Answer:
the question is?
Step-by-step explanation:
Perform the indicated operations. Write the answer in standard form, a+bi.
-4+4i / -3-6i
Answer:
[tex] \frac{ - 4 + 4i}{ - 3 - 6i} \\ multiply \: and \: divide \: by \: - 3 + 6i \\ \frac{ - 4 + 4i}{ - 3 - 6i} \times \frac{ - 3 + 6i}{ - 3 + 6i} \\ = \frac{ ( - 4 + 4i)( - 3 + 6i)}{ ( - 3 - 6i)( - 3 + 6i)} \\ = \frac{12 - 24i - 12i + 24 {i}^{2} }{ {( - 3)}^{2} - {(6i)}^{2} } \\ = \frac{12 - 24 - 36i}{9 + 36} \\ = \frac{ - 12 - 36i}{45} \\ \frac{ - 36i}{45} + \frac{ - 12}{45} \\ thank \: you[/tex]
EFGH is a rectangle. EA is 12 in. Find the length of the diagonal EH
26 in.
12 in.
24 in.
6 in.
Answer:
your answer is 24 in
I hope it's helps you
The length of the diagonal is 24 inches
From the given diagram, the length of the diagonal is twice the length EA
Mathematically;
EH = 2EA
Given the parameter:
EA = 12in
EH = 2(12)
EH = 24 in
Hence the length of the diagonal is 24 inches
Laern more on rectangle here: https://brainly.com/question/24438517
Identify the function family and describe the domain and range for g(x) = |x + 2|– 1.
The range of the function g(x) = |x + 2|– 1 is (-1,∞) and domain of the function is (-∞,∞).
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
For example f(x) = x²
Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.
Given the function g(x) = |x + 2|– 1
The minimum value of the function
At x = -2 ⇒ |-2+ 2|– 1 = -1
The maximum value of the function
At x = ∞ ⇒ |∞+ 2|– 1 = ∞
So,
The range will be (-1, ∞)
Now,
We can put x as -∞ and ∞ so the domain will be (-∞,∞).
Hence "The range of the function g(x) = |x + 2|– 1 is (-1,∞) and domain of the function is (-∞,∞)".
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The angle,2Θ, lies in the third quadrant such that cos2Θ=-2/5. Determine an exact value for tanΘ . Show your work including any diagrams if you plan to use them. (3 marks)
Answer:
[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]
Step-by-step explanation:
1. Approach
One is given the following information:
[tex]cos(2\theta)=-\frac{2}{5}[/tex]
One can rewrite this as:
[tex]cos(2\theta)=-0.4[/tex]
Also note, the problem says that the angle ([tex]2\theta[/tex]) is found in the third quadrant.
Using the trigonometric identities ([tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]) and ([tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]) one can solve for the values of ([tex]cos(\theta)[/tex]) and ([tex]sin(\theta)[/tex]). After doing so one can use another trigonometric identity ([tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]). Substitute the given information into the ratio and simplify.
2. Solve for [tex](cos(\theta))[/tex]
Use the following identity to solve for ([tex]cos(\theta)[/tex]) when given the value ([tex]cos(2\theta)[/tex]).
[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]
Substitute the given information in and solve for ([tex]cos(\theta)[/tex]).
[tex]cos(2\theta)=2(cos^2(\theta))-1[/tex]
[tex]-0.4=2(cos^2(\theta))-1[/tex]
Inverse operations,
[tex]-0.4=2(cos^2(\theta))-1[/tex]
[tex]0.6=2(cos^2(\theta))[/tex]
[tex]0.3=cos^2(\theta)[/tex]
[tex]\sqrt{0.3}=cos(\theta)[/tex]
Since this angle is found in the third quadrant its value is actually:
[tex]cos(\theta)=-\sqrt{0.3}[/tex]
3. Solve for [tex](sin(\theta))[/tex]
Use the other identity to solve for the value of ([tex]sin(\theta)[/tex]) when given the value of ([tex]cos(2\theta)[/tex]).
[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]
Substitute the given information in and solve for ([tex]sin(\theta)[/tex]).
[tex]cos(2\theta)=1-2(sin^2(\theta))[/tex]
[tex]-0.4=1-2(sin^2(\theta))[/tex]
Inverse operations,
[tex]-0.4=1-2(sin^2(\theta))[/tex]
[tex]-1.4=-2(sin^2(\theta))[/tex]
[tex]0.7=sin^2(\theta)[/tex]
[tex]\sqrt{0.7}=sin(\theta)[/tex]
Since this angle is found in the third quadrant, its value is actually:
[tex]sin(\theta)=-\sqrt{0.7}[/tex]
4. Solve for [tex](tan(\theta))[/tex]
One can use the following identity to solve for [tex](tan(\theta))[/tex];
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
Substitute the values on just solved for and simplify,
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
[tex]tan(\theta)=\frac{-\sqrt{0.7}}{-\sqrt{0.3}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{0.7}}{\sqrt{0.3}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]
Rationalize the denominator,
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}}}{\sqrt{\frac{3}{10}}}*\frac{\sqrt{\frac{3}{`0}}}{\sqrt{\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{7}{10}*\frac{3}{10}}}{\sqrt{\frac{3}{10}*\frac{3}{10}}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{\frac{21}{100}}}{\frac{3}{10}}[/tex]
[tex]tan(\theta)=\frac{\frac{\sqrt{21}}{10}}{\frac{3}{10}}[/tex]
[tex]tan(\theta)=\frac{\sqrt{21}}{10}*\frac{10}{3}[/tex]
[tex]tan(\theta)=\frac{\sqrt{21}}{3}[/tex]
2x + 5y = -10
rewrite the equation in slope intercept form then identify the slope and the y intercept of the line
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
2x + 5y = - 10 ( subtract 2x from both sides )
5y = - 2x - 10 ( divide the terms by 5 )
y = - [tex]\frac{2}{5}[/tex] x - 2 ← in slope- intercept form
with slope m = - [tex]\frac{2}{5}[/tex] and y- intercept c = - 2
Which of the following are rational numbers?
Step-by-step explanation:
square cube 214
I think this was your answer
If(2x,x+y)=(y,9)find x and y.
Answer:
the value of X is 3 and y is 6 .
Two numbers are in the ratio 1:2. If 7 is to be added to both, then ratio changes to 3:5, find the numbers
Let numbers be x and 2x
ATQ
[tex]\\ \rm\longmapsto \dfrac{x+7}{2x+7}=\dfrac{3}{5}[/tex]
[tex]\\ \rm\longmapsto 5(x+7)=3(2x+7)[/tex]
[tex]\\ \rm\longmapsto 5x+35=6x+21[/tex]
[tex]\\ \rm\longmapsto 6x-5x=35-21[/tex]
[tex]\\ \rm\longmapsto x=14[/tex]
2x=2(14)=28yearsMr. Mathman had a square frame with an area of 175.6 ft². Which measurement is the closest to the side length of Mr. Mathman’s frame?
A) 88 feet
B) 15 feet
C) 44 feet
D) 13 feet
Answer:
Fifteen feet is the closest to the side length of the frame, have a good day
18/73 and 4/16. Proportional or Not Proportional
Answer:
not proportional
Step-by-step explanation:
We can check using cross products
18/73 = 4/16
18*16 = 73*4
288=292
Since this is not equal, this is not proportional
solve 4m plus 2n equals 5n for m.
Answer:
m = (3/4) n
Step-by-step explanation:
4m + 2n = 5n
The subtraction property of equality states that we can subtract 2n from both sides to isolate the m and its coefficient to get
4m = 3n
The division property of equality states that we can divide 4 from both sides to isolate only the m (we divide by 4 because anything divided by itself equals 1) to get
m = (3/4) n
ok how do you add pictures
Given the following triangle. Find c
A.18v17
B.6v17
C.3v34
D.12
Answer:
The choose C.3√34
Step-by-step explanation:
15²+9²=c²
225+81=c²
306=c²
C= 3√34
I hope I helped you^_^
Find an equation for the line with the given properties. Express the equation in slope-intercept form. Containing the points P = (-4,4) and Q = (-3,2). What is the equation of the line?
y =
Answer:
[tex]y = - 2x - 4[/tex]
Step-by-step explanation:
Slope intercept eqn:
[tex]y - y1 = m(x - x1)[/tex]
P = (-4,4) and Q = (-3,2)
Let (x1, y1) = (-4,4) and (x2, y2) = (-3,2).
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{ 2 - 4}{ - 3 - ( - 4)} = \frac{ - 2}{1} = - 2[/tex]
Therefore the equation of the line in slope-intercept form :
[tex]y - 4 = - 2(x - ( - 4)) \\ y - 4 = - 2(x + 4) \\ y - 4 = - 2x - 8 \\ y = - 2x - 8 + 4 \\ y = - 2x - 4[/tex]
Graph the line that passes through the points (6,8) and (2,-2) and determine the equation of the line.
you buy 4 video tapes for 14.99 each and 3 dvds for 19.99 each find the total cost of the movies
Answer:
119.93
Step-by-step explanation:
I will assume the total of the cost of the movies will be the total.
the total = 4*14.99 + 3*19.99
total = 119.93
So like for integers when it’s only 28 - 19 do you change the negative to a positive like 28 - 19?
Answer:
Sorry I don't really understand your question, but 28-19 is 9 therefore 9 is more than 0
9 >0
Problem 2: Vector v has initial point (4, 3) and terminal point (-7, 9). Write v as a linear combination of the standard unit vectors i and j.
We have
v = (-7, 9) - (4, 3) = (-7 - 4, 9 - 3) = (-11, 6)
which as a linear combination of the i and j unit vectors is
v = -11i + 6j
Answer:
Step-by-step explanation:
The length of a sandbox is three feet longer than its width. What expression would represent the area of the sandbox
Expression represent the area of the sandbox is a² + 3a
GIven that;
Length of sandbox is three feet longer than its width
Find:
Expression represent the area of the sandbox
Computation:
Assume;
Width of sandbox = a feet
So,
Length of sandbox = (a + 3) feet
[tex]Area\ of\ rectangle = Length \times Width[/tex]
So,
Area of the sandbox = Length of sandbox × Width of sandbox
Area of the sandbox = (a + 3) × a
Area of the sandbox = a² + 3a
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Can you please show all your work plus the equation.
Answer:
25°
Step-by-step explanation:
20°--5°=
20°+5°=
25°
Answer: fell 25 degrees
Step-by-step explanation: 20-25= -5
//Give thanks(and or Brainliest) if helpful (≧▽≦)//
Which is an
appropriate estimate
for this addition
problem?
462
543
844
+ 921
PLEASE HELP DHEGDFEEHDB HELPP PLEASE
Answer:
B
Step-by-step explanation:
22/7 X 14 squared
-------------------------------- =308
2
406-308= 98cm ^2
what is line PR called
Answer:
A radius is a line segment with one endpoint at the center of the circle and the ... is called the midpoint, and arc PQ ≅ arc PR if and only if PQ ≅ PR.
Step-by-step explanation:
brainliest please
Answer:
A radius is a line segment with
Please help its due in 30 minutes will mark braniliest
Answer:
a point
Step-by-step explanation:
because it really seems like a point I dunno
n order to better manage his money, Joe kept track of his monthly grocery bills for the past six months to see how much he had spent. These amounts appear in the table.
Round each number in the table to the nearest hundred and estimate the total amount of money Joe should budget for groceries for the next 6 months.
Answer:
1,100
Step-by-step explanation:
200 + 200 + 200 + 200 + 100 + 200
Total amount after rounding off will be : 900
What is Rounding of numbers to nearest hundred ?
Rounding off a number to the nearest hundred means that you have to look or find the hundred which is closest to the given number and then write that as the rounded-off number .
Rounding off each number in the table to the nearest hundred :
1) 223 ( since , we have 223 and 223 < 250 . Since, 223 is closest to 200 as compared to 300 , after rounding it off we will get 200 instead of choosing 300) = 200
2) 189 =200
3) 210 = 200
4) 164 = 200
5) 148 = 100
6) 206 = 200
Total amount after rounding of numbers will be = 200 + 200 + 200 + 100 + 200
= 900
Learn more about rounding of numbers:
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To divide 5472 by 81 using the shortened form of the division algorithm, what should be your first thought? Select from the drop-down menus to correctly complete the thought. "How many times does 81 divides into Choose... ?"
5
54
547
5472
Answer:
"How many times does 81 divide into 547?"
How many meters does a runner cross in a circular runway with radious of 100 meters [R=3, 14]
What is the
range of the function graphed below? I am in desperate need of answer
Answer:
B
Step-by-step explanation:
look at where the line reaches on the y-axis
Please answer ASAP please and thank and also please draw it on the modle
Answer:
5/12
Step-by-step explanation:
1x5/2x6
Can Someone help me!
Answer:50 degree
Step-by-step explanation:
It is an isosceles triangle so two sides and angles are equal. The first line is facing the first angle so the second angle ( m<DEF) = 65 degrees because both angles are equal.
This implies that m<FED =
65 + 65+ <FED= 180( sum of angle in a triangle)
130 + <FED=180
<FED= 180- 130
<FED= 50 degree