Using the long division method, we have divide ([tex]x^3+x^2[/tex] +3x+5) ÷ (x+4) then the remainder is −55 and quotient is x^2−3x+15.
We have to divide ([tex]x^3+x^2[/tex] +3x+5) ÷ (x+4)
In general, long division of two integers without any variables is performed in the same way as long division of a polynomial by a binomial:
Divide the polynomial's highest degree term by the binomial's highest degree term. Over the division line, type the outcome.
Subtract the resulting binomial from the polynomial after multiplying this result by the divisor.
x+4) [tex]x^3+x^2[/tex] +3x+5 (x^2−3x+15
−([tex]x^3+4x^2[/tex])
−−−−−−−−−−−−−−−−−−−
−3[tex]x^2[/tex] +3x
−(−3[tex]x^2[/tex] −12)
−−−−−−−−−−−−−−−−−−−
15x+5
−(15x+60)
−−−−−−−−−−−−−−−−−−−
−55
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which expression is equivalent to xy ^ 2/9
The expression that is equivalent to xy^2/9 is [tex]x\sqrt[9]{y^{2} }[/tex] , the correct option is (d) .
an Algebraic Expression is defined as an expression that is written using the combination of variables and numbers joined by mathematical operators .
For Example : 2x+ 3y , 3y , 2xy are all algebraic expressions .
In the question ,
it is given that ,
the algebraic expression is xy^2/9 ,
we need to find an equivalent expression to the given expression .
we know that the x^(1/n) is written as [tex]\sqrt[n]{x}[/tex] .
So , xy^2/9 = [tex]x.(y^{2})^{\frac{1}{9} }[/tex] = [tex]x\sqrt[9]{y^{2} }[/tex]
Therefore , The expression that is equivalent to xy^2/9 is [tex]x\sqrt[9]{y^{2} }[/tex] , the correct option is (d) .
The given question is incomplete , the complete question is
Which expression is equivalent to xy^2/9 ?
(a) √(xy⁹)
(b) [tex]\sqrt[9]{xy^{2} }[/tex]
(c) x(√y⁹)
(d) [tex]x\sqrt[9]{y^{2} }[/tex]
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Select ALL the correct answers.
Observe the expression below and select the true statement(s).
The "3y" in the first term is a factor.
The "(7 + 2x)" in the first term is a factor.
The "10" in the third term is a coefficient.
The "x" in the second term is an exponent.
The "2" in the first term is a constant.
The "9" in the second term is a coefficient.
The correct statements are
The 3y in the first term is a factor The (7 + 2x) in the first term is a factor The 9 in the second terms is a coefficientThe expression is
3y(7 + 2x) + 9xy -10
The expression is the mathematical statement that consist of different variables, numbers and mathematical operators. The mathematical operators are addition, subtraction, division and multiplication
The expression is
3y(7 + 2x) + 9xy -10
From the expression 3y is the first term is a factor and (7+2x) is also the first term is a factor
Therefore,
The 3y in the first term is a factor.
The (7 + 2x) in the first term is a factor.
Consider the second term
The 9 in the second terms is a coefficient
Last term 10 is a constant, but there is not suitable statement is given
Hence, the correct statements are
The 3y in the first term is a factor The (7 + 2x) in the first term is a factor The 9 in the second terms is a coefficientLearn more about expression here
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Triangle abc ha a perimeter of 22cm
Ab =8cm
Bc=5
I triangle abc a right angle triangle
ΔABC is not a right angled triangle.
What is right angled triangle?
A right-angle triangle is one that has angles between its two sides that equal 90 degrees.
Main Body:
First let's find the length of the last side. We can do this by adding AB and BC together, then subtracting this amount from the perimeter of Triangle ABC, 22 cm.
ABC - (AB + BC) ⇒ 22 - (8 + 5)
=22 - 13 = 9 cm
The hypotenuse is always the longest side of a triangle, so we know that the side we figured out is the hypotenuse. Now we can use the Pythagorean Theorem to see whether the triangle is a right triangle.
Pythagorean Theorem: a² + b² = c², where a and b are legs and c is the hypotenuse.
If a² + b² do equal c², then the triangle is a right triangle.
⇒8² + 5² = 9²
⇒64 + 25 = 81
⇒89 > 81
Therefore triangle is not a right triangle, but we know that it is obtuse since a and b together are longer than c.
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If you are given a continuous function that has a domain of [-3, 4] which of the following values are included in the given domain?
A continuous function that has a domain of [-3, 4] will include all the values as -3,-2,-1,-0,-1,-2,3,4
What do you mean by continuous function?
In mathematics, a continuous function is one where a continuous variation of the argument results in a continuous variation of the function's value (i.e., a change without a leap). This indicates that there aren't any discontinuities, or sudden changes in value. More specifically, a function is continuous if it is possible to guarantee that its value will not vary significantly even with arbitrarily tiny changes to its parameter. Any function that is not continuous is said to be discontinuous.
It is given that a continuous function has a domain of [-3,4]
According to the definition of closed interval,
[-3,4] will contain all the elements between them and including them.
Therefore, [-3,4] will contain elements as -3,-2,-1,-0,-1,-2,3,4
Hence, a continuous function that has a domain of [-3, 4] will include all the values as -3,-2,-1,-0,-1,-2,3,4
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a 2 qaurt bucket of paint costs $20.32. What is the price per cup?
Answer:
$2.54
Step-by-step explanation:
2 qaurt = 8 cups
20.32/8=$2.54 percup
a function f is increasing on the interval (1 comma 4 )and decreasing on the interval (4 comma 9 ). determine and explain whether there is a local maximum or local minimum on the interval (1 comma 9 ).
As per the given function, the local minimum is 1 and the local maximum is 9 and it can be written as (1, 9)
Local Minimum and maximum
The term Local maxima and minima are the maxima and minima of the function that arises in a particular interval.
Here the Local maxima would be the point in the particular interval for which the values of the function near that point are always less than the value of the function at that point.
Whereas the local minima would be defined as the point where the values of the function near that point are greater than the value of the function at that point.
Given,
Here we have the function f is increasing on the interval (1, 4) and decreasing on the interval (4, 9).
Here we need to determine and explain whether there is a local maximum or local minimum on the interval (1, 9).
According to the definition of the local minimum and local maximum,
While we looking into the given point,
We have identified that the resulting point is
=> (1, 4) => 1 (minimum)
=> (4, 9) => 9 (maximum)
Therefore, the minimum and maximum is (1, 9).
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i need this, right now, please, is math
Answer:
The answer is eleven. 11
Determine the length of the line segment shown. line segment from negative 10 comma 9 to 5 comma negative 1
4 units
18 units
19 units
21 units
The length of the line is 18 units.
What is Distance Formula?If there are two point P( a, b) and Q (c, d) then the distance between P and Q is
d= √ ( c- a)² + ( d- b)²
Given points: ( -10 ,9 ) and ( 5, -1)
So, the distance between these two points
Using Distance formula
d= √ ( c- a)² + ( d- b)²
d = √(5 - (-10))² + (- 1- 9)²
d= √15² + (-10)²
d= √225+ 100
d= 18. 027 units
Hence, the length of the line is 18 units.
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Answer:
The solution to this problem is option (B) - 18 units
Step-by-step explanation:
I took the test and the test told me the answer is 18 so hence, choose option (B) as your answer.
Hope this helped:)
8 3/5 as an improper fraction
Answer: 43/5
Step-by-step explanation: I multiplied the 5 and 8, which gave me 40. Then I added 3 and got 43/5.
teen obesity: the 2013 national youth risk behavior survey (yrbs) reported that 13.7% of u.s. students in grades 9 through 12 who attend public and private school were obese. after seeing extensive efforts to educate parents and teens on healthy lifestyles, we want to know if the proportion has decreased this year. we select a random sample of 200 u.s. students and find that 11% are obese.after performing the hypothesis test for p
There is a 13.3% chance that a sample of 200 U.S students in grades 9 through 12 who attend public and private school will have 11% or fewer obese students if 13.7% of the population is obese this year.(Option D)
Given:
The 2013 national youth risk behavior survey (yrbs) reported that 13.7% of u.s. students in grades 9 through 12 who attend public and private school were obese.
consider the random sample:
200 US students
11% are obese.
Null hypothesis:
Null hypothesis = 13.7%
= 13.7/100
= 0.137
Alternative hypothesis = p < 0.137.
Therefore the null hypothesis = 0.137.
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There are 14 red jellybeans and 17 blue jellybeans in a bag. If you randomly select three jellybeans in a
row, without replacement, what is the probability that you get at least one red jellybean?
Fiugrie out the ratio missing table text back answer !
NO EXPLAIN HURRY THANK BYE
The ratio between the fruit and vegetable is 1:3
RatioRatio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14. The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.
We can simply say that a ratio is a fraction of one quantity over another quantity
In this case, we just have to figure the ratio between fruit and vegetables.
In the first column, we have fruit to vegetable as 2:6 = 1:3
In the second column, we have fruit missing. We can make that x.
Using the ratio between fruit and vegetable, when vegetable is 12, the fruit will be 12/3 = 4
The value of fruit in the second column will be 4.
In the third column, we have fruit as 6 and vegetable as y.
We can apply same ratio to get the vegetable which will be 6 * 3 = 18
In the third column, the vegetable is 18
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suppose you are standing such that a 63-foot tree is directly between you and the sun. if you are standing 240 feet away from the tree and the tree casts a 270-foot shadow, how tall could you be and still be completely in the shadow of the tree?
You could stand at 7 feet and still be completely in the shadow of the tree.
What is the property of a similar triangle?
Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion).
Given
You are standing such that a 63-foot tree is directly between you and the sun.
If you are standing 240 feet away from the tree and the tree casts a 270-foot shadow.
BC to be the height of the tree and DE to be the height of how tall you could be and still be completely in the shadow of the tree.
∠D = ∠B = 90 degrees
Therefore,
By the similar triangle property;
DE/BC = AD/AC
x/63 = (270-240)/270
x/63=30/270=0.11
x=63*0.11 = 7
Hence, you could stand at 7 feet and still be completely in the shadow of the tree.
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A department store buys 400 shirts at a cost of $10,800 and sells them at a selling price of $30 each. Find the percent markup. ... The percent markup is %.
The percent markup is 11.11%.
There is a department store. The total number of shirts bought by the department store is 400. The total cost of the shirts bought by the department store is $10,800. The department store sells all the shirts for $30 each. We need to find the percent markup.
We first need to find out the cost of each shirt. The cost price of each shirt is the total cost of all the shirts divided by the total number of shirts bought by the department store.
C = $10,800/400
C = $27
Hence, each shirt was purchased for a price equal to $27. To find the markup percentage, we need to find the percentage difference between the cost price and the selling price of the shirt.
M = [(30 - 27)/27]*100%
M = (3/27)*100%
M = 100/9%
M = 11.11%
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The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97% of the people who have a disease. However, it erroneously gives a positive reaction for 5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease". What is the probability of type i error if the new blood test is used?.
The probability of a type I error in the case of the new blood test is 0.022.
Given;
It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested who do not have the condition received an incorrectly positive response. Take into account the null hypothesis that "the person does not have the disease."
A: The individual does not have the disease
B: The individual does have the disease
We know that,
Type I Error is rejecting the true null hypothesis
P (Type I Error) = P(Positive reaction to an individual who does not have the disease)
=0.022
Hence, the probability of a type I error is 0.022.
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For the imaginary number, which of these is a possible value of " if n is greater than 6?
A 0
B 5
C -2
D 1
E 2
Answer:
A 0
Step-by-step explanation:
Melissa uses 3/5 as much water as Neil to water her plants. If Melissa uses 4 and 1/3 gallons of water, how much does Neil use?
Write an expression for the area of the following figure.
The expression for the area of the given figure is: 18x
Given, figure:
we are asked to determine the area of the expression of the given figure.
Label the given figure and join the points G and C
Draw the required figure.
Observe that from the figure that, the shape consists of a square ABCG and rectangle FCDE.
Find the area of the given shape.
area of the given shape = ar(ABCG) + ar (FCDE)
= 3 × x × 6
= 18x
Therefore, the expression for the area of the given figure is 18x.
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If heights of 3rd graders follow a normal distribution with a mean of 52 inches and a standard deviation of 2. 5 inches, what is the z score of a 3rd grader who is 47 inches tall?.
Z score of a 3rd grader who is 47 inches tall with mean of 52 inches and standard deviation of 2.5 inches is 2
Z- Score give an idea how far a data point is from mean .
z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .
Given , x = 47 inches
standard deviation = 2.5 inches
mean = 52 inches
z-score = x- μ / σ
putting all the values ,
z-score = 47 - 52 / 2.5
= -5 / 2.5
= -2
|Z| = 2
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Chee buys a two-pint bottle of juice for $3.52. What is the unit rate of the cost of the juice per fluid ounce?
The unit rate of the cost of the fluid per ounce is $0.11
How to calculate the cost of the fluid per ounce ?
Chee buys two pint bottle of juice
The two pints costs $3.52
The unit rate of the cost of the juice per fluid ounce can be calculated as follows
1 pint is equals to 16 fluid ounce
2 pints= 2 × 16
= 32
The cost per fluid ounce is
= 3.52/32
= 0.11
Hence the unit rate of the cost of the juice per fluid ounce is $0.11
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Select EVERY indeterminate form to which L'Hopital's Rule can be directly applied to (there may be more than one). 0.00 0° U U 1° oo U U 8 - 0 U 8|8 o 8
The indeterminant form to which the L'Hopital's Rule can be applied are 0/0 and ∞/∞ , the correct options are (d) and (f) .
L'Hopital's Rule in calculus is used to evaluate weird limits that result in indeterminate forms that are 0/0, ∞/∞ . These types of limits
(a) cannot be calculated by direct substitution of limit and/or
(b) can be evaluated but using a very long procedure .
that means if [tex]\lim_{x \to a} \frac{f(x)}{g(x)}[/tex] = 0/0 or ∞/∞ ,
then [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]
In the question ,
there are several indeterminant forms given which are 0.∞ , [tex]0^{0}[/tex] , [tex]1^{\infty}[/tex] , 0/0 , ∞ - ∞ , ∞/∞ , ∞⁰ .
By the definition of L'Hopital's Rule , the option that matches with the definition is 0/0 and ∞/∞ ,
So , the correct option is (d) 0/0 and (f) ∞/∞ .
Therefore , The indeterminant form to which the L'Hopital's Rule can be applied are 0/0 and ∞/∞ , the correct options are (d) and (f) .
The given question is incomplete , the complete question is
Select EVERY indeterminate form to which L'Hopital's Rule can be directly applied to (there may be more than one).
(a) 0.∞
(b) [tex]0^{0}[/tex]
(c) [tex]1^{\infty}[/tex]
(d) 0/0
(e) ∞ - ∞
(f) ∞/∞
(g) ∞⁰
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A pair of shoes usually sells for $58. If the shoes are 30% off, and sales tax is 7%, what is the total price of the shoes including tax?
A.
$43.44
B.
$40.34
C.
$46.55
D.
$44.66
Answer:
A
Step-by-step explanation:
1. calculate discount
30/100 × 58 = 17.4
2. calculate sell price
58 - 17.4 = 40.6
3. calculate sales tax
7/100 × 40.6 = 2.842
4. calculate total price
sell price + sales tax = 40.6 + 2.842 = 43.442
In quadrilateral ABCD, triangle ADC is congruent to CBA. Show
that ABCD is a parallelogram.
a shop has a sale microwave oven
Answer:
good i will buy
Step-by-step explanation:
math homework percentages help pls
Answer: 70 dollars in profit
Step-by-step explanation: 20 x 13.50 = 270 20 - 3 = 17 20 x 17 = 340 340 - 270 = 70
The price received for a bicycle is given by the equation b = 100 – 10x2, where x is the number of bicycles produced, in millions.
It costs the company $60 to make each bicycle.
What is the profit function for the company?
P = –10x2 – 60x + 100
P = –10x3 + 40x
P = – 10x2 + 40
Answer:
B
Step-by-step explanation:
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So a freshman in algebra 1 and im on unit 4 i been stuck on this question trying to find out how to solve it for almost over 15 minutes can you please help
Answer:
Step-by-step explanation:
Jada paints a circular table that has a diameter of 37 inches. What is the area of the table?
ola
The area of the circular table is 1075.21 square inches.
Jada has a table. The table is circular in shape. She paints the table. The diameter of the circular table is 37 inches. We need to find out the area of the table. We will, first of all, find the radius of the circular table. Let the radius and the area of the table be represented by the variables "r" and "A", respectively.
The radius of a circle is equal to half its diameter.
r = 37/2
r = 18.5 inches
To find the area of the table, we will use the formula for the area of a circle.
A = πr²
A = π(18.5)²
A = 1075.21
Hence, the area of the circular table is 1075.21 square inches.
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one of your cars is blue. it can travel 31 1/2 miles on 1 1/4 gallons of gas how many miles can it travel on one mile of gas
Answer:
25.2 miles per gallon
Step-by-step explanation:
[tex]\frac{31.5}{1.25}[/tex]
What is the equation of the blue line
The equation of the blue line in the given graph is y = -x/2 + 2 .
In the question ,
a line graph is given,
we have to find the equation of the blue line .
to find the equation of line , we need at least two points ,
So , from the graph we can see that the two points from where the blue line passes the graph are (4,0) and (0,2) .
the slope = (2-0)/(0-4)
m = 2/(-4)
m = -1/2
So , the equation of the line passing from the points (4,0) with slope -1/2 , is
(y - y₁) = m(x - x₁)
y - 0 = (-1/2)(x - 4)
y = -x/2 + 2
Therefore , The equation of the blue line in the given graph is y = -x/2 + 2 .
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