factor a number, variable, or expression out of the polynomial shown below. 15x^3 + 20x
a. 15x(x^2+5x)
b. 5x(3x^2+4x)
c. 5x(3x^2+4)
d. 15x(x^2+5)
Final answer:
To factor a number, variable, or expression out of the polynomial 15x³ + 20xa, you can factor out 5x to get 15x(x²+5x).
Explanation:
To factor a number, variable, or expression out of the polynomial 15x³ + 20xa, you need to identify a common factor.
In this case, the common factor is 5x. So, you can factor out 5x from each term to get: 15x(x²+5x)
Therefore, the correct answer is option a. 15x(x²+5x).
Which statement is true about this argument?
Premises:
If two angles form a linear pair, then they are supplementary. If two angles are supplementary, then the sum of their measures is 180°.
Conclusion:
If two angles form a linear pair, then the sum of their measures is 180°.
A) The argument is not valid because the premises are not true.
B) The argument is not valid because the conclusion does not follow from the premises.
C)The argument is valid by the law of syllogism.
D)The argument is valid by the law of detachment.
The given argument is valid by the law of syllogism which is the correct answer would be option (C).
What are supplementary angles?The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles. There are two types of supplementary angles.
Premise: If two angles form a linear pair, they are supplementary.
If two angles are supplementary, the total of their measurements equals 180.
Conclusion: If two angles form a linear pair, the total of their measurements equals 180.
If two angles form a linear pair, they are always supplementary.
Thus, if two angles form a linear pair, the total of their measures is 180°; however, if two angles are supplementary, it does not ensure that they will form a linear pair.
So the given argument is valid by the law of syllogism.
Hence, the correct answer would be option (C).
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Abdul's average speed is 40 mph in heavy traffic, and his average speed is 60 mph in light traffic. If he was in heavy traffic for 1 hour and light traffic for 3 hours, how far did Abdul travel?
Calculate the slope of the line that goes through the points (-15,70) and (5,10)
The slope of the line that goes through the point (-15,70) and (5,10) is - 3.
What is slope?The slope is the measure of the angle a line has with respect to the positive x-axis.
We know when two points of a line is given slope can be obtained by rise over run where the rise is the difference between the points of the y-axis and run is the difference of the points of the x-axis.
Given points are (-15,70) and (5,10) through which a line passes.
∴ Slope(m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
Slope(m) = (10 - 70)/(5 + 15).
Slope(m) = -60/20.
Slope(m) = -3.
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Which type of function best models the data in the table below?
A. inverse variation
B. linear
C. logarithmic
D. quadratic
Answer: Option A inverse variation
Explanation:
when we compare the values from the given table x is increasing and y is decreasing hence we can see it is an inverse variation.
In option B difference among all consecutive values of x is 2 but in y it is not same among all consecutive terms. In linear function change in y over change in x must be same.
In option C x is increasing but y is decreasing which is violating the property of logarithmic function. In logarithmic function if x increases then y should increase.
In option D first value of x is 2 following quadratic property meaning giving square of itself in y which is 4. But not all values of y are square of x except first value. In quadratic function value of y should be square of x.
The type of function that best models the table given is: A. inverse variation.
What is Inverse Variation?Inverse variation can be described as a relationship between two variables, whereby, the product of the two variables will give a constant. It is expressed as, k = xy.
In an inverse variation, if one variable increases, the other variable decreases.
The table shows an inverse variation because as x increases, y decreases, and can be expressed as k = xy.
Therefore, the type of function that best models the table given is: A. inverse variation.
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You can represent the measures of an angle and its complement as x° and (90 − x)°. Similarly, you can represent the measures of an angle and its supplement as x° and (180 − x)°. Use these expressions to find the measures of the angles described. The measure of an angle is equal to four times the measure of its supplement. The measure of the angle is ° and the measure of its supplement is °.
To determine the size of an angle and its supplement when the angle is four times the size of its supplement, we use the equation x = 4(180 - x) and solve for x to find that the angle measures 144 degrees and its supplement measures 36 degrees.
To find the measures of an angle and its supplement when the angle is four times its supplement, we use the expressions x and 180 - x. We can set up the equation x = 4(180 - x). Then we can solve for x to find the measures of the angle and its supplement.
By expanding and rearranging the equation, we get:
x = 720 - 4x5x = 720x = 144Thus, the angle measures 144 degrees and its supplement measures 36 degrees (since 180 - 144 = 36).
What percent of 10 is 6?
To determine what percent of 10 is 6, you multiply 6/10 by 100, which equals 60%, thus 6 is 60% of 10.
Explanation:To find what percent of 10 is 6, we can use the formula for percentage which is (Part / Whole) * 100.
In this case, the 'part' is 6 and the 'whole' is 10.
So the equation to find the percentage is (6 / 10) * 100.
Calculating that out, we get 0.6 * 100, which equals to 60%.
Therefore, 6 is 60% of 10.
This is a basic concept in mathematics where you are trying to find out how one number compares to another in terms of percentage.
The total weight of a tin and the cookies it contains is 2 pounds. after � of the cookies are eaten, the tin and the remaining cookies weigh 0.8 pounds. what is the weight of the empty tin in pounds?
Which relationship is continuous? A. the number of cows a farmer has owned over the years B. the number of cookies Stan baked for the party C. the number of people attending the assembly D. the distance a runner ran during training
The relationship that is continuous is the distance a runner ran during training.
Explanation:The relationship that is continuous is D. the distance a runner ran during training.
A continuous relationship is one in which the values of one variable change smoothly and consistently over a given interval. In the case of the distance a runner ran during training, the distance can be any real number and can be measured with great precision, allowing for smooth changes in the values.
The continuous relationship is the distance a runner ran during training.
A continuous relationship is one where the variable changes smoothly and can take any value within a given range. Let's analyze the options:
A. The number of cows a farmer has owned over the years:
This relationship is likely continuous, as the number of cows can change smoothly over time, and there are no discrete jumps in ownership.
B. The number of cookies Stan baked for the party:
This relationship is likely discrete, as the number of cookies is typically counted in whole numbers without smooth transitions. Stan would bake a specific, countable quantity of cookies.
C. The number of people attending the assembly:
This relationship is likely discrete, as the number of people is counted in whole numbers and does not change smoothly. Attendees come in whole individuals, not fractions.
D. The distance a runner ran during training:
This relationship is continuous, as distance can vary smoothly and take any real value within a given range. Runners can cover fractional distances, making it a continuous variable.
Therefore, the continuous relationship is D, the distance a runner ran during training.
A gardener has an area 320 sq ft. its width is 4 feet less than its length. what are the dimensions of the garden?
Answer: C
Step-by-step explanation:
How much simple interest is earned on 6,000 at an interest rate of 2.25% in 4 1/2
How do you find the missing value?
Tell whether the sequence is arithmetic. If it is, what is the common difference?
15, 19, 23, 27, . . .
A. yes; 15/19
B. yes; 4
C. yes; 34
D. no
Answer:
yes 4
Step-by-step explanation:
Square root of 1/121 simplified
The square root of the given number 121 is 11.
What is the square root?The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.
The given number is √121.
We need to find the square root of given numbers.
Here, 121=11×11
= 11²
So, √121 = √11²
= 11
Therefore, the square root is 11.
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The formula that describes an object's motion is given by S=ut+1/2at^2 , where S is the distance traveled, u is the initial velocity, a is the acceleration , and t is the time.
Which equation represents a in terms of the other variables?
A. a= 2S-2u/t
B. a=2S+2u/t
C. a=2S-2ut/t^2
D. a=2S+2ut/t^2
PLZ HELPPPPPPPPPPPPPPPPPPPP!!!!!!!!
The point (2, 4) is on the graph of f(x) = x^2. What is the value of b if the point (0.5, 4) is on the graph of f(bx)?
4
0.5
1
2.5
Answer:
A. 4
Step-by-step explanation:
12 inches increased by 36
John has 54 white marbles and nine yellow marbles Ben has 16 white marbles and 96 yellow marbles Noel has 12 white marbles and 72 yellow marbles
Answer: the question
Step-by-step explanation:Select the correct answer from the drop-down menu.
John has 54 white marbles and 9 yellow marbles. Ben has 16 white marbles and 96 yellow marbles. Noel has 12 white marbles and 72 yellow marbles.
The boys who have the same ratio of white marbles to yellow marbles are .
What is 4527 written in scientific notation?
Find the coordinates of the midpoint of the segment whose endpoints are H(8,2) and K(6,10).
The coordinates of the midpoint of the segment HK are (7, 6).
The midpoint coordinates of a line segment can be found using the midpoint formula:
Midpoint =[tex]\((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\)[/tex]
Given the endpoints of the segment as H(8,2) and K(6,10), let's plug these values into the formula:
Midpoint =[tex]\((\frac{8 + 6}{2}, \frac{2 + 10}{2})\)[/tex]
Midpoint =[tex]\((\frac{14}{2}, \frac{12}{2})\)[/tex]
Midpoint =[tex]\((7, 6)\)[/tex]
The coordinates of the midpoint of the segment HK are (7, 6).
To calculate the midpoint of a line segment, you can follow these steps:
1. Identify the coordinates of the endpoints of the segment. Let's call them[tex]\( (x_1, y_1) \) and \( (x_2, y_2) \).[/tex]
2. Use the midpoint formula:[tex]\( \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).[/tex]
3. Substitute the coordinates into the formula and calculate.
In this case, the endpoints are H(8,2) and K(6,10). Plug these values into the midpoint formula:
Midpoint = [tex]\( \left( \frac{8 + 6}{2}, \frac{2 + 10}{2} \right) \).[/tex]
Simplify the equation:
Midpoint =[tex]\( \left( \frac{14}{2}, \frac{12}{2} \right) \).[/tex]
Finally, calculate the values:
Midpoint =[tex]\( (7, 6) \).[/tex]
So, the coordinates of the midpoint of the segment HK are (7, 6).
complete question
Find the coordinates of the midpoint of the segment whose endpoints are H(8,2) and K(6,10).
A football team gained 6 yards on a first down, lost 15 yards on the second down, and gained 12 yards on the third down. how many yards do they need to gain on the fourth down to have a 10 yard gain from their starting position?
Answer:
They need to earn 7 yards on the fourth down to have a 10 yard gain from their starting position
Step-by-step explanation:
To gain a new set of downs, a football team has four downs(tries) to gain 10 net yards, in total.
Gained 6 yards on first down
Net of 6 yards gained
Needs 10-6 = 4 yards
Lost 15 yards on second down
6 - 15 = -9
In all, they have lost 9 yards, so they need
4 + 15 = 19 yards
Gained 12 yards on third down
-9 + 12 = 3 net yards(need 10)
19 - 12 = 7
They need to earn 7 yards on the fourth down to have a 10 yard gain from their starting position
If you're traveling 75 mph how many miles will you go in an hour
Math Help Please....
The sum of two consecutive odd integers is 72 write an algebraic equation to determine the two integers
Adam wrote a check for $38 to pay his monthly gas bill, but when balancing his checkbook, he accidently recorded it as a credit rather than his debit. How will his check register compare to his monthly bank statement when he receives it?
Answer:
76 dollars more
Step-by-step explanation:
Given that Adam wrote a check for $38 to pay his monthly gas bill.
Normally cheques issued would be debited to the account maintained by the customer thus making the balance less than the previous one.
If the customer had x as balance after cheque issued the balance would be x-38
This is a debit entry
But since Adam by mistake entered as credit, he would have recorded in his books balance as x+38
Thus as a result of this
Adam check register shows x+38-(x-38)
= 76 dollars more than monthly bank statement
In the diagram above, rectangles DEFG and WXYZ are similar. The ratio of the area of DEFG to WYXZ is 1:4. A student's work to find ZY is shown below. Describe and correct the error in finding ZY.
Given that v^y = 1/ 5 root v,
Work out the value of y.
what are the real solutions
Step-1 : Multiply the coefficient of the first term by the constant 1 • -2 = -2
Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is 1 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 2
x2 - 1x + 2x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-1)
Add up the last 2 terms, pulling out common factors :
2 • (x-1)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-1)
Which is the desired factorization
What are the coordinates of the x-intercept(s) of the graph of
y = (x - 6)(x + 5)?
A) (0, -30)
B) (-5, 0) and (6, 0)
C) (0, -5) and (0, 6)
D) (-6, 0) and (-5, 0)
Answer:
B. is the answer!!!!!!! (-5, 0) and (6, 0) is the correct answer.Step-by-step explanation:
(-5, 0) and (6, 0) is the correct answer.
To find the x-intercepts, use the Zero Product Property and solve for x:
x - 6 = 0
x = 6
x + 5 = 0
x = -5
Therefore, the x-intercepts are (6,0) & (-5,0).
What is the value of x and y in this parallelogram