Answer:
The excluded value is x=5.
Step-by-step explanation:
Given : Expression [tex]\frac{2x}{-5x+x^2}[/tex]
To find : Simplify the rational expression. State any excluded values.
Solution :
First we simplify the expression,
[tex]\frac{2x}{-5x+x^2}[/tex]
Taking x common from the denominator,
[tex]=\frac{2x}{x(-5+x)}[/tex]
Cancel the common term from numerator and denominator,
[tex]=\frac{2}{-5+x}[/tex]
To find the excluded value we put the denominator equal to zero to get the value of x in which given expression is not valid.
[tex]-5+x=0[/tex]
[tex]x=5[/tex]
Therefore, The excluded value is x=5.
A radio station is having a promotion in which every 12th caller receives a free concert ticket and every 15th caller receives a limo ride. Which caller will be first one to win both?
Answer: Every 60th caller would win both.
Step-by-step explanation:
Since we have given that
every 12th caller receives a free concert ticket.
And
every 15th caller receives a limo ride.
We need to find the first caller who would win.
So, for this we would find L.C.M. of 12 and 15.
And we know the least common multiple of 12 and 15 is 60.
Hence , every 60 th caller would win both.
5u - 5u =u -u help please
Answer:
it would cancel eachother out so infinite
Step-by-step explanation:
The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Which expression represents the volume of the following rectangular prism?
h=2x+9
l= x+2
w= 3x
A) 2x^2+13x+18
B) 6x^3+27x^2+54x
C) 6x^3+39x^2+54x
D) 18x^4+117x^3+162x^2
Solution: As given, Volume of a rectangular prism is given by the formula V = l w h, where l is the length of the prism, w is the width, and h is the height.
also , h=2x+9
l= x+2
w= 3 x
So, volume of prism= (2 x+9)(x+2)(3 x)= (3 x)(2 x+9)(x+2)→Using associative property
=3 x[2 x(x+2)+9(x+2)]→Using (x+a)(x+b)= x(x+a)+a(x+b)=x²+(a+b)x+ab
= 3 x [ 2 x²+ 4 x+ 9 x+18]
= 3 x[ 2 x² +13 x+18]
= (3 x)(2 x²) + (3 x)×(13 x) + (3 x)×(18)→ Using distributive property
= 6 x³+ 39 x² + 54 x → [ use [tex]x^{m} \times x^{n}= x^{m+n}[/tex]
Option (C) is correct.
The expression which represents the volume of the rectangular prism is; Choice C: 6x³+39x²+54x
Volume of a rectangular prismThe volume of the rectangular prism as given is;
V = lwhwhere, h=2x+9, l= x+2, and w= 3x
Therefore, Volume;
V = (2x+9) (x+2)(3x)V = (2x² +13x +18)(3x)V = 6x³+39x²+54xRead more on volume of rectangular prism;
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Find to slope of the line passing through the points 0,4 -8,-1
A,-8/5
B,-5/8
C, 5/8
D, 8/5
The amount of radioactive element remaining, r, in a 100-mg sample after d days is represented using the equation r=100[tex]( \frac{1}{2})^ \frac{d}{5} [/tex] . What is the daily percent of decrease?
87.06%
12.94%
3.13%
10%
Answer:
its 12.94%
Step-by-step explanation
jack purchases 12 gallons of gas on monday .he uses 2/3 of amount purchased communting to and from work during the week additional 2 gallons running errands. how many gallons of gas does john juse for work and errands
What is the value of X in the isosceles trapezoid below?
Answer:
D. 13Step-by-step explanation:
Remember that in a isosceles trapezoid, its angles on the base are always congruent.
Also, we know by definition that the sum of interior angles of a trapezoid is equal to 360°, so
[tex]2(2x)+2(10x+24)=360\\4x+20x+48=360\\24x=360-48\\x=\frac{312}{24}\\ x=13[/tex]
Therefore, the right answer is D.
Answer: 13
a p e x confirmed
When writing a two column proof you should always start with ________ Information.
Rounded to the nearest 3 decimal places, what is the value of r for this data set?
Between what two consecutive positive integers is the square root of 85
A number system is defined as a system of writing to express numbers. between 9 and 10 positive integers is the square root of 85 is there.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find the two consecutive positive integers which have square root of 85 in between.
Firstly we need to know meaning of consecutive numbers.
Numbers which follow each other continuously in the order from smallest to largest are consecutive numbers.
Let us take some perfect square numbers
1,4,16,25,36,49,64,81,100
We know that square root of 81 is 9
square root of 100 is 10
square root of 85 is in between 9 and 10
Hence between 9 and 10 positive integers is the square root of 85 is there.
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A scalene triangle has side side lengths of 12 feet, 8 feet, and 15 feet. what is the perimeter of the triangle
Answer:
gh
Step-by-step explanation:
Which of the quadratic functions has the widest graph? y = 0.3x2 y = –4x2
For the parent function y = f(x), the vertical stretching or compression of the function is a f(x).
If | a | < 1 (a fraction between 0 and 1), then the graph is compressed vertically by a factor of a units.
If | a | > 1, then the graph is stretched vertically by a factor of a units.
For values of a that are negative, then the vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis.
Thus, the equation with the widest graph is 0.3x^2.Yes, Y = 0.3x^2 is correct!!
Find the area of a trapezoid with bases of 8 and 16 and a height of 10. A)1,280 sq. Units B) 240 sq. units C)120 sq. units
Answer: The answer is (C) 120 sq. units.
Step-by-step explanation: We are given to find the area of a trapezoid with bases of lengths 8 units and 16 units and height of 10 units.
We know that the area of the trapezoid with 'a' and 'b' as lengths of the bases and height 'h' is given by
[tex]A=\dfrac{1}{2}(a+b)h.[/tex]
Here, a = 8 units, B = 16 units and h = 10 units.
Therefore, the area of the given trapezoid will be
[tex]a\\\\=\dfrac{1}{2}(a+b)h\\\\=\dfrac{1}{2}\times(8+16)\times 10\\\\=24\times 5\\\\=120~\textup{sq. units.}[/tex]
Thus, the correct option is (C).
What is the factored form of the expression? 4x2 – 81y2
If an organism had 200 atoms of carbon-14 at death, how many atoms will be present after 14,325 years
Answer:
If an organism had 200 atoms of carbon-14 at death, how many atoms will be present after 14,325 years? Round the answer to the nearest hundredth.
35.36
atoms
Gerry is a restaurant manager and plans to advertise her restaurant. The advertising budget is $5000, and she plans to run television and online ads. She would like to run at least 5 television ads and 10 online ads. A television ad costs $500 and an online ad costs $150. Let x represent the number of television ads and y represent the number of online ads. Two of the constraints for this situation are x≥5 and y≥10 . What is the other constraint for this situation?
We are given the two constraints:
x ≥ 5 and y ≥ 10
Now the other constraint must of course be based on the sum of the two. It was given that the budget is $5000 so the sum must be greater than that, that is:
500 x + 150 y ≤ 5000
Find the nth term of this sequence: 1,5,9,13,17
the equation y= -5.131x^2 +31.821x -3.333 approximates the number of people standing in line to catch a commuter train x hours after 5 a.m.
What is the best estimate for the number of people in line at 8 a.m?
A. 77
B. 46
C. 40
D. 32
Answer:
The answer is 42!!! I just took test.
Step-by-step explanation:
Pedro works as a newspaper deliverer. He receives a base pay plus an additional amount per newspaper delivered. Last week, Pedro delivered 5 newspapers and earned $37.50. This week, he delivered 20 newspapers and earned $75. Let x equal the number of newspapers Pedro delivers and y be the earnings he receives in dollars. Which linear function models the scenario? g(x) = 0.4x + 35.5 g(x) = 0.4x + 67 g(x) = 2.5x + 25 g(x) = 2.5x + 50
The linear function models the scenario is g(x) = 2.5x + 25 if He receives a base pay plus an additional amount per newspaper delivered option (C) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
Pedro works as a newspaper deliverer. He receives a base pay plus an additional amount per newspaper delivered.
x = the number of newspapers Pedro delivers
y = the earnings he receives in dollars.
From the data given the linear function can be framed as follows:
y = mx + b
Plug x = 5
y = 37.50
37.50 = 5m + b ...(I)
Plug x = 20, and y = 75
75 = 20m + b ...(II)
After solving equation (I) and equation (II):
m = 2.5
b = 25
y = 2.5x + 25
Replace y with g(x)
g(x) = 2.5x + 25
Thus, the linear function models the scenario is g(x) = 2.5x + 25 if He receives a base pay plus an additional amount per newspaper delivered option (C) is correct.
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What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2 + 8x + 2
Answer-
[tex]\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}[/tex]
Solution-
Given expression is [tex](x+2)^4[/tex]
Applying Binomial Theorem
[tex]\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
Here,
a = x, b = 2 and n = 4
So,
[tex]\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i[/tex]
Expanding the summation
[tex]=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4[/tex]
[tex]=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4[/tex]
[tex]=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16[/tex]
[tex]=x^4+8x^3+24x^2+32x+16[/tex]
Answer:
The answer to this question can be viewed in the images attached.
Hope it helps. Thanks
Write a linear factorization of the function. f(x) = x4 + 4x2
Final answer:
The function f(x) =[tex]x^4 + 4x^2[/tex] is factored using the difference of squares method to achieve its linear factorization. The final factorization over complex numbers is f(x) = x * x * (x + 2i) * (x - 2i).
Explanation:
To write a linear factorization of the function f(x) = [tex]x^4 + 4x^2[/tex] to find the factors of the polynomial that are linear, meaning each factor will be of the form (x - c) where c is a constant.
First, notice that the given polynomial is a quadratic in form, where [tex]x^2[/tex] is our variable. This gives us [tex]f(x) = (x^2)2 + 4(x^2)[/tex]which resembles the sum of squares [tex]a^2 + 2ab + b2 = (a + b)^2.[/tex] However, we only have [tex]a^2 + 2ab[/tex], with b being 2, and a being [tex]x^2[/tex].
To create a perfect square, we can write it as a difference of squares by adding and subtracting 4: [tex]f(x) = (x^2 + 2)^2 - (2)^2[/tex]. This can be factored further using the difference of squares formula, giving us[tex]f(x) = (x^2 + 2 + 2)(x^2 + 2 - 2)[/tex] which simplifies to [tex]f(x) = (x^2 + 4)(x^2).[/tex]
The linear factorization can be found by recognizing that x2 is already a product of linear factors x * x. Since [tex]x^2[/tex] + 4 cannot be factored over the real numbers, we need to use complex numbers to factor it further.
Using the sum of squares, we get [tex]x^2[/tex] + 4 = (x + 2i)(x - 2i), resulting in the final linear factorization over the complex numbers: f(x) = x * x * (x + 2i) * (x - 2i).
The product of two consecutive odd integers is 143. find all such pairs of integers.
How many square feet of carpeting are needed to carpet a 12-foot by 12-foot room
a golfer needs to hit a ball a distance of 500 feet, but there is a 60-foot tall tree that is 100 feet in front of the point where the shot needs to land. given that the maximum height of the shot is 120 feet, and that the intended distance of 500 feet is reached, by how much did the ball clear the tree?
We can create a parabola equation of the trajectory using the vertex form:
y = a (x – h)^2 + k
The center is at h and k, where h and k are the points at the maximum height so:
h = 250
k = 120
Therefore:
y = a (x – 250)^2 + 120
At the initial point, x = 0, y = 0, so we can solve for a:
0 = a (0 – 250)^2 + 120
0 = a (62,500) + 120
a = -0.00192
So the whole equation is:
y = -0.00192 (x – 250)^2 + 120
So find for y when the golf ball is above the tree, x = 400:
y = -0.00192 (400 - 250)^2 + 120
y = 76.8 ft
So the ball cleared the tree by:
76.8 ft – 60 ft = 16.8 ft
Answer:
16.8 ft
How to find the quadratic equation when given the vertex and y intercept?
a function is represented by the set of ordered pairs shown below.
{(-4,3), (-1,3), (0,3), (1,5), (3,7)}
what is the range of this function
Final answer:
The range of the given function is {3, 5, 7}.
Explanation:
The range of a function refers to the set of all possible output values (y-values) it can produce. Given the function represented by the set of ordered pairs {(-4,3), (-1,3), (0,3), (1,5), (3,7)}, to determine its range, we look at the second elements in each ordered pair since they correspond to the y-values produced by the function.
The y-values in the given set are 3, 3, 3, 5, and 7. Even though the value 3 is repeated, it is only counted once in the range. Thus, the range of this function is the set {3, 5, 7}.
Remember, the range includes all unique y-values that the function outputs. This set contains the different y-values that the function produces according to the given ordered pairs, which means these are the possible values that we can get as outputs from this function.
please help.
A doghouse is to be built in the shape of a right trapezoid, as shown below. What is the area of the doghouse?
A.45.5 square feet
B.63 square feet
C.66.5 square feet
D.84 square feet
Answer:
Option C
The area of the doghouse is [tex]66.5\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The area of trapezoid is equal to
[tex]A=\frac{1}{2}(b1+b2)h[/tex]
where
b1,b2 are the parallel bases of trapezoid
h is the height of trapezoid
in this problem we have
[tex]b1=7\ ft[/tex]
[tex]b2=7+5=12\ ft[/tex]
[tex]h=7\ ft[/tex]
substitute
[tex]A=\frac{1}{2}(7+12)7=66.5\ ft^{2}[/tex]
Charles has read 180 pages of book. This isn’t 3/4 of the total number of pages in the book. If p represents the number of pages in the book, what is p?
a.135
b.240
c.320
d. 420
Leo drank 8 servings of iced tea and espresso beverages containing a total of 482 mg of caffeine. How many servings of espresso did he drink?
Answer:
Hope it helps
Step-by-step explanation:
Realize income is ____.
A .The amount of income on hand
B.Income already spent
C. Income that comes from future investment
D. The amount of income you anticipate having
Realized income refers to the amount of income you expect to have, not yet received, including anticipated earnings and future investments.
Realized income represents the income an individual or entity expects to receive but has not yet received. It encompasses anticipated earnings, future investments, and any other income sources that have not yet materialized.
This includes income from salaries, investments, rental properties, or any other sources.
Unlike earned income, which refers to income already received, realized income is a forward-looking concept, reflecting the anticipated financial gains.
It plays a crucial role in financial planning and budgeting, guiding individuals and organizations in making decisions about expenditures, savings, and investment strategies based on expected future income streams.