The absolute value equation to represent the definition of betweenness is
AB + BC = AC ↔ B ∈ A,C
Absolute value equation:
An absolute value equation is a function that contains an algebraic expression within absolute value symbols.
Given,
Here we have the statement "If three points a, b, and c lie on the same line, then b is between a and c if and only if the distance from a to c is equal to the sum of the distances from a to b and from b to c.".
Here we need to find the absolute value function for this statement.
In order to find the absolute value equation,
First we have to identify the symbols for the terms mentioned in the statement they are,
between = ∈
if and only if = ↔
sum = +
Now, we have to divide the statement as two parts.
First one is, "c lie on the same line, then b is between a and c"
It can be written as,
B ∈ A,C
Then the second part is, "the distance from a to c is equal to the sum of the distances from a to b and from b to c."
Which can be written as
AB + BC = AC
When we combine it, the we get the absolute value equation as,
B ∈ A,C ↔ AB +BC = AC
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Describe the transformation.y = (x + 7)2 - 4
The parent function of the quadratic function is
[tex]y=x^2[/tex]∵ x is added by 7
∴ The graph of the function is translated 7 units to the left
∴ The image of the function will be
[tex]y=(x+7)^2[/tex]∵ The function is added by -4
∴ The graph of the function translated 4 units down
∴ The image of the function will be
[tex]y=(x+7)^2-4[/tex]The transformation is
Shift 7 units left and shift down 4
The answer is D
boxes of nails are stacked on top of each other on a work bench. The table below shows how the height above the floor of the topmost box depends on the number of boxes. What is a rule for the height? Give the rule in words and as an algebraic expression.
The height is the sum of 39 and 9 times the number of boxes, n. The rule is 9n + 39.
What is algebraic expression?An algebraic expression is defined as the type of expression that is made up of a variable, a coefficient and a constant.
From the given box of nails,
The height of 2 boxes of nails = (9× 2) + 39 = 57 In
The height of 3 boxes of nails = ( 9 × 3) + 39 = 66 In
The height of 4 boxes of nails = ( 9× 4) + 39 = 75 ln
That is to say that the height of the box above the floor can be calculated by the sum of 39 and 9 times the number of boxes, n.
Therefore, the rule of heights is 9n + 39 where n is the number of boxes present.
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For a ratio of 3:2, divide AB into 3 equal parts. Each equal part is 3 units, so the point that divides AB into a 3:2 ratio is 0. For a ratio of 3:2, divide AB into 3 equal parts. Each equal part is 3 units, so the point that divides AB into a 3:2 ratio is 3. For a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 1. For a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 2.
The correct option regarding the ratio is given as follows:
For a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 2.
RatioA ratio of an amount a over a total amount a + b is given as follows:
r = a/(a + b) = a:b.
In the context of this problem, the ratio is given as follows:
r = 3:2.
Hence the number of equal parts is given by:
equal parts = 3 + 2 = 5.
The length of the segment is:
B - A = 6 - (-4) = 10 units.
Hence the length of each equal part is:
length equal part = 10/5 = 2.
The point that is 3/5 of the way from point -4 to point 6 is found as follows:
x - (-4) = 3/5(6 - (-4))
x + 4 = 30/5
x + 4 = 6
x = 2.
Meaning that the correct option is given by the last one.
Missing informationThe coordinates of A and B are missing, and they are given as follows:
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A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes six revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? (Round your answer to one decimal place.)
The beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.
Given that, a lighthouse is located on a small island 4 km away from the nearest point P.
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
[tex]\frac{d\theta}{dt}[/tex] = 6 rev/min
= 6π rad/min
tan θ = x/6
[tex]\frac{d}{dt}tan\theta=\frac{d}{dt}(\frac{x}{6} )[/tex]
[tex]sec^2\frac{d\theta}{dt} = \frac{1}{6}(\frac{dx}{dt} )[/tex]
[tex]\frac{dx}{dt}=6sec^2\theta\frac{d\theta}{dt}[/tex]
At x=1 km; tan θ= x/6 = 1/6
[tex]sec^2 \theta= 1+tan^2 \theta= 1 + (\frac{1}{6})^2[/tex]
[tex]sec^2 \theta = \frac{10}{9}[/tex]
[tex]\frac{dx}{dt} = 6 sec^2\theta \frac{d\theta}{dt}[/tex]
dx/dt = 6 × 10/9 × 6π
dx/dt = 125.66 km/min
Therefore, the beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.
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save
The room numbers of two adjacent classrooms are two consecutive odd numbers. If their sum is 720, find the
classroom numbers.
The room numbers of two adjacent classrooms are 359 and 361.
What is consecutive odd numbers?
Consecutive odd numbers are odd integers that are separated by 2 and come after one another.
Suppose the first odd number is x, then the another consecutive odd number is x + 2.
The sum of these two numbers is 720.
So,
x + (x + 2) = 720
2x + 2 = 720
2x = 718
x = 359
Therefore, the first odd number is 359 and the second add number is 361 which gives the sum 720.
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The table shows the cumulative number of minutes Alice practices clarinet for the first part of the school year:The table shows the cumulative number of minutes Alice practices clarinet for the first part of the school year:
The correct option regarding the scale and the origin of the graph are as follows:
D.
x-axis scale: 1 unit = 1 week
y-axis scale: 1 unit = 150 minutes
origin: (0 weeks, 0 minutes)
Scale and originThe scale should be chosen focusing on improving the readability of the data-set by the reader, while the origin should be chosen according to the values assumed by the variables.
In the context of this problem, the values of x, in weeks, are:
2, 3, 4, 5, 6, 7, 8.
They increase by one, hence the scale of x should be of 1 unit = 1 week.
The values of y, in minutes are given as follows:
300, 450, 600, 750, 900, 1050, 1200.
They increase by 150, hence the scale of y should be of 1 unit = 150 minutes, which is the rate of change of the problem.
As the measures are both positive values, the origin should be of (0,0), hence the correct option for the scales and the origin is option D.
Complete problemThe table is:
Weeks Minutes
2 300
3 450
4 600
5 750
6 900
7 1,050
8 1,200
The options are:
A. x-axis scale: 1 unit = 2 weeks
y-axis scale: 1 unit = 50 minutes
origin: (0 weeks, 0 minutes)
B. x-axis scale: 1 unit = 2 weeks
y-axis scale: 1 unit = 150 minutes
origin: (2 weeks, 300 minutes)
C. x-axis scale: 1 unit = 1 week
y-axis scale: 1 unit = 50 minutes
origin: (2 weeks, 300 minutes)
D. x-axis scale: 1 unit = 1 week
y-axis scale: 1 unit = 150 minutes
origin: (0 weeks, 0 minutes)
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heeeeeeelp me please
Answer:
x=9
y=27
Step-by-step explanation:
the scale factor is [tex]\frac{4}{3}[/tex] so 6 × [tex]\frac{4}{3}[/tex] is x - 1
x-1 is 8
so x is 9.
Write the equation of the line that contains the point (-8,6) and has the same slope as the line represented by the table of values below.
step 1
Find the slope of the line represented by the table of values
take the points
(-8,13) and (-4,5)
m=(5-13)/(-4+8)
m=-8/4
m=-2
step 2
Write the equation of the line that contains the point (-8,6) and has the same slope as the line represented by the table
y=mx+b
we have
m=-2 -----> the same slope of the given line
point (-8,6)
substitute in the equation of the line in slope intercepot form
6=-2*(-8)+b
solve for b
6=16+b
b=-10
therefore
teh equatiion of the line is
y=-2x-10Can someone please help
-4x = -60 on a graph
The graph of the equation -4x = -60 is shown below.
How to Graph the Equation of a vertical Line?A vertical line is expressed as the equation, x = b. Here, the variable "b" is the point on the x-axis where the line intercepts the horizontal axis.
Thus, to plot the graph for a vertical line with the equation, x = b, we would simply draw a vertical line that crosses the x-axis at point b.
Given the equation, -4x = -60, rewrite the equation in the form x = b, to determine the value of b:
-4x/-4 = -60/-4 [division property of equality]
x = 15
This means that the graph of the equation, -4x = -60, would be a graph that has a vertical line that crosses the x-axis at 15.
the graph is shown below.
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true or false: (justify/explain your answer) state whether a or b is the true statement below and then explain why the other statement is false. a. with a large random sample, the sample histogram will closely resemble the normal curve. b. with a large random sample, the probability density function of the sample mean will close resemble the normal curve.
By central limit theorem ,with a large random sample, the sample histogram will not closely resemble the normal curve but with a large random sample, the probability density function of the sample mean closely resembles the normal curve.
The central limit theorem for samples says that if we keep drawing larger and larger samples and calculating their means, the sample forms their own normal distribution (the sampling distribution). The normal distribution will have the same mean as the original distribution and a variance that equals the original variance divided by the sample size. The variable n is the number of values that are averaged together,and not the number of times the experiment is done.
Hence,with a large random sample, the sample histogram will not resemble the normal curve but with a large random sample, the probability density function of the sample mean will closely resemble the normal curve.
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What graph represents the system of linear inequalities? y>3x+1 y≤−2x−4
Answer:
Step-by-step explanation:
y>3x+1
y≤-2x-4
By driving 10 miles per hour faster, Goldie was able to
Ishave 2 hours and 30 minutes off her 50-mile trip to visit
her grandmother who lives in the mountains. Select the
equation that could be used to solve this problem. Use x to
represent her faster driving rate.
The faster driving rate of Goldie is 20 miles/hour.
Given that, by driving 10 miles per hour faster, Goldie was able to have 2 hours and 30 minutes off her 50-mile trip.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Here, Speed = 10 miles/hour, Time = 2 hours and 30 minutes = 2.5 hours and Distance = 50 mile.
Now, Distance = Speed × Time
Let the faster driving rate be x.
50 = x × 2.5
⇒ x = 50/2.5
⇒ x = 20 miles/hour
Therefore, the faster driving rate of Goldie is 20 miles/hour.
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Answer:
Step-by-step explanation:
I don't agree with the other answer.
You need to you systems of equations
So
d=50 t=t-2.5 x=r+10
d=rt
50=(r+10)(t-2.5) (faster equation)
50=rt (slower equation)
t=[tex]\frac{50}{r}[/tex] (substitute into faster equation)
50 = (r+10)(50/r -2.5) mult both sides by r to get rid of fraction
50r = (r+10)(50-2.5r) FOIL
50r = 50r -2.5r² + 500 -25r Simplify
2.5r²+25r-500=0 divide all by 2.5
r²+10r-200 factor
(r-20)(r+10) eliminate negative answer
r=20
x=r+10 =20+10 =30 mph
Solve for the value of z.
(7z+7)°
(9z-7)°
Base on congruency of vertical angles, the value of z is 7.
What are vertically opposite angles?Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
In other words, vertically opposite angles are angles that opposed each other at one specific vertex, and are formed by two straight intersecting line.
Vertically opposite angles are congruent to each other.
Therefore,
7z + 7 = 9z - 7
subtract 9z from both sides of the equation
7z + 7 = 9z - 7
7z - 9z + 7 = 9z - 9z - 7
-2z + 7 = - 7
subtract 7 from both sides of the equation
-2z + 7 = - 7
-2z + 7 - 7 = - 7 - 7
- 2z = - 14
divide both sides by - 2
z = - 14 / -2
Therefore,
z = 7
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8x^{3}+26x^{2}+19x+38x
3
+26x
2
+19x+3 is divided by 4x+34x+3.
Applying synthetic division, the quotient between 8x³ + 26x² + 19x + 3 by 4x + 3 is:
2x² + 5x + 1.
Synthetic division algorithmIn the synthetic division algorithm, the coefficients of a polynomial are each divided by a value.This divisor is the zero of the divided polynomial, which goes into the far left box.In this context of this problem, the coefficients of the polynomial 8x³ + 26x² + 19x + 3 are given as follows:
8, 26, 19 and 3.
The divisor is found as follows:
4x + 3 = 0
4x = -3
x = -3/4
x = -0.75.
The resulting coefficients of the quotient are given as follows:
8, 20, 4 and remainder of 0.
Hence the quotient is:
8x² + 20x + 4.
Which can be simplified as:
2x² + 5x + 1.
The first coefficient of the polynomial, of 8, was moved down, the multiplied by -0.75 and added to 26, resulting in 20. Then the same procedure was done with 20(multiplied with -0.75 and added with the next coefficient of 19), until the last coefficient of 3.
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8. The equation below is the standard form of a linear equation. += ax+by=c Which of the following is an equivalent equation? A. =−+ y=−abx+cb B. =+ C. =+ y=bax+bc D. =−+
Answer:
A
Step-by-step explanation:
ax + by = c Subtract ax from both sides
by = -ax + c Divide all the way through by b
[tex]\frac{by}{b}[/tex] = [tex]\frac{-a}{b}[/tex] x + [tex]\frac{c}{b}[/tex]
y = - [tex]\frac{a}{b}[/tex] x +[tex]\frac{c}{b}[/tex]
Simplify 8a^2 ➗ 4a
Asap please
Answer:
2a
Step-by-step explanation:
8a² / 4a
8/4 a²-¹
2a
please rate as brainliest
Answer:
2a
Step-by-step explanation:
8a^2 = 4a x 2a
8a^2 ➗ 4a
= ( 4a x 2a )/4a
= 2a
67×73=1×3(mod 5)show works
Answer
Check Explanation
Explanation
a ≡ b (mod n)
This means a and b have the same remainder when they are divided by n
So, to check if this question works out, we divide what is on the left hand side and what is on the right hand side by what is after the mod.
1) 67 × 73 ≡ 1 × 3 (mod 5)
4891 ≡ 3 (mod 5)
So, to check,
(4891/5) = 978 remainder 1
(3/5) = 0 remainder 3
The remainders are different.
So, this equation is wrong and does not work.
This equation is false.
2) 83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)
Noting that it is the units digit that determines the remainder
3 raised to the power of a multiple of 4 gives 81 raised to the power of a positive integer
5 raised to power of a multiple of 4 gives 625 raised to the power of a positive integer
So, using these numbers,
83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)
81 ≡ 625 (mod 17)
(81/17) = 4 remainder 13
(625/17) = 36 remainder 13
The remainders are the same.
So, this equation is correct and it works.
This equation is true.
Hope this Helps!!!
assume that your kidneys can filter out of 10% of a medication in your blood every 6 hours, you take 200 milligrams dose of the medicine how many milligrams of the medicine are in your blood after 2 days
Answer: 160 mg
Step-by-step explanation:
10% of 200 is 20
therefore, every 6 hours, 20 milligrams of medicine filters into your blood.
there are 24 hours in a day, and 48 hours in 2 days.
6 * 4 = 24
20 * 4 = 80
you get 80 mg of medicine every day.
80 * 2 = 160
you get 160 mg of medicine in two days.
What’s the answer to this ???
ONLY ANSWER IF YOU KNOW !!!!
A polynomial function of degree 3 with real coefficients and given zeros of -3, -1, and 4 is 4(x - 4)(x + 3)(x + 1) for which f(-2) = 24.
Any modifying value connected to a variable through multiplication is referred to as a "coefficient." Any non-imaginary number is a "real" number
How do you locate a degree 3 polynomial with real coefficients?
A polynomial of degree 3 must take the form a(xr1)(xr2)(xr3) since it has three roots. We are provided with the roots 3, 1, and 4. So, all we have to do is change these to r1, r2, and r3. We now get a(x+3)(x+1)(x4).
We must first factor the provided polynomial equation into a linear and quadratic equation in order to obtain the roots of the three-degree polynomial. The zeros of the three-degree polynomial can then be easily found.
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If 4x-y=-10 is a true equation, what would be the value of 6+4x-y
Answer:
-4
Step-by-step explanation:
6 + 4x-y = 6 + (4x-y) = 6 + (-10) = -4
a list of 20182018 positive integers has a unique mode, which occurs exactly 1010 times. what is the least number of distinct values that can occur in the list?
The least number of distinct values that can occur in the list is 225.
what is mode?The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode.
The mode appears 10 times. That leaves 2008 numbers.
The least number of distinct values will occur if all but one of the remaining values appears 9 times
= 2008/9
=223 1/9.
So, The list can include a maximum of 225 distinct values, with the mode appearing 10 times, 223 other values nine times, and the last value once.
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I am not sure how to find out if the number is an integer or not I don’t need you to answer all those number that are in the pic I want to understand how to figure that out on my own
An integer number is a number that can be written without using a rational component. In other words, if a number can be written without using a fraction, then that number is considered an integer.
For example, let's take the first number:
[tex]-\frac{64}{8}[/tex]This number is written as a fraction. But, this is also equivalent to:
[tex]-\frac{64}{8}=-8[/tex]Since it can also be written without making use of a fraction then this number is an integer.
Also, there are numbers that are written in decimal form. For example:
[tex]-8.92[/tex]These types of numbers are not integers.
Which of the following belongs under the radical symbol in the quadraticformula below?-bt 土?X2a
The quadratic formula for a polynomial is given by:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Therefore, option (C) is correct.
devon has 15 dollars to spend on snacks. the corner store has candy bars for $1 and sports drinks for $3. he only wants to purchase at most 10 items.
Devon can have 6 candy bars and 3 sports drinks when he has $15 to spend.
According to the question,
We have the following information:
Devon has $15.
Cost of 1 candy bar = $1
Cost of 1 sports drink = $3
Devon wants to purchase at most 10 items.
It means that the total items should be less than or equal to 10.
Now, we have to spend $15 in such a way that number of items should be less than or equal to 10.
Now, we will look for the number of items for sports drink and change the number of candy bars accordingly.
Let's take 1 sports drink:
$3
We are left with $12. Now, there will be 12 candy bars.
So, this can not satisfy our conditions.
Let's take 2 sports drink:
$6
We are left $9. Now, there will be 9 candy bars. And the number of items is 11.
(This is not satisfying our condition.)
Let's take 3 sports drink:
$9
We are left with $6. Now, there will be 6 candy bars. And the number of items is 9.
This is satisfying all the conditions.
Hence, Devon can have 6 candy bars and 3 sports drinks when he has $15 to spend on snacks.
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What is the solution to the equation x\6 = 4\12?options:x = 2x = 6x = 4x = 1
SOLUTION
We want to solve the equation
[tex]\frac{x}{6}=\frac{4}{12}[/tex]cross multiplying, we have
[tex]\begin{gathered} 12\times x=6\times4 \\ 12x=24 \\ x=\frac{24}{12} \\ x=2 \end{gathered}[/tex]Hence the answer is x = 2, the first option
Chris and Sarah's dinner bill was $28.67. They want to leave an 18% tip. How much gratuity will they leave?
Please help me!
Answer:
Tip- $5.16
Total cost- $33.86
Step-by-step explanation:
To find a 18% tip, turn 18% into 0.18.
Multiply 28.67 by 0.18.
28.67x0.18=
5.16
If you add that to the bill, it would be 33.86
A woman saves $6000 at 2.5% compund interest. She adds $1000 to her amount at the end of each year. Find the total savings after 2 years
Answer:
$8303.75
Step-by-step explanation:
(6000x1.025^2)+2000=8303.75
Brainly keeps acting up if I go off or don't respond please understand it's brainly kicking me out. The last option for d is 309 yards
From the given diagram, let's find the length of the park's boundary.
We can see the side of the park's boundary is a circular arc and the top and bottom are the bases of triangles.
To find the length of the circular sides, apply the length of arc formula:
[tex]arc\text{ length=}2\pi r\ast\frac{\theta}{360}[/tex]Where:
Θ = 120 degrees
π = 3.14
radius, r = 50 yards
Hence, we have:
[tex]\text{arc length=2}\ast3.14\ast50\ast\frac{120}{360}=104.67\text{ yards}[/tex]This means the length of one circular side of the boundary is 104.67 yards.
We have two circular sides of the boundary.
The top and bottom sides form equilateral traingles.
Hence, the length of the top and bottom sides are 50 yards each.
To find the total length of the boundary, we have:
Total length = 104.67 + 104.67 + 50 + 50 = 309.34 yards
Rounding off to the nearest yard, the length of the park's boundary is:
309 yards
ANSWER:
D. 309 yards
If ADAB ACBA,
ZD = 132° and ZC = x + 18
Answer:
x = 114
Step-by-step explanation:
since the triangles are congruent then corresponding angles are congruent, then
∠ C = ∠ D , that is
x + 18 = 132 ( subtract 18 from both sides )
x = 114