) A = { odd numbers up to 9} B = {numbers less than 7). Write out the members of the following sets: (i) AUB (ii) An B (ii) A(prime) U B
Answers
Answer:
i. {1,2,3,4,5,6,7,9}
ii. {1,3,5}
iii. {1,2,3,4,5,6,8,10}
Step-by-step explanation:
U= {1,2,3,4,5,6,7,8,9,10}
A= {1,3,5,7,9}
B= {1,2,3,4,5,6}
A U B = {1,2,3,4,5,6,7,9}
A n B = { 1,3,5}
A (prime) U B =
A(prime)= {2,4,6,8,10}
Therefore A(prime)= {1,2,3,4,5,6,8,10}
determine which equation is parallel and perpendicular to jk
Answers
None of the equations are parallel or perpendicular to the line jk.
How to know equations that are parallel and perpendicular?The equation of a line can be interpreted as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
Parallel lines have the same slope(m).
Perpendicular line follows the principle below:
m₁ m₂ = -1Therefore, let's find equation of jk
(-5, 5)(1, -5)
m = -5 - 5 / 1 + 5 = -10 / 6 = - 5 / 3
using (1, -5)
-5 = - 5 / 3 (1) + b
b = -5 + 5 / 3 = -15 + 5 / 3 = -10 / 3
Therefore,
y = -5 / 3 x - 10 / 3
m = - 5 / 3
6x + 10y = 11
10y = -6x + 11
y = - 6 / 10 x + 11 / 10
y = - 3 / 5 x + 11 / 10
hence, m = - 3 / 5
5x - 3y = 8
3y = 5x - 8
y = 5 / 3 x - 8/3
m = 5 / 3
The equation
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The function y=3^x is called an_______ function because the exponent is a _______. Now, let’s look at how to graph the exponential function y=3^x
Answers
The function is called an exponential function became the exponent is a variable.
The function is called an exponential function became the exponent is a variable.
What is an exponential function?An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
So, here given a fill in the blank statement, we need to find the words to be filled in the blanks,
So, the whole statement is =
The function is called an exponential function became the exponent is a variable.
The function y = 3ˣ is an exponential function because it is having a power which is a variable.
The graph of the same is attached to the solution.
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EMERGENCY!! 25 POINTS!! Find 40th term of 5n - 3
Answers
Answer:
197
Step-by-step explanation:
the answers 197 because if an=5n-3 then a40= 197
PLEASS HELP!!
3 folders cost $2.91.
Which equation would help determine the cost of 2 folders?
Answers
Answer:
The answer is B
Step-by-step explanation:
By proportion , 3 : 2.91 = 2: x . then you write it in fraction
g Lovely Lawns, Inc., intends to use sales of lawn fertilizer to predict lawn mower sales. The store manager estimates a probable six-week lag between fertilizer sales and mower sales. The pertinent data are: PeriodFertilizer SalesNumber of Mowers Sold 11.915 21.612 31.713 41.915 52.116 61.813 71.914 81.713 91.815 101.412 111.814 121.714 131.714 141.612 a. Determine the correlation between the two variables.
Answers
The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.
What is correlation?The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when other data value is increased or decreased respectively.
The pertinent data are:
Period Fertilizer Sales Number of Mowers Sold
1 1.6 12.0
2 1.3 10.0
3 1.8 13.0
4 2.0 15.0
5 2.2 15.0
6 1.5 11.0
7 1.6 12.0
8 1.4 10.0
9 1.8 13.0
10 1.4 10.0
11 1.9 15.0
12 1.4 11.0
13 1.7 14.0
14 1.4 13.0
To determine the correlation between the two variables
Regression equation ( y ) = a + bx
y = dependent variable ( mower )
x = independent variable ( fertilizer)
a = intercept point ( y-axis and regression line )
b = slope ( regression line )
From the given data;
N = 14 , Σ x = 22.8,
Σy = 131, Σy^2 = 1269,
Σx^2 = 38.18, (Σx)^2 = 519.84
Σxy = 219.8, (Σy)^2 = 17161
Hence, The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.
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What is the standard form of 0.00849
Answers
Answer:
8.49 × 10⁻³
Explanation:
Standard form of a number: A. × 10ᵇ
(where 'A' is the number, b is the exponent over 10)
For the number "0.00849", move the decimal point 3 places right so the exponent of 10 is -3.
Standard form: 8.49 × 10⁻³
Other examples of standard/scientific forms are: standard forms
i) 0.043, move the decimal point 2 places right = 4.3 × 10⁻²
ii) 4030, move the decimal point 3 places left = 4.03 × 10³
Answer:
when a number is given in that manner you have to take that decimal between two whole numbers.
and that is the main reason why I took that decimal from 0.0 to 8.49 and since it went towards the right my answer is going to be 8.49 *10 raised to negative 3.
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Answers
Answer:
-9
Step-by-step explanation:
-9
Jacob traveled 171 miles in 3.8 hours. He wants to know how many miles he traveled in one hour, so he set up this problem:
171 divided by 3.8
Jacob started by multiplying the divisor and the dividend by 10. This is the new problem:
1710 divided by 38
Use long division to find the quotient.
0.45
4.5
45
450
Answers
The answer is 45
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Shapes F and G are similar
Shape F has a perimeter of 180mm and an area of 2196mm².
Shape G has a perimeter of 300mm
Work out the area of shape G.
Give your answer to 1.d.p if decimal
Answers
Shape F has a perimeter of 180mm and an area of 2196mm² is similar to shape G with perimeter 300mm then area of shape is 6100mm².
As given,
Shapes F and G are similar
Perimeter of shape F=180mm
Area of shape F=2196mm²
Perimeter of shape G=300mm
Let xmm²be the area of shape G
Square of ratio of perimeter of similar shape =Ratio of area of similar shape
⇒(180 /300)² =(2196/x)
⇒9/25=2196/x
⇒x=(2196×25)/9
⇒x=6100mm²
Therefore, shape F has a perimeter of 180mm and an area of 2196mm² is similar to shape G with perimeter 300mm then area of shape is 6100mm².
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Tahir purchase to toys for his children he buyS spider-man and barbie doll for rs. 3,000 and rs. 5,000 respectively if a discount of 20% is offered on all toys find amount of discount in the sale price for each toy
Answers
For the spider man the discount is of rs600, for the doll the discount is of rs1,000.
How to find the amount of discount for each toy?We know that the price of the spider-man is rs3,000, and we apply a discount of the 20%.
So the amount of discount for that toy is the 20% of rs3,000, which gives:
(20%/100%)*rs3,000 = rs600
So the amount discounted for the spider-man is rs600.
For the case of the doll, we know that its cost is rs5,000, the amount discounted is:
(20%/100%)*rs5,000 = rs1,000
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Determine the intercepts of the line.y=−2x−21
help please now
Answers
Answer:
( -10.5 , 0 ) and ( 0 , -21 )
Step-by-step explanation:
→ Determine where a line intersects
x and y intercept
→ Set x equal to 0 to find y - intercept
( 0 , -21 )
→ Set y equal to 0 to find x intercept
0 = -2x - 21
→ Add 21 to both sides
21 = -2x
→ Divide both sides by -2
-10.5 = x
can someone please help meee
Answers
Answer:
with a line accross the points
The price of a pack of kitchen rolls is reduced by 1/6
The new price is £1.20
Work out the original price.
Answers
Answer: 1.44
Step-by-step explanation:
(original price) - (1/6 of the original price) = 1.20
If you let x = original price, then the equation is:
x - 1/6 x = 1.20
5/6 x = 1.20
x = 1.44
the original price is £1.44.
Credits to the person who also answered :)
I hope this helps!
Answer:
£1.44
Step-by-step explanation:
Since the original price was reduced by 1/6, that means the new price is 5/6 of the original price.
Let x = original price.
Write an equation and solve it.
5/6 x = £1.20
x = £1.20 × 6/5
x = £1.44
If x is increased by 25% then, by what % is x² increased
Answers
By analytical methods and algebraic handling and on the basis that x is increased by 25 %, we conclude that the variable x² is increased by 18.75 %.
How to determine the percentage increase rate
In this case we have a linear variable x, whose increase is described by the following expression:
y = x · (1 + r/100) (1)
Where r is the increase rate.
If we square (1), then we find that:
y² = x² · (1 + r/100)² = (1 + r'/100) (2)
Where r' is the equivalent increase rate.
(1 + r/50 + r²/10000) = (1 + r'/100)
r'/100 = r/50 + r²/10000
r' = r/2 + r²/100
If we know that r = 25, then the equivalent increase rate is:
r' = 25/2 + 25²/100
r' = 18.75
By analytical methods and algebraic handling and on the basis that x is increased by 25 %, we conclude that the variable x² is increased by 18.75 %.
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Now evaluate f(x)=2x^4-4x^3-11x^2+3x-6 for x=-2.
F(-2)=
Answers
Answer:
8
Step-by-step explanation:
f(x)=2x^4-4x^3-11x^2+3x-6
f(-2)=2(-2)^4-4(-2)^3-11(-2)^2+3(-2)-6
f(-2)=2(16)-4(-8)-11(4)-6-6
f(-2)=32+32-44-12
f(-2)=64-44-12
f(-2)=20-12
f(-2)=8
During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon?
Answers
Answer:
30
Step-by-step explanation:
4 cups x 60 hours a min x 2 hours of lunch ÷ 16 cups per gallon = 30 gallons
The answer is 30 gallons.
Firstly, convert the hours to minutes so you know how many minutes you're working with. 2*60=120 minutes.
Then, multiply 120 with 4 to get the number of tea (in cups) that is poured. 120*4=480 cups.
Finally, divide 480 cups with 16 cups to find out the number of gallons poured. 480/16 equals 30 gallons.
Hope this helped.
Jacob traveled 171 miles in 3.8 hours. He wants to know how many miles he traveled in one hour, so he set up this problem:
Answers
Answer:
so first we have to divide each side by 38
4.5miles=0.1
45miles=1 hour
Hope This Helps!!!
