Step-by-step explanation:
(2x-y+3)(2x-y-3)=
4x²-2xy-6x-2xy+y²+3y+6x-3y-9=
4x²-4xy+y²-9=
(2x-y)²-9
Write the phrase as an algebraic expression and simplify if possible. Let x represent the unknown number
Three times a number, decreased by five
(Simplify your answer.)
To express the phrase "Three times a number, decreased by five" as an algebraic expression, we can use the variable x to represent the unknown number: 3x - 5
Now, let's simplify this expression: Given that the unknown number is represented by x, we can substitute it into the expression above. Substituting x into the expression, we have: [tex]3(x) - 5 3x - 5[/tex] Therefore, the algebraic expression representing "Three times a number, decreased by five" is [tex]3x - 5.[/tex] At this point, there is no further simplification possible since the expression is already in its simplest form.
For example, let's assume the unknown number x is 7. We can plug in this value to evaluate the expression: [tex]3(7) - 5 = 21 - 5 = 16[/tex] Similarly, if x is -2, the calculation would be: [tex]3(-2) - 5 = -6 - 5 = -11[/tex] In conclusion, the algebraic expression 3x - 5 represents the phrase "Three times a number, decreased by five."
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Find Length of x line OR
Both figures r similar (given )
so :-[tex] \frac{5}{2.5} = \frac{3}{1.5} = \frac{2}{1} = \frac{4}{x} \\ \frac{2}{1} = \frac{4}{x} \\ \frac{ \cancel{2}}{1} = \frac{ \cancel{4}^ { \tiny{2}}}{x} \\ x = 2 \: \: ans[/tex]
Construct a frequency polygon that represents the following data regarding the selling prices of houses sold in 2006 for a particular neighborhood find the midpoint
Class Frequency
78787 – 98786 9
98787 – 118786 8
18787 – 138786 9
138787 – 158786 4
158787 – 178786 8
Answer:
See attachment for polygon
Step-by-step explanation:
Given
[tex]\begin{array}{cc}{Class} & {Frequency} & 78787 - 98786 & 9 &98787 - 118786 & 8 & 118787 - 138786 & 9 & 138787 - 158786 & 4 & 158787 - 178786 & 8 \ \end{array}[/tex]
Required
The frequency polygon
First, we calculate the midpoint of each class.
This is the average of the class limits
So, we have:
[tex]x_1 = \frac{78787 + 98786}{2} = \frac{177573}{2} = 88786.5[/tex]
[tex]x_2 = \frac{98787 + 118786}{2} = \frac{217573}{2} = 108786.5[/tex]
----
--
-
[tex]x_5 = \frac{158787 + 178786}{2} = \frac{337573}{2} = 168786.5[/tex]
(138787 + 158786)/2
So, the table becomes:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {x} &78787 - 98786 & 9 & 88786.5 & 98787 - 118786 & 8 & 108786.5 & 118787 - 138786 & 9 & 128786.5 & 138787 - 158786 & 4 & 148787.5 & 158787 - 178786 & 8 & 168786.5\ \end{array}[/tex]
See attachment for frequency polygon
Which function is increasing and has a domain of (1,∞ )
The graph of a square root function has a domain of (0, ∞) and range of [1, ∞).
Answer:
f(x)=log(x-1)+2
Step-by-step explanation:
I did the test on plato and got it right.
What is 15 5/7 - 6 4/5
Answer:
8.9
Step-by-step explanation:
15.71428571-6.8=8.914285714
We round of to one significant figure because its addition n the lowest is 6.8
Answer:
[tex]8\frac{32}{35}[/tex]
Step-by-step explanation:
look at attachment below
Consider a species of bird that can be split into three age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years. The population is observed once a year. Given that the Leslie matrix is equal to
Answer: hello your question lacks some information attached below is the complete question
answer :
a) attached below
b) 65 students aged 1-2 years
Step-by-step explanation:
For a Leslie matrix ; there is a relation
Pn = L^n Po where ; Pn = population vector after n years , Po = initial population vector .
a) Initial population vector
attached below
[tex]\left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]
b) Number of birds aged 1-2 years are available after 10 years
i.e. P10 = L^10 Po
note : Po = Xo
∴ P10 = [tex]\left[\begin{array}{ccc}0&2&1\\0.2&0&0\\0&0.4&0\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]
we will apply MATLAB to resolve the above matrix
P10 = [tex]\left[\begin{array}{ccc}217.91\\65.24\\31.911\end{array}\right][/tex]
∴ Number of children between 1-2 years left after 10 years = 65.24 ≈ 65
The total number of birds aged between 1-2 years which are available after 10 years is 65 and this can be determined by using the Leslie matrix relation.
Given :
Consider a species of bird that can be split into three age groupings: those aged 0-1 years, those aged 1-2 years, and those aged 2-3 years. [tex]\rm L = \left[\begin{array}{ccc}0&2&1\\0.2&0&0\\0&0.4&0\end{array}\right][/tex]According to the given data, the initial population vector is given by:
[tex]x_0 = \left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]
Now, the total number of birds aged between 1-2 years which are available after 10 years is:
[tex]\rm P_{10} = \left[\begin{array}{ccc}0&2&1\\0.2&0&0\\0&0.4&0\end{array}\right] \left[\begin{array}{ccc}1100\\2400\\3200\end{array}\right][/tex]
Now, solve the above matrices in order to determine the value of [tex]\rm P_{10}[/tex].
[tex]\rm P_{10} = \left[\begin{array}{ccc}217.91\\65.24\\31.911\end{array}\right][/tex]
Therefore, the total number of birds aged between 1-2 years which are available after 10 years is 65.
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Simplify
x×x×x×у×у and
2×x×x×3×y×y×y
Step-by-step explanation:
1.x³y²
2. 6x²y³
hope it helps
A man, 1.5m tall, is on top of a building. He observes a car on the road at an angle of 75°. If the building is 30m, how far is the car from the building?
Answer:
The answer to this question is 8.44 m.
Step-by-step explanation:
This problem is best illustrated in the photo below.
First, we must know that the angle stated in the problem is the angle of depression. Angle of depression is the angle between the horizontal and the line of sight of the observer. On the other hand, if the observer is looking upward, then the angle between the horizontal and his line of sight is called the angle of elevation.
Since we have the given angle of depression, we must use its complementary angle to solve for the distance of the car from the building.
Let x = complementary angle of 75°
y = distance of the car from the building
To solve for x,
To solve for y, we need to use a trigonometric function that will relate the adjacent of 15° and the opposite of 15°. Let us look at the mnemonics
SOH: Sine =
CAH: Cosine =
TOA: Tangent =
Therefore we must use the tangent function to solve for y.
Diana is going to roll a 6-sided die. What's the probability she will role a 4 or
a 5? *
The probability of rolling any one number on a 6 sided die is 1/6
The probability of rolling a 4 is 1/6
The probability of rolling a 5 is 1/6
The probability of rolling a 4 or a 5 is the probability of rolling a 4 plus the probability of rolling a 5:
1/6 + 1/6 = 2/6 = 1/3
The answer is 1/3
A crew clears brush from 1/3 acre of land in 2 days. How long will it take the same crew to clear the entire plot of 2 1/ 2 acres?
Answer:
15 days
Step-by-step explanation:
Given that :
Time taken to clear 1/3 acre = 2 days
This means that, they will be able to clear ;
1/3 ÷ 2 = 1/3 * 2 /1 = 1/6 acre in one day
1/6 acres per day :
Hence, the number of days it will take to clear 2 1/2 acres will be :
2 1/2 acres ÷ 1/6
5 / 2 ÷ 1/ 6
5/2 * 6 /1 = (5*6) / (2*1) = 30/2 = 15
Hence, it will take 15 days to clear 2 1/2 acres
PLS HELP
the simplest form of this product has a numerator of
x + 2
x - 2
( x - 2 ) ( x - 2 )
( x + 2 ) ( x - 2 )
and a denominator of
x - 5
( x - 5 ) ( x - 1 )
x - 1
( x + 5 ) ( x + 1 )
the expression has an excluded value of x
- 5
2
-1
5
(x+2)(x-2) / (x-1)(x-5) this is the simplified form of the expression.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities. It is a way of expressing a number as a quotient of two integers, where the top number is called the numerator, and the bottom number is called the denominator.
x²-3x-10/x²-6x+5 • x-2/x-5
We can factor the numerator and denominator of the first fraction as follows: (x-5)(x+2) / (x-5)(x-1)
Notice that there's a common factor of x-5 in both the numerator and denominator. We can cancel them out, leaving: (x+2) / (x-1)
Now let's simplify the second fraction:
x-2 / x-5
We can't simplify this fraction any further, so we leave it as is.
Putting it all together, we get:
(x+2) / (x-1) * (x-2) / (x-5)
Multiplying the two fractions, we get:
(x+2)(x-2) / (x-1)(x-5)
This is the simplified form of the expression.
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subtract
a2-b2 from a2 +b2
Answer:
2b^2
Step-by-step explanation:
according to the question equation is
(a^2 + b^2 ) - (a^2 - b^2)
a^2 + b^2 - a^2 + b^2
plus a square and minus a square gets cancel
b^2 + b^2
since they are like terms they can be added
2b^2
Answer:
2b^2
Step-by-step explanation:
according to the question equation is
(a^2 + b^2 ) - (a^2 - b^2)
a^2 + b^2 - a^2 + b^2
= b^2 + b^2
like terms can be added
+2b^2
After being rejected for employment, Kim Kelly learns that the Bellevue Credit Company has hired only four women among the last 19 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men as qualified women.
Help her address the charge of gender discrimination by finding the probability of getting four or fewer women when 19 people are hired, assuming that there is no discrimination based on gender.
(Report answer accurate to 8 decimal places).
P(at most four) =
Answer:
P(at most four) = 0.00960541
Step-by-step explanation:
For each employee hired, there are only two possible outcomes. Either it is a women, or it is not. The probability of an employee being a women is independent of any other employee, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
19 new employees.
This means that [tex]n = 19[/tex]
Approximately equal number of qualified men as qualified women.
This means that [tex]p = 0.5[/tex]
Probability of getting four or fewer women when 19 people are hired
This is:
[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{19,0}.(0.5)^{0}.(0.5)^{19} = 0.00000191[/tex]
[tex]P(X = 1) = C_{19,1}.(0.5)^{1}.(0.5)^{18} = 0.00003624[/tex]
[tex]P(X = 2) = C_{19,2}.(0.5)^{2}.(0.5)^{17} = 0.00032616[/tex]
[tex]P(X = 3) = C_{19,3}.(0.5)^{3}.(0.5)^{16} = 0.00184822[/tex]
[tex]P(X = 4) = C_{19,4}.(0.5)^{4}.(0.5)^{15} = 0.00739288[/tex]
Then
[tex]P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.00000191 + 0.00003624 + 0.00032616 + 0.00184822 + 0.00739288 = 0.00960541[/tex]
So
P(at most four) = 0.00960541
An educational psychologist wondered whether there was a relationship between the amount of academic pressure a high school student felt and their plans for college. They surveyed a random sample of 300 high school students throughout the country about their college plans and whether they felt academic pressure. Here are the responses and partial results of a chi-square test (expected counts appear below observed counts):
Chi-square test:
Planned years of college vs. feeling academic pressure now
O years Up to 4 years Up to 4 years More than 4 years Total
Yes 31 48 161 240
31.2 48 160.8
No 8 12 40 60
7.8 12 40.2
Total 39 60 201 300
They want to use these results to carry out a xạ test of independence. Assume that all conditions for inference were met. What are the values of the test statistic and P-value for their test?
What are the values of the test statistic and P-value for their test?
A. x² = 0.002;
0.001 < P-value < 0.0025
B. x² = 0.002;
P-value > 0.25
C. x² = 0.007;
0.005 < P-value < 0.01
D. x² = 0.007;
P-value > 0.25
Answer:
D. x² = 0.007;
P-value > 0.25
Step-by-step explanation:
The observed and expected values are given below :
Yes____31 48 161 ____240
______31.2 48 160.8
No ____ 8 12 40_____ 60
______7.8 12 40.2
Total __ 39 60 201 ___300
The Chisquare statistic, χ²:
Σ(Observed - Expected)²/ Expected
Chi-Squared Values:
0.00128205 __ 0 __ 0.000248756
0.00512821 __ 0 __ 0.000995025
(0.00128205 + 0 + 0.000248756 + 0.00512821 + 0 + 0.000995025 )
= 0.007654041
The degree of freedom = (row - 1) * (column - 1)
Degree of freedom = (2-1)*(3-1) = 1*2= 2
The Pvalue = 0.9962
Pvalue > 0.25
Is 69 square routed a even number
WILL GIVE BRAINLIEST Solve for x
Answer:
Step-by-step explanation:
sin x° = [tex]\frac{17}{19}[/tex]
x° = [tex]sin^{-1}[/tex] [tex]\frac{17}{19}[/tex]
x° ≈ 63°
The interarrival time of nuclear particles in a Monte Carlo simulation of a reaction is designed to have a uniform distribution over an interval from 0 to 0.5 milliseconds. Determine the probability that the interarrival time between two particles will be:
Answer:
Incomplete question, but you can use the formulas given to solve it.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Uniform distribution over an interval from 0 to 0.5 milliseconds
This means that [tex]a = 0, b = 0.5[/tex]
Determine the probability that the interarrival time between two particles will be:
Considering [tex]a = 0, b = 0.5[/tex], and the question asked, you choose one of the three formulas above.
There is a bag filled with 3 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?
Answer:
its a three in seven chance, since there are seven total outcomes and there is only one favorable outcome. Hope that helps.
Step-by-step explanation:
what is 1+1+3+4+6+2+6+3+5=+8+2+5
Answer:
16
Step-by-step explanation:
baámmáy tính
Expand, and simplify the following expressions a. (2x+y)(x+y) + (2x-y)(x+y)
Step-by-step explanation:
2x²+2xy+yx+y²+2x²+2xy-yx+y²
2x²+2x²+2xy+2xy+yx-yx+y²+y²
2x²+2x²+2xy+2xy
4x²+4xy
Your Answer is in the above image.
Hope this solution may help you
I need help please anyone
Answer:
20
Step-by-step explanation:
l*w*h
4*5*1= 20
The ice cream man just ended his shift for the day. Let 1/2x^2 6/11x + 8 represent the amount of chocolate ice cream bars he sold. Let 5/9x^2 + 2/3 represent the amount of vanilla ice cream bars he sold. Finally let 1/3x^2 + 4x + 4/3 represent the amount of strawberry ice cream bars he sold. Select all the statements that are true
a. The total amount of ice cream bars sold can be represented by the expression 25/18x^2+ 50/11x +10
b. The total amount of ice cream bars sold can be represented by the expression 25/18x^2 + 172/33x +28/3
c. He sold 1/6x^2 + 50/11x + 28/3 more chocolate than strawberry ice cream bars.
d. He sold 1/6x^2 - 38/11x + 20/3 more chocolate than strawberry ice cream bars.
Answer:
A and D
Step-by-step explanation:
Total ice cream bars sold = sum of chocolate sold , vanilla and strawberry ice-creams sold.
=(1/2)x2 + (6/11)x + 8 + (5/9)x2 + (2/3) +(1/3)x2 + 4x +(4/3) (Given in the question)
=(25/18)x2 + (50/11)x + 10 (Adding terms corresponding to x2,x ,constant respectively)
Difference in chocolate and strawberry bars =[ (1/2)x2 + (6/11)x + 8] - [(1/3)x2 + 4x +(4/3)]
= (1/6)x2 - (38/11)x +(20/3)
So, the correct options are A and D
Which of the following represents the factorization of the trinomial below?
x2 - 14x + 49
O A. (x-7)
O B. (x-7)(x+7)
O C. (x+7)
O D. (x+2)(x+7)
ANSWER ASAP!!
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: ( {x - 7})^{2} }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] {x}^{2} - 14x + 49[/tex]
[tex] = {x}^{2} - 7x - 7x + 49[/tex]
Taking "[tex]x[/tex]" as common from first two terms and "7" from last two terms, we have
[tex] = x \: ( \: x - 7 \: ) - 7 \: ( \: x - 7 \: )[/tex]
Taking the factor [tex](x-7)[/tex] as common,
[tex] = ( \: x - 7\:) \: (\: x - 7\: )[/tex]
[tex] =( {x - 7})^{2} [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Có 7 cây hãy trồng thành 6 hàng, mỗi hàng 3 cây?
Answer:
Step-by-step explanation:
Bạn vẽ 1 tức giác ABCD lồi sau đó nối AB và CD cắt nhau tại E, AD và BC cắt nhau tại F, AC và BC cắt nhau tại G. Trồng 7 cây vào các điểm ABCDEFG l. Ta có sáu hàng là ABE, DCE, BCF, ADF, ACG, BDG
write the other side of this equation so its true for all values of x: 1/2(6x-10)-x=
9514 1404 393
Answer:
2x -5
Step-by-step explanation:
Any equivalent expression can be used. It is perhaps easiest just to simplify the given expression.
1/2(6x -10) -x = 3x -5 -x = 2x -5
Putting 2x-5 on the right will give an equation true for all x.
1/2(6x -10) = 2x -5
DO THIS FAST PLEASE I WILL GIVE BRAINLY CROWN
Use a model to divide. 5 ÷ 1/2 10 4 2 20
5 ÷ 1/2 => 5 x 2/1 => 10/1 => 10
Answer:
10
Step-by-step explanation:
In the pic, it shows ten half squares.
What is the volume in cubic centimeters of the figure below?
Answer:
so that you will multiply 15 * 4.
Step-by-step explanation:
15*4 = 60 now you divide 60 by 4 and the answer will be 15.
Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one kind. Do not solve.
a) dy/dx = (x − y)/x
b) (x + 1)dy/dx = −y + 20
c) dy/dx = 1/(x(x − y2))
d) dy/dx =(y^2 + y)/(x^2 + x)
e) dy/dx = 5y + y^2
f) y dx = (y − xy^2) dy
g) x dy/dx = ye^(xy) − x
h) 2xyy' + y^2 = 2x^2
i) y dx + x dy = 0
k) (x^2 + 2y/x) dx = (3 − ln x^2) dy
l) (y/x^2) dy/dx + e^(2x^3) + y^2 = 0
Here, we have to classify each differential equation based on their characteristics:
a) dy/dx = (x − y)/xThis is a separable differential equation because the variables can be separated on different sides of the equation.
It's of the form dy/dx = g(x) - f(y)/h(y), where g(x) = x/x and h(y) = 1.
b) (x + 1)dy/dx = −y + 20This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -1/(x + 1) and Q(x) = 20/(x + 1).
c) [tex]dy/dx = 1/(x(x - y^2))[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
d) [tex]dy/dx = (y^2 + y)/(x^2 + x)[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
e)[tex]dy/dx = 5y + y^2[/tex]This is a Bernoulli differential equation because it is of the form [tex]dy/dx = p(x)y + q(x)y^n[/tex], where p(x) = 0 and q(x) = 5x, n = 2.
f) [tex]y dx = (y - xy^2) dy[/tex]This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
g) [tex]x dy/dx = ye^{(xy)} - x[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -1/x and [tex]Q(x) = e^{(xy)} - x^{(-1)[/tex].
h) [tex]2xyy' + y^2 = 2x^2[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where P(x) = -2/x and Q(x) = 2x.
i) y dx + x dy = 0This is a separable differential equation because the variables x and y can be separated on different sides of the equation.
k) [tex](x^2 + 2y/x) dx = (3 - \text ln x^2) dy[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), although it's not immediately obvious what P(x) and Q(x) are.
l) [tex](y/x^2) dy/dx + e^{(2x^3)} + y^2 = 0[/tex]This is a linear first-order differential equation because it can be rearranged to the form y' + P(x)y = Q(x), where [tex]P(x) = -1/x^2[/tex] and [tex]Q(x) = -e^{(2x^3)} - y^2[/tex].
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I need help with this!
Answer:
1. y=5 x=1
2. y=4 x=4/5
3. y=2 x=2/5
Step-by-step explanation:
Plug the y-values in for y:
1. 5=5x
2. 4=5x
3. 2=5x
Then solve for x:
1. x=1
2. x=4/5
3. x= 2/5
Hope this helps!