Claire bought 3 bars of soap and five sponges for $2.31. Steve bought five bars of soap and three sponges for $3.05. Find the cost of each item
Is the sum of two monomials always a monomial? Is their product always a monomial?
Sum of two monomials is not necessarily always a monomial.
For example:
Suppose we have two monomials as 2x and 5x.
Adding 2x+5x , we get 7x.
So if two monomials are both like terms then their sum will be a monomial.
Suppose we have two monomials as 3y and 4x
Now these are both monomials but unlike, so we cannot add them together and sum would be 3y + 4x , which is a binomial.
So if we have like terms then the sum is monomial but if we have unlike terms sum is binomial.
Product of monomials:
suppose we have 2x and 5y,
Product : 2x*5y = 10xy ( which is a monomial)
So yes product of two monomials is always a monomial.
The sum of two monomials is not always a monomial and the product of two monomials is always a monomial.
Further explanation:
Explanation:
Consider the two monomials as [tex]5y{\text{ and }}7y.[/tex]
The sum of the two polynomials can be obtained as follows,
[tex]\begin{aligned}{\text{Sum}} &= 5y + 7y\\&= 12y\\\end{aligned}[/tex]
The sum of the two monomials is monomial.
Consider the two monomials as [tex]5y{\text{ and }}7x.[/tex]
The sum of the two polynomials can be obtained as follows,
[tex]{\text{Sum}} = 5y + 7x[/tex]
The sum of the two monomials is not monomial.
Consider the two monomials as [tex]4y{\text{ and }}6x.[/tex]
The product of the two polynomials can be obtained as follows,
[tex]\begin{aligned}{\text{Product}} &= 4y \times 6x\\&= 24xy\\\end{aligned}[/tex]
The product of the two monomials is monomial.
The sum of two monomials is not always a monomial and the product of two monomials is always a monomial.
Learn more
Learn more about the polynomial https://brainly.com/question/12996944 Learn more about logarithm model https://brainly.com/question/13005829 Learn more about the product of binomial and trinomial https://brainly.com/question/1394854Answer details:
Grade: High school
Subject: Mathematics
Chapter: Number system
Keywords: sum, two monomial, monomials, always monomial, product, always, monomial, factor, factorization, polynomial, quadratic, cubic, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.
6V3-16V3+21V-56 ANSWER
A flagpole that was originally 24 feet tall has cracked 9 feet from the ground and has fallen as if hinged. Find
out how far from the base of the flagpole the top of the flagpole touched after it had fallen.
Identify the hyperbolas (represented by equations) whose centers are at (2, 1)
A tailor cut 3/4 of an inch off a skirt and 1/6 of an inch off a pair of pants. How much more did the tailor cut off the skirt than the pants?
Final answer:
To find out how much more was cut from the skirt than the pants, convert fractions to have a common denominator and subtract: 3/4 inch minus 1/6 inch equals 7/12 inch.
Explanation:
To determine how much more the tailor cut off the skirt than the pants, we need to subtract the length cut from the pants from the length cut from the skirt. The tailor cut 3/4 of an inch off the skirt and 1/6 of an inch off the pants. To perform the subtraction, we need a common denominator, in this case, 12 is suitable. So we convert 3/4 to 9/12 and 1/6 to 2/12.
Now, we subtract the smaller fraction from the larger one:
9/12 - 2/12 = 7/12 of an inch.
Therefore, the tailor cut 7/12 of an inch more off the skirt than the pants.
In a circle with a radius of 6 m, an arc is intercepted by a central angle of 7π4 radians. What is the arc length? Use 3.14 for π . Enter your answer as a decimal in the box.
Answer:
[tex]Arc length=32.97m[/tex]
Step-by-step explanation:
It is given that In a circle with a radius of 6 m, an arc is intercepted by a central angle of [tex]\frac{7\pi}{4}[/tex] radians.
Then, the arclength of the circle is given as:
[tex]Arc length=radius{\times}central angle[/tex]
⇒[tex]Arc length=6{\times}\frac{7\pi}{4}[/tex]
⇒[tex]Arc length=\frac{21\pi}{2}[/tex]
⇒[tex]Arc length=10.5{\times}3.14[/tex]
⇒[tex]Arc length=32.97m[/tex]
Thus, the arc length of the given circle is 32.97m.
Rosa paints a wall in her bedroom. She puts green paint on 5/8 of the wall and blue paint on 3/8 of he wall. Compare fractions using <>=
Experts/ace/geniuses helpp
Zakir loans Panji $20,000 for one year at 8% simple interest. Three months later, Zakir sells the note to Ben at a simple discount rate of 7 3/4%. How much does Ben pay for the note?
A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.
What is the approximate area of the triangle? Round to the nearest tenth.
Area of a triangle = bh
68.7 cm2
161.7 cm2
381.3 cm2
450.0 cm2
Area of a triangle = [tex]\frac{1}{2} base*height[/tex]
In a right angle triangle the two legs are the base and height of the triangle.
One angle of the triangle is 23 degree and one adjacent leg is 27.6 cm.Let the other leg opposite to 23 degree angle by x.Sine of an angle is ratio of opposite and hypotenuse. Hypotenuse is given as 30 cm.
[tex]Sin 23=\frac{x}{30}[/tex]
x= 30 sin23.
x=11.72cm.
The legs of the triangle are 11.72 cm and 27.6 cm.
Area of triangle =[tex]\frac{1}{2} x11.72 x27.6 =161.7cm^{2}.[/tex]
given that 1 is a zero of p(x)=3x^4-x^3-8x^2+2x+4, factor the polynomial completely, and then list all its zeros.
What is the volume of a cube with an edge length of 2.7 centimeters?
Enter your answer, as a decimal, in the box.
cm³
Answer:
the answer is V≈19.68cm³
V=a3
a
Edge
cm
Step-by-step explanation:
If you laid 9 bolts end to end, that measure 7/8 inch how long would the row of bolts be?
The row of 9 bolts laid end to end would be 7 7/8 inches long.
To find the total length of 9 bolts laid end to end, we multiply the length of one bolt by the number of bolts.
Given:
- Length of one bolt: [tex]\( \frac{7}{8} \)[/tex] inch
- Number of bolts: 9
Total length:
[tex]\[ \text{Total length} = \text{Length of one bolt} \times \text{Number of bolts} \][/tex]
[tex]\[ \text{Total length} = \frac{7}{8} \times 9 \][/tex]
Now, multiply:
[tex]\[ \text{Total length} = \frac{7 \times 9}{8} \][/tex]
[tex]\[ \text{Total length} = \frac{63}{8} \][/tex]
To express this in mixed number form:
[tex]\[ \frac{63}{8} = 7 \frac{7}{8} \][/tex]
Therefore, the row of 9 bolts laid end to end would be [tex]\( 7 \frac{7}{8} \)[/tex] inches long.
Jenny spent 35 minutes doing research on the internet.she finished at 7:10 p.m. at what time did jenny start her research
what would be the dimensions of a new right rectangular prism that has 20 fewer unit cubes than the original prism
Please help with number 4 please !!
The circumference of a circular field is 229.22 yards. What is the radius of the field? Use 3.14 for π and do not round your answer.
(3x10^3)(2x10^5)
Write the answer in scientific notation
a rectangular prism has a top area of 20ft square and a height of 5ft. what is the volume of this rectangular prism
Leo paid $2400 in interest on an amount borrowed for 10 years at a 4% annual simple interest rate. How much did Leo borrow?
In one week, the Green Recycling Center
received 784 aluminum cans. They
received the same number of cans each
day. How many cans did the recycling
center receive each day?
A bale of hay in the shape of a rectangular prism has a length of 4 feet, a width of 2 feet, and a height of 2 feet. A cylindrical bale of hay has a diameter of 5 feet and a height of 6 feet. How many rectangular bales contain the same amount of hay as one cylindrical bale? Round your answer to the nearest tenth.
write an equation to represent the relationship between the time sabar walks and number of calories when he burns use x as the independent variable and use y as a dependent variable
The equation to represent the relationship between the time Sabar walks, denoted by [tex]x[/tex] , and the number of calories he burns, denoted by [tex]y[/tex], can be written as [tex]\( y = mx \),[/tex] where [tex]\( m \)[/tex] is the rate at which calories are burned per unit time.
To establish a relationship between the time Sabar spends walking and the number of calories he burns, we can use a simple linear equation. In this context, the independent variable [tex]x[/tex] represents the time spent walking, and the dependent variable [tex]\( y \)[/tex] represents the number of calories burned.
The rate at which calories are burned is typically constant for a given activity if the intensity remains consistent. This rate is represented by the coefficient [tex]\( m \)[/tex] in the equation [tex]\( y = mx \)[/tex]. The value of [tex]\( m \)[/tex] would be determined by how many calories Sabar burns per minute, hour, or any other time unit chosen for [tex]x.[/tex]
For example, if Sabar burns 5 calories per minute, then [tex]\( m = 5 \)[/tex]calories/minute, and the equation would be [tex]\( y = 5x \)[/tex]. If we measure time in hours and Sabar burns 300 calories per hour, then [tex]\( m = 300 \)[/tex]calories/hour, and the equation would be [tex]\( y = 300x \).[/tex]
This linear equation assumes that the relationship between time and calories burned is directly proportional, meaning that the number of calories burned increases at a constant rate as the time spent walking increases. This is a common assumption for steady-state aerobic activities like walking at a consistent pace.
Sven investigates the amount of damage to the head gaskets on the trucks in his fleet and find that the damage index depends on the ambient temperature. He develops the equation y = - 2 3 x + 14 to model the relationship. What does 14 mean? A) The temperature only adds 14 to the damage index. B) If there is no damage index then the ambient temperature is 14. C) If the damage index is 0, then the ambient temperature would be 0. D) If the ambient temperature is 0 then the damage index would be 14.
Given is the damage index equation, [tex] y=\frac{-2}{3} x+14 [/tex]
where y represents damage index, and x represents ambient temperature.
It is similar to slope-intercept form of linear equation given by y = mx + b.
Where m is said to be the slope of line and b is the y-intercept of the line. When x = 0, y = b.
Similarly, if plug x = 0 in the damage index equation, [tex] y=\frac{-2}{3} (0)+14=14 [/tex]
So, If ambient temperature, x = 0. Then damage index, y = 14.
Hence, option D is correct i.e. " If the ambient temperature is 0 then the damage index would be 14".
Answer:
The answer is D because 14 is the y-intercepts, which means that the x-value is 0. So the correct meaning is If the ambient temperature is 0 then the damage index would be 14. .
Step-by-step explanation:
This figure shows circle O with diameter QS .
mRSQ=280∘
What is the measure of ∠ROQ ?
What is BP? Enter your answer as a decimal in the box
find A if r = 3.6 femtometers
15% of the bands total ticket sales is $375. Which proportion should we use
On any given flight, an airline's goal is to fill the plane as much as possible, without overbooking. if, on average, 10% of customers cancel their tickets, all independently of each other, what is the probability that a particular flight will be overbooked if the airline sells 320 tickets, for a plane that has maximum capacity 300 people? what is the probability that a plane with maximum capacity 150 people will be overbooked if the airline sells 160 tickets?