Joelle should multiply 792 by 22 to get a perfect square
To figure out the smallest integer that Joelle could have multiplied by 792 to get a perfect square, we need to factorize 792 and ensure all prime factors appear in even powers.
First, we find the prime factorization of 792:
[tex]792 =2^3 \times 3^2 \times 11[/tex]
For a number to be a perfect square, all the exponents in its prime factorization must be even. The exponents of 2 and 11 are not even in this factorization, so we must multiply 792 by the smallest factors that will make these exponents even. So, we need an additional factor of 2 (to make [tex]2^4[/tex]) and an additional factor of 11 (to make [tex]11^2[/tex]). Therefore, we multiply as follows:
[tex]2 \times 11 = 22[/tex]
So, the smallest integer Joelle could have multiplied 792 by to get a perfect square is 22.
What is the value of g?
25(g−7)=3
25(g−7)=3
Distributive property
25g - 175 = 3
Add 175 to both sides
25g = 178
Divide both sides by 25
g = 178/25
g = 7.12
shannon walked 4 and 7/8 miles and ran 3 1/2 miles during the week. how much further did she walk than run
she walked 1 3/8 miles more than she ran, Hope this helps :D
If 800,000 was rounded to the nearest hundred thousand what is the largest number
The largest number of people that could have attended the event would be 849,999. If it was 850,000 it would be rounded up to 900,000.
The smallest number of people that could have attended would be 750,000. If there was 749,999, it would be rounded down to 700,000.
Hope this helps!
The greatest number that can be rounded to 800,000 when rounded on the nearest hundred thousand is 849,999.
Here,
The given number is 800,000.
We have to find the greatest number that can be rounded to 800,000 when rounded on the nearest hundred thousand.
What is Rounding number?
To making a number simpler but keeping its value close to what it was, is called Rounding.
Now,
The given number is 800,000.
When rounded to the nearest hundred thousand, then the largest number is 849,999.
Therefore, The greatest number that can be rounded to 800,000 when rounded on the nearest hundred thousand is 849,999.
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Which of the following terms correctly describes 4 : 1? A- Ratio B- Fraction C-Percent D- Factor
Sabrehalrubeai,
In order to find the correct answer to this question we need to go over all of the options to see which one is the correct answer.
Ratio: [tex]6 : 9[/tex] <---- Your answer....Fraction: [tex]\frac{6}{9}[/tex]Percent: [tex]35%[/tex]Factor: [tex]4 \times 3 = 12[/tex]Therefore your answer is option A "ratio."
Hope this helps!
evaluate f(x) when x = 6
when x = 6, you have to use the top equation .... because -6 < 6 < 9
f(x) = 6x² + 2
f(6) = 6(6)² + 2
= 6(36) + 2
= 216 + 2
= 218
Answer: D
Answer: Fourth option is correct.
Step-by-step explanation:
Since we have given that
[tex]f(x)=6x^2+2,-6<x<9\\\\f(x)=12,9\leq x<13[/tex]
We need to find the value of f(x) when x = 6.
As we can see that x = 6 is lie in the interval -6<x<9.
So, f(x) would be [tex]6x^2+2[/tex]
So, value of f(x) at x = 6 would be
[tex]f(x)=6(6)^2+2=216+2=218[/tex]
Hence, fourth option is correct.
Solve for x.
−(−2−5x)+(−2)=18
x=185
x=90
x=−185
x=−90
The correct solution to the equation is x = 18/5 that is option C is the correct answer.
1. Start with the given equation:
−(−2−5x)+(−2)=18
2. Simplify the expression inside the parentheses:
- (-2 - 5x) + (-2) = 18
3. Distribute the negative sign:
2 + 5x - 2 = 18
4. Combine like terms:
5x = 18
5. Divide by 5 to solve for x:
x = 18/5
Therefore, none of the given options (x=185, x=90, x=−185, x=−90) are correct, making the correct value of x = rac{18}{5} or 3.6.
Complete question:
Solve for x
- ( -2 - 5x) + (-2) =18
a. x = -90
b. x = -18/5
c. x = 18/5
d. x = 90
Sachiko is framing the border of a square picture. If she knows the area of the picture,
how could Sachiko determine the amount of framing material she needs to buy?
Answer:
Amount of framing material she need to buy = 4a, where a is the side of square.
a is found out by taking square root of area of picture.
Explanation:
Let the side of square be a. The area of a rectangle is breadth x width. Here breadth = width = side of square
Area of square = a x a = [tex]a^2[/tex]
It is given that area of picture is known, so she can find side of the square by finding square root of the area.
The perimeter of square is given by 4 times the side of square.
We know the side of the square, so we can calculate the perimeter.
Amount of framing material she need to buy = Perimeter of square = 4a
Is |-6| a negative integer
Answer:
NO. |-6| = 6 - a positive integer
Step-by-step explanation:
|a| = a for a ≥ 0
examples
|2| = 2, |0| = 0, |0.56| = 0.56
|a| = -a for a < 0
examples
|-2| = -(-2) = 2, |-100| = -(-100) = 100, |-0.25| = 0.25
Therefore your answer:
|-6| = 6 > 0
how many times is each basic property of associative commutative and distributive used to evaluate the expression 23 + 5x + 7y - x - 5 - 27 respectively
In evaluating the expression 23 + 5x + 7y - x - 5 - 27, the commutative property is used twice to rearrange terms, while the associative and distributive properties are not used.
Explanation:The student has asked how many times each basic property of associativity, commutativity, and distributivity is used to evaluate the expression 23 + 5x + 7y - x - 5 - 27. We can look at the expression and apply these properties to simplify it.
First, we'll combine like terms using the commutative property which states x + y = y + x and xy = yx. This allows us to rearrange terms:
Associative property: This property is not explicitly needed here since it involves the grouping of numbers, and this expression does not have parentheses to signify grouping for addition or multiplication.Commutative property: We use the commutative property twice to rearrange the x terms and the constant terms.Distributive property: This property is not used in this expression because there is no multiplication distributing over addition or subtraction.After rearranging, we get 23 - 5 + (5x - x) + 7y - 27. Now, simplifying the constants and combining the x terms, we have (23 - 5 - 27) + (5x - x) + 7y, which further simplifies to -9 + 4x + 7y.
Therefore, the commutative property was used twice in this simplification process, while the associative and distributive properties were not used.
erica paid $753.95 for dance classes. She paid $123.95 registration fee and $45 for each week. What is w,the number of weeks erica was enrolled in dance classes?
Erica was enrolled in dance classes for 14 weeks, as determined by subtracting the registration fee from the total amount paid and dividing by the weekly fee.
Explanation:Erica paid a total of 753.95 for dance classes, which included a $123.95 registration fee and a weekly fee of 45. To find out the number of weeks w Erica was enrolled in dance classes, we need to subtract the registration fee from the total amount and then divide the remainder by the weekly fee.
The equation to represent this situation is:
w = (Total amount paid - Registration fee) / Weekly fee
Plugging in the values, we get:
w = (753.95 - 123.95) / 45
Calculating the difference and then dividing by the weekly fee:
w = 630 / 45
So:
w = 14
Erica was enrolled in dance classes for 14 weeks.
The number of weeks Erica was enrolled in dance classes, w, is 14 weeks.
We need to subtract the registration fee from the total amount paid and then divide the remaining amount by the weekly fee.
First, we identify the total amount paid for the dance classes, which is $753.95. This includes the registration fee and the weekly fees for the classes.
Next, we identify the registration fee, which is $123.95.
The weekly fee for the dance classes is $45.
The total amount paid, excluding the registration fee, is the total cost minus the registration fee:
[tex]\[ \text{Total amount paid excluding registration} = \$753.95 - \$123.95 \][/tex]
[tex]\[ \text{Total amount paid excluding registration} = \$630.00 \][/tex]
Now, we divide this amount by the weekly fee to find the number of weeks Erica was enrolled:
[tex]\[ w = \frac{\$630.00}{\$45} \][/tex]
[tex]\[ w = 14 \][/tex]
The ratio of children to adults at family movie night is 5 to 4. A total of 72 people showed up at this weeks movie night. How many of them were children?
Someone Explain to me how 5. Is valid ???
This is valid through the law of syllogism. If you swap lines 1 and 2, then you'll have this argument:
If I step on a beehive, then I will get stung.
If I get stung by a bee, then it will hurt.
Therefore, if I step on a beehive, then it will hurt
------------------
So it's like connecting a chain together. Point A (stepping on the hive), leads to point B (getting stung), which leads to point C (getting hurt). We can take a shortcut to bypass point B to jump from A to C in one step. Check out the attached image for a visual of what I'm referring to.
Lauren’s bedroom measures 21 feet by 14 feet, with a closet that measures 3 feet by 6 feet. If carpet costs $4.25 per square foot, how much will it cost to carpet Lauren’s room & closet?
Lauren will need $1326 to cover 312 ft^2 of her room with carpet.
Final answer:
To carpet Lauren's room and closet, calculate the area of both then multiply by the carpet cost per square foot, resulting in a total cost of $1,326.
Explanation:
To calculate the cost of carpeting Lauren's room including the closet, we first need to find out the total area that needs to be carpeted. The area of Lauren's room is found by multiplying the length by the width: 21 feet × 14 feet, which equals 294 square feet. Similarly, the area of the closet is 3 feet × 6 feet, which equals 18 square feet.
To find the total area to be carpeted, we add the area of the room to the area of the closet: 294 square feet + 18 square feet equals 312 square feet. The cost to carpet this total area is then calculated by multiplying the total area by the cost per square foot: 312 square feet × $4.25 per square foot, which equals $1,326.
Therefore, to carpet both Lauren's room and the closet, it will cost $1,326.
Carol, Ann, and Liz each bought a toy fish. Carol's fish is 10 inches longer than Ann's fish. Liz's fish is 2 inches longer than twice the length of Ann's fish. Ann's fish is 12 inches long. Find the length of each toy fish.
Ann: 12 inches
Carol: 22 inches
Liz: 24 inches
Ann's fish is 12 inches long, Carol's fish, which is 10 inches longer than Ann's, is 22 inches long, and Liz's fish, which is 2 inches longer than twice the length of Ann's fish, is 26 inches.
Explanation:The subject of this question is
Mathematics
, particularly focusing on simple algebra. To solve the problem, let's first determine the length of each toy fish starting with Ann's. We know that Ann's fish is
12 inches long
. Carol's fish is 10 inches longer than Ann's, so Carol's fish would be
22 inches long
(12 + 10 = 22). Liz's fish is 2 inches longer than twice the length of Ann's fish, which means it's
26 inches long
(2*12 + 2 = 26). So, the lengths of the toy fish are: Ann's : 12 inches, Carol's: 22 inches and Liz's: 26 inches.
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two people begin traveling at the same time from opposite ends of a 20 mile trail. one person travels 3 miles per hour faster than the other. if they meet after 2 hours, what are the rates of the 2 people
Let us assume rate of other person = x miles per hour.
Rate of first person is 3 miles per hours faster than other.
Therefore, rate of first person = (x+3) miles per hour.
Total distance between them = 20 miles.
And total time taken by them is 2 hours.
We know, distance, time and rate relation:
Distance = Rate × Time.
Therefore, distance covered by other person = x * 2 = 2x.
Distnace covered by first person = (x+3)*2.
Total distance covered by both = 20 miles.
We can setup an equation
Total distance covered by both = Distnace covered by first person + distance covered by other person.
2(x+3) +2x = 20.
Now, we can solve the eqation for x.
2x +6 +2x = 20.
4x +6 =20.
Subtracting 6 from both sides, we get
4x +6-6 =20-6
4x = 14.
Dividing both sides by 4, we get
x=3.5
Rate of first person = (x+3) = 3.5+3 = 6.5 miles per hour.
Therefore, the rate of first person is 6.5 miles per hour and rate of second person 3.5 miles per hour.Can someone please answer this for me?!
how many solutions are there in the equation 7(x+2)=7x-10
a. 0
b. 1
c. infinitely many
A.0
These is no solution for the equation.
Find the slope of the line passing through the given points. (-7,2) (-8,7)
Your help would be appreciated!!!!!!!!!!!!!!!!!!!!!!!11
The slope of the line of the given points is y=-5x-33
If a container contains 18,000 ounces (oz) of beans, about how many pounds (lb) does it contain? [1 pound1 ounces)
There would be 1125 pounds of beans in the container.
Answer:
Your answer should be D, 288,000 lb.
Step-by-step explanation:
just simply multiply 16 by 18,000.
18,000
x 16
= 288,000
what is the opposite integer of-11
Answer: 11
Step-by-step explanation: Think of the opposite of an integer in terms of a number line. The opposite of an integer is the same distance from zero as the original integer but on the opposite side of zero.
On the number line, we can see that -11 is 11 units to the left of zero, so its opposite will be 11 units to the right of zero.
So the opposite of -11 is +11.
I have also attached my work in the image provided.
Final answer:
The opposite integer of -11 is 11. An opposite integer is simply the number with the opposite sign, and the opposite of a negative number is the same number but positive.
Explanation:
The opposite integer of -11 is 11. The opposite integer is simply the number with the opposite sign, so for any negative integer, the opposite is the same number but positive. Similarly, if you have a positive integer, its opposite would be negative. For example, the opposite of 5 is -5. To find the opposite, you change the sign of the number without changing its absolute value or magnitude. This is similar to finding the additive inverse of a number, which is what is added to the original number to result in zero. So, in the case of -11, adding 11 would give you zero: -11 + 11 = 0.
Twice the difference of a number and six is negative six, find the number
Let x = a number
3(6 - x) = -9
Divide both sides of equation by 3.
6 - x = -3
Subtract 6 on both sides of equation.
-x = -9
Divide both sides of equation by -1.
x = 9
The number is 9.
The difference between a number and six is [tex] x-6 [/tex]. Twice this difference is [tex] 2(x-6) [/tex]. If you want this difference to be negative, six, you have
[tex] 2(x-6)=-6 [/tex]
Divide both sides by 2:
[tex] x-6 = -3 [/tex]
Add 6 to both sides:
[tex] x = 3 [/tex]
Leena knits 10 rows in 12 min. At this pace, how long will it take her to knit the next 25 rows?
10 rows= 12 mins
there's 25 rows in all so break it down into 10, 10, and 5 to make it more simple
12+12= 24 minutes for 20 rows
since you only have 5 rows left (which is half of ten), you divide the 12 by two as well.
12mins/2= 6 minutes for 5 rows
24mins+6mins= 30 minutes
answer: It will take 30 minutes to knit 25 rows
Answer:
62.5 minutes
Step-by-step explanation:
10 rows
------------ = 2/5 row/min
25 min
This is equivalent to 5/2 minutes per row.
Mult. this by 25 min to determine how many rows Leena can knit in that period:
5 min 25 rows
---------- * --------------- = 125/2 minutes, or 62.5 minutes
2 row 1
41% of 78 is what? I dont really know this so could you help me out please..???.
Answer:
31.98
Step-by-step explanation:
Answer 31.98.
Step-by-step explanation: To convert a number to a decimal you must move the decimal point two spaces forward. 41.00----> .41. 41% would be .41 in decimal form. The next thing you do is multiply that decimal times whatever number you're trying to find the percent of. In this case it would be times 78 so the equation would look like this. .41*78=31.98
Hope this helps!
Which expression demonstrates the distributive property applied to the expression 4(x + y)?
A) 4x + y
B) 4x + 4y
C) 4(y + x)
D) 4 × (y × x)
Answer:
4x+4y i took the usa test prep
Step-by-step explanation:
Which of the following best describes the movement of an object
Point A is located at (0, 4), and point B is located at (−2, −3). Find the point that is 1 over 4 the distance from point A to point B.
(-1, 0.75)
(-0.75, 2)
(-0.5, 2.25)
(-0.25, 3)
The answer is (-0.5, 2.25).
Explanation:
A = (0,4)
B = (-2,-3)
The line joining the two points from A to B can be represented as a vector:
r (x) = A + x*(B - A) , where 0<= x <= 1
Now, r (x) can be written as:
r (x) = (0,4) + x[ (-2,-3) - (0,4) ] = (0,4) + x (-2,-7)
Assuming x to be 1/4 (given)
x(1/4) = (0,4) + 1/4* (-2,-7) = (0 -1/2, 4 -7/4) = (-1/2, 9/4)
= (−0.5, 2.25)
Solution
Find the mid point of A and B.
The mid point of A and B is (-1. 0.5)
Now find mid point of (0, 4) and (-1, 0.5)
= [(0 + (-1)/2 , (4 +0.5)/2 ]
= (-1/2, 4.5/2)
= (-0.5, 2.25)
The answer is (-0.5, 2.25)
Thank you.
Ronnie had a certain number of movies, m. One-fourth of those movies were action movies. He sold nine action movies to reach a grand total of four action movies. What was the original number of movies Ronnie had?
A. 52
B. 48
C. 26
D. 39
By adding the action movies Ronnie sold to the ones he kept, we determined he had 13 action movies, which was one-fourth of his total. Multiplying 13 by four revealed that he originally had 52 movies in total.
Explanation:The student's question pertains to finding the original number of movies Ronnie had given that one-fourth of those movies were action movies, and after selling nine of them, he was left with four action movies. To find the original number of action movies he had, we can add the four action movies he has left to the nine action movies he sold. This gives us a total of 13 action movies.
Since these 13 action movies represented one-fourth of his original collection, we multiply 13 by four to find the total number of movies Ronnie originally had. Therefore, Ronnie's original number of movies was 13 imes 4 = 52.
Consider the following graph of an absolute value function
A
The domain is -∞ < x < ∞
B
The range is -∞ < x ≤ 3
C
The graph is increasing from -∞ < y < 3
D
The graph is decreasing from 3 > y > -∞
E
The local maximum is at ( - 2, 3 )
F
There are no local minimums
The graph of an absolute value function is a V or inverted V. The x-coordinate of the V's vertex provides the function's line of symmetry, and the y-coordinate of the V's vertex shows the minimum or maximum value of the function.
Explanation:An absolute value function is a function that contains an algebraic expression within absolute value symbols. The graph of an absolute value function is a symmetrical V or inverted V, depending on the direction of the opening. The vertex of the V, which is the minimum or maximum point of the graph, provides two important pieces of information: the x-coordinate of the vertex gives us the equation's line of symmetry, and the y-coordinate represents the minimum or maximum value of the function, depending on the opening direction.
Let's say, for example, we have the graph of the function |x - 3| + 2. The vertex of this function is at the point (3, 2). Therefore, the line of symmetry is x = 3, and the minimum value of the function is 2.
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A cylindrical soup can has a radius of 1.5 in. and is 4.6 in. tall. Find the volume of the can.
Help me out please thank you
Well first you find the common denominatior of 1/7 and 4/9 which is 63 so then you see how many times does 7 go into 63 so this is part where you multiply 7 and 9 which gives you 63 and then you do how many times 9 go into 63 which is 7 so then you will take 7 times the 4 which is 28 so now your fractions should be 9/63 and 28/63 then now your next step is to add the 9 and 28 which is now 37/63 and you ask yourself and you divide that by any number to get a smaller number which is no so that is your answer