evaluate 3X^2-14X-49/X-7
the quotient of the equation is __X+__
Answers
Answer:
[tex]3x+7[/tex]
Step-by-step explanation:
[tex]\frac{3x^2-14x-49}{x-7}[/tex]
before dividing this fraction , lets factor the numerator
[tex]3x^2-14x-49[/tex]
Product is -49 and sum is -14, lets break the middle term using factors
[tex](3x^2+7x)+ (-21x-49)[/tex]
Take out GCF from each group
[tex]x(3x+7)-7(3x+7)[/tex]
[tex](3x+7)(x-7)[/tex]
Now we replace the factors in the numerator
[tex]\frac{(3x+7)(x-7)}{x-7}[/tex]
We have (x-7) at the top and bottom , so we cancel it out
[tex]3x+7[/tex]
Related Questions
An 8-pound bag of tomatoes costs $5.60. At the same rate, what would be the cost of 11 pounds of tomatoes?
A. $8.50
B. $7.00
C. $7.70
D. $6.50 ...?
Answers
Given that for an 8 pound bag of tomatoes costs $5.60, we would want to know how much will it be for 11 pounds. First, we should know how much does it cost per pound. So 5.60 divided by 8 is 0.7. So per pound of tomatoes costs $0.7. Now to know how much for 11 pounds, we multiply 0.7 by 11 and we get $7.70. The correct answer therefore would be option C. $7.70. Hope this answer helps.
Pears cost $1.25 per pound. What is the cost of 4.5 pounds of pears
Answers
So, 4.5 pound of pear will cost = 1.25 * 4.5 = $5.625
So, your final answer is $5.625
Hope this helps!
A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the cost of the fence?
smaller value? and larger value?
Answers
Kendra owns a restaurant. She charges $3.00 for 2 eggs and one piece of toast, and $1.80 for one egg and one piece of toast. How much does Kendra charge for an egg? A piece of toast?
Answers
Jaron paid 2.70 for 6 juice boxes how much should jaron expect to pay for 18 juice boxes
Answers
Answer:
8.10
Step-by-step explanation:
Justin is considering two websites for downloading music.The costs are detailed here.
Website 1: a yearly fee of $30 and $1.50 for each download
Website 2: $2 for each download
What is a system of equations to represent the costs for one year?
Express your equations in the form of y=mx+b where x is the number of downloads for the year and y is the total cost for the year.
Enter your equations in the boxes.
Website 1: ____
Website 2: ____
Answers
website 2. y=2
What is the first four terms of the sequence n squared + 5
Answers
The first four terms of the sequence defined by n squared plus 5 are 6, 9, 14, and 21.
The first four terms of the sequence defined by the expression n squared plus 5, which can be represented mathematically as n^2 + 5.
To find the terms, we simply substitute the first four positive integers (1, 2, 3, 4) for n and calculate:
For n = 1: 1^2 + 5 = 1 + 5 = 6
For n = 2: 2^2 + 5 = 4 + 5 = 9
For n = 3: 3^2 + 5 = 9 + 5 = 14
For n = 4: 4^2 + 5 = 16 + 5 = 21
F = 9/5 C + 32 : is the formula used to convert degrees Celsius to degrees Fahrenheit. Convert 35°C to degrees Fahrenheit.
A) 36°F
B) 63°F
C) 67°F
D) 95°F
Answers
Substitute for C = 35
F = 9/5 * 35 + 32
F = 63 + 32
F = 95
So, option D is your answer.
Hope this helps!
Converting 35°C to degrees Fahrenheit is equal to 95°F.
Option D is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Using the formula F = (9/5)C + 32, where C is the temperature in Celsius and F is the temperature in Fahrenheit.
Substituting C = 35°C into the formula:
F = (9/5) × 35 + 32
F = 63 + 32
F = 95°F
Therefore,
35°C is equal to 95°F.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
which equation when graph has x intercepts at (2,0) and (4,0) and a y-intercept of (0,-16)?
A. F(x)= -(x-2)(x-4)
B. F(x)= -(x+2)(x+4)
C. F(x)=-2(x-2)(x-4)
D. F(x)= -2(x+2)(x+4)
Answers
-2(0-2)(0-4)= -2(-2)(-4)=-16
Next set each factor equal to zero to get the x-intercepts.
(x-2)=0 x = 2 (2,0)
(x-4) = 0 x = 4 (4,0)
I hope this helps
Answer:
The answer is C. on Edgenuty.
How do you sketch this graph? Sketch the graph of y=xlnx
Answers
Greg went to the walmart to buy pencils and pens. each pencils costs $2 and each pen costs $3. he bought five items. he spent $12. how many pens and pencils did he buy?
Answers
however...
He bought
3 pencils and 2 pens
12/2=6
$6 on pens and $6 on pencils
6/2=3 pencils
6/3=2 pens
(3×2)+(2×3)=12
The daily dose of ampicillin for the treatment of an ear infection is 115mg/kg of body weight. what is the daily dose, in mg, for a 34-lb child? ...?
Answers
34 lg = 34*0,45 = 15,3 kg
1 kg.................115 mg
15,3 kg................x
x = 15,3*115
x = 1759,5 mg
A rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.
1] Find a function that models the total area of the four pens. (Let w be the width of the rectangular area and A(w) be the area.)
2]Find the largest possible total area of the four pens. (Round your answer to one decimal place.)
Answers
The function modeling the total area of the four pens is [tex]A(w) = w * ((750 - 3w) / 2)[/tex]. The maximum area can be found by taking the derivative of this function, setting it to zero, and solving for w.
Explanation:The subject in question is Mathematics, specifically calculus and problem-solving involving areas. The rancher with 750 ft of fencing intends to make a rectangular area divided into four pens. Let's define w to be the width and l to be the length of the rectangle.
1] Since the total length of the fence is 750 ft and it will be divided into 3 parts for the width and 2 parts for the length, the function for calculating length will be [tex]l = (750 - 3w) / 2[/tex]. Since the area of a rectangle is given by A=w*l, we can substitute our equation for l into our Area function. Therefore, our function will be [tex]A(w) = w * ((750 - 3w) / 2).[/tex]
2] To find the maximum area of the rectangles, you would need to find the derivative of the Area function and solve for w. After that, plug the value of w into the area function to get maximum area. The exact calculation requires calculus skills and could be taught in a high school Calculus course.
Learn more about Area of Rectangle here:https://brainly.com/question/8663941
#SPJ12
There are 24 children in a class, 16 brown-haired and 8 black-haired. Two students are randomly selected for a stage performance. Find the probability of the following selection. P(2 black haired children)
Answers
There are 8 black-haired children among 24 children. The probability of randomly selecting black haired children for the first time is:
P1 = 8/24 = 1/3
Now, there are 7 black-haired children left among 23 children. The probability of randomly selecting black haired children for the second time is:
P2 = 7/23
Since we want both of these events to occur together, we will multiply their probabilities:
P = P1 * P2 = 1/3 * 7/23 = 7/69
Sam decides to build a square garden. If the area of the garden is 9x2 − 24x + 16 square feet, what is the length of one side of the garden?
(3x + 4) feet
(3x − 4) feet
(4x − 3) feet
(4x + 3) feet ...?
Answers
Solve as a square:
(3x - 4)(3x - 4) = 9x² − 24x + 16
Answer: The correct option is (B) [tex](3x-4).[/tex]
Step-by-step explanation: Given that Sam decides to build a square garden whose area is as follows:
[tex]A=9x^2-24x+16~\textup{square feet}.[/tex]
We are to find the length of one side of the garden.
Since the given garden is of a square shape, so the length of each side is same.
That is, the area of the garden must be a perfect square trinomial.
We have
[tex]A\\\\=9x^2-24x+16\\\\=(3x)^2-2\times 3x\times 4+4^2\\\\=(3x-4)^2.[/tex]
Since the area of a square is (length)², so the length of one side of the garden is [tex](3x-4)~\textup{feet}.[/tex]
Thus, (B) is the correct option.
If each can costs $23.97 plus 6% tax, what is the total cost? Round to two decimal places.
Answers
__________________________________________________
Let us assume that we want to know the total cost of ONE CAN.
_____________________________________________
To calculate our answer:
_______________________________
$ 23.97 + [ (6/100) * 23.97)] = Our answer, in dollars.
__________________________________________
Note: "6%" = 6/100 = 0.06
_______________________
Rewrite as:
____________
$ 23.97 + [ (6/100) * 23.97)] = our answer, in dollars;
_____________________________________________
$ 23.97 + (0.06 * 23.97)
= $ 23.97 + 1.4382
= $ 25.4082 ; Round to decimal places, to get:
→ $ 25.41
__________________________________________
How many times does 50,000 go into 374,000,000,000?
Answers
A box contains four 40-W bulbs, five 60-W
bulbs, and six 75-W bulbs. If bulbs are se-
lected one by one in random order, what is
the probability that at least two bulbs must be
selected to obtain one that is rated 75W?
Answers
P(not a 75Wbulb)=(4+5)/(4+5+6)=9/15
P(a 75W bulb)=6/(15-1)=6/14
9/15*6/14=9/35
Answer: 0.99483
Step-by-step explanation:
Given : A box contains four 40-W bulbs, five 60-W bulbs, and six 75-W bulbs.
Total bulbs : 4+5+6=15
The probability of selecting a 75-W bulb :[tex]p=\dfrac{6}{15}=0.4[/tex]
Using the binomial probability :-
[tex]P(X)= ^nC_xp^x(1-p)^{n-x}[/tex], where P(x) is the probability of getting success in x trials , p is the probability of getting success in each trial and n is the total number of trials.
We have,
The probability that at least two bulbs must be selected to obtain one that is rated 75W :-
[tex]P(x\geq2)=1-(P(x<2))\\\\=1-(P(x=0)+P(x=1))\\\\=1-(^{15}C_0(0.4)^0(0.6)^{15}+^{15}C_{1}(0.4)^1(0.6)^{14})\\\\=1-((1)(0.6)^{15}+(15)(0.4)(0.6)^{14})\ \ [\because\ ^nC_0=1\ \&\ ^nC_1=n]\\\\\approx1-(0.00047+0.00470)\\\\=1-0.00517=0.99483[/tex]
Hence, the required probability = 0.99483
if you were ask to load 225 boxes onto a truck abd the boxes are crated, with each containing nine boxes how many creates would you need to load
Answers
Let x = the number of crates to be loader.
9x = 255
Divide both sides by 9
x = 25
3x-y=11
2x+5y=-4
systems of linear equations using substitution
find X and Y
Answers
The system of equations is:
3x - y = 11
2x + 5y = -4
_________
Rewrite the first equation:
y = 3x - 11
_________
Substitute y in the second equation and solve x:
2x + 5(3x - 11) = -4
2x + 5 * 3x + 5 * (-11) = -4
2x + 15x - 55 = -4
17x = 55 - 4
17x = 51
x = 51 / 17
x = 3
_______
Substitute x in the equation: y = 3x - 11
y = 3 * 3 -11
y = 9 - 11
y = -2
For the demand equation, express the total revenue R as a function of the price p per item.
q = −5p + 500
R(p) = ?
Answers
price = p
quantity sold = q = -5p + 500
R(p) = q*p = (-5p + 500) * p = -5p^2 + 500p
Answer: R(p) = -5p^2 + 500p
That is a quadratic function (parabola), which opens downward, so it has a maximum value, which represents the maximum revenue that can be obtained.
That point is the vertex of the parabola. It tells the price and the number of items sold to obtain the greatest revenue. You can obtain the vertex by several ways.
One is finding the roots of the quadratic function; then the vertex is at the middle of the roots.
-5p^2 + 500p = -5p(p-100) => p = 0 and p =100 => vertex is at p = 50 and maximum R = -5(50^2) + 500(50) = 12,500
The total revenue (R) can be expressed as a function of the price (p) per item by multiplying the price by the quantity demanded (q). Given the demand equation q = -5p + 500, the total revenue equation is R(p) = -5p^2 + 500p.
Explanation:The total revenue (R) can be expressed as a function of the price (p) per item by multiplying the price by the quantity demanded (q).
Given the demand equation q = -5p + 500, we can substitute q in the total revenue equation with -5p + 500:
R(p) = p * (-5p + 500)
Simplifying, we distribute p to both terms inside the parenthesis:
R(p) = -5p^2 + 500p
So, the total revenue (R) as a function of price (p) is R(p) = -5p^2 + 500p.
Learn more about demand equation here:https://brainly.com/question/34102394
#SPJ3
49 % is what of 70 and why do you get the answer of my question.
Answers
The diagram contains contradictory information. Explain the contradiction.
Answers
The true is that those angles are corresponding angles.
Additionaly statements C and D are contradictroy to each other, because on says that the sum of the corresponding angles is 180 and the other says that they are congruent.
The rigth statement is D: given that angles DEH and GHJ are corresponding angles, they are congruent
Optimization problem: what are the dimensions of the lightest open-top right circularcylindrical can that will hold a volume of 1000cm3?Compare the result with the result in example 2. ...?
Answers
Then lightest one means you have the smallest surface area. Which is one base and then the area of the surface. SA = pi*r^2 + 2pi*r*h
So now you have 2 equations, so:
h = 1,000/(pi*r^2)
So then SA = pi*r^2 + 2pi*r*(1,000/(pi*r^2) = pi*r^2 + 2,000/r
Derivative of SA is then 2pi*r -2,000/r^2. Set to 0
2pi*r-2,000/r^2 =0 --> 2pi*r^3 = 2,000 --> r^3 = 1,000/pi --> r = 10/pi^(1/3)
Now go back to the volume function: pi*r^2*h =1,000 --> 1,000/(pi*100/pi^(2/3)) = h
h = 10 / pi^(1/3)
Marty made a $220 bank deposit using $10 bills and $5 bills. She gave the teller a total of 38 bills, how many $5 bills were in the deposit? A) 6 five-dollar bills B) 28 five-dollar bills C) 32 five-dollar bills D) 34 five-dollar bills
Answers
You have to use your choices for this.
A: 6
B: 28
C: 32
D:34
Keep those numbers in mind.
She uses a total of 38 Bills.
Lets think of the first letter choice.
Letter Choice A:
If she uses 6 five-dollar bills ($30) she still needs to pay $190 more.
She would need 19 ten-dollar bills to pay this.
But then she would only have used 25 bills in total. It is stated she used 38.
Letter Choice B:
If she uses 28 five-dollar bills ($140) she still needs to pay $80 more.
She would need 8 ten-dollar bills to pay this.
But then she would only have used 36 bills in total. It is stated she used 38.
Letter Choice C:
If she uses 32 five-dollar bills ($160) she still needs to pay $60 more.
She would need 6 ten-dollar bills to pay this.
That would make it so that she used 38 bills, making this our answer.
Count the left-handed and right-handed spirals on the cacti in the photograph. You should get two consecutive terms of the Fibonacci sequence. What are the numbers? A. 34 and 55 B. 5 and 8 C. 8 and 13 D. 21 and 34 E. 13 and 21
Answers
The student's question involves counting the number of spirals in a cactus, which corresponds to two consecutive numbers in the Fibonacci sequence. The exact answer would depend on the actual count, which cannot be determined without the photograph.
Explanation:The question asks about the phenomenon related to the Fibonacci sequence observed in natural patterns, specifically in plant architecture such as cacti spirals. The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. It is often observable in nature, for example, in the arrangement of leaves or the spirals on sunflower heads and cacti.
In order to answer the question, one would need to physically count the number of left-handed and right-handed spirals on the cactus. The Fibonacci sequence relevant to this context begins with 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. Since the given answer choices are consecutive terms from this sequence, the correct numbers would be identified based on the actual spiral counts which are expected to be consecutive Fibonacci numbers.
Without the photograph, it is impossible to provide the specific numeric answer, but we can understand that the two numbers representing the left-handed and right-handed spirals on the cactus would be consecutive Fibonacci numbers as indicated by the options provided: A) 34 and 55, B) 5 and 8, C) 8 and 13, D) 21 and 34, e) 13 and 21.
Your friends borrowed 5 different movies from the library. In how many different orders can they watch the movies?
Answers
Slot A can be filled with 5 choices
Slot B can be filled with 4 choices (once you pick a movie you can't pick it again)
Slot C has 3 choices
Slot D has 2 choices
Slot E has 1 choice
In total, there are 5*4*3*2*1 = 120 different ways to order the movies
I have no idea what to do with this!
Given the function g(x) = 4x - 5, compare and contrast g(2) and g(-4). Choose the statement that is true concerning these two values.
Answer
The value of g(2) is smaller than the value of g(-4).
The values of g(2) and g(-4) cannot be compared.
The value of g(2) is larger than the value of g(-4).
The value of g(2) is the same as the value of g(-4). ...?
Answers
By substituting the x-values into the linear function g(x) = 4x - 5, we find g(2) = 3 and g(-4) = -21. Therefore, the value of g(2) is larger than the value of g(-4).
Explanation:To determine the values of g(2) and g(-4) for the function g(x) = 4x - 5, we simply substitute the x-values into the function.
For g(2):
g(2) = 4(2) - 5g(2) = 8 - 5g(2) = 3For g(-4):
g(-4) = 4(-4) - 5g(-4) = -16 - 5g(-4) = -21Now, we can compare the two values:
The value of g(2), which is 3, is larger than the value of g(-4), which is -21.
The statement that is true concerning [tex]\( g(2) \)[/tex] and [tex]\( g(-4) \)[/tex] is option a) : The value of [tex]\( g(2) \)[/tex] is larger than the value of [tex]\( g(-4) \)[/tex].
To compare and contrast [tex]\( g(2) \)[/tex] and [tex]\( g(-4) \)[/tex] for the function [tex]\( g(x) = 4x - 5 \)[/tex]:
1. Calculate [tex]\( g(2) \)[/tex] :
[tex]\[ g(2) = 4 \cdot 2 - 5 = 8 - 5 = 3 \][/tex]
2. Calculate [tex]\( g(-4) \)[/tex] :
[tex]\[ g(-4) = 4 \cdot (-4) - 5 = -16 - 5 = -21 \][/tex]
Now, let's analyze the values:
- [tex]\( g(2) = 3 \)[/tex]
- [tex]\( g(-4) = -21 \)[/tex]
Comparing these values:
- [tex]\( g(2) \)[/tex] is positive (3).
- [tex]\( g(-4) \)[/tex] is negative (-21).
Therefore, [tex]\( g(2) \)[/tex] is greater than [tex]\( g(-4) \)[/tex]. This means:
[tex]\[ \text{The value of } g(2) \text{ is larger than the value of } g(-4). \][/tex]
Explanation:
The function [tex]\( g(x) = 4x - 5 \)[/tex] calculates a linear relationship where [tex]\( g(2) \)[/tex] evaluates to 3 and [tex]\( g(-4) \)[/tex] evaluates to -21. This comparison clearly shows that [tex]\( g(2) \)[/tex] yields a larger value than [tex]\( g(-4) \)[/tex]. This result stems from the fact that when x = 2 , [tex]\( g(x) \)[/tex] outputs a positive value, while for x = -4 , [tex]\( g(x) \)[/tex]outputs a larger negative value. Therefore, option:
Complete question : Given the function g(x) = 4x −5, compare and contrast g(2) and g(−4). Choose the statement that is true concerning these two values.
a The value of g(2) is larger than the value of g(−4).
b The value of g(2) is smaller than the value of g(−4).
c The value of g(2) is the same as the value of g(−4).
d The values of g(2) and g(−4) cannot be compared.
"Which of the following are remote interior angles of 5? Check all that apply.
A.1
B.2
C.3
D.4
E.5
F. 6"
Answers
Answer:
A. 1
B. 2
Step-by-step explanation:
We have been given an image of a triangle. We are asked to find remote interior angles of angle 5 for our given triangle.
We can see that angle 5 is an exterior angle. We know that remote interior angles are those, which are inside the triangle and opposite to exterior angle.
We can see that angle 2 and angle 1 are are opposite angles of angle 5 and they are inside our given triangle.
Therefore, option A and B are correct choices.
Final answer:
Remote interior angles are non-adjacent angles within the same triangle. Relative to angle 5, angle 1 and angle 2 are remote interior angles because they are inside the triangle and do not share a vertex with angle 5.
Explanation:
In this mathematics problem, we are asked to find the remote interior angles of a given angle, which are angles that are inside the triangle and non-adjacent to the exterior angle being considered. For example, if we have a triangle with angles labeled 1, 2, 3, 4, 5, and 6, and we want to find the remote interior angles relative to angle 5, we would look for the angles inside the triangle that do not share a vertex with angle 5.
From the available options:
Angle 1 and angle 2 qualify as remote interior angles relative to angle 5 because they are non-adjacent to angle 5 and are within the same triangle.Angle 3 is adjacent to angle 5, so it is not a remote interior angle.Angles 4, 5, and 6 are not pertinent in this case because the question is specifically about the remote interior angles of angle 5, making angles 4 and 6 external to the triangle, whereas angle 5 is the angle in question itself.Therefore, options A (1) and B (2) are the correct answers to this problem.
George sold 18, 22, 26, 12, 25, 20, and 19 cars per month over the past seven months. He followed the steps below to determine the number of cars he needs to sell in the next month to have a mean number of sales per month of 24.
Answers
Final answer:
To find the number of cars George needs to sell in the next month to have a mean of 24, calculate the total number of cars he has sold in the past seven months. Subtract that total from 24 multiplied by 8 (including the past seven months and the next month). Divide the result by 1 to get the number of cars George needs to sell in the next month.
Explanation:
To find the number of cars George needs to sell in the next month to have a mean (average) number of sales per month of 24, we need to calculate the total number of cars he has sold in the past seven months. Then, we can subtract that total from 24 multiplied by 8 (as George wants a mean of 24 sales per month for a total of 8 months, including the past seven months and the next month). Finally, we divide the result by 1 to get the number of cars George needs to sell in the next month.
In this case, the total number of cars George has sold in the past seven months is 18 + 22 + 26 + 12 + 25 + 20 + 19 = 142.
So, to determine the number of cars George needs to sell in the next month to have a mean of 24, we perform the following calculation:
(24 * 8) - 142 = 192 - 142 = 50.
Therefore, George needs to sell 50 cars in the next month to have a mean number of sales per month of 24.