The simplified form of the expression 6! − 3! when it is simplify using the properties of factorial is 3!((6x5x4) − 1).
What is the simplified form of a term?Simplified form of a term is the simplest way of expression the term, which is obtained by applying the required operations of mathematics.
Factorial is the way to write the product of the numbers from its phase value to 1 in decreasing order. Suppose, the number is 3!. Then it can be written as,
3!=3×2×1
The expression which has to be simplified is,
6! - 3!
It can be written as,
6! - 3!
(6×5×4×3!)-3!
3!((6×5×4)-1)
Thus, the simplified form of the expression 6! − 3! when it is simplify using the properties of factorial is 3!((6x5x4) − 1).
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[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6! - 3!}\\\mathsf{\approx 6(5)(4)(3)(2)(1) - 3(2)(1)}\\\mathsf{\approx 30(4)(3)(2)(1)- 6(1)}\\\mathsf{\approx 120(3)(2)(1) - 6}\\\mathsf{\approx 360(2)(1) - 6}\\\mathsf{\approx 720(1) - 6}\\\mathsf{\approx 720 - 6}\\\mathsf{\approx 714}\\\mathsf{\approx 3!((6\times5\times4) - 1)}[/tex]
[tex]\huge\text{Answer: \boxed{\mathsf{3!((6\times5\times4) - 1)}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
(1+5²) –16 (1/2)³
Please help please and Thank you
Answer:
the answer simplified is 24
Step-by-step explanation:
3(2x + 8) = 0 what is x
Answer: Heyaa!
The Answer, x= −4
Step-by-step explanation:
Divide both sides by the numeric factor on the left side, then solve.
Hopefully this helps you~
- Matthew :)
have an amazing day <3
Answer:
X = - 4
Step-by-step explanation:
3(2x+8) =0
6x + 24 = 0
6x = 0 - 24
6x = - 24
X = - 24/6
X = - 4
Hope this helpssssss
Find the area of this circle. Use
3.14 for i.
72 in.
..
in.2
The area of the circle is about
(Round to the nearest hundredth as needed.)
Answer:
4,069.44 in squared
Step-by-step explanation:
pir^2
72/2 = 36
36^2 = 1,296pi
1,296*3.14 = 4,069.44
Miriam has 2 yellow tea cups and 5 brown teacups. Which ratio compares the number of brown tea cups to the total number of teacups?
A. 5:2
B. 2 to 7
C. 5 to 7
D. 2/5
F. 5:7
D. 5/7
The answer is 5:2 ration, it's already fully simplified
50 points for whoever could someone please assist me with this question
The first step to the proof is ∠QRS + ∠STQ = 180°
What is a cyclic Quadrilateral?A cyclic quadrilateral is a quadrilateral circumscribed by a circle in which all the vertices of the quadrilateral touch the circle.
Analysis:
Join line Qx and Sx together.
2∠QRS = reflex ∠QxS ( twice angle at the circumference is that at center)
2∠STQ = ∠QxS( twice angle at circumference is that at the center)
Also ∠QXS + reflex ∠QXS = 360(angle at a point)
2∠QRS + 2∠STQ = 360
2(∠QRS + ∠STQ) = 360
∠QRS + ∠STQ = 180°
In conclusion, ∠QRS + ∠STQ = 180°
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Kelsey had $65 to spend on books. Each book cost $5.50, and there was a $7.50 fee for shipping. She let b equal the number of books she can purchase and wrote the inequality 5.50 b + 7.5 less-than 65 to represent the situation. Which statements describe the reasoning used to determine if Kelsey’s inequality is correct? Select two options. The inequality symbol is correct because she must spend less than $65. The inequality symbol is incorrect because she can spend up to and including $65. The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price. The expression 5.50b + 7.5 is incorrect because $5.50 per book and $7.50 should be combined to $9.50b to determine the total purchase price. The inequality symbol is correct because she cannot spend more than $65. PLS NEED ASAP!!
Answer: Kelsey had $65 to spend on books. Each book cost $5.50, and there was a $7.50 fee for shipping. She let b equal the number of books she can purchase
Step-by-step explanation:
Answer:
its B and C
Step-by-step explanation:
Select the correct answer.
Which statement describes a relationship between these equations?
equation 1: y= 3x - 7
equation 2: y=-4x-7
O A.
The equations have the same y-intercept.
B.
The equations have the same slope.
OC.
Each equation represents a line that decreases from left to right.
OD.
Each equation represents a line that increases from left to right.
Answer:
A. Yes they do. Both equations have their opposing set of y-intercept. Where equation one has a y-intercept of +7, and equation two, +7.
B. No they do not. Equation one has a slope of +3, while equation 2 has a slope of -4.
C. Yes they do. Equation one represents that of a positive increasing graph, while equation two the opposite, decreasing.
Step-by-step explanation:
You can use the slope formula to identify and graph each equation simply by using y = mx + b. Where y is the the y coordinate, x is the x coordinate, m is the slope, and b is the y-intercept. With this you can start plotting by marking the y-intercept by putting the x as zero and seeing what number you get. In this case, 3x0-7 = -7. Meaning that would be the y-intercept. For the slope, depending on what the x coordinate is, that's how much the graph will increase or decrease whenever the x coordinate changes. Say the x coordinate is 1, so 3x1-7 = 3-7 = -4. Meaning your coordinate would be (1, -4) where you can keep doing this formula on and on to find the y coordinate for what x coordinate you want to find, or make it easier to graph with a ruler on paper once you have enough points.
please help me........asap
Answer:
If I had to guess I would choose "a group of employees determined by a random number generator"
Which of these equations shows the correct relationship between x and y?
X+y = 90
x + y = 180
x=y
x + 50 = y
A square has an area of square inch what is [tex]18x^{2}[/tex] the length of one of its sides
Answer:
18x
Step-by-step explanation:
18x times 18x
so the side is 18x because it was squared
pleasee helpp asapp!!!
The volume of a right cone is 3975\piπ units^3 3 . If its radius measures 15 units, find its height.
If its radius measures 15 units. Then the height of the cone will be 53 units.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The volume of a right cone is 3975π cubic units.
If its radius measures 15 units.
Then the height of the cone will be
The volume of the cone is given as
Volume = 1/3 x π x r² x h
Then we have
3975π = 1/3 x π x 15² x h
11925 = 225 x h
h = 53 units
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helpppppppppppppppppp 100 points
Answer:
Range = 4Mode = 3Step-by-step explanation:
The range is the difference between the maximum and minimum values:
5 - 1 = 4The mode is the most repeated value of the data set
This is 3 (repeated 5 times)Answer:
I attached a screen shot of the answer
Step-by-step explanation:
Find the length of the hypotenuse
Help please! Thank you
Answer:
A I might be wrong do
Step-by-step explanation:
A conservationist determines that a particular beach is eroding at a rate of 1.1% each year. when writing an explicit formula to represent the amount of beach remaining each year, which value should she use as the common ratio? 0.011 0.089 0.989 1.011
Using exponential function concepts, it is found that the common ratio would be given by 0.989.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.1 - r, also as a decimal, is the common ratio.In this problem, the amount decays 1.1% a year, hence:
r = 0.011.1 - r = 1 - 0.011 = 0.989.The common ratio would be given by 0.989.
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Answer: C
Step-by-step explanation:
Trust
What is the area of a circle with a Radius of 4 and a Diameter of 2?
(Its on Khan)
Answer:4^2≈50.26548
Step-by-step explanation:
πr2.
Where r is the radius and π≈3.14 , the ratio of a circle's circumference to its diameter.
Plugging in 4 from the radius, we get.
42π
⇒16π inches.
This is our exact answer. Alternatively, we can plug in 3.14 for π to get.
50.26 inches.
Guys, I beg you! How do you do these factoring quadratic equations!
Which is a solution to (x − 2)(x + 10) = 13
======================================================
Explanation:
There are at least three ways to solve this.
----------------------------------------------
Method 1:
We could graph y = (x-2)(x+10) using a tool like Desmos. Graph y = 13 as well which is a horizontal line.
Check out the screenshot shown below.
The parabola in red and the horizontal line in blue intersect at the locations (-11, 13) and (3, 13)
We only focus on the x coordinates of the intersection points.
Therefore, the two solutions are x = -11 and x = 3
The order of the solutions doesn't matter.
----------------------------------------------
Method 2:
Expand things out and get everything to one side
(x-2)(x+10) = 13
x^2 + 10x - 2x - 20 = 13
x^2 + 8x - 20 - 13 = 0
x^2 + 8x - 33 = 0
From here we can use the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-8\pm\sqrt{(8)^2-4(1)(-33)}}{2(1)}\\\\x = \frac{-8\pm\sqrt{64+132}}{2}\\\\x = \frac{-8\pm\sqrt{196}}{2}\\\\x = \frac{-8\pm14}{2}\\\\x = \frac{-8+14}{2} \ \text{ or } \ x = \frac{-8-14}{2}\\\\x = \frac{6}{2} \ \text{ or } \ x = \frac{-22}{2}\\\\x = 3 \ \text{ or } \ x = -11\\\\[/tex]
----------------------------------------------
Method 3:
Instead of using the quadratic formula, we could factor.
To factor x^2+8x-33, we need to find two numbers that
Multiply to -33Add to 8Through trial and error, you should get 11 and -3
11 times -3 = -3311 plus -3 = 8So,
x^2+8x-33 = 0
(x+11)(x-3) = 0
x+11 = 0 or x-3 = 0
x = -11 or x = 3
Please help asap! I don’t understand it
Step-by-step explanation:
From given graph
f(-3)= (-3)
f(1)=1
Answer:
f(-3) = -3
f(1) = 1
Step-by-step explanation:
f(x) means the "function of x".
Therefore, the number in the bracket after the letter f is the value of x.
f(-3) means find the value of the function (y-value) when x = -3
f(1) means find the value of the function (y-value) when x = 1
To find f(-3), find x = -3 on the x-axis.
Now trace vertically until you meet the line. Read the value of y at this point.
⇒ f(-3) = -3
To find f(1), find x = 1 on the x-axis.
Now trace vertically until you meet the line. Read the value of y at this point.
⇒ f(1) = 1
If 10% of a number is 16, find 5% of that number.
Answer:
5% = 8
Step-by-step explanation:
Since 10% of a number is 16, multiply that by 10 to get 160. In order to get 5%, divide 10% (16) by 2 to get 8, which is 5% of 160.
One line passes through the points \blueD{(-6,0)}(−6,0)start color #11accd, left parenthesis, minus, 6, comma, 0, right parenthesis, end color #11accd and \blueD{(-4,6)}(−4,6)start color #11accd, left parenthesis, minus, 4, comma, 6, right parenthesis, end color #11accd. Another line passes through points \green{(5,-2)}(5,−2)start color #28ae7b, left parenthesis, 5, comma, minus, 2, right parenthesis, end color #28ae7b and \green{(8,7)}(8,7)start color #28ae7b, left parenthesis, 8, comma, 7, right parenthesis, end color #28ae7b.
Are the lines parallel, perpendicular, or neither? its khan academy
Answer:
paralell
Step-by-step explanation:
The table shows the amount of money in your bank account over a period of 5
5
weeks. You plan to keep saving at the same rate until you have $800
$
800
in the account. Which equation could you use to find the number of weeks,
n
, it would take to reach your goal?
Math item stem image
CLEAR CHECK
100·=800
100
·
n
=
800
35·+100=800
35
·
n
+
100
=
800
100·+35=800
100
·
n
+
35
=
800
35·+800=100
The linear function that you could use to find the number of weeks it would take to reach your goal is:
35n + 100 = 800.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the table, we have that:
The intercept is the initial balance of 100.The slope is the rate of change of 35.Hence the balance after n weeks is given by:
B(n) = 100 + 35n.
You will have $800 when B(n) = 800, hence the equation is:
35n + 100 = 800.
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The ratio of width to length for an American flag is 10 to 19. How wide is a flag that is 66 cm long
Answer:
35cm
Step-by-step explanation:
The ratio of width:length is 10/19. Since the given length is 66cm long, we multiply by the ratio to get 66 x 10/19 = 34.7 = 35cm
I'm supposed to find the volume of a cube but the only number I am given is 6. Do I multiply 6 three times?
PLEASE HELP!!! 60 POINTS!!!
Otis measured the heights of several sunflowers. He found
that their heights were 2, 3, 5, 7, and 8 feet.
Otis found that the mean was 5 feet and the range was 6
feet.
Which numbers describe the center and spread of this data set?
A. 2 feet describes the center, and 8 feet describes the 8 spread.
B. 8 feet describes the center, and 2 feet describes the spread.
C. 6 feet describes the center, and 5 feet describes the spread.
O D. 5 feet describes the center, and 6 feet describes the spread. 6
Answer:
D
Step-by-step explanation:
the mean will describe the center and the range will describe the spread, I know this because the mean is in the middle, and the only other thing for the range would be the spread.
The table shows the ratio of people who ate a certain type of lunch to the total number of people who ate lunch. Lunch Type of Lunch Ratio to the Total Turkey sandwich 1 3 1 Vegetarian sandwich 6 4. Chicken sandwich 15 Salad 7 30 A total of 840 people ate lunch. Which statement is true? A Half as many people ate a turkey sandwich as ate a vegetarian sandwich. B One-fourth as many people ate a vegetarian sandwich as ate a salad. C There were 56 more people who ate a turkey sandwich than ate a chicken sandwich. с D There were 28 more people who ate a salad than ate a chicken sandwich.
Using proportions, it is found that the correct statement is given by:
C There were 56 more people who ate a turkey sandwich than ate a chicken sandwich.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, one third out of 840 people ate Turkey Sandwich, hence the number is given by:
nT = 840/3 = 280.
One sixth ate Vegetarian Sandwich, hence the number is given by:
nV = 840/6 = 140.
4/15 ate Chicken Sandwich, hence the number is given by:
nC = 4 x 840/15 = 224.
7/30 ate Salad, hence the number is given by:
nS = 7 x 840/30 = 196.
Thus, option C is correct.
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Write the following phrase as an algebraic expression. Use n for "a number."
three increased by the quotient of a number and two
a.
3+ n
2
b.
22
3 + -
2
C.
3(2 + 2)
d.
3 + 222
Please select the best answer from the choices provided
A
B
C
Answer:
3+(n/2) i think that is a? i cant rlly tell
Step-by-step explanation:
What is the first step when rewriting y = 3x2 + 9x – 18 in the form y = a(x – h)2 + k?
3 must be factored from 3x2 + 9x
x must be factored from 3x2 + 9x
9 must be factored from 9x – 18
3 must be factored from 3x2 – 18
Answer:
(a) 3 must be factored from 3x^2 + 9x
Step-by-step explanation:
The first step when rewriting a quadratic from standard form to vertex form is to factor out the leading coefficient from the variable terms.
__
y = 3x^2 +9x -18 . . . . . . given
y = 3(x^2 +3x) -18 . . . . . leading coefficient factored out
y = 3(x^2 +3x +2.25) -18 -3(2.25) . . . . . complete the square
y = 3(x +1.5)^2 -24.75 . . . . . simplify to vertex form
Answer:
3rd one
Step-by-step explanation: I am pretty sure becuase the other ones don't sound right hope this helps :)
Thirty-five students passed the test. If that’s 70% of the class how many students is in the class?
Answer:
50
Step-by-step explanation:
fr the question,
35 students----------------70%
x students-------------------100%
cross multiplying
x ×70 = 35×100
dividing bothsides by 70
x = 3500/70
x=50 students
therefore,
there are 50 students in the class
help i need the answer
Answer:
Step-by-step explanation:
