Barry walked a total of 3 miles to larry's house. if he walked for 45 minutes to get there, how fast was he traveling (r) in miles per hour?
Two times antonio's age plus three times sarah's age equals 34. Sarah's age is also 5 times antonio's age. how old is sarah
Jenna has $50 to spend at a local crafts fair. The entrance price for the fair is $10. At a pottery stand, Jenna finds some cups that she likes that are $4.50 each. what is the maximum number of cups she can buy?
Which binomial is not a devisor of x^3-11x^2+16x+84?
x + 4
Further explanationGiven:
The expression x³ - 11x² + 16x + 84
Question:
Which binomial is not a divisor of x³ - 11x² + 16x + 84?
x + 2x + 4x - 6x - 7The Process:
This is a problem about Remainder Theorem.
If x = a or (x - a) is one of the roots or factors (divisors) of the function f (x), then f(a) = 0.
Let us test one by one of the options available into the polynomial function.
[tex]\boxed{ \ x + 2 \ } \rightarrow \boxed{ \ x = -2 \ }.[/tex]
[tex]\boxed{ \ \rightarrow (-2)^3 - 11(-2)^2 + 16(-2) + 84 = ? \ }[/tex][tex]\boxed{ \ \rightarrow -8 - 44 - 32 + 84 = 0 \ }[/tex][tex]\boxed{ \ x + 4 \ } \rightarrow \boxed{ \ x = -4 \ }.[/tex]
[tex]\boxed{ \ \rightarrow (-4)^3 - 11(-4)^2 + 16(-4) + 84 = ? \ }[/tex][tex]\boxed{ \ \rightarrow -64 - 176 - 32 + 84 = -188 \ }[/tex][tex]\boxed{ \ x - 6 \ } \rightarrow \boxed{ \ x = 6 \ }.[/tex]
[tex]\boxed{ \ \rightarrow (6)^3 - 11(6)^2 + 16(6) + 84 = ? \ }[/tex][tex]\boxed{ \ \rightarrow 216 - 396 + 96 + 84 = 0 \ }[/tex][tex]\boxed{ \ x - 7 \ } \rightarrow \boxed{ \ x = 7 \ }.[/tex]
[tex]\boxed{ \ \rightarrow (7)^3 - 11(7)^2 + 16(7) + 84 = ? \ }[/tex][tex]\boxed{ \ \rightarrow 343 - 539 + 112 + 84 = 0 \ }[/tex]From the test results above, it was clearly observed that (x + 4) is not a divisor of x³ - 11x² + 16x + 84 because [tex]\boxed{ \ f (-4) \neq 0 \ }[/tex].
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Alternative Steps
We will use Horner's rule for polynomial division in finding factors as well as divisors.
To begin, let us try x = -2 to see if it is one of the roots of x³ - 11x² + 16x + 84. The complete process can be seen in the attached picture.Since there is no remainder when x³ - 11x² + 16x + 84 is divided by (x + 2), this binomial is a divisor (or a factor). The quotient is obtained x² - 13x + 42. After factorization, we get (x - 6) dan (x - 7 as factors and also the divisor.Learn moreThe remainder theorem https://brainly.com/question/9500387A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 https://brainly.com/question/12700460 The product of a binomial and a trinomial is x 3 + 3 x 2 − x + 2 x 2 + 6 x − 2.If y=1/2 when x=2, find y when x=3, given that y varies directly with x
If you purchase 100 items that cost $.25 each, how much would the items cost all together?
Larry Lazy purchased a one year membership at a local fitness center at the beginning of the year. It cost him $150. He goes twice a week for the first three months (13 weeks) of the year, but then goes only once a month for the rest of the year.
How much does each visit to the center cost?
If he continued going twice a week all year, how much would each visit cost?
Answer:
A. $4.29
B. $1.44
Step-by-step explanation:
A. We have been given that Larry goes to gym twice a week for 13 weeks. Let us multiply 13 by 2 to find the number of times Larry visited the gym for first 3 months.
[tex]\text{The number of Larry's visits to gym for the first 3 months}=13\times 2=26[/tex]
Since there are 12 months in a year, then Larry has gone to gym only 9 times for rest of month as 12-3=9.
Now let us add 26 and 9 to get the total number of Larry's visits to gym.
[tex]\text{Larry's total visits to gym}=26+9[/tex]
[tex]\text{Larry's total visits to gym}=35[/tex]
Now let us divide total cost (150) by total number of visits (35) to get the each visit's cost.
[tex]\text{Each visit's cost}=\frac{150}{35}[/tex]
[tex]\text{Each visit's cost}=4.2857142857142857\approx 4.29[/tex]
Therefore, each visit to the center costs $4.29 to Larry.
B. If Larry continued going twice a week all year, then total number of Larry's visits to center will be 52 times 2.
[tex]\text{Larry's total visits to center}=52\times 2[/tex]
[tex]\text{Larry's total visits to center}=104[/tex]
Now let us divide total cost (150) by total visits (104) to find the cost of each visit.
[tex]\text{Each visit's cost}=\frac{150}{104}[/tex]
[tex]\text{Each visit's cost}=1.4423076923076923\approx 1.44[/tex]
Therefore, If Larry continued going twice a week all year, it would cost him $1.44 for each visit.
It takes 36 minutes for 7 people to paint 4 walls. How many minutes does it take 9 people to paint 7 walls?
How to find out how likely it is to get 13% chance at something 13 times?
answer is center of rotation
Penny translate a trapezoid so that one of the vertices is at the origin. if the pre-image has a perimeter of 44 units what is the perimeter of the image
Translations are part of rigid motions which also include reflection and rotation. For these three, we can then assume that neither the perimeter nor the area of an object would change. This means that, once an object is translated it is not biased or distorted (either enlarged or diminished). Thus, making the perimeter of the original and the image are equal. So for this problem, the perimeter of the image would be the same as the pre-image, and that would be 44 units.
In the context of geometric transformations, the shape and size do not change, only position. Therefore, if the trapezoid's pre-image has a perimeter of 44 units, the image, as a result of translation, will have the same perimeter of 44 units.
Explanation:In the context of geometric transformations like translations, rotations, or reflections, the shape and size of the object do not change--only its position does. The pre-image and the image are congruent, so their perimeters are the same.
In the situation described in your question, Penny's trapezoid is translated so that one of its vertices is at the origin. Because a translation is a type of isometry (a transformation that preserves distance), the shape of the trapezoid and the lengths of its sides will not change in the translation process. As a result, if the perimeter of the pre-image is 44 units, then the perimeter of the image will also be 44 units, regardless of where the vertices are located.
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Write an inequality that represents the sentences:
What is the product of g and 2 is less than -6
The school bookstore sold 8 more pencils than pens one day. A pencil costs $0.05 and a pen costs $0.20. If the day's sales of pens and pencils totaled $8.90, how many pencils were sold?
To solve this problem, we use algebraic equations to represent the situation. By setting up an equation for the total sales and solving for the number of pens, we can then calculate the number of pencils sold based on the given information. In this case, 34 pens and 42 pencils were sold.
Explanation:Let's solve this problem using algebra. Let the number of pens sold be x. According to the problem, the number of pencils sold is x + 8. Now we can set up an equation to represent the total sales:
0.20x + 0.05(x + 8) = 8.90
Simplifying the equation, we get:
0.20x + 0.05x + 0.40 = 8.90
Combining like terms,
0.25x + 0.40 = 8.90
Next, we can subtract 0.40 from both sides of the equation to isolate x:
0.25x = 8.90 - 0.40
Subtracting, we find that
0.25x = 8.50
Finally, we can divide both sides of the equation by 0.25 to solve for x:
x = 8.50 / 0.25
Calculating, we find that x = 34. This means that 34 pens were sold. Since 34 pens were sold and there were 8 more pencils sold than pens, there must have been 34 + 8 = 42 pencils sold.
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5 hundred 25 thousand six hundred minutes
What are the steps for using a compass and straightedge to construct a regular hexagon inscribed in a circle?
Drag the steps and drop them in order from start to finish.
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Construct and JM⎯⎯⎯⎯⎯, MO⎯⎯⎯⎯⎯⎯⎯, OK⎯⎯⎯⎯⎯⎯⎯, KP⎯⎯⎯⎯⎯, PN⎯⎯⎯⎯⎯⎯, and NJ⎯⎯⎯⎯⎯ to complete regular hexagon JMOKPN .
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Construct a circle with its center at point H.
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Construct a circle with its center at point J and having radius HJ . Construct a circle with its center at point K having radius HJ .
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Construct horizontal line l and point H on line l.
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Label the point of intersection of circles H and J that lies above line l, point M, and the point of their intersection that lies below line l, point N. Label the point of intersection of circles H and K that lies above line l, point O, and the point of their intersection that lies below line l, point P.
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Label the point of intersection of the circle and line l to the left of point H, point J, and label the point of intersection of the circle and line l to the right of point H, point K.
In March, Rodney sold twice as many cars as Greg. In April Rodney sold 5 fewer cars than he did in March while Greg sold 3 more cars than he did in March. If they same number of cars in April how many cars did each sell in March
Final answer:
Rodney sold 16 cars and Greg sold 8 cars in March.
Explanation:
Let's start by representing the number of cars sold by Rodney and Greg in March as variables. Let R represent the number of cars sold by Rodney and G represent the number of cars sold by Greg.
Given that Rodney sold twice as many cars as Greg in March, we have the equation R = 2G.
In April, Rodney sold 5 fewer cars than he did in March, so we have the equation R - 5.
Greg sold 3 more cars than he did in March, so we have the equation G + 3.
Lastly, we know that they sold the same number of cars in April, so we can set R - 5 = G + 3.
Now, we can solve the system of equations to find the values of R and G. Substituting R = 2G into the last equation, we get 2G - 5 = G + 3. Solving for G, we find G = 8. Substituting this value back into the equation R = 2G, we get R = 16.
Therefore, Rodney sold 16 cars and Greg sold 8 cars in March.
Rodney: 16 cars
Greg: 8 cars
50 points!! help with justification of these steps please
Caitlyn needs to solve the equation: 2(3x+1)=3(2-x). She solves for x in 5 steps:
6x+2 = 6 - 3x
2 = 6 - 9x
-4 = -9x
4/9 = x
x = 4/9
What is the justification for each of the steps that Caitlyn took? Give the Algebraic Property for each step.
Answer:
combining like terms
Step-by-step explanation:
in 35 days a person saved $70 what was the person's average daily savings
The person's average daily savings is $2.00. The correct answer is option b $2.00.
Step 1
To find the average daily savings, we need to divide the total amount saved by the number of days over which the savings occurred.
Calculation:
1. Total savings: $70
2. Number of days: 35 days
Step 2
The average daily savings is calculated as:
[tex]\[\text{Average daily savings} = \frac{\text{Total savings}}{\text{Number of days}} = \frac{70}{35} = 2\][/tex]
The person's average daily savings is $2.00.
Complete question : In 35 days, a person saved $70. What was the person's average daily savings?
a $0.70
b $2.00
c $1.50
d $1.05
e $2.33
f none of these
Kaitlin brought 7 cans of cola to a party. lisa brought 18 packs of cola, and each pack had 6 cans. how many cans did they bring in all?
Please help with all 3 questions thank you.
Question 7 the length of a shadow of a building is 29 m . the distance from the top of the building to the tip of the shadow is 38 m . find the height of the building. if necessary, round your answer to the nearest tenth.
There are thirteen animals in a barn. Some are chickens and some are pigs there are 40 legs in all. How many of each animal are there
How to solve x^2+bx+c=0 when b and c are negative by factoring?
If you buy an IPod for $339, how much sales tax would you pay if the tax rate is 8.375%?
translate the following points 5 units up (-5,-2) (-2,1) (-4,-7)
BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. The tables below show the values of y corresponding to different values of x:
Table A
x 3 2 1
y 1 0 0
Table B
x 3 5 4
y −2 1 1
Which statement is true for the tables?
Both Table A and Table B represent functions.
Both Table A and Table B do not represent functions.
Table A does not represent a function, but Table B represents a function.
Table A represents a function, but Table B does not represent a function.
2. Which of the following statements best describes the effect of replacing the graph of f(x) with the graph of f(x) + 4?
The graph shifts 4 units up.
The graph shifts 4 units down.
The graph shifts 4 units left.
The graph shifts 4 units right.
Both Table A and Table B in the question represent functions, as each x value corresponds to exactly one y value in both tables. The operation of replacing the graph of f(x) with f(x) + 4 results in a vertical shift of the graph 4 units upward.
The subject of the question involves interpreting the data sets presented in Table A and Table B and understanding the behavior of functions. According to the definition, a function is a mathematical relationship wherein each input (x) corresponds to exactly one output (y).
Now, let's determine which tables represent functions. Table A: each 'x' corresponds to exactly one 'y', so this represents a function.
For Table B, each 'x' also corresponds to exactly one 'y', so this also represents a function.
This means both Table A and Table B represent functions.
As for the second question, the operation of replacing the graph of f(x) with f(x) + 4 will result in the graph shifting 4 units upward. The vertical shift is a result of adding 4 to the entire function f(x).
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Solve the inequality (show your work):
-5/2(3x + 4) < 6 - 3x
-5/2 (3x+4)<6-3x distribute
-15/2 x-10<6-3x move -15/2 to the other side by adding it to 3x
-10<6+9/2 x move 6 over by subtracting it from -10
-16<9/2 x divide 9/2 by 16 (or multiply 2/9)
-32/9<x
Jamie's parents have told him that he needs to pay his credit card bills on time to establish good credit. How will good credit help him in the future?
Simply C Because well Nowadays You Have To Have Credit For Everything And Its Crazy When Your A Teenager Living On Your Own Without Any Credit. I Had To Buy Things For Around The House And Eventually Bought A $5,000 Bed Set
an online movie streaming plan has no annual fee but charges $4.25 per movie watched. Another plan charges an annual fee of $36 plus $3.50 per movie watched. For how many movies is the cost of the plans the same?
You are planning to volunteer at a zoo that is 60 miles from your home. you can either take stephanie's car, which gets 20 miles to the gallon