Answer: x = -2
Step-by-step explanation:
4x=0.5(2x−12)
Use the distributive property to multiply 0.5 by 2x−12.
4x=x−6
Subtract x from both sides.
4x−x=−6
Combine 4x and −x to get 3x.
3x=−6
Divide both sides by 3.
x= 3−6
Divide −6 by 3 to get -2.
M(5, 7) is the midpoint of PS The coordinates of S are (6, 9). What are the coordinates of p2
The required coordinate of point p is (4,6) of line segment PS.
Given that
M(5, 7) is the midpoint of PS The coordinates of S are (6, 9).
To determine the coordinates of p.
Here,
Let the coordinate of P be (h, k)
Now, the coordinates of the midpoint is given by,
x = [x₁ + x₂] / 2 ; y = [y₁ + y₂] / 2
now, putting x = 5, x₁ = 6, x₂ = h; y = 7, y₁ = 9 y₂ = k
5 = 6 + h / 2 ; 7 = 9 + k / 2
10 - 6 = h ; 14 - 9 = k
h = 4 ; k = 5
Thus, the required coordinate of point p is (4,6).
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Which are the first five terms of a geometric sequence in which the second term is 6 and the fourth
term is 54?
3, 6, 27, 54, 108
3, 6, 54, 486, 4,374
-18, 6, 30, 54, 78
2, 6, 18, 54, 162
The first five terms of a geometric sequence in which the second term is 6 and fourth term is 54 are 2, 6, 18, 54, 162. Thus, the correct option is option D.
A Geometric progression may be defined as a series of terms in which the ratio between each succeeding term and the preceding term of the series is constant.
It is given that the second term of the series is 6 and the fourth term is 54.
The first five terms of geometric sequence are given by a, ar, ar², ar³ and ar⁴.
Thus, ar = 6 ......(1)
ar³ = 54 ......(2)
Divide equation (2) by (1)
ar³/ar = 54/6
r² = 9
=> r = 3
Putting value of r in equation (1)
ar = 6
=> a×3 = 6
=>a = 2
Now, substituting the values of a and r the terms of Geometric progression are given by:
a = 2, ar = 6, ar² = 18, ar³ = 54 and ar⁴ = 162.
Thus, the first five terms of Geometric sequence are given by 2, 6, 18, 54, 162.
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write and solve an equation to find the difference between the location of point a and point b on the ruler.
Using distance formula, distance between two points is √61 unit
Let's us consider an example first -
What is the the distance between A and B
Let A = (3,2) and B (9,7)
Given A (3,2) and B( 9,7) are the two points on a plane
We have find to distance between A and B
Put the distance formula in two points as we know -
Distance= d√(x^2-x^1)^2 + (y^2-y^1) ^2
Here X1= 3
X2 =9
Y1=2
Y2=7
Thus putting all these value x and y formula
d= √(9-3)^2+(7-2)^2
d=√(6^2+5^2)
d=√(36+25)
d=√61 unit
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Please Help me it is a major grade due today
Answer:
3x² + x
Step-by-step explanation:
collect the like terms first:
2x² + x² - 4x + 5x + 1 - 1
3x² + x
Answer:
the last answer. 3x to the second power + x
Step-by-step explanation:
The sum of three lengths of a fence ranges from 45 to 60 inches. Two side lengths are 9 and 18 inches. If the length of the third side is x inches, write
and solve a compound inequality to show the possible lengths of the third side.
09≤x≤18
O 18 ≤x≤ 33
036 ≤x≤ 42
045 ≤x≤ 60
If the sum of three lengths of a fence ranges from 45 to 60 inches and two side lengths are 9 and 18 inches, If the length of the third side is x inches, then the compound inequality to show the possible length of the third side is 18≤x≤33
Given,
The range of sum of three lengths = 45 to 60 inches
Length of other two side = 9 and 18 inches
Length of third side = x
Sum of three lengths = 9+18+x
= 27+x
The range of sum of three lengths is 45 to 60
then,
45≤27+x≤60
Subtract 27 from each part
18≤x≤33
Hence, if the sum of three lengths of a fence ranges from 45 to 60 inches and two side lengths are 9 and 18 inches, If the length of the third side is x inches, then the compound inequality to show the possible length of the third side is 18≤x≤33
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Answer:
B
Step-by-step explanation:
This is because 18 is less than or equal to x which is less than or equal to 33. Your welcome
−2(−x−3)−4x−1= 13 solve for x
2x+6-4x-1=13
2x+5=13
2x=8
x=4
Which of the following is the number form of thirty-eight and one hundred seven thousandths?
A.38.170
B.38.017
C.38.107
D.38.071
Number Form
C.) 38.107
___________________________________________________
The solution is simple. "Thirty-eight" is just 38, remaining on the left side of the decimal. Meanwhile, "one hundred seven thousandths" is 107, however on the right side of the decimal. Now you know this, put the two parts together and you have your number form; 38.107, aka. Option C.
___________________________________________________
Hope this helps! If so, lmk! Thanks and good luck!
A cafeteria is 6 squared ft wide and 7 squared ft long apply the laws of exponents to write two equivalent expressions for the area of the cafeteria
The two equivalent expressions for the area of the cafeteria are:
a. x = 6² + 7² feet
b. 36 + 49 = x feet.
Given the length of the cafeteria is 7² ft and
the width of the cafeteria is 6² ft.
Area = length × width
let the area be 'x'.
x = 6² × 7²
According to the law of exponents.
x = 36 × 49
x = 1764 ft
hence we get the area as 1764 ft of the cafeteria.
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How many unique trapezoids can be drawn with base angles that each measure 60° and sides that measure 4 cm, 4 cm, 8 cm, and 12 cm?
The number of unique trapezoids that can be drawn with base angles and side measures is 1
How to determine the number of unique trapezoids?The given parameters are
Base angle = 60 degrees
Side lengths = 4 cm, 4 cm, 8 cm, and 12 cm
From the question, we understand that the given angle is the base angle
Since the base angles are equal, then the trapezoids is an isosceles trapezoid
This also means that the nonparallel sides are equal i.e. 4cm each
While the parallel sides are not i.e. 8cm and 12 cm
Hence, the number of unique trapezoids that can be drawn with base angles and side measures is 1
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Analia wants to know which school has the higher SAT average relative to resources invested per student
A SAT average divided by number of sports medals won
B SAT average divided by number of students
C SAT average divided Budget per student
D SAT average divided by teachers per student
Anna is the middle of three siblings whose ages are consecutive integers. If the sum of their ages is 8181, find Anna's age.
Answer:
27
Step-by-step explanation:
Say the youngest sibling is a. Anna would be a+1, and the oldest would be a+2. If the sum of all of them are 81, then 3a+3 = 81. minus three on both sides, and you get 78. So 3a = 78/3 = 26. if the youngest is 26, then Anna will be a + 1 so 27.
The age of Anna where she is the middle of three siblings is 27 years.
Given data:
Let's represent Anna's age as "x." Since Anna is the middle sibling, the ages of her siblings would be x - 1 and x + 1, since they are consecutive integers.
According to the information given, the sum of their ages is 8181:
x + (x - 1) + (x + 1) = 81
Now, combine like terms:
3x = 81
Divide both sides by 3:
On simplifying the equation:
x = 81/3
x = 27
Hence, Anna's age is 27 years.
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The complete question is attached below:
Anna is the middle of three siblings whose ages are consecutive integers. If the sum of their ages is 81, find Anna's age.
in a famous experiment carried out in 1882, michelson and newcomb obtained 66 observations on the time it took for light to travel between two locations in washington, d.c. a few of the measurements (coded in a certain manner) were 31, 23, 32, 36, −2, 26, 27, and 31. (a) why are these measurements not identical? (select all that apply.)
These measurements are not identical due to confounding;
When the effects of two or more explanatory variables on a response variable cannot be distinguished from one another, confounding occurs in an experiment.
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your current wardrobe consists of eleven different items: three pairs of shoes, two pairs of pants, and six different shirts. your mom offered to buy you a new shirt or a new pair of shoes. which item (shoes or shirt) should your mom buy for you to maximize your total number of outfits (shoesshirt-pant)?
A pair of shoes gives us 48 different outfits.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." from Wolfram MathWorld: linearWe will employ the basic counting principle, which states that if one task can be completed in method A and another in way B, then both tasks may be completed in way A*B.
If mom buys 1 shirt, then total shirts(A) = 6+1 =7, total pants(B) = 2 and total shoes (C) = 3
By basic counting principle, number of outfits = A*B*C = 7*2*3 = 42 outfits possible
and
If mom buys 1 pair of shoes, then total shirts(A) = 6, total pants(B) = 2 and total shoes (C) = 3+1 = 4
By basic counting principle, number of outfits = A*B*C = 6*2*4 = 48 outfits possible
hence, buying a pair of shoes gives us 48 different outfits.
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2 and 8 supplementary or congruent
Answer: where's the pic?
A horses mane grows 1. 5 inches in 1 month. Lauras hair grows 0. 25 inch in 1 week
determine in the situation represents a proportional relationship
1:5:1 or 3:2 is the proportional relationship.
What is the proportional relationship?In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant. Two sequences are inversely proportional if corresponding elements have a constant product, also called the coefficient of proportionality.
Given Data
If considering that a month has 4 weeks approx, then Laura's hair grows( 0.25 inches×4)= 1 inch in a month.
Whereas the horse's mane grows 1.5 inches in a month.
Thus the proportional relation or ratio between growth of Horse's mane and Laura's hair for the same amount of time period is 1.5:1 or 3:2
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Important Please Help!!!!!!
Which is equivalent to √3+√12?
A. √15
B. 3√6
C. 2√3
D. 3√3
E. 5√3
Answer:
d is the correct answer to your question
Answer:
3√3
Step-by-step explanation:
√3 +√12
we can write 12 as 3 X 4
√3 + √(3+4)
√3 + √3 √4
√4 = 2
√3 + 2√3
= 3√3
In a class of 20 students, 5 are left handed. What percentage of students are right handed?
Answer: 75%
Step-by-step explanation:
20-5=15 right handed students
[tex]\displaystyle\\\frac{15}{20}*100\% =\\\\\frac{15*20*5}{20} \%=\\\\15*5\%=\\\\75\%\ -\ percentage\ of\ students\ are\ right\ handed[/tex]
A handyman company serves customers from two cities 60 miles apart, Jonesville and Bellevue. The company would like to position a new of
between the two cities using weighted averages based on the typical number of calls received from each city. If Jonesville has a weight of 3 a
Bellevue has a weight of 5, how far from Bellevue should the office be located?
miles
Using the weighted mean, it is found that the office should be located 13.85 miles from Bellevue.
What is the weighted mean?The weighted mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.
For this problem, the observations are given as follows:
Bellevue, at position 0, with a weight of 5.Jonesville, at position 60, with a weight of 3.These observations are the positions of the cities, considering that they are 60 miles apart, and their weights as given in the problem.
The weighted mean between these positions is found as follows:
M = (0 x 5 + 60 x 3)/(5 + 8) = 13.85.
The meaning of the weighted mean is that:
The office should be located 13.85 miles from Bellevue.
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What is the fractional equivalent of 34%?
A) 17/200
B) 35/10
C) 17/50
D) 35/1
What is the equation of the line that is parallel to the line y =
Oy=-x+3
O y=-x+7
Oy= 3x - 13
Oy= 3x +5
-x+4 and passes through the point (6, 5)?
Answer:
Step-by-step explanation:
x=4 is a vertical line.
horizontal line through (-6,5): y=5
y=6 is a horizontal line.
vertical line through (-6,5): x=-6
The equation of line parallel to y = -( 1/3 )x + 4 and passing through the point P ( 6 , 5 ) is y = -( 1/3 )x + 7
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = -( 1/3 )x + 4
Let the first point be P ( 6 , 5 )
Slope m = -1/3
The parallel lines have the same slope , so the point-slope form of the equation of a line to find the equation of the line passing through P(6,5) with slope -1/3 is
y - 5 = ( -1/3 ) ( x - 6 )
Adding 5 on both sides , we get
y = ( -1/3 )x + 2 + 5
y = -( 1/3 )x + 7
Hence , the equation of line is y = -( 1/3 )x + 7
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The complete question is attached below :
What is the equation of the line that is parallel to the line y = -1/3x + 4 and passes through the point (6, 5)?
A) y = -1/3x + 3
B) y= -1/3x + 7
C) y= 3x - 13
D) y= 3x + 5
Can u help me with this math plsss I will mark brainliest
Answer:
there.....................
Answer:
I4, C20, H6, O13, M3, V10, P23, G8, K19, H21, P16
What is the slope of the line represented by this equation?
-3X+ 8y = 12
The slope of the equation - 3 x+ 8 y = 12 is 0.375.
We are given an equation of the line:
- 3 x+ 8 y = 12
We need to find the slope of the equation.
x intercept:
- 3 x = 12
x = -4
Point 1 = ( - 4 , 0 )
y intercept:
8 y = 12
y = 1.5
Point 2 = ( 0 , 1.5 )
Slope = (y₂ - y₁) / (x₂ - x₁)
Substituting the values, we get that:
m = ( 1.5 - 0 ) / ( 0 - [-4])
m = 1.5 / 4
m = 0.375
Therefore, we get that, the slope of the equation - 3 x+ 8 y = 12 is 0.375.
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Who knows what a black widow spider can do
The 100 m world record was completed at an average speed of 37.6 km/h. Work out this speed in metres per second (m/s). Give your answer correct to one decimal place (1 d.p).
The average speed in meters per second is 10.4 m/s.
What is the average speed in meters per second?
Average speed is the total distance travelled per time. Average speed can be determined by dividing total distance by
Average speed = total distance / total time
The first step is to convert kilometer to meter: 1000 meter = 1 kilometer
The second step is to convert hours to seconds:
1 hour = 60 minutes
1 minute = 60 seconds
1 hour = 60 x 60 seconds
1 hour = 3,600 seconds
Multiply the average speed by 1000 meters and divide by 3,600 seconds.
37.6 x (1,000 / 3,600) = 10.44 m / s
10.4 m/s (1 d.p)
In order to round off to one decimal place, if the hundredth figure is less than 5, there is no change in the tenth digit. Digits that are less than the tenth digit are removed.
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Hector surveyed 20 students in his school and asked them whether they favor or oppose a new school dress code. He found that 5 students are in favor of a new school dress code. Based on these results, Hector wants to determine how many of the 200 students in the school would favor a new dress code.
50 students of the 200 students in the school would favor a new dress code.
We will use simple cross multiplication here
For first case
no. of students surveyed = 20
no. of student agreed for a new dress code = 5
This gives us 5/20
For second case
no. of students surveyed = 200
no. of student agreed for a new dress code = x
This gives us x/200
Lets us cross multiply
5/20 = x/200
20x = 200×5
x = (200×5)/20
x = 50
What is cross multiplication?Given an equation between two fractions or rational expressions in mathematics, particularly in primary arithmetic and elementary algebra, one might cross-multiply the equation to make it simpler or get the value of a variable.
The technique can be used to remember which things to multiply together by drawing lines that resemble the outline of a heart. It is also sometimes called as "cross your heart" technique.
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A lab technician is dividing a cell that has a diameter of 4.32×10−4 millimeters. Each of the new cells has a diameter measuring exactly one half of the diameter of the original cell. Which is the diameter of a new cell?
Answer:
I'm assuming that the number is supposed to be 4.32x10‾⁴, so if the new cell has half the diameter, then it's diameter would be 2.16x10‾⁴
Josh wanted to buy a new shirt for a school dance. At the store, he couldn't decide between a purple plaid shirt and a scarlet striped shirt. Since the shirts were on sale for $19.95 each, Josh decided to buy them both. He saved a total of $9.10. If he saved the same amount on each shirt, what was the original price of each one?
Answer:
$29.05
Step-by-step explanation:
First, you have to multiply $19.95 by 2 since he bought 2 shirts that were the same price. 19.95 times 2 is a total of $39.90. It says that he saved $9.10 on both shirts so, in order to see the original price of the shirts, you would have to multiply $9.10 times 2 which is $18.20. Now you need to add 39.90 to 18.20 which is $58.10. You just need to divide that by 2 which will give you $29.05. Each shirt's orignial price was $29.05
Hope that helps you out :D
Work out the value of each expressions.
a) 5(x³ - x) + 5x² /3 - 12x when x=3
b) 3y+16+ (y/2) -20/y when y=4
a) Simplification of the algebraic expression 5(x³ - x) + 5x²/3 - 12x when x = 3 is; 99
b) Simplification of the algebraic expression 3y + 16 + (y/2) - (20/y) is; 25
How to solve Algebraic Fractions?
a) We are given the algebraic expression;
5(x³ - x) + 5x²/3 - 12x
We want to simplify this when x = 3. Thus, we plug in 3 for x to get;
5(3³ - 3) + 5(3²)/3 - 12(3)
= 5(27 - 3) + (5 * 3) - 36
= 120 + 15 - 36
= 99
b) We are given the algebraic expression;
3y + 16 + (y/2) - (20/y)
We want to simplify this when y = 4. Thus, we plug in 4 for y to get;
3(4) + 16 + (4/2) - (20/4)
= 12 + 16 + 2 - 5
= 25
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Find the solution to the equation: 42-(3c+4)=2(c+4)+c
Answer:
5
Step-by-step explanation:
42-(3c+4)=2(c+4)+c
42-3c-4=2c+8+c
42-4-3c=3c+8
38-3c=3c+8
38-3c-3c=8
38-6c=8
6c=38-8
6c=30
c=30/6
c=5