[tex]\dfrac{x!-(x-3)!}{23}=1\\x!-(x-3)!=23\\(x-3)!((x-2)(x-1)x-1)=23\\(x-3)!((x^3-x^2-2x^2+2x)-1)=23\\(x-3)!((x^3-3x^2+2x)-1)=23[/tex]
23 is a prime number, therefore there are two possibilities:
[tex]\text{I.}\, (x-3)!=1 \wedge x^3-3x^2+2x-1=23[/tex]
or
[tex]\text{II.}\, (x-3)!=23 \wedge x^3-3x^2+2x-1=1[/tex]
[tex]\text{I.}\\(x-3)!=1\\x-3=0 \vee x-3=1\\x=3 \vee x=4[/tex]
Now, we check if any of these solutions is also a solution to the second equation:
[tex]3^3-3\cdot3^2+2\cdot3-1=23\\27-27+6-1-23=0\\ -18=0[/tex]
Therefore, 3 is not a solution.
[tex]4^3-3\cdot4^2+2\cdot4-1=23\\64-48+8-1-23=0\\0=0[/tex]
Therefore, 4 is a solution.
[tex]\text{II.}[/tex]
[tex](x-3)!=23[/tex]
We know that [tex]3!=6[/tex] and [tex]4!=24[/tex], therefore there isn't any [tex]n\in\mathbb{N}[/tex], for which [tex]n!=23[/tex], so there's no solution.
So, the only solution is [tex]x=4[/tex].
Graph the line passing through (6, 1) whose slope is m = 3.
Answer: [tex]y=3x-17[/tex]
Step-by-step explanation:
use point-slope form:
[tex]y_{1} -y=m(x_{1} -x)[/tex]
[tex]y-1=3(x-6)[/tex]
[tex]y-1=3x-18[/tex]
[tex]y=3x-17[/tex]
Answer:
equation: y = 3x - 17
[image attached]
Step-by-step explanation:
we know that the equation for a line is y = mx + b
we are given a point, (6, 1)
remember that a point is (x, y)
we can plug these sample x and y values into our equation, replacing x and y
y = mx + b
1 = m6 + b
we know that m = 3 [this was a given], so we can plug this into our equation
1 = (3)(6) + b
1 = (18) + b
1 = 18 + b [we can now solve for "b"]
1 = 18 + b
-18 - 18
-17 = b
so, we can re-write our equation so that we can graph it:
y = 3x - 17
we can now plug in x-values to graph this:
(you'll see these written in the table on the graph)
y = 3(0) - 17
y = -17
y= 3(1) - 17
y = 3 - 17
y = -14
y = 3(2) - 17
y = 6 - 17
y = -11
y = 3(3) - 17
y = 9 - 17
y = -8
y = 3(4) - 17
y = 12 - 17
y = -5
y = 3(-1) - 17
y = -3 - 17
y = -20
y = 3(-2) - 17
y = -6 - 17
y = -23
y = 3(-3) - 17
y = -9 - 17
y = -26
[there is an image attached of my graph]
hope this helps!! :)
A researcher is examining the claims made by a water softener salt manufacturer. He performs an experiment using water from a variety of sources. For each water source, he has a sample with no treatment and a sample treated with the recommended amount of the water softener salt.
He then tests each sample to measure the softness and compares the results, determining that the claims made by the manufacturer are true.
The conclusion drawn from the study is ___ because the sample is __ In this instance, an __ study was performed.
The conclusion drawn from the study is instance because the sample is homogenous and an experimental study was performed.
What is an experimental study?An experimental study deals with a dependent variable and there is a dependent variable.
Also, a control is used to establish the validity of the results.
The dependent variable is the level of softness after treatment while the independent variable is the type of water softener used.
The conclusion drawn from the study is instance because the sample is homogenous and an experimental study was performed.
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Triangle LMN is congruent to triangle FGH, as shown.
Go
65
Mark this and return
5-
4
3
321
2-
-6-5-4-3-2-14 2 3 4 5 6
یہ ب
-2
-3
FL
4
5
6
H
X
What is the length of side LM?
units
Next
Submit
Answer: 5
Step-by-step explanation:
If [tex]\triangle LMN \cong \triangle FGH[/tex], this means that [tex]\overline{LM} \cong \overline{FG}[/tex] by CPCTC.
Using the distance formula,
[tex]FG=\sqrt{(-3-0)^{2}+(-4-0)^{2}}=5\\\\\therefore LM=\boxed{5}[/tex]
What is the product?
2 3
5 9 -1 -7
11 5 -3
10 15 20
45 -5 -35
55
10
4 2
55
7
14
25 -15
45 -1 -7
315
+7 9
CO
8
9
4 1-2
Answer:
A.
Step-by-step explanation:
Hello, this is what we call matrix. multiplication matrix to be precised.
so it is;
5×2=10
5×3=15
5×4=20
5×9=45
5×-1= -5.
5×-7= -35
5×11=55
5×5=25
5×-3= -15.
i hope you understand. That is matrix for you but it has different categories
Give the “best” big-oh notation to describe the complexity of the algorithm that prints all bit strings of length n.
It is correct to state that a bit can be in one of 2 states, either 1 or 0.
What is a bit?A bit is is a single binary digit. A bit can either be "1" or "0".
What is the explanation to the above answer?We stated that It is correct to indicate that a bit can be in one of 2 states, either 1 or 0. This indicates that 2ⁿ strings must be created in total. The string must then be processed twice.
The first time, for generation andThe second for reading.Hence, Our time is now O(2ⁿ⁺¹) = O(2ⁿ)
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Please answer all 5 xoxo <3
Answer:
First Image: Option D
Second Image: Option D
Third Image: Option C
Fourth Image: Option B
Fifth Image: Option B
Step-by-step explanation:
First Image:
Supplementary angles is two angles whose sum is 180 degrees (straight line)180 - 47 = 133°? is an obtuse angle is any angle greater than 90° which checks the answerSecond Image:
A triangle angles adds up to 180° Two angles are already given72 + 45 + ? = 180° → 117 + ? = 180° → ? = 63°? is an acute angle is an angle that measures between 90° and 0°Third Image:
Supplementary angles is two angles whose sum is 180 degrees (straight line)180 - 110 = 70°? is an acute angle is an angle that measures between 90° and 0°Fourth Image:
Supplementary angles is two angles whose sum is 180 degrees (straight line)180 - 120 = 60°we are shown a right angle which = 90°A triangle adds up to 180° 180 - 90 - 60 = 30? = 30°? is an acute angle is an angle that measures between 90° and 0°Fifth Image:
Supplementary angles is two angles whose sum is 180 degrees (straight line)180 - 85 = 95°? is an obtuse angle is any angle greater than 90° which checks the answerLearn more about Triangles here: https://brainly.com/question/4186813
Mary Lou received $5,000 from her grandparents for her college education 8 years prior to her enrolling in college. Mary Lou invested the money at 5.5% compounded semiannually. How much money would she have in her savings account when she is ready to enroll in college? A: The balance in her account would be $__________ when she is ready to enroll in college. (Round your answer to the nearest cent.)
Answer:
The total amount , principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 5.5% per year compounded 2 times per year over 8 years is $7,717.55.
Step-by-step explanation:
Compound interest is based on the principal amount and the interest that accumulates on it in every period.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
First, convert R as a percent to r as a decimal
r = R/100
r = 5.5/100
r = 0.055 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 5,000.00(1 + 0.055/2)^(2)(8)
A = 5,000.00(1 + 0.0275)^(16)
A = $7,717.55
The total amount accrued, principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 5.5% per year compounded 2 times per year over 8 years is $7,717.55.
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A
Find the value of x.
Round to the nearest tenth.
19°
B
142°
X
x = [?]
Law of Sines: sin A
42
sin B
b
sin C
C
The value of x will be equal to x = 79.
What is the triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
For an isosceles triangle, the value of two opposite angles is equal and the opposite sides are also equal.
The Sum of the three angles is equal to 180 degrees so the third angle will be calculated as:-
Angle = 180 - 142 - 19 = 19
Now applying Lami's theorem in the triangle we will get the third side.
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
[tex]\dfrac{Sin 19}{42}= \dfrac{Sin142}{x}[/tex]
[tex]x = \dfrac{42\times Sin 142}{Sin19}[/tex]
x = 79
Therefore the value of x will be equal to x = 79.
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Answer:
Step-by-step explanation:
Solve the equation for x.
2(x + 4) = 2
5
x = [?]
Answer:
x=1
Step-by-step explanation:
(2(x+4))/5=2
Multiply both sides by 5
2(x+4)=10
Divide both sides by 2
x+4=5
subtract 4 from both sides
x=1
Given f(x)=2x^2-1 and g(x) =3x-5 what is f-g
[tex]f(x)-g(x)=(2x^{2}-1)-(3x-5)=2x^{2}-1-3x+5=\boxed{2x^{2}-3x+4}[/tex]
What is the equation of the line passing through the point (2,-4)
Answer:
y = m(x - 2) - 4
Step-by-step explanation:
Equation of a straight line is given by;
y = mx + c
Take a point on the line (x, y) and the given point (2, -4)
gradient = change x/ change in y
gardient(m) = y +4/ x - 2
m(x-2) = y + 4
y = m(x - 2) - 4
Need help with this geometric question
Answer: A
Step-by-step explanation:
[tex]V=\frac{1}{3}Bh\\\\V=\frac{1}[3}(6.3)(2.4)(3.6)=\boxed{18.144}[/tex]
If f(x) = 4x² + 1 and g(x)=x²-5, find (f+ g)(x). ( x ) = 4x² + 1 and g ( x ) = x² - 5 , find ( f + g ) ( x ) .
Answer: [tex]5x^{2}-4[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)=4x^{2}+1+x^{2}-5=\boxed{5x^{2}-4}[/tex]
A survey asked 20 mobile phone dealers how many mobile phones were sold during the previous week. Their answers are displayed in the Box-and-Whisker Plot and the Stem-and-Leaf Plot shown. Which graph can be used to find the mean? What is the mean of the data set?
A. Stem-and-Leaf Plot, Mean: 41.95
B. Stem-and-Leaf Plot, Mean: 42.55
C. Box-and-Whisker Plot, Mean: 43.65
D. Box-and-Whisker Plot, Mean: 38.80
Answer:
= B
Step-by-step explanation:
The percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 58.8% in 1980 to 50.5% in 1995.
(A) Predict when the percentage will be 47%.
(B) Predict the percentage in 2005.
Using a linear function, we have that:
a) The percentage will be 47% during the year of 2001.
b) The predicted percentage in 2005 is of 44.97%.
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.The percentage in 1980 is considered as the initial amount, hence b = 58.8. In 15 years, the percentage decreased from 58.8% to 50.5%, hence the slope is given by:
m = (50.5 - 58.8)/15 = 0.5533.
Hence the percentage in t years after 1980 is given by:
P(t) = 58.8 - 0.5533t.
Item a:
This is t + 1980, for which P(t) = 47, hence:
P(t) = 58.8 - 0.5533t
47 = 58.8 - 0.5533t.
0.5533t = 11.8.
t = 11.8/0.5533
t = 21.3.
1980 + 21 = 2001, hence the percentage will be 47% during the year of 2001.
Item b:
2005 is 25 years after 1980, hence the percentage is P(25), given as follows:
P(25) = 58.8 - 0.5533x25 = 44.97%.
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The number of measles cases has increased by 5.3% since 2000.
Express your answer rounded correctly to the nearest hundredth.
Stated another way, the number of measles cases is
times what it was in 2000.
Express your answer rounded correctly to the nearest tenth of a percent.
Stated another way, the number of measles cases was
% of what it is now.
The expressions for the number of measles are y = a(1.05)^x and y = a(1.1)^x
How to express the number of measles?Let the initial number of measles in 2000 be represented as:
Initial = a
The rate of increase is given as:
Rate, r = 5.3%
The number of measles in x years after 2000 is represented as:
y = a * (1 +r)^x
Substitute r = 5.3%
y = a * (1 + 5.3%)^x
So, we have:
y = a * (1 + 0.053)^x
Evaluate the sum
y = a * (1.053)^x
To express to the nearest hundredth, we approximate to 2 decimal places
y = a(1.05)^x
To express to the nearest tenth, we approximate to 1 decimal place
y = a(1.1)^x
Hence, the expressions for the number of measles are y = a * (1.05)^x and y = a * (1.1)^x
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Here is the histogram of a data distribution. All class widths are 1.
Which of the following numbers is closest to the mean of this distribution?
A.3
B.5
C.7
D.9
E.4
The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. suppose intensity is 8000 units at a distance of 2 miles. what will the intensity be at a distance of 11 miles? round your answer to the nearest unit.
The answer is B. 222 Units
factorise b^2 + 7b + 10
Step-by-step explanation:
b²+7b+10
Common factors are 5,2
b²+7b+10
b²+2b+5b+10
b(b+2)+5(b+2)
(b+2)(b+5)
Hope it helps.✨✨
Which of the numbers below are whole numbers? Check all that apply.
A. 734.895
B. 0.7538
C. 7
D. 5429.97
E. 616
F. 401119.8
Answer:
7, 616 because there is no floating point
what is the domain and range of this graph
Answer:
Domain: All real number
Range: y≤-4
An administrator is asked to file papers in a box which has the following dimensions height 15cm width 30cm and depth 20cm. Calculate the volume of the box.
The volume of the box is 9000 square cm if the box has the following dimensions height of 15cm width 30cm and depth of 20cm
What is a cuboid?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape.
We have:
An administrator is asked to file papers in a box that has the following dimensions height of 15 cm width of 30 cm and depth of 20 cm.
Let L be the length
W be the width
H be the height of the box:
Given:
L = 20 cm
W = 30 cm
H = 15 cm
The volume of the box
= 15×30×20
9000 square cm
Thus, the volume of the box is 9000 square cm if the box has the following dimensions height of 15cm width of 30cm, and depth of 20cm
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What is breaking probation?
Answer:
a probation violation occurs when someone who has already been sentenced for a crime breaks the terms or conditions of that probation
What is the value of
(X+Y) (X-Y) when x=3.5,y=-8.7
Answer:
[tex](x + y)(x - y)[/tex]
[tex](3.5 - 8.7)(3.5 + 8.7)[/tex]
[tex](-5.2)( 12.2)[/tex]
[tex]-63.44 [/tex]
Given the graph, find the initial value of the domain [ ___, 2].
Answer:
Looks to me like it should be -2
Pls help me with my math
Answer:
d.
Step-by-step explanation:
Left line is defined when x < 1 (x is less than 1). The point is not full and that means that x = 1 is not included.
Right line is defined when x is greater or equal to one x ≥ 1.
Options that have x < 1 and x ≥ 1 are b and d, so the answer is one of those.
Equations of the lines are in slope-intercept form y = mx + b, where m is slope and b is y-intercept.
Right line has steeper slope than left line, so the slope of right line will have bigger absolute value. That is the case with option d. (Left line has slope -1 and right one has slope -2, absolute value of right slope is bigger.)
You could also check with y-intercepts. Left line has y-intercept at y = 2 and left line is defined when x < 1. Only option d meets these conditions.
Enlarge the shape on scale factor 0
Answer:
Multiply with 2 to the original sides
The sum of 9 consecutive integers is 369. The middle integer is:
A. 38
B.35
C.41
D.10
PLEASE ANSWER QUICKKKk
We have an odd number of consecutive integers, therefore the middle one is equal to the average of all of them. And since the average is equal to the sum of the numbers divided by their number, the middle integer in this problem is equal to 369 divided by 9, which is equal to 41.
X+(x^2+2)+y=4
Find 2 coordinates
(X,y) (x,y)
Answer: (-2,0) and (1,0)
Step-by-step explanation:
If y=0, then:
[tex]x+x^2 + 2=4\\\\x^2 + x-2=0\\\\(x+2)(x-1)=0\\\\x=-2, 1[/tex]
So, the points (-2,0) and (1,0) lie on the curve.
The points (-2,0) and (1,0) lie on the curve.
If y=0, then:
[tex]x+(x^2+2)+0=4\\x^2+x+2=4\\[/tex]
What is the coordinate of the axis?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
[tex]x^2+x-2=0[/tex]
[tex]=\left(x^2-x\right)+\left(2x-2\right)[/tex]
[tex]=x\left(x-1\right)+2\left(x-1\right)[/tex]
[tex]=\left(x-1\right)\left(x+2\right)[/tex]
[tex]x=-2,x=1[/tex]
So, the points (-2,0) and (1,0) lie on the curve.
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a rhombus has perimeter 120 M and one of its diagonal is 50 M find the area of the Rhombus
The area of the rhombus is 829.1562m².
What is the area of the rhombus?A rhombus is a four sides quadrilateral with the four sides equal in length
The area of a rhombus = [tex]\frac{1}{4}d[/tex] ×√(p² - 4d²)
where p is the perimeter and d is the diagonal
1/4(50) x √(120² - 4 x 50²) =829.1562m²
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