Solve each of the following equations. Show its set on a number line. |4x-4(x+1)|=4
Answers
Solving this equation, we have:
[tex]\begin{gathered} |4x-4\mleft(x+1\mright)|=4 \\ |4x-4x-4|=4 \\ |-4|=4 \\ 4=4 \end{gathered}[/tex]Since the final sentence is always true, the solution set is all real numbers.
Showing it in the number line in blue, we have:
Related Questions
write an algebraic model for the statement then solve the model the sum of a number and -9 is -21
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Answer:
[tex]x + ( - 9) = - 21[/tex]
[tex]x - 9 = - 21[/tex]
[tex]x = - 12[/tex]
Write the equation of a line containing (3,-7) that is parallel to the line given by the equation -4x+8y=3
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Two lines are parallel is they have the same slope. In this case:
[tex]-4x\text{ + 8y = 3}[/tex]Solving the equation for y, and obtaining the slope-intercept equation for the line equation, we have:
[tex]8y\text{ = 3 + 4x}[/tex][tex]y\text{ = }\frac{3}{8}\text{ + }\frac{4}{8}x[/tex]Then,
lan is working two summer jobs, making $19 per hour lifeguarding and making $9per hour clearing tables. In a given week, he can work no more than 14 total hoursand must earn a minimum of $180. If x represents the number of hours lifeguardingand y represents the number of hours clearing tables, write and solve a system ofinequalities graphically and determine one possible solution.Inequality 1: y 24plot switch shadeInequality 2: y 24plotswitch shade2019181716151413121110Yes
Answers
Given:
Lan is working two jobs:
1) $19 per hour life guarding
2) $9 per hour clearing tables
The total hours per week = 14
He must earn a minimum of $180
Let x represents the number of hours life guarding and y represents the number of hours clearing tables
So, we have the following inequalities
[tex]\begin{gathered} x+y\le14 \\ 19x+9y\ge180 \end{gathered}[/tex]We need to solve the inequalities by graph
So, we will graph the lines: x + y = 14 and 19x + 9y = 180
The shaded area represents the solution of the system of inequalities
The following figure represents the solution of the system of inequalities
Can someone please help me on this question, I'm a little stuck? The question should be down below!
Answers
We have a right triangle with a missing side.
When we have two sides given sides on the right triangle and we need to find the missing side, we use the Pythagoras theorem:
The formula is given by:
[tex]a^2=b^2+c^2[/tex]Where:
a = Hypotenuse
b= Opposite side
c= Adjacent side
Now, we need to label the sides of the given triangle:
The largest side, represents the hypotenuse, in this case, a=15m.
The adjacent side is between the 90 degrees angle and the hypotenuse, in this case, c = 9m
Therefore, the missing side is the opposite side, let set b for this side:
Replacing these values:
[tex](15m)^2=b^2+(9m)^2[/tex][tex]225=b^2+81[/tex]Solve the equation for b:
[tex]225-81=b^2[/tex][tex]144=b^2[/tex][tex]\sqrt[]{144}=\sqrt[]{b^2}[/tex]Therefore, the missing side:
[tex]12=b[/tex]
What is the area in square feet ( of the rectangle) of 4 3/4 feet and 6 4/5 feet
Answers
Recall the area of a rectangle is determined by the formula
[tex]\begin{gathered} A_{\text{rectangle}}=lw \\ \text{where} \\ l\text{ and }w\text{ are the dimensions of the rectangle} \end{gathered}[/tex]Given the following
w = 4 3/4 ft
l = 6 4/5 ft
Convert the following given into improper fraction first
[tex]\begin{gathered} w=4\frac{3}{4}\text{ ft}\Longrightarrow w=\frac{19}{4}\text{ ft} \\ l=6\frac{4}{5}\text{ ft }\Longrightarrow l=\frac{34}{5}\text{ ft} \end{gathered}[/tex]Next, substitute those values to the given formula for solving the area of the rectangle
[tex]\begin{gathered} A=lw \\ A=\frac{34}{5}\text{ ft}\cdot\frac{19}{4}\text{ft} \\ A=\frac{646}{20}\text{ ft}^2 \\ \text{Convert the final answer back into mixed fractions} \\ A=\frac{646}{20}\text{ ft}^2\Longrightarrow A=32\frac{3}{10}\text{ ft}^2 \\ \\ \text{Therefore, the area of the rectangle is} \\ 32\frac{3}{10}\text{ ft}^2 \end{gathered}[/tex]A road sign is in the shape of a regular pentagon. What is the measure of each angle on the sign? Round to the nearest tenth. 540 252 54 Od 108
Answers
Internal angles of a polygon
The triangle has n=3 sides, and the sum of its internal angles is 180°
The rectangle has n=4 sides, and the sumo of its internal angles is 360°
There is a general formula to calculate the sum of the internal angles of any polygon of n sides:
Sum = 180° ( n -2 )
For a pentagon (n=5), the sum of angles is:
Sum = 180° ( 5 -2 ) = 180° * 3 = 540°
We are required to find the measure of each internal angle. Since the pentagon is regular, all of its internal angles measure the same, thus:
The measure of each angle = 540° / 5 = 108°
Can you please help me out with a question
Answers
AS shown in the figure:
The measure of arc RT = 27
The measure of arc FN = 105
The measure of angle FUN will be as follows:
[tex]m\angle\text{FUN}=\frac{1}{2}(105+27)=\frac{1}{2}\cdot132=66[/tex]So, the answer is option C. 66
Triangle ABC has vertices at A(−4, 3), B(0, 5), and C(−2, 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units down. A′(−4, −1), B′(0, 1), C′(−2, −4) A′(−4, 7), B′(0, 9), C′(−2, 4) A′(0, 3), B′(4, 4), C′(3, 0) A′(−8, 7), B′(−4, 9), C′(−6, 4)
Answers
Given:
The triangle is ABC
Vertices of ABC is
[tex]\begin{gathered} A=(-4,3) \\ \\ B=(0,5) \\ \\ C=(-2,0) \end{gathered}[/tex]Find-:
The vertex after 4 units down
Explanation-:
The triangle is down, which means changing the coordinates of the y-axis
The y axis reduce by 4 units, then coordinates is
[tex]\begin{gathered} A=(-4,3) \\ \\ A\rightarrow A^{\prime} \\ \\ A^{\prime}=(-4,(3-4)) \\ \\ A^{\prime}=(-4,-1) \end{gathered}[/tex]The B' is
[tex]\begin{gathered} B=(0,5) \\ \\ B^{\prime}=(0,(5-4)) \\ \\ B^{\prime}=(0,1) \end{gathered}[/tex]The C' is
[tex]\begin{gathered} C^{\prime}=(-2,(0-4)) \\ \\ C^{\prime}=(-2,-4) \end{gathered}[/tex]So, the new coordinates are
[tex]\begin{gathered} A^{\prime}(-4,-1) \\ \\ B^{\prime}(0,1) \\ \\ C^{\prime}(-2,-4) \end{gathered}[/tex]I tried it and got imaginary numbers in the answer.
Answers
Given the following equation:
[tex]\frac{x}{x-4}-\frac{4}{x}=\frac{3}{x-4}[/tex]First, we will identify the zeros of the denominator
So, the zeros are: x = {0,4}
Second, multiply the equation by x(x-4) to eliminate the denominators
[tex]x(x-4)*(\frac{x}{x-4}-\frac{4}{x})=x(x-4)*\frac{3}{x-4}[/tex]Simplify the equation:
[tex]x^2-4(x-4)=3x[/tex]Expand the equation and combine the like terms:
[tex]\begin{gathered} x^2-4x+16=3x \\ x^2-7x+16=0 \end{gathered}[/tex]The last quadratic equation will be solved using the quadratic rule:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Substitute a = 1, b = -7, c = 16
[tex]\begin{gathered} x=\frac{7\pm\sqrt{(-7)^2-4(1)(16)}}{2(1)} \\ \\ x=\frac{7\pm\sqrt{-15}}{2}=\frac{7\pm i\sqrt{15}}{2} \\ \\ x=\lbrace\frac{7+i\sqrt{15}}{2};\frac{7-i\sqrt{15}}{2}\rbrace \end{gathered}[/tex]So, the answer will be:
[tex]x=\lbrace\frac{7+i\sqrt{15}}{2};\frac{7-i\sqrt{15}}{2}\rbrace[/tex]need help with excerise step by step been 20 year's
Answers
Given:
Standard deviation
[tex]\sigma=5.18[/tex]Mean
[tex]\mu=129[/tex]Required:
Find the longest braking distance one of these cars could have and still in the bottom.
Explanation:
The z-score formula is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substitute the given values and find the value of z.
[tex]z=\frac{x-129}{5.18}[/tex]This is the first percentile which is X when Z has a p-value of 0.01, so z = -2.327.
[tex]\begin{gathered} -2.327=\frac{x-129}{5.18} \\ x-129=-2.327(5.18) \\ x-129=-12.054 \\ x=129+12.054 \\ x=116.946\text{ ft} \end{gathered}[/tex]Final answer:
The longest braking distance one of these cars could have and still in the bottom 1% is 116.946 ft.
A health club charges a one time initiation fee of $120.00 plus a membership fee of $30.00 per month. a. Write an expression for the cost function C(x) that gives the total for membership at the health club for x months. b. Draw a graph of the function in (a).c. The health club decided to give it's member an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, use a different color and draw on the same set of axes the cost graph under the plan. d. Determine after how many months the second plan is less expensive for the member. a. C(x) = _______ (Do not factor)
Answers
a.
Given that a health club charges a one-time initiation fee of $120.00 plus a membership fee of $30.00 per month.
The total cost will be equal to the fixed one-time charge plus the charge per month times the number of months.
It can be represented by the expression C(x);
[tex]C(x)=120+30x[/tex]b.
Graphing of the function, we would have;
c.
If the health club decided to give its members an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, we will have the function as;
[tex]F(x)=420+10x[/tex]graphing the above function, we have;
the first plan is represented by the blue line while the second plan is represented by the red line.
d.
The number of months after which the second plan is less expensive is the value of x when the two lines meet.
the two lines meet at point;
[tex](15,570)[/tex]The value of the x coordinate is 15.
So, The number of months after which the second plan is less expensive is
[tex]15\text{ months}[/tex]the jar's inner dimensions are approximately a rectangular prism with dimensions of 14cm by 12cm by 28cm. George estimates that the lowest amount of marbles possible to fill the jar 225 marbles and the highest amount is approximately 489 marbles. what is the reasonable lower limit and upper limit for the amount of marbles in the jar according to Fermi?
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Given: the dimensions of the rectangular prism is 14 x 12 x 28 in cm
Triangle ABC is shown with exterior ∠z.
Determine m∠z.
49°
97°
131°
146°
Answers
Answer:
(c) 131°
Step-by-step explanation:
Given exterior angle z of a triangle with remote interior angles 97° and 34°, you want the measure of angle z.
Remote interior anglesAn exterior angle is equal to the sum of the remote interior angles.
Applicationz = 97° +34°
z = 131°
CS 18 and 105 calories in each juice box The rules for two horseback riding packages are shown below. Go Galloping Horseback Rides $6 equipment fee plus S10 per hous hours horseback riding and let yepresent the total cost of the package. Write a system of equations to represent this situation let x represent the number of Lucky Horseshoe Stables $12 equipment fee plus hour 259 Calories What is the solution to the system of equations? What does the solution represent?
Answers
8A) Let x represent the number of hours of horseback riding.
Let y represent the total cost of the package
If Lucky horseshoe stables is used for x hours, the equation for the total cost would be
y = 7x + 12
If Go galloping horseshoe rides is used for x hours, the equation for the total cost would be
y = 10x + 6
Thus, the equations are
y = 7x + 12
y = 10x + 6
B) To solve the system of equations, we would substitute the first equation into the second equation. It becomes
7x + 12 = 10x + 6
10x - 7x = 12 - 6
3x = 6
x = 6/3
x = 2
y = 7x + 12 = 7 * 2 + 12
y = 14 + 12
y = 26
The solution of the system of equations is (2, 26)
the line AB is drawn on the grid.(i) Write down the coordinates of A
Answers
The coordinate of point A = (0, 1)
Explanation:Given:
the line AB is drawn on the grid
To find:
the coordinates of A
The coordinates of a point is in the form: (x, y)
To determine the coordinates of A, we will trace the y axis and x-axis.
At point A, x = 0, y = 1
The coordinate of point A = (0, 1)
15) If x and y satisfy both 9x + 2y = 8 and 7x + 2y = 4, then y =? * Hint: Use the elimination method to solve this system of equations
Answers
For the information given in the statement you have
[tex]\begin{cases}9x+2y=8\text{ (1)} \\ 7x+2y=4\text{ (2)}\end{cases}[/tex]Using the elimination method, multiply by -1 the equation (2) and then add the equations to eliminate one of the variables
[tex]\begin{cases}9x+2y=8\text{ (1)} \\ 7x+2y=4\text{ (2)}\cdot-1\end{cases}[/tex][tex]\begin{gathered} \begin{cases}9x+2y=8\text{ (1)} \\ -7x-2y=-4\text{ (2)}\end{cases} \\ ------------- \\ 2x+0y=4 \\ 2x=4 \\ \text{ Divide by 2 on both sides of the equation} \\ \frac{2x}{2}=\frac{4}{2} \\ x=2 \end{gathered}[/tex]Now plug the value of x found into any of the initial equations to find the value of y. For example in equation (1)
[tex]\begin{gathered} 9x+2y=8 \\ 9(2)+2y=8 \\ 18+2y=8 \\ \text{ Subtract 18 on both sides of the equation} \\ 18+2y-18=8-18 \\ 2y=-10 \\ \text{ Divide by 2 on both sides of the equation} \\ \frac{2y}{2}=\frac{-10}{2} \\ y=-5 \end{gathered}[/tex]Therefore, the solutions of the system of equations are
[tex]\begin{cases}x=2 \\ y=-5\end{cases}[/tex]If Lanny spins the spinner below 70 times, how many times can he expect is to land on a number divisible by 3? *
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From 1 to 10, there are 3, 6, and 9 are divisible by 3
Then we have 3 choices out of 10 numbers
Since the probability = an event/outcomes
Since the event is 3
Since the outcomes are 10, then
[tex]P(\frac{no}{3})=\frac{3}{10}[/tex]This is the probability for spinning the spinner one time
But we need to spin it 70 times
We will multiply 3/10 by itself 70 times, which means make it to the power of 70
[tex]P(\frac{no}{3})=(\frac{3}{10})^{70}[/tex]The answer is (3/10)^70 OR (0.3)^70
which numbers are all divisible by 5
Answers
Answer:
numbers that end with 0 or 5.
Answer: 5 35 790 55
Step-by-step explanation:
kekera pere
through: (5,-4), slope = -9/5
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The slope intersept form of a line is ,
[tex]y-y_1=m(x-x_1)[/tex]Given the point (x1,y1) is (5,-4) and slope is -9/5 implies,
[tex]undefined[/tex]Suppose the following bond quotes for IOU Corporation appear in the financial page of today’s newspaper. Assume the bond has a face value of $2,000 and the current date is April 19, 2021.
Company (Ticker) Coupon Maturity Last Price Last Yield EST volume (000s)
IOU (IOU) 6.3 April 19, 2037 112.97 ?? 1,857
a.
What is the yield to maturity of the bond? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b. What is the current yield? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Answers
a) The yield to maturity of the IOU Corporation's bond is -0.39%.
b) The current yield of the IOU Corporation's bond is 5.58%.
What is the yield to maturity?The bond's yield to maturity (YTM) is the total rate of return earned by a bondholder with all interest payments and the original principal repaid.
We can compute the yield to maturity using the following YTM formula:
Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]
Where:
FV = Face Value of the Bond
Price = Current Market Price
Maturity = Maturity Period.
Bond's face value = $2,000
Current date = April 19, 2021.
Company (Ticker) Coupon Maturity Last Price Last Yield EST volume
(000s)
IOU (IOU) 6.3 April 19, 2037 112.97 ?? 1,857
Annual interest = $126 ($2,000 x 6.3%)
Maturity period = 16 (2037 - 2021)
Price = $2,259.4 ($2,000 x 112.97/100)
Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]
= [$126 + {($2,000 - $2,259.4)/16}] / [($2,000 + 2,259.4)/2]
= [$126 -$259.4)/16] / [($4,259.4)/2]
= -8.3375/2,129.7
= -0.39%
Current yield = Annual Coupon/Current Price
= 5.58% ($126/$2,259.4 x 100)
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The point S is plotted on the coordinate grid below. Plot the point S', the reflection
of S over the x-axis.
Click on the graph to plot a point. Click a point to delete it.
Answers
Answer:
(1, -2)
Step-by-step explanation:
Reflecting a point over the x-axis means [tex](x,y) \longrightarrow (x, -y)[/tex].
Hugo averages 42 words per minute on a typing test with a standard deviation of 5.5 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(42,5.5). Suppose Hugo types 60 words per minute in a typing test on Wednesday. The z-score when x=60 is ________. This z-score tells you that x=60 is ________ standard deviations to the ________ (right/left) of the mean, ________. Correctly fill in the blanks in the statement above.
Answers
The z score when x = 60 is 3.27.
This z score tells you that x = 60 is 3.27 standard deviations to the right of the mean.
Given,
Consider as a normal distribution:
The mean should be equals to 42 (μ)
The standard deviation (σ) = 5.5
We have to find the z score when x = 60.
That is,
z = (x - μ) / σ = (60 - 42) / 5.5 = 18/5.5 = 3.27
Therefore,
The z score when x = 60 is 3.27.
This z score tells you that x = 60 is 3.27 standard deviations to the right of the mean.
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What is the value of 2(3x − 6) − 5y if x = −2 and y = 6?
−6 −18 −54 −78
Answers
Answer:
-54
Step-by-step explanation:
Finding a value means you will get a number answer. Since they said x
x = -2
fill in -2 in place of the x.
also they said
y = 6
so fill in 6 wherever you see a y.
2(3x - 6) - 5y
fill in -2 for x and 6 for y.
= 2(3•-2 - 6) - 5•6
Work on parentheses first. Multiply before adding or subtracting.
= 2(-6 - 6) - 5•6
= 2(-12) - 5•6
Again, multiply before adding or subtracting.
= -24 - 30
= -54
4. Betty Kusack and Theresa Peña together can do a job in 20 hours. Working alone,Betty can do the job in 60 hours. How long would it take Theresa, working alone, todo the job?AnswerH
Answers
Given:
Betty and Theresa together complete a job in 20 hours.
Betty alone does a work in 60 hours.
The aim is to find the time Theresa will take to complete the job alone.
Therefore,
Betty and Theresa's 1 day work:
[tex]=\frac{1}{20}[/tex]Betty's 1 day work when he works alone:
[tex]=\frac{1}{60}[/tex]Now, Theresa's 1 day work when he works alone is given by:
[tex]\begin{gathered} =\frac{1}{20}-\frac{1}{60} \\ =\frac{3-1}{60} \\ =\frac{2}{60} \\ =\frac{1}{30} \end{gathered}[/tex]Hence, Theresa can do the job in 30 hours working alone.
I need help with this practice problem solving The subject is trigonometry It asks to graph the functionIf you can, use Desmos to graph… it is recommend
Answers
In order to determine the graph of the given function, cosider:
The function f(x) is indetermined when the argument of the cot is 0.
[tex]\begin{gathered} x+\frac{\pi}{6}=0 \\ x=-\frac{\pi}{6} \end{gathered}[/tex]In this case, the period is 2pi. Then, not only for x=-pi/6, but for x=5pi/6 the function is indeterminate.
Then, the graph is:
help meeeeeeeeeeeeeeeee
Answers
For the given function f(x) = x³ +x +1,g(x) =-x, composition of the given function is given by ( fog)(x) = -x³ -x +1 , ( g of)(x) = -(x³ +x +1).
As given in the question,
Given function :
f(x) = x³ +x +1
g(x) =-x
Composition of the given function is equal to :
(fog)(x) = f(g(x))
= f(-x)
= (-x)³ +(-x) +1
= -x³ -x +1
(g of)(x) = g(f(x))
=g(x³ +x+1)
= -(x³ +x+1)
Therefore, for the given function f(x) = x³ +x +1,g(x) =-x, composition of the given function is given by ( fog)(x) = -x³ -x +1 , ( g of)(x) = -(x³ +x +1).
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Fill in the missing values to make the equations true.(a) log, 9-log, 11 = log5(b) log45 + log4 = log, 45(c) 5log72 = log7
Answers
(a)
[tex]\log _59-\log _511=\log _{5_{}}(\frac{9}{11})\text{ (}\because\log a-\log b=\log (\frac{a}{b})[/tex]Thus, the required value in the blank in 9/11/
(b)
[tex]\log _45+\log _4(9)=\log _445\text{ (}\because\log a+\log b=\log ab)[/tex]Thus, the required value in the blank is 9.
(c)
[tex]\begin{gathered} 5\log _72=\log _72^5(\because a\log b=\log b^a) \\ =\log _732 \end{gathered}[/tex]Thus, the requried value in the blank is 32.
Bobby was making a road trip to visit his parents. He stopped for gas and bought x number of gallons for $2.25 per gallon and a soda for $1.75. How much did he spend at the gas station if her purchased 15 gallons of gas?
Answers
Answer:
$35.5
Explanation:
If Bobby purchased 15 gallons of gas and each gallon cost $2.25, the total cost of the gallons of gas is:
15 x $2.25 = $33.75
Adittionally, Bobby bought a soda for $1.75, so he spend a total of:
$33.75 + $1.75 = $35.5
So, he spends $35.5
Larry says all numbers that have a 2 in the one's place are composite numbers. Explain if Larry is correct or incorrect.
Answers
A composite number is defined as a whole number that have more than two factors; from this definition we conclude that all whole numbers that are not prime are composite numbers.
Since all even numbers are not prime we conclude that Larry is correct; all numbers that have a 2 in the one's place are composite. In fact all even numbers are composite with exception of 2 itself.
Please help!
How many solutions does the following equation have?
6 (c+4) = 6c + 30
zero solutions
one solution
infinitely many
solutions
Answers
The number of solutions that this equation have is: A. zero solutions.
What are zero solution?Generally speaking, an equation is said to have zero solution or no solution when the left hand side and right hand side of the equation are not the same or equal. This ultimately implies that, an equation would have zero solution or no solution when both sides of the equal sign are not the same and the variables cancel out.
How to determine the number of solutions?In order to determine the number of solutions that this equation have, we would simplify the equation by opening the bracket and then compare both sides of the equation as follows:
6(c+4) = 6c + 30
6c + 24 = 6c + 30
6c - 6c = 30 - 24
0 = 6 (no solution).
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