To calculate 1/3 ÷ 4/5, switch the division operation to multiplication by flipping the second fraction. This gives us 1/3 * 5/4, which simplifies to 5/12.
Explanation:In mathematics, when we're asked to divide fractions, we often use the method of multiplying by the reciprocal of the second fraction.
In this case, the question asks you to perform the division operation of 1/3 ÷ 4/5.
To do this, you would first flip (or find the reciprocal) of the second fraction, which results in 5/4 instead of 4/5. Next, we perform the operation of 1/3 multiplied by 5/4 rather than division. Multiplication of these fractions gives us 5/12. Thus, 1/3 ÷ 4/5 = 5/12 is your answer in simplest form.Learn more about Divide Fractions here:https://brainly.com/question/18511795
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I spent 3/4 of my money and then I spent 1/5 of what was left.
a) What part of all my money did I spend?
b) What part of all my money do I have left?
Answers:
a) 4/5
b) 1/5
================================================
Let's say you start off with $100. If you spend 3/4 of that, then you spend 75 dollars (because 75/100 = 3/4). Think of it like 75 cents = 3 quarters. If you spend 75 dollars out of 100 total, then you have 100-75 = 25 dollars left after the first round of spending.
If you spend 1/5th of what is left, then you spend $5 on the second round leaving 25-5 = 20 dollars left at the end of the day.
Total up what you spend for both rounds: 75+5 = 80, which divides over the original amount 100 to get 80/100 = 8/10 = 4/5
If you had 20 dollars at he end of the day, out of 100 initially, then 20/100 = 2/10 = 1/5 is the fraction of what you have left.
note how 4/5 and 1/5 add to 5/5 = 1.00 = 100%. This is because the amount you spend and the amount you have left over must add to 100% of all the money you started with
Triangle ABC was dilated to triangle A'B'C'. What was the magnitude of the dilation?
A) 1
B) 2
C) 3
D) 4
Answer:
B) 2
Step-by-step explanation:
If you start from the origin and go to point B, you went up 2, and to the left 1. Now if you go from the origin to B', you went up 4, and to the left 4. Lets compare the ratios.
2/1 and 4/2
You had to multiply the first ration by 2 to get to the second ratio.
A line has a slope of -1/2 and a y-intercept of –2.
What is the x-intercept of the line?
a.–4
b.–1
c.1
d.4
Answer:
a.-4
Step-by-step explanation:
I pictured it as a graph and since the slope is negative, the line goes down and to the right. Since the slope is -1/2, for every 2 you move horizontally, you move one vertically. You have to move two up and unless the y intercept is 0, when the line intercepts y, you have 0 as x. You move two up and 4 backwards so the x intercept is -4
what kind of decimal is an irrational number give an example
Answer:
An irrational decimal is a decimal that cannot be written in fraction form
Ex: Pi or any decimal that keeps going and doesn't repeat
Step-by-step explanation:
I would give you more examples but they are all really long numbers and go on forever.
Answer:
Pi!
Step-by-step explanation:
I know it might sound silly but Pi and it's digits are part of the irrational decimal family! It's irrational because the digits of Pi seem like they never end, right? Hope this helped!
in my house, the ratio of dogs to fish is 1:10. the ratio of fish to cats is 6:1. What is the ratio of dogs to cats?
Answer:
The ratio of dogs to cats is 3 dogs to 5 cats
Step-by-step explanation:
dogs to fish: 1:10
fish to cats : 6:1
dogs to cats: 3:5
FISH:
llllllllll (10) llllllllll (10) llllllllll(10) (30 fish)
DOGS: 1 dog per 10 fish
D D D 3 dogs
CATS: 1 cat per 6 fish
C C C C C
Ratio represents partial data as some multiplies from numerator and denominator are lost due to simplification. You can assume them to be variables.
The ratio of dogs to cats is 3:5
How to get real quantity of ratio of first quantity to second quantity = a:b?We actually cannot get real quantities but we can use variables to partially get the information of how much their quantities were.
I said 'partially' since we don't get real values but with variables only.
Since the ratio is a:b, thus let the cancelled multiple during simplification was x.
Then we have:
First quantity = ax
Second quantity = bx
How to calculate the ratio of dogs to cats?It is given that:
Ratio of dogs to fish = 1:10
Then let number of dogs = 1x = x and number of fishes = 10x
Similarly,
Ratio of fish to cats = 6:1
Then let the multiple was y, then
Number of fishes = 6y,
Number of cats = 1y = y
But we have number of fishes = 10x and 6y both
Since number of fishes is constant, thus, they are equal. Or
[tex]10x = 6y\\\dfrac{x}{y} = \dfrac{6}{10} = \dfrac{3}{5}\\[/tex]
The ratio of dogs to cats = [tex]\dfrac{\text{Numbers of dogs}}{\text{Number of cats}} = \dfrac{x}{y} = \dfrac{3}{5}[/tex]
Thus, the ratio of dogs to cats is 3:5
Learn more about ratio here:
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after 8% discount from the list price, the sale price price of a poster was $17.48. what was the list price of poster.
Final answer:
To find the list price of the poster after an 8% discount, subtract 8% of the list price from the list price and set it equal to the sale price.
Explanation:
To find the list price of the poster, we need to first calculate the original price before the discount. Let's assume the list price is 'x' dollars. After an 8% discount, the sale price of the poster is $17.48.
We can set up an equation to solve for the list price: x - 8% of x = $17.48. To calculate 8% of x, we multiply x by 0.08.
So the equation becomes: x - 0.08x = $17.48. Combining like terms, we get 0.92x = $17.48. Dividing both sides by 0.92, we find that x = $19.
Which graph shows the solution set for 4x+3>-9
[tex]4x+3>-9\qquad\text{subtract 3 from both sides}\\\\4x>-12\qquad\text{divide both sides by 4}\\\\\boxed{x>-3}[/tex]
Deena decides to mark down prices at her jewelry store 20% for a clearance sale. She must add 6% to the sale price for state sales tax. Suppose an item was originally priced at x dollars. Which expression does not represent the total sale price, including sales tax, of the item?
The expression that does not represent the total sale price, including sales tax, of the item is x * (1 - 0.20 + 0.06). Hence the correct option is c.
1. Calculate the sale price after the markdown:
Original price: x dollars
Markdown rate: 20%
Sale price after markdown: x * (1 - 0.20) = 0.8x dollars
2. Calculate the amount of sales tax:
Sales tax rate: 6%
Sales tax amount: 0.06 * 0.8x = 0.048x dollars
3. Calculate the correct total sale price:
Sale price after markdown + Sales tax amount = 0.8x + 0.048x = 0.848x dollars
4. Analyze the given expressions:
x * (1 - 0.20) + 0.06x: This expression correctly calculates the discount and adds the sales tax to the original price, so it represents the total sale price.
x * (1 - 0.20) + 0.06 * 0.8x: This expression also correctly calculates the discount and adds the sales tax to the discounted price, so it represents the total sale price.
x * (1 - 0.20 + 0.06): This expression combines the discount and sales tax into a single percentage (14%), but it applies this percentage to the original price (x) instead of the discounted price (0.8x). This leads to an overestimation of the final sale price, so it does not represent the correct total price.
0.8x + 0.048x: This expression correctly calculates the sum of the discounted price and the sales tax amount, so it represents the total sale price.
Therefore, the expression that does not represent the total sale price, including sales tax, of the item is x * (1 - 0.20 + 0.06). Hence the correct option is c.
Complete question:
Deena decides to mark down prices at her jewelry store 20% for a clearance sale. She must add 6% to the sale price for state sales tax. Suppose an item was originally priced at x dollars. Which expression does not represent the total sale price, including sales tax, of the item?
x * (1 - 0.20) + 0.06x
x * (1 - 0.20) + 0.06 * 0.8x
x * (1 - 0.20 + 0.06)
0.8x + 0.048x
How do i graph the equation -x + 2y = 2
Step-by-step explanation:
Firstly, set the x value as 0:
-0 + 2y = 2
2y = 2
y = 1
So when x = 0, y = 1
Now set y to 0:
-x + 2(0) = 2
-x = 2
x = -2
So when y = 0, x = -2
Simply plot the two following points:
(0 , 1) and (-2 , 0)
And don't forget to join these two points up!
Attatched is an image of this graph.
5 days 6 hours 20 minutes minus 3 days 8 hours 40 minutes plz help will make brainliest
Answer:
1 day 21 hours 40 minutes
Step-by-step explanation:
5 days 6 hours 20 minutes
- 3 days 8 hours 40 minutes
============================
We will need to borrow minutes from the hours because we don't have enough.
1 hour = 60 minutes
6-1 = 5 hours
20 +60 = 80 minutes
5 days 5 hours 80 minutes
- 3 days 8 hours 40 minutes
==========================
We will need to borrow hours from the days because we don't have enough.
1 day = 24 hours
5 -1 =4 days
5 + 24 = 29 hours
4 days 29 hours 80 minutes
- 3 days 8 hours 40 minutes
==========================
1 day 21 hours 40 minutes
Answer:
1 day 21 hours 40 minutes
Step-by-step explanation:
you have to convert the days to hours, then convert the hours to minutes then subtract
4 days 29 hours 80 minutes - 3 days 8 hours 40 minutes = 1 day 21 hours 40 minutes
PLZ MARK BRAINIEST
Margo has a coin collection. She was given 1 coin as a gift, and she adds 3 coins per year. Which of the graphs below represents Margo's coin collection?
graph of line going through 1, 2 and 3, 4
graph of line going through 1, 1 and 3, 3
graph of line going through 1, 4 and 3, 10
graph of line going through 1, 2 and 2, 5
The graph that represents Margo's coin collection is:
Graph of line going through (1, 4) and (3, 10).
Step-by-step explanation:It is given that:
She was given 1 coin as a gift, and she adds 3 coins per year.
Let a_n denote the amount of Money Margo had in the end of the "nth" year.
According to the given information we have:
[tex]a_1=1+3=4[/tex]
[tex]a_2=4+3=7\\\\a_2=a_1+3[/tex]
[tex]a_3=10\\\\a_3=a_2+3\\\\\\a_3=a_1+3\times 2[/tex]
and so on.
Hence, we get:
[tex]a_n=a_1+3(n-1)[/tex]
Hence, we get a Arithmetic progression.
with first term as 4 and common difference as 3.
Hence, the graph is:
Graph of line going through (1, 4) and (3, 10).
( Since at n=1 we have: [tex]a_n=4[/tex]
and at n=3 we have: [tex]a_3=10[/tex] )
what is a equivalent expression for 2(c+c+c)
Answer: 2(C^3) or 2(C to the third power)
Step-by-step explanation: C^3 is the same thing a c+c+c
Hope this helps!
How do I solve this math problem?
Answer: 4x² + 4x - 2 - [tex]\frac{3}{2x+3}[/tex]
Step-by-step explanation:
You can use either synthetic or long division. I am using synthetic division:
2x + 3 = 0 ⇒ x = [tex]-\frac{3}{2}[/tex]
[tex]-\frac{3}{2}[/tex] | 4 10 4 -6
| ↓ -6 -6 3
4 4 -2 -3 ← -3 is the remainder
↓ ↓ ↓
4x² +4x -2 ← factored polynomial
how would you graph the following systems of equations ?
y= -3x -7
x- 2y=-14
Year 1 number sold 725
Year 2 number sold 579
Year 3 number sold in year 4 the store sold 112% of the total number of scooters sold during the previous three years combined determine the number of scooter sold in year 4
Answer:
2, 240
Step-by-step explanation:
In the table, the values should be
Year 1 725
Year 2 579
Year 3 696
Since Year 4 sold 112% of the previous 3 years combined, we add 725+579+696=2000. We can find 112% by writing a proportion.
[tex]\frac{112}{100} =\frac{x}{2000}[/tex]
We solve through cross multiplication of numerator and denominator of the opposite fraction.
[tex]112(2000)=100(x)\\224000=100x\\2,240=x[/tex]
Triangle CDE and triangle CFG are similar right triangles. Which proportion can be used to show that the slope of CE is equal to the slope of CG?
A) 2 − 3
2 − 0
= 3 − 1
4 −0
B) 3 − 2
2 − 0
= 3 − 1
4 − 0
C) 2 − 3
0 − 2
= 3 − 1
0 − 4
D) 3 − 2
0 − 2
= 3 − 1
0 − 4
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points E(2, 2), C(0, 3) and G(4, 1), C(0, 3).
Substitute:
[tex]\dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}\to\boxed{D}[/tex]
Answer: The correct option is (D) [tex]\dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}.[/tex]
Step-by-step explanation: Given that ΔCDE and ΔCFG are similar right triangles.
We are to select the correct proportion that can be used to show that the slope of CE is equal to the slope of CG.
We know that the slope of a line passing through two points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
From the given figure, we note that the co-ordinates of the points C, E and G are
C(0, 3), E(2, 2) and G(4, 1).
So, the slope of line CE is given by
[tex]m_1=\dfrac{2-3}{2-0},[/tex]
and the slope of line CG is given by
[tex]m_2=\dfrac{1-3}{4-0}.[/tex]
Since the lines CE and CG are same, they must be parallel and hence they have equal slopes.
Therefore,
[tex]m_1=m_2\\\\\\\Rightarrow\dfrac{2-3}{2-0}=\dfrac{1-3}{4-0}\\\\\\\Rightarrow \dfrac{3-2}{0-2}=\dfrac{3-1}{0-4}.[/tex]
Thus, (D) is the correct option.
The point (2,-2) and (-4,13) on the graph of a linear function of x. Which point also lies on the graph of this function?
A. (-6,18)
B. (-1,5)
C. (7,14.5)
D. (13, -4)
Answer:
A. (-6,18)
Step-by-step explanation:
The point (2,-2) and (-4,13) on the graph
First we frame an equation of the line using two points
y = mx + b where m is the slope and b is y intercept
slope = [tex]\frac{y_2-y_2}{x_2-x_1} =\frac{13+2}{-4-2} = \frac{15}{-6} = -2.5[/tex]
m = -2.5
Lets find out b
y = mx+b
y= -2.5x + b
Plug in (2,-2) and find out b
-2 = -2.5(2) + b
-2 = -5 + b (add 5 on both sides)
b = 3
so equation of line is y = -2.5 x + 3
Now we check with each option
(-6,18)
Plug in the x and y in our equation and check it
y = -2.5 x + 3
18 = -2.5(-6) + 3
18 = 15+3
18=18 true
So (-6,18) lies on the graph
if an equilateral triangle has an angle of 3 X what is the value of X
Answer:
x = 20
Step-by-step explanation:
In an equilateral triangle, everything is the same; line length and angles. Each angle in an equilateral triangle is:
180 ÷ 3 = 60
So 3x = 60
Divide both sides by 3 to get x:
x = 20
What is the range of AB?
a, b, c - sides of a triangle
Therefore:
a + b > c
a + c > b
b + c > a
---------------------------------
We have a = AB, b = 140mi, c = 100mi.
(1) a + b > c
AB + 140 > 100 subtract 140 from both sides
AB > -40 → AB > 0
----------
(2) a + c > b
AB + 100 > 140 subtract 100 from both sides
AB > 40
-----------
(3) b + c > a → a < b + c
AB < 140 + 100
AB < 240
Answer: 40 < AB < 240Thank you so much
I need the help
Answer:
g(x) is translated 6 units down from f(x)
Step-by-step explanation:
given a function f(x) then f(x) + c represents a vertical translation
• If c > 0 then vertical translation up ↑
• If c < 0 then vertical translation down ↓
select the angle that correctly completes the law of cosines for this triangle 24^2+25^2-2(24)(25)cos ____=7^2
a) 180 degrees
b) 90 degrees
c) 74 degrees
d) 16 degrees
The value of angle θ will be 16 degrees. Then the correct option is D.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
24² + 25² – 2(24)(25) cos θ = 7²
Then the value of angle θ will be
24² + 25² – 2(24)(25) cos θ = 7²
576 + 625 – 1200 cos θ = 49
1200 cos θ = 1152
cos θ = 1152 / 1200
θ = cos⁻¹ (1152 / 1200)
θ = 16°
Then the correct option is D.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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54d.
Change the following expression into a single fraction:
5b − 2/b
Which tool(s) are needed to construct a perpendicular bisector of a line segment?
Answer: compass and straightedge or ruler
Perpendicular bisector of a line segment
Geometry construction using a compass and straightedge
compass and straightedge or ruler
Step-by-step explanation:
Answer:
You need a straight edge and a compass.
Step-by-step explanation:
The straight edge should not be marked in any way. You are not allowed to put a mark on the straight edge at all. The only property it has is that it has no curvature in any direction.
The compass must be flexible and at the same time it must be able to stay at one radius unless changed by the owner. It's only property is that it can draw a perfect circle once the radius of the circle has been chosen,
Addison plays 1/2 of a song in 1/4 of a minute. How minutes will she need to play a full song?
Answer:
30 minutes
Step-by-step explanation:
She plays 1/2 of a song in 1/4 of a minute so that would be 15 minutes because if you divide 60 by 4 you would get 15. You would multiply 15 by 2 because if she plays a full song you multiply 1/2 by 2 to get a whole. So she will need 30 minutes to play a full song
The U.S. produces about 5.5 million tons of apples each year. Of the total, $20\%$ is mixed with other products, with $50\%$ of the remainder used for apple juice and the other $50\%$ sold fresh. How many million tons of apples are used for apple juice? Express your answer as a decimal to the nearest tenth.
Answer:
2.2 million tons
Step-by-step explanation:
20% of 5.5 million tons is 1.1 million tons. That is how many are mixed with other products. So that would leave you 4.4 million tons of apples.
50% of 4.4 is 2.2 so 2.2 million tons are used for apple juice.
Answer:
2.2 Million
Step-by-step explanation:
First, we wish to determine what percentage of the tons of apples are used for apple juice. After 20% is mixed with other products, 80% remains. Half of this is used for apple juice; therefore, 40% of the tons of apples is used for apple juice. To calculate 40% of 5.5 million tons, we find 10% and then multiply by four. 10% = 0.55, and 0.55* 4 = 2.2. Thus, 2.2 million tons are used for apple juice.
Lucy made a pumpkin pie to sell at a bake sale. She cut it into 6 slices and sold each slice for $1.25. How much money will she make if she sells the entire pie
Answer: $7.50
Step-by-step explanation: 1.25(6)
Which expression is equivalent to (5 × 6)×(3 × 2)?
A) (5 + 6) + (3 + 2)
B) (5 + 6)×(3 + 2)
C) (5 × 6) + (3 × 2)
D) (3 × 2)×(5 × 6)
Answer:
The original equation contains 3 multiplications.
When multiplying numbers, the order that they are in doesn't matter so 3 *2 is the same as 2 * 3.
This would make D, the same.
D) (3 × 2)×(5 × 6)
I need help with this question show steps! Quickly please!
Answer:
y+9 =-5(x-2) point slope form
y = -5x-1 slope intercept form
Step-by-step explanation:
If we have a slope and a point, we can use the point slope form of a line
y-y1 = m(x-x1)
y--9 = -5(x-2)
y+9 =-5(x-2)
If you want to write it in slope intercept form, distribute the -5
y+9 = -5x+10
Subtract 9 from each side
y+9-9 = -5x+10-9
y = -5x-1
Tom, Sally, Bob, and Jill ran a race. Toms time was 12.03 seconds, Sally's was 12.284 seconds, Bobs was 12.62 seconds, and Jills was 12.9 seconds. In what order did they finish? who won?
Answer:
1.Tom
2.Sally
3.Bob
4.Jills
can some one explain how to do these problems
Answer:
the slope is 0.
Step-by-step explanation:
You can use the slope equation
[tex]\frac{y-y}{x-x}[/tex]
and plug in your points
[tex]\frac{10-10}{4-1}[/tex]
[tex]\frac{0}{3}[/tex]
slope = 0