Answer:
Step-by-step explanation:
Let [tex] x[/tex] be the greater number and [tex] y [/tex] be the smaller number. We know that their difference is 15, so we have
[tex] x-y=15 [/tex]
Then, we have the following information: if we add twice the greater (2x) and 8 (2x+8), the result is 3 times the lesser (3y) minus four (3y-4). So, we have
[tex] 2x+8 = 3y-4 \iff 2x-3y = -12 [/tex]
So, we have the follwing system:
[tex] \begin{cases} x-y=15\\2x-3y = -12\end{cases} [/tex]
From the first equation, we can derive [tex] x = y+15 [/tex], and substitute this expression in the second equation to get
[tex] 2(y+15)-3y = -12 \iff 2y + 30 -3y = -12 \iff -y = -42 \iff y = 42 [/tex]
Substitute this value for y in the first equation to get
[tex] x-42=15 \iff x=15+42 \iff x = 57 [/tex]
Firstly, we need to write down the information given in the form of algebraic equations. We can represent our two unknown numbers, the greater and the lesser, as x and y respectively.
From the given information, we can form two equations. The first equation is from "the difference between the two numbers is 15", which gives us x - y = 15, where x is the larger number and y is the smaller one.
Also, we know that "If 8 is added to twice the greater number, the result is 4 less than 3 times the lesser number", this gives us the second equation: 2*x + 8 = 3*y - 4.
We now have a system of two equations that we can solve simultaneously:
1) x - y = 15
2) 2*x + 8 = 3*y - 4
To make it easier, let's multiply the first equation by 2, which gives us 2*x - 2*y = 30.
Now subtract the second equation (2*x + 8 = 3*y - 4) from the first (2*x - 2*y = 30), it yields: -2*y - 3*y = 30 - (-4 - 8).
This simplifies to -5y = 30 + 4 + 8, or -5*y = 42.
To get the value of y, divide by -5, therefore y = -42 / -5 = 42.
Now to find x, we can substitute y = 42 in the first equation (x - y = 15), so we get x = 42 + 15 = 57.
Hence, the greater number is 57 and the lesser number is 42.
Each jar contains 55 buttons. There are 16 jars on the shelf. How many buttons are there altogether
there are 6 cans in the box . there are 4 boxes how many cans in total
24 cans in total is your answer
6 times 4
6 · 4 = 24
24 cans in total
Please help I really need to give this in tomorrow I will give you a thanks please
(a) Lily: 5 * 2 - 12 + 3 = 1 pt
(b) Rose: -3 * 2 -1 + 6 + 7 = 6 pts
(c) Rose
Help I'm Timed!! PLZ!!!!!!!!
the question is in the pic!
The answer is X is greater than -2! <3
13 is the most points I can give but look I really need help I will give BrAInlIeSt AnSeR tO FIrSt OnE
which integer is √59 closer to
It is close to 8. When you look for the square root of 59 you should get about 7.6811457... Round up and thats 8 round down that 7 but it should be 8.
1.8499x10^9 move the decimal right 9 places
1.8499 × 10^9 = 1,849,900,000
To convert 1.8499 × 10^9 by moving the decimal nine places to the right, you get 1,849,900,000. This is achieved by shifting the decimal point and adding zeros as needed.
To move the decimal nine places to the right for the number 1.8499 × 10^9, you follow these steps:
Start with the number 1.8499Move the decimal point nine places to the right: 1,849,900,000.If there aren’t enough digits, add zeros as necessary.Thus, 1.8499 × 10^9 in standard notation becomes 1,849,900,000.
A number is squared. The result is squared, then that result is squared. The final number is 6561. What was the original number? What were the next 2 numbers? Wich of these numbers are perfect squares?
The original number is 3.
I actually began with the guess-and-check method, but seeing as that won't always work, let's go over the formal way. To get the original number, you first need to determine how many times the number was squared.
To make it simple, let's use x to focus on the exponents. The number was squared 3 times, so x^2, x^2, x^2. Basically, you need to multiply. 2 * 2 * 2 = 8. So, now find the 8th root of 6561 (depending on the calculator, you can just input it). You should come up with 3. Let me know if this part confuses you.
To find the next 2 numbers, you just need to continue the pattern.
6561^2 = 43,046,721
43,046,721^2 = 1,853,020,188,851,841
To my knowledge, which means this could be wrong, they're both perfect squares. Since the number to get them both were whole numbers, they should both have a square root that equals a whole number.
Original number (3): Not a perfect square (3 is not the square of any integer). First intermediate number (9): A perfect square (9 is the square of 3). Final number (6561): A perfect square (6561 is the square of 81). So, the only perfect square in the sequence is the first intermediate number, 9.
Here's why:
Original number: Starting with an unknown number, let's call it x. Squaring it gives us x^2.
First intermediate number: Squaring x^2 again, we get (x^2)^2 = x^4.
Final number: Finally, squaring x^4 one last time, we reach the given number, 6561: (x^4)^2 = x^8 = 6561.
Now, let's backtrack to find the original number x:
Since 6561 is the square of 81, and 81 is the square of 9, we can conclude that the original number x must be the square root of 9, which is 3.
Therefore, the sequence of numbers you provided is indeed correct:
Original number: 3 (squared to get 9)
First intermediate number: 9 (squared to get 81)
Final number: 81 (squared to get 6561)
Joshua swims 25 meters in one minute draw a graph of meters swam versus time
Let me know if you cant read anything
Hope it helps ❤️
The lines will keep going forever ❤️
Three time the sum of a number and 4 is the same as 18 more than the number.what is the number?
Let the nuber be x
According to question
3(x +4) = 18+ x
3x+ 12=18+x
3x-x=18-12
2x = 6
x =6/2
x = 3
what is the area of a square
The answer would be 108 because you multiply the 9 and the 12 together and get 108. I hope this helps.
Two rectangular adjacent rooms share a wall 1‘ x 1‘ tiles cover the floor of each room describe how the greatest possible length of the adjoining wall is related to the total number of tiles in each room
Answer:
Consider two adjacent rectangular rooms having Length=L, and, Breadth = B
Now Suppose the wall which is in between two rooms has a height or length =H.
Breadth of wall = B [ if the wall doesn't exceed the breadth of room]
Considering two rooms to be identical,
Area of each room= L × B square unit
Area of each tile = 1×1=1 square unit
Number of tiles required= L B ÷ 1= LB tiles( product of length and breadth of room is number of tiles required)
Suppose if,LB= N
B= N/L .................(1)
Area of wall(W) = B×H= B H square unit
B =W/H ......................(2)
Equating (1) and (2)
⇒N/L = W/ H
⇒H =[tex]\frac{WL}{N}[/tex]
⇒H =[tex]\frac{WL}{LB}[/tex]
⇒H = W/B
⇒ H =[tex]\frac {\text{ Area of Wall}}{\text{Breadth of room or wall}}[/tex]
is 3 gallon greater than 54 cups
No, 54 cups is equal to 3.4 gallons. Therefore, 54 cups>3 gallons
Draw a figure that contains at least three angles and requires three letters to name each angle PLEASE HELP
You can draw a triangle or a quadrilateral since they have at least three angles. For the second part, any angle can be named with three letters. After naming each corner/angle of the figure, name an angle so that the actual angle letter is the middle letter, surrounded by the letters of the corners that is just next to it.
There are Infinite number of figure , that contains at least three angles and requires three letters to name each angle
1.Any of the Triangle, either Acute, Obtuse, Right, Scalene, Isosceles, or Equilateral.
2. Any of the Quadrilateral, Parallelogram,Rectangle, Square, Trapezoid, and Kite.
→Or In General
Any of the Polygon whether it is Regular or Irregular.
→Because, A polygon is defined as ,a simple closed figure made up of three or more line segment.
39,189 rounded to nearest thousand
To round 39,189 to the nearest thousand, we need to look at the digit in the hundreds place. If the digit in the hundreds place is 5 or greater, we round up, if it is less than 5, we round down. In this case, 1 is less than 5, so we round 39,189 down to 39,000.
Explanation:To round 39,189 to the nearest thousand, we need to look at the digit in the hundreds place. In this case, it is 1. If the digit in the hundreds place is 5 or greater, we round up to the next thousand. If it is less than 5, we round down to the current thousand. Since 1 is less than 5, we round 39,189 down to 39,000.
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20 POINTS
Select equivalent or not equivalent to indicate weather the expression above is equivalent or not equivalent to the values or expressions in the last column
The correct expressions are as follows:
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]343[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}[/tex]
[tex]\texttt{ }[/tex]
Further explanationLet's recall following formula about Exponents and Surds:
[tex]\boxed { \sqrt { x } = x ^ { \frac{1}{2} } }[/tex]
[tex]\boxed { (a ^ b) ^ c = a ^ { b . c } } [/tex]
[tex]\boxed {a ^ b \div a ^ c = a ^ { b - c } }[/tex]
[tex]\boxed {\log a + \log b = \log (a \times b) }[/tex]
[tex]\boxed {\log a - \log b = \log (a \div b) }[/tex]
Let us tackle the problem!
[tex]\texttt{ }[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5}} \cdot (7^2)^{\frac{7}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5}} \cdot (7)^{2\times \frac{7}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = \boxed{7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5} + \frac{14}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{15}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{3}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = \boxed{343}[/tex]
[tex]\texttt{ }[/tex]
From the results above, it can be concluded that the correct statements are:
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]343[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}[/tex]
[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}[/tex]
[tex]\texttt{ }[/tex]
Learn moreCoefficient of A Square Root : https://brainly.com/question/11337634The Order of Operations : https://brainly.com/question/10821615Write 100,000 Using Exponents : https://brainly.com/question/2032116Answer detailsGrade: High School
Subject: Mathematics
Chapter: Exponents and Surds
Keywords: Power , Multiplication , Division , Exponent , Surd , Negative , Postive , Value , Equivalent , Perfect , Square , Factor.
Answer:
equivalent
not equivalent
equivalent
not equivalent
-step explanation:
Sanjay begins to correctly graph the function f(x) = (x + 1)2 – 3. Based on the axis of symmetry and the vertex, which graph could be Sanjay’s?
A.
For this case, the generic equation of a vertex shaped parabola is given by:
[tex]y = a (x-h) ^ 2 + k\\[/tex]
Where the vertex coordinates are (h, k)
Comparing with the given equation:
[tex]f (x) = (x + 1) ^ 2 - 3\\[/tex]
It is observed that h = -1 and k = -3 to obtain the form of the generic equation.
To find the axis of symmetry we derive the given function:
[tex]f '(x) = 2 (x + 1)\\[/tex]
We equate this derivative to zero and clear the value of x
[tex]2 (x + 1) = 0\\[/tex]
[tex]x = -1\\[/tex]
Therefore the vertice of the parabola is:
[tex](h, k) = (-1, -3)\\[/tex]
And the axis of symmetry is:
[tex]x = -1\\[/tex]
Answer:
Graphic 3
The graph third represents the vertex and axis of symmetry of the function f(x) = (x + 1)² - 3 option third is correct.
What is a quadratic function?Any function of the form [tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.
We have a function:
f(x) = (x + 1)² - 3
The above function is a quadratic function or parabolic function.
The vertex form of the function:
f(x) = (x - h)² + k
On comparing:
h = -1, k = -3
(h, k) = (-1, -3) is the vertex of the function.
Axis of symmetery:
x + 1 = 0
x = -1
Thus, the graph third represents the vertex and axis of symmetry of the function f(x) = (x + 1)² - 3 option third is correct.
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what is the greatest common factor or 21 and 84? explain what you did to get this.
Steve packed 350 containers of mealworms for the fishing store. Of those containers, 237 hold 6 mealworms each. The rest of the containes hold 8 mealworms each. How many mealworms did he pack in all.
[tex] \frac{17}{40} [/tex]
when divided what is the answer?
we are given
[tex]\frac{17}{40}[/tex]
we can use long division method
Firstly, we will try to make denominator either 10 , 100 , 1000 , 10000 form
and then we can put decimal accordingly
Here , we are given 40 in the denominator
[tex]40 \times 25=1000[/tex]
so, we will multiply both top and bottom by 25
[tex]\frac{17}{40}=\frac{25\times 17}{25\times 40}[/tex]
[tex]\frac{17}{40}=\frac{425}{1000}[/tex]
now, we can put decimal to three places because we have 1000 in bottom
so, we get
[tex]\frac{17}{40}=0.425[/tex]...............Answer
what is the product of −1/8*(1/8)
−1/8*(1/8) =
-(1/8)² =
-1/64
Write an inequality for each description.
1) Thirty subtracted from four times a number is greater than the opposite of ten.
And the 2nd one in the picture
1: Thirty subtracted from four times a number is greater than the opposite of ten.
Let the number be x, so equation becomes : [tex]30-4x>-10[/tex]
2: Given equation is [tex]27-2b\leq-6[/tex] this states that the result of 27-2b is less than equal to opposite of six.
6. Given the following equation , write a real-life problem about a gym that could be modeled by this equation. Remember to identify your variables.
No equation is given .
2/7 x 7/9 use greatest common factor
Answer: 2/9
Step-by-step explanation:
lt
2
7
×
7
9
=
2 × 7
7 × 9
=
14
63
=
14 ÷ 7
63 ÷ 7
=
2/9
Luis rides his bicycle 34 mile in 5 minutes, or 112 hour, along the bike trail. Assuming he rides at a constant rate, what is his speed, in miles per hour?
Answer:
[tex]408\frac{miles}{hour}[/tex]
Step-by-step explanation:
we know that
To find the speed divide the total distance by the time
so
[tex]\frac{34}{(1/12)}=34*12=408\frac{miles}{hour}[/tex]
What is 3/14 converting fractions to decimals
0.214285714
Hope this helps! :)
P.S- can you help me with my problem? LOL it's just that no one will help me! It's on planets. Hopefully, you know those stuff. :(
BRAINLIEST + POINTS ! Can someone help/explain to me why I got this wrong and solve it!
Standard deviation is the square root of the variance.
To find the variance from the standard deviation, raise it to the 2nd power:
Standard deviation = 4
Variance = 4^2 = 4x4 = 16.
|x-2|-5 <-2 help!!!!!!!!!!!
[tex]|x-2|-5 <-2 \\\\|x-2|<3\\\\x-2<3 \wedge x-2>-3\\\\x<5 \wedge x>-1\\\\x\in(-1,5)[/tex]
the number of pages in the US tax code exceeds the number of pages in The Bible by 18528 the combined number of pages in the tax code in the Bible is 21472 how many pages are in the US tax code
A student works no more than 25 hours each week at a part-time job. Write an inequality that represents how many hours the student can work each day. (how do you solve this)
Given that a student works no more than 25 hours per week, and that work is performed every day of a 7-day week, the maximum number of hours they can work per day is approximately 3.57, making it fair to say they can work up to 3 hours each day. This scenario can be represented by the inequality h ≤ 3.
Explanation:To answer your question, we need to find an inequality that represents how many hours the student can work each day given they work no more than 25 hours every week.
If we assume a typical week encompasses 7 days, and the student works every day of the week, then we should distribute the maximum hours worked per week over these seven days.
This results in 25 hours ÷ 7 days ≈ 3.57 hours/day. However, since you can't work a fraction of an hour, the student can work up to 3 hours a day.
The inequality representing this scenario would be h ≤ 3, where 'h' represents the number of hours the student can work each day.
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