Express the following division in the form of a + bi: (1+3i)(2+i)
Answer:
[tex](1 + i\,3) \cdot (2 + i) = -1 + i\,7[/tex]
Step-by-step explanation:
We proceed to present the procedure by algebraic means:
1) [tex](1 + i\,3)\cdot (2 + i)[/tex] Given
2) [tex]2\cdot (1 + i\,3) + i\,(1+i\,3)[/tex] Distributive and Commutative Properties
3) [tex]2 + i\,6 + i + i^{2} \,3[/tex] Distributive, Commutative and Associative Properties
4) [tex]2 + i\,7 -3[/tex] Definition of imaginary number/Distributive, Commutative and Associative Properties
5) [tex]-1 + i\,7[/tex] Commutative and Associative Properties
A 50 foot ladder is set against the side of a house so that it reaches up 48 feet. If Jack
grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the
side of the house will the ladder reach now? (The answer is not 44 ft.) Round to the
nearest tenth of a foot.
1.4 feet
let me know if you get it right hope i helped!
Answer:
14
Step-by-step explanation:
a2+(48)2=
502\,\,50^{2}502
Use the Pythagorean Theorem.
a2+2304=a^{2}+2304=a2+2304=
2500\,\,25002500
Simplify.
−2304-2304\phantom{=}−2304=
−2304\,\,-2304−2304
Subtract 2304 from both sides.
a2=a^{2}=a2=
196\,\,196196
a2=\sqrt{a^{2}}=a2
=
±196\,\,\pm\sqrt{196}±196
Square root both sides.
a=a=a=
14\,\,1414
Simplify. Ignore negative root, as length must be positive.
please answer its due tomorrow ill give brainiest no links or scam
Answer:
4: 1 2/3
5. 5/21 b. 1/4 c. 11/18 d. 3/20
6. 11/12 b. 10/12 < 11/12
7. 4/45
Step-by-step explanation:
4. 1/3 times 5
6. just add
7. 1/5 minus 1/9
Answer:
hey this is my alt acount im doing this so i can give brainiest
Step-by-step explanation:
-\frac{1}{10}-x^3+x^4+3x
−
10
1
−x
3
+x
4
+3x
Answer:
Its really simple
Step-by-step explanation:
first you take the 10 then turn it into joe then mama
Answer:
-1/10 - 1x^3 + x^4 + 3x
Step-by-step explanation:
negative one tenth minus 1x exponet 3 plus x exponent 4 plus 3x
You have 90 degree triangle and the adjacent is 24, the opposite is 32, and the hypotenuse is 40. What is the value of tan W rounded to the nearest hundredth, if necessary.
Answer:
sorry need points Step-by-step explanation:
sorry need points sorry need points
9. A building 62 feet tall casts a shadow 21 meters long. At what angle is the sun shining on the building?
A. 19.80
B. 18.71
C. 70.20
D. 71.29
First, we imagine a right triangle. Second, we are given that the building is 62 feet tall. Since the height of building is vertical straight - that means the height is opposite side of triangle. It also casts a shadow 21 meters long. Shadow should be the adjacent side because it casts on the ground and not on the air.
If we imagine the right triangle + the problem in our head, we'd get the triangle that the opposite side is 62 feet tall and the adjacent side is 21 meters long.
Use the tangent ratio to find the angle of sun shining.
[tex] \large \boxed{ \tan \theta = \frac{opposite}{adjacent} }[/tex]
Substitute adjacent = 21 and opposite = 62 in the ratio.
[tex] \large{tan \theta = \frac{62}{21} }[/tex]
For this part, you might need a calculator or trigonometric table because some values cannot be exactly found.
From the equation, we should get 71.288 which we round the answer to nearest hundreth and the answer would be 71.29
Answer
The answer is 71.29Answer:
71.29°
Step-by-step explanation:
By question its given that , a 62 feet tall tree cast a shadow of 21 m long. We need to find the angle at which the sun is shining on the building .
For this we gonna imagine a right angle triangle . Where , the length of the shadow will be the base of the triangle and the height of the building will be the perpendicular on the triangle .
Here since we have got perpendicular and base , we can use the ratio of tan . We know that tan is defined as perpendicular by base , that is ,
[tex]\implies tan \theta =\dfrac{perpendicular}{base}[/tex]
where theta is the angle between the Ray of the the sun and the the shadow of the building.Plug in the respective values , we have ,
[tex]\implies tan \theta =\dfrac{62}{21} \\\\\implies\theta = tan^{-1}\bigg( \dfrac{62}{21}\bigg) \\\\\implies \underline{\underline{\theta = 71.29^o }}[/tex]
Hence the required answer is 71.29° .
Question 1 of 10
Classify the following triangle. Check all that apply.
60
60
60
O A. Isosceles
B. Equilateral
O C. Scalene
O D. Acute
E. Right
Answer:
A, B, & D
Step-by-step explanation:
A. isosceles - 2 sides equal (actually) all sides are equal
B. equilateral - all sides equal and all angles are equal too
D acute - all angles are less than 90 degrees
Which expressions are equivalent to the one below? Check all that apply.
log 2 - log 6
A. log(2) + log(1/6)
B. log 2
C.log(1/3)
D. log 3
Answer:
is there a picture or something i cant understand
Step-by-step explanation:
Answer:
C. log(1/3)
Step-by-step explanation:
log a - log b = log(a/b)
Find the circumcenter of a triangle ABC with vertices at A(2, 2), B(0, -4), and C(7, -1)
20 POINTS PEOPLE
Answer:
just sum up the 3 sides.
quick side note: I lost my previews writing bc I waited too long too post it :(
but long story short: you get the length of, say, AB by using pythagoras theorem.
[tex] \sqrt{ {2}^{2} + {6}^{2} } [/tex]
do this with BC and CA too
the 2 is just the distance in x-direction and the 6 is just the distance in y-direction
and since a²+b²=c², we need to take the root to get the distance between 2 points
see screenshot for summing up the three distances. the part out of screen is written out above
the sum is 21.011 length units
hope it helps. have a nice day.
feel free to ask questions.
and maybe, if I'm feeling really nice and a lil bored, i leave greeting answers under yours to enable posters to give gives brainliests. if theres no 2and answer at least
(ii) 3x - 5y - 4 = 0 and 9x = 2y +7
Step-by-step explanation:
3×‐9×-5y-2y =0-7
-6x-7y =-7
Answer:
[tex]x = \frac{9}{13} \ , \ y = - \frac{5}{13}[/tex]
Step-by-step explanation:
3x - 5y = 4 ----------- ( 1 )
9x - 2y = 7 -----------( 2 )
______________________
( 1 ) x 9 => 27x - 45y = 36 ----------------- ( 3 )
( 2) x 3 => 27x - 6y = 21 -------------------( 4 )
_____________________
( 3 ) => 27x - 45y = 36
- ( 4 ) => -27x + 6y = - 21
____________________
( 3 ) - ( 4 ) => 0x - 39y = 15
-39y = 15
[tex]y = \frac{15}{-39} = -\frac{5}{13}[/tex]
Substitute y in ( 1 ) :
[tex]3x - 5y = 4\\\\3x - ( 5 \times -\frac{5}{13}) = 4\\\\3x + \frac{25}{13} = 4\\\\3x = 4 - \frac{25}{13}\\\\3x = \frac{52 - 25}{13}\\\\3x = \frac{27}{13}\\\\x = \frac{27}{13 \times 3}\\\\x= \frac{9}{13}[/tex]
Match the equation of circle with its center and radius.
Answer:
1- c=(-2,1) , R =9
2-c=(2,-1) , R=3
3-c=(-2,-1) , R=4
4-c=(2,1) , R=16
5-c=(0,0) , R=2
Given that a : b= 8:5 and 6: c= 3: 4,
find the ratio a : 6:c
Give your answer in its simplest form.
(3 marks)
Find the expression different from the others. Do this by showing that the other four are equivalent to each other using the properties of exponents. (4 points)
A)2^4x+2
B)4•16^x
C)2+4^4x
D)2^2 • 4^x (over) 4^-x
E)4^2x+1
Answer:
C) 2+4^4x
Step-by-step explanation:
A) 2^(4x+2) = 2^4x • 2² = 16^x • 4
B) 4 • 16^x = 16^x • 4 (already done)
D) 2^2 • 4^x (over) 4^-x
= 4 • 4^x • 4^x = 16^x • 4
E) 4^(2x+1) = 4^2x • 4¹ = 16^x • 4
3.
Find the value of x. If necessary, round to the nearest tenth.
A. 7.0 in.
B. 11.9 in
C. 9.9 in.
D. 14.0 in
Answer:
C. 9.9 in.
Step-by-step explanation:
Step-by-step explanation:
Alright, lets get started.
Area is given as 49 square inches.
The formula for area A =
base is given as x
Height is given as x
Hence area is A
A =
Multiplying 2 in both sides
Taking square root on both sides
hence the answer is x = 9.9 in : Answer
Hope it will help :)
The value of x is 9.9 in.
Solution:
The given image is a triangle.
Base of the triangle = x
Height of the triangle = x
Area of the triangle = 49 sq. in
To find the value of x:
Area of the triangle =
Substitute the given values in the formula.
Multiply by 2 on both sides, we get
Taking square root on both sides, we get
⇒ x = 9.9 in
Hence the value of x is 9.9 in.
For his phone service, Deshaun pays a monthly fee of $17, and he pays an additional $0.04 per minute of use. The least he has been charged in a month is $67.44.
how do i solve this
it’s geometry
Answer:
x=5, y=11
Step-by-step explanation:
> sum of interior angles of a polygon is (n-2)·180°, where n-is the number of sides, so our rhombus has sum of angles =(4-2)·180° =360°
>we know that the opposite angles are congruent so ...
>we have the sum of interior angles is
108+108+7y-5+7y-5 = 360, combine like terms
14y +206 =360, subtract 206 from both sides
14y = 154, divide both sides by 14
y= 11
>the sides are congruent therefore
4x+17 = 8x-3 , subtract 4x, and add 3 from both sides
17+3 =8x-4x, combine like terms
20 = 4x , divide by 4 both sides
5 =x
find the value of x.
Answer:
139 degrees
Step-by-step explanation:
we only have a central angle here (angle at the center of the circle).
and that angle remains the same along these 2 lines all the way out to the circle arc (and beyond, wherever these 2 lines take us).
so, if there is nothing missing in this graph, then x is the same as the inner angle : 139 degrees
Find the surface area
Answer:
352 m
Step-by-step explanation:
The area of a trapeze is (the biggest base + the smallest base) × height / 2
The area from rectangles are side a × side b
Trapeze: (6+12)×4/2 = 36
Rectangles: 5 × 10 = 50
6 × 10 = 60
12 × 10 = 120
There are two trapeze andtwo rectangles with the samesize, so you double their area:
2×36 + 2 × 50 + 60 + 120 = 352 m
The cost of 2 pounds
of coffee is $0.
True or False
Answer:
false
Step-by-step explanation:
the graph shows that 2 pounds of coffee would be about $4
Answer:
false.
Step-by-step explanation:
because if you look 1 pounds is 2 dollars
Darius is studying the relationship between mathematics and art. He asks friends to each draw a "typical” rectangle. He measures the length and width in centimeters of each rectangle and plots the points on a graph, where x represents the width and y represents the length. The points representing the rectangles are (6.1, 12.0), (5.0, 8.1), (9.1, 15.2), (6.5, 10.2), (7.4, 11.3), and (10.9, 17.5). Which equation could Darius use to determine the length, in centimeters, of a "typical” rectangle for a given width in centimeters?
y = 0.605x + 0.004
y = 0.959x + 0.041
y = 1.518x + 0.995
y = 1.967x + 0.984
Answer:
its the 4th one
Step-by-step explanation:
Answer:
the answer is C y=1.518x+0.995
Step-by-step explanation:
What is the value of x^2/y^1 when x=10 and y=5?
Fill in the blanks below in order to justify whether or not the mapping shown represents a function
Answer:
not a function because -3 maps to two different values 5 and 6
Step-by-step explanation:
The product of x and 8 is not less than 16
Answer:
x ≥ 2
Step-by-step explanation:
The inequality would be: x * 8 ≥ 16
8x ≥ 16
x ≥ 16/8
x ≥ 2
Hope this helps!
Answer:
x*8 > 16
Step-by-step explanation:
product means multiplaction and x and 8 are being multiplied so x*8 and the answer is not less than or at least 16
There are 4.5 litres of milk in a pot. The chef stirs in 2.5 g of salt and 1.2 litres of water. How much liquid is in the pot?
Answer:
5.7 litres
Step-by-step explanation:
The salt is not a liquid so you do not need to add it in.
4.5 litres + 1.2 litres = 5.7 litres
PLSS HELP ME ITS WORTH 20 POINTS!!
Answer:
suplementary
Step-by-step explanation:
By the distributive law 3 ✖ 2 + 3 ✖ 4 =
1. 9 + 8
2. 9 ✖ 8
3. 3 + 8
4. 3 ✖ 6
Need this quick as hell 25 points
(1.9)2 standard form
Answer:
-4
Step-by-step explanation:
hope this helps
have a great day/night :)
Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths.
Base 3 1/2 feet, altitude 3/4 feet.
Answer:
below
Step-by-step explanation:
base * height = area of a parallelogram
7/2 × 3/4
=21/8 feets
MATH HELP PLEASE ANSWER AND SHOW WORK ITS DUE SOON THANKS
Answer:
the area of the circle is the number of boxes in the box minus no .of boxes in circle....
hay claudia do u remember me
y = one-third (x + 2)
Answer:
Step-by-step explanation:
according to the question equation is
y=1/3*(x+2)
y=x+2/3
