Answer:
Kyle gave 2/7th of his money to his wife and spent 3/5 of the remainder. If he had $300 left, the money had by Kyle at first is $1050
Solution:
Step 1:
Consider “x” as the money which Kyle had initially.
From question, Kyle gave 2/7th of his money to his wife. So the remaining money left with Kyle is given as,
[tex]= 1 - \frac{2}{7}[/tex]
[tex]= \frac{7 - 2}{7} = \frac{5}{7}[/tex] ----- eqn 1
Now the remaining money left with Kyle is 5/7th.Given that Kyle spent 3/5 of the remaining money.
Now the remaining money left with Kyle is given as
[tex] = 1 - \frac{3}{5} = \frac{5 - 3}{5} = \frac{2}{5}[/tex]
Now kyle is left with $300, which is 2/5th of the initial money x .
We get equation as
[tex]\frac{2}{5} x=300[/tex]
2x = 1500
x = 750
Now Kyle is left with 750$ which is 5/7th of the initial amount x.( by using eqn 1)
We get equation as
[tex]\frac{5}{7} x = 750[/tex]
5x = 5250
x = 1050
So the amount had by Kyle at first is $1050
Final answer:
Working backward from the $300 Kyle had after spending and giving some away, we find that the original amount of money was $1050, which is determined by reversing the operations he performed on his money.
Explanation:
To solve how much money Kyle had at first, we need to work backwards from the amount he had left ($300) after he spent some and gave some to his wife. First, we determine how much was left before he spent the 3/5 of the remainder.
Let's denote Kyle's initial amount of money as x. The equation representing what Kyle did with his money is
x - (2/7)x = Remaining Amount After Giving to Wife
Kyle then spends 3/5 of this remaining amount, and is left with $300, so we can represent this as:
(1 - 3/5)(Remaining Amount After Giving to Wife) = $300
Substituting the first equation into the second we get:
(1 - 3/5)(x - (2/7)x) = $300
Simplifying, we find that (2/5)(5/7)x = $300.
This simplifies down to:
(2/5)(5/7)x = (10/35)x = $300
Finally, solving for x, we multiply both sides by the reciprocal of (10/35),
x = $300 × (35/10)
x = $300 × 3.5
x = $1050
So, Kyle originally had $1050.
Solve the system of equations
6x+7y = 5 2x-3y =7
Answer:
The solution is (2 , -1)
Step-by-step explanation:
* You have two ways to solve the system of equations
1. Elimination method:
By making the coefficients of one of the two variables equal in the 2
equations in magnitude and different in sign to eliminate it and find the
other variable
2. Substitution method:
By finding one of the two variables in terms of the other in one of the
two equations and substitute this value in the second equation
* Lets solve our system using the elimination method
∵ 6x + 7y = 5 ⇒ (1)
∵ 2x - 3y = 7 ⇒ (2)
- Multiply equation (2) by -3 to eliminate x
∵ (-3)(2x) - (-3)(3y) = (-3)(7)
∴ -6x + 9y = -21 ⇒ (3)
- Add equation (1) and (3)
∴ 7y + 9y = 5 + -21
∴ 16y = -16
- Divide each side by 16
∴ y = -1
- Substitute the value of y in equation (1)
∴ 6x + 7(-1) = 5
∴ 6x - 7 = 5
- Add 7 to both sides
∴ 6x = 12
- Divide both sides by 6
∴ x = 2
* The solution is (2 , -1)
What is the slope of x=18?
Answer:
Ø
Step-by-step explanation:
Anything that is set to equal x is what is known as an undefined rate of change [slope] because it is a vertical line.
I am joyous to assist you anytime.
Simplify
(2/3 +1/6) please
brnialest
.
Answer:
5/6
Step-by-step explanation:
Hey!
------------------------------------------------
Steps To Solve:
~Find common denominators
2/3 = 4/6
1/6
~Add
4/6 + 1/6
~Simplify
5/6
This cannot be simplified.
------------------------------------------------
Answer:
5/6
------------------------------------------------
Hope This Helped! Good Luck!
Mary invested 5,000 into a bank account that was earning 2.5 percent interest compound monthly what would her exact account balance be after 3 years?
Answer:
$12,162.68
Step-by-step explanation:
It's compounded monthly. 3 years is 36 months.
A = P (1 + r)^n
A = 5000 (1 + 0.025)^36
A ≈ 12162.68
Rounded to the nearest cent, her exact account balance would be $12,162.68.
Jackie brought 3/4 of a gallon of iced tea to the party. Bill brought 7/8 of a gallon of iced tea to the same party. How much iced tea did Jackie and Bill bring to the party?
Answer:
[tex]\frac{13}{8}=1\frac{5}{8}[/tex] gallons
Step-by-step explanation:
We have been given that Jackie brought 3/4 of a gallon of iced tea to the party. Bill brought 7/8 of a gallon of iced tea to the same party.
To find the total amount of iced tea, we will add both quantities as:
[tex]\text{Amount of ice tea brought to party by Jackie and Bill}=\frac{3}{4}+\frac{7}{8}[/tex]
Make a common denominator:
[tex]\text{Amount of ice tea brought to party by Jackie and Bill}=\frac{3*2}{4*2}+\frac{7}{8}[/tex]
[tex]\text{Amount of ice tea brought to party by Jackie and Bill}=\frac{6}{8}+\frac{7}{8}[/tex]
Add numerators:
[tex]\text{Amount of ice tea brought to party by Jackie and Bill}=\frac{6+7}{8}[/tex]
[tex]\text{Amount of ice tea brought to party by Jackie and Bill}=\frac{13}{8}[/tex]
[tex]\text{Amount of ice tea brought to party by Jackie and Bill}=1\frac{5}{8}[/tex]
Therefore, Jackie and Bill brought [tex]\frac{13}{8}=1\frac{5}{8}[/tex] gallons of ice tea to the party.
Which of the following statements uses the commutative property of addition?
2 + (3 + 4) = (2 + 3) + 4
2 + (3 + 4) = (2+ 3) + (2 + 4)
2 + (3 + 4) = 2 + (4 + 3)
The statement 2 + (3 + 4) = 2 + (4 + 3) is the one that uses the commutative property of addition, which states that changing the order of numbers being added does not affect the sum. So correct answer is first option.
The statement that uses the commutative property of addition is 2 + (3 + 4) = 2 + (4 + 3). The commutative property of addition states that the order in which two numbers are added does not change the sum.
This is represented by the equation A+B=B+A. In our specific example, changing the order of 3 and 4 does not affect the sum when added to 2.
This demonstrates the commutative property in a clear manner.
I need help please???
Answer:
63
Step-by-step explanation:
51 - ( - 12) (-)(-)=(+)
51 + 12
63
Answer:
63
Step-by-step explanation:
The question says 51 +12 becase two negatives make a positive.
For } (x) = 3x + 1 and g(x) = 72-6, find (f + g)(x).
the answer is f (-3x - 22) = -6x - 33
Which of the following are valid names for the triangle below? check all that apply
Answer:
E and F
Step-by-step explanation:
They are the only ones which use the appropriate triangle angles and points.
Have a nice day!!!!!!!! :-)
KA
E. ΔDMR & F. ΔMRD are valid names of the triangle.
Which are the valid names of the triangle ?
We know that, a triangle has 3 vertices.
Name of a triangle is always with the name of the vertices together in a clock or anticlockwise manner.
Example : If vertices of a triangle are A, B & C, then name of the triangle are like ΔABC, ΔBCA, ΔCAB, ΔBAC, ΔACB, ΔCBA.
Here, in the given diagram, vertices of the triangle are D, M, R
So, the names ΔDMR & ΔMRD are correct in all the options, others are not names of vertices, so they are not taken.
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Simplify the expression (6^2)^4
Answer:
6^8 = 1,679,616
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)^c = a^(bc)
__
Applied to this problem, the rule tells you ...
(6^2)^4 = 6^(2·4) = 6^8 = 1,679,616
__
Or, you can evaluate the expression according to the Order of Operations:
(6^2)^4 = 36^4 = 1,679,616
Answer:
6^8 = 1,679,616
Step-by-step explanation:
i looked it up and i did it on my own
Find the of x in each triangle.
First, it is important to know that there are 180 degrees in a triangle. The equation for this is 90+3x=180, since the small square means 90 degrees. From there on, you should be able to figure it out yourself.
. 50 cm =
0.005 of what
Answer:
It would be Meters, .50cm = 0.005 M
Order these numbers from least to greatest -1.264, -5/4,-1.015,-0.480,-14/25,-13/8
Your mother gave you $13.32 with which to buy a present. This covered 3/5 of the cost. How much did the present cost
Answer:
$22.20
Step-by-step explanation:
We are told that $13.32 only covered 3/5 of the cost. Does this mean it covered the whole cost? No. The 5 in the denominator represents the whole cost, and the 3 represents the fraction of the cost. In this case, 13.32 represents the 3, as it did not cover the whole cost.
Let's set up our equation by making 13.32 into a fraction.
13.32/x
We will represent the present's actual cost with the letter x.
13.32/x = 3/5
We want to make sure the 13.32 is in the numerator, equal to the 3 in the numerator in the 3/5 number, because we know that $13.32 only covered for a fraction of the present's cost, not the whole cost.
We solve this by doing cross multiplication. Multiply the 13.32 by the 5.
13.32 x 5 = 66.6
Next we divide 66.6 by 3 to get 22.2
66.6/3 = 22.2
This gives us our final answer of $22.20. This means that the cost of the original present was $22.20
The question involves setting up a proportion to find the total cost of the present. This was done step-by-step by dividing $13.32 by 3 to find 1/5 of the cost, and then multiplying by 5 to find the full cost. The present cost approximately $22.20
Explanation:The subject of your question is mathematics, particularly a topic in proportion. The information given is that $13.32 represents 3/5 of the cost of the present. We could set up a proportion to help calculate the full cost. If 3/5 is equal to $13.32, then 1 (or 5/5) would be equal to the full price of the present. We can solve for the full price by dividing $13.32 by 3 and then multiplying by 5 (since 5/5 represents the whole or full cost).
Step-by-step:
Divide $13.32 by 3. This gives you approximately $4.44, which represents the cost for 1/5 of the present. Multiply $4.44 by 5. This will give you the full cost of the present which is approximately $22.20.Learn more about Proportion here:https://brainly.com/question/31548894
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each situation to its corresponding expression.
Answer:
150(0.4),2,500(0.11)
Step-by-step explanation:The first question says 150 participants and 40%of the participants are eliminated. so it's 150(0.4)n
same goes for the second 2,500 bacteria in a colony the colony grows at a rate of 11% every hour so the answer to the question is 2,500(0.11)n
The student is tasked to match situations with their corresponding mathematical expressions, identifying key mathematical operations and formulating accurate representation for these operations
Explanation:The question is asking you to match given situations with their corresponding mathematical expressions. An example might be the situation 'Tom has twice as many apples as Tim' being matched to the expression '2T', where 'T' denotes the number of apples Tim has. To solve this, read each situation carefully and identify the key mathematical operations (addition, subtraction, multiplication, division) or relationships (equal to, greater than, less than) embedded within them. Then, formulate a mathematical expression that accurately represents these operations or relationships.
For example, if the situation is 'Sally has five more books than John,' the corresponding mathematical expression might be 'J+5' with 'J' representing the number of books John has.
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Figure ABCD is a parallelogram. Parallelogram A B C D is shown. Angle A is (4 p + 12) degrees and angle C is 36 degrees. What is the value of p? 6 7 8 9
Answer:
The value of p is 6
Step-by-step explanation:
we know that
In a parallelogram opposite angles are congruent
so
In the parallelogram ABCD
m∠A=m∠C ----> equation A
m∠B=m∠D ----> equation B
we have
m∠A=(4p+12)°
m∠C=36°
substitute the given values in equation A and solve for p
[tex](4p+12)\°=36\°[/tex]
[tex]4p=36-12[/tex]
[tex]4p=24[/tex]
[tex]p=6[/tex]
Answer:
6
Step-by-step explanation:
Tonka weighs 150 lb. He is loading a freight elevator with identical 67-pound boxes. The elevator can carry no more than 2000 lb. If Tonka rides up with the boxes, how many boxes can be loaded on the elevator?
Final answer:
Tonka can load a maximum of 29 boxes on the elevator.
Explanation:
To calculate the number of boxes Tonka can load on the elevator, we need to divide the maximum weight capacity of the elevator by the weight of each box. The weight capacity of the elevator is 2000 lb, and each box weighs 67 lb. Therefore, the number of boxes Tonka can load is found by dividing 2000 lb by 67 lb:
Number of boxes = 2000 lb ÷ 67 lb = 29.85
Since we can't have a fraction of a box, Tonka can load a maximum of 29 boxes on the elevator.
Madden and Jenn both worked at the coffee shop today. Madden's total cups of coffee made is represented by f(x); and Jenn's total cups of coffee made is represented by g(x). Use the functions below to write a function that represents the total cups of coffee they made today.
f(x) = 7x − 4
g(x) = 5x + 1
A. 9x + 5
B.9x − 3
C.12x + 5
D.12x − 3
Answer:
The answer is D. 12x - 3.
Step-by-step explanation:
To add these functions, we just add the terms.
f(x) + g(x) = (7x - 4) + (5x + 1)
7x - 4 + 5x + 1 | Simplify
7x + 5x - 3
12x - 3.
Answer:
Option D. (12x - 3)
Step-by-step explanation:
Madden's total cups of coffee made is represented by the function f(x).
f(x) = 7x - 4
Jenn's total cups of coffee made is represented by the function g(x).
g(x) = 5x + 1
Now we have to write a function that represents the total cup of coffee that represents they made.
That will be represented by f(x) + g(x) = (7x - 4) + (5x + 1)
f(x) + g(x) = 12x - 3
Therefore, option D. will be the answer.
vertices que tiene el prisma hexagonal
Answer:
12
Step-by-step explanation:
in geometry, the hexagonal prism is a prism with hexagonal base. This polyhedron has 8 faces, 18 edges, and 12 vertices. Since it has 8 faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces.
(se poquito de espanol, lo lamento)
40% of what number is 52?
A. 130
B. 200
C. 242
D. 1300
Answer:
130
Step-by-step explanation:
40 percent of what number is 52?
let this number be x
so, the equation is
40/100 x X= 52
divide 40/100 from both sides
X=52÷40/100
When you divide by a fraction, you multiply by its reciprocal
X=52 x 100/40
X=5200/40
X=130
40 percent of 130 is 52.
The value of the unknown number is 130.
Option A.
What is the value of the unknown number?Given the parameter:
"40% of what number is 52"
Let's represent the unknown number as "x."
To determine the number for which 40% is equal to 52, we can set up an equation and solve for the unknown number.
Hence:
40% of the number = 52
40% of x = 52
40% × x = 52
Convert the percentage to a decimal.
40% = 40/100 = 0.40
Now, rewrite the equation as:
0.40 × x = 52
0.4x = 52
To solve for the value of "x," divide both sides of the equation by 0.40:
x = 52/0.4
x = 130.
Therefore, 40 percent of 130 is 52.
Option A) 130 is the correct answer.
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math help pls!! will reward : )
Good evening ,
______
Answer:
A. x=all real numbers.
D. x = [tex]\frac{2-np}{2}[/tex]
___________________
Step-by-step explanation:
25-5x=5(-x+5)
25-5x=-5x+25
25-5x=25-5x
Then this equation is valid for all real number x
Note : If you replace x by any number you will get 0 = 0 and that always true.
:)
Answer:
a
Step-by-step explanation:
#1: In Picture!
#2: Explain Aaron's mistake using 1-3 complete sentences.
Please answer both :)
Answer:
1.45 in/h see belowStep-by-step explanation:
1. The appropriate "dimensional analysis" is ...
[tex]\dfrac{2.9\,ft}{1\,day}\cdot\dfrac{12\,in}{1\,ft}\cdot\dfrac{1\,day}{24\,h}=\dfrac{2.9\cdot 12\cdot 1\,day\cdot ft\cdot in}{1\cdot 1\cdot 24\,day\cdot ft\cdot h}=1.45\dfrac{in}{h}[/tex]
__
2. Aaron used the inverse of the correct days to hours conversion factor. The units he ends up with are in·h/day², not in/h. And the calculation he did does not match the expression he wrote.
what is the distributive property of 5x23
Answer:
see explanation
Step-by-step explanation:
We can express 5 × 23 as
5(20 + 3) ← distribute terms in parenthesis by 5
= 5 × 20 + 5 × 3
= 100 + 15
= 115
By distributive property , the number 5 x 23 = 115
What is Distributive Property?
The distributive property states that multiplying the sum of two or more addends by a number produces the same result as multiplying each addend individually by the number and adding the products together.
For a product of two numbers , a and d , d = b + c
By distributive property ,
a x ( b + c ) = a x b + a x c
Given data ,
Let the number be 5 x 23
Now , the number 23 can be split into ( 20 + 3 )
By opening the parentheses ,
5 x ( 20 + 3 )
The number 5 is first multiplied by 20 and then multiplied by 3 , and the sum of both the products will be taken
So ,
5 x 23 = 5 ( 20 + 3 )
5 x 23 = 5 ( 20 ) + 5 ( 3 )
5 x 23 = 100 + 15
5 x 23 = 115
Hence , by distributive property the product 5 x 23 is 115
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Andy and Sylvie each incorrectly simplified the expression -3 - 4(2x - 3). Andy wrote -14x + 21 and Sylvie wrote -8 - 6. Explain their errors and give the correct answer.
Answer:
Given the expression -3 - 4(2x- 3) the correct solution is -8x + 9.
Step-by-step explanation:
Andy wrote -14x + 21, so his error was to do de substraction (-3 -4) and then distribute -7(2x-3) = -14x+ 21.
Sylvie wrote -8x -6. Her error was to multiplied -4 only for 2x,
then -3 - 4(2x -3) = -3 -8x -3 = -8x -6.
Andy incorrectly distributed the negative sign and Sylvie made an error in simplifying the expression. The correct answer is -8x + 9.
Explanation:Andy's error: He incorrectly distributed the negative sign to both terms inside the parentheses. When distributing a negative sign to each term, the sign of each term should change. So, -4(2x - 3) becomes -8x + 12. However, Andy erroneously distributed the negative sign to only the first term, resulting in -14x + 21.
Sylvie's error: She incorrectly simplified the expression -8 - 6, which is equal to -14. However, this is not the correct result for the entire expression -3 - 4(2x - 3).
The correct answer is obtained by applying the distributive property and combining like terms. First, simplify the expression inside the parentheses: -4(2x - 3) = -8x + 12. Then, combine the terms outside the parentheses with the simplified expression: -3 - 8x + 12 = -8x + 9.
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hELP ASAP WILL MARK THE BRAINLIEST!
Write the equation of the quadratic function with roots -10 and -8 and a vertex at (-9, -3)
Answer:
y = 3x² + 54x + 240
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (- 9, - 3), thus
y = a(x + 9)² - 3
To find a substitute either of the roots into the equation
Using (- 8, 0), then
0 = a(- 8 + 9)² - 3
0 = a - 3 ( add 3 to both sides )
a = 3
y = 3(x + 9)² - 3 ← in vertex form
Expand factor and simplify
y = 3(x² + 18x + 81) - 3
= 3x² + 54x + 243 - 3
= 3x² + 54x + 240 ← in standard form
elena went bowling. elena's score in the first game was 127 she scored 16 more points in the second game than in the first game. wwhat was her total score?
Answer:
133
Step-by-step explanation:
127 + 16 = 133
If s(x) = 2 - x and f(x) = 3x, which value is equivalent to (s f) (-7)
The equivalent value for (s \\circ f) (-7), given s(x) = 2 - x and f(x) = 3x, is 23.
The question asks which value is equivalent to (s \\circ f) (-7), where s(x) = 2 - x and f(x) = 3x.
To solve for (s \\circ f) (-7), we first need to find f(-7). Since f(x) = 3x, we substitute x with -7:
f(-7) = 3(-7) = -21.
Next, we calculate s(f(-7)), which means we substitute x in s(x) with the value of f(-7):
s(-21) = 2 - (-21) = 2 + 21 = 23.
Therefore, the equivalent value is 23.
Azeneth is putting a fence around her rectangular garden. The width of the garden is 4x + 5 ft. and the
length is 2x^2 – 3x + 7 ft.
How much total fencing does Azeneth need to buy in terms of x?
Answer:
Azeneth needs to buy 4x² + 2x + 24 feet
Step-by-step explanation:
* Lets explain how to solve the problem
- Azeneth is putting a fence around her rectangular garden
- The width of the garden is 4x + 5 feet
- The length is 2x² – 3x + 7 feet
- We need to find how much total fencing Azeneth needs to buy in
terms of x
∵ The fence will put around the four sides of the rectangular garden
∴ The length of the fence is equal to the perimeter of the garden
- The perimeter of any rectangle = 2l + 2w, where l and w are its
dimensions
∵ The perimeter of the garden = 2 × its width + 2 × its length
∵ Width = 4x + 5
∴ 2 × width = 2(4x + 5) = 8x + 10
∵ Length = 2x² - 3x + 7
∴ 2 × length = 2(2x² - 3x + 7) = 4x² - 6x + 14
∴ The perimeter of the garden = 8x + 10 + 4x² - 6x + 14
- Add like terms
∴ The perimeter of the garden = 4x² + (8x - 6x) + (10 + 14)
∴ The perimeter of the garden = 4x² + 2x + 24
∵ The length of the fence = the perimeter of the garden
∴ The length of the fence = 4x² + 2x + 24 feet
* Azeneth needs to buy 4x² + 2x + 24 feet
Karel wants to buy a points card for his x-box
live account. He can buy a 200 point card
for $10.00 for a 300 point card to $15
W hich card is a better value?
Answer:
Both cards are the same value.
Step-by-step explanation:
$10 for 200 points = $5 for 100 points
$15 for $300 points = $5 for $100 points
Both cards are the same value.
Determine the area of each face of a cube 306.6
Answer: 51.1 units squared
Step-by-step explanation: the area of each face is 306.6 so then you would divided that by 6 since there are 6 sides in a cube so you get 51.1 and if multiplied by 6 it equals 306.6
The area of each face of a cube 306.6 is 51.1 square units.
What is a cube?A solid three-dimensional shape called a cube contains six square faces, eight vertices, and twelve edges.
A cube has 6 faces.
So the area of each face is (side x side).
So total area is equal to 6 times the area of each side.
Area = 6 x (side x side)
Now, substitute in your numbers and solve for the side length
306.6 = 6 (side)²
so first divide both sides by 6,
we get,
(side)² = 51.1
Therefore, the area of each face is 51.1 square units.
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