True, 4.62 is less than 4.67
A rectangle has a length of 10 inches and a width of 8 inches
will reward brainliest!
how many and what type of solutions does the equation have 17+3x^2=6x
A. no real solution
B. one real solution
C. two rational solutions
D. two irrational solutions
Option D: Two irrational solutions
Explanation:
The equation is [tex]17+3 x^{2}=6 x[/tex]
Subtracting 6x from both sides, we have,
[tex]3x^{2} -6x+17=0[/tex]
Solving the equation using quadratic formula,
[tex]x=\frac{6 \pm \sqrt{36-4(3)(17)}}{2(3)}[/tex]
Simplifying the expression, we get,
[tex]\begin{aligned}x &=\frac{6 \pm \sqrt{36-204}}{6} \\&=\frac{6 \pm \sqrt{-168}}{6} \\&=\frac{6 \pm 2 i \sqrt{42}}{6}\end{aligned}[/tex]
Taking out the common terms and simplifying, we have,
[tex]\begin{aligned}x &=\frac{2(3 \pm i \sqrt{42})}{6} \\&=\frac{(3 \pm i \sqrt{42})}{3}\end{aligned}[/tex]
Dividing by 3, we get,
[tex]x=1+i \sqrt{\frac{14}{3}}, x=1-i \sqrt{\frac{14}{3}}[/tex]
Hence, the equation has two irrational solutions.
How many solutions exist for the given equation?
12x + 1 = 3(4x + 1) – 2
zero
one
two
infinitely many
The equation have infinite solutions.
Data;
12x + 1 2(4x + 1) - 2Solution of EquationTo solve this problem, we can proceed to solve this equation by collecting like terms and then dividing through to know the coefficient of x.
[tex]12x + 1 = 3(4x + 1) - 2\\12x + 1 = 12x + 3 - 2\\12x + 1 = 12x + 1\\[/tex]
The equation have infinite solutions.
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Answer:
D. Infinitely many
Step-by-step explanation:
did on edge
hope this helps
the greatest common factor of 10 and 14 is 5 true or
Answer:
False
Step-by-step explanation:
Factors of 10 and 14:
10: 1 , 2, 5, 10
14: 1, 2, 7, 14
As you can see, 5 is not a common factor of 10 and 14
The greatest common factor is two
So the answer is false, 5 is not the greatest common factor of 10 and 14
Hope this helps :)
The greatest common factor of 10 and 14 is 2, not 5. The statement is false as 5 is not a factor of 14.
The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 10 and 14, we list the factors of each number:
Factors of 10: 1, 2, 5, 10Factors of 14: 1, 2, 7, 14The common factors of 10 and 14 are 1 and 2. Therefore, the GCF of 10 and 14 is 2, not 5. The statement that the greatest common factor of 10 and 14 is 5 is false.
A small acting club has 5 members. Three of the members are to be chosen for a trip to see a Broadway play. How many different 3-member groups are possible?
z(5 , 3) = 10
Step-by-step explanation:
x = 5
y = 3
z(x,y) = x/ y(x-y)
z (5, 3) = 5/ 3(5-3)
= 4x5/ 2
= 20/2
z (5- 3) = 10
The function f(x) = 2x + 210 represents the number of calories burned when exercising, where x is the number of hours spent exercising.
The function g(x) = 2x + 125 represents the calorie deficit that occurs when following a particular diet, where x is the number of hours spent exercising.
What is (f + g)(2)? Explain.
Hey there!
When we say (f + g)(2), we are adding both functions together and plugging in 2 for x.
Since f(x) is equal to 2x + 210 and g(x) is equal to 2x + 125, (f + g)(x) is equal to (2x + 210) + (2x + 125).
That can be simplified to 4x + 335.
So, (f + g)(x) = 4x + 335.
Let's plug 2 in for x and solve.
(f + g)(2) = 4(2) + 335
Multiply.
(f + g)(2) = 8 + 335
Add.
(f + g)(2) = 343
The x value is consistent for the values of both equations, in both x is defined as the number of hours spent exercising.
So, (f + g)(2), which is 343, is the amount of calories burned and the calorie deficit on a diet when 2 hours are spent exercising.
Hope this helps!
Answer:
Its D
Step-by-step explanation:
Which statements are true about the area of a circle check all that apply
Answer:
The correct answer is Area = Pir2, The area formula can be found by breaking apart the circle and forming a parallelogram, and The area formula can be found by breaking apart the circle and forming a parallelogram. B,D,and E.
Step-by-step explanation:
Answer:
B, D, E
Step-by-step explanation:
Thats the correct answer bye
Help I am so confused
1.)Which equation does not support the fact that polynomials are closed under multiplication?
−1⋅−1=1
1x⋅x=1
1⋅x=x
13⋅3=1
2.)Multiply and simplify.
x^2⋅x⋅x^5
3.)Multiply and simplify.
(3x+7)8x^2
Final answer:
The equation that does not support the fact that polynomials are closed under multiplication is 1x⋅x=1. To multiply and simplify [tex]x^2⋅x⋅x^5[/tex]onents are added. To multiply and simplify[tex](3x+7)8x^2,[/tex]ive property is used.
Explanation:
The equation that does not support the fact that polynomials are closed under multiplication is 1x⋅x=1. When multiplying two polynomials, the degree of the resulting polynomial is the sum of the degrees of the two original polynomials. In this case, the degree of the resulting polynomial would be 2, but the equation implies a polynomial of degree 0, which is not possible.
To multiply and simplify[tex]x^2⋅x⋅x^5[/tex]he exponents when multiplying the same base. So,[tex]x^2⋅x⋅x^5 = x^(2+1+5) = x^8.[/tex]
To multiply and simplify [tex](3x+7)8x^2,[/tex] distributive property. We multiply each term in the first polynomial by each term in the second polynomial. So, [tex](3x+7)8x^2 = 24x^3 + 56x^2.[/tex]
A $200 jacket went on sale for $140. What percentage was the reduction?
Question 1 options:
70%
35%
65%
60%
Answer:
Step-by-step explanation:
The dollar amount of the reduction was $200 - $140, or $60.
$60 is what percentage of $200?
$60
---------- = 3/10 = 0.30
$200
The reduction was 30%; the jacket sold for 70% of its original price.
Answer:
Step-by-step explanation: set up a proportion:
140/200 = x/100 answer is 70%
to cross check - .70 multiplied by 200 =140
Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula? Quadratic formula: x = -b
Answer:
shows correct substitution of the values a, b, and c from the given quadratic equation into quadratic formula.
Step-by-step explanation:
Given: The quadratic equation
We have to show the correct substitution of the values a, b, and c from the given quadratic equation into quadratic formula.
The standard form of quadratic equation is then the solution of quadratic equation using quadratic formula is given as
Consider the given quadratic equation
Comparing with general quadratic equation, we have
a = -3 , b = -2 , c = 6
Substitute in quadratic formula, we get,
Simplify, we have,
Thus, and x_{2}=\frac{2-\sqrt{76} }{-6}
Simplify, we get,
Thus, shows correct substitution of the values a, b, and c from the given quadratic equation into quadratic formula.
Answer:
shows correct substitution of the values a, b, and c from the given quadratic equation into quadratic formula.
Step-by-step explanation:
Given: The quadratic equation
We have to show the correct substitution of the values a, b, and c from the given quadratic equation into quadratic formula.
The standard form of quadratic equation is then the solution of quadratic equation using quadratic formula is given as
Consider the given quadratic equation
Comparing with general quadratic equation, we have
a = -3 , b = -2 , c = 6
Substitute in quadratic formula, we get,
Simplify, we have,
Thus, and x_{2}=\frac{2-\sqrt{76} }{-6}
Simplify, we get,
Thus, shows correct substitution of the values a, b, and c from the given quadratic equation into quadratic formula.
Two cargo ships spot a signal fire on a small island. The captains know they are 140 feet
away from each other and using angle measuring device they can determine the angle from
cach of their ships to the signal fire. The angle at ship A is 82º and the angle at ship B is 78°.
How far is it from Ship B to the signal fire at point C?
Hint: Use Law of Sines:
sin A = sinB = sin C
82
B
a.
b.
48.9 feet
400.4 feet
c. 405.3 feet
d. 673.4 feet
Answer:
[tex]\large \boxed{\text{c. 405.3 ft}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcr}\angle A + \angle B + \angle C & = & 180^{\circ}\\82^{\circ} + 78^{\circ} +\angle C & = & 180^{\circ}\\160^{\circ} + \angle C & = & 180^{\circ}\\\angle C & = & 20^{\circ}\\\end{array}[/tex]
[tex]\begin{array}{rcl}\dfrac{\sin A}{a} & = &\dfrac{\sin C}{c}\\\\\dfrac{\sin82^{\circ}}{a} & = &\dfrac{\sin20^{\circ}}{140}\\\\\dfrac{0.9903}{a} & = &\dfrac{0.3420}{140}\\\\a & = & \dfrac{0.9903 \times140}{0.3420}\\\\& = & \mathbf{405.3 ft}\\\end{array}\\\text{The distance from Ship B to the signal fire is $\large \boxed{\textbf{405.3 ft}}$}[/tex]
Order the integers from least to greatest.
7. 1, -3, -6,50
9. 11, -11,18, -18, -8
Answer:
7) -6, -3, 1, 50
9) -18, -11, -8, 11, 18
Solve for x. 4x-4<8 and 9x+5>23
Answer:
Step-by-step explanation:
hello :
the system is :
4x-4<8 ....(*)
9x+5>23...(**)
means :
4x < 12
9x > 18
x<3 and x>2 means : 2<x<3
What is the Value of x?
Enter your answer in the box.
⬜️ units
Answer: X = 28
Step-by-step explanation: The diagram shows a triangle which is actually in fact, two triangles placed into each other. The first one is triangle APR (the larger one) while the second one is triangle CDR (the smaller one).
Also the diagram shows line AP as being parallel to line CD. That makes triangle APR similar to triangle CDR.
We can now determine the ratios of the similar sides
If triangle APR = triangle CDR, then
Line PD/DR = AC/CR or
PD/PR = AC/AR or
CD/RD = AP/RP
Therefore to calculate X, we use the ratio,
PD/DR = AC/CR
15/42 = 10/x
{we reduce the left hand side to it's simplest form}
5/14 = 10/x
When we cross multiply we now have
5x = 14 × 10
5x = 140
Divide both sides of the equation by 5
x = 28
)
The diameter of the dart board is 50 centimeters. What is the approximate circumference? (Use 3.14 for
A 157 cm
B 78.5 cm
cc 1962.5 cm
D. 625 cm
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Answer:
a. 157 cm
Step-by-step explanation:
Multiply the diameter times 3.14
3.14 x 50=157 cm.
answer: 157 cm
To find the circumference of a circle given the diameter, multiply the diameter by π (approximately 3.14). Hence, the circumference of the dartboard is approximately 157 cm.
Explanation:The subject of the question is Mathematics and it covers a topic generally taught in Middle School. When given the diameter of a circle, you can calculate the circumference using the formula C=πd where C is the circumference, π (pi) is about 3.14, and d is the diameter. In this case, the diameter of the dartboard is 50 cm. So, we simply multiply the diameter (50 cm) by π (3.14) to get the circumference. This means the circumference of the dartboard is approximately
157 cm (Option A)
.
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A square prism measuring 6 km along each
edge of the base and 5 km tall. Find area
Final answer:
The total surface area of a square prism with a base edge of 6 km and height of 5 km is 192 km².
Explanation:
The question is about finding the surface area of a square prism (also known as a rectangular prism where the base is a square). A square prism has six faces: two square bases and four rectangular sides. To find the total surface area, we calculate the area of each face and sum them up.
The formula for the area of a square is side × side. Since the base of the prism is a square with each side measuring 6 km, the area of one square base is:
Area of one square base = 6 km × 6 km = 36 km²Since there are two square bases:
Total area of two square bases = 36 km² × 2 = 72 km²The formula for the area of a rectangle is length × width. The four rectangular sides each have one dimension that is the height of the prism (5 km), and the other dimension is the length of a side of the base (6 km), so:
Area of one rectangular side = 5 km × 6 km = 30 km²There are four such sides:
Total area of four rectangular sides = 30 km² × 4 = 120 km²Adding the areas of the bases and the sides:
Total surface area of the prism = 72 km² + 120 km² = 192 km²Cara went on a road trip. She set her cruise control for 65 miles per hour for 2 hours and then she lowered the cruise control to 60 miles per hour for the next 1.5 hours. What is the total distance she traveled during her drive?
Question 2 options:
227.5 miles
210 miles
220 miles
218.75 miles
Answer:220
Step-by-step explanation:
65+65+ 60+ 30
A Store has 8 fish tanks that each have 40 liters of water. What is the total number of liters of water in all of the fish tanks?
Answer:
320 liters
Step-by-step explanation:
Each tank = 40 liters
8 tanks = 40 × 8 = 320
Answer:
8 x 40 = 320
Step-by-step explanation:
since 1 fish tank has 40 liters of water, we are trying to find the total of all 8 which is why we multiply 8 x 40
Last month, Jim and Debbie earned $7,200. Debbie earned $1,600 more than Jim earned. How much did they each earn? Call the amount that Jim earned j and the amount that Debbie earned d.
Step-by-step explanation:
Let Jim earned $ x
Therefore, Debbie earned = $(x + 1600)
According to the given information:
[tex]x + (x + 1600) = 7200 \\ \therefore \: 2x = 7200 - 1600 \\ \therefore \: 2x =5600 \\ \\ \therefore \: x = \frac{5600}{2} \\ \\ \therefore \: x =2800 \\ [/tex]
Thus, Jim`s earning = $2800
Debbie`s earning = 2800 + 1600 = $4400
Lets Jim earn $ x
Therefore, Debbie earned=$(x+1600)
calculate Debbie's earnings
According to the given information :
[tex]x+(x+1600)=7200\\$$\therefore 2 x=7200-1600\\$$\therefore 2 x=5600\\$$\therefore x=\frac{5600}{2}\\$$\therefore x=2800\\$[/tex]
thus, Jim's earnings =$2800
Debbie's earnings =2800+1600=$4400
What is an example of Earning?An example of earning is to be paid five dollars for washing a car. An example of earning is getting a promotion for being very good at your job. An example of to earn is to take a vacation after completing a difficult and time-consuming project. To gain (success, reward, recognition) through applied effort or work.
What do you call earning?Definitions of earnings. something that remunerates. “they saved a quarter of all their earnings” synonyms: pay, remuneration, salary, wage.
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3. Add:
(-21) + (-37) + (-15)
O A. 73
O B. -58
O C. -43
O D.-73
Answer:
D) -73
Step-by-step explanation:
(-21)+(-37)+(-15)
-21-37-15
-58-15
-73
Solve this system of equations story problem by any method of your choice. Describe what the number solutions mean in terms of the real life application.
Jasmine and Stephanie are selling pies for a school fundraiser. Customers can buy cherry pies
and blackberry pies. Jasmine sold 12 cherry pies and 4 blackberry pies for a total of $136.
Stephanie sold 8 cherry pies and 1 blackberry pie for a total of $64. What is the cost each of one
cherry pie and one blackberry pie?
Please send a picture showing steps.
Answer:
Cost of each cherry pie = $6
Cost of each blackberry pie = $16
Step-by-step explanation:
Let x be the cherry pies and y be the blackberry pie.
Solution:
From the above statement Jasmine sold 12 cherry pies and 4 blackberry pies for a total of $136.
So, we write the first equation as.
[tex]12x+4y = 136 ------(1)[/tex]
And Stephanie sold 8 cherry pies and 1 blackberry pie for a total of $64.
So, we write the second equation as.
[tex]8x+y = 64 --------(2)[/tex]
First we solve equation 2 for y.
[tex]y = 64-8x[/tex] ------------------------(3)
Substitute [tex]y = 64-8x[/tex] in equation 1.
[tex]12x+4(64-8x) = 136[/tex]
[tex]12x+256-32x=136[/tex]
[tex]12x-32x=136-256[/tex]
[tex]-20x=-120[/tex]
[tex]x=\frac{120}{20}[/tex]
x = 6
Substitute x = 6 in equation 3.
[tex]y = 64-8(6)[/tex]
[tex]y=64-48[/tex]
y = 16
Therefore, cost of each cherry pie = $6 and cost of each blackberry pie = $16
By solving the system of equations, it is determined that the cost of one cherry pie is $6 and the cost of one blackberry pie is $16. These findings are crucial for pricing strategies in the school fundraiser.
Explanation:To solve the system of equations for the cost of cherry and blackberry pies sold by Jasmine and Stephanie for a school fundraiser, we can set up two equations based on the given information:
Let's denote the cost of one cherry pie as c and the cost of one blackberry pie as b. Therefore, we can form the following equations based on the problem statement:
Using the method of substitution or elimination, we solve for c and b.
For simplicity, let's use elimination. To eliminate b, we can multiply the second equation by -4 and add to the first:
-32c - 4b = -256
12c + 4b = 136
Combining these, we get -20c = -120, thus c = $6. Substituting c = 6 into the second equation, 8*6 + b = 64, gives us b = $16.
In real-life terms, this means one cherry pie costs $6, and one blackberry pie costs $16, which would be important for pricing and accounting in the fundraiser.
an average Scott makes a basket 9 times out of 12 when he is practicing how many baskets can he expect to make when he tried 200.
Answer:
150
Step-by-step explanation:
We know that Scott's ratio of making the basket is 9/12. All we need to do is find out how many baskets he'll make if he attempts 200 shots.
So, 9/12 needs to become x/200. We don't know what x is yet, but there's a shortcut.
9/12 can be simplified by dividing 3 on the top and bottom.
9/12 ÷ 3/3 = 3/4
We can then see how many times 4 can go into 200.
200/4 = 50
So, we multiply 3/4 by 50 on both the top and bottom.
3/4 × 50/50 = 150/200.
So, if he attempts 200 shots then he'll make 150 of them.
Scott can expect to make approximately 150 baskets if he attempts 200 shots with his success rate being 9 out of 12, which equates to a 75% success rate.
Explanation:The question asks how many baskets Scott can expect to make if he tries 200 shots given that his average success rate is 9 out of 12. To find the answer, we can set up a proportion because Scott's shooting is a matter of probability and ratios. First, we determine Scott's success rate as a fraction: 9/12 which simplifies to 3/4 or a success rate of 75%.
Then, we apply this success rate to the new number of attempts (200) to find the expected number of successful baskets:
Expected number of baskets = Success rate x Total attemptsExpected number of baskets = (3/4) x 200Expected number of baskets = 150Therefore, if Scott attempts 200 shots, he can expect to make approximately 150 baskets.
write the domain and range in interval notation.
Domain: [tex][-2,6][/tex]
Range: [tex][0,5][/tex]
Explanation:
Domain:
The domain of a function is the set of all possible values of the independent variable x. From the graph, we can see that the function has the set of all possible values from -2 to 6. Hence, the domain is from -2 to 6.
Thus, writing the domain in interval notation, we have,
[tex]-2\leq x\leq 6[/tex]
This also can be written as [tex][-2,6][/tex]
Hence, the domain is [tex][-2,6][/tex]
Range:
The Range of a function is set of all possible values of y obtained by substituting the values for x in the function. From the graph, we can see that the function has the set of all possible values from 0 to 5. Hence, the range is from 0 to 5.
Thus, writing the range in interval notation, we have,
[tex]0\leq y\leq 5[/tex]
This also can be written as [tex][0,5][/tex]
Hence, the range is [tex][0,5][/tex]
The domain and range in interval notation represent sets of possible values a function can take. For instance, for the function f(x) = 2x + 3 where x can be any real number, both the domain and range would be (-∞, ∞). Square brackets denote inclusive endpoints, while parentheses denote exclusive endpoints in interval notation.
Explanation:In mathematics, particularly in functions, the domain and range represent sets of possible input and output values respectively. When expressed in interval notation, domain and range convey a concise representation of these sets.
Let's illustrate with an example. If we have the function f(x) = 2x + 3, and x can be any real number, the domain in interval notation would be (-∞, ∞). As for the range, since the function can also output any real number, the range would also be (-∞, ∞).
To write the domain and range in interval notation, remember that square brackets [ ] represent inclusive endpoints, while parentheses ( ) represent exclusive endpoints. The symbol '∞' is always cloaked by parentheses.
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please someone help me with this
Answer:
See explanation
Step-by-step explanation:
Triangle ABC ahs vertices at points A(-4,-4), B(-1,-2) and C(-1,-4).
1 way: First reflect this triangle across the y-axis to form the triangle A''B''C'' which vertices are at points A''(4,-4), B''(1,-2) and C''(1,-4).
Then translate this triangle 7 units up to form the triangle A'B'C' with vertices:
[tex]A'(4,-4+7)=A'(4,3)\\ \\B'(1,-2+7)=B'(1,5)\\ \\C'(1,-4+7)=C'(1,3)[/tex]
2 way: First translate this triangle 7 units up to form the triangle A''B''C'' which vertices are at points A''(-4,3), B''(-1,5) and C''(-1,3).
Then reflect this triangle across the y-axis to form the triangle A'B'C' with vertices:
[tex]A'(-(-4),3)=A'(4,3)\\ \\B'(-(-1),5)=B'(1,5)\\ \\C'(-(-1),3)=C'(1,3)[/tex]
PLZ HELP!!!!!!!! BRANILY!!!!!!!!!!!!!! FOR THE PERSON WHO GETS THE ANSWER RIGHT!!!!!!!
IF M∠J = 82, M∠L = 57, AND M∠K = 41, list the sides of JLK in order from smallest to largest.
angle list: k,l,j:
sides are: LJ, KJ, KL
To find the sides of triangle JLK in order from smallest to largest, we need to compare the measures of the angles. The side opposite the largest angle is the longest side, so we can determine the order of the sides based on the angle measures.
Explanation:The triangle JLK has angles J, L, and K with measures 82, 57, and 41 degrees, respectively. To determine the sides of JLK in order from smallest to largest, we can use the fact that the side opposite the largest angle is the longest side. So, we need to identify the largest angle and its corresponding side.
Comparing the measures of the angles, we can see that M∠J is the largest angle. Therefore, the side opposite angle J, which is side JL, is the longest side. Next, we compare the measures of the remaining angles. M∠L is the next largest angle, so the side opposite angle L, which is side LK, is the second longest side. Finally, M∠K is the smallest angle, so the side opposite angle K, which is side JK, is the shortest side.
Therefore, the sides of triangle JLK in order from smallest to largest are JK, LK, JL.
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Select the correct answer.
What is the inverse of the function ?
A.
B.
C.
D.
Answer:
i think its d
Step-by-step explanation:
The question is asking about the inverse of a function, a crucial mathematical concept. We generally calculate this by switching x and y, then solving the new equation for y. Without specific function options, we cannot provide a correct answer.
Explanation:The question is about determining the inverse of a function, an important concept in Mathematics. Given that the question does not have any specifics about the function itself, it's impossible to determine the correct answer. In general, to find the inverse of a function, we follow a certain procedure: exchange the roles of y and x; once that is done, solve the function for y.
For instance, if you had a function like f(x) = 2x + 3, the inverse would be calculated by flipping x and y and solving the resulting equation for y: x = 2y + 3. Solving for y, you have y = (x - 3) / 2.
Unfortunately, without knowledge of the specific functions mentioned in the options A, B, C, D, we cannot select a correct answer.
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How do you get the number 24 with the numbers 2,6,4,1
Answer:
(2+6)*(4-1) = 24
(2-1)*(6*4) = 24
(2-1)*6*4 = 24
(2-1)*(4*6) = 24
(2-1)*4*6 = 24
(6+2)*(4-1) = 24
6*(2-1)*4 = 24
6*(2-1)*4 = 24
6/(2-1)*4 = 24
6/(2-1)*4 = 24
Find the slope of a line that goes through (3,-9) and (5,-1)
(1.3x + 2.4) - (6.1x - 3.2)
The expression (1.3x + 2.4) - (6.1x - 3.2) simplifies to -4.8x + 5.6 after distributing the negative sign and combining like terms.
To solve the expression (1.3x + 2.4) - (6.1x - 3.2), we'll distribute the negative sign inside the second parentheses and then combine like terms:
(1.3x + 2.4) - (6.1x - 3.2)
Distribute the negative sign:
1.3x + 2.4 - 6.1x + 3.2
Combine like terms:
(1.3x - 6.1x) + (2.4 + 3.2)
Combine the x terms:
-4.8x + 5.6
So, (1.3x + 2.4) - (6.1x - 3.2) simplifies to -4.8x + 5.6.
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The probable question may be:
Simplify (1.3x + 2.4) - (6.1x - 3.2)
The greatest integer that will divide both 4900 and 168 exactly
The greatest integer that will divide both 4900 and 168 exactly is 28.
What is Least Common Multiple?Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.
For example, the LCM of 6 and 8 is 24. Hence 24 is divisible by both 6 and 8.
First, Prime Factorizing 4900
4900 = 7 x 7 x 2 x 2 x 5 x 5
and, Prime Factorizing 168
168 = 2 x 2 x 2 x 3 x 7
So, the Common multiple of 4900 and 168 is 2 x 2 x 7 = 28.
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Final answer:
The greatest integer that will divide both 4900 and 168 exactly is 4.
Explanation:
The greatest integer that will divide both 4900 and 168 exactly is 4.
To determine this, we can use the concept of greatest common divisor (GCD). The GCD is the largest positive integer that divides two given numbers without leaving a remainder. In this case, the GCD of 4900 and 168 is 4.
One way to find the GCD is to factorize both numbers and determine the common factors. In this case, the prime factorization of 4900 is 2^2 * 5^2 * 7^2, and the prime factorization of 168 is 2^3 * 3 * 7.
The common factors are 2^2 and 7^1, which multiplied together give us 4. Therefore, 4 is the greatest integer that will divide both 4900 and 168 exactly.