When dividing both sides of an inequality by an integer we must reverse the inequality symbol
Your neighbor leaves his yard, which is 120 ft from the bus stop. He begins to walk toward you at the bus stop and then passes you. He walks at a speed of 4 ft/s. His distance d from you after t seconds is given by d = |120 − 4t|. After how many seconds is your neighbor 30 ft from you?
To find the amount of time it takes for your neighbor to be 30 ft from you, you set up and solve an equation using the given information.
Explanation:To find the amount of time it takes for your neighbor to be 30 ft from you, we need to set up an equation and solve for t. The distance d is given by d = |120 - 4t|. The absolute value represents the distance in one direction, so it does not matter if your neighbor is walking towards you or past you. We want to find when the distance is 30 ft, so we set up the equation 30 = |120 - 4t|.
Solving this equation gives us two possibilities: 30 = 120 - 4t and 30 = -(120 - 4t). We can solve each equation separately.
For the first equation, 30 = 120 - 4t, we subtract 120 from both sides to get -90 = -4t. Dividing both sides by -4 gives us t = 22.5.
For the second equation, 30 = -(120 - 4t), we multiply both sides by -1 to get -30 = 120 - 4t. Subtracting 120 from both sides gives us -150 = -4t. Dividing both sides by -4 gives us t = 37.5.
So your neighbor is 30 ft from you after 22.5 seconds and 37.5 seconds.
How long will it take for an investment to triple, if interest is compounded continuously at 4%?
Why do new cars costing $20,000 rent for $40 a day, while tuxedos costing only $500 rent for around $90?
A car is traveling at a speed of 90 kilometers per hour. What's the car's speed in meters per second? How many meters will the car travel in 10 seconds? Do not round your answers.
The pair of points (3,8) and (x, 6) are on the graph of am inverse variation. What is the missing value?
How many kilograms are in 500 grams? ...?
A laboratory technician needs to make a 72-liter batch of a 20% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 10% to get the desired concentration?
Answer: 8 L of 100% pure acid and 64 L of 10% acid must be combined
Step-by-step explanation:
According to the dilution law,
[tex]C_1V_1+C_2V_2=C_3V_3[/tex]
where,
[tex]C_1[/tex] = concentration of pure acid solution = 100 %
[tex]V_1[/tex] = volume of pure acid solution = x L
[tex]C_2[/tex] = concentration of another acid solution= 10%
[tex]V_2[/tex] = volume of another acid solution= (72-x) L
[tex]C_3[/tex] = concentration of resulting acid solution = 20 %
[tex]V_1[/tex] = volume of resulting acid solution = 72 L
Putting the values in the equation:
[tex]100\times x+10\times (72-x)=20\times 72[/tex]
[tex]x=8L[/tex]
Therefore, the laboratory technician must take 8 L of 100% pure acid and (72-8) = 64 L of 10% acid to get 72-liter batch of a 20% acid solution.
Explain why a point in the polar plane cannot be named by a unique ordered
pair (r, theta).
A point in the polar plane can have multiple representations due to the periodic nature of angles and the possibility of using negative radii to represent a point in the opposite direction from the pole.
Explanation:The question asks to explain why a point in the polar plane cannot be named by a unique ordered pair (r, θ). In the polar coordinate system, each point is determined by a radius (r) and an angle (θ).
However, a point can have multiple representations due to the periodic nature of angles. If you add or subtract multiples of 2π radians (or 360 degrees) from θ, you will land on the same point in the polar plane.
Additionally, if the radius (r) is negative, the direction is reversed, which also leads to the same point being represented by (-r, θ + π), where θ is the initial angle.
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Which of the following are solutions to the equation sinx cosx = 1/4? Check all that apply.
A. π/3+nπ/2
B. π/12+nπ
C. π/6+nπ/2
D. 5π/12+nπ ...?
Answer:
Its B and D.
Step-by-step explanation:
How is each function related to y=x? Graph the function by translating the parent function
1) y=x+2 2) y=x-1.2
I need help with this. I don't know what to do. I was sick and stayed home but I had homework and I wasn't taught how to do it could. Someone help me with this by explaining it step by step? Thank you.
Find x and y so that the ordered data set as a mean of 42and a median of 35.
17,22,26,29,34,x,42,67,70,56,y soln: 17+22+26+29+34+x+42+67+70+56+y= 363+x+y (363+x+y)/11=42 y=99/x x is median
Solve this problem
-2=c+2
the french club is sponsoring a bake sale. if their goal is to raise at least $135, how many pastries must they sell at $3.00 each in order to meet that goal? write and solve an inequality.
Answer:
45 or more
Step-by-step explanation:
If x is the amount of pastries they sell, we need to multiply it by $3.00 to know how much they raise. Total earnings: $3.00x
They need to raise at least $135, that is $135 or more.
So, $3.00x has to be greater than $135 or equal.
Written as an inequality is:
$3.00x [tex]\geq[/tex] $135
We divide both sides by $3.00 and we have:
x [tex]\geq[/tex] $135/$3.00 = 45
Therefore, they need to sell 45 or more pastries to meet the goal.
1. alicia and jamal completed the following "
given : 3x+7=x-5
prove: x=-6
Alicia's workt.
3x+7=x-5 : given
2x+7=-5: subtraction property of equality
2x=-12: subtraction property of quality
x=-6: division property of equality
jamal's work
3x+7=x-5 : given
7=-2x-5 : subtraction property of equality
12=-2x: addition property of equality
-6=x : division property of equality
who completed the proof correctly?
a) alicia only
b) jamal only
c) both alicia and jamal
d) neither alicia nor jamal
Answer:
both alicia and jamal
Step-by-step explanation:
From the given steps we can see that both Alicia and Jamal completed the proof correctly.
Option C
Given :
3x+7=x-5
prove: x=-6
Alicia's workout
3x+7=x-5 : given
2x+7=-5: subtraction property of equality
2x=-12: subtraction property of quality
x=-6: division property of equality
Alicia's steps are correct. She proved x=-6
jamal's work
3x+7=x-5 : given
7=-2x-5 : subtraction property of equality
12=-2x: addition property of equality
-6=x proved
Jamal's steps are also correct. Jamal started by subtracting 3x from both sides. That approach is also correct. He proved x=-6
so, both Alicia and Jamal are correct
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Why is the absolute value of a number always positive?
It's not. The absolute value of any number is the positive version of that number except for the absolute value of 0. This is the only situation where the absolute value of a number is not positive. The absolute value of 0 is just 0.
Lydia bought a shirt at 20% off its retail price of $40. She paid 5% tax on the price after the discount. How much did Lydia pay for the shirt?
$42
$36.60
$34
$33.60
Answer:
$33.60 is the correct answer.
Step-by-step explanation:
Price of the shirt = $40.00
discount rate = 20% or 20/100
so price of the shirt = 40 × 0.20 = 8
Shirt's price after 20% discount = 40 - 8 = $32.00
Now she paid 5% tax on the price after discount.
5% tax of 32.00
0.05 × 32 = $1.60
This amount will be added to his discounted price of a shirt.
= 32.00 + 1.60 = $33.60
Lydia pay $33.60 for the shirt.
why are both accuracy and precision important in making a measurement?
a number , x,rounded to 1 decimal place is 3.7 what is the error interval for x
The error interval will be [3.65,3.75).
What is an error interval?The error interval is the limit or range of accuracy where the number is truncated or rounded. This interval simply shows the range which it could be before rounding.
Given here the decimal number is 3.7 which is after rounded to 1 decimal place.
As the number is rounded to the nearest 0.1 unit, therefore, the error will be half of 0.1 which is 0.1/2= 0.05
Then the lower limit of the error interval will be 3.7-0.05= 3.65
the higher limit of the error interval will be 3.7+0.05= 3.75
the error interval will be 3.65≤x<3.75
As we are rounding 1st decimal unit, if the second decimal unit is greater than 5 then the first decimal unit will be 6. Similarly, if the second decimal unit is less than 5 then the first decimal unit will be 7.
There are the numbers below which on rounding give 3.7
3.65 ,3.66,3.67 ,3.68,3.69,3.70,3.71,3.72,3.73,3.74
Therefore the error interval will be [3.65,3.75).
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The error interval for a number x, which when rounded to one decimal place is 3.7, is [3.65, 3.75).
Explanation:When a number, x, rounded to one decimal place is 3.7, the error interval for x represents the range of actual values x could be to give that rounded figure. So, if x is rounded to 3.7, it means that the value must be at least 3.65 and less than 3.75 when considering rounding to one decimal place. Essentially, the number must be in the half-open interval [3.65, 3.75).
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The hypotenuse of a 30- 60- 90 triangle has length 13. What is the length of the side opposite the 60 angle? If necessary, round your answer to two decimal places.
Whats the product of 86 and the depth of the river?
Let the depth of the river = d
So in order to find the product, you simply multiply
so the product of 86 and the depth of the river would be 86 * d
or 86d.
Hope this answers your question. Have a great day!
name the property of real numbers illustrated by the equation step by step
-10+4=4+(-10)
Solve the following formula for R: C=2πR
Choose ALL equivalent variations of your answer.
To solve for R in the equation [tex]C=2\pi R[/tex] divide both sides by 2π to get [tex]R = C / (2\pi )[/tex].
To solve the equation [tex]C=2\pi R[/tex] for R, we need to isolate R on one side of the equation. Here are the steps to do this:
Start with the original equation: [tex]C=2\pi R[/tex]
Divide both sides of the equation by 2π to isolate [tex]R: R = C / (2\pi ).[/tex]
Given variation, this is also equivalent to [tex]r=1/2\pi C[/tex].
Now, R is the subject of the equation, and you can use this formula to find the radius (R) if you know the circumference (C) of a circle.
y = (1/4)x^2 - (1/2)lnx..over the interval (1, 7e) ...what is the arc length ?
What is 481 divided by 8?Is it 60 with a remainder of 1 ?
Solve for x: 3 − (2x − 5) < −4(x + 2)
x < −8
x > −8
x < −3
x > −3
I just need help because i don't know how i would do it with x on both sides
Answer: [tex]x<-8[/tex]
Step-by-step explanation:
The given inequality : [tex]3-(2x-5)<-4(x+2)[/tex]
To solve the inequality for x , first we open the parenthesis , we get
[tex]3-2x+5<-4x+(-4)2[/tex]
[tex]\Rightarrow\ 3-2x+5<-4x-8[/tex] [Note : (-)(+)=(-)]
[tex]\Rightarrow\ 3+5-2x<-4x-8[/tex]
[tex]\Rightarrow\ 8-2x<-4x-8[/tex]
Add 4x on both sides , we get
[tex]8-2x+4x<-4x-8+4x[/tex]
[tex]8+2x<-8[/tex]
Subtract 8 from both sides , we get
[tex]2x<-16[/tex]
Divide both sides by 2 , we get
[tex]x<-8[/tex]
Hence, the correct answer is : [tex]x<-8[/tex]
the slope of the line below is 0.8 write the equation of the line in point slope form using the coordinates of the coordinates of the labeled point do not use parenthesis on the y side
Final answer:
The equation of the line in point-slope form is y - y1 = 0.8(x - x1), where the point on the line and the slope are given.
Explanation:
To write the equation of a line in point-slope form, we need the slope of the line and the coordinates of a point on the line. In this case, the slope is given as 0.8. Let's assume the labeled point has coordinates (x, y). The equation in point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of the labeled point. Substituting the given slope and the coordinates of the point, the equation becomes:
y - y1 = 0.8(x - x1)
Remember to not use any parentheses on the y side of the equation.
each of the numbers from 1 to 50 is written on a tile and the tiles are placed upside down on the top of the table. if a tile is picked up at random, what is the probability that the number on the tile is multiple of 7 or a multiple of 8?
The probability that the number on the tile is a multiple of 7 or a multiple of 8 is 0.24 or 24%.
To find the probability that a tile picked at random has a number that is a multiple of 7 or a multiple of 8, we need to count the number of tiles that satisfy this condition and divide it by the total number of tiles.
First, let's find how many numbers from 1 to 50 are multiples of 7 and multiples of 8 separately.
Multiples of 7:
7, 14, 21, 28, 35, 42, 49
There are 7 multiples of 7 between 1 and 50.
Multiples of 8:
8, 16, 24, 32, 40, 48
There are 6 multiples of 8 between 1 and 50.
However, we need to be careful not to count the numbers that are multiples of both 7 and 8 (multiples of 56). There's only one such number in the range (56).
So, the total number of tiles with numbers that are multiples of 7 or multiples of 8 is 7 + 6 - 1 = 12.
The total number of tiles from 1 to 50 is 50.
Now, we can find the probability:
Probability = [tex]\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}[/tex]
Probability = [tex]\frac{12}{50}[/tex]
Probability = 0.24
So, the probability that the number on the tile is a multiple of 7 or a multiple of 8 is 0.24 or 24%.
Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled for the flowers to last the longest. Her cylinder vase has a radius of 4 inches and a height of 10 inches. How much water should Mary pour into the vase?
A ball is thrown horizontally at a speed of 24 meters per second from the top of the building. If the ball hits the ground 4.0 seconds later approximately how high is the building? ...?
The height of the building is approximately 78.4 meters.
Explanation:To find the height of the building, we can use the formula d = v0t + 1/2gt2, where d is the height, v0 is the initial horizontal speed, t is the time, and g is the acceleration due to gravity. In this case, since the ball is thrown horizontally, the initial vertical speed is 0 and there is no initial vertical acceleration. So, d = 0(4.0) + 1/2(9.8)(4.0)2. Solving this equation gives us a height of approximately 78.4 meters.