the sum of three consecutive odd numbers is 81.What is the smallest of the three numbers?
The three consecutive numbers are 25,27,29. The smallest is 25
12y+d=−19y+t
Solve for y
Hi!
Solve for d.
[tex]12y+d=-19y+t[/tex]
Subtract by 12y from both sides.
[tex]12y+d-12y=-19y+t-12y[/tex]
[tex]Answer---> d=-31y+t[/tex]
Solve for y.
Add 19y from both sides.
[tex]d+12y+19y=t-19y+19y[/tex]
[tex]d+31y=t[/tex]
Add d from both sides
[tex]d+31y+-d=t+-d[/tex]
[tex]31y=-d+t[/tex]
Divide by 31 from both sides.
[tex]\frac{31y}{31}=\frac{-d+t}{31}[/tex]
[tex]Answer ----> y=\frac{-1}{31} d+\frac{1}{31}t[/tex]
Hope this helps!
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Have a great day!
-Charlie
The number of employees of a company decreased from 225 to 189. Find the percent decrease
The number of employees at the company decreased by 16%. This was calculated by first finding the decrease in number of employees (36) and then calculating this as a percentage of the original number of employees.
Explanation:To find the percent decrease in the number of employees at the company, you need to follow these steps:
First determine how many employees there has been a decrease by subtracting the final number of employees from the original number. So 225 - 189 = 36.Next, calculate the percentage that this decrease represents out of the original number. You do this by dividing the decrease by the original number and then multiplying the result by 100 to get a percentage. So (36/225) * 100 = 16%.So the number of employees at the company decreased by 16%.
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Which line is a graph of the equation: 2x + 5y = –10? Number graph ranging from negative five to five on the x axis and negative six to two on the y axis. Four lines are drawn in blue on the graph. Lines a and c have a positive slope and are parallel to each other. Lines b and d have a negative slope and are parallel to each other. Lines a and b intersect at (zero, two), and lines c and d intersect at (zero, negative two). A. line a B. line b C. line c D. line d
First we find the slope of the given line by using slope intercept form.
Converting the equation into slope intercept form
[tex] 5y=-2x-10[/tex]
Divide both side by 5 we get
[tex] y==-\frac{2}{5}-2[/tex]
On comparing with [tex] y=mx+c[/tex]
We get slope [tex] m=-\frac{2}{5}[/tex]
as the slope of line is negative therefore the line will either "b" or "d"
As line "b" pass from (0,2)
On putting it in given equation we get
[tex] 2(0)+5(2)=10[/tex]
Which is not equL to RHS of the line
Therefore b is not the given line
Now putting point (0,-2)
We get [tex] 0+5(-2)=-10[/tex]
Satisfy the equation and line "d" pass from it
There the give equationis of line "d"
Answer:the answer is line D
Step-by-step explanation:took the test and got it right
Pls help forgot to do this
The surface area of a rectangular prism is the sum of the areas of its faces added together. From the picture, we can see that the prism is constructed of 4 faces that measure 7 cm by 9 cm and 2 faces that measure 7 cm by 7 cm.
The area of one 7 cm by 9 cm face is 63 cm². Together, all four of the faces add up to 252 cm².
The area of one 7 cm by 7 cm face is 49 cm². Together, the two faces add up to 98 cm².
Using these areas, we can say that the total surface area of the prism would be 252 cm² added to 98 cm², or 350 cm².
Y - 3 = 4(x + 12) slope and y intercept
The y-intercept will be (0,51)
In case, if you want the x-intercept it will be (-51/4,0)
I need help with the question above in the picture
First you would need to simplify.
4³=64
100/24=4
5 ^0= 1 (anything to the power of 0 is 1)
So your equation now looks like 64 * 4 - 1
Your answer would be 255.
PEMDAS: Parentheses, Exponents, Multiplication & Division, Addition & Subtraction. This is the order that operations are to be performed.
First, Parentheses
4³ * [tex](\frac{100}{25})[/tex] - 5⁰
= 4³ * 4 - 5⁰
Next, Exponents
4³ * 4 - 5⁰
= 64 * 4 - 1
Then, Multiplication & Division
64 * 4 - 1
= 256 - 1
Last step, Addition & Subtraction
256 - 1
= 255
Answer: 255
a plane flew 187 miles from New York city, to Boston Massachusetts. it therefore 273 miles from Boston to Philadelphia, Pennsylvania. the plane flew the same distance on the return trip. how many miles did the plane fly?
Answer:
920 miles
Step-by-step explanation:
Distance from New York City to Boston Massachusetts = 187 miles
Distance from Boston to Philadelphia, Pennsylvania = 273 miles
Total Distance of one side = 187 + 273
Total Distance of one side = 460 miles
The return distance will be the same that is 460 miles.
Total Distance of both sides = 460 + 460
Total Distance of both sides = 920 miles
Therefore, the plane flew total 920 miles.
!!
What is the maximum value of the objective function, P, with the given constraints?
P=20x+35y
x+y≤12
5x+y≤20
x≥0
y≥0
80
390
420
700
Answer:
Option C - 420
Step-by-step explanation:
Given : Objective function, P, with the given constraints
[tex]P=20x+35y[/tex]
Constraints,
[tex]x+y \leq 12[/tex]
[tex]5x+y \leq 20\\x \geq 0\\y \geq 0[/tex]
To find : What is the maximum value
Solution :
First we plot the graph through the given constrains.
As they all move towards the origin the common region of the equations is given by the points (0,0), (0,12), (2,10), (4,0)
Refer the attached figure.
So, we put all the points in P to, get maximum value.
[tex]P=20x+35y[/tex]
Point (0,0)[tex]P=20(0)+35(0)=0[/tex]
[tex]P=20x+35y[/tex]
Point (0,12)[tex]P=20(0)+35(12)=420[/tex]
Point (2,10)[tex]P=20(2)+35(10)=40+350=390[/tex]
Point (4,0)[tex]P=20(4)+35(0)=80[/tex]
Therefore, The value is maximum 420 at (0,12)
So, Option C is correct.
Answer:
420
Step-by-step explanation:
What is the least common denominator for the fractions 1/3 and 2/9
the LCD of the two is 9 what you do is this so 1/3,2/9 is simple its 1/3 2/3 1 then lets try the 2/9 2/9 4/9 6/9 and keep doing that until they both reach the SAME number.
The LCD (Least common denominator) is 9,
For the denominators (3, 9) the least common multiple (LCM) is 9.
Therefore, the least common denominator (LCD) is 9.
Hope This Helps :D
18.A ________ change occurred when a metal changed Color because it reacted with another substance.
The answer is a chemicl change.
A chemical change occured when a metal changed color because it reacted with another substance.
Benito saves $6 out of every $20 he earns. He earned $90 one month. How much did he save?
Set up a proportion:
6/20 = x/90
Meaning 6 saved over 20 and x saved over 90
Cross multiply
540 = 20x
x = 27
He saved $27
Evaluate the expression when x = 2
Plot the line for the equation on the graph. y−4=−14(x−5)
Answer:
Where do I plot it
Step-by-step explanation:
Answer:
Answer: Hopefully this helps other people! :) I got it right on the test!
Need help with number 60 plz. Multi-step math :)
Problem 60)
Solution
Part 1
Joy earns $8 per hour. She earns $128 per month.
The number of hours worked in each month = 128/8 = 16 hours.
She works 16 hours each month in order to earn $128.
Part 2
After six months she gets a $2 per hour raise.
Now her earning per become $10.
She works 16 hours each month.
Joy earning per month = 16*10 = $160.
Hope you will understand the solution. Thank you :)
Mr. McKay spent $2.60 for a box of crackers and then divided them evenly between the s students in his class. Write an expression for the cost of the crackers for each student. Find the cost for s=20 students
$2.60 was spent on a box of crackers. s = 20 students.
Let's have C be the cost of crackers for each student. To find the cost, we divide the total amount of money (2.60) by the number of students (20)
C = 2.6/20
C = 0.13
The cost of the crackers for each student in Mr. McKay's class, if divided evenly, would be $0.13 when there are 20 students.
Explanation:Mr. McKay's expenditure on the box of crackers can be written as an arithmetic expression where the total cost is divided by the number of students. This expression is 2.6 / s. By substituting the given number of students (s=20), we find that the cost of the crackers for each student is 2.6 / 20 = $0.13. Therefore, each student should pay $0.13 if the cost of the crackers is to be divided evenly among them.
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Choose the true statement.
-2 < -3
-2 > -3
-2 = -3
-2>-3
Because -2 is less far down than -3.
PLEASE HELP!! ASAP!!! 20 POINTS. David proved the Law of Cosines with reference to triangle abc using a different method.Arrange the steps of his proof in the correct sequence
Answer:
Top-to-bottom, the boxes have this order in the proof: 1, 7, 4, 3, 9, 8, 5, 2, 6.
Step-by-step explanation:
The basic idea is to use the Pythagorean theorem to write two expressions for the length of altitude BD, also called "k", then equate them and simplify the result. This leaves an expression for DC, also called "x", which is replaced by a cosine expression to complete the proof.
Finally, the variations involving other combinations of sides and angles are suggested as being provable in the same way.
How much of an alloy that is 10% copper should be mixed with 600 ounces of an alloy that is 60% copper in order to get an alloy that is 20% copper?
Answer:
1800 oz.
Step-by-step explanation:
There are already 600 ounces of alloy of nickel.
Of this 600 oz, 50% is pure i.e. copper content = 600(0.5) = 300 oz
Now available is
Copper Other metals
300 300
Let x oz of 10% copper is added.
Then new alloy will have 300+0.1x oz copper in total of 600+x oz.
Percentage pure = [tex]\frac{300+0.1x}{600+x} =20%[/tex]
Simplify to get
[tex]\frac{300+0.1x}{600+x} =\frac{20}{100} \\\\Cross multiply:\\20(600+x) =100(300+0.1x)\\12000+20x =30000+10x\\10x = 18000\\x = 1800[/tex]
Hence answer is 1800 oz should be added.
In a recent year the total sales at a restaurant a bar $350,000 worth in at restaurant be. Total sales at the two stores were $575 million. What were the sales for the year at each store?
Subtract the difference from the total:
575,000,000 - 350,000 = 574, 650, 000
Divide the difference by 2:
574, 650, 000 / 2 = 287,325,000
That is the lower one, then add the difference for the higher one:
Restaurant A = $287,325,000 + $350,000 = $287, 675,000
Restaurant B = $287,325,000
what is the mean of 5,10,15,20,25
5+10+15+20+25=75
75/5=15
15 is the mean
5+10+15+20+25=75
Your mean will be 75
Then divide by 5 = 15
Your answer will be 15
thirty students are eating at 5 lunch tables. each table had the same number of stdents. how many students are sittimg at each table?
Quiz: 4.12: Step Functions
I'll give brainliest!!!
Please Help me
#4 How does the graph of g(x)=2⌈x⌉ differ from the graph of f(x)=⌈x⌉?
Multiplying by 2 compresses the graph of g(x)=2⌈x⌉ vertically by a factor of 2.
Multiplying by 2 shifts the graph of g(x)=2⌈x⌉ up 2 units.
Multiplying by 2 shifts the graph of g(x)=2⌈x⌉ down 2 units.
Multiplying by 2 stretches the graph of g(x)=2⌈x⌉ vertically by a factor of 2.
#5 How does the graph of g(x)=⌊x⌋−3 differ from the graph of f(x)=⌊x⌋?
The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units.
The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted right 3 units.
The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted left 3 units.
The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted up 3 units.
Question 4: The correct option is d. Multiplying by 2 stretches the graph of g(x) = 2⌈x⌉ vertically by a factor of 2.
Question 5: The correct option is a. The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units.
Question 4:
The graph illustrates the functions f(x) = ⌈x⌉ and g(x) = 2⌈x⌉. Multiplying by 2 does not compress or shift the graph vertically, but rather stretches it. Each step on f(x) has a height of 1 unit, while on g(x), the steps have a height of 2 units.
This indicates that g(x) is a vertical stretch of f(x) by a factor of 2. The red dotted lines highlight the vertical distance between corresponding steps of f(x) and g(x), showing that g(x) is indeed twice the height of f(x) at every step. Therefore, the correct statement is:
Multiplying by 2 stretches the graph of g(x) = 2⌈x⌉ vertically by a factor of 2.
The representation of the graph is given below.
Question 5:
The graph demonstrates the functions f(x) = ⌊x⌋ and g(x) = ⌊x⌋−3. The graph of g(x) is identical in shape to the graph of f(x), but it is shifted downward by 3 units. This is visually represented by the dashed line of g(x), which follows the same step pattern as f(x) but is consistently 3 units lower across the entire domain.
Therefore, the correct statement is:
The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units.
The representation of the graph is given below.
Nine less than five times a number is equal to -30
To solve this question, we can start to set up an equation using what the question is telling us. Since we don't know what the number is, let's make it equal to x.
The phrase "5 times a number" means that we're multiplying our unknown, x, by 5. That is equal to 5x. 9 less than that would be 5x - 9. Since we know that it's equal to -30, we can solve.
5x - 9 = -30
Get all terms with x on one side and the constants on the other
5x - 9 +9 = -30 + 9
Simplify
5x = -21
Now, we can divide both sides by 5 to get our answer of x = -[tex]\frac{21}{5}[/tex]
An equation can be formed with the given information.
"Nine less than" → -9
"Five times a number" → 5x
"Is equal to -30" → =-30
So our given equation is: 5x-9=-30
To solve this, first add 9 on both sides of the equation.
5x-9+9=-30+9
5x=-21
Divide both sides by 5 for x.
[tex]\frac{5x}{5}[/tex]=[tex]\frac{-21}{5}[/tex]
x=[tex]\frac{-21}{5}[/tex] , or -4.2.
If you roll a die, what is the probability that a one will appear on top
you will have a 1 in 6 chance to roll a 1 on a die
A standard Die has 6 sides.
The probability of any number being on top is 1/6.
The probability of having a one on top would be 1/6.
Which ordered pair is a solution of the equation Y=- 7X +2
Answer:
neither
Step-by-step explanation:
Olivia ordered cupcakes and a layer cake. Together she paid $52. She paid $12 more on the layer cake than on the cupcakes. What was the price of each?
Hey there!!
The total cost is $52.
She paid $12 more for the layer cake than the cupcake.
Let's take the price of the cupcake as $x. Then, the price of the layer cake would be $12 + x
The sum of these would result in $52.
... x + x + 12 = 52
... 2x + 12 = 52
... 2x = 52 - 12
... 2x = 40
... x = 20
Hence, the price of the cupcake is $20 and the price of the layer cake is $32.
Hope my answer helps!!
A bookstore manager marks down the price of older hardcover books,which originally sell for b dollars,by 46 percent. What is the markdown as a decimal. Write an expression for the sale price of the hardcover book. What is the same price of a hardcover book for which the original retail price was $29.00? If you buy the book in part c, how much do you save by paying the sale price?
We are given original selling price of book = $b.
Price is marked down by 46%.
46% can be written as 46/100 in decimals it would be 0.46.
Therefore, markdown as a decimal is 0.46
Now, markdown is 0.46 of original price = 0.46b
Therefore, new price after marked down can be written by expression =
b - 0.46b = 0.56b.
Therefore, the expression for the sale price of the hardcover book is 0.56b.If original retail price was = $29.00.
The sale price would be 0.56b = 29*0.56 = $15.66.
Total saving = 29-15.66 = $13.34.
Therefore, you save $13.34 by paying the sale price $15.66.
Where does 56 come from ?
Solve the system by the substitution method.
X+Y=-3
Y=-4x
x = 1, y = - 4
substitute y = - 4x into the other equation
x - 4x = - 3
- 3x = - 3 ( divide both sides by - 3 )
x = 1
substitute x = 1 into y = - 4x ⇒ y = - 4
How to solve |3x-6|<30
[tex]|3x-6|<30 \\\\|x-2|<10\\\\x-2<10 \wedge x-2>-10\\\\x<12 \wedge x>-8\\\\x\in(-8,12)[/tex]
[tex]Solution, solve\:for\:x,\:\left|3x-6\right|<30\quad :\quad -8<x<12[/tex]
[tex]Steps:[/tex]
[tex]|f\left(x\right)|<a\quad \Rightarrow \:f\left(x\right)<a\quad \mathrm{and}\quad \:f\left(x\right)>-a, 3x-6<30\quad \quad \mathrm{and}\quad \:\quad \:3x-6>-30[/tex]
[tex]3x-6<30\quad :\quad x<12[/tex]
[tex]3x-6>-30\quad :\quad x>-8[/tex]
[tex]\mathrm{Combine\:the\:ranges}, -8<x<12[/tex]
The correct answer is -8<x<12