Answers
The number line for [tex]\fbox{\begin\\\ \bf \text{option 1}\\\end{minispace}}[/tex] represents the solution for the equation [tex]|x+4|=2[/tex].
Further explanation:
The equation is given as follows:
[tex]|x+4|=2[/tex]
In the above equation [tex]||[/tex] represents the modulus function.
Modulus function is defined as a function which gives positive value of the function for any real value of [tex]x[/tex].
For example: The function [tex]y=|x|[/tex] is a modulus function in which [tex]y>0[/tex] and [tex]x<0[/tex] or [tex]x>0[/tex].
In the given equation [tex]|x+4|[/tex] is a modulus expression.
There are two cases formed for [tex]|x+4|[/tex].
First case: [tex]x>-4[/tex]
If [tex]x>-4[/tex] then [tex]|x+4|\rightarrow (x+4)[/tex].
Substitute [tex]|x+4|=(x+4)[/tex] in [tex]|x+4|=2[/tex].
[tex]\begin{aligned}x+4&=2\\x&=2-4\\&=-2\end{aligned}[/tex]
Therefore, for [tex]x>-4[/tex] the value of [tex]x[/tex] which satisfies the equation [tex]|x+4|=2[/tex] is [tex]x=-2[/tex].
Second case: [tex]x<-4[/tex]
If [tex]x<-4[/tex] then [tex]|x+4|\rightarrow -(x+4)[/tex].
Substitute [tex]|x+4|=-(x+4)[/tex] in [tex]|x+4|=2[/tex].
[tex]\begin{aligned}-(x+4)&=2\\-x-4&=2\\-x&=2+4\\-x&=6\\x&=-6\end{aligned}[/tex]
Therefore, for [tex]x<-4[/tex] the value of [tex]x[/tex] which satisfies the equation [tex]|x+4|=2[/tex] is [tex]x=-6[/tex].
This implies that the solution for the equation [tex]|x+4|=2[/tex] or the value of [tex]x[/tex] which satisfies the given equation are [tex]\fbox{\begin\\\ \math x=-2\ \text{and}\ x=-6\\\end{minispace}}[/tex].
Option 1:
The number line in option 1 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
This implies that option 1 is correct.
Option 2:
The number line in option 2 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=2[/tex] and [tex]x=4[/tex].
As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
This implies that option 2 is incorrect.
Option 3:
The number line in option 3 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=2[/tex] and [tex]x=6[/tex].
As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
This implies that option 3 is incorrect.
Option 4:
The number line in option 4 shows that the solutions of the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-4[/tex].
As per our calculation made above the solutions for the equation [tex]|x+4|=2[/tex] are [tex]x=-2[/tex] and [tex]x=-6[/tex].
This implies that option 4 is incorrect.
Therefore, the number line for [tex]\fbox{\begin\\\ \bf \text{option 1}\\\end{minispace}}[/tex] represents the solution for the equation [tex]|x+4|=2[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Functions
Keywords: Functions, modulus, modulus function, number line, real line, |x+4|=2, equation, root, zeroes, solutions, absolute function, x=-6 and x=-2.
Option A is correct, the values of [tex]x[/tex] staisfying the given equation [tex]|x+4|=2[/tex] are [tex]-2[/tex] and [tex]-6[/tex].
Modulus function always returns a positive value to the equation.
Here, [tex]|x+4|[/tex] will give positive result if [tex]x>-4[/tex] and negative value if, [tex]x<-4[/tex].
Case 1: When [tex]x>-4[/tex]
According to the given equation,
[tex]|x+4|=2\\x=2-4\\x=-2[/tex]
So, the value of [tex]x[/tex] which satisfies the given equation [tex]|x+4|=2[/tex] for [tex]x>-4[/tex] is [tex]x=-2[/tex].
Case 2: When [tex]x<-4[/tex]
According to the given equation,
[tex]|x+4|=2\\-x-4=2\\x=-6[/tex]
So, the value of [tex]x[/tex] which satisfies the given equation [tex]|x+4|=2[/tex] for [tex]x<-4[/tex] is [tex]x=-6[/tex].
Hence, the values of [tex]x[/tex] staisfying the given equation [tex]|x+4|=2[/tex] are [tex]-2[/tex] and [tex]-6[/tex].
Now, according to the options, Option A is correct.
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Related Questions
[11 (y- 10)] = (4y- 5) what is y
Answers
11y-110 = 4y -5
+110 +110
11y = 4y + 105
-4y -4y
7y = 105
y= 15
Before a sale, an item’s price was $38.00. After the sale discount, the price became $32.30. What was the percent of the sale discount
Answers
Answer:
15%
Step-by-step explanation:
Before a sale, an item’s price was $38.00.
Original price, p = $38.00
After the sale discount, the price became $32.30.
After discount price, q = $32.30
Difference of sale = 38.00 - 32.30
= $5.70
% of sale distance [tex]=\dfrac{difference}{original price}\times 100[/tex]
[tex]=\dfrac{5.70}{38.00}\times 100[/tex]
[tex]=15\%[/tex]
Hence, The sale discount is 15%
Before a sale, an item’s price was $38.00. After the sale discount, the price became $32.30. The percentage of the sale discount is 15%.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
Before a sale, an item’s price was $38.00.
Original price, p = $38.00
After the sale discount, the price became $32.30.
After discount price, q = $32.30
Difference of sale = 38.00 - 32.30
= $5.70
The percent of the sale discount = difference/ original x 100
= 5.70 / 38.00 x 100
= 15%
Thus, The percentage of the sale discount is 15%.
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If a snail can move 3/10 of a meter every 1/12 hour, what is the speed of the snail, in meters per hour?
1/4
5/18
1 1/2
3 3/5
Answers
60 divided by 12 = 5
5 = 1/12 of an hour
1000 cm divided by 10 is 100 cm
3/10 so 100 + 100 + 100 = 300 cm or 3/10 of a meter
A snail can go 300 centimeters in 5 minutes.
By seeing this I can estimate my answer and that would be 1 1/2 meters in one hour
Hpe I helped
Brainliest if satisfied
would mean a lot
I take K12 by the way
The speed of the snail, in meters per hour 3 3/5 meters/hour.
Given that, a snail can move 3/10 of a meter every 1/12 hour.
We need to find the speed of the snail, in meters per hour.
What is speed?Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took. The formula for speed is Speed = Distance ÷ Time.
Now, speed = 3/10 ÷ 1/12
=3/10 × 12/1
=18/5
=3 3/5
Therefore, the speed of the snail, in meters per hour 3 3/5 meters/hour.
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The parent function of a graph is f(x) = x2. The graph shifts a units to the left and down b units. Which function models the transformed function?
A) y = x2 - a + b
B) y = (x - a)2 - b
C) y = (x + a)2 - b
D) y = (x - b)2 - a
B was incorrect, whats answer?
Answers
5,550 divide 10 to the power of 3
Answers
This would be 5.55
5550÷10^3=5.55
Hope this helps
The solution involves dividing 5,550 by 1,000, which gives 5.55. The expression 10³ represents 1,000, simplifying the division. Therefore, 5,550 divided by 10 to the power of 3 equals 5.55.
To solve the problem 5,550 divided by 10 to the power of 3, follow these steps:
First, understand that 10 to the power of 3 is equivalent to 10³.Calculate 10³: 10 × 10 × 10 = 1,000. Now, divide 5,550 by 1,000: 5,550 ÷ 1,000 = 5.55.Therefore, 5,550 ÷ 10³ = 5.55.
Define a new random variable by y = 2px. show that, as p l 0, the mgf of y converges to that of a chi squared random variable with 2r degrees of freedom by showing that
Answers
To show that the moment generating function (mgf) of a random variable y = 2px converges to that of a chi-squared random variable with 2r degrees of freedom as p approaches 0, we need to find the mgf of y using the definition of the mgf and substitute the new random variable. Then, by applying the limit as p approaches 0, we can demonstrate the convergence.
In this question, we are asked to define a new random variable, y = 2px, and show that as p approaches 0, the moment generating function (mgf) of y converges to that of a chi-squared random variable with 2r degrees of freedom.
To show this, we need to find the mgf of y by using the definition of the mgf and substituting the new random variable.
Then, as p approaches 0, we need to simplify the mgf and show that it converges to the mgf of a chi-squared random variable with 2r degrees of freedom.
By applying the limit as p approaches 0, we can demonstrate that the mgf of y converges to the mgf of a chi-squared random variable with 2r degrees of freedom.
If f(x)=-2(5)^x what is f(2)
Answers
f(2) = -2(5)²
does this equation describe a linear function
Y=2/x-28
Answers
Billy picked 18 oranges. Taylor picked 3 times as many oranges as Billy did. They want to put them in bags with 9 oranges in each bag.
How many bags will they need for all the oranges?
Answers
54/9 = 6
So, they would need 6 bags.
Martene got a small aquarium for her birthday. The aquarium is a right rectangular prism 18.5cm long by 15cm wide. Martene put 3885 cm3 of water in the aquarium. How deep is the water in the aquarium -
Answers
hope it helps
Mary bought 20 bowls and plates for $96. each bowl cost $4.50 and each plate cost $1.50 more than a bowl. she bought more bowls than plates. how many bowls and how many plates did she buy?
Answers
Let x represent the bowls and y represent the plates.
Your equations will be:
4.50x + 6y = 96
x + y = 20
We can solve this problem by either the substitution method or elimination method.
Substitution method:
1) Solve for x.
x + y = 20
x = 20 - y
2) Substitute x with 20 - y in the other equation.
4.50x + 6y = 96
4.50(20 - y) + 6y = 96
3) Distribute the outside term through the terms inside the parenthesis and simplify the rest of the equation.
90 - 4.50y + 6y = 96
90 + 1.50y = 96
1.50y = 6
y = 4
4) Now that we know the numerical value of y, solve for the numerical value of x by substituting once more.
a) x + 4 = 20
x = 16
b) 4.50x + 6(4) = 96
4.50x + 24 = 96
4.50x = 72
x = 16
*The solution is that:
Mary bought 16 bowls and 4 plates.
The top of a manhole cover is shaped like a circle. The area of the manhole cover is 380 square inches. What is the circumference of the manhole cover, to the nearest inch?
Answers
need to find the radius first
area = pi*r^2
380 = PI *r^2
380/PI = r^2
r^2 = 121
r = sqrt(121) = 11 inches
radius is 11 inches
now calculate circumference:
c = 2*PI*r
C = 2 * 3.14 * 11
circumference = 69.08 = 69 inches
How would I solve -x^2 = -36?
Answers
-x^2 = -36
Step 1: Divide both sides by -1.
-x^2/-1 = -36/-1
x^2 = 36
Step 2: Take square root.
x=±√36
x=6 or x=−6
Answer: x=6 or x=−6
I hope this helps you! :)
Audrey has $120 dollars to spend on a tennis racket and lessons. The racket costs $45 and the lessons cost $15 dollars per hour. Define a variable. The write and solve an equation to find how many hours of lessons she can afford.
Answers
15x is the variable since it is a reoccurring fee.
120 = 45 + 15x
first you subtract 45 from both sides
75 = 15x
divide both sides by 15
5 = x
so audrey can afford 5 hours of lessons
i hope this helps!!
At tennis practice, Tim practices his backhand and his serve at least 2 hours each day. He works less on his backhand than his serve and practices his serve more than 1/2 hour daily.
Which system of inequalities represents Tim’s daily tennis practice if x represents the number of hours spent practicing his backhand and y represents the number of hours practicing his serve?
The images below are the possible answers,
Answers
x+y≥2
He practices his backhand(x) LESS THAN(<) his serves(y)
x<y
He practices his serves(y) MORE THAN(>) .5 hours
y>.5
Answer:
[tex]\left\{\begin{matrix}x+y\geq 2\\ x< y\\ y> \frac{1}{2}\end{matrix}\right.[/tex]
Step-by-step explanation:
Let x represents the number of hours spent practicing his backhand
Let y represents the number of hours practicing his serve.
Since we are given that Tim practices his backhand and his serve at least 2 hours each day i.e. he practices his backhand and serves for two hours or more than two hours
⇒ x+y≥2 --(a)
We are also given that He works less on his backhand than his serve
⇒x < y --(b)
And we are also given that he practices his serve more than 1/2 hour daily.
⇒ y > 1/2 --(c)
Thus the inequalities are :
[tex]\left\{\begin{matrix}x+y\geq 2\\ x< y\\ y> \frac{1}{2}\end{matrix}\right.[/tex]
Thus the Option C is correct .
If it takes 4 men 6 hours to repair a road, How long will it take 7 men to do the job if they work at the same rate ?
Answers
now, how long will it take for 7 men working at the same rate?, 24/7 <--- that many hours.
the division will give how long each man worked, and since it will be the same amount for each, that many hours it took for the whole job being done by the 7 of them.
[tex]\bf \cfrac{24}{7}\implies 3\frac{3}{7}\implies \textit{about 3 hours 25 minutes and 43 seconds}[/tex]
in february,Robbins and Myers,Inc.executed a 2-for-1 split.janine had 470 shares before the spilit.each share was worth $69.48. A.how many shares did she hold after the split? B.what was the post-split price per share? C.show that the split was a monetary non-event for janine?
Answers
Janine held 940 shares after the split. The post-split price per share was $34.74. The split was a monetary non-event as the total value of Janine's shares remained the same.
Explanation:A 2-for-1 split means that for every one share of stock owned, an investor receives two shares in return. In this case, Janine had 470 shares before the split. After the split, she would have 470 x 2 = 940 shares.
The pre-split price per share was $69.48. Since the split was 2-for-1, the post-split price per share would be $69.48 / 2 = $34.74.
To show that the split was a monetary non-event for Janine, we can calculate the total value of her shares before and after the split. Before the split, Janine's shares were worth 470 x $69.48 = $32,621.60. After the split, her 940 shares would be worth 940 x $34.74 = $32,621.60. Therefore, the total value of her shares remained the same.
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How do you construct a line segment perpendicular to the segment given through the point given?
Answers
3.4−2.8d+2.8d−1.3 Combine like terms to simplify the expression
Answers
answer
After 2 months on a diet, John’s weight dropped from 168 pounds to 147 pounds. By what percent did John’s weight drop?
Answers
Final answer:
John's weight dropped by 12.5%.
Explanation:
To calculate the percent by which John's weight dropped, we need to find the difference between his initial weight and final weight, and then divide that difference by his initial weight. We can then multiply the result by 100 to express it as a percentage.
Initial weight = 168 pounds
Final weight = 147 pounds
Difference = 168 - 147 = 21 pounds
Percent drop = (Difference / Initial weight) x 100
Percent drop = (21 / 168) x 100 = 12.5%
Therefore, John's weight dropped by 12.5%.
Final answer:
To calculate the percent by which John's weight dropped, subtract his final weight from his initial weight, and divide the difference by his initial weight, then multiply by 100. John's weight dropped by 12.5%.
Explanation:
To calculate the percent by which John's weight dropped, you need to find the difference between his initial weight and his final weight, then divide that difference by his initial weight and multiply by 100.
Difference in weight = Final weight - Initial weight = 147 - 168 = -21 Percent weight drop = (Difference in weight / Initial weight) * 100 = (-21 / 168) * 100 = -12.5%So, John's weight dropped by 12.5%.
What is the percent increase of 2826 to 3324?
Answers
You will get the decimal 1.17622 etc.
round to the nearest thousandths place 1.18%
The answer is provided in the image attached.
Have a great day!
At 1 P.M., there were 16 seagulls on the beach. At 3p.m., there were 40 seagulls. What is the constant rate?
Answers
24 birds in 2 hrs = 24/2 = 12 birds per hr....ur constant rate is 12 per hr
Please help and show all work.
Answers
1. Since r and t are each perpendicular to s, angles 1 and 5 are right angles and therefore are congruent corresponding angles. Since two lines cut by a transversal are parallel if the corresponding angles are congruent, lines r and t are parallel.( make sure you re word this some)
2. No, they will not be parallel because in order to form a 90 degree angle on each corner (to allow the sides to be parallel to each other), the angles have to add up to 90 degrees. When you add 37 degrees to 50 degrees, you are left with 87 degrees, which means that they will ever so slightly tilt away from each other, therefore not being parallel.
Find the measure of Angle 1
Answers
so
m<1 = m<66
Answer:
66º
Step-by-step explanation:
From the picture we know that AB║CD. Therefore, the line BD is a transversal line between two parallels.
We know that in these cases, the alternate interior angles are the same.
In the picture, angle 1 and the angle that measures 66º are alternate interior angles. Therefore, angle 1 measures 66º as well.
∠1 = 66º
Show why the function f(x) = 3rad x is not differentiable at x=0
Answers
[tex]f'(x) = -\frac{3}{2\sqrt{x}}[/tex]
When x = 0, f'(0) becomes undefined. Thus, we know that there is no derivative at x = 0. You could also show it by taking the limits, which is the fundamental of calculus. Show that as x approaches 0 from the negative side is not equal to the value as x approaches 0 from the positive side.
What this tells us is that there is no uniquely distinct point that satisfies the continuity of the curve in order for the graph to have a specific gradient at x = 0; thus, this means there is no gradient at x = 0, and hence, the function is not differentiable at x = 0
The revenue from selling x shirts is r(x) = 15x.
The cost of buying x shirts is c(x) = 7x + 20.
The profit from selling x shirts is p(x) = r(x) – c(x).
What is p(x)?
A. p(x) = 22x – 20
B. p(x) = 22x + 20
C. p(x) = 8x – 20
D. p(x) = 8x + 20
Answers
The answer would be...
C. p(x) = 8x-20
The profit function, p(x) is the difference between the revenue and cost function of the shirt sales, Hence, the profit function is 8x - 20
Given the Parameters :
Revenue function, R(x) = 15x Cost function, C(x) = 7x + 20The profit function can be expressed thus ::
Revenue function - Cost FunctionP(x) = R(x) - C(x)
P(x) = 15x - (7x + 20)
P(x) = 15x - 7x - 20
P(x) = 8x - 20
Therefore, the profit function is 8x - 20.
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what is w reduced by 22? f(w)=
Answers
So, to every w-value corresponds a value equal to w - 22.
Using the notation of functions, w is the independent variable or input and f(w) is the function that returns the dependent value or output:
inpunt otuput
w f(w) = w - 22
Answer: f(w) = w - 22
WHO IS GOOD AT MATH!!!!! Solve this problem.
326-9²+32= ?
Answers
20 less than 5 times a number
Answers
Let the number be [tex]x[/tex]
The expression would be [tex]5x - 20 [/tex]
Hope this helps!
Have a great day!
What is the doubling time of prices which are increasing by 7 percent per year?
Answers
About 14 years and 4 months
Since it is doubling, it must increase by 100%.
100 divided by 7 = 14.28
The doubling time of prices increasing at a rate of 7% per year can be calculated using the Rule of 70, which states that the doubling time of a variable undergoing exponential growth is approximately 70 divided by the growth rate. Thus, the doubling time for these prices would be about 10 years.
Explanation:The question pertains to the concept of doubling time in the field of finance and economics, specifically how quickly something (prices, in this case) doubles in size or value at a constant growth rate. The doubling time for a variable growing at a 7% annual growth rate can be calculated using the Rule of 70. This rule states that the doubling time of a variable undergoing exponential growth is approximately 70 divided by the growth rate (in this case, 7).
So, to calculate:
Doubling Time = 70 / 7
Doubling Time = 10 years
This means that the prices will double approximately every 10 years if they increase at a constant rate of 7% per year.
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