m = [tex]\frac{5}{6}[/tex] , y - 7 = [tex]\frac{5}{6}[/tex] ( x - 12), y = [tex]\frac{5}{6}[/tex] x - 3
(a) calculate the slope using the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 6, - 8) and (x₂, y₂) = (12, 7)
m = [tex]\frac{7+8}{12+6}[/tex] = [tex]\frac{15}{18}[/tex] = [tex]\frac{5}{6}[/tex]
(b) the equation of a line in point-slope form is
y - b = m(x - a )
where m is the slope and (a, b) a point on the line
using m = [tex]\frac{5}{6}[/tex] and (a , b) = (12, 7 )
y - 7 = [tex]\frac{5}{6}[/tex] (x - 12)
(c) the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange (b ) into this form
y - 7 = [tex]\frac{5}{6}[/tex] - 10
y = [tex]\frac{5}{6}[/tex] x - 3
Please hel 15 points!
parent graph: f(x) = |x|
shifted 6 units down: f(x) = |x| - 6
then shifted 4 units to the right: f(x) = |x - 4| - 6
then vertically stretched by 2: f(x) = 2|x - 4| - 6
This means the vertex (0, 0) has moved to (4, -6) and the slope is 2
**************************************************************************************
f(x) = |x| f(x) = 2|x - 4| - 6
x y x y new coordinate
-2 2 -2 + 4 = 2 2(2) - 6 = -2 (2, -2)
-1 1 -1 + 4 = 3 1(2) - 6 = -4 (3, -4)
0 0 vertex 0 + 4 = 4 0(2) - 6 = -6 vertex (4, -6)
1 1 1 + 4 = 5 1(2) - 6 = -4 (5, -4)
2 2 2 + 4 = 6 2(2) - 6 = -2 (6, -2)
Plot the NEW COORDINATES for the transformed graph.
How long is the piece of string?
Answer:
C) 14 units
Step-by-step explanation:
The equation is in standard form, so the larger denominator is the square of the semi-major axis. That length is √49 = 7, so the major axis length is 2·7 = 14. This length is the length of the string.
Which statement is true?
A dilation is a function because every point on the pre-image corresponds to exactly one point on the image.
A dilation is a function because the scale factor is always greater than 1.
A dilation is not a function because a point on the pre-image could be mapped to more than one point on the image.
A dilation is not a function because the image is not congruent to the pre-image.
Answer:
Dilation : The meaning of Dilation is that by taking a fixed center and certain real number we can either enlarge an image or reduce it's size without actually changing it's shape. it totally depends on amount by which we are dilating if it is a real number greater than 1 the size of image increases otherwise shrinks means smaller in size.
The original image is called Pre-image and after dilation that changed image is called image.
So, we can say that Dilation is a function because for each different scale factor or different real number we get different images.
So, Out of all the four options given first looks completely true about Dilation.
i.e A dilation is a function because every point on the pre-image corresponds to exactly one point on the image.
A dilation is a function because every point on the pre-image corresponds to exactly one point on the image. This is the definition of a function in mathematics. The scale factor and the congruity of the image to the pre-image are irrelevant to the classification of dilation as a function.
Explanation:The correct statement is:
A dilation is a function because every point on the pre-image corresponds to exactly one point on the image
. In mathematics, dilation is a transformation that changes the size, but not the shape, of a figure. For a dilation to qualify as a function, each point in the pre-image must correspond to exactly one point in the image, without any point in the pre-image being mapped to more than one point in the image. This is the definition of a function: a relation from a set of inputs (the pre-image) to a set of possible outputs (the image) where each input is related to exactly one output. The scale factor and the congruity of the image to the pre-image have no bearing on whether a dilation is a function or not.
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THIS one u probably have to choose more than one
Replace [tex]a_{n}[/tex] with 27, solve for [tex]a_{n-1}[/tex], and see if the result is a whole number.
27 = 2a ⇒ [tex]\frac{27}{2}[/tex] = a not a whole number NO
27 = 2a + 1 ⇒ 26 = 2a ⇒ 13 = a 13 is a whole number YES
27 = 3a ⇒ 9 = a 9 is a whole number YES
27 = 3a + 6 ⇒ 21 = 3a ⇒ 7 = a 7 is a whole number YES
27 = 3a + 1 ⇒ 26 = 3a ⇒ [tex]\frac{26}{3}[/tex] = a not a whole number NO
Answer: B, C, D
A single person earns a gross biweekly salary of $840 and claims 5 exemptions. What is the person's net pay. a. It is the same as the gross pay. b. It is $11 more than the gross pay. c. It is $11 less than the gross pay. d. It is $13 less than the gross pay.
Answer:
D. It is $13 less than the gross pay.
Step-by-step explanation:
To find the net pay, you have to look at the table h
We are given that table.
Step 1: Biweekly gross salary is $840 and the number of claimed is 5.
Step 2: Look for claimed number to the corresponding wage $840. It is 13, which is rounded by blue circle in the given table.
Thank you.
Answer:
D. It is $13 less than the gross pay.
Step-by-step explanation:
To find the net pay, you have to look at the table h
We are given that table.
Step 1: Biweekly gross salary is $840 and the number of claimed is 5.
Step 2: Look for claimed number to the corresponding wage $840. It is 13, which is rounded by blue circle in the given table.
Thank you.
i copied the other dued lol
60 POINTS
Does the following table show a proportional relationship between the variables g and h?
No I don't believe so, a proportional relation ship would be h= g x 3. So I believe it would be g3=h9 g6=h18 g9=h27. So that when you divide h by 3 it will always equal g. I hope this helped and wasn't too confusing.
The relationship between these 2 g and h is that h=gxg but that is not really constant with it, I hope that helps
A music store sold 300cds and 100cd players. If each cd cost $12 and each cd player cost $35, what was the store total earnings
So with what we know we can set up two equations to solve for the CDs and the players.
$12(300) = total earnings for cds
= $3600 total cds sold
$35(100) = total earnings for cd players
=$35000
add both of the totals of the CDs and the CD players to get the total earnings
$3600+$3500 = $7100 gained in total from both products sold
The underwater Terror toller-coaster tide takes passengers up to a 123 feet above ground. It then quickly drops the riders 154 feet into a underwater passageway. Next, the coaster immediately takes everyone straight up again 187 feet before it drops 175 feet into the second underwater passageway. What is the elevation of the 2nd underwater passageway relative to the ground? Please show your work.
up (+) 123 187
down (-) -154 -175
(123 + 187) - (154 + 175)
= 310 - 329
= -19
Answer: 19 feet below ground
I have the picture of the equation.
find (f+g)(x)=
find (f-g)(x)=
find (f·g)(x)=
[tex]f(x)=\dfrac{5x+7}{7x-5},\ g(x)=\dfrac{8x}{7x-5}\\\\(f+g)(x)=f(x)+g(x)=\dfrac{5x+7}{7x-5}+\dfrac{8x}{7x-5}=\dfrac{5x+7+8x}{7x-5}=\dfrac{13x+7}{7x-5}\\\\(f-g)(x)=f(x)-g(x)=\dfrac{5x+7}{7x-5}-\dfrac{8x}{7x-5}=\dfrac{5x+7-8x}{7x-5}=\dfrac{-3x+7}{7x-5}\\\\(f\cdot g)(x)=f(x)\cdot g(x)=\dfrac{5x+7}{7x-5}\cdot\dfrac{8x}{7x-5}=\dfrac{(5x+7)(8x)}{(7x-5)(7x-5)}\\\\=\dfrac{40x^2+56x}{(7x)(7x)+(7x)(-5)+(-5)(7x)+(-5)(-5)}=\dfrac{40x^2+56x}{49x^2-70x+25}[/tex]
helppppppppppppppppppppp
6. Mike and his best friend Dan have the same birthday, but Mike is three years older than Dan. Let the variable x represent Mike's age and y represent Dan's age. Which graph represents the relationship between Dan's age and Mike's age?
also can anyone tell me all the answers for Solving Equations Unit Test please I really need the help.
Answer:
A linear graph will be plotted to show the relation between ages of Mike and Dan.
Step-by-step explanation:
As the age of Mike increase, the age of Dan will also increase. There is a relation of direct proportionality and a linear graph line will be plotted. When x=3, y=0, therefore the line will be at a distance of 3 x-intercept from origin.
Please try to answer quickly :) thanks
A and B are two events.
Let P(A)=0.5 , P(B)=0.25 , and P(A and B)=0.15 .
Which statement is true?
A and B are not independent events because P(A|B)≠P(A) .
A and B are not independent events because P(A|B)=P(A) and P(B|A)=P(B) .
A and B are independent events because P(A|B)=P(B) and P(B|A)=P(A) .
A and B are not independent events because P(A|B)=P(B) and P(B|A)=P(A) .
Answer:
A and B are not independent events because P(A|B)≠P(A)
is the correct answer.
Step-by-step explanation:
If A and B are independent then we must have
P(AB) = P(A) P(B) and also
P(A/B) = P(A)
We are given that
A and B are two events.
Let P(A)=0.5 , P(B)=0.25 , and P(A and B)=0.15 .
P(A/B) = P(AB)/P(B) = 0.15/0.5 = 0.3
i.e. P(A/B) is not equal P(A)
Similarly P(B/A) = P(AB)/P(A) = 0.15/0.25 = 0.6 not equal to P(B)
Hence A and B are not independent.
Answer:
Step-by-step explanation:
A and B are not independent events because P(A|B)≠P(A)
is the correct answer.
How is the number 123,789 written in words?
A group of 485 people take a canoe trip. They fill up all avalible canoes that each hold 3 people with 273 people. The rest of the group will ride in canoes
that each hold 2 people. How many canoes will the group need? Write equations with unknown to show your steps.
Answer:
They will need 197 canoes.
Step-by-step explanation:
The first step is to find the ''3-people canoes'' that they filled.
Given that 273 people filled a certain number ''a'' of canoes that each hold 3 people, we know that is we multiply the number of canoes ''a'' by the number of people that can each canoe hold, we will obtain the number of people who
will take the canoe trip in the ''3-people canoes''. We write :
[tex]3a=273[/tex] ⇒
[tex]a=\frac{273}{3}=91[/tex]
We find that [tex]a=91[/tex] canoes. This means that 91 ''3-people canoes'' were filled each one with 3 people in order to hold 273 people in total.
The second step is to find the remaining people that won't take the ''3-people canoes''. We do this by subtracting 273 people to the total 485 people.
[tex]485-273=212[/tex]
We know that 212 people will travel in the ''2-people canoes''. Using a similar reasoning and defining as ''b'' to the total number of ''2-people canoes'' we write :
[tex]2b=212\\b=\frac{212}{2}=106\\ b=106[/tex]
We find that [tex]b=106[/tex] canoes is the total number of ''2-people canoes'' that we need If we want them to be filled up with 212 people.
The total number of canoes that the group will need is the sum of ''3-people canoes'' and ''2-people canoes'' :
[tex]Total=a+b=91+106=197[/tex]
The group of 485 people will need 197 canoes.
Write the perimeter of the floor plan shown as an algebraic expression in x.
Answer:
Perimeter = 2x + 64
Step-by-step explanation:
Perimeter = Sum of the lengths of the borders
From the given figure, we need to find the missing length.
Missing length = 18 - 10 = 8
Another missing length = (x + 14) - (x + 8) = x + 14 - x - 8
= 14 -8
= 6
Now let's add all the sides.
Perimeter = x + 14 + 8 + 6 + 10 + x + 8 + 18
Now add all the x terms and constants
Perimeter = 2x + 64
Solve for x.
2x^2-4x=0
Hey there!!
Equation given :
2x² - 4x = 0
Taking the common terms
2x ( x - 2 ) = 0
Divide by 2x on both sides
x - 2 = 0
Adding 2 on both sides ...
x = 2
And another answer would be zero as the whole equation is zero,
Hence the answer : ( 0 , 2 )
Hope it helps@+!!
The value x for equation 2x² - 4x = 0 is 2.
Given equation:
2x² - 4x = 0
Add 4x on both side,
2x² = 4x
Divide x on both side
2x = 4
Divide 2 on both side,
x = 2.
Therefore, the value x for equation 2x² - 4x = 0 is 2.
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Evaluate:
6!
A.
60
B.
120
C.
360
D.
720
[tex]n!=1\cdot2\cdot3\cdot...\cdot n\\\\6!=1\cdot2\cdot3\cdot4\cdot5\cdot6=720\\\\Answer:\ \boxed{D.\ 720}[/tex]
Answer: D.
720
Step-by-step explanation:
We know that the value of n factorial or n! is given by :-
[tex]n!=n\times(n-1)\times(n-2)\times(n-3)\times...........................\times1[/tex]
We are given to find the value of 6! (or 6 factorial )
Using the above formula , the value of 6! is given by :-
[tex]6!=6\times(6-1)\times(6-2)\times(6-3)\times\times(6-4)\times(6-5)\\\\\Rightarrow\ 6!=6\times5\times4\times3\times2\times1\\\\\Rightarrow\ 6!=720[/tex]
Therefore , the value of 6! = 720
How to know what to do next in a geometry two column proof?
To do a two-column proof, you must know the definitions of the terms that are being used. Also, you must know the postulates and theorems you have learned so far. You look at the given information, and using the definitions, postulates, and theorems, you reason in your mind how to go from the given to the conclusion, step by step. You write each step and the accompanying reason that allows you to conclude each step.
What is the midpoint of ?
point M
point N
point P
point Q
Answer:
the answer is point N
Step-by-step explanation:
i dont have a graph to explain
The midpoint of a line segment is calculated using the formula Midpoint = ((x1 + x2)/2 , (y1 + y2)/2), which finds the average of the x-coordinates and y-coordinates of the two points. Unfortunately, without specific points, we can't provide a concrete midpoint.
Explanation:Unfortunately, your question is slightly unclear as we need more detail to accurately determine the midpoint of the segment. Generally, if you want to find the midpoint of a segment, you need two defined points. Knowing these two points, you can calculate the midpoint using the formula: Midpoint = ((x1 + x2)/2 , (y1 + y2)/2). This formula calculates the average of the x-coordinates and y-coordinates of the two points, which gives you the coordinates of the midpoint.
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The ratio of cats to dogs seen by a veterinarian on one day is 2 to 5. If the vet saw 40 dogs in one day how many cats did he see
Answer:
He sees 16 cats that day
Step-by-step explanation:
If the veterinarian sees 5 dogs a day then he also sees 2 cats.
If he sees 40 dogs a day then,
⇒[tex]\frac{2}{5} *40[/tex]
=[tex]16[/tex] Cats
He sees 16 cats that day.
The correct option is C.
Approximately 29 dogs were seen by the vet in one day.
To solve this problem, we first need to find the fraction of dogs among the total animals seen by the vet.
Given that the ratio of cats to dogs is 2 to 5, the total parts in this ratio is 2 + 5 = 7.
Now, to find the fraction representing dogs, we divide the number of parts representing dogs (5) by the total parts (7). This gives us 5/7.
Next, to find out how many of the 40 animals were dogs, we multiply the total number of animals seen (40) by the fraction representing dogs:
40 animals × (5/7) = (40 × 5) / 7 = 200/7 ≈ 28.57
Since we're looking for an approximation, we round this to the nearest whole number, which is 29.
So, approximately 29 of the animals seen were dogs, which corresponds to option C.
The complete question is here:
The ratio of cats to dogs seen by a vet in a day is about 2 to 5. If a vet saw 40 animals in one day, about how many were dogs?
A. 5
B. 12
C. 29
D. 40
Which statement is false?
A. The number zero is a rational number.
B. Some irrational numbers are also rational numbers.
C. Every irrational number is a real number.
D. Every integer is a rational number.
Need answers ASAP, Thanks!
The false statement is B: 'Some irrational numbers are also rational numbers.' This is incorrect because a number cannot be both rational and irrational by definition.
The false statement among the options provided is option B: Some irrational numbers are also rational numbers. This is false because by definition, irrational numbers and rational numbers are distinct sets of numbers with no overlap. A rational number can be written as a ratio of two integers, which means it can be expressed as a fraction. On the other hand, an irrational number cannot be written as a ratio of integers. Thus, a number cannot be both rational and irrational at the same time.
To clarify the other options, option A is true because zero can be represented as the ratio 0/1, making it a rational number. Option C is true because irrational numbers such as π (pi) and √2 (the square root of 2) are indeed part of the set of real numbers. Option D is true because all integers can be expressed as a ratio where the denominator is 1, making every integer a rational number.
Which of the following is the simplified form of the expression -x(x - y) + 4xy - x2?
A.2x2 - 3xy
B.-2x2 + 3xy
C.-2x2 + 5xy
D.2x2- 5xy
Find the sum of the polynomials (5y^3+2y^2-7y) + (12y^3-4y^2+8)
[tex](5y^3+2y^2-7y) + (12y^3-4y^2+8)\\\\=5y^3+2y^2-7y+12y^3-4y^2+8\\\\=(5y^3+12y^3)+(2y^2-4y^2)+(-7y)+(8)\\\\=17y^3-2y^2-7y+8[/tex]
Deon plans to ride a 15-mi bicycle trail. If his average is 20mi/h, with equation can he use to find the time T, in hours, for the ride ?
Distance traveled by Deon to ride a bicycle trail = 15 mile
Average speed of Deon to ride a bicycle trail = 20 mi/hour
Let 'T' be the time taken to ride the bicycle trail.
We will use distance speed formula to write the equation to find the time 'T' in hours, for the ride.
Distance =[tex]\frac{Speed}{time}[/tex]
[tex]15 = \frac{20}{T}[/tex]
So, [tex]T = \frac{20}{15}[/tex]
This equation will be used to find the time 'T' in hours for the ride.
A car drives at a speed of 90km/h for 2 hours and 20 mins how far does the car travel
Final answer:
The car travels approximately 210 kilometers in 2 hours and 20 minutes by multiplying its speed of 90km/h by the time duration converted to hours (2.333 hours).
Explanation:
The student's question involves calculating the distance a car travels at a constant speed over a given period of time. In this case, the car drives at a speed of 90km/h for 2 hours and 20 mins. To find the distance, you can use the formula: distance = speed × time. First, convert 2 hours and 20 mins into hours, which is 2 hours + 20/60 hours = 2.333 hours.
Next, multiply the speed by the time to get the distance:
Distance = 90km/h × 2.333 hours = 209.97 km
So, the car travels approximately 210 kilometers in 2 hours and 20 minutes.
find the 26 term is a1=30 and d =-2
Answer:
[tex]a_{26}=-20[/tex]
Step-by-step explanation:
The formula of a nth term of an arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]
We have:
[tex]a_1=30,\ d=-2,\ n=26[/tex]
Substitute:
[tex]a_{26}=30+(26-1)(-2)=30+(25)(-2)=30-50=-20[/tex]
30 points + Brainliest
Your answer is A. If we find the slope of the line and draw it out farther, we can see that the points 4,7,10, and 13 would fall on that line.
Answer:
The answer is A. Hope I helped ^-^
Step-by-step explanation:
The temperature changed from -7 degrees f at 6:00 am to 7 degrees f at noon write an expression. How much did the temperature increase?
I just need it to be written in an expression and then simplified
The temperature increase can be represented by the expression 7°F + 7°F, which simplifies to 14°F.
Explanation:The expression to represent the temperature increase from -7 degrees Fahrenheit at 6:00 am to 7 degrees Fahrenheit at noon is as follows:
Temperature increase = Final temperature - Initial temperature
Substituting the values, we get:
Temperature increase = 7°F - (-7°F)
Simplifying, we have:
Temperature increase = 7°F + 7°F
Temperature increase = 14°F
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Check all of the polynomial functions that have 2 as a root.
A. h(m) = 8 – m^3
B. f(g) = g^3 – 2g^2 + g
C. f(a) = a^3 – 4a^2 + a + 6
D. f(x) = x^3 – x^2 – 4
A,C,D those were the answers i put and they were correct.
Answer:
A. h(m) = 27 – m3
C. f(a) = a3 – 4a2 + a + 6
D. f(x) = 2x3 – 5x2 – 9
Step-by-step explanation:
did review on edg2020