Answer:
(11a^5 - 3b^4) (3b^4 + 11a^5) = 121a^10 - 9b^8
Step-by-step explanation:
I got the 11 part by doing √121 = 11
I got the a^5 by knowing that a needs to have the same exponent both times and 5+5=10. Thats how I got the a^5 part.
Answer: (11a^5 - 3b^4) (3b^4 + 11a^5) = 121a^10 - 9b^8
I need help anyone with graphs
The given function shows imply that the graph g(x) is shifted two units right and three units up.
Option B is correct.
What is the transformation of a function?The transformation of a function occurs in a fancy way such that a function maps itself. f: x → x.
From the given information:
Let's take a look at the function f(x) that goes through 0 just when x = 0. Now we want to move it to the right by 2. It implies that it has to go through 0 when x = +2.
Now, we have to add 2 to x, then the function becomes f'(x) = f(x-2) will be shifted by 2 units to the right.
Similarly, the same scenario occurs when shifting up. Again imagine your function passes 0 when x = 0. We have to add 3. Now, the function f’’(x) = f(x) + 3 will be shifted by 3 units up.
Combining the two transformations, we have:
g(x) = f(x-2) + 3Therefore, we can conclude that the function implies that the graph g(x) is shifted two units right and three units up.
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You are investigating having business cards printed for your new game store. A local printing company charges $250 for the cardboard used and an hourly rate for labour of $40.
a. If h is the number of hours of labour required to print the cards, construct an equation for the cost
of the cards, C.
b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give
your answer to the nearest minute.
c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you
get printed with your current budget?
d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?
Answer:
See below.
Step-by-step explanation:
a. If h is the number of hours of labour required to print the cards, construct an equation for the cost of the cards, C.
C = $250 + ($40/hr)*h
b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give your answer to the nearest minute.
$1000 = $250 + ($40/hr)*h
($40/hr)*h = $750
h = 18.75 hours
(18.75 hours)(60 min/hr) = 1125 minutes
c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you get printed with your current budget?
(18.75 hr)*(1000 cards/hr) = 18,750 cards
d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?
Photocopy Cost for the first 1000 single-sided cards is:
(1000 cards)*($0.15) = $150
Photocopy Cost for the final 17,750 single-sided cards is:
(17,750)*($0.10) = $1,775
Totoal photocopy cost for 18,750 single-sided cards is $1,925. [1775+150]
The cheapest option for 18,750 cards is printing: $1,000
Printing is (1,925 - 1000) $925 cheaper than photocopying.
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 2 more than 5 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 110
Mark and Don have 18 and 92 marbles respectively.
What is the solution of the equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
Let the number of marbles Mark has be x.
According to the question,
Don has (5x+2) marbles.
Total number of marbles=110
Thus, the required equation is:
x+5x+2=110
6x=108
x=108/6
x=18
Mark has 18 marbles.
Don has (5*18+2)=92 marbles.
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What is the slope?
Please help!! Thankss
Answer:
slope = 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0,2) ← 2 points on the line
m = [tex]\frac{2-0}{0-(-1)}[/tex] = [tex]\frac{2}{0+1}[/tex] = [tex]\frac{2}{1}[/tex] = 2
what is x
x =x=x, equals
^\circ
∘
degrees
Kindly solve this please!
Diagram for both the questions are given.
Answer:
Q9 - B) 8Q10 - D) 4.5========================
Question 9We have a diagram and need to find the number of routes without repeat paths:
[tex]ABCA[/tex] or [tex]ACBA[/tex]We can see that there is one route from A to B, two routes from B to C and two routes from C to A. This is same on reverse order.
This gives us the number of routes:
[tex]ABCA = 1*2*2 = 4[/tex][tex]ACBA = 2*2*1 = 4[/tex]Total number is:
[tex]4 + 4 = 8[/tex]The matching answer choice is B
---------------------------------------------------------------------------
Question 10From the given we can observe that:
ABC and DCE are similar triangles, since they have same angle at vertex E (vertical angles are equal) and both are right triangles.
From similarity we get same ratio of corresponding sides:
[tex]AE/DE = AB/CD = 3/9 = 1/3[/tex]We can find areas of triangles ACD and ECD and subtract to get the area of triangle AEC:
[tex]S_{ACD} - S_{ECD} = S_{AEC}[/tex]As per ratio of corresponding sides:
[tex]AE/DE = 1/3[/tex]As per segment addition:
[tex]AE + DE = AD = 4[/tex]From the two equations above we get:
[tex]DE = 3/4*AD = 3/4*4 = 3[/tex]Now, the required area is:
[tex]S_{ACD} - S_{ECD} = 1/2(4*9) - 1/2(3*9) = 4.5[/tex]This is matching the answer choice D
Answer:
9) B. 8
10) D. 4.5
Step-by-step explanation:
Question 9
For ease of visualization, label the different legs of the journey on the diagram (see attachment).
The journey needs to start and end at point A, go through points B and C (in any order), and not travel any road twice.
The different routes are:
AB (u), BC (x), CA (w)AB (u), BC (y), CA (w)AB (u), BC (x), CA (z)AB (u), BC (y), CA (z)AC (w), CB (x), BA (u)AC (z), CB (x), BA (u)AC (w), CB (y), BA (u)AC (z), CB (y), BA (u)Therefore, there are 8 different routes.
Question 10
Triangles EDC and EAB are similar since they have congruent angles:
∠EDC ≅ ∠EAB (both right angles)∠DEC ≅ ∠AEB (vertical angle theorem)Therefore, their corresponding sides are in proportion.
⇒ CD : BA = ED : EA
⇒ 9 : 3 = ED : EA
⇒ 3 : 1 = ED : EA
Since we know that AD = 4:
⇒ ED = 3
⇒ EA = 1
Area of a triangle
[tex]\sf Area = \dfrac{1}{2} \times base \times height[/tex]
To find the area of triangle AEC, subtract the area of triangle EDC from the area of triangle ADC.
[tex]\begin{aligned}\textsf{Area of triangle AEC} & = \sf Area\:of\:\triangle ADC - Area\:of\:\triangle EDC\\& = \sf \dfrac{1}{2} \cdot CD \cdot AD-\dfrac{1}{2} \cdot CD \cdot ED\\& = \sf \dfrac{1}{2}(9)(4)-\dfrac{1}{2}(9)(3)\\& = \sf 18-13.4\\& = \sf 4.5\:\:units\:squared\end{aligned}[/tex]
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Find a polynomial function of lowest degree with
rational coefficients that has the given numbers
as some of its zeros.
- 5i, 4
Answer:
x^3-4x^2+25x-100
Step-by-step explanation:
We have 2 roots -5i and 4. Using the conjugate root theorem for the root -5i, we know that 5i should be another root
Combining the roots into a polynomial gives us:
(x+5i)(x-5i)(x-4)
Expand:
(x^2 + 25)(x-4)
x^3-4x^2+25x-100
You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. The sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. Think about how each function is related to its reciprocal function.
How are the graphs of the reciprocal functions related to their corresponding original functions? What happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? Describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions.
The graphs of the reciprocal functions are related to their corresponding original functions based on the information illustrated below.
What are trigonometric functions?It should be noted that the trigonometric functions are the real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
There are six functions of an angle. They are sine (sin), cosine (cos), tangent (tan), cotangent, secant, and cosecant (csc).
It should be noted that all the y-coordinates of a reciprocal function will be the reciprocals of the y-coordinates of the original function. Then, the graph of a reciprocal function has a vertical asymptote at each zero of the original function. For example, y=arcsinx reflects against y=sinx.
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Please please answer following question and show work
The y-intercept of the function f(x) is (0, 10/3)
The limits of the functionThe function is given as:
[tex]f\left(x\right)=\frac{30}{1+2^{3-x}}[/tex]
As x approaches infinity, we have:
[tex]\lim_{x \to \infty} \frac{30}{1+2^{3-x}}[/tex]
This gives
[tex]\lim_{x \to \infty} \frac{30}{1+2^{3-\infty}}[/tex]
[tex]\lim_{x \to \infty} \frac{30}{1+2^{-\infty}}[/tex]
Evaluate
[tex]\lim_{x \to \infty} \frac{30}{1}[/tex]
[tex]\lim_{x \to \infty} 30[/tex]
As x approaches negative infinity, we have:
[tex]\lim_{x \to -\infty} \frac{30}{1+2^{3+x}}[/tex]
This gives
[tex]\lim_{x \to -\infty} \frac{30}{\infty}[/tex]
Evaluate
[tex]\lim_{x \to -\infty} 0[/tex]
Hence, the limits of the function are [tex]\lim_{x \to \infty} 30[/tex] and [tex]\lim_{x \to -\infty} 0[/tex]
The horizontal asymptoteRemove the denominator
f(x) = 30
Also, set the numerator to 0
f(x) = 0
Hence, the horizontal asymptotes are y = 30 and y = 0
The y-interceptSet x = 0
[tex]f\left(0\right)=\frac{30}{1+2^{3-0}}[/tex]
Evaluate
[tex]f\left(0\right)=\frac{30}{9}[/tex]
Divide
[tex]f\left(0\right)=\frac{10}3[/tex]
Hence, the y-intercept is (0, 10/3)
How the numerator is related to (b)The numerator of f(x) is 30.
In (b), we have
The horizontal asymptotes are y = 30 and y = 0
This means that the horizontal asymptotes and the numerator are the same
The graphSee attachment for the graph of f(x)
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The function G(x) = 2-sin(x) is the result of the application of
transformations on the original function F(x) = cos(x). Which of the following options correctly describes the transformations applied to F(x)?
The transformations applied to F(x) is a vertical shift of 2 and a phase shift of π/2.
What are transformations?When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects."
Function transformations are highly useful for graphing functions without having to start from scratch because they allow you to move, extend, compress, or reflect the curve.
The graph of the parent function is either "moved," "resized," or "reflected" by a function transformation. The three primary categories of function transformations are as follows:Translation,Dilation and Reflection.
The given function F(x)=cos x is transformed to G(x)=2-sin x, by applying a vertical shift of 2 units upwards and a phase shift of π/2.
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I dont know how to do this
Answer:
Option C = 78,125Step-by-step explanation:
First prime factorize 135,
135 = 5×3×3×3
Now prime factorize 128,
128=2×2×2×2×2×2×2 = 2^7
the highest prime factor of 135 is 5,
Let 5 be x
the highest power of the lowest prime factor of 128 which is the power 2 is 7
Let 7 be y
According to the question x^y = 5^7
= 78,125Charlize accidentally omitted two consecutive integers when adding the elements of the arithmetic sequence, $\{1, 2, 3, \ldots, n\}$. If the sum she obtained is $241$, what is the smallest possible value of $n$
The smallest possible value of N is 23.
According to the statement
we have given that the sequence {1,2,3.....n}
and the sum is 241. we have to find the smallest value of n.
So, for this purpose we use summation formula of an arithmetic sequence
Sn = n /2 ( a1 +an )
Put the values in it then.
Note that the sum of the first 21 integers is 21 * 22 /2 = 231...this isn't large enough as compare to given value.
And the sum of the first 22 integers = 22 * 23 / 2 = 253
So 253 - 241 = 12 = omitted sum.....
but the sum of two consecutive integers must be odd
And......the sum of the first 23 integers is 23 * 24 / 2 = 276
So.......276 - 241 = 35 = omitted sum
So....the consecutive integers omitted must be 17 and 18
So....... the smallest value of n is 23
So, The smallest possible value of N is 23.
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A sample of 20 pages was taken from a Yellow Pages directory. On each page, the mean area devoted to display ads was measured in square millimeters (mm2). The sample mean is 346.5 mm2 and sample standard deviation is 170.38 mm2. The 95 percent confidence interval for the mean is:
The 95 percent confidence interval for the mean is (266.76,426.24).
A confidence interval is how much uncertainty there is with any particular statistic. Confidence intervals are often used with a margin of error. It tells you how confident you can be that the results from a poll or survey reflect what you would expect to find if it were possible to survey the entire population. Confidence intervals are intrinsically connected to confidence levels.
The formula of Confidence Interval = Mean ± [tex]t\frac{Standard Deviation}{\sqrt{number of observations} }[/tex]
where t is a constant
Given:
Mean = 346.5
Standard Deviation = 170.378
t-critical value for 95% Confidence interval with degrees of freedom(df)=n-1= 19 is 2.093
∴ Substituting values in formula we get
E = [tex]2.093 X170.378/\sqrt{20}[/tex] = 2.0931.96 x 38.0976=79.74
95% Confidence interval : (346.5-79.74,346.5+79.74)
95% Confidence interval : (266.76,426.24)
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Solving equations with fractions- how do i solve this
Answer:
[tex]x=\frac{83}{36}[/tex]
Step-by-step explanation:
1) Convert [tex]2\frac{1}{4}[/tex] to improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].
[tex]x-\frac{2\times4+1}{4} = \frac{1}{18}[/tex]
2) Simplify [tex]2\times4[/tex] to 8.
[tex]x-\frac{8+1}{4} =\frac{1}{18}[/tex]
3) Simplify [tex]8+1[/tex] to 9.
[tex]x-\frac{9}{4} =\frac{1}{18}[/tex]
4) Add [tex]\frac{9}{4}[/tex] to both sides.
[tex]x=\frac{1}{18} +\frac{9}{4}[/tex]
5) Simplify [tex]\frac{1}{18} +\frac{9}{4}[/tex] to [tex]\frac{83}{36}[/tex].
[tex]x=\frac{83}{36}[/tex]
Decimal Form: 2.305556
Answer:
83/36
Step-by-step explanation:
x - 2 1/4 = 1/18
x = 1/18 + 9/4
L.C.M= 36,
x = 1x2/18x2 + 9x9/4x9
x = 2/36 + 81/36
x = 83/36
Decimal form = 2.305556
1. Mrs Ratu bought a Twin-Tub Washing Machine from M.H Homemaker in Suva. The washing machine's Cash Price is $650.00. She paid a deposit of $250.00 and agrees for a 24 monthly payments of $25.50 per month. a. Calculate the monthly instalment of 24 months. b. How much would she have to pay altogether for the Washing Machine? C. How much could she save if she had bought in cash?
Answer:
925.5
Step-by-step explanation:
Hope it helps!
<3
PLLLLLLLLEASEEEEEEEEE
Answer:
[tex]x^2+8x+8+\frac{-9}{x+4}[/tex]
Step-by-step explanation:
it would be simpler to do synthetic division by removing the variables and using the coefficients:
i hope this helped!
Mrs. fresneda sells homemade soap at the farmers' market for $4.00 per bar. write an expression for how much mrs. fresneda earns selling bars of soap. then, evaluate the expression to determine how much money she will earn if she sells 26 bars of soap.
The expression which shows the earning of Mrs. Fresneda is 4x and the money that she will earn by selling 26 bars of soap is $144.
Given that price of soap is $4.00 per bar.
We have to find the expression which shows the earning of Mrs. Fresneda after selling soap bars and the money that she will earn by selling 26 bars of soap.
let the number of soap bars be x.
We know that the revenue is the product of price and quantity.
Money that Mrs.Fresneda earns is 4*x
=4x
Expression is 4x which shows that money that Mrs. Freneda will earn by selling soap bars.
We have to just put x=26 in the expression to calculate the money after selling 26 bars of soap.
Money=4*26
=$144
Hence the expression is 4x and the money that Mrs.Freneda will earnby selling 26 bars of soap is $144.
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When calculating correlation and regression both sets of data must be __________
When calculating correlation and regression both sets of data must be Statistical.
According to the statement
we have to find the type of data when we calculate the correlation and regression both sets.
so, The difference between these two statistical measurements is that correlation measures the degree of a relationship between two variables (x and y), whereas regression is how one variable affects another.
And when we calculate both then data sets must be a statistical data. because correlation summarizing direct relationship between two variables and regression predict or explain numeric response. So, without statistical data this is not possible to calculate correlation and regression both sets.
so, When calculating correlation and regression both sets of data must be Statistical.
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Please please help me dayson is covering a package in the shape of a rectangular prism with wrapping paper. the package is 50 centimeters by 20 centimeters by 18 centimeters. he has 1 square meter of wrapping paper. can he completely cover the package with wrapping paper? complete the explanation to show your answer. dayson has 1 m2 of wrapping paper, which is cm2. the package has a surface area of cm2. does dayson have enough paper? enter yes or no.
The package has a surface area of 4520cm². The area of the package is less than the area of the wrapping paper. So, dayson can cover the package with the wrapping paper.
According to the question,
The first step is to determine the surface area of the package.
Total surface area of a cuboid = 2 (l w + w h + l h)
where:
• l = length
• w = width
• h = height
2[(50 x 20) + (50 x 18) + (20 x 18)] = 4520cm²
The second step is to convert 1 square meter to cm
1m² = 100 cm²
100 x 100 = 10,000
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In a zoo, the ratio of female to male tiger is 2:3.
There are 30 male tigers.
How many tigers are female?
The results of a poll show that the true proportion of students who prefer the new schedule is likely in the interval (0.195,0.245).
What is the point estimate of the proportion of students who prefer the new schedule
The point estimate of the proportion of students who prefer the new schedule is 0.22.
Definition of Point Estimate
Point estimation is a technique used in statistics to determine a single value that will serve as the "best guess" or "best estimate" of an unidentified population characteristic, known as the point estimate. More precisely, in order to produce a point estimate, we apply a point estimator to the data.
For the confidence interval (0.195, 0.245), point estimate is calculated as follows,
p = (0.195 + 0.245) / 2
p = 0.44 / 2
p = 0.22
Hence, the point estimate of the proportion of students who prefer the new schedule comes out to be 2.2.
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Which expression is equivalent to (m-4/m+4)/(m+2)?
A) m-4/(m+4)(m+2)
B) (m+4)(m+2)/m-4
C) (m-4)(m+2)/m+4
D) m+4/(m-4)(m+2)
Hello,
[tex] \frac{ \frac{m - 4}{m + 4} }{m + 2} = \frac{ \frac{m - 4}{m + 4} }{ \frac{m + 2}{1} } = \frac{m - 4}{m + 4} \times \frac{1}{m + 2} = \frac{m - 4}{(m + 4)(m + 2)} [/tex]
PLS SOLVEEEEEEEE!!! This is urgent :(
Answer:
B) 16
Step-by-step explanation:
12/3 = x/4
48 = 3x Divide both sides by 3
16 = x
Factor the greatest common factor: 28a3b4 20a2b2 − 16ab3. 4ab(7a2b 5a − 4b2) 4ab2(7a2b 5a − 4b) 4ab2(7a2b2 5a − 4b) 4ab(7a2b3 5a − 4b)
Answer:
4ab2(7a2b2 5a - 4b)
Step-by-step explanation:
28a3b4 20a2b2 − 16ab3
The GCF of 28, 20 and 16 is 4.
GCF of the variables is ab2
So the answer is
4ab2(7a2b2 5a - 4b)
Answer:
4ab2(7a2b2 5a - 4b)
Step-by-step explanation:
Transform the given equation into a system of first order equations. (Let x1 = u, x2 = u', x3 = u'', and x4 = u'''. Enter your answers in terms of x1, x2, x3, and x4.) u(4) − u = 0
a) x1' =
b) x2' =
c) x3' =
d) x4' =
Given the 4th order linear ODE
[tex]u^{(4)} - u = 0[/tex]
we substitute
[tex]x_1 = u[/tex]
[tex]x_2 = {x_1}' = u'[/tex]
[tex]x_3 = {x_2}' = {x_1}'' = u''[/tex]
[tex]x_4 = {x_3}' = {x_2}'' = {x_1}''' = u'''[/tex]
Then the given equation transforms to
[tex]{x_4}' - x_1 = 0[/tex]
but we also need to relate this to the other derivative substitutions. This gives the system of differential equations
[tex]\begin{cases} {x_1}' = x_2 \\ {x_2}' = x_3 \\ {x_3}' = x_4 \\ {x_4}' = x_1 \end{cases}[/tex]
In matrix form,
[tex]\begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{bmatrix}' = \begin{bmatrix} 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \\ x_4 \end{bmatrix}[/tex]
A house is octagon-shaped, and each side measures 22 feet long. How many lineal feet of exterior wall does this house have
Length of each side is 176 feet ² .
What is octagon ?A polygon of eight angles and eight sides.It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of a regular octagon is 135° ( radians). The central angle is 45° ( radians).each side of house = 22 feet long
Perimeter of octagon = 8 × sides
Length of each side of house = 8 × 22 ⇒ 176 feet²
Therefore, length of each side is 176 feet ² .
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Solve the rational equation by multiplying both sides by the lcd. check your results for extraneous solutions. 3 x2 5x 6 x − 1 x 2 = 7 x 3 x = is a solution. x = is an extraneous solution.
The solution and extraneous solution of the equation as given are; x=7 and x=-2 respectively.
What is the solution of the equation?It follows that the equation given is;
(3/(x²+5x+6)) + ((x-1)/(x+2)) = 7/(x+3)
Hence, by multiplying both sides by (x²+5x+6); we have;
3 + x² +2x -3 = 7x + 14.
x²-5x -14 = 0
On this note, the solutions of the quadratic equation are; x =7 and x=-2.
It therefore follows that x= 7 is a solution while x=-2 is an extraneous solution because it renders (x-1)/(x+2) undefined.
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Answer:
x=7
x=-2
Step-by-step explanation:
Vic is standing on the ground at a point directly south of the base of the CN Tower and can see the top when looking at an angle of elevation of 61°. Dan is standing on the ground at a point directly west of the base of the tower and must look up at an angle of elevation of 72° in order to see the top. If the CN Tower is 553.3 m tall,how far apart are Vic and Dan to the nearest meter? Include a well-labeled diagram as part of your solution.
The angle of elevation of 61° and 72° with the height of the tower being 553.3 m. gives Vic's distance from Dan as approximately 356 meters.
How can the distance between Vic and Dan be calculated?Location of Vic relative to the tower = South
Vic's sight angle of elevation to the top of the tower = 61°
Dan's location with respect to the tower = West
Dan's angle of elevation in order to see the top of the tower = 72°
Height of the tower = 553.3m
[tex]tan( \theta) = \frac{opposite}{adjacent} [/tex]
[tex]tan( 61 ^{ \circ}) = \frac{553.3}{ Vic' s\: distance \: to \: tower} [/tex]
[tex]distance = \frac{553.3}{tan ( {61}^{ \circ} )} = 306.7[/tex]
Vic's distance from the tower ≈ 306.7 mSimilarly, we have;
[tex] Dan's distance = \frac{553.3}{tan ( {72}^{ \circ} )} = 179.8[/tex]
Dan's distance from the tower ≈ 179.8 mGiven that Vic and Dan are at right angles relative to the tower (Vic is on the south of the tower while Dan is at the west), by Pythagorean theorem, the distance between Vic and Dan d is found as follows;
d = √(306.7² + 179.8²) ≈ 356Therefore;
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A system of linear equations is given by the tables. one of the tables is represented by the equation . x y 0 5 3 6 6 7 9 8 x y -6 9 -3 8 0 7 3 6 the equation that represents the other equation is y = x . the solution of the system is ( , )
The solution of the system would be (3,6).
Lets solve the problem,
Other equation: y = 1/3x+5
Slope-Intercept Form: y = mx + b
Slope Formula:
y2-y1/x2-x1 = m
Have to find equation now:
m = (6 - 5)/(3 - 0)
m = 1/3
y = 1/3x + b
5 = 1/3(0) + b
b=5
y = 1/3x + 5
Lets put the substituition method here,
1/3x + 5 = -1/3x + 7
2/3x + 5 = 7
2/3x = 2
x = 3
y = 1/3(3) + 5
y = 1 + 5
y = 6
Therefore the coordinates are (3,6)
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What is the difference? startfraction x 5 over x 2 endfraction minus startfraction x 1 over x squared 2 x endfraction
The difference between the two given fractions is [tex]\frac{x^{2} +4x-1}{x^{2} +2x}[/tex].
What is fraction?Fraction if a part of whole. It is represented in the form of numerator and denominator.
Given that,
[tex]\frac{x+5}{x+2} -\frac{x+1}{x^{2} +2x}[/tex]
= [tex]\frac{x+5}{x+2} -\frac{x+1}{x(x+2)}[/tex]
Take the LCM of the denominators is [tex]x(x+2)[/tex].
= [tex]\frac{x(x+5)-(x+1)}{x(x+2)}[/tex]
= [tex]\frac{x^{2}+5x -x-1}{x^{2} +2x}[/tex]
= [tex]\frac{x^{2}+4x-1}{x^{2} +2x}[/tex]
Thus, the difference between the two given fractions is [tex]\frac{x^{2}+4x-1}{x^{2} +2x}[/tex] .
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The given question is not in correct form.