Jane and jill collect yo-yo’s. the ratio of the number of jane’s yo-yo’s to the number of jill’s yo-yo’s is 5:4. if jane will give 15 of her yo-yo’s to her little brother, jane and jill will have the same number of yo-yo’s in their collections. how many yo-yo’s do both girls have together?
The number of yo-yo's Jane and Jill have is required.
The number of yo-yo's Jane has is 75 and Jill has 60 yo-yo's.
The ratio of Jane's yo-yo to Jill's yo-yo is [tex]\dfrac{5}{4}[/tex]
Let x be the number of yo-yo's Jane has
y be the number of yo-yo's Jill has
[tex]\dfrac{x}{y}=\dfrac{5}{4}[/tex]
When Jane's gives 15 of her yo-yo's away both will have the same number of yo-yo's so
[tex]x-15=y[/tex]
substituting in the first equation
[tex]\dfrac{x}{x-15}=\dfrac{5}{4}\\\Rightarrow 4x=5x-75\\\Rightarrow x=75[/tex]
[tex]y=x-15=75-15\\\Rightarrow x=60[/tex]
The number of yo-yo's Jane has is 75 and Jill has 60 yo-yo's.
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What is the answer 1/2k+6=4k–8
To solve the equation 1/2k + 6 = 4k - 8, subtract 1/2k from both sides, combine like terms, add 8 to both sides, combine constant terms, divide by 3.5, and solve for k to get k = 4.
Explanation:To solve the algebraic equation 1/2k + 6 = 4k - 8, we need to isolate the variable 'k' on one side of the equation. Here are the steps:
Subtract 1/2k from both sides: 6 = 4k - 1/2k - 8.Combine like terms on the right side: 6 = 3.5k - 8.Add 8 to both sides to get all constant terms on the left side: 6 + 8 = 3.5k.Combine the constant terms: 14 = 3.5k.Divide both sides by 3.5 to solve for k: k = 14 / 3.5.Calculate the division: k = 4.Therefore, the solution to the equation is k = 4.
Nathan is making beaded bracelet for every 5 red beads there are 3 white beads. What is the ratio red to white beads?
choose exactly two that are correct
To calculate the mean of the data shown in the stem and leaf plot, paper and pencil to record work and technology to add and divide are required.
What is stem and leaf plot?A stem-and-leaf display or stem-and-leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution.
A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).
The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values.
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The cost of 4 pounds of patatoes is 3.50. How many pounds of potatoes can you buy with $14.
Don breaks a 4×7 array into a 2×7 and another array. What is the fact for Don's second array?
The fact for Don's second array is 2x7, indicating there are 2 rows and 7 columns in the array.
Explanation:In this question, the student is splitting a 4x7 array into a 2x7 array, and another array.
The 4x7 array has 28 elements. After removing a
2x7 array with 14 elements, we're left with an array that also has 14 elements.
We're not given its dimensions, but if we follow the pattern of the original breakup, it could also be a 2x7 array. Therefore, the fact for the second array is 2x7.
By representing this as multiplication, we're showing that there are 2 rows and 7 columns in the array, which represents the total number of elements.
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A car uses 20 gallons of fuel to travel 440 miles. How much fuel will the car use to travel 1054 miles
Two patterns start at 0. The rule in Add 3. The rule for the other pattern is Add five. Examine the number in each pattern. Explain how the numbers in each pattern are similarly
solve the system of linear equations by substitution.
4x−2y=14
y=12x−1
Answer: x=-3/5 y=-41/5
Step-by-step explanation: Rewrite equations:
y=12x−1;4x−2y=14
Step: Solvey=12x−1for y:
y=12x−1
Step: Substitute12x−1foryin4x−2y=14:
4x−2y=14
4x−2(12x−1)=14
−20x+2=14(Simplify both sides of the equation)
−20x+2+−2=14+−2(Add -2 to both sides)
−20x=12
−20x
−20
=
12
−20
(Divide both sides by -20)
x=
−3
5
Step: Substitute
−3
5
forxiny=12x−1:
y=12x−1
y=12(
−3
5
)−1
y=
−41
5
(Simplify both sides of the equation)
The system of linear equations is solved by substitution, resulting in the solution x=-3/5 and y=6.2.
Explanation:To solve the system of linear equations by substitution, start with the given system:
4x − 2y = 14
y = 12x − 1
Since y is already isolated in the second equation, substitute (12x − 1) for y in the first equation:
4x − 2(12x − 1) = 144x − 24x + 2 = 14−20x + 2 = 14−20x = 12x = −1/20 × 12x = −6/10x = −3/5Now substitute x = −3/5 into the second equation to find y:
y = 12(−3/5) − 1y = −36/5 − 1y = −7.2 − 1y = 6.2The solution for the system of equations is x = −3/5, y = 6.2.
find the value of x and the measure of angle MNQ
The angle is given as 3x - 13 and 58. The measure of angle MNQ (3x - 13) is 32 degrees.
What are complementary angles?Two angles whose sum is 90° are called complementary angles.
The angle is given as 3x - 13 and 58.
Since the two angles within MNP equal to 90 degrees:
3x - 13 + 58 = 90
3x = 90 - 45
3x = 45
x = 15
Therefore, The measure of angle MNQ (3x - 13) = 32 degrees.
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a student did a 340 page essay for 3/4 hours. how much would it take to do 1 page
Every week, Colin mows the lawn, edges the lawn, and pulls weeds. List all the possible orders in which he can take care of the yard.
Colin can complete his yard work in 6 different orders.
Colin has three tasks to complete for his yard work: mowing the lawn, edging the lawn, and pulling weeds. We can list all possible orders in which he can complete these tasks by considering each task as an item in a permutation. Since there are three tasks to arrange, there are 3! (3 factorial) possible ways to order them, which is 3 × 2 × 1 = 6 possible orders.
Mow, Edge, WeedsMow, Weeds, EdgeEdge, Mow, WeedsEdge, Weeds, MowWeeds, Mow, EdgeWeeds, Edge, MowThis list represents all the combinations that Colin can take to complete his yard work.
What is standard form
which blue word comes between apple and car in the dictionary
The word that comes between apple and car in the dictionary is blue.
What is a dictionary?A dictionary is a reference book that contains an alphabetical list of words in a language or a specific field, along with their definitions, and pronunciation. It serves as a valuable tool for writers, students, and anyone who wants to improve their vocabulary and communication skills.
Dictionaries can be found in both print and digital formats. They can cover a wide range of languages, dialects, and specialized fields such as law, medicine, or science.
Some dictionaries also include other features such as synonyms, antonyms, and usage examples. They also contain illustrations to help users understand the meaning and context of words better.
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The number of flowers which blossom varies directly as the number of seeds planted. When 55 seeds are planted, 5 flowers blossom.
What is the number of flowers that blossom when 550 seeds are planted?
A.
545
B.
250
C.
50
D.
11
I want to be smart at school and I am getting really for the test too.
At a concert, you purchase 3 T-shirts and a concert program for a total cost of $90.The program for a total cost $15 and the T-shirts all cost the same. Write and solve an equation to find the cost of one T-shirt
To solve the problem, we created an equation representing the total cost of 3 T-shirts and a program, and then solved it to find the cost of one T-shirt, which is $25.
Explanation:Let's denote the cost of one T-shirt as 'T'. Since the total cost of 3 T-shirts and a program is $90, and we know that the cost of the program is $15, we can write our equation as follows: 3T + 15 = 90.
To solve for 'T', we start by subtracting 15 from both sides of the equation, getting us 3T = 90 - 15 = 75.
Next, we would divide both sides by 3 to find the cost of one T-shirt. Hence T = 75 / 3 = $25. So, the cost of one T-shirt is $25.
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A relay team of 4 people runs 3 miles.If each person runs the same distance,How many miles does each person run?
the class had a pizza party 3/8 of a pizza was left over and 4/8 of a pizza with other pizza was left over you put them both into a box how much pizza do you have all together
Simplify 0.75 (5v+11)-0.25 (11+v)
what is 2.25 as a fraction
If an angle measures 100 degrees, through what fraction of a circle does the angle turn?
A. 1/100
B. 1/4
C. 100/360
D. 1/2
you should have $16 and a coupon for a $5 discount at a local supermarket. a bottle of olive oil costs$7. how many bottles of olive oil can you buy?
With a total of $21, including the discount coupon, and each bottle of olive oil costing $7, you can buy 3 bottles of olive oil.
Explanation:In your case, you start with $16 and a $5 discount coupon to use at the local supermarket. This gives you an effective total of $16 + $5 = $21 to spend. Each bottle of olive oil costs $7. So, if you divide your total amount of money $21 by the cost of one bottle of olive oil $7, you get 21 ÷ 7 = 3. This means you can buy 3 bottles of olive oil.
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How many weeks will the cat food last?
What is 6476 divided by 12?
NEEDED ASAP PLEASE
A relation is plotted as a linear function on the coordinate plane starting at point C (0,−1)(0,−1) and ending at point D (2,−11)(2,−11) . What is the rate of change for the linear function and what is its initial value? Select from the drop-down menus to correctly complete the statements.The rate of change is -11, -5, 0, 5.and the initial value is -11, -2, -1, 0.
Answer:
-5,-1
Step-by-step explanation:
I took the test!
0-<
How many times does 19 go into 115
Is this Scientific Notation? 0.4 x 10^25
I need help :( with this it's kinda confusing
What is the value of 2x{6+[12 divided by (3+1)]}-1
The value of the given expression 2x{6+[12 divided by (3+1)]}-1 is 17 when following the order of operations.
Explanation:To solve the mathematical expression 2x{6+[12 divided by (3+1)]}-1, the first thing you have to do is follow the order of operations, which is abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Step 1: Solve the operation within parentheses, 12 ÷ (3+1) = 12 ÷ 4 = 3.
Step 2: Subtitute the result back into the equation, 2x{6+[3]}-1.
Step 3: Solve the operation within brackets, {6+[3]} = {9}.
Step 4: Substitute the result back into the equation, 2x{9}-1 = 2x9 - 1 = 18 -1 = 17.
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