We can conclude that ΔWXZ ≅ ΔXZY under ASA condition.
What do we mean by the congruency of a triangle?Two triangles are said to be congruent if all three corresponding sides and angles are equal in size.To appear identical, these triangles can be moved, rotated, flipped, and turned.They will coincide if they are moved.Congruence exists when two triangles satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
To Prove: ΔWXZ ≅ ΔXZY
ZX = ZX = (Common)∠WZX = ∠YZX = (Equal as ZX bisects ∠WZY)∠ZXW = ∠ZXY = (Equal as XZ bisects ∠WXY)So, ΔWXZ ≅ ΔXZY under ASA consition.
Therefore, ΔWXZ ≅ ΔXZY.
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Which number is greater, 23 x 10³ or 11 x 104? How do you know? Show your work and explain your steps
Answer:
23x10
Step-by-step explanation:
Its 23x10^3 because its basically because 10 times 10 is a 100 and 100x10 is 10000 and 11x104 will be like 1000 smth (calculate it if u want)
PLS HELP RIGHT ANSWER ONLY ill give 500 points
Determine the value of x in the diagram below.
Question 1 options:
A. 4
B. -6
C. 10
D. 12
By applying the triangle midpoint theorem to the triangle, the value of x is equal to: D. 12.
The properties of similar triangles.In Geometry, two (2) triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.
Corresponding parts of two congruent figures.In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.
What is triangle midpoint theorem?Triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.
By applying the triangle midpoint theorem to the triangle, we have:
8x = 2(2x + 24)
8x = 4x + 48
8x - 4x = 48
4x = 48
x = 48/4
x = 12.
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On October 1, Nadia starts a push-up challenge by doing 18 push-ups. On October 2, she does 21 push¬ups. On October 3, she does 24 push-ups. She continues until October 16, when she does the final push-ups in the challenge. a. Write an explicit definition to model the number of push-ups Nadia does each day. b. Write a recursive definition to model the number of push-ups Nadia does each day. c. How many push-ups will Nadia do on October 16? d. What is the total number of push-ups Nadia does from October 1 to October 16?
Answer:
[tex]\textsf{a)} \quad a_n=3n+15[/tex]
[tex]\textsf{b)} \quad \begin{cases}a_n=a_{n-1}+d\\a_1=18\end{cases}[/tex]
[tex]\textsf{c)} \quad 63[/tex]
[tex]\textsf{d)} \quad 648[/tex]
Step-by-step explanation:
Part (a)An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.
Explicit Formula
[tex]\boxed{a_n=a+(n-1)d}[/tex]
where:
[tex]a_n[/tex] is the nth term.a is the first term.n is the number of the term.d is the common difference.Given information:
October 1 = 18 push-upsOctober 2 = 21 push-upsOctober 3 = 24 push-upsNadia increases the number of push-ups each day by 3. Therefore:
a = 18d = 3Substitute the values of a and d into the formula to create an explicit formula to model the number of push-ups Nadia does each day:
[tex]\implies a_n=18+(n-1)3[/tex]
[tex]\implies a_n=18+3n-3[/tex]
[tex]\implies a_n=3n+15[/tex]
Part (b)A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.
Recursive Formula
[tex]\boxed{a_n=a_{n-1}+d}[/tex]
where:
[tex]a_n[/tex] is the nth term.[tex]a_{n-1}[/tex] is the (n-1)th term.d is the common difference.We already know the common difference from the previous calculations.
Therefore:
[tex]\implies a_n=a_{n-1}+3[/tex]
When giving a recursive rule we have to define the first term of the sequence, as it is not part of the formula. Therefore, the full recursive rule for the given scenario is:
[tex]\begin{cases}a_n=a_{n-1}+d\\a_1=18\end{cases}[/tex]
Part (c)To calculate how many push-ups Nadia will do on October 16, substitute n = 16 into the recursive formula from part (a):
[tex]\implies a_{16}=3(16)+15[/tex]
[tex]\implies a_{16}=48+15[/tex]
[tex]\implies a_{16}=63[/tex]
Therefore, Nadia will do 63 push-ups on October 16.
Part (d)Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac12n(a+a_n)}[/tex]
To find the total number of push-ups Nadia does from October 1 to October 16, substitute n = 16, a = 18 and a₁₆ = 63 into the formula:
[tex]\implies S_{16}=\dfrac12(16)(18+63)[/tex]
[tex]\implies S_{16}=8(81)[/tex]
[tex]\implies S_{16}=648[/tex]
Therefore, Nadia does a total number of 648 push-ups from October 1 to October 16.
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A model airplane takes off at an angle of elevation of 30°C. How high will the plane be after traveling 100 feet horizontally? Round to the nearest tenth. Show your work.
A model plane would be 57.7 feet high.
In this question,
A model airplane takes off at an angle of elevation of 30°C
We need to find how much the plane will be high after traveling 100 feet horizontally.
Consider the following diagram.
Let angle ACB is the angle of elevation.
∠ACB = 30°
the horizontal distance CB = 100 feet
We need to find the distance AB.
Consider tangent of angle ACB.
⇒ tan(30) = AB / BC
⇒ 0.577 = AB / 100
⇒ AB = 0.577 × 100
⇒ AB = 57.7 feet
Therefore, a model plane would be 57.7 feet high.
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8x1,000=8x_____=_____ i need help btw thanks last person by the way who helped me on my last question
The value of the expression 8 x `1000 is 8000
How to evaluate the expression?The expression is given as
8 x `1000
The above expression implies that we multiply 8 by 1000
This can be done directly using a calculator, and it can be solved step by step
The step by step procedure is as follows
Express 1000 as 10 x 100
So, we have
8 x `1000 = 8 x `10 x 100
Evaluate 8 x 10
8 x `1000 = 80 x 100
Evaluate 80 x 100
8 x `1000 = 8000
Hence, the value of the expression 8 x `1000 is 8000
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Find the distance between pair of parallel lines with the given equations.
y=x+2 y=x-4
The distance between pair of parallel lines with the following equation
y=x+2 y=x-4 is [tex]3{\sqrt 2 }[/tex]
Definition of parallel linesParallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.
The fundamental characteristics listed below make it simple to recognize parallel lines.
Straight lines which are always the same distance apart from one another are known as parallel lines.No matter how far apart they are from one another, the parallel lines can never intersect.The slope of a line which is perpendicular to both the lines will be -1. Check what are the y-intercept of any of the two lines and write the equation of the perpendicular line through it.
The y-intercept of the line y = x − 4 is (0,−4).
So, the equation of a line with slope −1 and a y-intercept of −4 is y = −x −4.
The perpendicular intersects or meets the line y = x - 4 at (0, 4).
Now, to find the point of intersection of the perpendicular & the other line, solve the two equations. Solve the right sides & solve for x.
x + 26 = -x - 6
2x = -6 (combine them like terms)
x = -3 (divide both the side by 2)
Find y:
y = -3 - 4
= -7
So, the point of intersection is (−3,−7).
Use the Distance Formula to find the distance between the points (-3, -7) and (0,−4).
[tex]{\displaystyle d={\sqrt {\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}[/tex]
[tex]={\sqrt {\left(0-(-3\right)^{2}+\left(-4-(-7\right))^{2}}}[/tex]
[tex]={\sqrt {3^2 +3^2}}[/tex]
[tex]=3{\sqrt 2 }[/tex]
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URGENT HELP MARKING BRAINIST
if a polynomial f(x) has a remainder of 8 qhen divided by x-3 what is f(x)
The value of f(x)= (x-3).g(x)+8
A division algorithm is an algorithm which, given two integers N and D, computes their quotient and/or remainder, the result of Euclidean division.
dividend= divisor x quotient+ remainder
given that, f(x) has remainder 8 and divided by x-3
as per division algorithm we can say that
dividend= divisor x quotient+ remainder
f(x)= (x-3).g(x)+ 8
if we need to find f(3) then put 3 in the place of x
that gives you f(3) = (3-3).g(x)+ 8
f(3)= 8
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The answer to f(x)= (x-3). g(x)+8
An algorithm for dividing two integers, N and D, into their quotient and/or remainder, or the product of Euclidean division, is known as a division algorithm.
Dividend equals Divisor x Quotient plus Remainder.
Given that, f(x) is divided by x-3 and has a remainder of 8.
The division algorithm allows us to state that
Dividend equals Divisor x Quotient plus Remainder.
f(x)= (x-3) (x-3).
g(x)+ 8
If we need to find f(3), we should substitute 3 for x.
giving you f(3) = (3-3).
g(x)+ 8
f(3)= 8
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Help me solve for 28/x = 12/18
Answer:
hope u get it............
Is the solution shown below correct? Explain.
9x+2=8x²+6x
Answer:
The solution below is wrong. The correct solution is [tex]x = \frac{-b (+-)\sqrt{73} }{16}[/tex]
Step-by-step explanation:
Rearrange the numerals :
[tex]9x + 2 = 8x^2 + 6x\\8x^2 + 6x - 9x - 2 = 0\\8x^2 - 3x - 2 = 0\\[/tex]
Use quadratic formula :
Solution 1: (Note: the -b"+".... is actually "±" as the system has some problem of adding "±" symbol)
[tex]x = \frac{-b+\sqrt{b^2 - 4ac}}{2a} \\x = \frac{-(-3)+\sqrt{(-3)^2 - 4(8)(-2)}}{2(8)} \\x= \frac{3+\sqrt{9 + 64 }}{16} \\\\x= \frac{3+\sqrt{73 }}{16} \\\\[/tex]
Hope this helps, it would really help me if u mark me as the brainliest.
) What happens if both bags weigh over 50 pounds when the passenger approaches the check in counter? Think. This is real life.
When both bags weigh over 50 pounds when the passenger approaches the check in counter, the person will pay an extra charge.
How to illustrate the information?It should be noted that one will pay for an excess luggage when the luggage is heavier than the allowance when the person checks in.
It should be noted that every airline has a restriction on how heavy the luggage can be.
Therefore, when both bags weigh over 50 pounds when the passenger approaches the check in counter, the person will pay an extra charge.
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The vasquez family visits their grandmother every 3 weeks and hosts a neighborhood party every 8 weeks. every 16th week, the vasquez family takes a day to go hiking
The problem statement provides information about the Vasquez Family, who pay visits to their grandmother every three weeks and host a neighborhood party every eight weeks.
The number of weeks combined when the Vasquez Family visits their grandmother and hosts the neighborhood party is 24 weeks.
The total number of weeks with all the three events occurring together (visit, neighborhood party, hiking) is 48 weeks.
Now we concluded that the number of weeks is 24 because we know that the Vasquez family visits their grandmother every three weeks and hosts a neighborhood party every eight weeks.
Therefore, we will look for a least common factor of both 3 (visit) and 8 (party) and that LCM (least Common Factor) is 24.
Therefore, the number of weeks when the Vasquez family visits their grandmother and hosts the neighborhood party is 24.
Complete Problem Statement:
The Vasquez family visits their grandmother every three weeks and hosts a neighborhood party every eight weeks. Every 16 weeks, the Vazquez family takes a day to go hiking. After how many weeks will the Vasquez family visit their grandmother and host the neighborhood party? After how many weeks will all three events occur?
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PLEASE HELP SOLVEEEEEE
The area of the parallelogram is approximately equal to 59.994 square units.
How to determine the area of a parallelogram by using Heron's formula
The area of a parallelogram is equivalent to the sum of the areas of the two triangles by adding a diagonal. Then, the area of each triangle can be found in terms of side terms by Heron's formula. First, find the length of each side:
Side AB
AB = (4, 6) - (- 2, 6)
AB = (6, 0)
AB = √(6² + 0²)
AB = 6
Side CD
CD = (- 1, - 4) - (5, - 4)
CD = (- 6, 0)
CD = √(6² + 0²)
CD = 6
Side AD
AD = (- 1, - 4) - (- 2, 6)
AD = (1, 10)
AD = √(1² + 10²)
AD = √101
Side BC
BC = (5, - 4) - (4, 6)
BC = (1, - 10)
BC = √[1² + (- 10)²]
BC = √101
Side AC
AC = (5, - 4) - (- 2, 6)
AC = (7, - 10)
AC = √[7² + (- 10)²]
AC = √149
Second, determine the areas of the two triangles.
Triangle ABC
s = 0.5 · (AB + BC + AC)
s ≈ 14.128
A = √[s · (s - AB) · (s - BC) · (s - AC)]
A ≈ 29.997
Triangle ACD
s = 0.5 · (AC + CD + AD)
s ≈ 14.128
A = √[s · (s - AC) · (s - CD) · (s - AD)]
A ≈ 29.997
Third, find the area of the parallelogram by adding the two areas calculated in the previous step:
A' = 29.997 + 29.997
A' = 59.994
The area of the parallelogram is approximately equal to 59.994 square units.
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Prove the following.
If SC ≅ HR and HR ≅ AB , then SC ≅ AB.
The congruent segments, [tex] SC \cong HR [/tex] and [tex] HR \cong AB[/tex], according to the substitution property of equality, gives; [tex] SC \cong AB [/tex]
How can the definition of congruency and equality property prove [tex] SC \cong AB [/tex]?The given parameters are;
[tex] SC \cong HR [/tex] [tex] HR \cong AB[/tex]Required;
To prove;
[tex] SC \cong AB[/tex]
Solution;
From the given parameters, and the definition of congruency, we have;
SC = HRHR = ABAccording to the symmetric property of equality, we have;
SC = HR
Therefore;
HR = SCAccording to the substitution property of equality, we have;
If a = b and a = c, therefore;
b = c
Which gives;
HR = SC
HR = AB
Therefore;
SC = AB
Which gives;
[tex] SC \cong AB [/tex] (Inverse of the definition of congruency)
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5. For f(x) = 5x + 1, find f-4). (1 point)
O-19
01
O-21
021
Answer: 19 ==> 1st option
Step-by-step explanation:
f(x) = 5x + 1
f(-4)=5(-4) + 1
f(-4)=-20 + 1
f(-4)=-19 ==> 1st option
Solve for x.
A. 8
B. 4.8
C. 4
D. 7.2
Answer: x=8 ==> A
Step-by-step explanation:
15x-6=114 ==> both angles are congruent angles, so they're equal
15x-6+6=114+6
15x=114+6
15x=120
15x/15=120/15
x=120/15
x=8 ==> A
For every 21 litres of petrol a car can run for 80 km.
How much petrol do you need (to 1 DP) to ensure the car has enough petrol of a trip that is 224 km?
Determine the values of m in the equation m2 = 36.
please helppp
Answer:
m = 6
Step-by-step explanation:
➟ m² = 36
in order to find the value of m take square root from both side
➟ [tex] \sf \: \sqrt{ {m}^{2} } = \sqrt{36} [/tex]
Calculate the values
➟ m = 6
∴ the value of m is 6
Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition.
Measures greater than m ∠ 8
The exterior angle ([tex]\angle[/tex] 5) is larger than either remote interior angle
([tex]\angle[/tex] 7 and [tex]\angle[/tex] 8) then m [tex]\angle[/tex] 2 > m [tex]\angle[/tex] 8 and m [tex]\angle[/tex] 5 > m [tex]\angle[/tex] 8 .
What is meant by Exterior Angle Inequality Theorem?
According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles. The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.
A triangle's exterior angle is always greater than its two remote interior angles.
By the Exterior Angle Inequality Theorem, the exterior angle ([tex]\angle[/tex] 2) is larger than either remote interior angle ([tex]\angle[/tex] 6 and [tex]\angle[/tex] 8).
Similarly, the exterior angle ([tex]\angle[/tex] 5) is larger than either remote interior angle ([tex]\angle[/tex] 7 and [tex]\angle[/tex] 8).
Therefore, m [tex]\angle[/tex] 2 > m [tex]\angle[/tex] 8 and m [tex]\angle[/tex] 5 > m [tex]\angle[/tex] 8 .
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A -4 nc point charge is located at -3 m along the x-axis. what is the electric potential at the origin?
The electric potential at the origin is 11.9834 ×[tex]10^{9}[/tex] .
What is electric potential?V = k (q/r)
V = 8.98755 × [tex]10^{9}[/tex] ×(-4/3)
V= 11.9834 ×[tex]10^{9}[/tex] is the the electric potential at the origin.
The effort required to transfer a unit charge against an electric field from a reference point to a specified spot.
Electric potential difference is the potential created when a charge is moved from one point to another within the field itself, whereas electric potential is the effort done per unit charge to transport the charge from infinity to a point in the electric field.
The amount of work required to move a unit positive charge from infinity to a particular point in an electric field is called the electric potential.
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11. Lang withdrew half of his money from his
bank account on the last day of January.
Then he withdrew half of the remaining
amount on the last day of February. He
continued withdrawing half of his money
on the last day of March, April, May, and
June. His final balance was $1.50. How
much money did Lang have in his bank
account before his first withdrawal?
Land withdrew money in the form of an geometric series and he had $96 in his account in January.
A geometric series in mathematics is made up of an unlimited number of terms with a fixed ratio between them.
Each term is connected to the previous term by a simple ratio.
if the first term of an Geometric series be a, and the common ratio r then the second term is ar, third term is ar² and so on.
the nth term of a Geometric series is calculated by
[tex]a_n=ar^{n-1}[/tex]
Now here we know that the final term of the Geometric series is $1.50.
So each month Lang withdrew half of his money.
So the common ratio of each terms is [tex]\frac{1}{2}[/tex].
Number of months=6(n=7)
Now we have to find the initial term of the Geometric series.
We know that [tex]a_n=ar^{n-1}\\[/tex]
Given n=7 and r=1/2 and aₙ=1.5
Substituting the values we get:
[tex]1.5=a\times(\frac{1}{2})^{7-1} \\or, 1.5=a \times (\frac{1}{2} )^6\\or, 1.5=a\times \frac{1}{64} \\or,a=96[/tex]
Hence Lang had $96 in his bank account before his first withdrawal.
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Anyone know how to solve please
If the coordinates are rotated 90 degrees clockwise, the resulting expression will be;
B' = (0, -5)
K' = (-3, 0)
U' = (2, -2)
Y' = (-3, 4)
Rotation of coordinate pointWhen a coordinate (x, y) is rotated 90 degrees clockwise around the origin is (-y, x)
Given the coordinates points
B = (5, 0)
K = (0, 3)
U = (2, -2)
Y = (4, 3)
If the coordinates are rotated 90 degrees clockwise, the resulting expression will be;
B' = (0, -5)
K' = (-3, 0)
U' = (2, -2)
Y' = (-3, 4)
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Kendra and Ann shared 200 apples such that Kendra received 50 apples more than Ann I)calculate their share Ii)find the ratio of their share
pls help Asap
Step-by-step explanation:
this is the solution above
Maria is going for a run. She runs for 4 hours at a speed of 6.4 miles per hour. For how many miles does she run?
The number of miles that Maria ran is 25.6 mile.
How to calculate the value?From the information given, she runs for 4 hours at a speed of 6.4 miles per hour.
It should be noted that distance is calculated as the speed multiplied by the time taken.
In this case,the distance will be:
= Speed × Time
= 6.4 × 4
= 25.6 miles
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HELPPP ASAPPPP
which expression is equivalent to 5(2.47y − 2.03)?
A.)12.35y + 10.15
B.)12.35y − 10.15
C.) 12.35y + 2.03
D.) 12.35y − 2.03
Answer:
5(2.47y−2.03)
Use the distributive property to multiply 5 by 2.47y−2.03.
12.35y−10.15
Step-by-step explanation:
f(x)=x², g(x)=2x²
The points (-1, 1), (0, 0), and (1, 1) of f(x) translate to the points ‘blank’ of g(x).
The coordinate points of g(x) are (-1, 2), (0, 0), (1, 2).
Which are the coordinates of the new points?
We know that the points (-1, 1), (0, 0), and (1, 1) belong to f(x) graph, where:
f(x) = x^2
Notice that the inputs in these points are x = -1, x = 0, x = 1.
Function g(x) is:
g(x) = 2x^2
Using the given inputs, we have:
g( -1) = 2*(-1)^2 = 2
g(0) = 2*0^2 = 0
g(1) = 2*(1)^2 = 2
Then the coordinate points of g(x) are (-1, 2), (0, 0), (1, 2).
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A school playground is in the shape of a rectangle 800 feet long and 700 feet wide. If fencing costs $18 per yard, what will it cost to place fencing around the playground?
Answer:
pomogło dzięki xxxxxxxxxx
Jayden is a songwriter who collects royalties on his songs whenever they are played in
a commercial or a movie. Jayden will earn $30 every time one of his songs is played
in a commercial and he will earn $120 every time one of his songs is played in a
movie. Jayden's songs were played on 4 more commercials than movies, and his total
earnings on the royalties from all commercials and movies was $420. Write a system
of equations that could be used to determine the number of commercials and the
number of movies on which Jayden's songs were played. Define the variables that use to write the system.
The system of equations that could be used to determine the number of commercials and the number of movies on which Jayden's songs were played is illustrated as 30(x + 4) + 120(x) = 420.
The variable is that the number of times the song was played in movies is represented by x.
How to illustrate the information?From the information, Jayden is a songwriter who collects royalties on his songs whenever they are played in
a commercial or a movie and she will earn $30 every time one of his songs is played in a commercial and he will earn $120 every time one of his songs is played in a movie
Let the number of times the song was played in movies be x.
Jayden's songs were played on 4 more commercials than movies. This will be x+4.
Therefore, the equation to solve the question will be:
30(x + 4) + 120(x) = 420
30x + 120 + 120x = 430
150x + 120 = 430
150x = 430 - 120
150x = 310
x = 310/150
x = 2.1
Number of movies = 2
Number of commercial = x + 4 = 6
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Answer:
Step-by-step explanation:
Find the solution(s) of the system of equations:
y = x2 + 6x + 9
y = 2x + 6
(–3,12) and (–1,8)
(3,12) and (1,8)
(3,0) and (1,4)
(–3,0) and (–1,4)
The solutions are (0, - 6) ,(7, 8)
The given system of equations is expressed as
y = x² - 5x - 6- - - - - - - - - - - - (1)
y = 2x - 6- - - - - - - - - - - (2)
We would apply the method of substitution by substituting equation 2 into equation 1. It becomes
x² - 5x - 6 = 2x - 6
x² - 5x - 6 = 2x - 6
x² - 5x - 2x - 6 + 6 = 0
x² - 7x = 0
x(x - 7) = 0
x = 0 or x - 7 = 0
x = 7 or x = 0
Substituting x = 0 into equation 2, it becomes
y = 2 × 0 - 6
y = - 6
Substituting x = 7 into equation 2, it becomes
y = 2 × 7 - 6
y = 14 - 6
y = 8
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bisects ∠PQT.
7. If m∠PQT = 60 and m∠PQS =
4x + 14, find the value of x.
The value of x in the question is 4
How to find the value of x?The given parameters are
PQT = 60
PQS = 4x + 14
The line bisects PQT
So, we have
PQS = 1/2 * PQT
This gives
4x + 14 = 1/2 * 60
Evaluate
4x + 14 = 30
Evaluate the like terms
4x = 16
Divide by 4
x = 4
Hence, the value of x in the question is 4
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the temperature in sudbury was 4c. what was the temperature after a rise of 5c followed by a fall of 10c
By the use of arithmethic, the final temperature in Sudbury is - 1 °C.
What is the final temperature of Sudbury?
In this problem we know that initial temperature and two consecutive changes in time. A temperature rise represents a positive change, whereas a temperature fall represents a negative change, then the final temperature is equal to sum of the initial temperature and its two changes:
T = T' + ΔT₁ + ΔT₂
T = 4 °C + 5 °C - 10 °C
T = 9 °C - 10 °C
T = - 1 °C
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