The measure of the angle rst is [tex]105^{o}[/tex].
What is the inscribed quadrilateral theorem?According to the theorem, a quadrilateral can be inscribed by a circle if and only if its opposing angles are supplementary. A quadrilateral that may be encircled by a circle is known as a cyclic quadrilateral.
The sum opposite angles of a quadrilateral is 180 degrees.
We can see that the angles rst and angle tqr are opposite angles of quadrilateral qrst, hence supplementary angles.
Therefore,
<RST + <TQR = 180
5x+15 + 4x+ 3 = 180
9x + 18 = 180
9x = 180 - 18
9x = 162
x = 162/9
x = 18
Since <RST = 5x+15
<RST = 5(18) + 15
<RST = 90 + 15
<RST = 105degrees
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Mrs. Gurung allowed 10% discount on her fancy items to make 25% profit and sold a lady bag for Rs 5,085 with 13% VAT. Due to the excessive demands of her items, she decreased the discount percent by 2%. By how much was her profit percent increased?
Her profit % was increased by 2.77%
Answer:
Solution Given:
discount =10%
profit =25%
S.P with 13% vat = Rs 5,085
S.P+Vat% of S.P= Rs 5,085
S.P(1+13%)=Rs 5,085
S.P=Rs 5,085/1.13
S.P =Rs 4,500
Again
M.P = S.P+discount% of M.P
M.P- discount% of M.P= Rs 4,500
M.P(1-10%)=Rs 4,500
M.P=Rs 4,500/0.9
M.P = Rs 5,000
Now
C.P= (S.P*100)/(1+profit%)
C.P=(4,500*100)/(100+25%)
C.P= Rs 3,600
Again
profit =S.P- C.P= Rs 4,500-Rs 3,600=Rs 900
Again
Due to the excessive demands of her items, she decreased the discount percent by 2%.
So,
New discount = 10%-2%=8%
New S.P= M.P -discount% of M.P
=M.P(1-discount%)
=Rs 5,000(1-8%)
=Rs 4,600
Again
Profit=S.P- C.P
New profit =Rs 4,600 - Rs 3,600=Rs 1,000
Profit% =profit/C.P*100%= 1000/3600*100=27.77%
Profit % increased =New profit%- profit%
=27.77-25
=2.77%
Amal used the tabular method to show her work dividing –2x3 11x2 – 23x 20 by x2 – 3x 4.
The true statement is (c) Amal's work is incorrect because it includes a positive two instead of a negative two in the answer
How to determine the true statement?The complete question is added as an attachment
From the table, we have
Divisor = x^2 - 3x + 4
Quotient = 2x + 5
Dividend = -2x^3 + 11x^2 - 23x + 20
See that the signs of the leading coefficients of the dividend and the divisor are different
This means that the leading coefficient of the quotient must be negative
From the question, we have:
Quotient = 2x + 5
The expression 2x + 5 has a positive leading coefficient
Hence, the true statement is (c) Amal's work is incorrect because it includes a positive two instead of a negative two in the answer
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Find the radius of convergence R, then determine the interval of convergence
By the ratio test, the series converges for all [tex]x[/tex], since
[tex]\displaystyle \lim_{k\to\infty} \left|\frac{(k+1)^2 x^{k+4}}{(k+1)!} \cdot \frac{k!}{k^2 x^{k+3}}\right| = |x| \lim_{k\to\infty} \frac{(k+1)^2 k!}{k^2 (k+1)!} = |x| \lim_{k\to\infty} \frac1{k+1} = 0 < 1[/tex]
Then the radius of convergence is R = ∞, and the interval of convergence is the entire real line, -∞ < x < ∞.
The radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series. This can be obtained by using ratio test.
Find the radius of convergence R and the interval of convergence:Ratio test is the test that is used to find the convergence of the given power series.
First aₙ is noted and then aₙ₊₁ is noted.
For ∑ aₙ, aₙ and aₙ₊₁ is noted.
[tex]\lim_{n \to \infty} | \frac{a_{n+1} }{a_{n} } |[/tex] = β
If β < 1, then the series convergesIf β > 1, then the series divergesIf β = 1, then the series inconclusiveHere aₙ = (n²/n!) xⁿ⁺³ and aₙ₊₁ = ((n+1)²/(n+1)!) xⁿ⁺¹⁺³ = ((n+1)²/(n+1)!) xⁿ⁺⁴
Now limit is taken,
[tex]\lim_{n \to \infty} | \frac{a_{n+1} }{a_{n} } |[/tex] = [tex]\lim_{n \to \infty} | \frac{((n+1)^{2} /(n+1)!) x^{n+4} }{(n^{2} /n!) x^{n+3} } |[/tex]
= [tex]\lim_{n \to \infty} | \frac{((n+1)^{2} ) n!x^{n+4} }{(n+1)!(n^{2} ) x^{n+3} } |[/tex]
= [tex]\lim_{n \to \infty} | \frac{((1+1/n)^{2} ) x }{(n+1)} |[/tex]
= [tex]\lim_{n \to \infty} | \frac{ x }{(n+1)} |[/tex] = 0 < 1
Since the limit is less than 1 the series is converging.
We get that,
interval of convergence = (-∞, ∞)
radius of convergence R = ∞
Hence the radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series.
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Use a comparison test (either normal or limit) to determine whether the following series converges or diverges. Be sure to clearly identify what you are comparing too and if that converges or diverges.
By the comparison test, the series converges.
We have
[tex]\dfrac1{k\sqrt{k+2}} \le \dfrac1{k \sqrt k} = \dfrac1{k^{3/2}}[/tex]
so we can compare to a convergent [tex]p[/tex]-series,
[tex]\displaystyle \sum_{k=1}^\infty \frac1{k\sqrt{k+2}} \le \sum_{k=1}^\infty \frac1{k^{3/2}} < \infty[/tex]
By the comparison test, the series converges.
What are convergence series and diverging series?
If the infinite series converges to a real number it is called converging if not then it is called diverging series.
If the larger series is convergent the smaller series must also be convergent. Likewise, if the smaller series is divergent then the larger series must also be divergent.
For this series to be converging it must follow the following :
⇒ [tex]| \frac{t_{n+1} }{t_{n} } | \leq 1[/tex]
⇒Putting n = 1
[tex]| \frac{t_{2} }{t_{1} } | \leq 1[/tex]
[tex]\t_{2} t_{1}[/tex] [tex]t_{2}[/tex]= 1/4
[tex]t_{1}[/tex]=1/[tex]\sqrt{2}[/tex]
[tex]\frac{t_{2} }{{t_{1} }}[/tex] = 1/2[tex]\sqrt{2[/tex]
⇒ t₂/t₁≤1
⇒ Hence it converges
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The temperature during a day can be modeled by a sinusoid. Answer the following question given that the low temperature of 7 degrees occurs at 5 AM and the high temperature for the day is 45 degrees.
Find the temperature, to the nearest degree, at 9 AM.
The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)
What is the temperature of a place at a given time?
Sinusoids are expressions with trascendent functions, to be more specfic, trigonometric functions, whose form is described below:
T(t) = A · sin (2π · t / T + C) + B (1)
Where:
A - Temperature amplitude, in degrees.B - Middle temperature, in degrees.T - Period, in hours.C - Angular phase, in radians.The temperature amplitude and the middle temperature can be found by the following expressions:
A = (t' - t'') / 2 (2)
B = (t' + t'') / 2 (3)
Where t' and t'' are maximum and minimum temperatures, in degrees.
Then, we proceed to find each constant of the sinusoidal model:
A = (45 - 7) / 2
A = 38 / 2
A = 19
B = (45 + 7) / 2
B = 52 / 2
B = 26
We assume a period of 24 hours (T = 24).
If we know that t = 0, T = 24, A = 19, B = 26, T(t) = 7, then the angular phase is:
7 = 19 · sin [(π / 12) · 0 + C] + 26
- 19 = 19 · sin C
sin C = - 1
C = π
T(t) = 19 · sin (π · t / 12 + π) + 26
Then, the temperature at 9 AM is: (t = 4)
T(4) = 19 · sin (π · 4 / 12 + π) + 26
T(4) ≈ 9.545
The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)
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I am a 2-dimensional shape with all my sides of equal length.
I have an angle sum of 180 degrees.
What am I?
Answer:
=> Equilateral Triangle
Step-by-step explanation:
Equilateral Triangle is having 2-d shape with all equal sides and the sum of angles of any triangle is 180° .
Which of the following equations represents the area of a sector?
1.) A360nxr², where n is the central angle of the sector
2.)A = n², where n is the central angle of the sector
n
3.) A= TT, where n is the central angle of the sector
360°
4.) A =
360
T², where n is the central angle of the sector
From the given options we can say that the only one that represents the area of the sector is; A = n/360 * πr²
What is the Area of the Sector?
In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.
The formula for Area of a sector is given as;
θ/360 * πr²
where;
θ is the central angle of the sector
r is radius
Now, looking at the given options we can say that the only one that represents the area of the sector is;
A = n/360 * πr²
where n is the central angle of the sector
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Answer:
A!
Step-by-step explanation:
Find the area of the figure with the coordinates, S(-3, 5), A (1, 5), L(2, 1) and T(-6, 1).
Answer: a = 24 units²
Step-by-step explanation:
Let us graph the figure given. This shape appears to be a trapezoid. Now, we can solve for the area. This shape also has a height of 4, which I forgot to show in the picture.
In the formula, h is the height, a is a base, and b is the other base.
[tex]\displaystyle a=\frac{a+b}{2} h[/tex]
[tex]\displaystyle a=\frac{4+8}{2} 4[/tex]
[tex]\displaystyle a=\frac{12}{2} 4[/tex]
[tex]\displaystyle a=(6)4[/tex]
[tex]\displaystyle a=24\; \text{units}^{2}[/tex]
(Sequences and Summations) How would you solve this? Please give an explanation rather than just answering the question.
Step-by-step explanation:
To find the Tth term of an arithmetic progression, you should use the formula: Tn: a + (n-1)d, whereby 'a' is the first term, you have to find 'n' and 'd' is the difference between the first 2 numbers to find out by how much the arithmetic progression is increasing or decreasing. Hence, 29/30 minus 4/5 equals to 1/6. 'a' is 4/5 and 'd' is 1/6.
Use the above formula by replace a and d then you'll get the answer. Hope this helps.
If ph term of A.P. is q and qth term is p, then (p+q) term is??
If the pth term of an arithmetic progression is q and qth term is p then the (p+q) th term is 0.
Given that the p th term of an A.P is q aand q th term is p.
We are required to find the (p+q) th term of that A.P.
Arithmetic progression is a sequence in which all the terms have common difference between them.
N th term of an A.P.=a+(n-1)d
p th term=a+(p-1)d
q=a+(p-1)d-------1
q th term=a+(q-1)d
p=a+(q-1)d---------2
Subtract equation 2 by 1.
q-p==a+(p-1)d-a-(q-1)d
q-p=pd-qd-d+d
q-p=d(p-q)
d=(p-q)/(q-p)
d=-(p-q)/(p-q)
d=-1
Put the value of d in 1.
q=a+(p-1)(-1)
q=a-p+1
a=q+p-1
(p+q) th term=a+(n-1)d
=q+p-1+(p+q-1)(-1)
=q+p-1-p-q+1
=0
Hence if the pth term of an A.P is q and qth term is p then the (p+q) th term is 0.
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35*71+71*65+51*23+23+49
Answer:
35x71+71x65+51x23+23+49=8,345
Step-by-step explanation:
Answer:
8345
Is the correct answer
Step-by-step explanation:
hope it will help you
Find the midpoint of UV thanks so much
Answer:
(0, -5/2).
Step-by-step explanation:
The coordinates of the mid point of (x1, y1) and (x2, y2) are
(x 1 + x2)/2 , (y1 + y2)/ 2
So here we have:
(-3 + 3)/ 2, (-4 + -1)/2
= 0/2, -5/2
= (0, -5/2).
The amount of unexplained variance in a relationship between two variables is called?
Answer:
The amount of unexplained variance in a relationship between two variables is called: coefficient of alienation also called coefficient of nondetermination. A positive correlation between two variables would be represented in a scatterplot as. line sloping upwards. .
Step-by-step explanation:
What is the equation in slope-intercept form for the line that passes through the points (-2, -1) and (1, 5)?
Answer:
Step-by-step explanatio
Rewrit using factored form solve using zero product property
Answer:
Step-by-step explanation:
a. d^2 - 7d + 6 = 0
(d - 1)(d - 6) = 0
d - 1 = 0, d - 6 = 0 therefore:
d = 1, 6.
b, x^2 + 18x + 81 = 0
(x + 9)(x + 9) = 0
x = -9 multiplicity 2.
c u^2 + 7u - 60 = 0
(u + 12)(u - 5) = 0
u = -12, 5.
What values of c and d make the equation true? rootindex 3 startroot 162 x superscript c baseline y superscript 5 baseline endroot = 3 x squared y (rootindex 3 startroot 6 y superscript d baseline endroot)
Values of c and d make the equation true are c=6, d=2
Equations
We must find the values of c and d that make the below equation be true[tex]\sqrt[3]{162x^{c}y^{5} } = 3x^{2} y^{3} \sqrt[3]{6y^{d} }[/tex]
cubing on both sides -[tex](\sqrt[3]{162x^{c}y^{5} })^{3} = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}[/tex]
The left side just simplifies the cubic root with the cube:[tex]{162x^{c}y^{5} } = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}[/tex]
On the right side, we'll simplify the cubic root where possible and power what's outside of the root:[tex]{162x^{c}y^{5} } = 27x^{6} y^{3} ({6y^{d})[/tex]
Simplifying[tex]{x^{c}y^{5} } = x^{6} y^{3} ({y^{d})[/tex]
[tex]{x^{c}y^{5} } = x^{6} y^{3+d}[/tex]
On equating,c = 6
d = 2
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6x+4y-3z,7x-11y-9z,14x+8y-6z
Step-by-step explanation:
i donot know
sorry about this
Matrix a is a 6 × 5 matrix. which order of matrix can be multiplied by matrix a to create matrix ab?
Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.
What is a matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics. For instance, consider a matrix with two rows and three columns.To find the order of matrix:
We must first check the dimension of two matrices, say matrix A by matrix B, before we may multiply them.Multiplication is achievable if the number of columns in the first matrix, A, equals the number of rows in the second matrix.Dimension is assigned to the provided matrix: 6 × 5This means the given matrix contains six rows and five columns.As a result, the second matrix MUST have 5 rows in order for multiplication to be POSSIBLE.The only matrix with 5 rows among the above alternatives is the matrix with dimension (B) 5 × 6.To prove:
In other words, the inner products of the dimensions should be equal.That is; (a × b)(b × a) is possible but (a ×b)(c × b) is impossible.The dimensions of the matrix are given by, row × column.Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.
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If ABC = 2x and BAC = 3x + 10 what is the value of x ?
The value of x from the given diagram is -10
Similar triangleTwo triangles are known to be similar if the ratio of their similar sides is equal. The diagram shown is similar to the required diagram.
Given the following parameters
<ABC = 2x
<BAC = 3x + 10
Equate the expression since both angles are equal. Substitute;
2x = 3x + 10
Subtract 3x from both sides
2x-3x = 3x-3x+10
-x = 10
x = -10
Hence the value of x from the given diagram is -10
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14. The average age of 4 siblings is 12.5 years. If 3 of the siblings are 12-year-old triplets, how old is the fourth sibling? (A) 11.5 (B) 13 (C) 13.5 (D) 14
Answer:
D) 14
Step-by-step explanation:
12+12+12 is 36 we don't know hold old the fourth sibling is so they are X
to get the average of 12.5 you need to add all the siblings ages then divide it by 4
(36+X)/4=14 so the other sibling is 14
Answer:
B
Step-by-step explanation:
12.5x3=37.5
37.5 +11.5 =49
49÷4 =12.25
Pls help I keep getting this wrong
Answer:
x = 8
y = -3
Step-by-step explanation:
Multiply the first equation with (-2)
(-2) * (x - 4y) = 20
-2x + 8y = -40 now find the sum of it with second equation
2x + 5y - 2x + 8y = 1 - 40 add like terms (2x will eliminate -2x)
13y = -39 divide both sides by 13
y = -3
Now we can use this to find the value of x
x - 4y = 20 rewrite the equation using the value we found for y
x - 4(-3) = 20 multiply (-4) and (*3) (product will be positive because we are multiplying two negatives)
x + 12 = 20 subtract 12 from both sides
x = 8
The function yp(t)=ln(3 2t), t>−32, is a particular solution to the differential equation y′′ 7y=g(t). find g(t)?
This might help a bit, i hope
Simplify the expression:
-2(-1 + 2w) =
Submit please
[tex]-2(-1+2w)[/tex]
distribute
[tex]2-4w[/tex]
put in standard form
[tex]-4w+2[/tex]
Name a pair of vertical angles
Name a pit of adjacent angles
If m
Can someone help I’m confused I never learned this
Answer: Vertical: angles ABF and DBE. Adjacent: angles ABC and CBD
Step-by-step explanation:
vertical angles are angles that share a common point. they are right across from each other, and in this case, share point B. adjacent angles are angles that are directly next to each other, and share a line or segment. in this case, the two angles share the segment BC. hope this helps.
What is the vertex of the graph of the function f(x)=x^2+8x-2 !?
Answer:
(-4, -18).
Step-by-step explanation:
f(x = x^2 + 8x - 2 Completing the square on x^2 + 8x:-
= (x + 4)^2 - 16 - 2
= (x + 4)^2 - 18
- which is the vertex form of f(x)
The vertex of
(x - h)^2 + k is at (h, k)
So the vertex of f(x) is at (-4, -18)
Let f(x, y) = x2 6y2. find the maximum and minimum values of f subject to the given constraint?
The minimum and maximum values are (16/9)√3 and -(16/9)√3.
According to the statement
we have given that the function
First of all, since the constraint's graph is a circle, which is a closed loop, and f is continuous in [tex]R^2[/tex], there must exist a constrained global maximum and minimum value.
Lagrange Multipliers:
f(x,y) = xy^2
g(x,y) = x^2 + y^2
We want ∇f = λ∇g so we get the following system of equations
1. y^2 = 2λx
2. 2xy = 2λy
3. x^2 + y^2 = 4 ← The constraint.
Equation 2 implies that y = 0 or λ = x
We can ignore y = 0, since that will make f(x,y) = 0 and clearly f(x,y) takes on both positive and negative values subject to the constraint.
Plugging in the alternative, λ = x to equation 1 gives y^2 = 2x^2.
Plugging this into the constraint gives 3x^2 = 4 so that x^2 = 4/3 and y^2 = 8/3
Taking square roots gives
x = ±√(4/3) = ±(2/3)√3
y = ±√(8/3) = ±(2/3)√6
At the points < (2/3)√3 , ±(2/3)√6 >, f(x,y) = (16/9)√3 ← Maximum
At the points < -(2/3)√3 , ±(2/3)√6 >, f(x,y) = -(16/9)√3 ← Minimum
So, The minimum and maximum values are (16/9)√3 and -(16/9)√3.
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Logistic regression analyses require that your single dependent variable is a ratio variable.
a. true
b. false
Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9 and the length of T Q is 16. The length of S R is x.
What is the value of x?
The value of x from the given diagram is 20
Triangular altitude theoremAccording to theorem, the right triangle altitude theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse.
Using the theorem above;
RT^2 = 9 * 16
RT^2 = 144
R = 12 units
Determine the value of x using the Pythagoras theorem;
x² =12² + 16²
x² = 144 + 256
x² = 400
Take the square root of both sides
x = √400
x = 20
Hence the value of x from the given diagram is 20
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Find the standard deviation for the set of data. {15,17,23,5,21,19,26,4,14} a. 7.17 b. 7.39 c. 7.1 d. 6.65
The standard deviation exists as the positive square root of the variance.
So, the standard deviation = 6.819.
How to estimate the standard deviation?Given data set: 15, 17, 23, 5, 21, 19, 26, 4, 14
To calculate the mean of the data.
We know that mean exists as the average of the data values and exists estimated as:
Mean [tex]$=\frac{15+17+23+5+21+19+26+4+14}{9}[/tex]
Mean [tex]$=\frac{144}{9}[/tex]
Mean = 16
To estimate the difference of each data point from the mean as:
Deviation:
15 - 16 = -1
17 - 16 = 1
23 - 16 = 7
5 - 16 = -11
21 - 16 = 5
19 - 16 = 3
26 - 16 = 10
4 - 16 = -12
14 - 16 = -2
Now we have to square the above deviations we obtain:
1 , 1, 14, 121, 25, 9, 100, 144, 4
To estimate the variance of the above sets:
variance [tex]$=\frac{1+ 1+14+ 121+25+ 9+ 100+ 144+ 4}{9}[/tex]
Variance [tex]$=\frac{419}{9}[/tex]
Variance = 46.5
The standard deviation exists as the positive square root of the variance.
so, the standard deviation [tex]$\sqrt{46.5} =6.819[/tex] .
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Six pyramids are shown inside of a cube. The height of the cube is h units. The lengths of the sides of the cube are b.
The area of the base of the cube, B, is
square units.
The volume of the cube is
cubic units.
The height of each pyramid, h, is
. Therefore,
b = 2h.
There are
square pyramids with the same base and height that exactly fill the given cube.
Therefore, the volume of one pyramid is
or One-thirdBh.
We are required to fill in the solution to the question that we have here.
this is done below
Six pyramids are shown inside of a cube. The height of the cube is h units. The lengths of the sides of the cube are b. The area of the base of the cube,
B, is (b)*(b) square units.
The volume of the cube is (b)*(b)*(b) cubic units.
The height of each pyramid, h, is b/2
b = 2h.
There are 6 square pyramids with the same base and height that exactly fill the given cube.
Therefore, the volume of one pyramid is (1/6)(b)(b)(2h)
or One-third Bh.
What is a pyramid?This is the term that is used to refer to the shape that is known to have a square base and the base could also be triangular. The parts of the base are known to have a connection at the top of the pyramid.
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answer is in the attachment below :)
goodluck!!