F(v) =2x if g(x)=5x then f(g(x)
Answer:
10x
Step-by-step explanation:
g(x)=5x
f(x)=2x
f(g(x))=f(5x)
f(g(x))=2*5x=10x
Which of the following statements is equivalent to 10x – 30? 10(x – 30) 10(x – 3) 10 + (x – 20) 10(x – 20)
Answer:
10(x-3) is equivalent to 10x – 30
Step-by-step explanation:
First you have to take everything of out the parentheses and then simplify if needed.
10(x – 30) is not equivalent to 10x – 30 because, 10 times x is 10x, but 10 times 30 is 300. So, 10(x – 30) is not equivalent to 10x – 30.10(x – 3) is equivalent to 10x – 30 because, 10 times x is 10x, and 10 times 3 is 30. So, 10(x – 3) is equivalent to 10x – 30.10 + (x – 20) is not equivalent to 10x – 30 because, 10 minis 20 plus x are -10 + x. So, 10+(x – 20) is not equivalent to 10x – 30.10(x – 20) is not equivalent to 10x – 30 because, 10 times x is 10x, but 10 times 20 is 200. So, 10(x – 20) is not equivalent to 10x – 30.Answer: 10(x-3) is equivalent to 10x – 30
CAN SOMEONE HELP PLEASE!
Answer:
None of these
Step-by-step explanation:
[tex]\frac{360}{n}=24 \implies n=15[/tex]
This is called a pentadecagon.
Could you please help me solve this question?
pleaseeeee help me with this algebra question! select the solutions for the quadratic equation!
Answer:
I dont know if this is right but i got -7/3.
Sorry if its wrong
If 4 out of 7 students at
Johnson High play sports,
about how many of the 504
students at the school play
sports?
[tex]\frac{4}{7}(504)=\boxed{288}[/tex]
An investment pays 10% interest compounded monthly. What percent, as a decimal, is the effective annual yield? Enter your answer as a decimal rounded to four decimal places.
[tex]~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ APY=\left(1+\frac{r}{n}\right)^{n}-1 ~\hfill \begin{cases} r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12 \end{cases} \\\\\\ APY=\left(1+\frac{0.1}{12}\right)^{12}-1\implies APY=\left( \frac{121}{120} \right)^{12}-1\implies APY\approx 0.1047[/tex]
What is the smallest odd number of using 9,3,6,8,1,9
Answer: well one is
Bc its the smallest besides zero, but zero is neither odd or even
Step-by-step explanation:
Will mark brainliest
Using the given definition and [tex]\Delta x=\frac{0-(-2)}n=\frac2n[/tex], we have
[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \lim_{n\to\infty} \sum_{i=1}^n \left(7\left(-2+\frac{2i}n\right)^2 + 7\left(-2+\frac{2i}n\right)\right) \frac2n \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac2n \sum_{i=1}^n \left(14 - \frac{42i}n + \frac{28i^2}{n^2}\right)[/tex]
Recall the well-known power sum formulas,
[tex]\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + 1 + \cdots + 1}_{n\,\rm times} = n[/tex]
[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]
[tex]\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + 9 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6[/tex]
Reducing our sum leads to
[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \lim_{n\to\infty} \frac2n \left(\frac{7n}3 - 7 + \frac{14}{3n}\right) = \lim_{n\to\infty} \left(\frac{14}3 - \frac{14}n + \frac{28}{3n^2}\right)[/tex]
As [tex]n[/tex] goes to ∞, the rational terms containing [tex]n[/tex] will converge to 0, and the definite integral converges to
[tex]\displaystyle \int_{-2}^0 (7x^2+7x) \,dx = \boxed{\frac{14}3}[/tex]
Identify the vertex of the parabola ?
Step-by-step explanation:
second one
explanation: trust me bro
if u=–s^2rt then what does r equal?
The required rewritten equation in terms of variable 'r' is r = -u/s²t. By applying simple arithmetic operations, the required equation is obtained.
How to rewrite an equation in terms of another variable?Consider an equation c = ax + by. Solving for variable 'a'.
Step1: Write the required variable terms on one side
Step2: Add/Subtract like terms if any or take common if any
Step3: Divide/Multiply the coefficient of the required variable
Step4: simplify the obtained terms for the required variable
As follows:
c = ax + by
⇒ ax = by - c
⇒ ax/x = (by - c)/x
∴ a = (by - c)/x
Calculation:The given equation is u = -s²rt
dividing by 't' on both sides:
⇒ u/t = -s²rt/t
⇒ u/t = -s²r
dividing by 's²' on both sides:
⇒ u/s²t = -s²r/s²
⇒ u/s²t = -r
∴ r = -u/s²t
Thus, the required equation for variable 'r' is r = -u/s²t.
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Help me with this please asap?!
Answer:
None of these answers are correct.
Step-by-step explanation:
[tex]QR=\frac{25+45}{2}=35[/tex]
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
By Trapezoid mid - segment theorem :
[tex] \qquad❖ \: \sf \:QR = \cfrac{MN+ OP}{2} [/tex]
[tex] \qquad❖ \: \sf \:QR= \cfrac{25+ 45}{2} [/tex]
[tex] \qquad❖ \: \sf \:QR = \cfrac{70}{2} [/tex]
[tex] \qquad❖ \: \sf \:QR= 35 \: \: units[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
length of segment QR = 35Brandon enters bike races. He bikes 91 half miles every1 half hour. Complete the table to find how far Brandon bikes for each time interval.
Help,
Using proportions, it is found that he bikes:
19 miles in one hour.28.5 miles in one and a hour.38 miles in two hours.47.5 miles in two and a hours.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, the proportion is that he bikes 9.5 miles each half hour, hence:
In one hour, he bikes 2 x 9.5 = 19 miles.In one and a half hour, he bikes 3 x 9.5 = 28.5 miles.In two hours, 4 x 9.5 = 38 miles.In two and a half hours, he bikes 5 x 9.5 = 47.5 miles.More can be learned about proportions at https://brainly.com/question/24372153
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1+r+r²+...........+r^n+1=1-r^n/1-r
mathematical induction mesthod
Answer + Step-by-step explanation:
the correct question:
For r ≠ 1 ,Prove using the mathematical induction method that :
[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]
………………………………………………………………………………………………………………
for n = 0 :
1⁰ = 1 and (1 - r⁰⁺¹)/(1 - r) = (1 - r)/(1 - r) = 1
Then the property is true for n = 0.
For n ≥ 0 :
Suppose
[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]
And prove that
[tex]1+\cdots+r^{n+1} =\frac{1-r^{n+2}}{1-r}[/tex]
Since :
[tex]1+\cdots+r^{n+1} =(1+\cdots+r^n)+r^{n+1}[/tex]
Then
[tex]1+\cdots+r^n+r^{n+1} =\frac{1-r^{n+1}}{1-r}+r^{n+1}[/tex]
[tex]= \frac{1-r^{n+1}+r^{n+1}(1-r)}{1-r}[/tex]
[tex]= \frac{1-r^{n+2}}{1-r}[/tex]
Then according to the mathematical induction method
[tex]1+\cdots+r^n =\frac{1-r^{n+1}}{1-r}[/tex]
Where n is a natural number and r ≠ 1.
Determine if the series converges or diverges. If the series converges, find its sum.
9
Σ n(n+3)
n=1
OA. The series diverges.
OB. The series converges to
11
2
7
OC. The series converges to
2
D. The series converges
15
-
2
The true statement about the series [tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex] is that (a) the series diverges
How to determine if the series diverges or converges?The series is given as:
[tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex]
Take the limit of the function to infinity
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)}[/tex]
This gives
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty * (\infty +3)}[/tex]
Evaluate the sum
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty * \infty}[/tex]
Evaluate the product
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = \frac{9}{\infty}[/tex]
Evaluate the quotient
[tex]\lim_{n \to \infty} \frac{9}{n(n +3)} = 0[/tex]
Since the limit is 0, then it means that the series diverges
Hence, the true statement about the series [tex]\sum\limits^{\infty}_{n=1} \frac{9}{n(n +3)}[/tex] is that (a) the series diverges
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Answer:
B. The series converges to [tex]\displaystyle{\frac{11}{2}}[/tex].
Step-by-step explanation:
Before evaluating the infinite series, the expression can be decomposed as the sum of two fractions (partial fraction decomposition) as follows.
Let [tex]\textit{A}[/tex] and [tex]\textit{B}[/tex] be constants such that
[tex]{\displaystyle{\frac{9}{n\left(n+3\right)}}}} \ \ = \ \ \displaystyle{\frac{A}{n} \ \ \ + \ \ \frac{B}{n+3}}[/tex]
Multiply both sides of the equation by the denominator of the left fraction,
[tex]n\left(n+3\right)[/tex], yielding
[tex]9 \ \ = \ \ A\left(n+3\right) \ \ + \ \ B \-\hspace{0.045cm} n[/tex]
Now, let [tex]n \ = \ 0[/tex], thus
[tex]\-\hspace{0.2cm} 9 \ \ = \ \ A\left(0 + 3\right) \ + \ B\left(0\right) \\ \\ 3 \-\hspace{0.035cm} A \ = \ \ 9 \\ \\ \-\hspace{0.11cm} A \ \ = \ \ 3[/tex].
Likewise, let [tex]n \ = \ -3[/tex], then
[tex]\-\hspace{0.5cm} 9 \ \ = \ \ A\left(-3 + 3\right) \ + \ B\left(-3\right) \\ \\ -3 \-\hspace{0.035cm} B \ = \ \ 9 \\ \\ \-\hspace{0.44cm} B \ \ = \ \ -3[/tex]
Hence,
[tex]\displaystyle{\sum_{n=1}^{\infty} {\frac{9}{n\left(n+3\right)}}} \ = \ \displaystyle\sum_{n=1}^{\infty} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right)[/tex].
First and foremost, write the nth partial sum (first nth terms) of the series,
[tex]\displaystyle\sum_{n=1}^{n} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \displaytstyle{\frac{3}{1} \ - \frac{3}{4} + \ \frac{3}{2} \ - \frac{3}{5} \ + \frac{3}{3} \ - \frac{3}{6} \ + \frac{3}{4} \ - \frac{3}{7}} \\ \\ \\ \-\hspace{3.58cm} + \ \displaystyle{\frac{3}{5} \ - \ \frac{3}{8} \ + \ \frac{3}{6} \ - \ \frac{3}{9} \ + \ \frac{3}{7} \ - \ \frac{3}{10}} \\ \\ \\ \-\hspace{3.58cm} + \ \ \dots[/tex]
[tex]+ \ \ \displaystyle{\frac{3}{n-3} \ - \ \frac{3}{n} \ + \ \frac{3}{n-2} \ - \ \frac{3}{n+1}} \\ \\ \\ \ + \ \frac{3}{n-1} \ - \ \frac{3}{n+2} \ + \ \frac{3}{n} - \ \frac{3}{n+3}}[/tex].
Notice that the expression forms a telescoping sum where subsequent terms cancel each other, leaving only
[tex]\displaystyle\sum_{n=1}^{n} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \displaytstyle{\frac{3}{1} \ + \ \frac{3}{2} \ + \frac{3}{3} \ - \ \frac{3}{n+1}} - \ \frac{3}{n+2} \ - \ \frac{3}{n+3}}}[/tex].
To determine if this infinite series converges or diverges, evaluate the limit of the nth partial sum as [tex]n \ \rightarrow \ \infty[/tex],
[tex]\displaystyle\sum_{n=1}^{\infty} \left(\frac{3}{n} \ - \ \frac{3}{n+3}\right) \ \ = \ \-\hspace{0.33cm} \lim_{n \to \infty} \left(\displaytstyle{\frac{11}{2} \ - \ \frac{3}{n+1} \ - \ \frac{3}{n+2} \ + \ - \ \frac{3}{n+3}\right) \\ \\ \\ \-\hspace{3.25cm} = \ \ \ \displaystyle{\frac{11}{2} \ - \ 0 \ - \ 0 \ - \ 0} \\ \\ \\ \-\hspace{3.25cm} = \ \ \ \displaystyle{\frac{11}{2}[/tex]
Consider the following figure:
The value of a is
Answer:
125
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation according to this information and that will help us find the value of x:
65 + 60 = x add like terms
125 = x is the answer we are looking for.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{equation:}[/tex]
[tex]\large\textsf{a = 60 + 65}[/tex]
[tex]\huge\textsf{solving:}[/tex]
[tex]\large\textsf{a = 60 + 65}[/tex]
[tex]\large\textsf{60 + 65 = a}[/tex]
[tex]\huge\textsf{simplify it:}[/tex]
[tex]\large\textsf{a = 125}[/tex]
[tex]\huge\textsf{therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{a =} \frak{125}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
2. What is the value of x? Show your work.
can someone explain this to me? how would I find X? Thank you in advance!
Answer:
7
Step-by-step explanation:
→ Find the scale factor
30 ÷ 25 = 1.2
→ Multiply answer by 20
20 × 1.2 = 24
→ Equate equation to 24
4x - 4 = 24
→ Add 4 to both sides
4x = 28
→ Divide both sides by 4
x = 7
Simplify [tex]\frac{6a^2 b^-^2}{8a^-^3 b^3}[/tex] Assume a≠0 and b≠0
Answer:
sorry i thought i knew it
Step-by-step explanation:
Answer:
3rd option
Step-by-step explanation:
using the rules of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] : nm > n
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex] : n > m
[tex]\frac{6a^2b^{-2} }{8a^{-3b^3} }[/tex] ← separate the variables
= [tex]\frac{6}{8}[/tex] × [tex]\frac{a^2}{a^{-3} }[/tex] × [tex]\frac{b^{-2} }{b^3}[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{2-(-3)}[/tex] × [tex]\frac{1}{b^{3-(-2)} }[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{2+3}[/tex] × [tex]\frac{1}{b^{3+2} }[/tex]
= [tex]\frac{3}{4}[/tex] × [tex]a^{5}[/tex] × [tex]\frac{1}{b^{5} }[/tex]
= [tex]\frac{3a^{5} }{4b^{5} }[/tex]
8 ft
10 ft
20 ft
A trapezoid has a height of 10 feet,
and base measurements of 20 feet and
8 feet. What is the area?
[?] square feet
Hint: The formula for the area of a trapezoid is: (b₁b2). h
Enter
ग
15
The area of the trapezoid is 140 square feet
What are areas?The area of a shape is the amount of space on that shape
How to determine the area of the trapezoid?The dimensions of the trapezoid are given as:
Height = 10 feet
Parallel bases = 8 feet and 20 feet
The area of a trapezoid is calculated using
Area = 0.5 * (Sum of parallel bases) * Height
Substitute the known values in the above equation
Area = 0.5 * (8 + 20) * 10
Evaluate the equation
Area = 140
Hence, the area of the trapezoid is 140 square feet
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The length and width of a rectangle must have a sum of 60. Find the dimensions of the rectangle that will have the maximum area. [Hint: Let x and 60-x be the length
and width. The area can be described by the function f(x)=x(60-x).]
The length is… and the width is…
If the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.
Given that the sum of length and breadth of rectangle is 60.
We are required to find the dimensions of the rectangle that will have the maximum area. Area is basically how much part of surface is being covered by that particular shape or substance.
Let the length of rectangle be x.
According to question the breadth will be (60-x).----2
Area of rectangle=Length *Breadth
A=x(60-x)
A=60x-[tex]x^{2}[/tex]
Differentiate A with respect to x.
dA/dx=60-2x
Again differentiate with respect to x.
[tex]d^{2} A/dA^{2}[/tex]=-2x
-2x<0
So the area is maximum because x cannot be less than or equal to 0.
Put dA/dx=0
60-2x=0
60=2x
x=30
Put the value of x in 2 to get the breadth.
Breadth=60-x
=60-30
=30
Hence if the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.
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3. What is f(2) if f(x) = 2x³ - 19x² +28x + 47?
O 45
O 40
O 43
O 37
Answer: C: 43
Step-by-step explanation:
As we are calling the function with 2 for x, we can substitute 2 for every x we see in the function and solve.
[tex]f(2)=2(2)^3-19(2)^2+28(2)+47\\=2(8)-19(4)+28(2)+47\\=16-76+56+47\\=43[/tex]
Hence, f(2) is 43.
Find the solution of the system of equations
shown on the graph.
Answer: (0,6)
Step-by-step explanation:
The solution is where the graphs intersect.
Melissa is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Melissa has been adding money. Suppose that x and y are related by the equation y = 550+20x.
Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
What is the change per week in the amount of money in the account?
What was the starting amount of money in the account?
Check the picture below.
if a rectangular piece of metal has 27.75 square inches what is the length and width?
We cannot get further information about the dimensions of the piece since the number of variables is greater than the number of equations.
What are the dimensions of a rectangular piece of metal?
By geometry we know that the area of the piece of metal is equal to the product of its length and width, then we must find two real numbers such that:
l · w = 27.75, where l, w > 0.
Unfortunately, we cannot get further information about the dimensions of the piece since the number of variables is greater than the number of equations. We need at least one equation to find an unique solution.
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What is the equation of the line described below in slope-intercept form?
The line passing through point (-1, 5) and parallel to the line whose equation is x + y = 10
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]x + y = 10\implies y = -x+10\implies y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+10 \leftarrow \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so, we're really looking for the equation of al ine whose slope is -1 and that passes through (-1 , 5)
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-1}( ~~ x-\stackrel{x_1}{(-1) ~~ }) \\\\\\ y-5 = -(x+1)\implies y-5=-x-1\implies y=-x+4[/tex]
Find the upper quartile summary for the data. {51, 49, 52, 46, 50, 38, 38, 45, 34, 52, 46}
The upper quartile for the given data is 51 .
Given data: {51,49,52,46,50,38,38,45,34,52,46}
Data in arranged form: {34,38,38,45,46,46,49,50,51,52,52}
Find the median first, then the upper quartile. There are eleven data points, thus look at term six to determine the median as there are five data points on any side. The median is 46 because the sixth term is 46.
The upper extreme, 52, and the median are then used to determine the upper quartile; make sure not to include the median data point when dividing the groups. The upper quartile is the third term (between the median and upper extreme) because there would be two data points on each side if there were only five data points from the median to the upper extreme. The third term, which is 51, falls into the upper quartile.
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Solve the inequality for x.
OA.
X S
5- 2/2 x ²
x 2
28
OB. x ≤ 7
OC.
28
9
OD. x ≥ 7
The solution to the inequality x-13<=7+4x is x >= -20/3
How to solve the inequality?The inequality expression is given as:
x-13<=7+4x
Add 13 to both sides of the inequality
x <= 20 + 4x
Subtract 4x from both sides of the inequality
-3x <= 20
Divide both sides of the inequality by -3
x >= -20/3
Hence, the solution to the inequality x-13<=7+4x is x >= -20/3
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Complete question
Solve the inequality for x
x-13<=7+4x
Suppose a stock qualifies as having moderate risk if the standard deviation of its monthly rate of return is less
than 10%. A stock rating agency randomly selects 36 months and decides the rate of return for a specific fund.
The standard deviation of the rate of return is computed to be 4.95%. Is there sufficient evidence to conclude
that the fund has moderate risk at the α=0.05 level of significance? A standard probability plot shows that the
monthly rates of return are typically distributed.
Test the claim using a hypothesis test.
What are the null and alternative hypotheses for the hypothesis test?
What is the conclusion based on the hypothesis test?
The conclusion of the Hypothesis Conclusion is; that there is sufficient evidence to support the claim that the fund has moderate risk.
How to test hypothesis claim?
We are given;
Sample size; n = 36
Population standard deviation; σ₀ = 10
Sample standard deviation; s = 4.95
Significance level; α = 0.05
Claim: Standard deviation less than 10
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis needs to contain an equality and the value mentioned in the claim. If the claim is the null hypothesis, then the alternative hypothesis states the opposite of each other. Thus;
Null Hypothesis; H₀: σ = 10
Alternative Hypothesis; H₁: σ < 10
Compute the value of the test statistic:
χ2 = [(n - 1)/(σ²)] * s²
χ2 = [(36 - 1)/(10²)] * 4.95²
χ2 = 8.576
The critical value of the left-tailed test is given in the row with df = n - 1 = 36 - 1 = 35 and in the column with 1 − α = 0.95 of the chi-square distribution table online, we have;
χ2_{1 - α} = 21.77
The rejection region then contains all values smaller than 21.77
If the test statistic is in the rejection region, then reject the null hypothesis:
8.576 < 13.848
Thus, we will reject H₀ and conclude that there is sufficient evidence to support the claim that the fund has moderate risk.
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I need help with this question:
Simplify
The simplified form of the given expression as a fraction is 7x/x-7
Simplification of fractionsFractions are written as a ratio of two integers. For instance a/b is a fraction where a and b are integers.
Given the expression below;
(1/7+1/x)/(1/49+1/x²)
Find the LCM to have:
(x+7/7x)/(x²-49)/49x²
Divide to have:
x+7/7x * 49x²/(x²-49)
(x+7) * 7x/(x+7)(x-7)
Cancel out the like terms to have:
1 * 7x/x-7
= 7x/x-7
Hence the simplified form of the given expression as a fraction is 7x/x-7
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what is the solution I need help
Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is less than 0.4
Square root of numbersThe square root of numbers is is expressed using the square root sign. In order to determine the square root os 0.15 given, we need need to determine the square of perfect square before and after the given number.
For the square root of √0.09
√0.09 = 0.3
Similarly for the square root of √0.16
√0.16 = 0.4
Since the resulting value is 0.3 and 0.4, hence the square root of 0.15 must be between these two values on the number line.
Since Hassan's estimation is between 0.4 and 0.5, hence the Hassan is incorrect because √0.15 is less than 0.4
Learn more on square root of decimal here: https://brainly.com/question/16694048
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