Answer:
[tex]\textsf{1.} \quad 5x+3-\dfrac{3}{x-4}[/tex]
[tex]\textsf{2.} \quad 2x^2-4x+3[/tex]
[tex]\textsf{3.} \quad x^3+3x^2-2x+4+\dfrac{25}{2x-5}[/tex]
Step-by-step explanation:
Long Division Method of dividing polynomials
Dividend: The polynomial which has to be divided.Divisor: The expression by which the divisor is divided.Quotient: The result of the division.Remainder: The part left over.Divide the first term of the dividend by the first term of the divisor and put that in the answer.
Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.
Repeat until no more division is possible.
Write the solution as the quotient plus the remainder divided by the divisor.
Question 1[tex]\large \begin{array}{r}5x+3\phantom{)}\\x-4{\overline{\smash{\big)}\,5x^2-17x-15\phantom{)}}}\\{-~\phantom{(}\underline{(5x^2-20x)\phantom{-b)..}}\\3x-15\phantom{)}\\-~\phantom{()}\underline{(3x-12)\phantom{}}\\-3\phantom{)}\\\end{array}[/tex]
Solution
[tex](5x^2-17x-15) \div (x-4)=\dfrac{5x^2-17x-15}{x-4}=5x+3-\dfrac{3}{x-4}[/tex]
Question 2[tex]\large \begin{array}{r}2x^2-4x+3\phantom{)}\\3x-2{\overline{\smash{\big)}\,6x^3-16x^2+17x-6\phantom{)}}}\\{-~\phantom{(}\underline{(6x^3-4x^2)\phantom{-bbbbbbbb.)}}\\-12x^2+17x-6\phantom{)}\\-~\phantom{()}\underline{(-12x^2+8x)\phantom{))))).}}\\9x-6\phantom{)}\\-~\phantom{()}\underline{(9x-6)\phantom{}}\\0\phantom{)}\end{array}[/tex]
Solution
[tex](6x^3-16x^2+17x-6) \div (3x-2)=\dfrac{6x^3-16x^2+17x-6}{3x-2}=2x^2-4x+3[/tex]
Question 3[tex]\large \begin{array}{r}x^3+3x^2-2x+4\phantom{)}\\2x-5{\overline{\smash{\big)}\,2x^4+x^3-19x^2+18x+5\phantom{)}}}\\{-~\phantom{(}\underline{(2x^4-5x^3)\phantom{-bbbbbbbbbbb.bb.)}}\\6x^3-19x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(6x^3-15x^2)\phantom{))))bbbb..).}}\\-4x^2+18x+5\phantom{)}\\-~\phantom{()}\underline{(-4x^2+10x)\phantom{)))..}}\\8x+5\phantom{)}\\-~\phantom{()}\underline{(8x-20)}\\25\phantom{)}\end{array}[/tex]
Solution
[tex]\begin{aligned}(2x^4+x^3-19x^2+18x+5) \div (2x-5) & =\dfrac{2x^4+x^3-19x^2+18x+5}{2x-5}\\ & =x^3+3x^2-2x+4+\dfrac{25}{2x-5}\end{aligned}[/tex]
Exponential form is a shorter form of _______________ multiplication.
Answer:
repeated
Step-by-step explanation:
Please answer questions 10-16. It would help me a whole bunch! You would be a total lifesaver! DUE TONIGHT!
Answer:uh I think its a carrot
Step-by-step explanation:
hi, 12 points available
I was just wondering if anyone knows the answer to this question?
Two numbers, Greater than 1, which have A lowest common Multiple of 48?
Answer:16 and 24
Step-by-step explanation:
Simplify the equation please
Answer:
[tex]4(5) {m}^{3} \times {m}^{2} \times {n}^{2} \times {n}^{1} [/tex]
since you know the rules of exponents we are multiplying powers of the same bases meaning we will add the exponents.
[tex] = 20 {m}^{3 + 2} {n}^{2 + 1} \\ = 20 {m}^{5} {n}^{3} [/tex]
mark wants to paint a mural. he has 1 1/3 gallons of yellow paint, 1 1/4 gallons of green paint, and 7/8 gallon of blue paint. Mark plans to use 3/4 gallons of each paint color. how many gallons of paint will he have left after painting the mural
Mark has: 1 1/3 = 4/3 gallons of Yellow
1 1/4 = 5/4 gallons of Green
7/8 gallons of Blue.
Total = (4/3 + 5/4 + 7/8) LCM = 24
= (32 + 30 + 21)/24 = 83/24 Gallons of Paint in total.
If he used 3/4 of each, he would have = 1/4 of each left.
Therefore gallons left = 1/4 * (83/24) = 83/96 gallons left.
= 0. 8646 gallons left in total.
Jasmine wants to use her savings of $1,128 to buy video games and movies. The total price of the movies she bought was $72. The video games cost $43 each.
Choose the inequality that would be used to solve for the maximum number of video games Jasmine can buy with her savings.
The last one.
It states that "The video games cost $43 each." and the total price was $72 in movies meaning that the x would go with the 43 and 1,128 would have to be greater than the amount she's buying or she won't be able to buy it.
What is 7 12/13 as a improper fraction?? I rlly need help
Answer: 103/13
Step-by-step explanation:
7 * 13 = 91
91 + 12 = 103
what is 20x-14x=21-10
:))
20x-14x=21-10
6x=11
x=11/6
☞ user58580~ ♥
Answer:
The Answer is x=11/6
Step-by-step explanation:
Hope this helps!!
A movie theater is open x hours Monday through Thursday and y hours Friday through Sunday. Write an algebraic expression that represents the number of hours per week the theater is open.
The algebraic expression for total hours that represents the number of hours per week the theater is open is 4 x + 3 y
Number of hours the theatre is opened on Monday to Thursday = x hours.
Number of hours the theatre is opened on Friday to Sunday = y hours.
Number of hours from Monday to Thursday = 4 x hours.
Number of hours from Friday to Sunday = 3 y hours.
Total hours will be represented by the algebraic expression:
Total hours = 4 x + 3 y.
Therefore, the algebraic expression for total hours that represents the number of hours per week the theater is open is 4 x + 3 y
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The feasible solution is the best solution possible for a mathematical model.
a. true
b. false
The feasible solution is the best solution possible for a mathematical model , the statement is False.
Feasible Solution for a mathematical model is defined as the solution that satisfies all the constraints of the linear program.
Whereas an Optimal Solution is a feasible solution that minimizes or maximizes the function.
Optimal Solution is a part of feasible Solution .
So , an Optimal Solution can also satisfy all the constraints of the linear program.
Hence, The feasible solution is the best solution possible for a mathematical model statement is False .
Therefore , the correct option is (b) false.
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-4(x+7)+7x+2
combine like terms
Answer:
3x-26
Step-by-step explanation:
-4(x+7)+7x+2
Multiple -4 By 7
-4x -28 +7x +2
Group like terms
-4x +7x -28+2
-4+7= 3
3x -28 +2
-28+2=-26
3x-26
Hope this helps! ^^
Ann, Claire and Josh collect stickers. One week, Ann collects 7 more stickers than Josh. Josh collects twice as many stickers as Claire. If they collect a total of 157 stickers, how much stickers did each collect?
Josh collected 60 stickers, Ann collected 67 stickers and Claire collected 30 stickers.
How to find the number of stickers each collect using variables?Ann, Claire and Josh collect stickers. One week, Ann collects 7 more stickers than Josh.
let use variables to represent the amount of stickers they collected.
Therefore, Ann collects 7 more stickers than Josh. Josh collects twice as many stickers as Claire
Josh stickers = x
Ann stickers = 7 + x
Claire stickers = 1 / 2 x
Total stickers collected = 157
Therefore,
x + 7 + x + 1 / 2 x = 157
x + x + 1 / 2 x = 157 - 7
2.5x = 150
divide both sides by 2.5
x = 150 / 2.5
x = 60
Therefore, Josh collected 60 stickers, Ann collected 67 stickers and Claire collected 30 stickers.
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A farmer raises chickens and pigs. If his animals have a total of 120 heads and a total of 300 feet, how many chickens does the farmer have?
F. 60 G. 70 H. 80 J. 90
The number of chickens are J. 90.
Let the chickens be represented by x and the pigs be represented by y.
Forming the equation according to first information -
Equation 1 : x + y = 120
x = 120 - y
Both chicken and pig has one head. Chicken has 2 feet while pig has 4 feet. Forming the equation according to second information -
Equation 2 : 2x + 4y = 300
Simplifying the equation 2 by dividing by number 2
x + 2y = 150
Keep the value of x from equation 1 in equation 2
120 - y + 2y = 150
Performing subtraction
120 + y = 150
Further shifting the value and performing subtraction
y = 150 - 120
Performing subtraction
y = 30
Now, 30 is the number of pigs.
Number of chickens = 120 - y
Number of chickens = 120 - 30
Number of chickens = 90
Hence, the number of chickens the farmer has is J. 90.
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Solve x³ = 27. A x=9. Bx = 19,683 C_x=3√3. DX = 3
Answer:
D. x = 3
Step-by-step explanation:
[tex] {x}^{3} = 27[/tex]
[tex]x = \sqrt[3]{27} = 3[/tex]
Myra is reading an article about the success of introduced species of animals into the United States.
Which person is most likely considered the authority on the subject?
a zoologist
a microbiologist
a physicist
a chemist
The person that is most likely considered the authority on the subject is A. a zoologist.
Who is a zoologist?It should be noted that a zoologist simply means the individual that study animals and how they interact with their ecosystem.
In this case, Myra is reading an article about the success of introduced species of animals into the United States.
Therefore, the person that is most likely considered the authority on the subject is a zoologist.
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Which line on the graph below has an undefined slope?
On a coordinate plane, line Q is horizontal, line P has a positive slope, line R is vertical, and line S has a negative slope.
P
Q
R
S
The line which has an undefined slope among the answer choices given in the task content as described is; the line R which is a vertical line.
Which line among the given answer choices is that which has an undefined slope?It follows from the task content that the line which has an undefined slope is to.be determined among the answer choices.
Since, the slope of a graph is the rate of change in the vertical axis to that in the horizontal axis; it follows that the slope of vertical lines is undefined.
The statement above is true because, no change is recorded in the X axis of vertical lines. Hence, the denominator in the slope formula is; 0 and ultimately, the slope is undefined.
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Answer:
Step-by-step explanation:
The answer is R
Angels (LIne). I'm unsure of what to do.
Based on the linear pair theorem, the value of x is: 42°.
How to Apply the Linear Pair Theorem?A linear pair is a pair of two angles that are formed adjacent to each other on a straight line. These two angles, according to the linear pair theorem, have a sum of 180d degrees when their measures are added together.
From the image, we see that x° and 138° are a linear pair as they lie on a straight line.
Therefore:
x + 138 = 180 [linear pair theorem]
Subtract 138 from both sides of the equation
x + 138 - 138 = 180 - 138
x = 42°
Therefore, based on the linear pair theorem, the value of x is: 42°.
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If w = 24, what is the value of 2w − 18?
30
8
206
66
Answer:
30
Step-by-step explanation:
Substitute 24 for w
2(24) - 18
multiply 24 by 2
48 - 18
Subtract 18 from 48
Answer: 30
Solve each equation. 3(w-8)=36
The solution of the given linear equation 3(w -8) = 36 in one variable is at w = 20.
According to the given question.
We have a linear equation in one variable 3(w - 8) = 36.
Since, we have to solve the above equation for w.
As we know tha, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Therefore, the solution of the linear equation in one varibale 3(w - 8) = 36 is given by
3(w - 8) = 36
⇒3w - 24 = 36 ( by distributive property)
⇒ 3w = 36 + 24 (adding 24 both the sides)
⇒ 3w = 60
⇒ w = 60/3 (dividing both the sides by 3)
⇒ w = 20
Hence, the solution of the given linear equation 3(w -8) = 36 in one variable is at w = 20.
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A bicycle has tires that are 24 inches in diameter.
b. How many inches does the tire travel after 100 rotations?
The tire travels 7536 inches.
We are given the diameter of tire of bicycle. Now, to find the distance traveled, we will use the following formula -
Distance = number of rotations × circumference of tire.
Now, further calculating the circumference of tire using the formula -
Circumference = π×diameter.
Firstly keep the values in the formula of circumference to calculate it.
Circumference = 3.14×24
Performing multiplication
Circumference = 75.36 inch
Now, keep the values in formula to find the distance traveled by the tire of bicycle.
Distance = 100×75.36
Again performing multiplication
Distance = 7536 inches
Hence, the distance traveled by the tires 7536 inches.
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Find measure.
m ∠ 5
Measure of angle 5 i.e. m∠5 = 50°
What is measurement of an angle ?The measurement of angle is the degree of that angle or we can also say that the angles are always measured in degree. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.
How to find angle measurement ?As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360 or 180 for a straight line.
In the question,
Let given angle is ∠8.
Given, ∠8 = 50°
Now, according to vertical angle property
∠5 = ∠8
therefore, ∠5 = 50°
Thus, m∠5 = 50°
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The complete question is :
Find measure m∠5
what positive number raised to the second power is equal to 64
solve for x in terms of y
4x+2y=7
Answer: [tex]x=\frac{7-2y}{4}\\[/tex]
Step-by-step explanation:
4x+2y-2y=7-2y
4x= 7-2y
[tex]\frac{4x}{4}=\frac{7}{4}-\frac{2y}{4}[/tex]
Simplify: [tex]\mathrm{Divide\:the\:numbers:}\:\frac{4}{4}=1[/tex] = x / [tex]\frac{7}{4}-\frac{2y}{4}[/tex] x = [tex]\frac{7-2y}{4}[/tex]
Find L in the cone
please hurry
The length of slant height l is √98 ft. when diameter of cone and height of cone is 7 ft.
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.
Here, the diameter of cone is given as : 14ft.
also, the height of cone is : 7 ft.
the radius r of base will be half of diameter :
r = b/2
r = 14/2 = b
Now to find the slant height of the cone we use Pythagoras theorem between the base of cone b, height of cone h and slant height l that is :
h² + r² = l²
7² + 7 ² = l²
l² = (2x7²)
l = 7 √2 ft. or √98 ft.
Therefore, the length of slant height l is √98 ft.
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We can use the pythagorean theorem to answer this question.
We know that [tex]l[/tex] is the hypotenuse, and the 2 sides are 7 and 7.
So, we can build the equation:
[tex]7^2+7^2 = l^2[/tex]
[tex]98 = l^2[/tex]
[tex]\sqrt{98} = l[/tex]
.
please help me I need help i have problems
Answer:
3.6cm
Step-by-step explanation:
the points lie in order like this
A.....B.....C
we know that A......B......C total spans 4cm (or 40mm)
we know that A......B spans 4mm
we need to know the length of B......C
B......C = A.......B.......C - A.....B = 40mm - 4mm = 36mm = 3.6cm
Sadie worked 14 hours last weekend at Pickles and Onions sub shop. On Saturday, her gross
income was $90 but her net income was only $77.75. On Sunday, her gross income was $120
and her net income was $101.38.
How much did Sadie pay in payroll taxes for the weekend? /PLS HELP
Answer:
$30.87
Step-by-step explanation:
Saturday
- gross: $90
- net: $77.75
Sunday
- gross: $120
- net: $101.38
Total gross: 90 + 120 = $210
Total net: 179.13
Total tax: 210 - 179.13 = 30.87
what are the vertex and range of 7= |x +2| -3
The vertex and range are (-2, -3) and y >= -3 respectively
How to determine the vertex and range?The equation is given as:
y = |x +2| - 3
The above equation is an absolute value equation
An absolute value equation is represented as:
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
Vertex = (-2, -3)
Also, we have
a = 1
Since a is positive, then the vertex is a minimum
Hence, the vertex and range are (-2, -3) and y >= -3 respectively
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What is 2,520 divide 36
What are the coordinates of the point on the
directed line segment from (-8, 8) to (7,-7)
that partitions the segment into a ratio of 1 to 4?
The coordinates of the point on the directed line segment is (-5,5)
In the given sum we are using the internal division formula which goes like: (x,y) = (nx₁ + mx₂)/(m+n), (ny₁ + my₂)/(m+n)
with the available data we can interpret that where m = 1 , n = 4 , (x₁,y₁) = (-8,8) , (x₂,y₂) = (7,-7)
substituting the given values in the above formulae
The coordinates of the point is :
(x,y) = (4(-8) + 1(7))/(1 + 4) , (4(8) + 1(-7))/(1 + 4)
= ( -32 + 7)/5, (32 - 7)/5
= (-25/5) , (25/5)
= (-5,5)
∴ (x , y) = (-5 , 5)
So here the coordinates are (-5 , 5) which directed line segment from (-8,8) to (7,-7) that partions the segment into a ratio of 1 to 4
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Solve -4(3x-7)=52 for x
Answer:
x = -2
Step-by-step explanation:
First, distribute:
-12x + 28 = 52
Then, subtract 28 on both sides:
-12x = 24
Finally, divide -12 on both sides:
x = -2
Step-by-step explanation:
hope it helps