Answer: 24x² + 20x + 4
Step-by-step explanation:
Area of a rectangle can be found with A = L * W;
A = L * W
A = (8x + 4) * (3x + 1)
Now we can use the "FOIL" method, which is used to multiply binomials.
[F] First ➜ 8x * 3x = 24x²
[O] Outside ➜ 8x * 1 = 8x
[I] Inside ➜ 4 * 3x = 12x
[L] Last ➜ 4 * 1 = 4
Lastly, we add it all together for our final answer.
24x² + 8x + 12x + 4 = 24x² + 20x + 4
Answer:
24x^2+20x+4
Step-by-step explanation:
Area is length times width.
The length is (8x+4) and the width is (3x+1).
If we follow the formula for the area of a rectangle, then it would be
(8x+4)(3x+1).
Next, you would foil.
Take the first and multiply it by the second equation as follows
8x*3x+8x*1 which would give you
24x^2+8x
Then, you would take the second from the first equation and multiply it with the second equation as well.
4*3x+4*1 which would give you
12x+4
Combine all of it together
24x^2+8x+12x+4
Combine like terms
24x^2+20x+4
That's the area.
Hope this helps.
in how many different ways can the letters of the word detail' be arranged in such a way that the vowels occupy only the odd positions?
The number of ways in which the word detail can be arranged in such a way that the vowels occupy only the odd positions is 36.
We will find the number of permutations in which the word DETAIL can be arranged such that the vowels occupy odd positions.
The vowels are E, A and I. They can occupy 1st, 3rd and 5th position in any order. Hence, the number of ways to do that is 3! = 6.
Now, the consonants D, T and L can occupy 2nd, 4th and 6th position in any order. Hence, the number of ways to do that is 3! = 6.
Hence,
Total number of ways = 3! * 3! = 6*6 = 36.
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Simplify 2x(3x^2+5x-2)
Answer:
6x^2+6x
Step-by-step explanation:
2x(3x^2+5x-2)
6x^2+10x-4x
6x^2+6x
A+B=0 and AB= -36
What is the value of A-B?
Please help me with step by step explanation.
The value of A - B is - 12
It is given that A + B = 0 .......... ( Eq . 1 )
⇒ A = - B ............ ( i )
Another equation which is given is :
AB = - 36 ........... ( Eq . 2 )
Using (i) in Eq . 2
- B ( B ) = - 36
- B ² = - 36
B ² = 36
B = √ 36
B = 6 .......( ii )
Using B = 6 in ( i ) ,
A B = - 36
A ( 6 ) = - 36
A = -6
This implies, A = - 6 and B = 6
Now to find the value of A - B , we need to put the values
A - B = - 6 - 6
= - 12
Hence, the value of A - B is - 12 .
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If x= -2 , calculate the value of x squared - x
Answer:
x= -2
Step-by-step explanation:
A square number is the result when a number has been multiplied by itself
Mr. harris is adding tiles to his patio area. on monday, he tiled 1/3 of his patio, and on tuesday, he tiled 1/2 of the patio area. how much would he have left to tile on wednesday?
The area left to be tiled on Wednesday is 1/6
Let the total area to tile be 60 sq feet
We have taken 60 sq feet as the LCM of 2 and 3 is 6. So taking up 60 makes our calculation part easy.
Area tiled on Monday = 1/3*60 = 20 sq feet
Area tiled on Tuesday = 1/2*60 = 30 sq feet
Area remaining to be tiled = 10 sq feet
So, a fraction of the area left to be tiled = Area left to be tiled/Total area to be tiled
= 10/60 = 1/6
Hence, 1/6 of the area is left to be tiled
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Answer:1/6
Step-by-step explanation:
Solve the equation. Show all steps of your work and justify each step with an algebraic property of equality.
4x-8/2=10
Answer:
Question 4x-8/2=10 Answer X=7
Step-by-step explanation:
Frist Multiply both sides :by 2[tex]\frac{2\left(4x-8\right)}{2}=10\cdot \:2[/tex]
Simplify4x-8=20
Add 8 to both sides4x-8+8=20+8
Simplify4x=28
Divide both sides by 4[tex]\frac{4x}{4}=\frac{28}{4}[/tex]
SimplifyX= 7
Hope this helps
Pls mark brainliest
Please help 1 through 4
Answers:
1.) Plot the numbers on the y-axis (vertical line) and the countries on the x-axis (horizontal). Then, put "Cars (billions)" to label the y-axis and put "Country" to label the x-axis. There is an example attached.
2.) Do the same thing as #1 but label the y-axis with "People (hundreds)" and the x-axis as "Colonies".
3.) Japan because 8 is the greatest amount comparing to the other countries.
4.) Japan made 6 million more cars than Spain since 8 - 2 = 6. (We are counting the cars in millions)
The probability that john,beth, and avery will be elected secretary of the key club are 1/8,2/5, and 1/3 what is the probability that one of the three will be elected?
the probability that one of the three will be elected = [tex]\frac{19}{30}[/tex]
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.
As per the question, it is given that :
Probability of John (A) = [tex]\frac{1}{8}[/tex]
Probability of Beth (B) = [tex]\frac{2}{5}[/tex]
Probability of Avery (C) = [tex]\frac{1}{3}[/tex]
The probability that one of the three will be elected :
P(A) * P(B') * P(C') + P(A') * P(B) * P(C') + P(A') * P(B') * P(C) = P(A) * (1 - P(B)) * (1 - P(C)) + (1 - P(A)) * P(B) * (1 - P(C)) + (1 - P(A)) * (1 - P(B)) * P(C).
here, P(A) = Probability of A happening
P(A') = Probability of A not happening
= [tex](\frac{1}{8} * \frac{3}{5} * \frac{2}{3}) + (\frac{7}{8} * \frac{2}{5} * \frac{2}{3}) + (\frac{7}{8} * \frac{3}{5} * \frac{1}{3})[/tex]
= [tex]\frac{1}{20} + \frac{7}{30} + \frac{7}{20}[/tex]
= [tex]\frac{3 + 14 + 21}{60}[/tex]
= [tex]\frac{38}{60}[/tex] = [tex]\frac{19}{30}[/tex]
Therefore, the probability that one of the three will be elected = [tex]\frac{19}{30}[/tex]
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what is -10 minus -4 with counters
-10 minus -4 = -6
Subtraction in mathematics is the process of subtracting one number from another. This is a first-order arithmetic operation, represented by the subtraction sign (-), and is a method of calculating the difference between two numbers and the length of a segment. Subtraction is an operation which is used to find the difference between numbers. If you have a group of objects and remove some objects from it, the group will be smaller. For example, you bought 9 cupcakes for your birthday party and your friend ate 7 cupcakes. Now he has two cupcakes left. This can be written in the form of the subtraction formula 9 - 7 = 2, read as "9 minus 7 is equal to 2". If you subtract 7 from 9, (9 - 7) becomes 2.Solving the equation
-10 minus -4
= -10 - (-4)
= -10 + 4
= -6
-10 minus -4 = -6
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4. jamaal is collecting data on freddie's on-task behavior. he looks to see if freddie is on-task for an entire 10-second interval. if he is, he marks yes. if freddie looks around during the 10 seconds, he marks no. what type of data recording is jamaal using?
Jamaal using whole interval type of data recording to collect the data on Freddie’s on-task behavior.
What do you mean by whole interval data collection?One form of interval recording technique is whole interval recording. An interval recording approach involves watching to see if a behavior happens or not within predetermined intervals of time. After determining the duration of an observation session, the time is divided into shorter segments that are all of the same length. To record the incidence of behavior, ten boxes may be utilized to divide a 10-minute observational session into 1-minute intervals. A whole interval recorder uses a X for occurrence and a O for no non-occurrence to indicate if a behavior occurred during the entire interval.
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Brittany says she can read about 220 words per minute. She has a book that is 300 pages long and each page has about 370 words per page. How many hours will it take Brittany to finish the book?
We want to do a change of units of a rate, from words per minute to words per hour.
We will find that the answer is 22,200 words per hour.
The rate that we need to modify is:
370 words/minute
So the time is in the denominator.
Also, remember that:
1 hour = 60 minutes.
Then:
1 minute = (1/60) hours.
Using the above relation, we can replace the "minute" in the denominator by (1/60) hours, so we get:
370 words/minute = 370 words/((1/60) hours.) = 60*370 words/hour
22,200 words/hour.
Then the rate is 22,200 words per hour.
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Answer:
We want to do a change of units of a rate, from words per minute to words per hour.
We will find that the answer is 22,200 words per hour.
The rate that we need to modify is:
370 words/minute
So the time is in the denominator.
Also, remember that:
1 hour = 60 minutes.
Then:
1 minute = (1/60) hours.
Using the above relation, we can replace the "minute" in the denominator by (1/60) hours, so we get:
370 words/minute = 370 words/((1/60) hours.) = 60*370 words/hour
22,200 words/hour.
Then the rate is 22,200 words per hour.
Step-by-step explanation:
I’m stuck on this question can somebody help me
Answer:
X=10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
A triangle with vertices at (-6, 5), (-5, 1), and (-8, 2) is reflected over the y-axis. What are the coordinates of the vertices of the reflected image? Enter the correct answers in the boxes. Show Hints Preimage coordinates Image coordinates (-6,5) (-5,1) (-8,2)
The coordinates of the vertices of the reflected image are
A' ( 6,5) , B' ( 5,1), C' ( 8,2)
given that
a triangle has vertices A ( -6,5 ) , B (-5, 1) , C( -8,2 )
it is reflected over Y axis
we have to find the coordinates of the vertices of the reflected image
since it is reflected over Y axis then only the sign of x coordinates changes
the rule for a reflection over the Y axis is (x, y) -> ( -x , y)
the y coordinate in this case is unchanged
the vertices changes and it become
A( -6, 5) -> A' ( 6,5)
B ( -5, 1) -> B' ( 5,1)
C ( -8,2) -> C' ( 8,2)
preimage of coordinates attached below
Hence the coordinates of the vertices of the reflected image are
A' ( 6,5) , B' ( 5,1), C' ( 8,2)
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it is not always helpful to rewrite a quadratic equation in standard form as a first step in solving it.
The given statement is True.
"It is not always helpful to rewrite an equation in standard form as a first step in solving it."
Briefing:In standard form, the right side of an equation should be 0 and every component on the left side should be 1. For example, x2 = 4; to express this in standard form, move the number 4 to the left side of the equation, resulting in x2 - 4 = 0.
If you are asked to find x in this circumstance, there is no need to write the equation in standard form; simply take this same real number of both of the equation's sides to find x.
How do I write a standard form equation?Ax+By=C is the common structure for linear equations in two variables. 2x+3y=5, for example, is a simple linear equation. It is rather simple to find both intercepted communications when an equation is stated in this way (x and y). This form is indeed useful for solving two-linear equation systems.
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I understand that the question you are looking for is:
It is not always helpful to rewrite an equation in standard form as a first step in solving it.
True/False
During this time, helen barnes from tri-state realty called for information about a stone listing. what should the assistant do?
During this time, Helen Barnes from tri-state realty called for information about a stone listing. The assistant should give Helen the information she is asking for.
Who is an unlicensed assistant broker?An unlicensed assistant broker does a number of responsibilities. Nonetheless, it is vital that every broker understands what an unlicensed broker is legally allowed to do when compared to a licensed assistant broker, in order to avoid getting into trouble.
Therefore, we conclude that in this question, the assistant should give Helen the information she is asking for.
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Complete question is; all of the licensees at stone realty are attending an off site conference for the afternoon. the broker’s unlicensed assistant remained at the office to answer the telephone. during this time, helen barnes from tri-state realty called for information about a stone listing. what should the assistant do?
using the following quantities, calculated from these data, estimate the correlation between the percentage of dopamine receptors blocked and subjects’ ratings of the cocaine high. provide a standard error with your estimate. sum of products: 957.5 sum of squares (receptors blocked): 8145.441 sum of squares (rating of high): 372.5
correlation coefficient,r = 0.5497
Standard Error,[tex]SE_{r} = 0.1477[/tex]
What is dopamine?Dopamine, also known as DA or 3,4-dihydroxyphenethylamine, is a neuromodulatory chemical with a variety of crucial functions in cells. It is an organic substance that belongs to the phenethylamine and catecholamine families. About 80% of the catecholamines in the brain are made up of dopamine. It is an amine produced by removing a carboxyl group from a molecule of L-DOPA, which is used as a precursor and is produced in the kidneys and brain. Plants and the majority of animals can produce dopamine as well. Dopamine performs the role of a neurotransmitter in the brain, which is a substance secreted by neurons (nerve cells) to communicate with other nerve cells. Although neurotransmitters are only produced in some parts of the brain, they have a systemic impact on numerous areas.
Let the random variable, X = % of dopamine receptors blocked and Y= subject's ratings of cocaine high.
The correlation coefficient, r
Given:
[tex]SS_{XY}[/tex] = 957.5
[tex]SS_{X}[/tex] = 8145.441
[tex]SS_{Y}[/tex]= 372.5
The correlation coefficient between the variables, X and Y is obtained using the following formula,
[tex]r=\frac{SS_{XY} }{\sqrt{SS_{X} \times SS_{Y} } }[/tex]
[tex]r=\frac{957.5 }{\sqrt{{8145.441} \times372.5 } } }[/tex]
r = 0.5497
The standard error for the estimate of the correlation coefficient is obtained using the following formula,
[tex]SE_{r} = \sqrt{\frac{1-r^{2} }{n-2} }[/tex]
From the scatterplot, the sample size, n = 34
[tex]SE_{r} = \sqrt{\frac{1-(0.5497)^{2} }{34-2} }[/tex]
[tex]SE_{r}=0.1477[/tex]
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Ranger Raul is thinking of two numbers. When he adds them, he gets 40. When he multiplies them, he
gets 351. What are the numbers?
Answer:27 and 13
Step-by-step explanation: 27 + 13= 40
27 x 13= 351
A shop has 5 different shirts and 7 different jeans. how many ways are there to select two items so that at least one jeans is chosen?
There are 56 number of possible ways are there to select two items so that at least one jeans is chosen.
Combinations:
Combinations is the number of ways in which you can choose r elements out of a set containing n distinct objects.
The combination formula that will allow you to determine the number of combinations in no time:
C(n,r) = n! / (r! (n-r)!)
where:
C(n,r) is the number of combinations;
n is the total number of elements in the set; and
r is the number of elements you choose from this set.
Given,
A shop has 5 different shirts and 7 different jeans.
Here we need to find how many number of ways ways are there to select two items so that at least one jeans is chosen.
Let's say,
First, you picked up 1 jeans and 1 shirt …
Then the number of ways to do that is
=> ⁵C₁ x ⁷C₁
=> 5 x 7
=> 35
Similarly, in second case you picked up the only 2 jeans
number of ways to do that is
=> ⁷C₂
=> 21
So the final answer will be sum of both the cases that is
=>( ⁵C₁ x ⁷C₁ ) + (⁷C₂)
=> 35+21
=> 56 ways
Therefore, there are 56 possible ways to select two items so that at least one jeans is chosen.
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a traffic study has shown that the probability that 55 cars will pass over a small bridge in a 4-4-minute period is 0.16.0.16. what are the odds against exactly
Final answer:
The odds against exactly 5 cars passing over the bridge in that time is calculated as 4:21
Why don't we use probability instead of odds ?
A probability must be between 0 and 1 (nothing can happen with a greater than 100% likelihood). The chances are not as limited. Odds can be any positive number; for example, a chance of 2/3 is equivalent to odds of 2/1. By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.
By dividing the odds in the first group by the odds in the second group, the odds ratio is calculated. For many clinicians, odds and odds ratios are difficult to comprehend. Odds are calculated by dividing the likelihood of an event happening by the probability that it won't.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
When designing a rectangular patio, a landscaper places a coordinate grid on top of the design.
One side of the patio is represented by the line
y=2/3x+5/3
The other three sides of the patio will be represented by one line with a slope of (BLANK) and two lines with a slope of (BLANK).
The other three sides of the patio will be represented by one line with a slope of 2/3 and two lines with a slope of -3/2.
What is general equation of a Straight line?The general equation of a straight line is -
y = mx + c
Given in the question is a equation that describes the one side of a rectangular patio. From the question, we can write -
Equation representing a side of Patio - y = 2/3x + 5/3
If we compare the equation representing a side of Patio with the general equation of line, we get -
y = 2/3 x + 5/3
[y] = [m] x + [c]
From this we can conclude that -
m = 2/3 = slope of line
c = 5/3 = y - intercept
The patio is in the shape of a rectangle. Therefore, the side opposite to the line of slope → 2/3 will be equal in length and parallel to it. We know, that the slope of two parallel lines are same. So, the slope of line parallel to y = 2/3x + 5/3 will be 2/3.
The remaining two sides are perpendicular to both the side of slope → 2/3. The remaining sides are also parallel to each other, indicating they both have same slope. The slope of a line perpendicular to a given line (L) is given by -
m [p] x m [L] = -1
m [p] = - 1 / m [L]
m [p] = - 3/2
Therefore, the remaining two sides will have slope of -3/2.
Therefore, the other three sides of the patio will be represented by one line with a slope of 2/3 and two lines with a slope of -3/2.
[Refer to the graph attached]
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6. Draw the rotated image on the same graph.
Rotate 180° about (0, 0).
A
b
C
Answer:
Answer in the photo
Step-by-step explanation:
Hope this helps x :)
PLEASE HELP ITS URGENT
Answer:
Hi, it's 8^9
Step-by-step explanation:
[tex]8^5\cdot \:8^4\\8^5\cdot \:8^4=8^{5+4}\\8^{5+4}\\=8^9\\[/tex]
a pencil at a stationery store costs $1, and a pen costs $1.50. stella spent $21 at the store. she bought a total of 18 items. which system of equations can be used to find the number of pencils (x) and pens (y) she bought?
Answer:x+1.5y=21
Step-by-step explanation:
We know that a pencil is $1, so let's represent that as 1x or just x. We also know that each pen costs $1.50, and let's represent this as 1.5y for the number of pens Stella bought. Your equation would be x+1.5y=21.
Andre performs a 90-degree counterclockwise rotation of polygon p and gets polygon p but he does not say what center of the rotation is
The center of rotation for the polygon p is shown as the red point in the attached graph below.
A plane figure spins around a point known as the center of rotation. Throughout the rotation, this point remains stationary.
The fixed point that the rotation revolves around in a figure or object with rotational symmetry is referred to as the center of rotation. As an illustration, we consider the point in the middle of a windmill where the blades start to rotate.A rotation is a transformation in which every point of a figure is turned through a predetermined angle and in a predetermined direction around a fixed point. The fixed point is referred to as the rotational center. The term "angle of rotation" refers to the rotation's amount and is expressed in degrees.To learn more about center of rotation visit:
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Heellppp I cant figure it out
Answer:
It will be 29/1000
Step-by-step explanation:
Because each kg equal 1000 milie gram
Sofias bank account statement said she had -25$ she dopsited 47$ Into her account what is Sofias balance after she made that deposite
Answer: $22
Step-by-step explanation:
47- 25= 22
choose the correct answer to fill in the blank. an outlier is an observation which is less than iqr or greater than q3 ( )times iqr.
According to the given statement Outliers would be any sightings that are more than 1.5 IQR below Q1 or more then 1.5 IQR above Q3.
What does the term "outlier" signify in statistics?An outlier is a value that is significantly different from the other values in a random sampling of a population. In some ways, this definition leaves it up towards the analyst (or a consensus process) to determine what is abnormal.
What is the significance of identifying outliers?Identifying potential outliers is critical for such following reasons. An outlier could imply faulty data. For example, the data could have been wrongly coded, or an experiment could have been done erroneously.
According to the given data:An outlier is defined as an observation that is less than or more than Q3 times IQR.
We need to look for place variances in Q1 and Q3.
When we utilize the IQR approach to discover outliers outside of Q1 and Q3, we create a "fence." Outliers are any values that fall outside of the defined boundary.
To construct this fence, we take 1.5 times the IQR, deduct it from Q1, and add it to Q3.
IQR = (1.5 - Q1)
IQR = (1.5 + Q3)
This provides us with the minimum and maximum fence posts to which we can compare every observation.
the given statement Outliers would be any sightings that are more than 1.5 IQR below Q1 or more then 1.5 IQR above Q3.
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Cool Down: Drawing a Pool
A rectangular swimming pool measures 30 meters in length and 15 meters in width.
1. Make a scale drawing of the swimming pool where 1 centimeter represents 5 meters
11-1
1=201
The pool's new dimensions will be 10cm by 5cm, where 1 centimeter equals 5 meters.
What do we mean by dimensions?The dimension of a mathematical space is defined informally in physics and mathematics as the smallest number of coordinates required to specify any point within it. A line has a dimension of one because it only requires one coordinate to specify a point on it, such as the point at 5 on a number line.So, scaling is a technique for resizing an object. It can either enlarge or decrease the size of the object.
A rectangular pool's dimensions of 50m by 25mMaking a scale drawing of the pool in which 1cm equals 5 meters, that is:
1 cm = 5m .... (1)The length:
L = 50 m ..... (2)Subtraction of both expressions 1 and 2:
1/L = 5/505L = 50L = 50/5L = 10cmIn terms of width:
The original width was 25 meters.Obtain new width:
1/W = 5/255W = 25W = 25/5W = 5cmTherefore, the pool's new dimensions will be 10cm by 5cm, where 1 centimeter equals 5 meters.
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The correct question is given below;
A rectangular swimming pool measures 50 meters in length and 25 meters in width. Make a scale drawing of the swimming pool where 1 centimeter represents 5 meters.
(x-4) |x-4| i am looking for the simplification of this. i think the answer should be x^2 - 16, my teacher gave us an answer, but i don't believe it is correct. she gave us -x^2 +8x - 16.
It depends on the sign of [tex]x-4[/tex].
Recall the absolute value function's definition:
[tex]|x| = \begin{cases}x & \text{if } x \ge 0 \\ -x & \text{if } x < 0\end{cases}[/tex]
Now, if [tex]x-4\ge0[/tex], then
[tex](x-4)|x-4| = (x-4)(x-4) = x^2 - 8x + 16[/tex]
On the other hand, if [tex]x-4<0[/tex], then
[tex](x-4)|x-4| = -(x-4)(x-4) = -(x-4)^2 = -x^2 + 8x - 16[/tex]
What you first suggested is incorrect. We have
[tex]x^2 - 16 = (x - 4) (x + 4)[/tex]
but [tex]|x-4| \neq x + 4[/tex].
We can show this using the definition again. If [tex]x-4\ge0[/tex], then
[tex]x-4 = x+4 \implies -4=4[/tex]
which is a contradiction; on the other hand, if [tex]x-4<0[/tex], then
[tex]-x+4 = x+4 \implies 2x = 0 \implies x =0[/tex]
holds for only one value of [tex]x[/tex].
you are currently in dept to your friend by $50. You pay your friend back $15 the first week, then $25 the next week do you still owe your friend money and how much?(help me please)
Answer:
Well that depends
Step-by-step explanation: