The prime factorization of the number 126 is 2,3,3, and 7.
What is prime factorization?Any number can be represented as a sum of prime numbers by prime factorization. A number with exactly two factors, 1 and the number itself, is said to be a prime number. As an illustration, the prime factorization of 18 is 2,3, and 3.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the number is 126. The prime factorization of the number 126 will be calculated as:-
126 = 2 x 3 x 3 x 7
Hence, the prime factorization of the number 126 is 2,3,3, and 7.
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A painting crew bought 30 gal of paint for a job. The crew members used 3 gal of paint per hour until they used all the paint.
Which sketch represents this situation?
If the crew members used 3 gal of paint per hour and bought 30 gal of paint for a job, then they will work 30:3=10 hours.
They start at x=0 hours with y=30 gal of paint;They end at x=10 hours with y=0 gal of paint (they worked until they used all the paint).The dependence between x and y is linear.Conclusion: the only possible sketch is A.
Answer: correct choice is A.
How do you use the half angle formula for
sin (5π/12)?
To determine sin(5π/12) using the half-angle formula, we establish a known cos value for the double of the angle, i.e., cos(5π/6)=-√3/2. Substituting it into the half-angle sin formula: Sin(5π/12)=±√{(1+√3/2)/2}. Simplifying gives Sin(5π/12)=√{3+√3/4}.
Explanation:The half angle formula for sine is given by:
Sin(x/2) = ±√{(1 - cos x) / 2}
To solve for sin(5π/12) using the half angle formula, we would look for an angle whose double is easily recognized in terms of standard angles (multiples of 30° or 45°). Luckily, the double of 5π/12 is 5π/6, a recognizable angle, and we know that cos(5π/6) = -√3/2.
Step 1: Substitute cos x value (-√3/2) into the formula:
Sin(5π/12) = √{(1 - (-√3/2 )) / 2}
Step 2: Simplify the expression inside the square root:
Sin(5π/12) = √{(1 + √3 / 2) / 2}
Step 3: Calculate the square root:
Sin(5π/12) = ± √{3 + √3 / 4}
Usually, we choose the positive root for a result in the first or second quadrant and the negative root for a result in the third or fourth quadrant. Since the angle 5π/12 is in the first quadrant, we choose the positive root:
Sin(5π/12) = √{3 + √3 / 4}
So, sin(5π/12) using the half angle formula is √{3 + √3 / 4}.
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What is 9 x ( 3 x 5 ) = ( 9 x n ) x 5?
Answer:
n=3
Step-by-step explanation:
You purchase a home for $125,000. The value of the property increases by 1.9% every year. After ten years, you decide to sell the home. In the meantime, you have made renovations and improvements to the house which increase its sale value by $48,300. How much will you sell the house for, to the nearest hundred dollars?
We can use the formula:
F = P · ( 1 + i )^n
where: P = $125,000, i = 0.019 ( 1.9 %), n = 10
F = $125,000 · ( 1 + 0.019 )^10
F = $125,000 · 1.019^10
F = $125,000 · 1.207096
F = $150,887
And we have to add $48,3000 ( for renovations and improvements )
$150,887 + $48,300 = $199,187 ≈ $199,200
Answer: You will be sell the house for $199,200.
Answer:
$199,200
Step-by-step explanation:
What is the additive inverse of the polynomial 9xy^2 + 6x^2y – 5x^3?
A.9xy2 – 6x2y + 5x3
B. 9xy2 – 6x2y – 5x3
C. 9xy2 + 6x2y + 5x3
D. 9xy2 – 6x2y + 5x3
Answer:
The answer is B.
Step-by-step explanation:
The additive inverse of the given polynomial is:
-9xy^2 - 6x^2y + 5x^3
How to find the additive inverse of a polynomial?The additive inverse of a polynomial would be another polynomial, such that when we add the two, the outcome is zero.
For a given polynomial the additive inverse is given by multiplying the given polynomial by -1.
Here we have:
p(x) = 9xy^2 + 6x^2y – 5x^3
Then the additive inverse is:
q(x) = -p(x) = -9xy^2 - 6x^2y + 5x^3
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HELP ASAP!!!
The markup on candy at the discount store is 45%. A bag of candy has a wholesale cost of $1.15. What will be the retail price for the candy?
A. $1.45
B. $1.60
C. $1.67
D. $1.78
Answer:
Option C. $1.67
Step-by-step explanation:
The price of a bag of candy at wholesale = $1.15
The markup on candy at the discount store = 45%
The retail price for the candy = 1.15 +(45% × 1.15)
= 1.15 + ([tex]\frac{45}{100}[/tex]×1.15)
= 1.15 + (0.45 × 1.15)
= 1.15 + 0.5175
= 1.6675 ≈ $1.67
The retail price for the candy would be $1.67.
Four milliliters of ink A is added to 10 milliliters of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B contains an unknown percentage of blue pigment. The mixture of the two inks contains 35% blue pigment.
What percentage of blue pigment is in the mixture of the two inks?
45%
49%
60%
75%
Answer:
45%
Step-by-step explanation:
I took the test!
Witch Decimal is equal to six-tenths?
0.6 0.15 0.2 0.3 0.4
The Sky High Ski Club dues are $450 per season. This fee includes transportation to and from the slopes and lift tickets. Skis cost $159.90, boots $78.25, and poles $19. What is the total cost?
Answer:
The total cost is $707.15.
Step-by-step explanation:
The Sky High Club dues are = $450 per person
and the Skis costs = $159.90
Cost for boots = $78.25
Cost of poles = $19.00
To find the total cost we will add all the amounts.
Total cost = 450 + 159.90 + 78.25 + 19.00
= $707.15
The total cost is $707.15.
10. Mr. Falcone's pizza shop offers three sizes of pizza. The small, medium and large pizzas have diameters of 8 inches, 10 inches and 12 inches. Small Medium Large a) What is the circumference of each size of pizza? Small = _________________ Medium = ___________________ b) What is the area of each size of pizza? Small = _________________ Medium = _________________ Large = _______________ Large = _________________ c) Joey is very hungry. He says he wants to eat a 100-square-inch area of pizza. Which size(s) of pizza should he order? Why?
Answer:
Step-by-step explanation:The employees must sell 78 pizzas in order to get the bonus.
The percentage decrease is 0.05%
Step-by-step explanation:
Number of pizzas sold yesterday is 65 pizzas.
The owner offers the employees a bonus if the number of pizzas sold increases by 20%
So 20% of 65 pizzas is, pizzas.
Therefore, the employees must sell 65+13=78 pizzas in order to get the bonus.
But the actual number of pizzas sold today was 60. So the number of pizza sold has decreased. Then the percent decrease is,
Therefore, the percentage decrease
which of the following comparisons is false 4 liters< 1 gallon, 1 foot< 1 meter, 25 grams< 1 ounce, 10 kilometer< 9 miles
At a pet show, the ratio of dogs to cats is 4:3. if the number of cats is 45, find the number of dogs at the show.answer:
The number of dogs would be 60 when the ratio of dogs to cats is 4:3.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
Given that the ratio of dogs to cats is 4:3. if the number of cats is 45
We have to determine the number of dogs.
Let the number of dogs would be x
As per the given condition, we can write a proportion as
4 dogs : 3 cats = x : 45 cats
⇒ 4 / 3 = x / 45
Apply the cross-multiplication operation,
⇒ 45 × 4 = x × 3
⇒ x = (45 × 4)/3
⇒ x = 15 × 4
⇒ x = 60
Therefore, the number of dogs would be 60.
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Create a trinomial that can be factored and write it in standard form.
To create a trinomial, use a basic factored form like (x+a)(x+b), and expand this via the distributive property. This yields as an example x²+8x+15, a trinomial in standard form.
Explanation:To create a trinomial that can be factored and to write it in standard form, we need to consider a basic factored form first. Let's use (x+a)(x+b) as our basic factored form. In this form, 'a' and 'b' are the roots of the trinomial.
To create the trinomial, we then expand this expression by using the distributive property: (x+a)(x+b) = x² + bx + ax + ab, which simplifies to x² + (a+b)x + ab. This is now our trinomial in standard form.
Let's take a concrete example. If we let 'a' be 3 and 'b' be 5, our factored form is (x+3)(x+5). Expanding this, we get x² + 5x + 3x + 15, which simplifies to x² + 8x + 15. Thus, x² + 8x + 15 is a trinomial that can be factored and is written in standard form.
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How much of the circle is shaded? Write your answer with as a simplified fraction, with an explanation. Thank you.
What is the value of the expression when a = 5 and b = 2? a 2b−3
Which is the most accurate name for the polygon shown?
concave pentagon
convex pentagon
concave hexagon
convex hexagon
becky works 16 days each month.how many days will she work in 6 months
Becky will work 96 days in 6 months.
Explanation:To find out the number of days Becky will work in 6 months, we need to multiply the number of days she works each month by the number of months. Given that Becky works 16 days each month, we can calculate the number of days she will work in 6 months as follows:
Number of days Becky works each month = 16Number of months = 6Number of days Becky will work in 6 months = 16 days/month * 6 months = 96 daysLearn more about number of days worked here:
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FIRST ANSWER IS BRAINIEST QUICKKK FIRST ANSWER IS BRAINIEST QUICKKK FIRST ANSWER IS BRAINIEST QUICKKK
What is the equation in point slope form of the line that passes through the point (1, –2) and has a slope of 3?
y−2=3(x+1)
y+2=3(x−1)
y+1=3(x−2)
y−1=3(x+2)
To get to work, matt walks 0.75 miles from his house to the bus stop and rides the bus 3.8 miles to his office. if he walks at a pace of 3.6 miles per hour and the bus drives at an average speed of 15 miles per hour, how long is his commute?
The diagonals of a rhombus divide it into four triangles of equal area.
True
False
Answer:
True
Step-by-step explanation:
The altitude dropped to the base of an isosceles triangle is a median, an angle-bisector, and a perpendicular bisector?
True
False ...?
The triangle PQR shown on the coordinate grid below is reflected once to map onto triangle P´Q´R´.
If vertex P’ is at (7, -6), what are the coordinates of vertex R’?
A)(5, -3)
B)(3, -5)
C) (3, -2)
D)(5, -2)
The answer is (5,-2)
To find the coordinates of vertex R' in the reflected triangle, we can use the midpoint formula. Using the given point P' at (7, -6) and the original point P at (x, y), the x-coordinate of vertex R' is 5. Similarly, using the given point P' at (7, -6) and the original point R at (x, y), the y-coordinate of vertex R' is -2.
Explanation:To find the coordinates of vertex R', we need to map the reflection of triangle PQR onto triangle P'Q'R'. Since vertex P' is at (7, -6), we can use the midpoint formula to find the coordinates of the reflected point R'.
The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints.
Using the given point P' at (7, -6) and the original point P at (x, y), we can write the equation:
(x + 7) / 2 = 7
Solving for x, we get x = 5.
Similarly, using the given point P' at (7, -6) and the original point R at (x, y), we can write the equation:
(y - 6) / 2 = -2
Solving for y, we get y = -2.
Therefore, the coordinates of vertex R' are (5, -2).
What is 43/50 as a percent?
Choose the words or phrases that best complete the sentences.
A fifth degree polynomial (could or must) have 5 linear factors. The factors (could, but do not have to be, or must) be distinct.
Answer: A fifth degree polynomial could have 5 linear factors. But the factors do not have to be be distinct.
Step-by-step explanation:
The fundamental theorem of algebra tells that every non-constant single-variable polynomial with complex coefficients has at least one complex root.Corollary to the fundamental theorem tells that every polynomial of m>0 degree has exactly m zeroes.Thus by corollary to fundamental theorem of algebra, a fifth degree polynomial must have 5 zeroes . But A fifth degree polynomial could have 5 linear factors if all zeroes are real numbers.
The factors could be distinct or similar.
Thus , The factors do not have to be distinct .
Rock music accounted for 30.5% of the total sales of recorded music in 1999 , and 20.4% of the total sales of recorded music in 2009 . Find the average rate of change of the percentage of sales of rock music from 1999 to 2009 .
Round to the nearest hundredth of a percent. Note that the percentage sign is already given in the answer, so you do not need to enter it.
The average rate of change is
Integrate (2 ln x)/x ...?
**PLEASE HELP??? ****STUCK ON THIS!!!!
Suppose that f(w) varies inversely with w and f(w) = 0.75 when w= 8.
What is f(w) when w= 2?
A.) 12
B.) 6
C.) 3
D.) 1.5
My answer choice is C.) 3. I'm not very confident in my answer so..... :/
Answer:
C.3
Step-by-step explanation:
We are given that
f(w) varies inversely with w.
f(w)=0.75 when w=8
We have to find the value of f(w) when w=2
According to question
[tex]f(w)\propto\frac{1}{w}[/tex]
[tex]f(w)=\frac{k}{w}[/tex]
Where k=proportionality constant
Substitute the given values then, we get
[tex]0.75=\frac{k}{8}[/tex]
[tex]k=0.75\times 8[/tex]
[tex]k=6[/tex]
Substitute the value of k then, we get
[tex]f(w)=\frac{6}{w}[/tex]
Substitute the value of w=2
Then, we get
[tex]f(w)=\frac{6}{2}=3[/tex]
[tex]f(w)=3[/tex]
Hence, option C is true.
When point E (-9, 3) is rotated 180� about the origin, its coordinate becomes (3, 9).
True
False
...?
solve for x. 27^(2x)=9^(x-3) ...?
The length of a rectangle is five centimeters more than its width w if the perimeter of the rectangle is 26 centimeters what is the area of the rectangle i'm square centimeters