Answer:
To solve this question, we first have to know that we are trying to assemble
and solve equations with two variables: x
and y.
Assuming x
is the number of dimes and y
is the number of quarters, we
can assemble the equations.
since the number of dimes is 3 more than three times the number of quarters,
we get x=3y+3.
Additionally, multiplying the number of dimes by 0.1 and the number of
quarters by 0.25,
we get the total value of x
and y
which appears by this
equation 0.1x+0.25y=11.30
.
Substituting the value of x
in the second equation, we get 0.1(3y+3)+
0.25y=11.30
.
Solving this equation, we get that the value of x,
we get x=3×20+3=
Using the first equation to get the value of x,
we get x=3×20+3=
60+3=63
dimes.
Chapter 9
Math Models and Geometry
Section 2
Solve Money Applications
Prealgebra
Step-by-step explanation:
At an amusement park, 25 riders ride the race cars every 30 minutes and 20 riders ride the spinning swings every 20 minutes. Which ride will have more riders each hour and how many more? Use the drop-down menus to answer the problem. The Choose... will have Choose... more riders each hour.
Answer:
The spinning swings will have 10 more riders each hour.
Step-by-step explanation:
1. If 25 riders ride the race car every 30 mins, that would mean each hour 50 riders ride the race car.
2. If 20 riders ride the spinning swings every 20 mins, that would mean each hour 60 riders ride the spinning swings.
Lets say 4 hours have passed. We could say 25 × 8. I don't know if this would make sense but there would be 8 30 mins in 4 hours. If you multiply 25 × 8 you would get 200 riders riding the race cars in 4 hours.
Lets do the same thing with the spinning swings. There are 12 20 mins in 4 hours. So we could do could do 20 × 12. That would equal 240 riders riding the spinning swings in 4 hours.
So if the race cars got 200 riders in 4 hours, each hours they will have 50 riders. And If the spinning swings got 240 riders in 4 hours, each hour they got 60 riders. So that would mean the spinning swings got more riders each hour. They also got 10 more riders each hour. Hopefully I didn't confused you.
(x +y)^5
Complete the polynomial operation
Answer:
Please check the explanation!
Step-by-step explanation:
Given the polynomial
[tex]\left(x+y\right)^5[/tex]
[tex]\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
[tex]a=x,\:\:b=y[/tex]
[tex]=\sum _{i=0}^5\binom{5}{i}x^{\left(5-i\right)}y^i[/tex]
so expanding summation
[tex]=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5[/tex]
solving
[tex]\frac{5!}{0!\left(5-0\right)!}x^5y^0[/tex]
[tex]=1\cdot \frac{5!}{0!\left(5-0\right)!}x^5[/tex]
[tex]=1\cdot \:1\cdot \:x^5[/tex]
[tex]=x^5[/tex]
also solving
[tex]=\frac{5!}{1!\left(5-1\right)!}x^4y[/tex]
[tex]=\frac{5}{1!}x^4y[/tex]
[tex]=\frac{5}{1!}x^4y[/tex]
[tex]=\frac{5x^4y}{1}[/tex]
[tex]=\frac{5x^4y}{1}[/tex]
[tex]=5x^4y[/tex]
similarly, the result of the remaining terms can be solved such as
[tex]\frac{5!}{2!\left(5-2\right)!}x^3y^2=10x^3y^2[/tex]
[tex]\frac{5!}{3!\left(5-3\right)!}x^2y^3=10x^2y^3[/tex]
[tex]\frac{5!}{4!\left(5-4\right)!}x^1y^4=5xy^4[/tex]
[tex]\frac{5!}{5!\left(5-5\right)!}x^0y^5=y^5[/tex]
so substituting all the solved results in the expression
[tex]=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5[/tex]
[tex]=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
Therefore,
[tex]\left(x\:+y\right)^5=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
a tank containing 50 liter of water develops a leak and loss water at a constant rate. after 20 minutes it contains 40 liter. after a further 30 minutes the tank is 5% of its full capacity. determine the tanks capacity
Answer:
The tank's capacity is 500 liters
Step-by-step explanation:
Proportions
The tank initially contains 50 liters of water. The tank's capacity is more than that, as we'll show later.
We know after 20 minutes of leaking from the tank, 40 liters still remain. This means 10 liters have leaked in 20 minutes. The loss of water occurs at a constant rate or 10/20=0.5 liters per minute.
After 30 more minutes, the tank has lost 0.5*30 = 15 more liters of water and now has 40 - 15 = 25 liters remaining.
We are told those 25 liters correspond to 5% of the tank's full capacity. Thus, the full capacity of the tank is:
[tex]\displaystyle \frac{25 }{ (5 / 100)} = 500~liters[/tex]
The tank's capacity is 500 liters
(03.01) Match the two numbers with their least common multiple (LCM). Match Term Definition 8 and 4 A) 24 8 and 6 B) 8 8 and 10 c) 40 Previous Question Question 1 (Not Answered)
Answer:
LCM of 8 and 4 = [tex]8[/tex]
LCM of 8 and 6 [tex]=24[/tex]
LCM of 8 and 10 = [tex]40[/tex]
Step-by-step explanation:
Least common multiple (LCM) of numbers is their smallest common multiple.
First find prime factorization of [tex]4,6,8,10[/tex]
[tex]4=2^2\\6=2(3)\\8=2^3\\10=2(5)[/tex]
LCM of 8 and 4 = [tex]2^3=8[/tex]
LCM of 8 and 6 [tex]=2^3(3)=8(3)=24[/tex]
LCM of 8 and 10 = [tex]2^3(5)=8(5)=40[/tex]
If you know why i got the point wrong for A and B please let me know right now i need it.
Thank you!
I’ll be giving extra points who ever explain it and has the answer correctly
Answer:
a.(-1,8), (2,9) b. (2,0) (3,5)
Step-by-step explanation:
a.
for (-4, 7) slope is [tex]\frac{1}{3}[/tex]
slope is m=rise /run =rise 1/run3 so to go to the next point
from (-4,7)
rise 1 so now you are at (-4,8) and run 3 and you are at (-1,8)
from (-1,8)
rise 1 to (-1, 9) and run 3 to (2,9)
b
(1,-5) slope is [tex]\frac{5}{1}[/tex]
from (1,-5) rise 5 to (1,0) and run 1 to (2,0)
from (2,0) rise 5 to (2,5) and run 1 to (3,5)
I NEEEDDDD HELP PLZZZZZZZZZZZZZZZZZZZZZZZZZ
The shorter diagonal of a rhombus measures 18cm. The side of the rhombus measures 41cm. Find the length of the longer diagonal.
Answer:
80 cm
Step-by-step explanation:
The diagonals divide the rhombus into four congruent triangles. The height of each triangle is 18/2 = 9, and the hypotenuse is 41. Using Pythagorean theorem, the width of each triangle is:
c² = a² + b²
41² = 9² + x²
x = 40
Therefore, the longer diagonal is 2×40 = 80.
How do you do b and c?
Answer:
b) 18
c) 80.78
Step-by-step explanation:
While we can solve this equation with separation of variables, it isn't necessary. The coffee is originally at 95°, and the ambient temperature is 18°. The top right graph is the only one that shows this trend.
As t approaches infinity, y approaches the ambient temperature of 18°.
yₙ₊₁ = yₙ + Δt F(tₙ, yₙ)
yₙ₊₁ = yₙ + 2 (-0.02 (yₙ − 18))
yₙ₊₁ = yₙ − 0.04 (yₙ − 18)
yₙ₊₁ = 0.96 yₙ + 0.72
When n=0:
y₁ = 0.96 y₀ + 0.72
y₁ = 0.96 (95) + 0.72
y₁ = 91.92
When n=1:
y₂ = 0.96 y₁ + 0.72
y₂ = 0.96 (91.92) + 0.72
y₂ = 88.96
When n=2:
y₃ = 0.96 y₂ + 0.72
y₃ = 0.96 (88.96) + 0.72
y₃ = 86.12
When n=3:
y₄ = 0.96 y₃ + 0.72
y₄ = 0.96 (86.12) + 0.72
y₄ = 83.40
When n=4:
y₅ = 0.96 y₄ + 0.72
y₅ = 0.96 (83.40) + 0.72
y₅ = 80.78
1.x(x+4)=5
2.(x+3)raise to 2=36
3.(t+2)raise to 2+(t-3)raise to2 =9
4.3 4
--+-- =x-1
x 2x
5. 3 4
-------+------- =x-1
m-2 m+5
how did you transform each equation into a quadratic equation what concepts or principles did you employ
x (x + 4) = 5
x² + 4x = 5
x²+ x + (-5) = 0
(x+3)²+(t+3)²=9
x² + 6x + 9 + t² + 6t + 9 = 9
x² + t² + 6x + 6t + 18 + (-9) = 0
x² + t² + 6x + 6t + 9 = 0
x² + t² + 6(x + t) + 9 = 0
3/x + 4/2x = x - 1
6/2x + 4/2x = x - 1
10/2x = x - 1
10 = (x - 1) 2x
10 = 2x² - 2x
0 = 2x² + (-2x) + (-10)
When is subtraction always the first operation done in an expression?
Answer:
When it is in parentheses.
Step-by-step explanation:
In PEMDAS, first is always parentheses, no matter what operation.
If it is subtraction, do that first.
hope this helped!
Answer:
the 3rd one
Step-by-step explanation:
this is only true when it is in perenthisis because when you do PEDMAS you go in that order. P (perenthisis) beng first. so TECHNECLY perenthisis is first, but the first actual MATH PROBLEM being done is subtraction.
5
Select the correct answer.
Tom gets $12 off a box of chocolates that had an original price of $48. What percentage is the discount?
OA.
12%
OB.
25%
Ос.
50%
OD
60%
Reset
Next
Answer:
B
Step-by-step explanation:
12 is 1/4 of 48 so when you take $12 off $48 you take 1/4 of 25% away
Carter's trampoline has a diameter of 10 ft. Its circumference is twice as great as the circumference of Reed's trampoline. What is the circumference of Reed's trampoline.
Answer:
no
Step-by-step explanation:
nsjdjfhfjskskdknxiwiwfbrbbewiisaksndbbfeueiaooand
one school purchased 18 gallons of blue paint to decorate several of its classrooms. if each classroom needs 1 4/5 gallons of paint, then how many classrooms will get painted.
Answer:
18 gallons of paint could paint 10 classrooms.
Step-by-step explanation:
Given that the school bought 18 gallons of paint, and that each classroom requires 1 4/5 of paint to be painted, to determine how many classrooms can be painted with that amount of paint, the following calculation must be performed:
4/5 = 0.8
1 + 0.8 = 1.8
18 / 1.8 = 10
Therefore, 18 gallons of paint could paint 10 classrooms.
please help asap question 9()
___ x 2 = 30
12 divided by ___ = 4
Just a practice :)
15 x 2 = 30
12 ÷ 3 = 4
Have a wonderful day!
- Audrey :)
1 point
Find the slope of each line that passes through the points (4.0) and (7.9),
Answer:
[tex]m=3[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (4, 0)
Point (7, 9)
Step 2: Find slope m
Substitute: [tex]m=\frac{9-0}{7-4}[/tex]Subtract: [tex]m=\frac{9}{3}[/tex]Divide: [tex]m=3[/tex]The half-life of a radioactive substance is 200 years. There are 8000 grams of the substance initially. How many grams of the substance are left after 300 years?
Answer:
There are 2,000 grams left after 300 years.
Step-by-step explanation:
Giving the following information:
The half-life of a radioactive substance is 200 years. There are 8000 grams of the substance initially.
First, we need to calculate the reduction of the substance each year:
Yearly reduction= 8,000/400= 20 grams per year
Now, for 300 years:
300 year reduction= 20*300= 6,000
There are 2,000 grams left after 300 years.
Find the area of a compound shape
Can you please explain
Answer:
Bruh the answer is there so uh yea
Step-by-step explanation:bruh sorry for being a little rude.
You and your friend skate at the same rate. You complete 6 laps in 5 minutes. How long does your friend take to complete 18 laps?
Answer:
15 minutes
Step-by-step explanation:
Answer:
69
Step-by-step explanation:
haha 69= funny number
12 movie tickets cost $36. At this rate, what is the cost per ticket?
Answer:
3
Step-by-step explanation:
36÷12=3
sooo EACH ticket is 3$ PER ticket
Find the equation of a line that has a slope of -3/7 and goes through the point (49,-17)
Mia went into a fair with $55.75 in her pocket. She bought a hot dog and drink for $2.975 each and then wanted to spend the rest of her money on rids tickets, which costs $0.95 each. Write an inequality to represent the total where r is the number of tickets purchased.
What is the maximum number of tickets mia can buy or purchesed_______?
Graphs how many rides tickets can mia buy without going over her budget.?
Answer: Maximum tickets she can buy is 52
Step-by-step explanation:
After she bought the fries and drinks she was left with $49.81. If she spent the rest of her money on rides/tickets for the rides then she bought 52 tickets to be exact. 0.95x52=49.40
Your boss asks you to design a Boolean circuit that verifies
Answer:
hello your question is incomplete attached below is the complete question
answer : attached below
Step-by-step explanation:
A) The given output would be : 1 for 0, 5,10,15 also the output will be = 0 for every other value
attached below is the truth function of the Boolean truth table
B) attached below is the Boolean expression
Two system of equations 2y =14-2x and y=-x + 7 is graphed. What is the solution to the system of equations
To solve this system, we will use the graphing method.
Based on the graph shown below, we can conclude that this system has infinite solutions, because they are the same line.
Answer:
Infinitely many solutionsStep-by-step explanation:
Given equations
2y =14-2x and y= -x + 7Rewriting the first equation
2y = 14 - 2x2y = -2x + 14y = -x + 7As we see it is same as the second equation. So same two lines, overlapping when graphed and the system has infinitely many solutions
Which expression can be used to represent the phrase “Maren increases the number of servings by six”? A. n-6 B. 6-n C. n+6 D. 6n HURRY PLEASE
Answer: C) n+6
Step-by-step explanation:
You’re increasing so it means you want to add and you must have a serving 6+ and the only one that’s increasing is C
Answer: c is n+6
Step-by-step explanation:
HELP PLZ
i need help with this math side i just need b,c,d a =4x+2y=16
Answer:
Please check the explanatio.
Step-by-step explanation:
Solving Part b)
We know that the slope-intercept form of the equation line is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
Given the equation
[tex]4x+2y=16[/tex]
Re-writing the equation in the slope-intercept form
[tex]4x+2y=16[/tex]
[tex]y=-2x+8[/tex]
Here, m=-2 and b=8
Thus, the equation in the slope-intercept form will be:
[tex]y=-2x+8[/tex]
Solving Part c)
As you sold two pounds of cheddar cheese.
i.e. y=2
substituting y=2 in the slope-intercept form of the line equation
[tex]y=-2x+8[/tex]
[tex]2=-2x+8[/tex]
Subtract 8 from both sides
[tex]-2x+8-8=2-8[/tex]
[tex]-2x=-6[/tex]
Divide both sides by -2
[tex]\frac{-2x}{-2}=\frac{-6}{-2}[/tex]
[tex]x=3[/tex]
You sold 3 pounds of swiss cheese.
Solving Part d)
[tex]y=-2x+8[/tex]
putting x=2.5 in the equation
[tex]y=-2x+8[/tex]
[tex]2=-2\left(2.5\right)+8[/tex]
[tex]2=3[/tex]
The sides are not equal
FALSE
Thus, x=2.5 does not make any sense in the context of the problem.
Write the slope intercept form of the equation of each line plz
(Ill give brainliest)
Solve 9,396 ÷ 18 = __________ Using partial quotients.
Draw it out
Answer:
522
Step-by-step explanation:
POINTS AND POINTS AND POINTS. ANSWER ONLY IF U TOOK THE TEST ON K12 AND POST PICTURE OF CORRECT ANSWERS.
The coordinates of the vertices of quadrilateral ABCD are A(−1, −1), B(−3, 3), C(1, 5), and D(5, 2). Drag and drop the choices into each box to correctly complete the sentences. The slope of AB⎯⎯⎯⎯⎯ is Response area, the slope of BC⎯⎯⎯⎯⎯ is Response area, the slope of CD⎯⎯⎯⎯⎯⎯ is Response area, and the slope of AD⎯⎯⎯⎯⎯ is Response area. Quadrilateral ABCD is Response area because Response area.
Answer:
AB=-2
BC=1\2
CD=-3\4
AD=1\2
Step-by-step explanation:
The slope of AB is - 2,
Slope of BC is
Slope of CD is
Slope of AD is ,
ABCD is trapezoid because one pair of opposite sides is parallel.
Answer:
slope of AB: -2
slope of BC: 1/2
slope of CD: -3/4
slope of AD: 1/2
Quadrilateral ABCD is a trapezoid because there is one pair of parallel sides.
Step-by-step explanation:
I solved for the slopes using slope formula. Also, I determined that the quadrilateral was a trapezoid since there was at least one pair of parallel sides. I'm sorry that I don't have a k12 account, but I hope this helps.
What is the slope and y-intercept of the equation: y = -2/3x + 5
Answer:
-2/3 is slope and y-intercept is 5
The difference between two same side interior angles of two parallel lines is 35 degrees. Find the measures of these two angles.
Answer: 2x+43
Step-by-step explanation:
Answer:
107.5 degrees and 72.5 degrees (Don't forget the degrees symbol)
Please mark me Brainliest if I'm right :D