Answer:
[tex]x=2\text{ (or) }x=11[/tex]
Step-by-step explanation:
We have been given factors of a polynomial as [tex](x-2)[/tex] and [tex](x-11)[/tex]. We are asked to find the values of x that would make the polynomial equal to zero.
We will use zero product property of polynomials to solve our given problem. The zero product property of polynomials states that if any of two factors of a polynomial is zero, then their product will be equal to zero.
Upon equating our given factors to zero, we will get:
[tex](x-2)(x-11)=0[/tex]
[tex](x-2)=0\text{ (or) }(x-11)=0[/tex]
[tex]x-2=0\text{ (or) }x-11=0[/tex]
[tex]x-2+2=0+2\text{ (or) }x-11+11=0+11[/tex]
[tex]x=2\text{ (or) }x=11[/tex]
Therefore, [tex]x=2\text{ (or) }x=11[/tex] will make the polynomial equal to zero.
Explain why the equation (x-4)^2-10=15 has two solutions. Then solve the equation to find the solutions.
Please show all your work! (30 points)
how many ounces of 30% hydrochloric acid solution and 80% hydrochloric acid solution must be mixed to get 10 oz of 50% hydrochloric acid solution
How to solve this please?
2x - 5 = 4
pleae help thanks a bunch
If a+5=b, then what is the value of (b−a)^4?
PLZ HURRY!!
If a Professional basketball player earns $3 million playing 125 games per year and plays an average of 40 minutes per game, how much does he earn per second of playing time?
A cutlery manufacturer producer produces 200 units of output at a total cost of $1,500. if total variable costs are $500, the average variable cost (per unit) is ______. $2.5 $3.00 $2.00 $1.00 $7.50
Since there are 200 units and variable costs are $500, we do a simple division, like this:
500/200 = 2.5.
So the answer is: 2.5
Hope this helped! c:
After being rearranged and simplified, which two of the following equations could be solved using the quadratic formula?
Answer:
The Answer will Be B and D
Step-by-step explanation:
A bookstore costs $90 a day to keep open, and spends $12 for each book it sells. the store charges $18 for each book it sells. If n represents the number of books sold, which equation represents the revenue function for this bookstore?
Answer:
[tex]R=6n-90[/tex]
Step-by-step explanation:
Let
R------> the revenue function
n------> the number of books sold per day
we know that
In this problem
[tex]18n[/tex] -----> represent the profit
[tex](12n+90)[/tex] -----> represent the cost
so
The revenue is equal to the profit minus the cost
[tex]R=18n-(12n+90)[/tex]
[tex]R=n(18-12)-90[/tex] ------> equation that represent the revenue function
Simplify
[tex]R=6n-90[/tex]
Lupe has 14 stickers that she wants to give to 2 friends. She wants each friend to have the same number of stickers. Select the three statements that describe how Lupe should give the stickers to her friends. Each friend gets 14÷2 stickers. Each friend gets 2 of the 14 stickers. Each friend gets 142 stickers. Each friend gets 7 of the 14 stickers.
Answer:
The correct options are 1, 3 and 4.
Step-by-step explanation:
It is given that Lupe has 14 stickers that she wants to give to 2 friends.
Total number of stickers Lupe has is 14.
The number of friends is 2.
She wants each friend to have the same number of stickers. It means each friend will get half of 14.
The number stickers Lupe should give to her friends is 14 divided by 2.
[tex]\text{Number of stickers}=14\div 2[/tex]
Write this value in fraction form.
[tex]\text{Number of stickers}=\frac{14}{2}[/tex]
[tex]\text{Number of stickers}=7[/tex]
It means the correct statements are
1. Each friend gets 14÷2 stickers.
3. Each friend gets (14)/2 stickers.
4. Each friend gets 7 of the 14 stickers.
Hence correct options are 1, 3 and 4.
ILL MARK YOU THE BRAINLIST PLS HELP a man who is 6 feet tall casts a shadow that is 15 feet long. A tree casts a similar shadow is 22 FT how tall is the tree?
hello can you please help me posted picture of question
5,895÷36
show all your work
If all of the diagonals are drawn from a vertex of a hexagon, how many triangles are formed?
There are 5 different triangles formed by drawing all of the diagonals from a vertex of a hexagon.
Explanation:To find the number of triangles formed by drawing all of the diagonals from a vertex of a hexagon, we need to determine the number of different combinations of vertices that can form triangles.
For a hexagon, there are 4 vertices that can be chosen as one of the vertices of the triangle. The other 2 vertices can be chosen from the remaining 5 vertices. The order in which the vertices are chosen doesn't matter, so we need to divide by 2 to avoid overcounting.
Using the combination formula, we get:
C(5, 2) / 2 = 10 / 2 = 5
Therefore, there are 5 different triangles formed by drawing all of the diagonals from a vertex of a hexagon.
Joseph buys a bag of 60 pieces of taffy. In the bag, there are 6 cinnamon pieces, 18 raspberry pieces, 12 key lime pieces, and the rest are candy apple pieces. If he randomly draws one piece of taffy, what is the probability that it is a piece of key lime taffy?
A. 0.1
B. 0.4
C. 0.02
D. 0.2
Answer:0.2
Step-by-step explanation:
Mrs. Daly's reading classes were surveyed about their reading preferences. the data is summarized in the table below.
given that a student is in 9th grade, what is the probability that they like to read non-fiction novels, based on this data?
Answer:
0.60
Step-by-step explanation:
I WILL MARK BRAINLIEST PLEASE HURRY
For a test of : p 0.50, the sample proportion is 0.36 based on a sample size of 100. use this information to complete parts (a) through (c) below.
The question involves hypothesis testing for proportions. The p-value is calculated using the normal distribution for proportions. In this case, the p-value is found to be 0.0417.
The question involves hypothesis testing for proportions. The null and alternative hypotheses need to be defined for the study.
The p-value is calculated using the normal distribution for proportions.
In this case, the p-value is found to be 0.0417. We can conclude that there is sufficient evidence to reject the null hypothesis and conclude that there is a difference between the proportions of households in the two communities.
PLEASE HELP!!!! THIS LINEAR EQUATIONS!!!
Use multiplying by 1 to find an expression equivalent to 3/14 with a denominator of 14 y.
What is the mode of these numbers? A 40. B 43. C 26 and 31. D. 31 and 43
What are the zeros of the polynomial function f(x) = (x – 6)(x – 2)(x + 7)?
Dynatashia has a list of items she needs to buy at the store. She has written down the items and the advertised prices as shown: Hamburger – $3.99 per pound Hamburger buns – $1.29 2-liter soda – 3 for $2.00 Dynatashia buys 1.5 pounds of hamburger, 1 package of buns and 3 of the 2-liter bottles of soda. Her receipt is shown below. 2-ltr soda 2@3/$2 $1.34 Hambrg 1.5 lb@3.99 $5.99 Hbuns 1@1.69 $1.69 2-ltr soda 1@3/$2 $0.67 Determine if Dynatashia's receipt is correct. a. Yes, Dynatashia's receipt is correct. b. No, Dynatashia paid too much for soda. c. No, Dynatashia paid too much for hamburger. d. No, Dynatashia paid too much for buns.
Answer:
D. No, Dynatashia paid too much for buns.
Step-by-step explanation:
We are given that,
The actual cost of the items are,
Items Cost
Hamburger $3.99 per pound
Buns $1.29 per packet
2-liter soda $2 per 3 bottle
As, she bought 1.5 pounds of hamburgers, 1 packet of buns and 3 bottles of 2-liter soda.
So, she has to pay,
For hamburger = 1.5 × 3.99 = $5.99
For buns = 1.29 × 1 = $1.29
For soda bottles = $2
But from the receipt, we see that she pays,
For hamburger = 1.5 × 3.99 = $5.99
For buns = 1.69 × 1 = $1.69
For soda bottles = 1.34 + 0.67 = $2
That is, she has to pay $1.29 for the packet of the buns but she paid $1.69 for the buns.
Hence, the receipt is not correct as Dynatashia paid too much for the buns.
Answer: D
Step-by-step explanation:
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At Jason's car rental shop it costs a flat rate of $100 to rent a car, which covers the cost of driving up to 75 miles. For every mile over 75 it costs an additional $0.10. Write a piecewise function modeling this situation, where x represents the miles driven and y represents the total cost.
Andrew drove 55 mph on his trip. Which of the following equations best represents the distance he drove if x stands for the number of hours?
Answer
Using speed formula:
[tex]\text{Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]
Let y represents the distance in miles and x represents the time in hours.
As per the given statement:
Andrew drove 55 mph on his trip.
Using formula;
we have;
[tex]55 = \frac{y}{x}[/tex]
Multiply both sides by x we have;
[tex]y = 55x[/tex]
Therefore, the equation best represents the distance he drove is [tex]y = 55x[/tex]
how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 30% alcohol solution
To create 9 gallons of a 30% alcohol solution, mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution by setting up and solving a system of equations based on volumes and concentrations.
Explanation:To find out how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of a 30% alcohol solution, we can set up a system of equations based on the volumes and concentrations of the solutions. Let's let x represent the volume of the 20% solution and y represent the volume of the 50% solution.
Since the total volume of the mixture should be 9 gallons, we have our first equation:
x + y = 9Next, we consider the concentration of alcohol in the final mixture. The amount of pure alcohol from the 20% solution is 0.20x gallons, and from the 50% solution, it is 0.50y gallons. The final mixture has a concentration of 30%, so the total amount of alcohol in the 9 gallons mixture is 0.30 * 9 gallons. This gives us our second equation:
0.20x + 0.50y = 0.30 * 9Now we have a system of two equations with two variables that can be solved using methods such as substitution or elimination. After solving, we find that x = 6 gallons and y = 3 gallons. Therefore, to obtain 9 gallons of a 30% alcohol solution, you'd need to mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution.
Which expression is equivalent to 10x^6y^12/-5x^-2y^-6? Assume .x=0.y=0.
Answer:B on edge
Step-by-step explanation:
What is the surface area of a cylinder with a radius of 5 ft and a height of 2 ft?
Answer:
Its B.
Have a great day! OwO
Marta wants to use her mothers recipe. Her mother's recipe makes enough soup for 10-12 people, but Marta wants to make only 1/3 of that amount. If the original recipe requires 2 1/2 pounds of chicken, how many pounds of chicken will Marta need for her soup?
Simplify (3x+8)(x+1) using a table, the Distributive Property, and the FOIL
method. Which method is most efficient? Explain.
Final answer:
To simplify (3x+8)(x+1), we can use the FOIL method, the Distributive Property, or a multiplication table, all leading to the same simplified expression: 3x² + 11x + 8. The FOIL method is typically the most efficient for binomials.
Explanation:
The question asks to simplify the expression (3x+8)(x+1) using a table, the Distributive Property, and the FOIL method and to determine which method is most efficient.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last and represents a quick way to multiply two binomials:
First: Multiply the first terms in each binomial (3x×x = 3x²).
Outer: Multiply the outer terms (3x×1 = 3x).
Inner: Multiply the inner terms (8×x = 8x).
Last: Multiply the last terms in each binomial (8×1 = 8).
Adding these products together, we get 3x² + 3x + 8x + 8, which simplifies to 3x² + 11x + 8.
Using the Distributive Property
This involves expanding the expression by multiplying each term in the first polynomial by each term in the second: (3x+8)(x) + (3x+8)(1), which also simplifies to 3x² + 11x + 8.
Using a Table
Create a table where you list each term of the first polynomial in the first row and the terms of the second polynomial in the first column, and then fill in the table with the products of the intersecting terms. The sum of these products will also yield 3x² + 11x + 8.
While all three methods will give the correct answer, the FOIL method is generally seen as the most efficient for this particular problem, as it provides a straightforward, step-by-step process that is easy to follow and remember for multiplying two binomials.