Which of the following are solutions to the following solutions to the following solutions?
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We have to find the solutions to the equation:
[tex]|x+4|=8[/tex]The absolute value function is in fact a piecewise function, so it may have two solutions.
We consider for the first solution that the argument inside the absolute function is positive, that is x + 4 > 0. Then, we will have:
[tex]\begin{gathered} x+4=8 \\ x=8-4 \\ x=4 \end{gathered}[/tex]Now, we consider that the the argument is negative and is made positive by the absolute value function (it will shift the sign, which can be represented by a multiplication by -1). This means that x + 4 < 0, and the solution will be:
[tex]\begin{gathered} -(x+4)=8 \\ -x-4=8 \\ -x=8+4 \\ -x=12 \\ x=-12 \end{gathered}[/tex]We can see it in a graph as:
Answer: the solutions are x = 4 and x = -12.
Related Questions
Which of the following inequalities would have solutions of -1, 1, 3, 4?Mark all that apply.A e > -1Bf <6c d < 4Db> -1EC < 5Fa> 0
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Notice that for option B
f< 6 means that all numbers less than 6 are solution to the inequality, also notice that -1,1,3 and 4 are less than 6.
An analogous reasoning apllies for option E, all numbers less than 5 are solution to the inequality c<5 then -1,1,3 and 4 are solution.
For the rest of the inequalities at least one of the provided numbers are no solution for the inequality.
a student teacher is given a guideline that a student should be able to finish a 32 question test in 28 minutes if the student teacher is planning to give a test that contains 160 questions and the average students complete question of the same rate as previously State how many minutes should you plan for the average student to complete the test.
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since the student do 32 questions in a time of 28 minutes, then the rate of response is 32/28=8/7 questions/minute ,then the students will be able to complete 160 questions in 20(7)= 140 minutes
simplify x⁹ divided by x^5
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Answer:
[tex]x^{4}[/tex]
Step-by-step explanation:
Whenever it comes to the division of the same variable, we subtract their powers in order to get the correct answer:
[tex]x^{9}/x^{5}[/tex]
[tex]x^{9-5}[/tex]
[tex]x^{4}[/tex]
Chloe's car used 15 gallons to travel 570 miles. How many gallons of gas would she need to travel 380 miles?
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Answer:
10
Step-by-step explanation:
I divided 570 by 15 to see how many miles she can travel per gallon of gas which came out to be 38.
After that i divided the 380 by the 38. 380÷38 is 10.
Answer:
Need:
10 gallons
Step-by-step explanation:
Proportions:
15 gallons ⇒ 570 miles
A gallons ⇒ 380 miles
A = 15gallons * 380miles / 570miles
A = 10 gallons
two integers a and b have a product of 36 what is the least possible answer
Answers
Answer:
the answer is 12
Step-by-step explanation:
In short, a = 6 and b = 6. We can make a table of various values to help confirm that 12 is the smallest sum.
Answer: 1
Step-by-step explanation: 1 is the least possible answer because an integer is any number and 1x36 would be the least possible answer for the product.
The function g is defined as follows for the domain given g(x) = 3x - 2 , omain = \{- 2, - 1, 0, 1\} Write the range of g using set notation. Then graph g
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Given: The function below
[tex]\begin{gathered} g(x)=3x-2 \\ Domain:\lbrace-2,-1,-0,1\rbrace \end{gathered}[/tex]To Determine: The range and the graph of g
Solution
The range is as given below
[tex]\begin{gathered} x=-2 \\ g(-2)=3(-2)-2=-6-2=-8 \\ x=-1 \\ g(-1)=3(-1)-2=-3-2=-5 \end{gathered}[/tex][tex]\begin{gathered} x=0 \\ g(0)=3(0)-2=0-2=-2 \\ x=1 \\ g(1)=3(1)-2=3-2=1 \end{gathered}[/tex]Hence, the range is
{-8, -5, -2, 1}
Let us form a table showing the domain(x) and the range (g(x))
Let us use the table to plot graph of the domain(x) against the range(g(x)) as below
Compute the square root of 532 to the nearest tenth. Use the "divideand average method.
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ANSWER:
[tex]\sqrt[]{532}\cong23.065[/tex]STEP-BY-STEP EXPLANATION:
We have the following square root
[tex]\sqrt[]{532}[/tex]We calculate by means of the divide and average method.
The first thing is to look for exact roots between those two values
Step 1 estimate
[tex]\begin{gathered} \sqrt[]{539}<\sqrt[]{532}<\sqrt[]{576} \\ 23<\sqrt[]{532}<24 \\ \text{Estimate 23.5} \end{gathered}[/tex]Step 2 divide
[tex]\frac{532}{23.5}=22.63[/tex]Step 3 average:
[tex]\frac{23.5+22.63}{2}=\frac{46.13}{2}=23.065[/tex]Therefore:
[tex]\sqrt[]{532}\cong23.065[/tex]You need to measure the depth of a large lake. Since the sonar equipment is very expensive, you decide to use your friend's boat. The boat has an anchor on a 100 ft line. You take the boat out to the middle of the lake on a
windy day. You drop the anchor and let the wind push the boat until the anchor line is tight. Your GPS tells you that the boat has moved 82 feet. Assuming the bottom of the lake is flat, what is the depth of the lake?
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Using the Pythagorean Theorem, the depth of the lake is 57.24 feet.
What is the depth?According to the Pythagorean Theorem, the depth or height is the difference between the squared root of the hypothenuse and the base.
The Pythagorean Theorem Formula is as follows:
a² + b² = c²
Where:
a = side of the right triangle (height, depth, or perpendicular)
b = side of the right triangle (the base)
c = hypotenuse (the longest part or hypothenuse)
Therefore, the depth is:
a² = c² - b²
a² = 100² - 82²
a² = 10,000 - 6,724
a² = 3,276
a = √3,276
a = 57.24
= 57.24 feet
Thus, assuming a flat-bottom lake, its depth is 57.24 feet.
Learn more about the Pythagorean Theorem at https://brainly.com/question/343682
#SPJ1
Word Problems: Define your variable, write and solve the equation. 9. You have $75 to spend at the grocery store. You get $23 in change. How much money do you spend? Define your variable: Equation: Answer:
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ANSWER
Variable : how much money was spent (x)
Equation: x + 23 = 75
Answer: $52
EXPLANATION
Let the variable (amount of money spent) be x.
Initially, you had $75 and you spend some money (x) and you are left with $23 in change.
This means that the sum of the money you spent and the change you received is $75.
That is:
x + 23 = 75
That is the equation.
To find how much money you spent, we have to find the value of x by collecting like terms:
=> x = 75 - 23
x = $52
You spent $52.
Find the domain of the function represented by the list of ordered pairs
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The domain of a function is always represented by the values of X. In the ordered pair, they are always the first value of the pair.
The domain is the first number of each pair.
Domain: {-1, -10, 8, 6}.
Jackson deposited $160 a month into an account earning 7.2% compounded monthly for 12 years. He left the accumulated amount for another 3 years at the same interest rate. How much total interest did he earn?
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Using the formula for the compound interest, we have:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{ A:amount,P:principal,r:rate,n: number of times interest is compounded per year,t:time in years.} \\ A=160(1+\frac{0.072}{12})^{12\cdot15}\text{ (Replacing the values)} \\ A=160(1+0.006)^{180}\text{ (Dividing and multiplying)} \\ A=160\cdot2.935\text{ (Adding and raising the result to the power of 180)} \\ A=469.63\text{ (Multiplying)} \\ \text{Interest}=\text{ Amount - Principal=469.63}-160=309.63 \\ \text{The answer is \$309.63} \end{gathered}[/tex]Round to the nearest thousand.52.60552,605 rounded to the nearest thousand is
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Find the equation of the axis of symmetry of the following parabola using graphingtechnology.y = x^2 – 8x + 32
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Explanation:
If we graph this parabola we can see the vertex at point (4, 16)
The axis of simmetry is a vertical line that passes through the vertex of the parabola.
Any vertical line's equation is:
[tex]x=a[/tex]'a' is any value of x.
Answer:
The equation of the axis of simmetry is x = 4
One-third of a number b multiplied by -11 is more than 3 2
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reduce 45/10 to halves
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5. (a) The table below shows the cumulative frequency distribution of the weight of 80 deer recorded by the zookeeper. Weight, w kg Cumulative Frequency 6 15 61-80 36 niger 81-100 58 y Determine the upper class boundary for the class 21-40. Determine the class width for the class 41-60. How many deer were recorded in the class 81-100. (iv) A deer was chosen at random from the 80 deer. What is the probability that the weight of the deer is more than 100.5 kg. Leave your answer as an EXACT value. [2]
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STEP - BY - STEP EXPLANATION
What to find?
• The upper class boundary for the class 21 - 40
,• Class width for 41 - 60
,• The number of deer recorded in the class 81 - 100
Given:
(i) To find the class boundary for the class 21 - 40, we will first subtract 0.5 from 21 and then add 0.5 to 40.
That is;
20.5 - 40.5
Hence, the upper class boundary is 40.5
(ii) The class width for the class 41 - 60
The class width can be determine by subtracting 41 from 60.
That is;
[tex]60-41=19[/tex]Hence, class width = 19
(iii) Number of deer recorded in the class 81 - 100
This can be obtain by subtracting the cumulative frequency in the class from the cumulative frequency before it.
58 - 36 =22
Hence, we have 22 numbers of deer in the class 81 - 100.
(iv) A deer was chosen at random from the 80 deer. What is the probability that the weight of the deer is more than 100.5 kg.
We can solve this by first determining the number of deer that are above 100.5 kg.
Number of beer above 100.5 kg = 15 + 7 = 22
Total number of deer = 80
[tex]Probability=\frac{required\text{ outcome}}{all\text{ possible outcome}}[/tex][tex]=\frac{22}{80}[/tex][tex]=\frac{11}{40}[/tex]ANSWER
(i) 40.5
(ii) 19
(iii) 22
(iv) 11/40
The average number of moves a person makes in his or her lifetime is 12 and the standard deviation is 3.1. Assume that the sample is taken from a large population and the correction factor can be ignored. Round the final answers to four decimal places and intermediate z value calculations to two decimal places.Find the probability that the mean of a sample of 25 people is less than 10.Find the probability that the mean of a sample of 25 people is greater than 10.Find the probability that the mean of a sample of 25 people is between 11 and 12.
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The z-score is given by the following formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where x is the data point, μ is the mean, and σ is the standard deviation.
First
well I'm stuck on this homework question and need help please thank you
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15. x=m<1=I'll upload a picture of my HW
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Opposite angles are the same
Then:
[tex]\begin{gathered} 6x+4=8x\text{ - }18 \\ 18+4=8x\text{ -}6x \\ 22=\text{ 2x} \\ x=\text{ 22/2} \\ x=11 \end{gathered}[/tex]So: (Remember the line has a 180º degrees
y varies inversely as x. y = 18 when x = 7. Find y when x = 3.y=(Simplify your answer.)
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Which is the equation of the line that passes through the points (-4, 8) and (1, 3)?A. Y=x+4B. Y=-x+12C. Y=-x+4D. Y=x+12
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In order to find the equation that passes through both points, we can use the slope-intercept form of the linear equation:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Using the given points on this equation, we have:
[tex]\begin{gathered} (-4,8)\colon \\ 8=m\cdot(-4)+b \\ b=8+4m \\ \\ (1,3)\colon \\ 3=m+b \\ 3=m+8+4m \\ 5m=3-8 \\ 5m=-5 \\ m=-1 \\ b=8+4\cdot(-1)=8-4=4 \end{gathered}[/tex]Therefore the equation is y = -x + 4 (correct option: C)
Please see photo checking my work I think it is all the students attending the college
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Answer:
A population is the entire group that you want to draw conclusions about.
So, in this exercise, the population is all the students attending the college.
Ethan and Evan are twins. They each deposit $3,000 into separate bank accounts.Their accounts each accrue interest annually as shown in the tables below.
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Part A.
Ethan's account can be model as a linear equation since it is increasing at a constant rate of the form:
[tex]y=240x+3000[/tex]And Evan's account can be model as a exponential equation of the form:
[tex]y=3000(1.08)^x[/tex]Part B:
Evaluate the 1st and 2nd equation for x = 5:
[tex]\begin{gathered} y=240(5)+3000=4200 \\ y=3000(1.08)^5=4407.98 \\ so\colon \\ \frac{4407.98}{4200}=1.05 \end{gathered}[/tex]It would be 1.05 higher
How do I use the calculator to find log10 6, to 3 decimal places please?
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Your calculator uses base 10 for its logs
There should be a button that says log
That is a base 10 log
log 6 = .77815125
To 3 decimal places
log 6 = .778
The base 10 is implied
The drama club was selling ticketsto the school play. Adult ticketscost $8.00 each, and studenttickets cost $5.00 each. The littletheater holds 142 people and wassold out for both Friday andSaturday. The total sales for thetwo days was $1,948.00.1. How many adult tickets weresold out over the two days?2. How many student tickets weresold out over the two days?
Answers
We are given a problem that can be solved using a system of linear equations. Let A, be the number of adults, and S the number of students. Since there are in total 142 people and there were two days, this means that the sum of the number of adults and the number of students must be 284, which can be written mathematically as follows:
[tex]A+S=284,(1)[/tex]This is our first equation. The second equation is found using the total sales of $1948. Since the ticket per adult is $8 and per student is $5, we have the following equations:
[tex]8A+5S=1948,(2)[/tex]To solve this equation we will solve for A in equation (1), by subtracting S to both sides;
[tex]\begin{gathered} A+S-S=284-S \\ A=284-S \end{gathered}[/tex]Now we will replace this value in equation (2):
[tex]8(284-S)+5S=1948[/tex]Now we will apply the distributive property:
[tex]2272-8S+5S=1948[/tex]Addins like terms:
[tex]2272-3S=1948[/tex]Subtracting 2272 to both sides;
[tex]\begin{gathered} 2272-2272-3S=1948-2272 \\ -3S=-324 \end{gathered}[/tex]Dividing both sides by -3:
[tex]S=-\frac{324}{-3}=108[/tex]Now we replace this value in equation (1), where we have already solved for A:
[tex]\begin{gathered} A=248-108 \\ A=140 \end{gathered}[/tex]Therefore, there were sold 108 student tickets and 140 adult tickets.
In 1990, there were 1330 registered alpacas in the United States. By summer of 2000, there were 29,856. What was the percent of increase in registered alpacas?
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answer - 214% increase
explanation
formula = big number - small number ÷ original number
29856 - 1330 = 28,526 ÷ 1330 = 21.45
21.45 to percent = 214% then if rounded to nearest
Graph the inequality and give interval notation for the solution. Use two o's (as in octopus) forinifinity and a U for union as needed.-- 5x + 4 >I 19 OR – 22 - 15 – 3-8 -7 -6 -5-4-3-2-] 022345678Clear All Draw:Interval notation for the above inequality and graph is
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- 5x + 4 > 19
1st step let us move 4 to the other side by subtracting both sides by 4
- 5x + 4 - 4 > 19 - 4
- 5x > 15
2nd step is move - 5 to the other side by dividing both sides by -5, BUT when we divide the sides of an inequality by a negative number we must reverse the sign of inequality
[tex]\frac{-5x}{-5}<\frac{15}{-5}[/tex]x < -3
The solution is all values smaller than -3
On the number, line draw an empty circle at -3 then draw from it an arrow pointing to the left ( - ve infinity)
The solution is {x : x < -3} or (-00, -3)
Round 13.134 to the nearest tenth.
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Answer: 13.1
13.1
Rounded to the nearest 0.1 or
the Tenths Place.
Explanation:
13.134
You rounded to the nearest tenths place. The 1 in the tenths place rounds down to 1, or stays the same, because the digit to the right in the hundredths place is 3.
13.1
When the digit to the right is less than 5 we round toward 0.
13.134 was rounded down toward zero to 13.1
Write the equation of each line in slope intercept form (see attached)
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As we can see we have a horizontal line, the slope of the horizontal line is zero
the form of the equation of the line in slop-intercept form is
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
In our case m=0
[tex]\begin{gathered} y=(0)x+b \\ y=b \end{gathered}[/tex]in this case the y-intercept is b=-4
Therefore the equation is
[tex]y=-4[/tex]ANSWER
y=-4
Which fraction is represented by point A on the numb 0 -1 O- 1 4. 4 1 1
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The fraction that represent the point A is -1/4.
Since there are 4 divition in between -1 and 0.
Thus the length of one division is,
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