We are given the following polynomial
\((x+3)(3x-1)(x-5)_{}\)Let us multiply and simplify the polynomial.
First, multiply any two parentheses and simplify
\((x+3)(3x-1)(x-5)_{}=(x\cdot3x+x\cdot-1+3\cdot3x+3\cdot-1)(x-5)_{}=(3x^2-x+9x-3)(x-5)=(3x^2+8x-3)(x-5)\)Now, multiply the remaining two parentheses
\((3x^2+8x-3)(x-5)=3x^2\cdot x+3x^2\cdot-5+8x\cdot x+8x\cdot-5-3\cdot x-3\cdot-5=3x^3-15x^2+8x^2-40x-3x+15=3x^3-7x^2-43x+15\)Therefore, the expanded polynomial is
\(3x^3-7x^2-43x+15\)The price of an item has dropped to 27$ today. Yesterday it was 90. Find the percentage decrease
The percentage decrease would be 70 percent.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
The price of an item has dropped to 27$ today. Yesterday it was 90.
90 - 27 = 63
The percentage decrease;
63 / 90 x 100= 70%
Hence, The percentage decrease would be 70 percent.
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round 427963 to the nearest thousand
Answer:
428,000
Step-by-step explanation:
427,963
If the number behind what number you're trying to round is greater than 4 then the number you're rounding goes up once while everything behind it goes to zero. If it's below 5 than the it well stay the same. Ex. Round nearest tenth--> 14--->10 instead of it going up to 20 it stays 10.
427,963
^
This number is higher than 4 so the number in front or the thousand mark goes up a number.
428,000
Someone else already answered so I figured I'll tell you how to round it, hope this helps.
A tune up automotive facility marks up its part by 25% suppose that the facility charges its customers $1.75 for each spark plug it's sells which is the facility cost for each spark plug?
Answer:
$1.4
Step-by-step explanation:
wat factor of 26 is between 4 and 26
Answer:
13
Step-by-step explanation:
cos 13 x 2 = 26
13 is a factor that is more than 4 and less then 26
The factor of the number 26 that is between 4 and 26 is 13. Factors are the numbers that can divide into a number without leaving a remainder. In this case, the factors of 26 are 1, 2, 13, and 26.
Explanation:In mathematics, a factor of a number is a number that divides into another number without leaving a remainder. In the case of the number 26, its factors include 1, 2, 13, and 26. The factor of 26 that is between 4 and 26 is 13.
To find this, you can go through the factors of 26 one by one. The factors are found by dividing 26 by all the numbers up to 26, and the numbers that give a remainder of 0 are the factors. In this case, 1, 2, 13, and 26 divide evenly into 26, and so are the factors of 26. Of these, only 13 lies between 4 and 26.
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What is an equation of the line that passes through the points (-7, 7) and (3, 7)(
Answer:
y=7
Step-by-step explanation:
The slope is (7-7)/(3+7) = 0. So, the line is a horizontal line.
The y value of both points is 7.
PLEASE HELP WITH THIS ONE QUESTION
6 / 3/5 ITS FOR A 20 PIONT
Answer:
10
Step-by-step explanation:
I'm guessing you meant this, but tell me if I'm wrong and I'll fix it
6 / (3/5)
6 * 5/3
30/3
=10
Hope it helped!
Answer:
thanks
Step-by-step explanation:
Select the 3 options below that are equal in value. For example, if one of the terms
equals 0.85, so do the other two.
sample size
area under the curve
proportion
probability
One of the terms equals 0.85, so do the other two:
sample size
proportion
probability
How can sample size be determined?
to calculate the sample size in five easy steps
Define population size or total population.Indicate your error margin.You should assess your level of confidence.Calculate the anticipated variance.finalize the size of your sampleCalculating sample size requires knowledge of or estimation of three or four factors:
the effect size (often the difference between two groups); the population standard deviation (for continuous data); the required power of the experiment to detect the supposed effect; the significance threshold.To learn more about sample size refer to:
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linearise cos^5(x). Help asap please
use exponential
Answer:
Step-by-step explanation:
To linearize the function cos^5(x), we can use the following identity:
cos^5(x) = (cos^2(x))^2 * cos(x) = (1 - sin^2(x))^2 * cos(x)
Now, we can use the identity e^(ix) = cos(x) + i sin(x) to rewrite the expression as follows:
(1 - sin^2(x))^2 * cos(x) = ((1 - e^(ix) * e^(-ix))/2)^2 * (e^(ix) + e^(-ix))/2
= (1/16) * (e^(4ix) - 4e^(2ix) + 6 - 4e^(-2ix) + e^(-4ix))
This expression is now linear in terms of e^(ix) and e^(-ix). Therefore, we have linearized the function cos^5(x) as:
(1/16) * (e^(4ix) - 4e^(2ix) + 6 - 4e^(-2ix) + e^(-4ix))
Find the rank of the matrix [
2 − 1 − 3 − 1
1 2 3 − 1
1 0 1 1
0 1 1 − 1
]
The rank of the matrix is 3, since there are three linearly independent rows.
The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.
To find the rank of the matrix:
[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]
We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.
\(R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2\)
This gives us the following matrix:
[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]
We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.
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Geometry need help asap
On solving the provided question, we can say that - here in quadrilateral we have x + 146 + 47 + y = 360 => \(x= 83.5\)
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
here,
x + 146 + 47 + y = 360
2x + 193 = 360
2x = 167
\(x= 83.5\)
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hbgvfcdbfvnhjmkhbgtfr
Answer:
C
Step-by-step explanation:
84 - (15+13)/4
84 - 28/4
56/4
14
Answer:
14
Step-by-step explanation:
84-(15+13)
84-(28)=56
56/4 = 14
FIRST TO ANSWER CORRECTLY GETS BRAINLIEST
Answer:
d
Step-by-step explanation:
2*4.5=9
scale1:30
=9*30 =270
Convert to actual scale based on proportion of 1:30
4.5 x 30 = 135 inches
2 x 30 = 60 inches
135 x 60 = 8100 inches^2 though we need this in feet and because we solved for area we need to divide by 12in^2*12in*^2
8100/144 = 56.25 or roughly 56 ft^2
I hope this helps! Let me know if you have any questions. Have a very nice day/night :).
order of operations (pemdas) question (8 + 7) ÷ 3
Answer:
Step-by-step explanation:
(8 + 7) ÷ 3
15 ÷ 3
= 3
Lauren hiked 16,900 feetin the morning and 14850 feet in the afternoon. Estimate the total number of miles Lauren hiked that day.
Answer: 6 miles!
Step-by-step explanation:
There are 5280 ft in a mile (you can remember this by saying five to-mat-os haha). In total, Lauren walked 16,900+14,850= 31,750 ft. To find how many miles she hiked you would simply divide by 5,280. I plugged this division problem into my calculator and got about 6 miles.
you can continue to tranform 12=5x-3 into simpler form by adding 3 to both sides to get 15=5x when x =3 do youu get true statement
Answer:
yes
Step-by-step explanation:
12+3=5x-3+3
15=5x
15=5(3)
15=15
what is the solution: y=x and y=-x+4
Answer:
(2, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Coordinates (x, y)Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = x
y = -x + 4
Step 2: Solve for x
Substitution
Substitute in y: x = -x + 4[Addition Property of Equality] Add x on both sides: 2x = 4[Division Property of Equality] Divide 2 on both sides: x = 2Step 3: Solve for y
Define original equation: y = xSubstitute in x: y = 2Find the value of n in each of the following proportions.
1. 18/n = 21/28
2. 12/16 = n/64
Answer:
24
Step-by-step explanation:
18/n = 21/28 You can cancel, but calculators make that unnecessary. Cross multiply
21n = 18 * 28
21n = 504 Divide by 21
n = 504 / 21
n = 24
==================
12/16 = n / 64 Cross Multiply
16n = 12 * 64
16n = 768 Divide by 16
n = 768/16
n = 48
HELP ME!!!!
ZEARN!!!!!!!!!
A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.
Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.
Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.
Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of
To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).
First, let's convert the fractions 1/5 and 2/3 to fifteenths:
\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)
\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)
Now we can rewrite the expression using the common denominator:
\(3 + \frac{3}{15}+\frac{10}{15}\)
x/3-1/2=5/6 solve for the variable
Answer:
4/3 - 1/2= 5/6 hope this helped
Try These questions out and I’ll give you brainliest
The expressions are simplified to;
1. 72n² + 63n
2. 18t - 18t²
3. -18b² - 18b
4. -56r - 21r²
5. -6m + 9m²
What are algebraic expressions?Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.
These algebraic expressions are also made up of mathematical or arithmetic operations.
These operations are;
BracketParenthesesAdditionMultiplicationDivisionSubtractionFrom the information given, we have;
1. -9n (-8n -7)
expand the bracket
72n² + 63n
2. -2t(-9 + 9t)
expand the bracket
18t - 18t²
3. -3b(6b + 6)
expand the bracket
-18b² - 18b
4. -7r(8 + 3r)
expand the bracket
-56r - 21r²
5. 3m(-2 + 3m)
expand the bracket
-6m + 9m²
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Differentiate the following four levels of measurement and give an example of each: nominal, ordinal, interval and ratio.
-Nominal: a level of measurement describing a variable that has attributes that are merely different, as distinguished from ordinal, interval, or ratio measures. Gender is an example.
-Ordinal: a level of measurement describing a variable with attributes we can rank-order along some dimension. An example is socioeconomic status as composed of the attributes high, medium, and low.
-Interval: a level of measurement describing a variable whose attributes are rank-ordered and have equal distances between adjacent attributes. There is however, no "true" zero point. Like the difference in temperature.
-Ratio: a level of measurement describing a variable with attributes that have all the qualities of nominal, ordinal, and interval measures and in addition are based on a "true zero" point. Ex. Number of children you have, makes sense to have a zero
The process of associating numbers with physical quantities and phenomena. Measurement is used in our day-to-day life
Nominal: A level of measurement describing a variable that has attributes that are merely different, as distinguished from ordinal, interval, or ratio measures.
Gender is an example.
Ordinal: A level of measurement describing a variable with attributes we can rank-order along some dimension.
An example is socioeconomic status as composed of the attributes high, medium, and low.
Interval: A level of measurement describing a variable whose attributes are rank-ordered and have equal distances between adjacent attributes. There is however, no "true" zero point. Like the difference in temperature. An example will be the measuring temperature.
Ratio: A level of measurement describing a variable with attributes that have all the qualities of nominal, ordinal, and interval measures and in addition are based on a true zero point. An example will be Number of children you have, makes sense to have a zero
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Write an equation of the line that passes through (-3, 3) and is perpendicular to the line 2y = 8x - 6.
Answer:
2y = 8x - 6
2y/2 = 8x/2 - 6/2
y = 4x - 3
y = -1/4x + 389.80 divided 4 plz help٩(๑❛ᴗ❛๑)۶
Answer:
22.45
Step-by-step explanation:
Answer:
89.80 divided by 4 is 22.45
Step-by-step explanation:
im just cool
Sara receives a 10% commission on the first $4000 in sales and 15% on all sales beyond $4000. If Sara receives a commission of $2530, how much did she sell?
Answer:
Step-by-step explanation:
$4000(0.10) = $400
which is less than her paid commission
so we know that she sold more than $4000 worth
if s is sales above $4000
$2530 = 400 + 0.15s
$2130 = 0.15s
s = $14200
so total sales x is
x = $4000 + $14200 = $18200
How do you subtract a fraction?
Answer: It's easy.
Step-by-step explanation: When the denominators of the two fractions you're subtracting are the same, in your answer they should also stay the same. Just subtract the numerators [top numbers].
When the denominators are not the same, if you can simplify the denominators so they can be the same number, do it.
For example: 2/4 - 1/2
Change 2/4 to 1/2 so that the equation turns into 1/2 - 1/2.
heidi claims that the prime viewing plan is the most expensive without purchasing additional movies. do you agree or disagree with heidi's claim?
Answer:
disagree
Step-by-step explanation:
purchasing extra movies = spend more money
Answer:
agree
Step-by-step explanation:
For a population with a mean of f = 40 and σ= 12, find the z-score for each of the following
X values.
X = 45: z =
X = 52: z =
X = 41: z =
X = 30: z =
X = 25: z =
X = 38: z =
The z-scores for the given X values are approximately:
X = 45: z ≈ 0.4167
X = 52: z = 1
X = 41: z ≈ 0.0833
X = 30: z ≈ -0.8333
X = 25: z ≈ -1.25
X = 38: z ≈ -0.1667
To find the z-score for each X value given a population with a mean (μ) of 40 and a standard deviation (σ) of 12, we can use the formula:
z = (X - μ) / σ
where X is the given value, μ is the population mean, and σ is the population standard deviation.
Let's calculate the z-scores for each X value:
X = 45:
z = (45 - 40) / 12 = 5 / 12 ≈ 0.4167
X = 52:
z = (52 - 40) / 12 = 12 / 12 = 1
X = 41:
z = (41 - 40) / 12 = 1 / 12 ≈ 0.0833
X = 30:
z = (30 - 40) / 12 = -10 / 12 ≈ -0.8333
X = 25:
z = (25 - 40) / 12 = -15 / 12 ≈ -1.25
X = 38:
z = (38 - 40) / 12 = -2 / 12 ≈ -0.1667
Therefore, the z-scores for the given X values are approximately:
X = 45: z ≈ 0.4167
X = 52: z = 1
X = 41: z ≈ 0.0833
X = 30: z ≈ -0.8333
X = 25: z ≈ -1.25
X = 38: z ≈ -0.1667
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if ⅚ of a certain number is -6⅔. what is the number?
The answer would be -3 4/3
Step-by-step explanation:
ok ok ok ok I'm very sorry if i get it wrong at least I tried on this app most of the people don't even do the homework they do it to cheat.
Answer:
Dan and Paul share some money in the ratio 13:5.
Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1.
How much did Paul originally have
URGENT! PLEASE HELP!
Answer:
Let's define the East as the x-axis, and the North as the y-axis
Now we can write the speed of the plane as:
(Vx, Vy)
Such that the total velocity of the plane is 350mph
This means that, if the plane flies at an angle of A degrees from the East, then:
Vx = 350mph*cos(A)
Vy = 350mph*sin(A)
We know that the speed of the wind is 65mph at 43° North from East.
This velocity, (Wx, Wy), can be written in components as:
Wx = 65mph*cos(43°) = 47.54 mph
Wy = 65mph*sin(43°) = 44.33 mph
Now, when the plane flies with the wind, the velocity of the plane will be equal to the velocity of the plane plus the velocity of the wind.
This is:
Velocity = (Vx, Vy) + (Wx, Wy) = (Vx + Wx, Vy + Wy)
The plane wants to keep going to the East, then the y-component must vanish (remember that the y-component is the one associated with the North)
Then we must have that:
Vy + Wy = 0
replacing the correspondent values, we have:
350mph*sin(A) + 44.33 mph = 0
350mph*sin(A) = -44.33 mph
Sin(A) = -44.33 mph/350mph
A = Arcsin(-44.33 mph/350mph) = -7.27°
This means that the plane must fly at -7.27° degrees North of East (Or 7.27° South of East)
That is the direction at which the plane must fly.