Answer:
So, the GCF of 12x^5 and 8x^3 is 4x^3.
Step-by-step explanation:
To find the greatest common factor (GCF) of 12x^5 and 8x^3, you can break down each term into its prime factors and then identify the common factors:
12x^5 = 2^2 * 3 * x^5
8x^3 = 2^3 * x^3
Now, identify the common factors is this :
The common factor of 2^2 (4) and 2^3 (8) is 2^2 (4).
The common factor of x^5 and x^3 is x^3.
So, the GCF of 12x^5 and 8x^3 is 4x^3.
The GCF of 12x^5 and 8x^3 is 4x^3.
Explanation:The GCF (Greatest Common Factor) of 12x^5 and 8x^3 can be found by factoring out the common factors of the two terms. In this case, the common factor between the two terms is 4x^3.
To find the GCF, we need to find the highest power of x that can be divided into both terms: 12x^5 and 8x^3. Since 4x^3 is the highest power of x that can be divided into both terms, it is the GCF.
Therefore, the GCF of 12x^5 and 8x^3 is 4x^3.
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-1/2x>4 solve for x
Answer:
X<-8
Step-by-step explanation:
-1/2x>4
Multiple both sides by -2
-2(-1/2)x<-2(4)
Multiple even numbers of negative terms
2(1/2)x<-2(4)
Cancel out the 2
(2 this is out)(1/(2 this is out))x<-2(4)
x<-2×4
Multiple
x<-8
(9+q)(8-q)= polynomial in standard form
Answer:
- q² - q + 72
Step-by-step explanation:
To express the given expression as a polynomial in standard form, we would first multiply the individual elements in one parenthesis with the elements in the second.
We would then rearrange the outcome and simplify it algebraically.
The arrange it in the order of the unknown variable.
As such,
(9+q)(8-q) = 9(8-q) +q(8-q)
= 72 -9q + 8q - q²
= 72 - q - q²
= - q² - q + 72
To form the expression (9+q)(8-q) into a polynomial in standard form, we multiply the terms using the distributive property to get -q² - q + 72.
The student has asked for the expansion of a binomial expression into polynomial form, in this case, expanding (9+q)(8-q). The process involves using the distributive property, also known as the FOIL method (First, Outer, Inner, Last), to multiply each term in the first binomial by each term in the second.
Expanding the binomials, we have:
First: 9 × 8 = 72
Outer: 9 × (-q) = -9q
Inner: q × 8 = 8q
Last: q × (-q) = -q²
Combining like terms (-9q and 8q) gives -q and then adding to the remaining terms, we have:
72 - q - q²
Reordering to get the polynomial in standard form (highest degree first), the result is:
-q² - q + 72
how do you select a month of the year at random what is the probability that the month ends with the ER
Answer:
4/12 or 1/3
Step-by-step explanation:
Answer:
1:3 or 1/3
Step-by-step explanation:
September, October, November, December
4 moths out of twelve
4/12 reduces to 1/3
The answer could be written 1/3 or 1:3.
If Ezra works less than or equal to 50 hours doing lawn care, he must spend at least __ hours walking dogs.
Final answer:
If Ezra works less than or equal to 50 hours doing lawn care, he must spend at least [answer] hours walking dogs.
Explanation:
To determine the minimum number of hours Ezra must spend walking dogs when he works less than or equal to 50 hours doing lawn care, we need to refer to the given information and apply it to the situation
According to the exercise, Louis requires one hour to cut a typical lawn, while Carrie Anne needs one and one-half hours. Therefore, Louis is more efficient at cutting grass. Carrie Anne, on the other hand, can wash a car in half an hour, while Louis requires three-quarters of an hour. So, Carrie Anne is more efficient at cleaning cars.
If they each specialize in the task they are most efficient at, Louis should cut the grass, and Carrie Anne should wash cars. This way, they can maximize their output in a given amount of time.
Now, if they each work a twelve-hour day, we can calculate how many lawns they can cut and how many cars they can wash based on their efficiency. Louis can cut 12 lawns (since he requires 1 hour per lawn), and Carrie Anne can wash 24 cars (since she can wash a car in 0.5 hours).
Therefore, if they specialize in their most efficient tasks, they can cut 12 lawns and wash 24 cars in a twelve-hour day.
Answer:
IT IS 35
Step-by-step explanation:
What is the scale factor ASAP
and why
Answer:
The SF is 2/3
Step-by-step explanation:
You can find this out by creating a ratio between the points and it's image. The one with the apostrophe is the image, and the bigger one is the pre-image.
The supply and demand curves for a product line of bicycles are shown. Approximately where is the equilibrium point?
Answer:
The answer is B (132,220)
Step-by-step explanation:
I got it correct on the test
Plato tests
The required equilibrium point for the supply and demand curves for a product line of bicycles is (135, 225).
What is the graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
here,
The graph shows the supply and demand curves for a product line of bicycles.
To determine the equilibrium point we to locate the intersection point of supply and demand.
From the graph, the intersection point is (135, 225), which is the approximate equilibrium point.
Thus, the required equilibrium point for the supply and demand curves for a product line of bicycles is (135, 225).
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What number must you add to complete the square?
x^2+12x=5
Answer:
36
Step-by-step explanation:
12/2 = 6
6^2 = 36
3x-4y=1 and x=2y+1 using substitution
Answer:
x =-1
y =-1
Step-by-step explanation:
to solve this system of equation, using substiution method
3x-4y=1 ........................ equation 1
x=2y+1 ............................ equation 2
subbstitute for x into equation 1
3x-4y=1 ........................ equation 1
3(2y + 1) - 4y = 1
6y + 3 -4y = 1
2y + 3 = 1
collect the like terms
2y = 1- 3
2y= -2
divide both sides by the coefficient of y which is y
2y/2 = -2/2
y = -1
put the value of y =-1 into equation 2
x=2y+1 ............................ equation 2
x = 2(-1) + 1
x = -2 + 1
x = -1
therefore x =-1 y = -1
If you flip a coin and roll a six sided die what is the probability that you flip a heads and roll a five?
Answer:
you have a 50-50% of landing heads and a 5 out 6 % chance of rolling a 5
Step-by-step explanation:
Answer: 1/12
Step-by-step explanation:
Which of the following formulas could be used to find the perimeter, P, of a regular hexagon? plz
Answer:
Just add up all the sides and you get the perimeter.
Students in middle school and high school were surveyed about whether they have taken the SAT. Some of the survey results are listed here.
37% of middle school students have taken the SAT.
4% of high school students have not taken the SAT.
This information is shown in the two-way frequency table below. Drag numbers into the empty spaces to complete the table.
Answer:
Step-by-step explanation:k so high school total should be 100%
middle school not taken SAT should be 63%
high school have taken SAT should be 96%
basically just use your basic math. Turn the problem around and take the total(100%) and subtract what number you already know. So like This:
100-37=63
100-4=96
The subject of this question is SAT and it is related to middle school and high school. The answer provides an explanation of the survey results regarding students taking the SAT.
Explanation:The subject of this question is SAT. The grade level of this question is Middle School, High School.
The table provided shows the survey results of whether middle school students and high school students have taken the SAT. From the information given, we can determine the missing values in the table:
Middle School Students Taken SAT = 37%
High School Students Not Taken SAT = 4%
*Please note that the table was not provided with the question, so we are unable to fill in the missing values.
Write an expression for the sequence of operations described below.
divide w by 3, then subtract 10 from the result
Do not simplify any part of the expression.
Answer:
(w/3)-10
Hope this helps!
w/3 - 10 is an expression for the above-described series of operations.
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given, divide w by 3, then subtract 10 from the result Do not simplify any part of the expression.
We need to Create an expression for the above sequence
divide w by 3
=> w/3
then subtract 10
=> w/3 - 10
Since it's written in the problem that does not simplify hence, we would simplify this equation further.
Therefore, an expression for the sequence of operations described above is w/3 - 10
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Grace had 4 3/8 yards of elastic. She used 1 2/3 yards of the elastic to make bracelets for her friends. How many yards of elastic does she have now?
6 1/24 yards
3 7/24 yards
2 17/24 yards
3 17/24 yards
Answer:
Exact form: 65/24
Decimal form: 2.7083
Mixed number form: 2 17/24
Step-by-step explanation:
4 3/8 - 1 2/3 = 2 17/24
A block is set in motion hanging from a spring and oscillates about its resting position
x = 0
according to the function
x = 0.6sin(2t)+0.4cos(2t),
where x is in centimeters and t is in seconds. For what values of t in the interval [0,3] is the block at its resting position
x =0?
Answer:
t = 1.277 sec and t = 2.848 sec
Step-by-step explanation:
This problem is much more easily done by graphing it than by computing it using algebra.
The values of t we're looking for are the ones that make x = 0, so we want the solutions of [tex]0.6sin(2t)+0.4cos(2t)=0[/tex] on the interval [0, 3].
According to the graph, this is true when t = 1.277 seconds and t = 2.848 seconds.
Answer:
t = 1.28, 2.85
Step-by-step explanation:
x = 0.6sin(2t)+0.4cos(2t)
x = 0, so
0.6sin(2t)+0.4cos(2t) = 0
0.6sin(2t) = -0.4cos(2t)
Convert into tan(2t) by dividing both sides by 0.6cos(2t):
tan(2t) = -0.4/0.6
tan(2t) =-2/3
Since t lies in [0,3] ,
2t lies in [0,6]
tan(2t) =-2/3
Basic angle:
0.5880026035
Tan is negative is second and fourth quadrants
2t = 2.553590005, 5.695182704
t = 1.276795025, 2.847591352
Re-write the quadratic function below in Standard Form
y = -7(x + 9) (x - 1)
Answer:
-7x squared -56x+63.
Step-by-step explanation:
Hope this helps!
A pool is in the shape of a rectangular prism. On Monday, water was pumped out of the pool at a constant rate, starting at 12:00pm. At 12:15 pm, the water in the pool was 45 inches deep. At 12:35 pm, the water in the pool was 41 inches deep.
Part A
How many inches does the depth of the water decrease each minute?
Part B
Write an equation that represents y, the depth of the water (in inches) after x minutes.
Answer:
the equation is y = (-2/15 in/min)x + 43 in
Step-by-step explanation:
We'll represent elapsed time with the letter t. Then 12 p.m. corresponds to t = 0 sec. Between 12 p.m. and 12:15 p.m., the change in time was 15 min and the change in water depth was (45 - 41) in., or 4 in.
Thus, the water depth changes by 4 in (a decrease) over 30 min.
Part A: The water depth rate of change is -4 in/30 min, or -2 in/15 min, or
(-2/15 in)/min (the depth is decreasing).
Part B: We need to derive a linear function that describes the water depth at any given time x (or t). Two points on the graph of this line are
(15 min, 45 in) and (35 min, 41 in): the 'run' is 30 min and the 'rise' is -4 in.
As in Part A, the slope of this line is (-2/15 in)/min.
The desired equation is then y = mx + b, or 45 in = (-2 in/15 min)(15 min) + b, or 45 in = 2 in + b, or 43 in = b. Then, in its most general form,
the equation is y = (-2/15 in/min)x + 43 in
Find the domain of the rational function 9x/(x+5)(x+3)
Answer:
the domain is : D = ]-∞ , -5[ U ]-5 , -3[ U ]-3 , +∞[
Step-by-step explanation:
hello :
f(x) = 9x/(x+5)(x+3)
f exist for : (x+5)(x+3) ≠ 0
(x+5)(x+3)=0
x+5=0 or x+3=0 means : x= - 5 or x= -3
the domain is : D = ]-∞ , -5[ U ]-5 , -3[ U ]-3 , +∞[
I’m lost and unsure what is the first step to do find width of da roof
Answer:
You set up an equation, using the trig function "tan" to find half of the roof (the equation would be tan(24) = 3.5/x, where x = 1/2 roof width)
Step-by-step explanation:
That would be the first step.
You solve the equation for x, and then multiply x by 2 to get the width of the roof.
Two of the world's longest rivers are the Nile, which is 4100 miles long, and the Rio
Grande, which is 1900 miles long. Find how much longer the Nile is than the Rio
Grande.
Answer:
The Nile River is 2,200 miles longer than the Rio Grande.
Step-by-step explanation:
4100-1900=2200
Answer:
Answer:
The Nile River is 2,200 miles longer than the Rio Grande.
Step-by-step explanation:
4100-1900=2200
Step-by-step explanation:
Which BEST describes the representation of the data on the given graph?
A) The graph represents the data appropriately.
B) The graph is misleading because the size of the sample is not shown.
C) The graph is misleading because the vertical scale does not begin at 0.
D) The graph is misleading because the scale is disproportional to the data.
Answer:
A) The graph represents the data appropriately.
Step-by-step explanation:
The graph above is a true representation of data showing the percent of political parties people who agreed with court.
From the graph above, three categories of political parties people are concerned; which are, the Democrats, the Republicans and the Independents.
It can therefore be deduced that 62% of the Democrats agreed with court. By implication, the percent of the Democrats who disagreed with court is 38%. Conversely, 54% of people agreed with court for both the Republicans and the Independents respectively. This implies that the percent of both the Republicans and the Independents who did not agree with court is 46% respectively.
However, the graph fails to provide us with information about what the people agree on; probably the outcome of an election or appointment of a minister.
The graph is not misleading in any way and it is not necessary that the vertical scale begin at zero. Therefore, the data represents the graph appropriately.
What is the length of Line A B? On a coordinate plane, point A is (negative 4, 3), point B is (2, 3), and point C is (2, negative 1). 4 units 5 units 6 units 7 units
Answer:
6 units
Step-by-step explanation:
Answer:
6 units
Step-by-step explanation:
Which sample size of a population of 200 is most likely to give a reliable conclusion?
Therefore, the sample size of a population of 200 is most likely to give a reliable conclusion is 80.
Answer:
80
Step-by-step explanation:
The bedroom is 13ft. by 10ft. Determine the perimeter and area
Perimeter formula: 2b + 2h
Area formula: b * h
Perimeter:
2(13) + 2(10)
26 + 20
46
Area:
13 * 10
130
The perimeter is 46ft.²
The area is 130ft.²
Best of Luck!
In mathematics, the perimeter of the 13ft by 10ft bedroom would be 46ft and the area would be 130 square feet.
Explanation:The perimeter of a rectangle (which a bedroom is 13ft. by 10ft. mostly is) can be determined by adding up all the sides. So, the formula for a rectangle is: Perimeter = 2(length + width). Given that your length is 13ft and width is 10ft, the calculation would be Perimeter = 2(13ft + 10ft), resulting in a perimeter of 46ft.
The area of a rectangle is calculated by multiplying the length by the width. In this case: Area = length * width, therefore Area = 13ft. * 10ft., resulting in an area of 130 square feet.
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I need help:
The width of this rectangle is 1/3 of the length. Find the length and the width of the rectangle.
Answer:
3(y-4) =2y+6
3y - 12 = 2y +6
y = 18
so length is 42 in.
width is 14 in.
After solving the given equations, the length of the rectangle is 42 inches and the width of the rectangle is 14 inches.
What is an equation?Equations are mathematical expressions that have two algebra on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
The given data in the question,
According to the given diagram,
Length of the rectangle, L = 2y + 6 inches (i)
Width of the rectangle, W = y - 4 inches (ii)
The width of the rectangle is 1/3 of the length,
1/3(2y + 6) = (y - 4)
2y + 6 = 3y - 12
y = 18.
Substitute y = 18 in equation (i)
L = 2(18) + 6
L = 42 inches
Substitute y = 18 in equation (ii)
W = (18 - 4)
W = 14 inches.
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2c = 112
A. c = 2
B. c = 42
C. c = 56
D. C = 224
Answer:
The answer is C. 56
Step-by-step explanation:
So if we replace C with 56, the equation would look like this, 2(56)=112.
i really need help :( i dont get help from anyone :(
Answer:
D.) 12x -6x 90
Step-by-step explanation:
because it's right angle
(giving 30 points/need answers STAT!!)
Four transformations of the function f(x) = 3x + 2 are given below.
For each transformation, drag the expression that shows the result of that transformation into the box under it.
Transformations can be applied to functions to change the appearance of
the (slope and intercept) of the function.
The result of the transformation are presented as follows;
[tex]\begin{tabular}{|c|c|c|c|}f(x-5)&f(x) - 5&-5 \cdot f(x) &f(-5\cdot x)\\3\cdot (x - 5) + 2&3 \cdot x - 5 + 2&-5\cdot (3 \cdot x + 2)&3 \cdot (-5\cdot x) + 2 \end{array}\right][/tex]Reasons:
The given function is; f(x) = 3·x + 2
The function -5·(3·x + 2) is the same as -5 × f(x) = -f(x)
Therefore;
-5·(3·x + 2) → -5·f(x)
The function 3·x - 5 + 2 = 3·x + 2 - 5 = f(x) - 5
Therefore;
3·x - 5 + 2 → f(x) - 5
The function 3·(x - 5) + 2 by comparison to 3·x + 2 is obtained when x is replaced by (x - 5), therefore;
f(x) = 3·x + 2
f(x - 5) = 3·(x - 5) + 2
3·(x - 5) + 2 → f(x - 5)
The function 3·(-5·x) + 2 is obtained when x in f(x) is replaced by (-5·x),
which gives;
f(x) = 3·x + 2
∴ f(-5·x) = 3·(-5·x) + 2
Which gives;
3·(-5·x) + 2 → f(-5·x)
The completed table is therefore;
[tex]\begin{tabular}{|c|c|c|c|}f(x-5)&f(x) - 5&-5 \cdot f(x) &f(-5\cdot x)\\3\cdot (x - 5) + 2&3 \cdot x - 5 + 2&-5\cdot (3 \cdot x + 2)&3 \cdot (-5\cdot x) + 2 \end{array}\right][/tex]
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A car traveling 9/10 of a mile per minute will travel _____ miles in 10 minutes
Answer:
It will travel 9 miles in 10 minutes
Step-by-step explanation:
A car travels 9/10 miles/minute
In 10 minutes, it will travel
10*9/10 = 9 miles
Final answer:
A car traveling at 9/10 of a mile per minute will travel 9 miles in 10 minutes by simply multiplying the car's speed by the time traveled.
Explanation:
To calculate how far a car traveling at a speed of 9/10 of a mile per minute will travel in 10 minutes, we simply multiply the speed of the car by the amount of time it travels.
Speed of car = 9/10 mile/minute
Time = 10 minutes
Distance traveled = Speed of car × Time
Distance traveled = (9/10) mile/minute × 10 minutes
Now we perform the multiplication:
Distance traveled = 9/10 × 10
Distance traveled = 9 miles
Which point on the number line represent 42?
A.P
B.Q
C.R
D.S
Answer:
Q
Step-by-step explanation:
because 42 square rooted is between 6 and 7.
What is the positive negative square roots of 64?
The answer explains the positive and negative square roots of 64.
When dealing with the square roots of a number like 64, remember that the square root of 64 is 8, both positive and negative. This is because (-8) x (-8) equals 64 just like (8) x (8) equals 64, following the rule that multiplying two negative numbers results in a positive number.