The prime factorization of 18 is 2 x 3², dividing 18 first by 2 and then by 3 twice.
Explanation:The prime factorization of a number represents that number written as the product of its prime factors. Let's take 18 as an example. First, we will find the smallest prime number that can divide 18, which is 2. When 18 is divided by 2, the quotient is 9. Then, we continue to divide 9 by the smallest possible prime number, which is 3. We can divide 9 by 3 two more times. Therefore, the prime factorization of 18 is 2 x 3², where 2 and 3 are the prime factors and ² is an exponent indicating that 3 is a factor twice.
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shirts are onsale at 3 for $15.50. how many shirts can you buy with $139.50.
First you take the $139.50 and divide it by $15.50
139.50 / 15.50 = 9
Then you take the 9 and multiply it by 3, be cause there are 3 shirts per $15.50
9 x 3 = 27
You can buy a total of 27 shirts with $139.50
what is 3x times x???
3 x squared:) hope this helps
Jon performs 3 transformations on a pentagon. First, he reflects it over the x-axis. Then, he translates it 3 units to the left and 4 units up. Finally, he reflects the image over the line x = 1. Are the original and transformed images congruent? Justify your answer.
yes; Reflections and translations are rigid motions. Rigid motions preserve the size of the original image.
Suppose N represents a power of 10. what is the value of n when 31,100 is rounded to the nearest power of 10?
We get the approximate value of [n] as 5.
What is logarithm? What is a mathematical equation and expression?A quantity representing the power to which a fixed number (the base) must be raised to produce a given number. We can write -[tex]$\log_{b}({b^x})=x[/tex]
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have 31,100 is rounded to the nearest power of 10 and [N] represents a power of 10.
We can write -
10ⁿ = 31100
10ⁿ = 311 x 10²
10ⁿ ⁻ ² = 311
log(10ⁿ ⁻ ²) = log(311)
(n - 2) log 10 = log (311)
n - 2 = log(311)/log(10)
n - 2 = 2.5
n = 4.5
n = 5 (approx.)
Therefore, we get the approximate value of [n] as 5.
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When rounding 31,100 to the nearest power of 10, we get the value of n is 4.
To find the value of n when 31,100 is rounded to the nearest power of 10, we first need to determine which powers of 10 are closest to 31,100. The nearest powers of 10 to 31,100 are 104 (10,000) and 105 (100,000). Since 31,100 is closer to 104 than to 105, we round it down to 104.
Therefore, when 31,100 is rounded to the nearest power of 10, the value of n is 4.
The process involves converting the number into scientific notation and then adjusting the exponent, which represents the number of places the decimal point moves. In our case, to convert 31,100 to a number between 1 and 10, we would express it as 3.11 × 104, confirming that the value of n is 4.
What is the middle term of the product of (x - 4)(x - 3)?
Answer:
The middle term of the product of (x - 4)(x - 3) is -7
Step-by-step explanation:
Consider the given expression (x - 4)(x - 3)
We have to find the middle term of the product of (x - 4)(x - 3).
First multiply the given terms, we get,
[tex](x - 4)(x - 3)=x(x-3)-4(x-3)[/tex]
Simplify, we get,
[tex]x(x-3)-4(x-3)=x^2-3x-4x+12[/tex]
Simplify further, we get,
[tex]x^2-3x-4x+12=x^2-7x+12[/tex]
Thus, the middle term of the product of (x - 4)(x - 3) is -7
Multiply the polynomials.
(x – 7)(x2 + 3x – 3)
A. x3 – 4x2 – 3x + 21
B. x3 – 7x2 – 24x + 21
C. x3 – 4x2 – 24x + 21
D. x3 – 7x2 – 3x + 21
Answer:
C) x³ -4x² - 24x + 21.
Step-by-step explanation:
Given : (x – 7)(x² + 3x – 3).
To find : Multiply the polynomials.
Solution : We have given (x – 7)(x² + 3x – 3).
Distributes x over (x² + 3x – 3) and -7 over (x² + 3x – 3).
Then
x (x² + 3x – 3) -7(x² + 3x – 3).
x³ + 3x² -3x - 7x² - 21x +21.
Combine like terms
x³ + 3x² - 7x² -3x -21x + 21.
x³ -4x² - 24x + 21.
Therefore, C) x³ -4x² - 24x + 21.
Answer:
x³ -4x² - 24x + 21.
Step-by-step explanation:
Ape-x
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What is the correct order of operations for simplifying the expression (x+3)^2-(x^2+9)/2x^2
The correct order of operations for simplifying the expression (x+3)^2 - [tex](x^2+9)/2x^2[/tex] is as follows:
1. Square the binomial (x+3) to get x^2 + 6x + 9.
2. Divide each term in (x^2+9) by [tex]2x^2[/tex] to get [tex]1/2 + 9/2x^2[/tex].
3. Substitute the simplified expressions back into the original expression: [tex]x^2 + 6x + 9 - (1/2 + 9/2x^2).[/tex]
The correct order of operations for simplifying the expression (x+3)^2 - (x^2+9)/2x^2 is as follows:
1. Start by simplifying the expression within the parentheses: (x+3)^2. This means squaring the binomial (x+3). To do this, you multiply the binomial by itself: (x+3) * (x+3). This results in [tex]x^2 + 6x + 9.[/tex]
2. Next, simplify the expression within the second set of parentheses: (x^2+9).
3. Now, divide [tex](x^2+9)[/tex] by 2x^2. To do this, divide each term in (x^2+9) by 2x^2. This gives us [tex](x^2/2x^2)[/tex] [tex]+ (9/2x^2)[/tex]. Simplifying further, we get 1/2 + [tex]9/2x^2[/tex].
4. Finally, substitute the simplified expressions back into the original expression: [tex]x^2 + 6x + 9 - (1/2 + 9/2x^2).[/tex]
Bill buys a red marble and a blue marble. If the total weight of 3 such red marbles and 2 such blue marbles is 84g, and the total weight of 12 such red marbles and 5 such blue marbles is 282g, what is weight of the red marble and the blue marble respectively?
Final answer:
The weight of the red marble is 16 grams, and the weight of the blue marble is 18 grams, based on the solution of the system of linear equations derived from the given total weights of the marbles.
Explanation:
To solve the problem of determining the weight of each marble, we can set up a system of linear equations based on the given information:
Let r be the weight of a red marble in grams.
Let b be the weight of a blue marble in grams.
The total weight of 3 red marbles and 2 blue marbles is 84g.
The total weight of 12 red marbles and 5 blue marbles is 282g.
Based on these statements, we can write two equations:
3r + 2b = 84 (1)
12r + 5b = 282 (2)
We can solve this system of equations by multiplying equation (1) by 4 to eliminate variable b.
(4)(3r + 2b) = (4)(84)
12r + 8b = 336 (3)
Subtract equation (2) from equation (3) to solve for r:
(12r + 8b) - (12r + 5b) = 336 - 282
3b = 54
b = 18 (weight of blue marble)
Substitute value of b in equation (1) to solve for r:
3r + 2(18) = 84
3r + 36 = 84
3r = 48
r = 16 (weight of red marble)
Therefore, the weight of the red marble is 16 grams and the weight of the blue marble is 18 grams.
A jacket is discounted 40% the jacket is now 38.70 dollars what was the original price
(5x^2+38x+18) divided (x+7) what is the quotient and the remainder
To determine the quotient and remainder for (5x^2+38x+18) divided by (x+7), polynomial long division must be used, involving dividing terms, multiplying and subtracting until the remainder is obtained.
Explanation:To find the quotient and remainder of the division of polynomials (5x2+38x+18) by (x+7), we can use polynomial long division.
Divide the first term of the dividend, 5x2, by the first term of the divisor, x, to get the first term of the quotient, which is 5x. Multiply the entire divisor (x+7) by 5x and subtract from the dividend. Bring down the next term from the dividend and repeat the process until there are no more terms to bring down. The last line after the subtraction will be the remainder.
By doing this, you will obtain the quotient and the specific remainder for this division.
The sum of two consecutive numbers is 131 .What are the two numbers ?
The sum of two consecutive numbers is 131. What are the two numbers?
Answer is provided in the image attached.
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Without graphing, classify the following system as independent, dependent, or inconsistent. y=-3x+4 and 6x+2y=8
a. independent
b. dependent
c. inconsistent
please help
Answer:
Dependent
Step-by-step explanation:
[tex]y=-3x+4[/tex] and [tex]6x+2y=8[/tex]
Lets solve the second equation for y and then substitute it in first equation
[tex]6x+2y=8[/tex]
Subtract 6x on both sides
[tex]2y=-6x+8[/tex]
Divide by 2 on both sides
[tex]y=-3x+4[/tex]
Now we plug it in first equation for y
[tex]-3x+4=-3x+4[/tex]
Add 3x on both sides
[tex]4=4[/tex]
Both sides are same, they are equal. the system has infinite solutions.
They are said to be dependent
the dimensions of a rectangle can be expressed as x-3 and x+8. If the area of the rectangle is 42 square feet. Find the dimensions of the rectangle.
The radius of this ball is 24 inches. Which equation gives the ball's surface area, in square inches?
Find the length of the hypotenuse of a right triangle whose legs are 5 and sqare root of 2
Answer:
The length of the hypotenuse is 3√3 units.
Step-by-step explanation:
It is given that the length of the legs of a right triangle are 5 units and √2 units.
According to the Pythagoras theorem, in a right angled triangle
[tex](hypotenuse)^2=(leg_1)^2+(leg_2)^2[/tex]
Substitute leg₁=5 and leg₂=√2 in the above formula.
[tex](hypotenuse)^2=(5)^2+(\sqrt{2})^2[/tex]
[tex](hypotenuse)^2=25+2[/tex]
[tex](hypotenuse)^2=27[/tex]
Taking square root both the sides.
[tex]hypotenuse=\sqrt{27}[/tex]
[tex]hypotenuse=3\sqrt{3}[/tex]
Therefore the length of the hypotenuse is 3√3 units.
Find the quotient of 3/5 and 9/10 . Express your answer in simplest form.
The quotient of 3/5 and 9/10 is the value obtained by dividing both values, Hence, the quotient of the division is 2/3
The numerator = 3/5 The denominator = 9/10The division operation can be expressed thus :
3/5 ÷ 9/10
Take the reciprocal of the denominator and change the sign to multiplication ;
Reciprocal of 9/10 = 10/9
Hence, we have ;
3/5 × 10/9 = 30/45
In simplest form ; 30/45 = 10/15 = 2/3Therefore, the quotient is 2/3
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What is the measure of ∠F, to the nearest degree?
44°
57°
71°
78°
Answer:
Option A. 44°
Step-by-step explanation:
In a given triangle FGH sides have been given as FG = 7 yards, FH = 6 yards, and GH = 5 yards.
We have to calculate the approximate value of ∠F.
We apply the cosine rule in the given triangle.
5² = 7² + 6² - 2×7×6×cosF
25 = 49 + 36 - 84× cosF
25 = 85 - 84 cosF
84cosF = 85 - 25 = 60
[tex]cosF=\frac{60}{84}=0.71428[/tex]
[tex]F=cos^{-1}( 0.71428) = 44.4[/tex]
F = 44°
Therefore option A. 44° is the correct answer.
Need help on this asap!!
Find the inverse function f^-1(x) for the given function f(x). f(x) =3x-8
Final answer:
To find the inverse of the function f(x) = 3x - 8, you swap x and y and solve for y, resulting in the inverse function f^-1(x) = (x + 8) / 3.
Explanation:
To find the inverse function f-1(x) for the given linear function f(x) = 3x - 8, we will follow these steps:
Replace f(x) with y: y = 3x - 8.
Swap x and y to make it x = 3y - 8.
Solve for y to get the inverse function.
Starting with x = 3y - 8, we add 8 to both sides to obtain x + 8 = 3y. Then, we divide both sides by 3 to isolate y, resulting in y = (x + 8) / 3. Therefore, the inverse function is f-1(x) = (x + 8) / 3.
How many of the first 1992 prime numbers have reciprocals less tahn 0.05?
Consider the multiple regression model with two regressors x1 and x2, where both variables are determinants of the dependent variable. when omitting x2 from the regression, there will be omitted variable bias for modifyingabove beta with caret 1:
a. if upper x 2 is measured in percentages.
b. only if upper x 2 is a dummy variable.
c. if upper x 1 and upper x 2 are correlated.
d. always.
Identify intervals on which the function is increasing, decreasing, or constant.
g(x) = 1 - (x - 7)^2
Select one:
a. Increasing: x < 7; decreasing: x > 7
b. Increasing: x < -7; decreasing: x > -7
c. Increasing: x > 1; decreasing: x < 1
d. Increasing: x < 1; decreasing: x > 1
Write an equation of the line with the given slope and containing the given point. write the equation in the slope-intercept form yequals=mxplus+b. slope negative 3−3; through (22,negative 10−10)
Solve for v in the formula v = u + 10t when u = 16 and t = 4. a. v = -22 c. v = 56 b. v = 3 d. v = 40
Drag and drop the symbols to enter the equation of the circle in standard form with center and radius given. Center (-8, -3), radius = 2 times the square root
please answer before 1:00
How do I factorise
6-42x
Answer:
[tex]6(-7x+1)[/tex]
Step-by-step explanation:
Given: The equation [tex]6-42x[/tex].
To find: Factorize the given equation.
Solution:
The given expression is:
[tex]6-42x[/tex]
which can be rewritten as:
[tex]-42x+6[/tex]
Upon solving the above expression and Taking 6 common from both the terms of the expression ,we get
[tex]6(-7x+1)[/tex]
which is the required factorized form of the given expression.
Please help, I need to turn in today
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A rectangle has a width of 3 cm and a length of 10 cm.
What is the effect on the perimeter when the dimensions are multiplied by 10?
A) The perimeter is increased by a factor of 10.
B) The perimeter is increased by a factor of 40.
C) The perimeter is increased by a factor of 100.
D) The perimeter is increased by a factor of 400.
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