For this case we have that by definition, the Greatest Common Factor or GFC of two or more numbers, is the largest number that divides them without leaving residue.
So:
We look for the factors of 18 and 36:
18: 1,2,3,6,9,18
36: 1, 2,3,4, 6,9,18 ...
Thus, the GFC of both numbers is 18.
Then, the GFC of[tex]18x ^ 2[/tex] and [tex]36x[/tex] is:
[tex]18x[/tex]
Answer:
[tex]18x[/tex]
Final answer:
The Greatest Common Factor of 18x² and 36x is 18x, which is the product of shared prime factors to the lowest powers and includes the variable x.
Explanation:
Finding the Greatest Common Factor (GCF)
To find the Greatest Common Factor of 18x² and 36x, we need to break down each term into its prime factors and include the variable parts:
18x² can be factored into 2 × 3 × 3 × x × x (or 2 × 3² × x²)36x can be factored into 2 × 2 × 3 × 3 × x (or 2² × 3² × x)The GCF is the product of the lowest powers of common factors in both terms. Hence, the GCF of 18x² and 36x is 18x, which consists of 2 × 3 × 3 × x (or 2 × 3² × x).
A piece of ribbon is cut into two shorter pieces in the ratio 2.8:1.25. The divfference in the length of the two shorter pieces is 80.6 centimmeters. What is the length of the original piece of ribbon?
Answer:
210.6 cm
Step-by-step explanation:
Given that a piece of ribbon is cut into two shorter pieces in the ratio 2.8:1.25.
So that means length of the first smaller piece = 2.8x
and length of the second smaller piece = 1.25x
Then difference between their lengths = 2.8x-1.25x = 1.55x
Given that difference is equal to 80.6 centimeters then we get
1.55x=80.6
or x= 80.6/1.55
or x=52
then length of the original piece = 2.8x+1.25x
= 2.8*52+1.25*52
= 145.6+65
= 210.6 cm
Refer to the picture below, sorry for constant questions, btw.
Answer:
1 inch : 5 yards.
Step-by-step explanation:
Paco's first scale was 2 : 5 which is 1 : 2.5.
Now as the length of the pool on the drawing was reduced from 10 in to 5 ins, that means the scale was doubled so the answer is:
1 : 2*2.5 = 1 : 5 .
Without using a protractor to measure exactly, choose the BEST possible measurement of the angle above.
A. 90°
B. 45°
C. 85°
D. 160°
Answer:
Step-by-step explanation:
The slanting line has a slope of approximately 1, so the angle this line makes with the horiz. axis is approx. 45 degrees.
Answer:
B
Step-by-step explanation:
It's not going to be a right angle. The two lines of a right angle are perpendicular. A is incorrect.
C is incorrect. 85o is pretty close to 90 degrees. That angle is nowhere's near that large.
D is incorrect. 160 degrees is nearly a straight line. The angle shown isn't.
That leaves B.
B looks to be 45 degrees and since the others are incorrect, B must be your answer.
La edad de 4 miembros de una familia suman 70. Mamá es 6 veces más grande que su hijo y 10 veces más grande que su hija. Papá es 2 años más grande que mamá. ¿Qué edad tienen cada uno de los miembros de la familia? Escribe el resultado en orden ascendente y separados por un espacios
explicación por favor
Answer:
3 5 30 32
Step-by-step explanation:
The question in English is
The age of 4 members of a family adds up to 70. Mom is 6 times bigger than her son and 10 times bigger than her daughter. Dad is 2 years older than Mom. How old are each of the family members? Write the result in ascending order and separated by spaces
Let
x----> Mon's age
y----> Son's age
z----> Daughter's age
w---> Dad's age
we know that
x+y+z+w=70 -----> equation A
x=6y ----> y=x/6 -----> equation B
x=10z ----> z=x/10 -----> equation C
w=2+x -----> equation D
substitute equation B, C and D in equation A and solve for x
x+(x/6)+(x/10)+(2+x)=70
Multiply by 60 both sides
60x+10x+6x+120+60x=4,200
136x=4,200-120
x=4,080/136
x=30 years
Find the value of y
y=x/6 -----> y=30/6=5 years
Find the value of z
z=x/10 ----> z=30/10=3 years
Find the value of w
w=2+x ----> w=2+30=32 years
Write the result in ascending order and separated by spaces
3 5 30 32
so
Daughter Son Mon Dad
Solve for x. 4x − 3/ 3 =7 Enter your answer in the box. x =
Answer:
x = 6
Step-by-step explanation:
(4x - 3)/3 = 7
4x - 3 = 21
4x = 24
x = 6
Answer:
6
Step-by-step explanation:
I'm going to assume you mean (4x - 3) / 3 = 7
If that is not correct, could you please correct it.
Multiply both sides by 3
3*(4x - 3) / 3 = 7*3
The 3s cancel on the left
4x - 3 = 21
Add 3 to both sides.
4x - 3 + 3 = 21 + 3
combine
4x = 24
Divide by 4
4x/4 = 24/4
x = 6
A merchant paid $3 each for golfing hats that he sold for $4 each. He therefore earned a
gross profit of $1 per hat. By what per cent was the cost price increased to provide for this
profit?
20%
O 30%
331%
300%
o none of these
Step-by-step explanation:
The cost increase is:
(4 - 3) / 3 × 100%
33%
The answer is none of these.
Answer:
Option E. None of these.
Step-by-step explanation:
A merchant paid $3 each for golfing hats and sold for $4 each. He earned a gross profit of $1 per hat.
We have to calculate the percent of increase in cost price Or percentage profit.
Percentage profit = [tex]\frac{\text{(Selling price - Cost price)}}{\text{cost price}}(100)[/tex]
= [tex]\frac{(4-3)}{3}.(100)[/tex]
= [tex]\frac{100}{3}=33.33[/tex]%
Which not in any option.
Therefore, Option E. None of these is the answer.
(HELP ASAP PLEASE)
Zoe often orders party trays from her favorite Mexican food restaurant for company events. For a recent company party, she spent $239 on 4 burrito platters and 5 taco platters. For a company meeting, she spent $208 on 3 burrito platters and 5 taco platters. How much does each type of platter cost?
Each burrito platter costs $___ and each taco platter costs $___ .
Answer:
Each burrito platter costs $_31_ and each taco platter costs $_23__ .
Step-by-step explanation:
Let's first express both orders into equations. Let's simply use b for the burritos platters and t for the tacos platters:
4b + 5t = 239
3b + 5t = 208
We can use the subtraction method easily on this one:
4b + 5t = 239
-
3b + 5t = 208
==============
1b + 0t = 31
b = 31
So, the burrito platters ost $31 each.
Now, let's find how much are the tacos ones. Just take the first equation:
4(31) + 5t = 239
124 + 5t = 239
5t = 115
t = 23
Taco platters cost $23.
Let's test that with the second equation:
3b + 5t = 208
3(31) + 5(23) = 208
93 + 115 = 208
208 = 208
Verified!
The coordinates R(1, -3), S(3, -1) T(5,-7) form what type of polygon?
a right triangle
an acute triangle
an equilateral triangle
an obtuse triangle
Answer:
A right triangle
Step-by-step explanation:
Suppose a, b, c are the sides of a triangle,
If a² = b² + c² or b² = a² + c² or c² = a² + b²
Then the triangle is called a right angled triangle,
If a² + b² > c², a² + c² > b², b² + c² > a²
Then the triangle is called an acute triangle,
If a = b = c
Then the triangle is called an equilateral triangle,
If a² + b² < c², where c is the largest side of the triangle,
Then the triangle is called an obtuse triangle,
Now, In triangle RST,
By the distance formula,
[tex]RS=\sqrt{(3-1)^2+(-1-(-3))^2}=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{8}\text{ unit }[/tex]
Similarly,
ST = √40 unit,
TR = √32 units,
Since, ST² = RS² + TR²
Hence, by the above explanation it is clear that,
Triangle RST is a right angled triangle,
First option is correct.
Answer:
this isa right triangle!!!
Step-by-step explanation:
this isa right triangle!!!
The difference between the roots of the equation 2x^2−5x+c=0 is 0.25. Find c.
Answer:
[tex]c=\frac{99}{32}[/tex]
Step-by-step explanation:
The given quadratic equation is [tex]2x^2-5x+c=0[/tex].
Comparing this equation to: [tex]ax^2+bx+c=0[/tex], we have a=2,b=-5.
Where: [tex]x_1+x_2=\frac{5}{2}[/tex] and [tex]x_1x_2=\frac{c}{2}[/tex]
The difference in roots is given by:
[tex]x_2-x_1=\sqrt{(x_1+x_2)^2-4x_1x_2}[/tex]
[tex]\implies 0.25=\sqrt{(2.5)^2-4(\frac{c}{2})}[/tex]
[tex]\implies 0.25^2=6.25-2c[/tex]
[tex]\implies 0.0625-6.25=-2c[/tex]
[tex]\implies -6.1875=-2c[/tex]
Divide both sides by -2
[tex]c=\frac{99}{32}[/tex]
Answer:
The value of c is 3.09375.
Step-by-step explanation:
Given : The difference between the roots of the equation [tex]2x^2-5x+c=0[/tex] is 0.25.
To find : The value of c?
Solution :
The general quadratic equation is [tex]ax^2+bx+c=0[/tex] with roots [tex]\alpha,\beta[/tex]
The sum of roots is [tex]\alpha+\beta=-\frac{b}{a}[/tex]
The product of roots is [tex]\alpha\beta=\frac{c}{a}[/tex]
On comparing with given equation, a=2, b=-5 and c=c
Substitute the values,
The sum of roots is [tex]\alpha+\beta=-\frac{-5}{2}[/tex]
[tex]\alpha+\beta=\frac{5}{2}[/tex] .....(1)
The product of roots is [tex]\alpha\beta=\frac{c}{2}[/tex] ....(2)
The difference between roots are [tex]\alpha-\beta=0.25[/tex] .....(3)
Using identity,
[tex]\alpha-\beta=\sqrt{(\alpha+\beta)^2-4\alpha\beta}[/tex]
Substitute the value in the identity,
[tex]0.25=\sqrt{(\frac{5}{2})^2-4(\frac{c}{2})}[/tex]
[tex]0.25=\sqrt{\frac{25}{4}-2c}[/tex]
[tex]0.25=\sqrt{\frac{25-8c}{4}}[/tex]
[tex]0.25\times 2=\sqrt{25-8c}[/tex]
[tex]0.5=\sqrt{25-8c}[/tex]
Squaring both side,
[tex]0.5^2=25-8c[/tex]
[tex]0.25=25-8c[/tex]
[tex]8c=25-0.25[/tex]
[tex]8c=24.75[/tex]
[tex]c=\frac{24.75}{8}[/tex]
[tex]c=3.09375[/tex]
Therefore, the value of c is 3.09375.
Which best describes a system of equations that has infinitely many solutions
Answer:
see explanation
Step-by-step explanation:
Either both equations are equal or are multiples of each other
As an example consider the 2 equations
4x - y = 2 → (1)
- 12x + 3y = - 6 → (2)
Multiply (1) by - 3
- 12x + 3y = - 6 → (3)
Subtract (3) from (2) term by term
(- 12x - (- 12)x) + (3y - 3y) = (- 6 - (- 6)), that is
(- 12x + 12x) + 0 = - 6 + 6
0 = 0
This indicates the solution has infinite solutions
let x = k, k is a real number then from (1) y = 4x - 2 ⇒ y = 4k - 2
Thus (k, 4k - 2) will generate solutions to the system of equations
Three cars are for sale.
Car A
£12380
Car B
£16760
Car C
£14580
The price of each car is rounded to the nearest £100.
Which price changes by the greatest amount?
Answer:
Car B
Step-by-step explanation:
Car B's price changes by the greatest amount (£40) when rounded to the nearest £100 among the three cars.
To determine which price changes by the greatest amount when rounded to the nearest £100, let's first calculate the rounded prices for each car:
Car A: £12380 rounds to £12400
Car B: £16760 rounds to £16800
Car C: £14580 rounds to £14600
Now, let's compare the differences between the original prices and the rounded prices:
- For Car A: £12400 - £12380 = £20
- For Car B: £16800 - £16760 = £40
- For Car C: £14600 - £14580 = £20
The greatest difference is £40, which occurs for Car B. Therefore, the price of Car B changes by the greatest amount when rounded to the nearest £100.
How many solutions does this linear system have?
y = x+ 2
6x – 4y = –10
Answer:
no solutions
Step-by-step explanation:
Answer:
Exactly one solution.
Step-by-step explanation:
We have been given a system of equations. We are asked to find the number of solutions for our given system.
[tex]y=x+2...(1)[/tex]
[tex]6x-4y=-10...(2)[/tex]
We can see that equation (1) in slope-intercept form of equation.
We will convert equation (2) in slope-intercept form of equation as shown below:
[tex]6x-6x-4y=-10-6x[/tex]
[tex]-4y=-6x-10[/tex]
Divide both sides by [tex]-4[/tex].
[tex]\frac{-4y}{-4}=\frac{-6x}{-4}+\frac{-10}{-4}[/tex]
[tex]y=\frac{3}{2}x+\frac{5}{2}[/tex]
We can see that slopes of both lines are different, therefore, our given lines will intersect exactly at one point and our given system of equations has exactly one solution.
Miss Diego has three cups of sugar she needs to divide the sugar equally into containers of 1/3 of a cup of sugar how many containers will miss Diego be able to fill? can you please help because my little sis needs help but I haven't done this a while so yeah....
Answer:
9
Step-by-step explanation:
if every container needs 1/3 of one cup and you have 3 cups then multiply 3 by 3 and you have your answer
Miss Diego will be able to fill 9 containers.
How to find the number of containers?We must divide the quantity of sugar by the quantity of sugar each container can hold to find the total number of containers.
We can find the total number of containers below:It is given that Miss Diego has three cups of sugar.
It is also given that the containers can hold 1/3 of a cup.
We are asked to find the total number of containers she can fill.
This can be done as shown below:
Total number of cups = Total cups of sugar/quantity of sugar each container can hold
= 3 / (1/3)
= 3 * 3
= 9
The number of containers that can be filled is found. The total number of containers that can be filled is equal to 9 containers.
Therefore, we have found that Miss Diego will be able to fill 9 containers.
Learn more about division here: https://brainly.com/question/1622425
#SPJ2
Good Afternoon I have a couple of problems I need help one. Can someone help on this ASAP. (It would be greatly appreciated if you showed your work)
Thank you have a good day
Answer:
C. [tex]y=3\cdot 5^x[/tex]
Step-by-step explanation:
First two options show linear function and last two options show exponentioal functions. From the table you can see that
[tex]\dfrac{3}{5}=5\cdot \dfrac{3}{25}\\ \\3=5\cdot \dfrac{3}{5}\\ \\15=5\cdot 3\\ \\75=5\cdot 15[/tex]
This gives you that the function is exponential. Let the expression for the function be [tex]y=ab^x.[/tex] Substitute two values:
at x=0:
[tex]y=a\cdot b^0\\ \\3=a\cdot b^0\\ \\3=a\cdot 1\\ \\a=3[/tex]
at x=1:
[tex]y=a\cdot b^1\\ \\15=a\cdot b\\ \\15=3\cdot b\\ \\b=\dfrac{15}{3}\\ \\b=5[/tex]
Hence
[tex]y=3\cdot 5^x[/tex]
What is the 25th term of the arithmetic sequence where a1 = 8 and a9 = 48?
Answer: [tex]a_{25} = 128[/tex]
Step-by-step explanation:
You need to use this formula:
[tex]a_n = a_1 + (n - 1)d[/tex]
Where [tex]a_n[/tex] is the nth] term, [tex]a_1[/tex] is the first term,"n" is the term position and "d" is the common diference.
You must find the value of "d". Substitute [tex]a_1=8[/tex], [tex]a_9=48[/tex] and [tex]n=9[/tex] into the formula and solve for "d":
[tex]48 = 8 + (9 - 1)d\\48=8+8d\\48-8=8d\\40=8d\\d=5[/tex]
Now, you can calculate the 25th term substituting into the formula these values:
[tex]a_1=8[/tex]
[tex]d=5[/tex] and [tex]n=25[/tex]
Then you get:
[tex]a_{25} = 8 + (25 - 1)5[/tex]
[tex]a_{25} = 8 + 120[/tex]
[tex]a_{25} = 128[/tex]
Point E(3,3) is reflected in the line x = -2. What are the coordinates of E’?
Answer:
(3, -7) are the coordinates
What is the scale factor ? And given that QY’ = 4.125 what is QY?
Answer:
4
Step-by-step explanation:
Answer:
first q is 2.75
second q is 1.5
Step-by-step explanation:
Find the lateral area of this pyramid whose base is a regular hexagon with a side length of 3cm and whose slant height is 12cm.
Answer:
108 cm²
Step-by-step explanation:
The lateral area of this pyramid is the addition of the six triangle areas formed on its lateral side.
The area of each triangle is:
Area = (1/2)*side*slant
Area = (1/2)*3*12 = 18 cm²
Then the lateral area is 6*18 = 108 cm²
Answer:
108cm2
Step-by-step explanation:
Please help?
Which statement can you be sure is true
Answer:
the answer is C
Step-by-step explanation:
which student solved the equation w/13.5 = 9.7 correctly?
Answer:
Kwan's work
Step-by-step explanation:
The given equation is:
[tex]\frac{w}{13.5}=9.7[/tex]
We multiply both sides by 13.5 to obtain:
[tex]\frac{w}{13.5}\times 13.5=9.7\times 13.5[/tex]
We simplify to get;
[tex]w=9.7\times 13.5[/tex]
We multiply out the RHS to get:
[tex]w=130.95[/tex]
Answer:
kyan's work
Step-by-step explanation:
i did the test
Daryl took out a single payment loan for $890 that charged a $40 fee. How
much does he have to pay by the time the loan reaches maturity?
Answer:
$930
Step-by-step explanation:
The amount payable at maturity of the loan is simply the sum of the loan amount and the fee charged on the loan.
The loan amount is 890 while the fee charged on the loan is 40. The amount repayable at maturity is thus;
890 + 40 = 930.
Therefore, he has to pay $930 by the time the loan reaches maturity.
Answer:
$930
Step-by-step explanation:
Daryl took out a single payment loan for $890.
That charged a $40 fee.
He takes loan of $890 that charged a $40 fee for a single time, so his maturity amount = loan amount + fees of $40
He have to pay by the time the loan reaches maturity = 890 + 40
= $930
He have to pay $930 by the time of maturity.
Write as a single logarithm
ANSWER
[tex]c. \ln( \frac{2 {x}^{3} }{3y}) [/tex]
EXPLANATION
We want to write
[tex] ln(2x) + 2 ln(x) - ln(3y) [/tex]
as a single logarithm.
Use the power rule to rewrite the middle term:
[tex]n \: ln(a) = ln( {a}^{n} ) [/tex]
[tex]ln(2x) + ln( {x}^{2} ) - ln(3y) [/tex]
Use the product rule to obtain:
[tex]ln(a) + ln(b) = ln(ab) [/tex]
[tex]ln(2x \times {x}^{2} )- ln(3y) [/tex]
[tex]ln(2{x}^{3} )- ln(3y)[/tex]
Apply the quotient rule:
[tex] ln(a) - ln(b) = ln( \frac{a}{b})[/tex]
[tex]ln(2{x}^{3} )- ln(3y) =\ln(\frac{2 {x}^{3} }{3y})[/tex]
If lines AB and CD are parallel, then angels c and e are?
A. complementary
B. congruent
C. corresponding
D. supplementary
Answer:
D
Step-by-step explanation:
Given that AB and CD are parallel lines, then
∠c and ∠e are same side interior angles and are supplementary
Answer:
D. Supplementary
Step-by-step explanation:
Consecutive Interior Angles Theorem:
If two parallel lines are cut by a transversal, then consecutive interior angles are supplementary.
Supplementary means the sum of the angles is 180 degrees.
Another name for consecutive interior angles is same side interior angles. The angles are on the same side of the transversal (in this case to the left) and they are in between the parallel lines which is the interior.
Lisa and Julia are selling cookie dough for a school fundraiser. Customers can buy packages of sugar cookie dough and packages of chocolate chip cookie dough. Lisa sold 13 packages of sugar cookie dough and 6 packages of chocolate chip cookie dough for a total of $252. Julia sold 8 packages of sugar cookie dough and 12 packages of chocolate chip cookie dough for a total of $288. Find the cost of each of one package of sugar cookie dough and one package of chocolate chip cookie dough.
x = ______________________________ y = _______________________________
Equations:
1.
2.
solution: _______________________
Final answer:
The problem is a linear system where we find the cost of sugar cookie dough (x) at $12 per package and chocolate chip cookie dough (y) at $16 per package by forming and solving two linear equations.
Explanation:
The problem presented is one of linear systems, where we are asked to find the cost of one package of sugar cookie dough (x) and one package of chocolate chip cookie dough (y). To solve for x and y, we need to create two equations based on the information given:
13x + 6y = $252 (Lisa's sales)
8x + 12y = $288 (Julia's sales)
By solving this system of equations, we can determine the cost of each type of cookie dough. Using either substitution or elimination method will lead us to the solution. For this example, I'll use the elimination method:
Multiply each side of the first equation by 2, and the second equation by -1, and then add them together to eliminate y:
26x + 12y = $504
-8x - 12y = -$288
18x = $216
x = $216 / 18
x = $12
Substitute x back into any one of the original equations to find y:
13($12) + 6y = $252
$156 + 6y = $252
6y = $252 - $156
6y = $96
y = $96 / 6
y = $16
So the cost per package is $12 for sugar cookie dough and $16 for chocolate chip cookie dough.
n the table below, x represents miles traveled and y represents the cost to travel by train.
Miles, x
Cost, y
2
8.50
5
15.25
8
22.00
12
31.00
Which linear equation represents the situation?
B. y=2.25x+4.00 (eg. 2020)
What is the value of x?
Answer:
[tex]\large\boxed{x=8\sqrt2}[/tex]
Step-by-step explanation:
[tex]\bold{METHOD\ 1}\\\\\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\ leg=8,\ leg=8,\ hypotenuse=x.\\\text{Substitute:}\\\\x^2=8^2+8^2\\\\x^2=2(8^2)\to x=\sqrt{2(8^2)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x=\sqrt2\cdot\sqrt{8^2}\qquad\text{use}\ \sqrt{a^2}=a\\\\x=8\sqrt2[/tex]
[tex]\bold{METHOD\ 2}\\(look\ at\ the\ picture)\\\\\text{We have}\ a=8.\ \text{Therefore}\ a\sqrt2=8\sqrt2[/tex]
If komal's salary of $2000per month is increased by 5.5%,what is his new salary
Answer:
2110 dollars / month
Step-by-step explanation:
Formula
New Salary = Old Salary * (1 + 5.5/100)
Solution
New Salary = 2000 * (1 + 0.055)
New Salary = 2000 * 1.055
New Salary = 2110 dollars / month
What’s the y-intercept for the quadratic equation:y=3x^2+5x-2? Would really appreciate it if someone knew. :)
recall that to find the x-intercept we set y = 0 and solve for "x".
and to find the y-intercept, we set x = 0 and solve for "y", so let's do so
x = 0, so then the equation turns into
y = 3x² + 5x - 2
y = 3(0)² + 5(0) - 2
y = -2
when x = 0, y = -2, ( 0 , -2 ).
You want to hang a painting in the center of a 12-
foot wall. The painting is 2 feet wide. How far from
the edge of the wall do you place the nail to hang the
painting?
Answer:
6 feet from the edge of the wall
help plz ...................................
Answer:
Last Choice: 6 * 3 * 3 square inches
Step-by-step explanation:
The net is made up of 6 squares. Each square measures 3 inches by 3 inches. The area of one square is 3 * 3 square inches. The total surface is 6 times the area of one square.
Answer: 6 * 3 * 3 square inches