If the GCF of a term and 12x²y is 4xy , then (a) The term is 8xy , The expression is 4xy(2 + 3x) .
The Greatest Common Factor of the two terms is 4xy ,
where , the first term is 12x²y , we have to find the second term ,
Consider Option(a) : where the second term is 8xy ,
So , GCF of 8xy and 12x²y is
= 2(4xy) and 3x(4xy)
= 4xy(2 + 3x ) ....taking 4xy common from both the terms ,
Therefore , Yes , the second term is 8xy and the expression is 4xy(2+3x) .
The given question is incomplete , the complete question is
What term and 12x²y have a GCF of 4xy? Write an expression that shows the monomial factored out of the polynomial , choose the correct answer below :
(a) The term is 8xy , The expression is 4xy(2 + 3x)
(b) The term is 16xy , The expression is 4xy(4xy + 3x)
(c) The term is 3x , The expression is 12x²y(3x + 4xy)
(d) The term is 4x²y , the expression is 4xy(1 + 3x) .
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mentum.com
Lxpre3310113, 1931
ial Expressions: Mastery Test
5
Drag each tile to the correct box.
Using the order of operations, what are the steps for solving this expression?
40+8+32+(15-7) × 2
Arrange the steps in the order in which they are performed.
3²
5+9
40+8
14+ 16
8x2
KNOW
15-7
The order in which they performed be
14 + 16 . . . . add 5 + 9
30 . . . . . . . add 14 + 16
What is meant by expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. There are four possible math operations here: addition, subtraction, multiplication, and division.
Given: 40/8 + 3² + (15 - 7) × 2
The order of operations instructs you to begin by assessing parenthesized expressions. This is done by deducting 7 from 15.
40/8 + 3² + 8 × 2 . . . . (15 - 7) = 8
Then you evaluate exponential terms.
40/8 + 9 + 8 × 2 . . . . . 3² = 9
Next, multiply and divide from left to right. In this case, division comes before multiplication.
5 + 9 + 8 × 2 . . . . . divide 40/8 = 5
5 + 9 +16 . . . . . . multiply 8 × 2 = 16
The order in which they performed be
14 + 16 . . . . add 5 + 9
30 . . . . . . . add 14 + 16
The complete question is:
Using the order of operations, what are the steps for solving this expression?
40/8+3^2+(15-7)*2
Arrange the steps in the order in which they are performed.
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a tank holds 4000 liters of water in which 100 grams of salt have been dissolved. saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. write initial the value problem for:
The mass of salt in the tank at time t.
dS/dt = 10 - S/400
S(0) = 100 grams
The solution is S(t) = 4000 - 3900[tex]e^{\frac{-t}{400}}[/tex]
A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.
So dS/dt = S(in) - S(out)
S(in) = 1 × 10 = 10 gram/liters
S(out) = S/V × 10 = 10S/V gram/liters
V = V(0) + q(in) - q(out)
V = 4000 + 10t - 10t
V = 4000 liters
dS/dt = 10 - 10S/V
dS/dt = 10 - 10S/4000
dS/dt = 10 - S/400
Now given; S(0) = 100.
Here, p(t) = 1/400, q(t) = 10
[tex]\int p(t)dt = \int\frac{1}{400}dt[/tex][tex]\int p(t)dt = \frac{1}{400}t[/tex]
[tex]\mu=e^{\int p(t)dt}[/tex]
[tex]\mu=e^{\frac{t}{400}}[/tex]
So, S(t) = [tex]\frac{\int\mu q(t)dt+C}{\mu}[/tex]
S(t) = [tex]\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}[/tex]
S(t) = [tex]e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)[/tex]
S(t) = [tex]e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)[/tex]
S(t) = [tex]e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)[/tex]
Now solving the bracket
S(t) = 4000 + [tex]e^{\frac{-t}{400}}[/tex]C.....(1)
At S(0) = 100
100 = 4000 + [tex]e^{\frac{-0}{400}}[/tex] C
100 = 4000 + [tex]e^{0}[/tex] C
100 = 4000 + C
Subtract 4000 on both side, we get
C = -3900
Now S(t) = 4000 - 3900[tex]e^{\frac{-t}{400}}[/tex]
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The complete question is:
A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:
The mass of salt in the tank at time t.
dS/dt =
S(0) =
The solution is S(t) =
What is the equation of the line that passes through the point (1, 8) and has a slope
of 1?
Answer:
y = x + 7
Step-by-step explanation:
Equation of line:[tex]\boxed{(y-y_1)=m(x -x_1)}[/tex]
m = 1
(1 , 8) ; x₁ = 1 & y₁= 8;
y - 8 = 1*(x - 1)
y - 8 = x - 1
y = x - 1 + 8
y = x + 7
Printing company purchases an ad- vanced color copier/printer for $113,000 After 7 years, the equipment will be obsolete and have no value.
Write a linear equation giving the value of the equipment in terms of the time t
A linear equation giving the value of the equipment in terms of the time t is calculated to be v = 117000 - 16714.3t.
The value of the colour printer is 117000 $ and machine has no value after 7 years.
As it is given that the machine has no value after 7 years. That mean rate is decreasing every year. So, the decreasing rate is, 117000/7 = 16714.3.
Let us assume v is the value of the machine and t is the time. Then, the linear equation for the given problem is, v = 117000 - 16714.3t
Thus, the required linear equation is v = 117000 - 16714.3t.
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anna leaves her house on her bike traveling at an averge speed of 6 mph. an hour later, her mother sets out after her on the same road, traveling by car. how fast must she drive to reach anna in twn minutes
The mother must drive at a speed of 6 mph to reach Anna in ten minutes.
To find the speed required for the mother to reach Anna in ten minutes, you need to calculate the distance between them and the time it takes to close the gap.
Let x be the speed of the mother's car in mph.
In one hour, Anna will have covered 6 miles.
In ten minutes, the mother will have covered x * 10/60 miles.
The total distance between them is 6 + x * 10/60 miles.
The mother must cover this distance in ten minutes, so:
x * 10/60 = 6 / (10/60)
x = 6 * (10/60) / (10/60)
x = 6 mph
Therefore, the mother must drive at a speed of 6 mph to reach Anna in ten minutes.
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Clare describes her morning at school yesterday: “ I entered the school on the first floor . Then walked up to the third floor floor and stayed for my class for an hour afterwards, I had an hour long class in the basement, and after I went back to the ground level and sat outside to eat my lunch “. Sketch a possible graph of her height from the ground floor as a function of time
The Centers for Disease Control and Prevention (CDC) states that the average height for men and women in the United States is around 5 feet, 9 inches and 5 feet, 4 inches, respectively.
What height do you think is normal?The Centers for Disease Control and Prevention (CDC) states that the average height for men and women in the United States is around 5 feet, 9 inches and 5 feet, 4 inches, respectively.14-year-old boys typically stand 162.4 cm (5 ft 3 in) tall, compared to 159.8 cm for girls (5 ft 2). At this age, you should expect a sizable range in height. Puberty, however, will vary from person to person; some may have already passed through it, while others may not.The Centers for Disease Control and Prevention (CDC) states that the average height for men and women in the United States is around 5 feet, 9 inches and 5 feet, 4 inches, respectively.To learn more about height refer to:
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A man walks due west for 4km. he then changes direction and walks on a bearing of 197 degrees until he is southwest of his starting point. how far is he to the then from his starting point
Step-by-step explanation:
To solve this problem, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and an angle C opposite side c,
c² = a² + b² - 2abcos(C)
In this problem, we can consider the man's starting point as the origin, and the distance he travels in the first leg as the first side of the triangle (a = 4km). The distance he travels in the second leg is the second side of the triangle (b). The angle between the two legs is the angle opposite side c, which is 90 degrees since the man changes direction from due west to southwest.
Therefore, we can use the law of cosines to find the distance he traveled in the second leg:
c² = a² + b² - 2abcos(90)
c² = 4² + b²
c = √(4² + b²)
c = √(16 + b²)
We know that the bearing of the second leg is 197 degrees, which is equivalent to a bearing of -163 degrees, since bearing measurements are taken clockwise from due north.
So we can use the law of cosines to find the distance he traveled in the second leg:
b = √(c² + a² - 2ac cos (-163))
We can now plug in the values we know:
b = √(c² + 4² - 24c*cos(-163))
We can now solve for c:
c = √(b² + 16 - 8bc)
The man is then southwest of his starting point, so the distance from his starting point to the final point is c.
be sure to answer all parts. a small hole in the wing of a space shuttle requires a 21.9 cm2 patch. (a) what is the patch's area in square kilometers (km2)? enter your answer in scientific notation. (b) if the patching material costs nasa $3.91/in2, what is the cost of the patch to the nearest cent?
(a) The area of the space shuttle is:2.07x10⁻⁹km²
(b) $11.0321 is the cost of the patch.
Area of the patch of the space shuttle = 21.9cm²
a) 1 cm=0.00001 km
1cm²=(0.00001 km)²=10⁻¹⁰km²
21.9cm²=21.9x10⁻¹⁰km²=21.9x10⁻⁹km²
the patch's area =21.9x10⁻⁹km²
b) 1 cm = 0.393701 inch
1cm²=0.1550inch²
21.9cm²=21.9x0.1550inch²=3.3945inch²
The cost of patching area = 3.3945inch²
The cost of patching is are: 3.3945inch²
3.25inch²x3.3945inch²=11.0321
the cost of the patch to the nearest cent=11.0321
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FIELD TRIP A school is planning a field trip to a museum. Tickets cost $4 for students and $8 for adult chaperones. There must be at least 1 adult chaperone for every 9 students and no more than 1 adult Up to 100 people may go on the field trip. chaperone for every 4 students. What is the maximum total cost for tickets?
Answer:
The maximum total cost for tickets is $320 + $160 = $480.
Step-by-step explanation:
The maximum number of people that can go on the field trip is 100, so the maximum number of students is 100 - (100/5) = 80 students.
The maximum number of adult chaperones is 1 adult chaperone for every 4 students, so the maximum number of chaperones is 80/4 = 20 chaperones.
The total cost for student tickets is $4 x 80 = $320.
The total cost for adult chaperone tickets is $8 x 20 = $160.
The maximum total cost for tickets is $320 + $160 = $480.
Answer:
the maximum amount for the equation is 320+160=480
using the multiple linear regression model you developed in part (a), what is the predicted freshman gpa of bobby engle, a student who has been admitted to ruggles college with a 660 sat score on critical reading and at a 630 sat score on mathematics?
y= -2.6717 + 0.0043(660) + 0.0045(630) = 3.00 is the GPA Score for Bobby Eagle.
A statistical method known as multiple linear regression (MLR), usually referred to as multiple regression, employs a number of explanatory variables to forecast the result of a response variable. One explanatory variable is used just once in multiple regression, an extension of linear (OLS) regression. Financial and econometric inference both make heavy use of MLR.
Score on critical reading = 660
Score on mathematics = 630
Intercept = -2.6717
Reading(x1) = 0.0043
Mathematics(x2) = 0.0045
Hence, y = -2.6717 + 0.0043(660) + 0.0045(630) is the GPA score for Bobby.
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You are ask to solve 12x-18 =126
The solution to an inequality is graphed on the number
ne.
-5 -4 -3 -2 -1 0 1 2 3 4 5
Mark this and return
What is another way to represent this solution set?
{xx<4.5}
Ox|x≤4.5}
Oxx> 4.5)
O{x|x24.5)
Save and Exit
Next
The solution set to the inequality as represented in another way is {x | x ∈ ≤ 4.5}. The second option is correct from the photo.
Representation of sets into a set builder notation:The set builder form is the representation of components of a set by a statement or an expression. The represented element(s) will be written using a variable, accompanied by a vertical line or colon, then the general attribute of the same represented element. This approach avoids listing the elements as seen in the roster method or the listing method.
From the given sets in roster form:
{-5,-4, -3, -2, -1, 0, 1, 2, 3, 4.5}
The same set above can be denoted by x, where x represents all the elements in the set and can be written as:
= {x | x ∈ ≤ 4.5}
This is read as x is an element of x such that x represent all the values from negative infinity to 4.5.
Therefore, we can conclude that the second option is correct from the photo.
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FInd the simple interest earned on a deposit of $2800 after 5 years at a 2% annual rate.
The simple interest earned on a deposit of $2800 after 5 years at a 2% annual rate is $280.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
We have,
P = $2800
T = 5 years
R = 2%
Now,
The formula for simple interest.
SI = PRT/100
Now,
SI = (2800 x 2 x 5) / 100
SI = 28 x 10
SI = $280
Thus,
Simple interest is $280.
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In a survey, a group of students were asked to name their favorite world language class. There were 25 students who chose "other" languages. How many students participated? french:42. 5% spanish:45 students participated
Spanish 45 and french 42.5. When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common.
When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common. After that, input how many items are still there in each pair of sets' overlapping zone.
The quantity of each set's leftover pieces should be entered. Lastly, locate any missing numbers using any known totals.
Using a Venn diagram to determine probabilities: The Venn diagram's subset's components should be identified. Figure out the subset's frequency. Work out the larger set's overall frequency.
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If I Got 7 "(tokens or whatever you prefer) a minute for 9 hours/ 540 minutes, how many tokens would I have
make x the subject for 8x+7=2y-1
In a group of 60 tudent, 25 play table tenni, 16 do wimming and 22 play cricket, 8 play table tenni and do wimming, 6 play cricket and do wimming, 5 play table tenni and cricket, and 12 tudent do not play any of thee game
12 students do not play any of the games. Number of students who do not play any of the games = 60 - 82 = 12
A group of 60 students, 25 play table tennis, 16 do swimming and 22 play cricket, 8 play table tennis and do swimming, 6 play cricket and do swimming, 5 play table tennis and cricket.
25 play table tennis
16 do swimming
22 play cricket
8 play table tennis and do swimming
6 play cricket and do swimming
5 play table tennis and cricket
Find the number of students who do not play any of the games
Total number of students = 60
Number of students who play any of the games = 25 + 16 + 22 + 8 + 6 + 5 = 82
Number of students who do not play any of the games = 60 - 82 = 12
12 students do not play any of the games.
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necesito esto para hoy,porfavor x-3(x+5)=3x+10
No hay solución para la ecuación algebraica 3 · x + 15 = 3 · x + 10.
¿Cómo resolver una ecuación algebraica?
En este problema tenemos el caso de una ecuación algebraica con una variable única y es nuestra labor determinar su solución, en caso de existir, por métodos algebraicos. Primero, escriba la ecuación algebraica correspondiente:
3 · (x + 5) = 3 · x + 10
Segundo, halle la solución por propiedades algebraicas:
3 · x + 15 = 3 · x + 10
15 = 10 (CRASH!)
La ecuación algebraica 3 · x + 15 = 3 · x + 10 no tiene solución.
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Quadrilaterals Q and P are similar. What is the scale factor of the dilation that takes P to Q?
A. 3/5
B. 4/5
C. 5/4
D. 5/3
Answer:
C. 5/4
Step-by-step explanation:
Let s = the scale factor
4s = 5 divide both sides by 4
s = 5/4
– 0.2× – 5÷( – 1– – 0.5)
Answer:
Step-by-step explanation:
35
A shipping container is in the form of a right rectangular prism, with
dimensions of 20 ft by 8 ft by 8 ft 9 in. How many cubic feet of shipped goods
would it hold when it's a quarter full? Round your answer to the nearest tenth
if necessary.
When it's a quarter full, the shipping container holds a volume of 350 cubic feet.
How many cubic feet of shipped goods would it hold when it's a quarter full?Bassically, we want to find one quarter (1/4) of the volume of the rectangular prims.
The dimensions are 20ft by 8ft by (8ft + 9in)
Let's rewrite that last part only using feet.
Remember that 12 in = 1ft
Then:
9 in = (9/12)ft = 0.75 ft
Then we can rewrite the dimensions as:
20ft by 8ft by 8.75 ft
The volume is the product between these numbers, and we want one fourt of the volume, so we need to find:
V = (1/4)*(20ft)*(8 ft)*(8 .75 ft) = 350ft³
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In 2012, it was estimated that the number of U. S. Households that had dogs as pets was [tex]4. 33 x 10^7[/tex], and the average number of dogs per household was 1. 6. Based on the information, approximately how many dogs were household pets in the U. S. In 2012, in scientific notation?
[tex]2. 71 x 10^7[/tex]
[tex]3. 70 x 10^8[/tex]
[tex]5. 33 x 10^8[/tex]
[tex]6. 93 x 10^7[/tex]
6.93 × 10⁷ dogs were household pets in the U. S. In 2012.
To find the total number of dogs as household pets in the U.S. in 2012, we need to multiply the number of households by the average number of dogs per household.
Number of households = 4.33 × 10⁷
The average number of dogs per household = 1.6
Total number of dogs = (4.33 x 10⁷) × (1.6) = 6.93 × 10⁷
Therefore, approximately 6.93 × 10⁷ dogs were household pets in the U.S. in 2012.
Hence, the correct answer is D.
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Tyson must complete 30 hours of community service. She does 2 hours each day. Write a liner equation to represent the hours Tyson has left after x days?
Tyson has (30-2x) hours left after x days .
Linear equation: What is it?A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).
A first-degree polynomial is described as the sum of a collection of terms, each of which is the product of a constant and the first power of a variable in a linear equation.
She works out for two hours per day for a total of x days.
She has thus worked for two hours.
She has 30 hours left to accomplish, of which she has already worked for two of them.
She now has 30 2 hours to finish the task.
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Please help me!!! Sorry about small photo!
Answer:
I think 9/10 but I am not sure
Determine the solution to the following system of linear equations by inspecting the graph below. Enter the solution set as an ordered pair in the form (x,y). If there are no solutions, enter None and enter ALL if there are infinitely many solutions.
The solution set to the system of linear equations as an ordered pair is (3, -3).
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines cross each other (intersect), which is represented as an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.
Note: Each interval on this graph represents 1 unit.
By critically observing the graph of the lines representing the system of linear equations, we can reasonably infer and logically deduce that the correct solution set lies in Quadrant IV and it is denoted by the point of intersection of both the x-coordinate and y-coordinate, which is given by the ordered pair (3, -3).
In conclusion, the ordered pair (3, -3) represents the solution set to the system of linear equations represented by the graph.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
An open circle is at 5 and a bold line starts at 5 and is pointing to the right. Therefore, option B is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -3(2x - 5) < 5(2 - x).
Here, -6x+15<10-5x
Add 5x on both the sides of an inequality, we get
-x+15<10
Subtract 15 on both the sides of an inequality, we get
-x<10-15
-x<-5
Multiply -1 on both the sides of an inequality, we get
x>5
Therefore, option B is the correct answer.
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how to find
127.98+35.261
(for my cuz)
The simplification of the given expression after addition would be = 163.241.
What is addition?Addition is the combination of two or more given values and it's one of the major arithmetic operations in mathematics.
The given expression is a s follows;
127.98+35.261 = 163.241
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What is ths measure of z. 3
How many teaspoons are there in 6 milliliters?
Answer:
70
Step-by-step explanation:
you divide the intergert and div8de its easy
Answer: 70
Step-by-step explanation:
Sheila collect pokemon card. A of 2018, he ha a Mewtwo card that i twice a old a her Snorlax card. Two year ago, her rare Raichu card wa five time a old a the Snorlax card. If the Raichu card i even year older than the Mewtwo card in what year wa the Raichu card made?
The Raichu card was made 8 years ago.
To calculate this, we need to take into account the age of the Mewtwo card, the Snorlax card, and the Raichu card.
The Mewtwo card is twice as old as the Snorlax card, so the Mewtwo card is two years old. The Raichu card is five times as old as the Snorlax card, so it must be ten years old.
Since the Raichu card is two years older than the Mewtwo card, it must be eight years old. Therefore, the Raichu card was made eight years ago.
To summarise, the Mewtwo card is two years old, the Snorlax card is one year old, and the Raichu card is ten years old. Therefore, the Raichu card was made eight years ago.
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