Work Shown:
x³ + x² + x + 1
(x³ + x²) + (x + 1)
x²(x+1) + 1(x + 1)
(x² + 1)(x + 1)
The basic outline is to pair up the terms into two groups. We factor each group separately, and then factor out the overall GCF (x+1). You can use the FOIL rule to verify the answer.
The factored form of x³ + x² + x + 1 is (x²+1)(x+1).
What is Factorization?A number or other mathematical item is factored (or factorised; see English spelling changes) or factored by a number of factors, usually smaller or simpler things of the same kind.
We have,
x³ + x² + x + 1
Now, making groups as
(x³ + x²) + (x + 1)
= x² (x + 1) + (x+1)
= (x²+1)(x+1)
So, resulting expression is (x²+1)(x+1).
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If you apply the changes below to the quadratic parent function, f(x) = x², which of these is the equation of the new function? Shift 1 unit right. • Vertically stretch by a factor of 3. • Reflect over the x-axis. A. g(x)=-3(x-1)2 B. g(x)=-3(x+1)2 c. g(x)=-3x²-1 D. g(x) = (-3x+1)2
Equation of the new function -3(x+1)².
The correct option is (B)
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given function:
f(x) = x²
The given condition are shift one unit right+ 1.
i.e., x+1
Vertically stretch 3 units= -3
i.e., -3(x+1)
So, reflect over x- axis = square the function'
So, new function= -3(x+1)²
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Which expression is equivalent to
(5ab)^3
30a b-7? Assume a≠0, b≠0.
1. a7b¹0/6
2. 125a¹8b21/30
3. 25a³b4/6
4. 25a9b¹0/6
The equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex]\frac{(5ab)^3}{30ab^{-7}}[/tex]
Expand the numerator
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{125a^3b^3}{30ab^{-7}}[/tex]
Divide 125 and 30 by 5
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^3b^3}{6ab^{-7}}[/tex]
Apply the law of indices
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{3-1}b^{3+7}}{6}[/tex]
Evaluate the exponent
[tex]\frac{(5ab)^3}{30ab^{-7}} =\frac{25a^{2}b^{10}}{6}[/tex]
Hence, the equivalent expression of [tex]\frac{(5ab)^3}{30ab^{-7}}[/tex] is [tex]\frac{25a^{2}b^{10}}{6}[/tex]
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MATH!!! Volume of prisms stuff
Neyha has six number cards. Here are four of Neyha's cards. 8;8;8;8 The mean of all six cards is 8 The range of all six cards is 4 What are the other two cards?
After considering the given data we come to the conclusion that the two other cards are 6 and 10, under the condition that Neyha has six number cards. Here are four of Neyha's cards. 8;8;8;8.
Let us assume that the other two cards x and y.
The given mean of all six cards is 8. Then, the sum of all six cards is 48 (8×6). We have that four of the cards are 8s.
So, the summation of these four cards is 32 (8×4).
The dedicated range of all six cards is 4. Therefore, the difference between the largest and smallest card is 4.
Furthermore, we know that four of the cards are 8s, the other two cards must be different from 8.
Hence, we can consider that x and y are the smallest and largest numbers in the set.
Here we have to apply basic algebraic expression
We can perform the setting up two equations:
x + y = 48 - 32 = 16 (the summation of x and y is equivalent to the summation of all six cards minus the summation of the four 8s)
y - x = 4 (the difference considering y and x is equal to the range of all six cards)
Evaluating these equations simultaneously gives us:
y = 10
x = 6
Therefore, the other two cards are 6 and 10.
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There is a set of 10 jobs in the printer queue. One of the jobs in the queue is called job A. How many ways are there for the jobs to be ordered in the queue so that job A is the first to finish or the last to finish
The number of ways for the jobs to be ordered in the queue so that job A is the first to finish or the last to finish is; 2 * 9!
How to solve permutation and combination?We are told that;
There is a set of 10 jobs in the printer queue.
One of the jobs is job A. Thus, there are 9 other identified jobs.
Number of ways to order this nine jobs = 9!
Since the job A has to be ordered first or last, then;
Number of ways to order job A = 2 ways.
Thus;
Total number of ways to order the jobs in the given order = 2 * 9!
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(x + a)(x + 3a) = x ^ 2 + bx + 75
(x+a)(x+3a)= x²+bx+75
x²+4a+3a²=x²+bx+75
by comparing 3a²=75 and b= 4a
a= ±5
possible values of b= ±20
Two possible values of b are 20 and -20.
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
Given that;
The mathematical expression as;
(x + a)(x + 3a) = x² + bx + 75
Now,
The mathematical expression is;
(x + a)(x + 3a) = x² + bx + 75
Solve the expression as;
(x + a)(x + 3a) = x² + bx + 75
x² + 3ax + ax + 3a² = x² + bx + 75
x² + 4ax + 3a² = x² + bx + 75
After comparison we get;
4a = b ... (i)
And, 3a² = 75 .. (ii)
Solve the second equation for a as;
3a² = 75
Divide by 3;
a² = 25
Take square root both side, we get;
a = ± 5
So, By equation (i) we get;
b = 4a
Substitute a = 5;
b = 4 x 5
b = 20
And, Substitute b = -5;
b = 4 x -5
b = -20
Thus, Two possible values of b are 20 and -20.
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What is .63 as a fraction
There are 973 dozen M&M's in a jar.
How many M&M's are in the jar?
Answer:
11,676 M&M's
Step-by-step explanation:
A dozen is 12
the problem is saying that in the jar, there are 973 (12-M&M's)
973 * 12 is 11676
There are 11,676 M&M's in the jar
Answer:
they are 11,676
Step-by-step explanation:
A dozen is 12 so since there are 973 dozen, we multiply by 12.
This table shows the number of points a high school basketball team scored during each of its last 10 games.
Which measure(s) of central tendency is most affected by the lowest score?
A. the mean
B. the median
C. the mode
D. both the mean and the median
The measure of central tendency that is most affected by the lowest score is; A: The mean.
How to find the measures of Central Tendency?
The points table is missing and so I have attached it.
The 3 main measures of central tendency are called mean, median and mode.
Now, from the table attached, if we find the average which is the mean, we will get 56.6.
Now, the mode is the number that occurs the most times. In this case, there is no mode because no number appears more than the other.
For the median, if we arrange in ascending order, we have;
42, 48, 49, 53, 55, 56, 58, 66, 68, 71.
The median = (55 + 56)/2 = 55.5
Now, if we remove the lowest score, the measure that will be most affected will be the mean as the median will only change by 0.5 to 56.
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Answer:
B
Step-by-step explanation:
What is the length of segment XZ?
Answer:
24 is the length of segment XZ
Find a possible formula for the trigonometric function represented by the given table of values. (enter your answer in the form y = a cos(bx − c) d or y = a sin(bx − c) d. )
A function assigns the values. The function will be 8cos(2x-π)+4.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the maximum value is 12, while the minimum value is -4, therefore,
A = (Max-Min)/2 = 12-(-4)/2 = 8
D = (Max+Min)/2 = (12-4)/2 = 4
Period=π, but since x =-4 at 0 or π, therefore,
(2π/B) = π
B = 2π/π = 2
C/B = π/2, {∴At π/2 maximum}
C=π
Hence, the function will be 8cos(2x-π)+4.
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A bag contains 4 blue balls, 7 yellow balls and 4 white balls. Event A is defined as drawing a blue ball on the first draw and event B is defined as drawing a white ball on the second draw. If two balls are drawn from the bag, one after the other and not replaced, what is P(B|A) expressed in simplest form? A. B. C. D.
P(B|A) expressed in simplest form is 8/105.
What is the probability?Probability determines the chances that an event would happen. The chance of the event happening lies between 0 and 1.
P(B|A) = (number of blue balls / total number of balls) x (number of white balls / total number of balls - 1 )
(4/15) x 4/14 = 8/105
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Ava earns 9.20 per hour for the first 6 hours she works each day then time and a half.
What is her pay if she works for 9 hours?
Decide whether quadrilateral ABCD with vertices 4(3,1), B(-1,-1) C(1,3), and D(5.5) is a rectangle, rhombus,square, or parallelogram.
Answer: rhombus
Step-by-step explanation:
By inspection, we can tell that there are no right angles, so we can determine it is not a square or a rectangle.
From the options, it is implied that it is a parallelogram, so to determine if it is a rhombus, we can determine if there is a pair of consecutive congruent sides.
By the distance formula,
[tex]AB=\sqrt{(-1-3)^{2}+(-1-1)^{2}}=\sqrt{16+4}=2\sqrt{5}\\BC=\sqrt{(-1-1)^{2}+(-1-3)^{2}}=\sqrt{4+16}=2\sqrt{5}[/tex]
As AB=BC, there is indeed a pair of consecutive congruent sides, and thus the most specific classification is a rhombus
Can a parabola have both a minimum and a maximum point? Explain.
Which of the following choices is a reference angle to θ = 225º?
30 degrees
45 degrees
60 degrees
90 degrees
Answer:
45 degrees
Step-by-step explanation:
A reference angle can be found by identifying its terminal side and see by what angle the terminal side is close to the x-axis.
To do this, we can subtract this given angle by the nearest 90° angle.
270° is the closest.
[tex]\textsf {Solving :}[/tex]
[tex]\implies \textsf{Reference angle = 270 - 225}[/tex]
[tex]\implies \textsf {45 degrees}[/tex]
The reference angle is the angle from the x-axis thus 45 degrees will be the reference angle to θ = 225°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
As per the given angle,
θ = 225°
It is going to the third quadrant as shown below,
The reference angle is the angle from x-axis.
The angle from the negative x-axis will be as,
180° + x = 225°
x = 225° - 180° = 45°
Hence "The reference angle is the angle from the x-axis thus 45 degrees will be the reference angle to θ = 225°".
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Find the value of x.
Round to the nearest tenth.
B
63
142°
61
A
C
X
x = [?
X
Law of Cosines: c² = a² + b² - 2ab cos C
The value of x in the triangle using the cosine rule is 22.1 degrees.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Cosine rule is used to show the relationship between the sides and angles of a triangle. It is given by:
c² = a² + b² - 2ab cos C
Where a, b, c are the sides and C is the angle opposite side c.
Using cosine rule:
8² = 14² + 19² - 2(14)(19) * cos(x)
cos(x) = 0.9267
x = 22.1°
The value of x in the triangle using the cosine rule is 22.1 degrees.
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Using the law of Cosines, the value of x to the nearest tenth is 77.8
Law of CosinesFrom the question, we are to determine the value of x
Using the law of Cosines
c² = a² + b² - 2ab cos C
c is the unknown side length
a and b are the given side lengths
and C is the included angle
From the given information,
a = 63
b = 62
C = 142°
Then,
x² = 63² + 61² -2×63×61 cos 142°
x² = 3969 + 3721 -7686(-0.788)
x² = 7690 + 6056.568
x² = 13746.569
x = √13746.569
x = 77.8
Hence, the value of x to the nearest tenth is 77.8
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What is the end behavior of the function f(x)=−1/4x^2?
Answer:
As x approaches infinity, f(x) approaches negative infinity
As x approaches negative infinity, f(x) approaches negative infinity
Step-by-step explanation:
Because the function goes in the downward direction on both sides, it would be negative infinity for both.
It's basically saying, as the x values go towards the positives, the y values go towards the negatives
and as the x values go towards the negatives, the y values go towards the negatives.
Please help is a choose al that apply
Answer:
Your answers are:
A, B and C
Step-by-step explanation:
So 12 over 3 is equal to 4 which is a Whole number. meaning Not a fraction, an Integer is a whole number (not a fractional number) that can be positive, negative, or zero. Rational numbers would include this example as well
Hope this helped have a wonderful day/night/afternoon
B Which of the statements is true about the polygons below E D 120 degrees C 90 90 60 60 120 degrees 90 90 F D Polygon A Polygon B A. It is possible to circumscribe a circle around each polygon because they are both quadrilaterals. B. It is not possible to circumscribe a circle about either polygon because they are both quadrilaterals. C. It is possible to circumscribe a circle about the parallelogram on the left only, because opposite angles must be supplementary D. It is possible to circumscribe a circle about the rectangle because its opposite angles are supplementary
Answer:
hope you can understand
Which of the following functions describes the graph of h(x)?
Answer:
2x+4/ x-1 C
Step-by-step explanation:
Because the y-intercept is -4
6. Find the principal value of each of the following to the nearest minute:
Arccsc (1.607)
A. 38°64
B. 39°24'
C. 38°48'
D. 38°32'
E. 39°37'
F. 38°29'
The principal value of Arccsc (1.607) to the nearest minute is 38°29'
To answer the question, we need to know what arccsc is
What is arccsc?Arccsc is the inverse of the cosec of an angle.
Let x = arccsc(1.607)
So, taking the inverse, we have
csc(x) = 1.607
Since csc(x) = 1/sinx, we have
1/sinx = 1.607
sinx = 1/1.607
sinx = 0.6223
The value of x
Taking inverse, we have
x = arcsin(0.6223)
x = 38.483°
Since 60' = 1°, we have
x = 38 + 0.483° × 60'/1°
x = 38° + 28.98'
x = 38°28.98'
x ≅ 38°29'
So, the principal value of Arccsc (1.607) to the nearest minute is 38°29'
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Use the drop-down menus to identify whether the mean, median, mode, and range are always, sometimes, or never one of the data values in a data set.
the mean is
choose...
one of the data values.
the median is
choose...
one of the data values.
the mode is
choose...
one of the data values.
the range is
choose...
one of the data values.
The information shows that:
The mean is sometimes of the data values.The median is sometimes one of the data values.The mode is always one or the data values.The range is sometimes one of the data values.What is a mean?It should be noted that the mean is the average of the numbers that are given.
The median is the number in the middle when they are arranged in ascending or descending order. The mode is the number that appears most.
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On the blue prints for a house, 2 inches represents 3 feet. If the width of a room on
the plan is 6½ inches, what is the actual width of the room?
Please help!!
Answer:
The actual width would be 9.75 feet. (I think).
Step-by-step explanation:
If two inches represents three feet, then two inches also represents thirty-six inches. You would then have to set up the proportion [tex]\frac{2}{36} = \frac{6.5}{x}[/tex]. Solving that proportion would get you an answer of 117 inches, equal to 9.75 feet. I hope this helps! :)
Which three ordered pairs describe points that are 5 units away from P(-1,2)?
A. (1,5)
B. (-6,7)
C. (-1,-3)
D. (4,2)
E. (2,-2)
The ordered pair that is 5 units away is (-1, -3)
What is a line?
A line is a distance between two points.
Analysis:
see attached file.
In conclusion, the ordered pair is (-1, -3)
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The table shows values for a quadratic function.
What is the average rate of change for this function for the interval from x = 1
to x = 3?
The average rate of change for this function for the interval from x = 1
to x = 3 will be 8. Therefore option B is correct.
How to find the average rate of change of something?Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:
[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where when
[tex]x = x_1, y = y_1\\and \\x = x_2, y = y_2[/tex]
The average rate of change can be calculated as;
From x=1 to x=3,
y = 2 and y = 18
Therefore, based on the table, when:
[tex]x_1 = 1 y_1 = 2 \\and \\x_2 = 3, y_2 = 18[/tex]
Then:
[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]\text{Average rate} = \dfrac{18 - 2}{3-1}\\\\\text{Average rate} = \dfrac{16}{2}\\\\\text{Average rate} = 8[/tex]
Therefore option B is correct.
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Find the sum of the cubes of first 15 natural numbers.
The sum of the cubes of first 15 natural numbers.
Solution:[tex]( \frac{(15 \times 16)}{2} {)}^{2} [/tex]
[tex] = (15 \times 8 {)}^{2} [/tex]
=14400
Hence, the sum of the cubes of first 15 natural numbers is 14400
anyone know the answer
Answer:
y=x+4
Step-by-step explanation:
pretty sure
10m−p=−n, for m
10m−p=−n, for m
10m−p=−n, for m
10m−p=−n, for m
Answer:
[tex]m=\dfrac{-n+p}{10}[/tex]
Step-by-step explanation:Solve for 'm'
To solve for 'm', we have to isolate 'm'.
First add p to both sides to cancel (-p) in the left side10m - p = -n
10m = -n + p
Now, divide the equation by the coefficient of 'm', which 10[tex]\sf\dfrac{10m}{m}=\dfrac{-n+p}{10}\\[/tex]
[tex]\sf \boxed{\bf m = \dfrac{-n+p}{10}}[/tex]
need help fast given lim x→c f(x) = "-4" and lim x→c g(f) =1/5 what is lim x→c [g(f)/f(x)]
Work Shown:
[tex]\displaystyle \lim_{x \to c}f(x) = -4\\\\\\\lim_{x \to c}g(x) = 1/5\\\\\\L = \lim_{x \to c}\frac{g(x)}{f(x)}\\\\\\L = \frac{\displaystyle \lim_{x \to c}(g(x))}{\displaystyle \lim_{x \to c}(f(x))}\\\\\\L = \frac{1/5}{-4}\\\\\\L = (1/5)*(-1/4)\\\\\\L = -1/20\\\\[/tex]
Put simply, we divide the two given values g(x) = 1/5 over f(x) = -4 to end up with -1/20