The correct property of equality to solve each equation. 3 + x = 27 and x + 6 = 5 is subtraction property of equality.
The property of equality defines an equivalence relationship between two variables. The subtraction property of equality refers to the property that two sides of the equation remain equal when the same number is subtracted from both sides of an equation. According to the subtraction property of equality, if two quantities a and b are equal, and if c is subtracted from both a and b, then the difference of a and c and the difference of b and c are equal. Hence, if a = b, a – c = b – c. Using the subtraction property of equality:
3 + x = 27
3 + x -3 = 27 - 3
x = 24
Similarly,
x + 6 – 6 = 5 – 6
x = -1
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Answer:
3+x=27
✔ subtraction property of equality with 3
x/6 = 5
✔ multiplication property of equality with 6
Step-by-step explanation:
Find the values of the variables. Then find the side length of the square 
Answer:
x = 4y = 8side length = 4Step-by-step explanation:
You have a square with sides labeled (y-4), (3x-8), (2y-12), and you want to know the values of the variables as well as the side length.
SetupAll sides of the square are the same length. Equating two different y-expressions, we get ...
y -4 = 2y -12
We can use the solution to that to find x:
y -4 = 3x -8
SolutionAdding 12-y to the first of these equations gives us ...
8 = y
Using this value in the second equation, we have ...
8 -4 = 3x -8
12 = 3x . . . . . . add 8
4 = x . . . . . . . . divide by 3
The side length is ...
y -4 = 8 -4 = 4
The values of the variables are x = 4, y = 8, and the side length of the square is 4.
A textbook store sold a combined total of 382 chemistry and biology textbooks in a week. The number of biology textbooks sold was 58
less than the number of chemistry textbooks sold. How many textbooks of each type were sold?
Number of chemistry textbooks sold:
Number of biology textbooks sold:
Answer:
chemistry books is 220 and number of biology books is 220
Step-by-step explanation:
let y be biology books
let x be the number of chemistry books
x-58=y
equation 1 ) x+y=382
sub in x-58 for y
2. x+(x-58)=382
3. 2x-58= 382
4. 2x=382-58
5. 2x = 324
6. x/2 =324/2
7. x = 162
for x=y+58
y=162
x 220
220+162=382
y+x=382
Convert this Slope Intercept Form equation into Standard Form. y=2x-12
Answer: -2x+y=-12
Step-by-step explanation:
After what I did this is what i got. Can't really explain it
Hope this helps :)
Jace left his house at time zero and drove to the store, which is 2 blocks away, at a speed of 1 block per minute. Then he stopped and went into the store for 6 minutes. From there, he drove in the same direction at a speed of 3 blocks per minute until he got to the bank, which is 6 blocks away from the store. He stopped at the bank for 7 minutes. Then he drove home at a speed of 2 blocks every minute. Make a graph of showing the number of blocks away from home that Jace is xx minutes after he leaves his house, until he gets back home.
The total time it took Jace to out home and return home is 21 minutes and the graph represents that the total distance was 8 blocks.
What is a graph?In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty). Charts and graphs come in a variety of styles. Line graphs, bar graphs and histograms, pie charts, and Cartesian graphs are likely the four most popular types. They serve quite diverse purposes and are best suited for very different uses.So, the total number of minutes Jace takes to get back home after going out:
From Home to store = 2 minutes (1 blocks/min) + 6 minute (stop)From store to bank = 2 minutes (3 blocks/min) + 7 minutes (stop)From bank to home = 4 minutes (2 blocks/min)Total minutes:
2 + 6 + 2 + 7 + 4 = 21 min(Refer to the graph attached below)
The graph represents that Jace travels a total of 8 blocksTherefore, the total time it took Jace to out of home and return home is 21 minutes and the graph represents that the total distance was 8 blocks.
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On a math test student, Jake, has to identify all the coefficients and constants of the expression 9b+7+n. Jake says that 9 is a coefficient and 7 is a constant. Identify all the coefficients and constants of the expression. What error might Jake have made?
The coefficient(s) of the expression is/are _.
Answer:
The coefficient is 9 in 9b.
Step-by-step explanation:
A coefficient is a number before a variable.
Examples: 9 in 9b, 5 in 5y, 3 in 3x.
Practically anything before a variable is declared a coefficient.
Pls vote brainliest if this was helpful!
It helps a lot :)
Hi if someone can help me that would be great
The diagrams are shown in the solution.
What is a rectangle?A rectangle is a quadrilateral with all four interior angles 90°.
(1) The rectangle diagram of 1/2 × 5/6 can be drawn by converting the fractions into integers.
The dimension can be written as:
1/2 : 5/6
Multiply the ratio by 6:
3 : 5
Hence, the rectangle of 1/2 × 5/6 is proportional to 3×5.
The diagram is shown.
Similarly, the diagrams of other rectangles are shown.
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(Factoring Algebraic Expressions MC) Factor −4x2 + 12x. 4x(−x + 3) −4x(x + 3) x(4x + 12) 4(−x2 + 12x)
The factorization of given polynomial is 4x(-x+3). Therefore, option A is the correct answer.
The given algebraic expression is -4x²+12x.
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The factorization of the given polynomial is
-4x²+12x
= 4x(-x+3)
The factorization of given polynomial is 4x(-x+3). Therefore, option A is the correct answer.
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researchers want to decrease the margin of error by adjusting the confidence level. which confidence interval will have the smallest margin of error (moe)?
One-sided confidence interval which have the smallest margin of error.
Given that;
Researchers want to decrease the margin of error by adjusting the confidence level.
You cannot be completely certain of the true value of a parameter, such as the mean, if your confidence interval is too broad. However, there are a number of methods you may do to narrow a confidence interval and improve the accuracy of your estimate. The following characteristics have an impact on the confidence interval's width.
one-sided confidence interval:
The margin of error is lower for a one-sided confidence interval than a two-sided confidence interval. A one-sided interval, however, merely shows whether a parameter is larger or less than a cut-off number. A one-sided interval does not reveal anything regarding the parameter's value when viewed from the other direction. Therefore, only use a one-sided confidence interval to boost an estimate's precision when you are concerned that it will either be higher or lower than a cut-off value, but not both.
Hence, we use one-sided confidence interval which have the smallest margin of error.
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a company wants to study the effectiveness of a new pain relief medicine. they recruit 100100100 volunteers with chronic pain. each subject takes the new pain relief medicine for a 222-week period, and a placebo for another 222-week period. subjects don't know which pill is the actual medicine, and the order of the pills is randomly assigned for each subject. researchers will measure the difference in the overall pain level for each subject. what type of experiment design is this?
Completely random design is used in this experiment.
In the given question,
A business wants to investigate the efficacy of a novel painkiller.
100 participants who suffer from chronic discomfort are enlisted.
Each participant takes the brand-new painkiller for two weeks before switching to a placebo for an additional two weeks.
The order of the tablets is chosen at random for each participant, and the subjects are unaware of which pill contains the actual medication.
Each subject's variance in total pain will be measured by researchers.
We have to check what type of experiment design is this.
As we can see in the question that they recruit 100 volunteers with chronic pain and each subject they use new pain relief medicine for a 2-week period and a placebo for another 2-week period.
They assign each subject randomly.
As we know that in a completely random design, treatments are randomly assigned to sampling material. The usual method for doing this is to make a list of the treatments and give each one a random number.
So we can see that completely random design is used in this experiment.
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The image of ΔABC after a reflection across Line E G is ΔA'B'C'.
2 triangles are shown. Line E G is the line of reflection. Line segment D D prime has a midpoint at point F. Line segment C C prime has a midpoint at point G. Points B and B prime share a point. Angle C G F is a right angle.
Which triangle must be a right triangle and why?
ΔBGC is right because Line EG is perpendicular-to CC'.
What is Reflection?A reflection image or reflection point is the mirror image of a figure in the axis or plane of reflection.
Each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the other side of the line. This transformation is known as a reflection over line. The size and form of the image in a reflection are identical to those of the pre-image.
Given:
On the line of reflection will be the midpoints of the segments connecting a triangle vertex with its reflected image. The segment will be parallel to the reflection's line.
A triangle will be considered correct in this situation if it has a leg that is a part of the segment connecting the reflected points and a leg that is on the line of reflection. Such a triangle is the BGC.
Hence, BGC is right triangle.
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Answer: D
Step-by-step explanation: Trust
the annual salaries of workers in a large manufacturing factory are normally distributed with a mean of rs. 48,000 and a standard deviation of rs. 1500. find the probability of workers who earn between rs. 35,000 and rs. 52,000. a. 0.42
The probability of workers who earn between rs. 35,000 and rs. 52,000 is 99.62 %.
What is defined as the normal distribution?A data set with a normal distribution has the majority of its values clustered in the middle of the distribution and the remaining values tapering off symmetrical toward either end.
For the given question;
z = (x - μ)/σ
In which,
x = sample mean
μ = mean (48,000)
σ = standard deviation (1500)
x = 35,000 and x = 52,000
For x = 35,000.
z = (35,000 - 48,000)/1500
z = -8.66
Check the p value from table
p(z = -8.66) = 0
For x = 52,000
z = (52,000 - 48,000)/1500
z = 2.66
p(z = 2.66) = 0.99617
P(35,000 < x < 52,000) = 0.99617 - 0
P(35,000 < x < 52,000) = 0.99617
Thus, the probability of workers who earn between rs. 35,000 and rs. 52,000 is 99.62 %.
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Write an equation of a line that passes through (-1,2) and is parallel to a line with x-intercept (3,0) and y-intercept (0,1).
The Equation of line is y= -1/3x + 5/3
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
x-intercept = (3,0) and y-intercept = (0,1).
slope, m= 0-1/ 3-0= -1/3
so, The slope-intercept form of the equation of a line is
y= mx + b
y= -1/3x +b
Now, the passes through (-1, 2) we get
2= -1/3(-1) + b
2- 1/3= b
b= 5/3
So, the Equation of line is y= -1/3x + 5/3
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Which number is a multiple of 4?
A.) 6
B.) 9
C.) 15
D.) 12
Answer:
D: 12
Step-by-step explanation:
multiples of 4: 4,8,12,16,20
12 is the only number that can be divided by 4 on the list
Hopes this helps please mark brainliest
Answer:
D. 12
Step-by-step explanation:
12 is a multiple of 4 because 4 goes into 12 (evenly, with no remainder).
That's what being a multiple means.
All the "answers" to 4 times table questions are multiples of 4. Here they are:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48...
Can't actually list them all because the list goes on forever.
(b) Write down the value of 12⁰
(c) Write down the value of 3-²
Answer:
b) 1 c) 0.1Step-by-step explanation:
b) The value of 12⁰ will be?
→ 12⁰ = ?
→ 12⁰ = 1
Hence, the solution is 1.
c) The value of (3)^(-2) will be?
→ (3)^(-2) = ?
→ (3)^(-2) = 0.1
Hence, the solution is 0.1.
What is the perimeter of a pentagon ABCDE with given vertices at A(4, -2), B(4, 10), C(7, 10), D(15, 4), E(7, -2)
Answer:
38 units
Step-by-step explanation:
You want the perimeter of pentagon ABCDE with vertices at A(4, -2), B(4, 10), C(7, 10), D(15, 4), E(7, -2).
PerimeterThe perimeter of a plane figure is the sum of the lengths of its sides.
Vertical, Horizontal sidesBy counting grid squares, or subtracting coordinates, you can find the lengths of the vertical and horizontal segments easily:
AB = 12, BC = 3, EA = 3
Diagonal sidesThe lengths of the diagonal segments can be found using the distance formula or your knowledge of Pythagorean triples. Counting grid squares (or subtracting coordinates), you see that each diagonal side has a vertical distance of 6 and a horizontal distance of 8. These correspond to twice the lengths of the sides in a 3-4-5 triangle, so you know the diagonal length is twice the hypotenuse: 2·5 = 10.
The Pythagorean theorem, or the distance formula, will tell you the same thing:
c² = a² +b² . . . . . . Pythagorean theorem for sides a, b, hypotenuse c
c = √(a² +b²)
diagonal length = √(6² +8²) = √100 = 10
Then the remaining two sides are ...
CD = 10, DE = 10
ApplicationThe perimeter is ...
perimeter = AB +BC +CD +DE +EA
= 12 +3 +10 +10 +3 = 38 . . . units
The perimeter of pentagon ABCDE is 38 units.
guys i seriously need help with this one
The option(1) that is g(1) is 3 is True and remaining are false.
Explain the function by its graph?Function of a variable is when a change in one is accompanied by a change in the other. The graph's x-axis denotes the function's domain, and the y-axis its range.
What kinds of functions can you find on a graph?Eight distinct types of regularly used functions correspond to eight distinct types of function graphs. They include linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal function graphs.
According to given data in the question:we have,
g(x) = f(x - 3)
The value of g(1) is 3As graph in question,
g(1) = f(1-3) = f(-2) = 3
This option is true.
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The sum of twice a number "x" and sixteen is
negative fifty six. Translate and find the number.
Answer:
The number is -36 or x = -36
Step-by-step explanation:
2x + 16 = -56
2x = -72
x = -36
What is the equation of the line that passes through the points (-4, -6) and (2, 8)
The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
A linear equation or function is given as ;
y = mx + c
Here, m is the slope and is given as (y₂ - y₁)/(x₂ - x₁).
The slope of the line passing through (-4, -6) and (2, 8) will be,
m = (8 + 6)/(2 + 4)
m = 14/6
So, y = (14/6)x + c
Substitute, (2, 8)
8 = (14/6)2 + c
c = 8 - 14/3 = 10/3
Therefore, y = (14/6)x + 10/3
Hence "The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3".
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a toy manufacturer inspects boxes of toys before shipment. each box contains 17 toys. the inspection procedure consists of randomly selecting three toys from the box. if one or more of the toys are defective, the box is not shipped. suppose that a given box has two defective toys. what is the probability that it will be shipped? a) 0.1765 b) 0.6691 c) 0.3309 d) 0.0221 e) 0.4341 f) none of the above.
The probability that it toys will be shipped is option b ) 0.6691 .
Hypergeometric Distribution will be used
P ( X = x ) = h ( x , N , n , k ) = [tex]C_{k,x}[/tex][tex]C_{N-k,n-x}[/tex] / [tex]C_{N,n}[/tex]
[tex]C_{n,x}[/tex] = n! / [ x! ( n - x ) !
According to question,
N = 17
k = 2
n = 3
To find : P ( X = 0 ) ,
P ( X = 0 ) = h ( 0 , 17 , 3 , 2 )
= [tex]C_{2,0} C_{15,3} / C_{17,3}[/tex]
= 455 / 680
= 0.6691
So there is 66.91 % probability that toys will be shipped .
Hence , option b ) 0.6691 is the correct answer .
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A health food store makes trail mix using dried fruit and nuts.the cost of the dried fruit is $2.50 per pound,and the cost of the nuts is $2.00 per pound .the total cost to make the trail mix is $225.if the total cost can be represented by the equation 2.5x +2y=225,what does the term 2.5x represent?
I need help:’)
The equation 2.5x + 2y = 225 represents the total cost and 2.5x represents the cost of dried fruit when its quantity is x.
A health food business prepares trail mixes out of dried fruit and nuts. The dried fruit costs $2.50 per pound, while the nuts cost $2.00 per pound. The overall cost of making the trail mix is $225.
Let the quantity of the dried fruit is x,
And the quantity of nuts is y,
As per the given question, the equation would be as:
2.5x + 2y = 225
The above equation represents the total cost and 2.5x represents the cost of dried fruit when its quantity is x.
Thus, 2.5x represents the cost of dried fruit when its quantity is x.
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8,40,200,...
Find the 10th term.
The sequence has the 10th term of 15625000
How to find the 10th term for the arithmetic sequence?The sequence is given as:
8,40,200,...
The above sequence has the following parameters
First term, a = 8
Common ratio, r = 5 i.e. 40/8 = 5
Number of terms , n = 10
This means that the sequence is a geometric sequence
The nth term of an geometric sequence is calculated as
f(n) = ar^(n - 1)
Substitute the known values in the above equation
So, we have the following equation
f(10) = 8 * 5^(10 - 1)
Evaluate
f(10) = 15625000
Hence, the 10th term for the sequence is 15625000
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daysha loves the caramel macchiato at the coffee shop. the 16 oz. medium size has 260 calories. how many calories will she get if she drinks the larger 20 oz. size?
After using proportion method 325 calories will she get if she drinks the larger 20 oz. size.
What is proportion?
Ratio and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers. The ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics. Numerous challenges in daily life can be solved with proportion, including those in business when handling transactions or in the kitchen, among other situations. It creates a relationship between two or more quantities and aids in comparing them.
Here 16 oz medium size has 260 calories.
Then
=> [tex]\frac{size of coffee}{ calories}[/tex]
=>[tex]\frac{16}{260}=\frac{20}{x}[/tex]
=>x=[tex]\frac{20*260}{16}[/tex]
=> x = 325
Hence 325 calories will she get if she drinks the larger 20 oz. size.
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A line includes the points (1, 10) and (0, 8). What is its equation in slope-intercept form?
Answer:
Y = 2x+8
Step-by-step explanation:
Y=mx=b equations
#12 all parts please!!
Answer:
Step-by-step explanation:
a find the interpret the slope and the y-intercept of the graph
Given:-16=m-18;Prove:m=10
Answer:
m=2
Step-by-step explanation:
-16=m-18
-16+18=m
2=m
What is the simplest positive form of
-35(mod 6)?
13) Mr. Harrington wants to buy a new TV for $500. He has a 10% off coupon and knows the tax
be 13.5%. How much money will he need to save to buy the TV?
a) $510.75
c) $450
b) $432.50
d) $567.50
Mr. Harrington will need $510.75 to buy the TV
The correct answer is an option (a)
In this question, Mr. Harrington wants to buy a new TV for $500
He has a 10% off coupon.
After applying this coupon, the cost of TV would be,
500 - (10 percent of $500)
= 500 -[ (10/100) * 500]
= 500 - 50
= 450
He knows the tax be 13.5%.
13.5 percent of 450 would be,
(13.5/100) * 450
= 60.75
So, the amount he will need to save to buy the TV,
$450 + $60.75 = $510.75
Therefore, Mr. Harrington will need $510.75 to buy the TV
The correct answer is an option (a)
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Identify three segments parallel to AE using the figure shown. Assume lines and planes that appear to be parallel or perpendicular are parallel or perpendicular, respectively
From the figure, the lines parallel to AE are DH, CG, and EF.
What are parallel and perpendicular lines?Geometry is heavily reliant on parallel and perpendicular lines, and they can be easily distinguished thanks to a few unique qualities. If two lines never cross each other, are in the same plane, and are at the same distance from one another, then they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees.
If two straight lines are in the same plane and never intersect, they are said to be parallel lines.
So from the figure, we can see that the lines parallel to AE are DH, CG, and EF, as the lines are in the same plane.
As equidistant lines, they are always the same distance apart.
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Solve for x.
9x3x36
0-6
O-4
O
4
6
Answer:
[tex]9x = 3x - 36 \\ 6x = - 36 \\ x = - 6[/tex]
hopefully this will u...^_^
When you answer, could you just put the letter of the number you have? Thank you.
In the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.
As given in the question,
In the given triangle KLM,
Coordinates of the triangle KLM are given by :
K(0,2) ,L(2 ,9) ,M(4,2)
Dilation from the origin is represented by:
a. K'(0,2) , L'(8,9) , M'(16, 2)
Dilation scale factor does not effect on all the coordinates .
Not a correct option.
b. K'(0,2) , L'(2,36) , M'(16, 2)
Dilation scale factor does not effect on all the coordinates .
Not a correct option.
c. K'(0,8) , L'(8,36) , M'(16, 8)
Multiply by scale factor 4.
Dilation exist.
d. K'(4,6) , L'(6,13) , M'(8, 6)
Scale factor of addition of 4.
Dilation does not exist.
Therefore, in the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.
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