Start with definition of absolute value, |x|.
It says,
|x| = x, for any x >= 0 and
|x| = -x, for any x < 0
Now, instead of x, we have the expression x+120 inside the absolute value brackets:
|x+120|
Play the same game as above - what is the absolute value here?
|x+120| = x+120 for (x+120)>=0 and
|x+120| = -(x+120) for (x+120)<0
Now, recognize that the last condition (x+120)<0 is the same as writing x<-120. That is the condition in the question. Therefore the absolute value |x+120| will equal the second expression (for that condition), namely -(x+120), or -x-120.
To simplify |x + 120| when x is less than -120, you change the sign of the expression inside the absolute value to get the simplified form as -x - 120.
To simplify |x + 120| when x < -120, we need to consider the definition of absolute value. The absolute value of a number is the non-negative value of that number without regard to its sign. Since x is less than -120, x + 120 is a negative number, and to find its absolute value, we change the sign to positive.
Therefore, the simplification of |x + 120| when x < -120 is simply -(x + 120), which equals -x - 120.
The number of students at Bedrock Middle School decreased to 90 % last year's number. Last year, there were 1,500 students. How many students are there this year?
Answer:
1,350 students
Step-by-step explanation:
The number of students this year is 90% of the number from last year. Find 90% of 1500....
90% is 0.9 as a decimal,
0.9(1500) = 1,350 students
Answer: 2i50 students
Step-by-step explanation:
Do 90% of 1,500
10% = 150
150 x 9 = 1350
We need the total amount of students
So do 1350 + 1500 = 2850 students
Sasha bought 3 and 1/2 pints of blueberries to make jelly she ate 3/4 of a pint of varies on her way home how many pints of berries does she have left to make jelly
3 1/2 pints - 3/4 pints
3 1/2 = 3 2/4
3 2/4 = 2 6/4
2 6/4 - 3/4
2 3/4
Answer: 2 3/4 pints of berries
Sasha bought 3 and 1/2 pints of blueberries, ate 3/4 of a pint, and after calculating, she has 2 and 3/4 pints left for making jelly.
The student, Sasha, initially bought 3 and 1/2 pints of blueberries and then ate 3/4 of a pint. To find out how many pints of berries she has left, we need to subtract the amount eaten from the amount bought.
We calculate:
Convert the mixed fraction to an improper fraction:Converting 11/4 pints back to a mixed number, we get 2 and 3/4 pints. Therefore, Sasha has 2 and 3/4 pints of blueberries left to make jelly.
How Find the solution set of the inequality
−4x+35>2
Answer:
[tex]x<8\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]-4x+35>2\\-4x>-33\\x<\frac{33}{4} \\x<8\frac{1}{4}[/tex]
Remember to flip the sign when you divide or multiply both sides by a negative number! You don't need to flip the sign with adding or subtracting as in the case of step one subtracting 35 from both sides.
The solution of the inequality −4x+35>2 will be x < (33 / 4).
What is inequality?The relationship between two phrases using a symbol like "not equal to," "greater than," or "less than" indicates that they are not equal.
The given inequality will be solved as below:-
−4x+35>2
−4x>- 35 + 2
−4x > - 33
−4x > - 33
x < ( 33 / 4 )
Therefore, the solution of the inequality −4x+35>2 will be x < (33 / 4).
To know more about inequality follow
https://brainly.com/question/24372553
#SPJ2
Find a linear equation in your life?
My life is not linear. Time is not constant. My life (and time included) is just a series of times that do not run parallel to each other. Instead, they drift further or closer as a function of velocity and curvature of space time.
Answer: If you are looking for a linear equation in your life, an example could be the rate of the grass growing in your lawn. The y axis could be the height and the x axis could be the time. As it grows, the line representing the grass could go up gradually; when you cut it, the line can stop. Keep doing that for however long you'd like to represent the grass growing/getting cut.
the sum of two numbers is 21 and their difference is 5
X+Y = 21 ---> Y = 21-x
X-y = 5
x - (21-x) = 5
2x - 21 = 5
2x = 26
x = 13
13 and 8
The two numbers are 13 and 8.
13 + 8 = 21
The difference (13 - 8) is 5.
Subtract 6 ounces from 3 pounds.
5 lb., 7 oz.
6 lb., 3 oz.
2 lb., 10 oz.
2 lb., 13 oz.
Answer:
the answer is c
Step-by-step explanation:
Final answer:
To subtract 6 ounces from 3 pounds, convert 3 pounds to ounces (3 x 16 = 48 ounces), subtract 6 ounces (48 - 6 = 42 ounces), then convert back to pounds and ounces (42 ounces = 2 pounds and 10 ounces). The answer is 2 pounds, 10 ounces.
Explanation:
Subtracting Ounces from Pounds
The question asks to subtract 6 ounces from 3 pounds. In order to compare or subtract different units of weight, it is essential to convert them to the same unit. Firstly, we must remember the unit equivalence where 1 pound = 16 ounces. Now, to start the conversion, we multiply the number of pounds by 16 to get the total number of ounces, which is a step in solving these types of conversion problems.
Therefore, for 3 pounds:
3 pounds × 16 ounces/pound = 48 ounces.
Now subtract the given ounces: 48 ounces - 6 ounces = 42 ounces.
Since we know there are 16 ounces in a pound, we divide the total ounces by 16 to convert back to pounds and ounces.
42 ounces ÷ 16 ounces/pound = 2 pounds with a remainder of 10 ounces.
Hence, subtracting 6 ounces from 3 pounds gives us 2 pounds, 10 ounces.
Find the mean and the median of this data set: 9, 6, 5, 3, 28, 6, 4, 7
Answer:
The means is 8.5 The Median is 6
Step-by-step explanation:
1) to find the mean just Simply add all the numbers together and divided by how many numbers that is giving. (Because you are simply finding the average)
9+6+5+3+28+6+4+7=68
68 divided by 8 = 8.5
2) to find the median simply organize the numbers from least to greatest Like this: (3,4,5,6,6,7,9,28) Then keep crossing out from both sides teal you find the middle Number.
If there a odd amount of number the median will be one Number, if even 2 numbers ( if 2 numbers just add them both and divide by 2)
In This Case the Median is 6,6 but Its actually 6 Why (6+6=12) and (12/2=6) so your median is 6.
Hopes This helps!
The mean of the given data 9, 6, 5, 3, 28, 6, 4, 7 is 8.5 and the median is 6.
The mean is defined as the average of all the values or the mean can be defined as the sum of all observations by the total number of observations.
[tex]Mean =\dfrac {\ Sum \ of \ all \ observation}{Total \ number \ of \ observation}[/tex]
[tex]Mean = \dfrac{9 + 6 + 5 + 3 + 28 + 6 + 4 + 7}{8}[/tex]
Mean = [tex]\dfrac{68}{8}[/tex]
Mean = 8.5
Therefore, the mean of the data set is 8.5.
The median is defined as:
The median is the middle value when the data set is arranged in ascending or descending order.
If there are two middle values, the median is the average of those two values.
Arrange the data set in ascending order: 3, 4, 5, 6, 6, 7, 9, 28.
Here n = 8, since n is even so the median is calculated as:
Median = [tex]\dfrac{(\dfrac{n}{2}) \ th \ observation + (\dfrac{n}{2}+1) \ th \ observation}{2}[/tex]
Median =[tex]\dfrac{( 4 \ th \ observation + 5 \ th \ observation)}{2}[/tex]
The 4th observation is 6 and the 5th observation is 6.
So, this mean will be 6.
Therefore, the median of the data set is 6.
The Mean is 8.5 and the median is 6.
Learn more about the median here:
https://brainly.com/question/1157284
#SPJ4
The coordinates of 3 of the vertices of a parallelogram are (–7, 3), (–6, 1), and (–4, 5). What is the equation for the line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a parallelogram are parallel.)
Answer: [tex]y=-2x-3[/tex]
Step-by-step explanation:
The equation of the line in slope-intercept form, is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
By definition, parallel lines have the same slope.
Then:
- Find the slope of the the line that connects the points (-7,3) and (-6,1), as following:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1-3}{-6-(-7)}=-2[/tex]
- We know that the other line is connected with the point (-4,5), therefore, you can substitute values and solve for b:
[tex]5=-2(-4)+b\\5=8+b\\5-8=b\\b=-3[/tex]
Then, the equation for the line containing the side opposite the side containing the first two vertices is:
[tex]y=-2x-3[/tex]
Suppose you buy an appliance costing $2450 at a store charging 9% add-on interest, you make a down payment of $ 600, and you agree to monthly payments over 4 years.
Find the total cost for the appliance plus interest.
Answer:
$3116
Step-by-step explanation:
First off, we need to find the value of the appliance after the down payment.
$2450 - $600 = $1850
This then makes our principal $1850.
P = $1850
r = 9% or 0.09
t = 4 years
To find the total cost of the appliance plus interest, we need to look for our accrued amount first.
A = P + Prt
A = $1850 + $1850(0.09)(4)
A = $1850 + $666
A = $2516
Now that we know our accrued amount, we then add our down payment to find the total cost.
Total cost = $2516 + $600
Total cost = $3116
To calculate the cost of an appliance with added interest, subtract the down payment from the purchase price to determine the amount of the loan. This is followed by the calculation of the total interest over the length of the loan. Adding these two amounts provides the total cost of the appliance plus interest, which in this case is $2516.
Explanation:The total cost of the appliance plus interest can be calculated by first determining the amount of the loan made, which is the cost of the appliance minus the down payment. This comes out to $2450 - $600 = $1850.
Then, the add-on interest over 4 years is calculated by multiplying the amount of the loan by the annual interest rate and by the number of years. For this question, that is $1850 * 0.09 * 4 = $666.
So, the total cost of the appliance with interest added is the sum of the amount of the loan and the amount of the interest. Therefore, $1850 + $666 = $2516 is the total cost for the appliance plus interest.
Learn more about Interest Calculation here:https://brainly.com/question/29011216
#SPJ3
Last option is none of the above
Answer:
A and B
Step-by-step explanation:
When rotating a point (or any shape around a certain point), none of the diameters of the shape will change. So for example, with this circle, when you rotate it around a point, the radius and circumference will not change because it has just rotated. It wont be on the x-axis though because point P is not on the x-axis an it is being rotated 180 degrees about point P. Just know that when you are rotating, nothing about the shape changes, all angles or measurements will be the same, it is just moving to a different place.
Hope this helped ^-^
SOMEONE PLEASE HELP ME!!!
if f(x)=x^2+2x-3 and g(x)=x^2-9, find (f/g)(4) and (f+g)(4)
Replace x in each equation with 4:
f(x) = x^2 +2x-3 = 4^2 + 2(4) -3 = 16 + 8 -3 = 21
g(x) = x^2-9 = 4^2 -9 = 16-9 =7
Now you have values for f(x) and g(x) now you can solve for f/g and f+g:
f/g = 21 / 7 = 3
f+g = 21 + 7 = 28
For this case, we have that by definition:
[tex](f + g) (x) = f (x) + g (x)\\(\frac {f} {g})(x) = \frac {f (x)} {g (x)}[/tex]
We have the following functions:
[tex]f (x) = x ^ 2 + 2x-3\\g (x) = x ^ 2-9[/tex]
So:
[tex](f + g) (x) = x ^ 2 + 2x-3 (x ^ 2-9)\\(f + g) (x) = x ^ 2 + 2x-3 x ^ 2-9\\(f + g) (x) = 2x ^ 2 + 2x-12\\(f + g) (4) = 2 (4) ^ 2 + 2 (4) -12\\(f + g) (4) = 2 * 16 + 8-12\\(f + g) = 32 + 8-12\\(f + g) (4) = 28[/tex]
On the other hand:
[tex](\frac {f (x)} {g (x)}) = \frac {x ^ 2 + 2x-3} {x ^ 2-9}\\Evaluated\ at\ x = 4[/tex]
[tex](\frac {f (x)} {g (x)}) = \frac {4 ^ 2 + 2 (4) -3} {4 ^ 2-9} = \frac {16 + 8-3} {16 -9} = \frac {21} {7} = 3[/tex]
Answer:
[tex](f + g) (4) = 28\\(\frac {f} {g}(4)) = 3[/tex]
Hey can someone answer this ASAP
Answer:
csc θ = [tex]\sqrt{85}[/tex]/6
sec θ = [tex]\sqrt{85}[/tex]/7
tan θ = 6/7
Step-by-step explanation:
The first thing to do will be to compute the length of the hypotenuse using the Pythagoras theorem;
6^2 +7^2 = hypotenuse^2
hypotenuse = [tex]\sqrt{85}[/tex]
csc θ = 1/sinθ
sinθ = opposite side/hypotenuse
= 6/[tex]\sqrt{85}[/tex]
csc θ = [tex]\sqrt{85}[/tex]/6
sec θ = 1/cosθ
cosθ = adjacent side/hypotenuse
sec θ = hypotenuse/adjacent side
= [tex]\sqrt{85}[/tex]/7
tan θ = Opposite side/adjacent side
= 6/7
Which function is represented by the graph
f(x)= -|x|+4
f(x)= -|x|-4
f(x)= -|x+4|
f(x)= -|x-4|
It’s the forth one
The answer is -|x-4|.
Answer:y=-|x-4|
Step-by-step explanation:
we know the graph of y=|x| touches at x=0 and opens upward towards y axis
but this graph is facing downwards therefore it should be of form
y=-|x|
but it touches the x axis at x=4
therefore the graph is represented by
y=-|x-4|
4 is added inside the mod because it intersect x axis at x=4
The graph would be y=-|x-4|+1 if it shifts 1 unit upwards.
Which numbers are factors of 4? Select all that apply.
1
4
2
3
Answer:
1,2,4
Step-by-step explanation:
Factors are the numbers that we can multiply together to make 4
1*4 = 4
2*2 = 4
The factors are 1,2 and 4
Answer:
1, 2 and 4Step-by-step explanation:
[tex]Factors\ of\ 4:\ 1,\ 2,\ 4\\\\4=4\cdot\boxed{1}\\4=2\cdot\boxed2\\4=1\cdot\boxed4[/tex]
the point slope form of the equation of a line that passes through (8,4) and (0,2) is y-4=1/4(×-8) what is the slope intercept form of the equation for this line.
Answer:
[tex]\large\boxed{y=\dfrac{1}{4}x+2}[/tex]
Step-by-step explanation:
The slope-intercept form of the equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The point-slope form of the equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
We have the equation of a line:
[tex]y-4=\dfrac{1}{4}(x-8)\to m=\dfrac{1}{4}[/tex]
and the point (0, 2) → b = 2.
Substitute:
[tex]y=\dfrac{1}{4}x+2[/tex]
Answer:
Step-by-step explanation:
DDD
Solve for the roots in the following equation. Hint: Factor both quadratic expressions. (x 4 + 5x 2 - 36)(2x 2 + 9x - 5) = 0 x = a0 a1, ± a2, - a3, ± a4 i
Answer:
The final solution is all the values that make
( x 4 + 5 x 2 − 36 ) ( 2 x 2 + 9 x − 5 ) = 0 true. x = − 2 , 2 , 3 i , − 3 i , 1 2 , − 5
Step-by-step explanation:
x 4 + 5 x 2 − 36 = 0 2 x 2 + 9 x − 5 = 0
Answer:
1,2,2,5,3
Step-by-step explanation:
it's right you idiots
A right triangle has coordinates A(6, 0), B(0, 0), and C(0, 8). What is the perimeter of the triangle?
A. 18 units
B. 20 units
C. 24 units
D. 28 units
Answer:
C
Step-by-step explanation:
From the given coordinates
A(6, 0), B(0, 0) then AB = 6 - 0 = 6
B(0, 0), C(0, 8) then BC = 8 - 0 = 8
To calculate AC use Pythagoras' theorem on the right triangle formed
AC² = AB² + BC² = 6² + 8² = 36 + 64 = 100
Take the square root of both sides, hence
AC = [tex]\sqrt{100}[/tex] = 10
Perimeter = AB + BC + AC = 6 + 8 + 10 = 24 → C
Jack rolls two standard number cubes.find the probability that the sum of the roll is 5, given that one cube up even and the other came up odd
Answer:
[tex]\frac{4}{36}[/tex] or [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
We are given that Jack rolls two standard number cubes and we are to find the probability that the sum of the roll is 5, given that one cube up even and the other came up odd.
A sum of two from two rolls would always be one even and one odd, whatsoever is the case.
To have a sum of five, we can have (1, 4), (2,3), (3,2) or (4,1) out of a sample space of 36 so the probability will be [tex]\frac{4}{36}[/tex] or [tex]\frac{1}{9}[/tex].
URGENT! Which of the following correctly expresses sin(2θ)−sin(6θ) as a product?
Select the correct answer below:
2sin(4θ)cos(2θ)
2sin(2θ)cos(4θ)
−2sin(2θ)cos(4θ)
−2sin(2θ)sin(4θ)
Answer:
−2sin(2θ)cos(4θ)
Step-by-step explanation:
sin(2∅)-sin(6∅)
Sum product Identity
sinα - sinβ = 2cos((α+β)/2)sin((α-β)/2)
Putting α= 2∅ and β= 6∅ in the identity we get
sin(2∅)-sin(6∅) = 2cos((2∅+6∅)/2)sin((2∅-6∅)/2)
=2cos(8∅/2)sin(-4∅/2)
=2cos(4∅)sin(-2∅)
= -2sin(2∅)cos(4∅)
2. The amount of fertilizer in a landscaping company’s warehouse decreases at a rate of 3% per week. The amount of fertilizer in the warehouse was originally 78,000 cubic yards. What function models the amount of fertilizer in cubic yards left after w weeks?
Exponential Growth: y=a*b^x where a initial amount and b is the growth factor.
Sarah identified the initial amount as 78000 and the rate as 3%. She wrote her equation as: y=78,000 〖(3)〗^x.
Error:
Correct solution:
The error is the way she wrote 3%
3% = 0.03
The correct equation should be y = 78,000(0.03)^x
X-10<6-5x , I need the inequality solved please:)
Answer:
x < [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
Given
x - 10 < 6 - 5x ( add 5x to both sides )
6x - 10 < 6 ( add 10 to both sides )
6x < 16 ( divide both sides by 6 )
x < [tex]\frac{16}{6}[/tex], that is
x < [tex]\frac{8}{3}[/tex]
Length of the missing leg is:
Pythagorean theorem - Integers -
Find the missing leg
PLEASE HELP
(need to show work)
Im so confused!!
The lengths of the legs of each triangle are:
1) Leg = √19
2) Leg = √105
3) Leg = √60
How to use Pythagoras Theorem?
Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
a = √(c² - b²)
1) We are given that:
Hypotenuse = 10
Opposite side = 9
Thus, using Pythagoras Theorem, we have:
Leg = √(10²- 9²)
Leg = √19
2) We are given that:
Hypotenuse = 19
Opposite side = 16
Thus, using Pythagoras Theorem, we have:
Leg = √(19²- 16²)
Leg = √105
3) We are given that:
Hypotenuse = 8
Opposite side = 2
Using Pythagoras Theorem, we have:
Leg = √(8²- 2²)
Leg = √60
Simplify.
38√
3√4
6√8
24√8
6√4
Answer:
the first one i believe
Step-by-step explanation:
hope this helps
Answer:
3√4
Step-by-step explanation:
explain how to convert numbers from standard form to scientific.
Answer:
Start by moving the decimal place in the number until you have a coefficient between 1 and 10. The number of places to the left that you had to move the decimal point is the exponent. so for example, 0.000345 would be 3.45(10)^4
Step-by-step explanation:
Hope that helps!
2pt 4 fl oz, 5 cups 39fl oz. What is the greatest amount of paint?
Answer:
5 cups 39 fl oz
Step-by-step explanation:
There are 2 cups to a pint, so 2pt 4 fl oz becomes 4 cups 4 fl oz, which is less than 5 cups 39 fl oz
Josephina is five years older than Cameron and the sum of their ages is 31. Can you write or type an equation and solve it to figure out their ages? Or, must you use the 5-D process to solve? Either way, find a way to solve it. How old are Josephina and Cameron? Show that your answer is correct.
Cameron - х years
Josephina is five years older than Cameron = х+5 years
sum of their ages is 31
х+х+5=31
2х=31-5
2х=26
х=13 Cameron
13+5=18 Josephina
The age of Josephina and Cameron is 13 and 18.
The calculation is as follows:
here Cameron be х years
And, Josephina is five years older than Cameron so х+5 years
Also,
The sum of their ages is 31
Now
х+х+5=31
2х=31-5
2х=26
х=13 Cameron
13+5=18 Josephina
learn more: https://brainly.com/question/18269454?referrer=searchResults
If Kayla babysits for 3 hours, she will earn$27. How much will she earn for 4 hours?
Answer:
kayla will earn $26
She will earn $36.00 in 4 hours.
27 divided by 3 = 9
9 x 4 = 36
Hope this makes sense and helps.
There are 12 contestants in a coloring contest. Three ribbons will be awarded. How many different ways could the ribbons be awarded?
Answer:
1320 ways
Step-by-step explanation:
Here we have a situation where 3 ribbons will be awarded to 3 of the 12 contestants. We can use the permutation formula, because the order of awarding the ribbons matters.
The permutation formula is:
[tex]_{n}P_{k}=\dfrac{n!}{(n-k)!}[/tex]
n = 12
k = 3
Now that we have our variables, let's plug them into the formula.
[tex]_{12}P_{3}=\dfrac{12!}{(12-3)!}[/tex]
[tex]_{12}P_{3}=\dfrac{12!}{9!}[/tex]
[tex]_{12}P_{3}=1320[/tex]
So there are 1320 different ways that the contestants will be awarded.
Lina bought x rolls of film at $5.00 per roll and spent $25. How many rolls of film did Lina buy? (MUST SHOW WORK)
Answer:
Step-by-step explanation:
If Lina supposedly bought 10 rolls, we would show it by the following equation,5*10=50, and since 25 is half of 50, we would have 5 as our solution.
25/5=5
5 rolls of films is our solution
Which type of function is the result of adding a quadratic function and a linear function?
A. a linear function
B. a quadratic function
C. a rational function
D. a cubic function
Answer:
B
Step-by-step explanation:
D: You will not get a cubic function. Nothing adds to give a term with x^3 in it.
C: A rational function is of the form (x^2 + 3x + 2) / (x^2). In other words it has a numerator and a denominator that are polynomials. Unless one or both started out like that, the answer is not a rations function.
A: It can't be linear. The x^2 term will carry over after addition.
The answer is B. One of the polynomials started out as a quadratic. It will remain that way.