which can be used to expand the expression below?
5(3x-6/7)
-
associative property
commutative property
distributive property
subtracting
According to the distributive property, Multiplying each value in the bracket by 5 ls equivalent to taking the sum of the values, then multiply the sum by 5. Hence, the distributive property is used for the expansion.
Given the expression :
5(3x - 6/7)To expand, use the distributive property, such that ;
5(3x - 6/7)
5*3x - 5*6/7
15x - 30/7
Therefore, the distributive property would be used in expanding the expression above.
Learn more : https://brainly.com/question/10169393
how much would 500 invested at 4 interest compounded continuously be worth after 7 years round your answer to the nearest cent?
Please help :( 2 questions..
If c(x)=5/x-2 and d(x)=x+3 what is the domain of (cd)(x)?
And, if f(x)=7+4x and g(x)=1/2x, what is the value of (f/g)(5)?,
A watch manufacturer has two factories (FA, FB) and 60% of their watches are made at FA. It is known that 10% of them are made at FA and 15% made at FB are defective. What is the probability that a selected defective watch was manufactured at FB?
You purchased 8 gal of paint and 3 brushes for 152.5. the next day, you purchased 6 gal of paint and 2 brushes for 113. how much does each gallon of paint and each brush
−7y−6y
3
+2y+4y
3
−5−1−2y
3
Which of the following is a polynomial?
x² + 2
Further explanationLet us determine whether each algebraic expression is a polynomial or not.
[tex]\boxed{ \ A. \ x^2 + 2 \ }.[/tex] is a polynomial. [tex]\boxed{ \ B. (x^8 - 2)/(x^{-2} + 3) \rightarrow \frac{(x^8 - 2)}{(x^{-2} + 3)} \ }[/tex] is not a polynomial, but a rational function.[tex]\boxed{ \ C. \ 7x^7 - 2x^{-4} + 3 \ }[/tex] is not a polynomial, because - 4 is not a whole number power. [tex]\boxed{ \ D. \ x^{-x} - 1 \ }[/tex] is not a polynomial, because - x is not a power of integer but a variable as well.Let us rephrase the following definitions.
A monomial is an algebraic expression which comprises a single real number, or the product of a real number and one or more variables raised to whole number powers. For example, [tex]\boxed{-2} \boxed{3x^2} \boxed{4a^3b^4} \boxed{-5xy^3z^2} \boxed{\frac{3}{5}}[/tex]A coefficient is each real number preceeding the variable(s) in a monomial. In the examples above [tex]\boxed{ \ -2, 3, 4, -5, \frac{3}{5} \ }[/tex] are the coefficients.A polynomial is the sum or difference of a set of monomials. For example, [tex]\boxed{ \ 2x^2 - 3xy^2 + 4x^2y \ }[/tex]Each monomial that forms a polynomial is called a term of that polynomial. For example, the term of polynomial [tex]\boxed{ \ 2x^2 - 3xy^2 + 4x^2y \ }[/tex] are [tex]\boxed{ \ 2, - 3, and \ 4. \ }[/tex]The constant term is the term of polynomial that does not contain a variable.The leading coefficient is the coefficient of the term containing the variable raised to the highest power.For example, consider the polynomial [tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex]
[tex]\boxed{ \ 2x^4, - 3x^2, - 4x, and \ - 5 \ }[/tex] are the terms of polynomial.[tex]\boxed{ \ 2, - 3, - 4 \ }[/tex] are the coefficients.- 5 is the constant term.2 is the leading coefficient.A polynomial is said to be in standard form if the terms are written in descending order of degree. For example:
[tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex] is a polynomial in standard form.[tex]\boxed{ \ - 3x^2 + 2x^4 - 5- 4x \ }[/tex] is the polynomial, but it is not in standard form.Learn moreThe remainder theorem https://brainly.com/question/950038768.32 divided by 2.8 is divisible https://brainly.com/question/5022643#Which expression is equivalent to the product of a binomial and a trinomial after it has been fully simplified https://brainly.com/question/1394854Keywords: which of the following is a polynomial, a monomial, terms, the leading coefficient, constant, in a standard form, rational function, whole number power, integer
Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers, (k), she can drive with 12 liters of fuel. She assumes the relationship between kilometers and fuel is proportional. How many kilometers can Pamela drive with 12 liters of fuel?
Suppose a normal distribution has a mean of 16 and a standard deviation of 4.
A value of 26 is how many standard deviations away from the mean?
−2.5
−1.5
1.5
2.5
Answer:
Correct Answer is 2.5
Step-by-step explanation:
The rate of change of y with respect to t is proportional to 50 - y
Find the amount of Social Security deducted: $37890 annually.
The current social security tax is 12.4% so the answer is $2349.18
Step-by-step explanation:Social security deduction is a federal tax imposed on employers, employees and self-employed individuals. Employers and employees both get the equal shares. The current tax rate for social security is 6.2% for the employer and 6.2% for the employee and 12.4 % in total so the social security tax for $37890 is 4698.36 in total and $2349.18 on each party i.e employer and employee.
If a pair of perpendicular lines are rotated, which is true?
A) Rotating perpendicular lines result in parallel lines.
B) The lines remain perpendicular only if rotated 180°.
C) The lines remain perpendicular only if rotated 360°.
D) Rotated perpendicular lines always remain perpendicular lines.
Perpendicular lines remain perpendicular after any rotation around a point on either line because rotation is a rigid motion that preserves angles and distances. Therefore, the correct answer is option D).
When a pair of perpendicular lines is rotated around any point on either line, the two lines will always remain perpendicular to each other, regardless of the angle of rotation. This is because rotation is a rigid motion, which preserves angles and distances. Consequently, if the two lines were originally perpendicular, they would continue to form a 90-degree angle with each other after any amount of rotation. In other words, the nature of perpendicular lines is such that they form four right angles at the point of intersection, and rotation around that point does not alter these angles.
What is the measure of angle C?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
°
Write the expression as either the sine, cosine, or tangent of a single angle. tan5x - tan2y / 1 + tan5x tan2y
Final answer:
The expression tan5x - tan2y / 1 + tan5x tan2y simplifies to tan(5x + 2y) using the tangent sum formula, illustrating how two tangent values can be combined into a single tangent of the sum of two angles.
Explanation:
The expression given is tan5x - tan2y / 1 + tan5x tan2y. This can be simplified using the tangent sum formula, which is a key concept in trigonometry. The tangent sum formula states that tan(a + b) = (tan a + tan b) / (1 - tan a tan b).
By comparing the given expression to this formula, we can see that the expression represents the tangent of the sum of two angles, specifically tan(5x + 2y). This simplification uses trigonometric identities to represent the combination of two different tangent values as a single tangent value of the sum of the angles.
(2x - 3y)(4x - y) Please help
100 POINTS!!!!!!!!!!!!!!! whats is 9 times 7 times 4777 times 2 plus 3636363636363 times 700 times 4 minus 5 time 6999999996950 plus 300 times 400
Jenny said i'm thinking of fraction that is equivalent to 2/6 the numerator is 8 less than the denominator what fraction is jenney thinking of
The town recreation department ordered a total of 100 baseballs and bats for the summer baseball camp. Baseballs cost $4.50 each and balls cost $20 each. The total purchase was $822. How many of each item was ordered
76 baseballs and 24 bats were ordered.
Explanation:Let's assume that 'x' represents the number of baseballs ordered and 'y' represents the number of bats ordered.
We can set up two equations to solve for 'x' and 'y':
x + y = 100 (since the total number of items ordered is 100)4.50x + 20y = 822 (since the total cost of the purchase is $822)We can solve the system of equations using the substitution or elimination method. Let's use the elimination method by multiplying the first equation by 4.50:
4.50x + 4.50y = 4504.50x + 20y = 822Subtracting the first equation from the second equation eliminates 'x' and we can solve for 'y':
15.50y = 372
y = 24
Substituting the value of 'y' back into the first equation, we can solve for 'x':
x + 24 = 100
x = 100 - 24
x = 76
Therefore, 76 baseballs and 24 bats were ordered.
76 baseballs and 24 bats were ordered for the summer camp, costing $822 in total.
Let's denote the number of baseballs as [tex]\( B \)[/tex] and the number of bats as [tex]\( T \)[/tex].
We're given two pieces of information:
1. The total number of items ordered is 100, so [tex]\( B + T = 100 \)[/tex].
2. The total cost of the items is $822, so [tex]\( 4.50B + 20T = 822 \)[/tex].
We can solve this system of equations by substitution or elimination. Let's use the elimination method.
1. Multiply the first equation by 20 to match the coefficient of [tex]\( T \)[/tex] in the second equation:
[tex]\[ 20(B + T) = 20(100) \][/tex]
[tex]\[ 20B + 20T = 2000 \][/tex]
2. Subtract this modified first equation from the second equation:
[tex]\[ (4.50B + 20T) - (20B + 20T) = 822 - 2000 \][/tex]
[tex]\[ 4.50B + 20T - 20B - 20T = -1178 \][/tex]
[tex]\[ -15.50B = -1178 \][/tex]
3. Divide both sides by -15.50 to solve for [tex]\( B \)[/tex]:
[tex]\[ B = \frac{-1178}{-15.50} \][/tex]
[tex]\[ B \approx 76 \][/tex]
4. Now, substitute the value of [tex]\( B \)[/tex] back into the first equation to find [tex]\( T \)[/tex]:
[tex]\[ 76 + T = 100 \][/tex]
[tex]\[ T = 100 - 76 \][/tex]
[tex]\[ T = 24 \][/tex]
So, there were 76 baseballs and 24 bats ordered.
Which graph shows a line that is perpendicular to line QR?
Last winter Armand had mc009-1.jpg of a row of stacked logs. At the end of the winter he had mc009-2.jpg of the same row left. How much wood did he burn over the winter?
Answer:
the answer is 3/10 slime
Step-by-step explanation:
What is the slope of the line passing through the points (-4, 3) and (5, -3)?
Answer:
2/3
Step-by-step explanation:
My cousin just took this on odyssey
which expression is equivalent to 6a+12
Answer:
2(3a + 6) would be correct.
Hope this was helpful !
Step-by-step explanation:
What is the range of the function in the graph?
(I'VE NEVER BEEN GOOD AT THESE, COULD SOMEONE HELP?)
20+3/4(12-y)=3/2y-10
a)156/7
b)26
c)52/3
algebra 2
What is the height of cylinder with a surface area of 226.08 square meters and a radius of 3 meters? (Use 3.14 for π.)
Which relationship shows an inverse variation?
x: 2,3,4,5
f(x):1,4,9,16
x:1,2,3,4
f(x):2,8,18,32
x:1,2,3,4
f(x):4,3,2,1
X:2,4,6,8
f(x):12,6,4,3,
Answer:
x : 2,4,6,8
f(x) :12,6,4,3
This table represents the relationship of an inverse variation.
Step-by-step explanation:
We are asked to find which relationship shows an inverse variation.
Inverse variation means that there exist a constant 'k' such that:
f(x)=k/x
or, k=x·f(x)
1)
x : 2, 3, 4, 5
f(x): 1, 4, 9, 16
if x=2 and f(x)=1
k=2
but if x=3 and f(x)=4
we get: k=12.
Hence, we do not obtain a same constant k.
2)
x: 1,2,3,4
f(x):2,8,18,32
when x=1 , f(x)=2
⇒ k=2
when x=2 , f(x)=8
⇒ k=16
Hence, we did not get a same constant 'k'.
3)
x: 1,2,3,4
f(x):4,3,2,1
when x=1, f(x)=4
⇒ k=4
when x=2 , f(x)=3
⇒ k=6
Hence, we did not get a same constant 'k'.
4)
x :2,4,6,8
f(x) :12,6,4,3
when x=2 f(x)=12
⇒ k=2×12=24
when x=4 f(x)=6
⇒ k=4×6=24
when x=6 f(x)=4
⇒ k=6×4=24
when x=8 f(x)=3
⇒ k=8×3=24
Hence, we get a constant 'k=24' for all the values of x.
Hence, option: 4 shows relationship of an inverse variation.
x :2,4,6,8
f(x) :12,6,4,3
What is the area of a sector with a central angle of 3π5 radians and a diameter of 21.2 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
cm²
The area of the sector has a diameter of 21.2 cm and a central angle of 3π/5 radians is 105.90 square cm.
What is a circle?It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
The central angle of 3π/5 radians and a diameter of 21.2 cm.
Then the area of the sector will be
[tex]\rm Area = \dfrac{\theta}{2\pi} *\dfrac{\pi}{4} d^2[/tex]
Then put the values, we have
[tex]\rm Area = \dfrac{\frac{3\pi}{5}}{2\pi} *\dfrac{\pi}{4} (21.2)^2\\\\\\\rm Area = \dfrac{3\pi}{10\pi} *\dfrac{3.14}{4} *449.44\\\\\\Area = \dfrac{3}{10} *\dfrac{3.14}{4} *449.44\\\\\\Area = 105.8968 \approx 105.90 \ cm^2[/tex]
The area of the sector has a diameter of 21.2 cm and a central angle of 3π/5 radians is 105.90 square cm.
More about the circle link is given below.
https://brainly.com/question/11833983
A segment with the endpoint X(-6,2) and Y(-1,-3) is rotated 90 degrees about the origin. What are the coordinates of X' and Y'?
1- X' (-1,-3) Y'(-6,2)
2- X' (2,6) Y' (-3,1)
3- X' (-2,-6) Y' (3,-1)
4- X' (6,-1) Y' (1,3)
Thank you for helping, and looking. Thanks,
The length of the minute hand is 200% of the length of the hour hand.
In 1 hour, how much farther does the tip of the minute hand move than the tip of the hour hand? Round your answer to the nearest hundredth.
In one hour, the minute hand, being twice as long as the hour hand, covers a distance of 4π times its length, while the hour hand covers 1/12 of its circumference. The difference, 23π/6 times the length of the hour hand, translates to approximately 12.09 times the length of the hour hand, rounded to the nearest hundredth.
The question asks about the relative movement of clock hands, which is a concept related to geometry and ratios. We need to determine how much farther the tip of the minute hand moves than the tip of the hour hand in one hour. Given that the length of the minute hand is 200% of the length of the hour hand, the minute hand's tip covers a greater distance due to its longer radius.
In one hour, the minute hand makes one complete revolution, which is 360 degrees around the clock. The hour hand, however, moves only 1/12th of this distance because there are 12 hours on a clock. To find the actual distances, we calculate the circumference each hand moves through, knowing that the length of the minute hand is twice that of the hour hand.
Let's denote the length of the hour hand as L. Therefore, the length of the minute hand is 2L. The circumference for the minute hand is 2π(2L) and for the hour hand is 2π(L). The minute hand travels 2π(2L) = 4πL, whereas the hour hand travels 1/12 of its circumference, which is approximately 2π(L)/12 = πL/6.
The difference in the distance covered in one hour is 4πL - πL/6. Simplifying this:
4πL - πL/6 = (24πL - πL)/6
(24πL - πL)/6 = 23πL/6
23πL/6 is approximately 23πL/6 = 12.09L (using π ≈ 3.14)
The tip of the minute hand moves approximately 12.09 times the length of the hour hand farther in one hour. This result would then be rounded to the nearest hundredth as per instruction.
A valve in a full 6000 gallon water tank is slowly opening. Water flows out of the tank through the valve. The flow rate in gallons per hour is given by the function f(t)=300 t^2 where t is in minutes.
How much water flows out the tank in the first 7 minutes?
How many minutes does it take for the tank to be completely empty?,
Water flows: 34300 gallons in 7 minutes. Tank empties in about 3.914 minutes. (Rounded to three decimal places.)
To find out how much water flows out of the tank in the first 7 minutes, we need to integrate the flow rate function, [tex]\(f(t)\)[/tex], from [tex]\(t = 0\)[/tex] to [tex]\(t = 7\)[/tex]. The flow rate function is given as [tex]\(f(t) = 300t^2\)[/tex].
So, the amount of water that flows out of the tank in the first 7 minutes, denoted as [tex]\(W_{\text{out}}\)[/tex], is given by the integral of [tex]\(f(t)\)[/tex] over the interval [tex]\([0, 7]\)[/tex]:
[tex]\[W_{\text{out}} = \int_{0}^{7} f(t) \, dt\][/tex]
[tex]\[= \int_{0}^{7} 300t^2 \, dt\][/tex]
[tex]\[= 300 \int_{0}^{7} t^2 \, dt\][/tex]
To find the integral of [tex]\(t^2\)[/tex], we use the power rule for integration:
[tex]\[= 300 \left[\frac{t^3}{3}\right]_{0}^{7}\][/tex]
[tex]\[= 300 \left(\frac{7^3}{3} - \frac{0^3}{3}\right)\][/tex]
[tex]\[= 300 \left(\frac{343}{3}\right)\][/tex]
[tex]\[= 34300\][/tex]
So, [tex]\(W_{\text{out}} = 34300\)[/tex] gallons.
Now, to find out how many minutes it takes for the tank to be completely empty, we need to find the time, [tex]\(T\)[/tex], at which the tank is empty. The tank will be empty when the integral of the flow rate function from [tex]\(t = 0\)[/tex] to [tex]\(t = T\)[/tex] is equal to the total volume of the tank, which is 6000 gallons.
So, we have:
[tex]\[6000 = \int_{0}^{T} f(t) \, dt\][/tex]
[tex]\[= \int_{0}^{T} 300t^2 \, dt\][/tex]
[tex]\[= 300 \int_{0}^{T} t^2 \, dt\][/tex]
Using the power rule for integration again:
[tex]\[6000 = 300 \left[\frac{t^3}{3}\right]_{0}^{T}\][/tex]
[tex]\[= 300 \left(\frac{T^3}{3} - \frac{0^3}{3}\right)\][/tex]
[tex]\[= 100T^3\][/tex]
Now, solving for [tex]\(T\):[/tex]
[tex]\[T^3 = \frac{6000}{100}\][/tex]
[tex]\[T^3 = 60\][/tex]
[tex]\[T = \sqrt[3]{60}\][/tex]
[tex]\[T \approx 3.914\][/tex]
So, it takes approximately 3.914 minutes for the tank to be completely empty.