Answer:
the answer would be 23/13 - 15/13i
Step-by-step explanation:
The result of the complex expression (10 – 4i) ÷ (5 + i) is [tex]\frac{23}{13} - i\frac{15}{13}[/tex] .
Given, complex expression (10 – 4i) ÷ (5 + i)
Complex roots: When the roots are complex in nature then they appear in complex conjugate pair.
Complex roots: a ± ib
Complex number pair : a ± ib
i = iota(imaginary number)
a = real part
b = imaginary part
Value of iota :
[tex]i = \sqrt{-1}\\ i^2 = -1[/tex]
Complex expression : (10 – 4i) ÷ (5 + i)
Apply rationalization,
Use formula [tex](a^2 - b^2) = (a+b)(a-b)[/tex].
[tex]\frac{ (10 - 4i) }{(5 + i)} \times \frac{5-i}{5-i} \\\\= \frac{(10 - 4i) \times (5-i) }{(5+i)(5-i)} \\\\=\frac{50 -30i -4}{5^2 - i^2}\\ \\= \frac{46 - 30i}{25 +1 } \\\\= \frac{46 - 30i}{26} \\\\[/tex]
[tex]= \frac{23}{13} - i\frac{15}{13}[/tex]
The real part is positive and imaginary part is negative.
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Explain how to determine if Carlos’s allowance is directly proportional to the number of chores he completes.
Answer:
if the ratio allowance/chores is constant, it is proportional
Step-by-step explanation:
The values x and y are directly proportional if they satisfy the equation ...
y = kx
for some constant k, the constant of proportionality.
__
If the relation that produces ordered pairs (chores, allowance) is directly proportional, all of the ratios (allowance)/(chores) will have the same value: the constant of proportionality (k).
If the ratios are not constant, Carlos's allowance is not directly proportional to the number of chores he completes.
Find the surface area of the cone in terms of 1.
15 cm
3 cm
In terms of l?
TSA
πr²+πrlπr(l+r)π(3)(3+l)9.42(3+l) cm²LSA
πrl9.42l cm²Answer:
[tex]\sf SA=54\pi\:\:\:cm^2[/tex]
Step-by-step explanation:
Surface Area of a Cone
[tex]\sf SA=\pi r l+\pi r^2[/tex]
where:
r is the radiusl is the slant heightGiven:
r = 3 cml = 15 cmSubstitute the given values into the formula and solve for SA:
[tex]\implies \sf SA=\pi (3)(15)+\pi (3)^2[/tex]
[tex]\implies \sf SA=45\pi+ 9 \pi[/tex]
[tex]\implies \sf SA=54\pi\:\:cm^2[/tex]
Therefore, the surface area of the cone in terms of pi is:
[tex]\sf SA=54 \pi\:\:\:cm^2[/tex]
40. Se desea distribuir las bancas dentro de un salón de clases cada 1.5 m como
se muestra en la imagen, ¿de qué forma se puede saber el área requerida para
conservar la separación de las bancas?
1.5m
La forma adecuada para saber el área requerida para conservar la separación de las sillas es multiplicar (7.5) (4.5) opción B.
¿Cómo calcular el área requerida para mantener la separación?Para identificar la operación necesaria para calcular el área requerida para ubicar las sillas con su respectiva separación de 1.5 metros es:
7.5 × 4.5 = 33.75Esta expresión nos va a permitir calcular el área necesaria debido a que la separación entre sillas es 1.5 metros y tenemos 6 sillas a lo largo y 4 sillas a lo ancho, es decir:
1.5 × 5 = 7.5 distancia a lo largo1.5 × 3 = 4.5 distancia a lo anchoNota: Esta pregunta está incompleta porque falta la imagen y las opciones. Aquí está la información faltante:
Opciones:
A. Multiplicar (6)(4)
B. Multiplicar (7.5)(4.5)
C. Multiplicar (9)(6)
D. Multiplicar (9.5)(4.5)
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HELP!!!!!
The graph of g(x) is the result of translating the graph of f(x) = 3x six units to the right. What is the equation of g(x)?
g(x) = 3x-6
g(x) = 3x+6
g(x)=3*-6
g(x)=3*+6
The answer is g(x) = 3x - 6
What is the area of this triangle?
1375 ft²
1500 ft²
3300 ft²
4500 ft²
Answer:
Area of a triangle = 1/2 * base * height
here ,
base = 120 ft
height = 25 ft
Area = 1/2* 120*25
= 60 * 25
= 1500 ft²
Answer 2
Answer:
1/2 * base * height
so 1/2 * 25 * 120
= 1500
Which statement is true?
O When an altitude is drawn from the right angle in a right triangle it creates two similar triangles.
O When an altitude is drawn from an acute angle in a right triangle it creates three similar triangles.
O When an altitude is drawn from the right angle of a right triangle it creates three similar triangles.
O When an altitude is drawn from an acute angle in a right triangle it creates two similar triangles.
Answer:
C) When an altitude is drawn from the right angle of a right triangle it creates three similar triangles.
Step-by-step explanation:
The Inscribed Similar Triangles Theorem states that if an altitude is drawn from the right angle of any right triangle, then the two triangles formed are similar to the original triangle and all three triangles are similar to each other.
Homework Progress 46 / 90 Marks Work out the length of AB. Give your answer to 3 significant figures. A (-1, 6) B (5, 3) X + Homework Progress 46 / 90 Marks Work out the length of AB . Give your answer to 3 significant figures . A ( -1 , 6 ) B ( 5 , 3 ) X +
Answer: 6.71
Step-by-step explanation:
[tex]AB=\sqrt{(-1-5)^{2}+(6-3)^{2}} \approx \boxed{6.71}[/tex]
The height of a tank is 3 meter and volume is 12 million centimeters. find the area of the square base of the tank in square meters
Answer:
75
Step-by-step explanation:
Given that 2x − 1∶ − 4 = 16x + 1 ∶ 2x − 1 find the possible values of
The possible values of x are 5 and -1/12
Complete questionGiven that 2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1 find the possible values of x
How to determine the possible values of x?The ratio is given as:
2x − 1∶ x − 4 = 16x + 1 ∶ 2x − 1
Express as fraction
[tex]\frac{2x - 1}{x-4} = \frac{16x + 1}{2x -1}[/tex]
Cross multiply
4x^2 -4x + 1 = 16x^2 + x -64x - 4
Collect like terms
-16x^2 + 4x^2 + 64x - x - 4x + 1 + 4 = 0
Evaluate the like terms
-12x^2 + 59x + 5 = 0
Divide through by -1
12x^2 - 59x - 5 = 0
Expand
12x^2 + x - 60x - 5 = 0
Factorize
x(12x + 1) - 5(12x + 1) = 0
Factor out 12x + 1
(x - 5)(12x + 1) = 0
Expand
x - 5 = 0 or 12x + 1 = 0
Solve for x
x = 5 or x = -1/12
Hence, the possible values of x are 5 and -1/12
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if sin theta=-3/5 in quadrant III what is cos theta
Answer:
Just simply input in your calculator arcsin of -5/6. Arcsin is the sign that looks like sin to the power of -1, even though it doesn't mean sin to the power of -1. This comes out to 303.6 degrees. So, it actually isn't in quadrant 3, it's in quadrant 4.
Step-by-step explanation:
1. Select all the true statements.
A. √-I is an imaginary number.
-1
B. There are no real numbers that satisfy the equation x = √√-1.
C. Because √-I is imaginary, no one does math with it.
D. The equation x² = -1 has real solutions.
E. √-T = -1 because -1 -1 = -1.
Answer:
A , B , D
Step-by-step explanation:
Jerry plans to keep up this saving pattern until he can no longer afford it. At that time he hopes to have enough in his account for his trip. How much will be in the account, after making the down payment, if the most he will be able to contribute in a month is $1,200?
please help i just started summer school online Part F
Several minutes later, Raul decides to measure the water temperature again. He finds that the temperature changed by -0.6°F. What is the temperature of the water now? Show your work.
Answer:
Step-by-step explanation:
basically all you do is
Please someone do this for me
Answer:
A = -12
Step-by-step explanation:
A put in -2 for 'x' in the equation to find value
2(-2) - y = 8 add 4 to both sides
-y = 12
y = -12
I think YOU can now find B and C with this method !
find the length of CB
A. 7
B. 4
C. 14
D. 2
Answer:
7
Step-by-step explanation:
5x-3 = 3x+1
2x=4
x=2
plug in
5(2)-3
10-3
7
answer: 7
A climber is on a hike. After an hour he is at an altitude of 150 feet. After 2 hours, he is at an altitude of 275 feet. After 4 hours, he is at an altitude of 525 feet and after 6 hours, he is at an altitude of 700 feet. Which table could be used to model his climb?
The table that could be used to model his climb will consist of 125 ft/h for the first two hours and 87.5 ft/h for the next 4 hours.
Equation of motion of the climberThe equation that can be used to model the motion of the climber is calculated as follows;
(1, 150)
(2, 275)
(4, 525)
(6, 700)
Slope for the first two hoursm = (275 - 150)/(2 - 1) = 125 ft per hour
Slope for the next 4 hoursm = (700 - 525)/(4 - 2) = 87.5 ft/hr
Thus, the table that could be used to model his climb will consist of 125 ft/h for the first two hours and 87.5 ft/h for the next 4 hours.
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What's an algorithm ?
Answer:An algorithm is a set of instructions for solving a problem or accomplishing a task.
Step-by-step explanation:
Any series of well defined steps that shows a procedure for solving a given type of problem is called an algorithm.
Step-by-step explanation:
Hope it helps you !!The terminal side of an angle in standard position passes through p(–3, –4). what is the value of tangent theta?
Answer:
4/3
Step-by-step explanation:
The tangent of any angle (θ) in standard position that has point (x, y) on its terminal ray is ...
tan(θ) = y/x
__
For the given point on the terminal side, the tangent is ...
tan(θ) = (-4)/(-3) = 4/3
_____
Additional comment
There are several ways this can be explained. One of them makes use of the relation between rectangular and polar coordinates:
(x, y) = (r·cos(θ), r·sin(θ))
Then the ratio y/x is ...
y/x = (r·sin(θ))/(r·cos(θ)) = sin(θ)/cos(θ) = tan(θ)
Calculate the lenth of AC to 1 decimal place in the trapezium below.
Answer:
18.1cm
Step-by-step explanation:
Please refer to the attached photo for a better understanding. Apologies for the terrible drawing.
First we will find the length of BE by using pythagoras' Theorem.
[tex]c^{2} =a^{2} +b^{2} \\AB^{2} =BE^{2} +EA^{2} \\16^{2} =BE^{2} +7^{2} \\256=BE^{2} +49\\BE^{2} =256-49\\BE=\sqrt{207} cm[/tex]
We will leave BE as it is as it is not the final answer.
Since we know CD = BE,
CD = [tex]\sqrt{207} cm[/tex]
Now from the photo, draw a line from C to A or A to C, you will see another triangle.
Now we will use Pythagora's Theorem again to find AC.
[tex]AC^{2} =AD^{2} +DC^{2} \\AC^{2} =11^{2} +(\sqrt{207}) ^{2} \\AC^{2} = 121+207\\AC^{2} =328\\AC=\sqrt{328} \\=18.1cm (1dp)[/tex]
Given log subscript 4 baseline 3 almost-equals 0.792 and log subscript 4 baseline 21 almost-equals 2.196, what is log subscript 4 baseline 7?
The value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.
We are given the logarithmic functions:
log₄3 = 0.792 ,,, (i), and log₄21 = 2.196 ... (ii),
and we are asked to find the value of the logarithmic function log₄7.
On subtracting (i) from (ii), we get:
log₄21 - log₄3 = 2.196 - 0.792.
Using the quotient law of logarithms, according to which:
logₓa - logₓb = logₓ(a/b), we can write the above equation as:
log₄(21/3) = 1.404,
or, log₄7 = 1.404.
Therefore, the value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.
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Answer:
A.
1.404
Step-by-step explanation:
area of rectangle = l×b find area of rectangle in sq cm
a) l=7cm,b=4cm
Answer:
[tex]28{cm}^{2} [/tex]
Step-by-step explanation:
we know
area of rectangle=l*b=(7*4)sq cm=28sq cm
What is the surface area of the cylinder with height 4 yd and radius 5 yd? Round your answer to the nearest thousandth.
Answer:
282.743 yd²
Step-by-step explanation:
Surface Area of the Cylinder: Top Base + Bottom Base + Side
Area of Top Base (Circle): πr² = π(5 yd)² = 25π yd²
Area of Bottom Base (Circle): same as top base = 25π yd²
Area of Side (Rectangle): Circumference*Height = (2πr)*(4 yd) =
2π(5 yd)*(4 yd) = 40π yd²
Total Surface Area = 25π yd² + 25π yd² + 40π yd² = 90π yd² = 282.743 yd²
The image of ABC is A'B'C. What transformations would result in this image?
ABC is rotated 180° around the origin, then T: ( x, y) → ( x - 1, y - 1).
ABC is reflected over the line x = 1, then is reflected over the line y = -1.
ABC is rotated -90° around the point, then T: ( x, y) → ( x + 5, y + 3).
ABC is rotated -90° around the origin, then T: ( x, y) → ( x + 5, y - 1).
(multi choice)
Triangle ABC was rotated 90° around the point, then translated using the rule (x, y) → ( x + 5, y + 3) to form triangle A'B'C'.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and translation.
Triangle ABC was rotated 90° around the point B, then translated using the rule (x, y) → ( x + 5, y + 3) to form triangle A'B'C'.
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HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
write and solve a proportion to complete the statement. Round to the nearest hundredth if necessary.
1. 6km ≈ ?mi
2. 2.5 L≈ ?gal
3. 90lb ≈ ?kg
pls help
From unit conversion, it is found the following results:
6km ≈ 3.73 mi
2.5 L≈ 0.66 gal
90 lb ≈ 40.82 kg
Unit Conversion
Units of measurement are part of our daily lives. There are different units for area, length, volume, mass, and others. Because of this, it is important to know converting them.
For solving this question you need some information as:
1 km = 0.621371 mi ( unit for length and distance)
1 L = 0.2641722 gallons (unit for volume)
1 lb = 0.453592 kg (unit for mass)
Therefore,
If 1 km = 0.621371 mi, you will have:1 km -------- 0.621371 mi
6 km -------- x mi
x= 6* 0.621371
x=3.73 mi
Thus, 6km ≈ 3.73 mi.
If 1 L = 0.2641722 gallons, you will have: 1 L-------- 0.2647122 gal 2.5L -------- x gal x= 2.5* 0.2647122 x=0.66 galThus, 2.5 L≈ 0.66 gal.If 1 lb = 0.453592 kg, you will have: 1 lb-------- 0.453592 kg 90 lb -------- x kg x= 90* 0.453592 x=40.82 kgThus, 90 lb≈ 40.82 kg.Read more about unit conversion here:
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please help me solve this LCM
Note that
[tex]x^2 - y^2 = (x - y) (x + y)[/tex]
and
[tex]x^2 + 2xy + y^2 = (x + y)^2[/tex]
Then their LCM is [tex]\boxed{x + y}[/tex].
Calculate the cost of the number of units used
Step-by-step explanation:
calculated the cost of numbers of units usex
Venn diagram in maths ! !
Answer:
People surveyed: 79
a) p(s) = 46/79
b) p(snv) = 13/79
c) p(suv) = 96/79
hope this helps, and tell me if you get it right! It's prob wrong though, im bad at venn diagrams (×_×)⌒☆
100 points helpppp now
Solve the inequality hurrry show your work
33+6f<33
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:f < 0 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 33 + 6f < 33[/tex]
[ subtract 33 on both sides ]
[tex]\qquad \tt \rightarrow \: 33 - 33+ 6f < 33 - 33[/tex]
[tex]\qquad \tt \rightarrow \: 6f < 0[/tex]
[tex]\qquad \tt \rightarrow \: f < 0[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
3. Complete the square for the following equations:
a. y = 2x² 12x + 1
b. y = 4x² + 48x - 10
The square for the equation: [tex]y=2x^{2} + 12x +1[/tex] is [tex]y=2(x+3)x^{2} -17[/tex]
The square for the equation: [tex]y=4x^{2} +48x-10[/tex] is [tex]y=4(x+6)x^{2} -154[/tex]
a)
[tex]y=2x^{2} +12x +1[/tex]
[tex]y = 2[(x^{2} + 6x)] + 1[/tex] ( taking common)
[tex]y = 2[(x+3)^{2} - 9] + 1[/tex] ( adding and subtracting 9 to make a square term
[tex]y = 2(x+3)^{2} - 18 + 1[/tex] ( multiplying by 2)
[tex]y=2(x+3)x^{2} -17[/tex]
b)
[tex]y=4x^{2} +48x-10[/tex]
[tex]y = 4[(x^{2} + 12x)] - 10[/tex] (taking 4 common)
[tex]y = 4[(x+6)^{2} - 36)] - 10[/tex] (adding and subtracting 36)
[tex]y = 4(x+6)^{2} - 144 - 10[/tex](multiplying by 4)
[tex]y=4(x+6)x^{2} -154[/tex]
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On tax-free weekend, Ben buys school supplies totaling $47.50. He has a sale coupon for 15% off his entire purchase. What will Ben final cost be after the 15% discount?
