Answers
ANSWER
A. True
EXPLANATION
Let the complex number be z = a+ ib, so its complex conjugate is z* = a - ib, where a and b are real numbers. Let's find the product,
The product is,
[tex](a+ib)(a-ib)=a\cdot a-a\operatorname{\cdot}ib+ib\operatorname{\cdot}a-ib\operatorname{\cdot}ib[/tex]Solve the products,
[tex](a+ib)(a-ib)=a^2-iab+iab-i^2b^2[/tex]Simplify: note that the second and third terms are opposites, so they cancel out. Remember that i² is equal to -1,
[tex](a+ib)(a-ib)=a^2+0-(-1)b^2=a^2+b^2[/tex]Since a and b were real numbers, then the sum of their squares is also a real number.
Hence, this statement is true.
Related Questions
uncle grandpa once said, “400 reduced by twice my age is 262.” what is his age? Show work
Answers
Answer:
69
Step-by-step explanation:
400-262=138
138÷2=69
which graph represents the equation x - 4y = -16
Answers
the given equation is
x - 4y = -16
put x = 0
0 - 4y = -16
y = 4
so at x = 0 ,, y is 4
put x = 4
4 - 4y = -16
-4y = -16- 4
y = 20/4
y = 5
so, at x = 4 the value of y is 5
thus, the correct graph is option B
A ball is thrown in the air from a platform that is 96 feet above ground level with an initial vertical velocity of 32 feet per second. The height of the ball, in feet, can be represented by the function shown where t is the time, in seconds, since the ball was thrown. Rewrite the function in the form that would be best used to identify the maximum height of the ball and find Approximately when the object lands on the ground when rounded to the nearest tenth.
Answers
Answer:
y = -16 (x - 1)^2 + 112
The object lands on the ground in approximately 3.6s
Explanation:
The equation given is that of a parabola.
Now the maximum (local) point of a parabola is the vertex. Therefore, if we want to rewrite our function in the form that would be used to find the maximum height, then that form must be the vertex form of a parabola.
The vertex form of a parabola is
[tex]y=a(t-h)^2+k[/tex]where (h, k) is the vertex.
The only question is, what is the vertex for our function h(t)?
Remember that if we have an equation of the form
[tex]y=ax^2+bx+c[/tex]then the x-coordinate of the vertex is
[tex]h=-\frac{b}{2a}[/tex]Now in our case b = 32 and a = -16; therefore,
[tex]h=\frac{-32}{2(16)}=1[/tex]We've found the value of the x-coordinate of the vertex. What about the y-coordinate? To get the y-coordinate, we put x = 1 into h(t) and get
[tex]k=-16(1)+32(1)+96=112[/tex]Hence, the y-coordindate is k = 112.
Therefore, the vertex of the parabola is (1, 112).
With the coordinates of the vertex in hand, we now write the equation of the parabola in vertex form.
[tex]h(t)=a(t-1)^2+112[/tex]The only problem is that we don't know what the value of a is. How do we find a?
Note that the point (0, 96) lies on the parabola. In other words,
[tex]h(0)=-16(0)^2+32(0)+96=96[/tex]Therefore, the vertex form of the parabola must also contain the point (0, 96).
Putting in t = 0, h = 96 into the vertex form gives
[tex]96=a(0-1)^2+112[/tex][tex]96=a+112[/tex]subtracting 112 from both sides gives
[tex]a=-16[/tex]With the value of a in hand, we can finally write the equation of the parabola on vertex form.
[tex]\boxed{h\mleft(t\mright)=-16\left(t-1\right)^2+112.}[/tex]Now when does the object hit the ground? In other words, for what value of t is h(t) = 0? To find out we just have to solve the following for t.
[tex]h(t)=0.[/tex]We could either use h(t) = -16t^2 + 32t + 96 or the h(t) = -16(t - 1)^2 + 112 for the above equation. But it turns out, the vertex form is more convenient.
Thus we solve,
[tex]-16\left(t-1\right)^2+112=0[/tex]Now subtracting 112 from both sides gives
[tex]-16(t-1)^2=-112[/tex]Dividing both sides by -16 gives
[tex](t-1)^2=\frac{-112}{-16}[/tex][tex](t-1)^2=7[/tex]taking the square root of both sides gives
[tex]t-1=\pm\sqrt{7}[/tex]adding 1 to both sides gives
[tex]t=\pm\sqrt{7}+1[/tex]Hence, the two solutions we get are
[tex]t=\sqrt{7}+1=3.6[/tex][tex]t=-\sqrt{7}+1=-1.6[/tex]Now since time cannot take a negative value, we discard the second solution and say that t = 3.6 is our valid solution.
Therefore, it takes about 3.6 seconds for the object to hit the ground.
Solve by factoring: f(x) = 2x² + 7x+6
Write the final answers in the two blanks. Do NOT write x =, just the number. If there is a fraction in your answer, write as #/#.
Answers
The factoring of the expression 2x² + 7x + 6 is (2x + 3)(x + 2).
How to illustrate the information?It should be noted that a factor of a number is a number that can be multiplied with another number to get the original number.
In this case, 2x² + 7x - 6 will be factored thus:
= 2x² + 7x + 6
= 2x² + 4x + 3x + 6
= 2x(x + 2) + 3(x + 2)
= (2x + 3)(x + 2)
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I don't understand this at all. Solve the equation for T1.
Answers
Answer:
T1 = P2 * V2 / T2 * P1 * V1
−8−x=−3(2x−4)+3x (with dcmam)
Answers
x = 10 is the solution to the equation -8 - x = -3( 2x - 4 ) + 3x using DCMAM method.
What is the solution to the given equation?
Given the equation in the question;
-8 - x = -3( 2x - 4 ) + 3xx = ?First, apply the distributive property to eliminate the parenthesis.
-8 - x = -3( 2x - 4 ) + 3x
-8 - x = -3×2x -3×-4 + 3x
Multiply -3 × 2x
-8 - x = -6x -3×-4 + 3x
Multiply -3 × -4
-8 - x = -6x + 12 + 3x
Next, combine like terms.
Add -6x and 3x
-8 - x = -3x + 12
Next, move variable to one side and constant terms to the other.
-x + 3x = 12 + 8
Add -x and 3x
2x = 12 + 8
Add 12 and 8
2x = 20
Divide both sides by 2
2x/2 = 20/2
x = 20/2
x = 10
Therefore, the value of x is 10.
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There are multiple choices. but they didn’t fit in the picture
Answers
Explanation
In the question,
The number of tomatoes is described as x
The number of lettuce is described as y
As per the question, the number of vegetables Aneil can plant in the garden is modelled by:
[tex]2x+3y=60[/tex]The graph of the above model can be seen above.
From the graph, we have the y-intercept to be 20 and the x-intercept to be 30.
Answer:
Y-intercept = 20 ---- This is the number of lettuce plants Aneil can plant if he plants zero tomatoes
X- intercept =30 ---- This is the number of tomatoes plants Aneil can plant if he plants zero lettuce
B. f(x) = x² + 1
4. Evaluate f(-3).
5. Evaluate f (6).
6. Circle any ordered pairs
that are included in the
function:
(0, -1) (5, 17) ((-7,50)
Answers
A mixture of 20 pounds of candy sells for $1.15. The mixture consists of chocolates worth $1.45 a pound and chocolatesworth $0.90 a pound. If x represents the pounds of $0.90 chocolates used, then which of the following represents thepounds of $1.45 chocolates used?20 - x20 xOX-20
Answers
Answer
The 1.45 dollar chocolates will weigh (20 - x) pounds.
Explanation
We are told that the mixture weighed 20 pounds and one of the chocolates in the mixture weighed x pounds.
We are then to cslculate the weight of the other type of chocolate in the mixture.
Total mixture = 20 pounds
0.90 dollar chocolate weighed x pounds
The 1.45 dollar chocolates will weigh (20 - x) pounds.
Hope this Helps!!!
Find the dimensions of a rectangular Persian rug whose perimeter is 18 ft and whose area is 20ft^2. *Answer fill in*The Persian rug has a length (longerside) of [___]ft and a width (shorter) of [__]ft
Answers
Perimeter = 18 ft
Area = 20 ft ^2
Perimeter = 2l + 2w
Area = lw
Substitution
18 = 2l + 2w
20 = lw
Solve for l
20/w = l
18 = 2(20/w) + 2w
18 = 40/w + 2w
18w = 40 + 2w^2
2w^2 - 18w + 40 = 0
w^2 - 9w + 20 = 0
(w - 5)(w - 4) = 0
w1 = 5 w2 = 4
Conclusion
width = 4 ft
length = 5 ft
6. Solve for x. **THINK! a) what type of angles do you have? b) what is theirrelationship (add up to 90, add up to 180, or congruent)? c) set up an equationand solve *
Answers
a) The types of angles present are:
- 1 right angle
- 1 angles of 50 degrees and 1 angle of 4x degrees
b) their relationship is add up to 90°
c) 50° + 4*x° = 90°
4*x° = 90 - 450
x° = 40/4 = 10
x = 10°
Picture listed below help.
Answers
Answer:
Perimeter = 65.12 inches, Area = 292.48 square inches
Step-by-step explanation:
Perimeter:
Total perimeter = perimeter of semicircle + perimeter of rectangle (note: excluding the shared line, since that is not on the outside of the shape).
= [tex]\frac{1}{2} 2\pi r[/tex]
= [tex]\frac{1}{2} *2*3.14*8[/tex]
= 25.12
Perimeter = 25.12 + 12 + 12 + 16 = 65.12 inches
Area:
Total area = area of semicircle + area of rectangle
Area of semicircle = [tex]\frac{1}{2} \pi r^{2}[/tex]
= [tex]\frac{1}{2} *3.14* 8^{2}[/tex]
= 100.48
Area of rectangle = l * w
= 16 * 12
= 192
Total area = 100.48 + 192 = 292.48
a. pi/3 b. pi/2c. 2pi/3d. 3pi/2 These are 4 options but there can be more than 2 or 3 correct answers.Find the solution of each equation the interval
Answers
so the answer is pi/2, 3pi/2, and pi/3
if A(-3,4) is on BC and divides it in the ratio of BA:AC = 1:2 find C if B is (-9,8)
Answers
The coordinate of the point C on the line segment is (9, -4)
How to determine the coordinates of the endpoint C?On the segment, we have the following endpoints
A = (-3, 4)
B = (-9, 8)
The ratio of point A on the line is given as
Ratio, B : C = 1 : 2
Rewrite as
m : n = 1 : 2
The coordinate of point A is calculated using
A = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)
Where x and y are the coordinates defined above
So, we have
(-3, 4) = 1/(1+2) * (1 * x + 2 * -9, 1 * y + 2 * 8)
Evaluate
(-3, 4) = 1/3 * (x - 18, y + 16)
So, we have
(x - 18, y + 16) = (-9, 12)
This means that
x - 18 = -9
y + 16 = 12
Solve
x = 9
y = -4
Hence, the location of the point C is (9, -4)
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To indirectly measure the distance across a lake, Ethan makes use of a couple
landmarks at points B and C. He measures AE, EC, and DE as marked. Find the
distance across the lake (BC), rounding your answer to the nearest hundredth of a
meter.
Answers
To the nearest tenth, the distance across the lake is DE = 207.68 m.
The corresponding side lengths of two triangles that are similar are always proportional to each other.
ΔCDE and ΔCFG are similar to each other
FG = 142.1 m
FC = 130 m
DF = 60 m
DC = 130 + 60 = 190 m
Therefore,
DE/FG = DC/FC
Substitute
DE/142.1 = 190/130
Cross multiply nearest hundredth
Therefore, applying the similarity theorem, the distance across the lake to the nearest hundredth is DE = 207.68 m
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Cuanto es 2 1/2 + 1 3/4 + 1/2=?
Ayudaaa
Answers
Answer:
2 2/4 + 1 3/4 + 2/4 = 4 3/4
4 3/4
Answer:
4 and 3/4
Step-by-step explanation:
2 1/2
+1 3/4
+ 1/2
_____
4 and 3/4
The quadratic function -2x ^ 2 + 4x + 6 is shown below. What are the solutions of this function? *
Answers
The solution for this function will be x = -1 and x = 3
Describe the quadratic function.Quadratic polynomials are those with at least one variable and a variable with a maximum exponent of two. Since the second-degree term is the highest degree term in a quadratic function, it is sometimes referred to as the polynomial of degree 2. In a quadratic function, at least one term must be of the second degree. It has qualities in algebra.
The given function is -2x² + 4x + 6
So, we'll employ the middle term splitting strategy.
-2x² + 4x + 6 = 0
- 2x² + 6x - 2x + 6 = 0
-2x ( x-3) -2 (x-3) = 0
(-2x-2) (x-3) = 0
So, the solution will be
-2x - 2 = 0
-2x = 2
x = 2/-2
x = -1
And, x-3 =0
x = 3
So, the solution of the quadratic function will be
x =-1 and x = 3
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What term must go in the space to complete the statement?
Answers
The term that should go in the space to complete the statement is 5.
The complete statement is 5c + 15 = 5(c + 3).
What exactly does it mean to simplify an expression?Simplifying an expression is the same as solving a math problem. When you simplify an expression, you are attempting to write it in the simplest feasible manner.Combining similar terms is a frequent strategy for reducing algebraic expressions. Like Terms have identical variable components (same variable(s) and same exponent(s)).The given statement is 5c + 15 = __(c + 3).
Now, we will combine the like term from the left side of the expression which is 5, and place it on the right side space to make the expression equivalent.
Hence, the complete statement is 5c + 15 = 5(c + 3).
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can you please solve this practice problem for me I really need assistance. the original slope is blue and the parallel slope is green
Answers
Answer:
The original slope is 1, so the slope of the parallel line will also be 1.
A farmer harvested 192 pounds of Yukon Gold potatoes and 138 pounds of russet potatoes. He divided the Yukon
Gold potatoes evenly among 8 baskets. He divided the russet potatoes evenly among 6 baskets. He then filled a
sack with one basket of Yukon Gold potatoes and one basket of russet potatoes.
Which equation could be used to solve for n, the number of number of pounds of potatoes the farmer put in the
sack?
Answers
The farmer put a total of 47 potatoes in one sack.
Here, we are given that a farmer harvested 192 pounds of Yukon Gold potatoes and 138 pounds of russet potatoes.
He divided the Yukon Gold potatoes evenly among 8 baskets.
Thus, the number of pounds of potatoes in each basket = 192/8
= 24
Similarly, he divided the russet potatoes evenly among 6 baskets.
Thus, the number of pounds of russet potatoes in each basket = 138/6
= 23
Now, he fills a sack with one basket of Yukon Gold potatoes and one basket of russet potatoes.
n = the number of pounds of potatoes the farmer put in the sack
Thus, n = 24 + 23
n = 47
Thus, the farmer put a total of 47 pounds of potatoes in one sack.
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Transit Technologies plans to produce 2-way radios that will sell for $59 per radio. They estimate fixed costs
in manufacturing the radios to be $41,500. The variable costs of producing each radio will be $14. How many
radios must the company sell to break even?
Answers
The company should must sell 923 radios to break even.
Fixed cost refer to those costs which do not vary directly with the level of output. For example salary given to staff.
Variable cost that cost which vary directly with the level of output..
The selling price of radio is $59.
Total radios sell are of value $41500. This is the fixed cost.
Let us say that they sell x number of radios,
As we know,
For break even point,
Total revenue = Total cost
Cost of one radio x number of radio = fixed cost plus variable cost of all radios
54x = 41500 + 14x
40x = 41500
x = 922.22~923
So, they should sell 923 radio to break even.
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The turning points of the graph are (-1.73, -10.39) and (1.73, 10.39). What is the range of the Polynomial function f?
Answers
Given the turning points of the graph:
(-1.73, -10.39) and (1.73, 10.39).
Let's determine the range of the graphed function.
The range of a function is the set of all possible values of y.
The y-values are represented on the vertical axis.
From the graph, we can see the function goes up continuously and goes down continuously.
Therefore, we can say the range of the function is real numbers.
Therefore, the range of the function in interval notation is:
(-∞, ∞)
ANSWER:
rRange: (-∞, ∞)
Least squares regression line is y=4x-8 what is the best predicted value for y given x =7?
Answers
We have a regression model to predict y from the value of x.
The equation of this regression line is:
[tex]y=4x-8[/tex]We then can calculate y for x = 7 as:
[tex]y(7)=4(7)-8=28-8=20[/tex]Answer: the predicted value of y when x = 7 is y(7) = 20
subtract 5x from 7x-6
Answers
We can subtract 5x from 7x - 6 like this:
7x - 6 - 5x
Now, we just have to combine like terms, in this case, the terms that have the x variable, like this:
7x - 5x - 6
2x - 6
Then, after subtracting 5x from 7x - 6 we get 2x - 6
Answer this please I really need you to do this
Answers
Answer:
x ≥ 2
Step-by-step explanation:
Given inequality:
[tex]-\dfrac{4(x+3)}{5} \leq 4x-12[/tex]
Values of x less than 2
Substitute two values where x < 2 into the inequality:
[tex]\begin{aligned}x=1 \implies -\dfrac{4(1+3)}{5} & \leq 4(1)-12\\\\ -\dfrac{4(4)}{5} & \leq 4-12\\\\ -\dfrac{16}{5} & \leq -8 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]
[tex]\begin{aligned}x=0 \implies -\dfrac{4(0+3)}{5} & \leq 4(0)-12\\\\ -\dfrac{4(3)}{5} & \leq 0-12\\\\ -\dfrac{12}{5} & \leq -12 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]
The values of x < 2 are not solutions to the inequality.
--------------------------------------------------------------------------------
Substitute the value of x = 2 into the inequality:
[tex]\begin{aligned}x=0 \implies -\dfrac{4(2+3)}{5} & \leq 4(2)-12\\\\ -\dfrac{4(5)}{5} & \leq 8-12\\\\ -\dfrac{20}{5} & \leq -4\\\\ -4 & \leq -4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]
The value of x = 2 is a solution to the inequality.
--------------------------------------------------------------------------------
Values of x more than 2
Substitute two values where x > 2 into the inequality:
[tex]\begin{aligned}x=3 \implies -\dfrac{4(3+3)}{5} & \leq 4(3)-12\\\\ -\dfrac{4(6)}{5} & \leq 12-12\\\\ -\dfrac{24}{5} & \leq 0 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]
[tex]\begin{aligned}x=4 \implies -\dfrac{4(4+3)}{5} & \leq 4(4)-12\\\\ -\dfrac{4(7)}{5} & \leq 16-12\\\\ -\dfrac{28}{5} & \leq 4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]
The values of x > 2 are solutions to the inequality.
--------------------------------------------------------------------------------
Therefore, the solution to the inequality appears to be x ≥ 2.
To check, solve the inequality:
[tex]\begin{aligned} \implies -\dfrac{4(x+3)}{5} &\leq 4x-12\\-4(x+3) &\leq 5(4x-12)\\-4x-12 &\leq 20x-60\\ -24x & \leq-48\\x & \geq 2\end{aligned}[/tex]
When graphing inequalities on a number line:
< or > : open circle.≤ or ≥ : closed circle.< or ≤ : shade to the left of the circle.> or ≥ : shade to the right of the circle.To graph the solution to the inequality on number line, place a closed circle at x = 2 and shade to the right. (See attachment).
May u please help me with my geometry study guide Only 2 questions
Answers
Answer:
4.
[tex]x=AB=\frac{5\sqrt[]{2}}{2}[/tex]5.
[tex]BC=x=5\sqrt[]{3}[/tex]Step-by-step explanation:
Relationships in a right triangle:
The sine of an angle is the length of the opposite side to the angle divided by the hypotenuse.
The cosine of an angle is the length of the adjacent side to the angle divided by the hypotenuse
The tangent of an angle is the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
Question 4:
hypotenuse is 5.
AB is adjacent to an angle of 45º. So
[tex]\sin 45^{\circ}=\frac{x}{5}^{}^{}[/tex][tex]\frac{\sqrt[]{2}}{2}=\frac{x}{5}[/tex]Applying cross multiplication:
[tex]2x=5\sqrt[]{2}[/tex][tex]x=AB=\frac{5\sqrt[]{2}}{2}[/tex]Question 5:
Hypotenuse is 10.
BC is opposite to an angle of 60. So
[tex]\sin 60^{\circ}=\frac{x}{10}[/tex][tex]\frac{\sqrt[]{3}}{2}=\frac{x}{10}[/tex][tex]2x=10\sqrt[]{3}[/tex][tex]x=\frac{10\sqrt[]{3}}{2}[/tex][tex]BC=x=5\sqrt[]{3}[/tex]Find the equation of the line with slope −3/5 and y-intercept (0,−3).
Answers
The equation of the line will be [tex]y = -\frac{3}{5}x -3[/tex]
In the question given, It is stated that the slope of the line is m = -3/5, and the y-intercept of the line is (0, -3). We have to find out the slope-intercept form of the line. To find out the equation of line first the standard equation for slope intercept form is y = mx + b, where m is the slope, and b is the y-intercept.
Now, we have slope m = -3/5 and y-intercept is -3. Putting these values in the slope intercept form we get:
=> y = mx + b
=> [tex]y = -\frac{3}{5}x -3[/tex]
Hence, we get equation of line [tex]y = -\frac{3}{5}x -3[/tex]
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A map is drawn using the scale 2cm: 100miles. On the map, Town B, is 3.5 cm from Town A and Town C is 2 cm past Town B. How many miles apart are Town A and Town C
Answers
SOLUTION
From the question, town B is 3.5cm from town A and town C is 2cm from town B. Therefore C is 5.5 cm from town A.
The scale is 2cm for every 100miles. This means 1cm for every 50 miles.
You get this by dividing 100 by 2.
Now 5.5 cm becomes 5.5 x 50 miles = 275miles.
So town A and town C are 275 miles apart
Hey! Can anybody help me with this?I don't need a very big explanation just a very brief explanation leading to the answer as I already kinda know this stuff. Thanks!
Answers
In an ordered pair (x,y), x denotes the domain of the relation, and y denotes the range of the relation.
Knowing this, the three ordered pairs that will form a relation with a range of {-3, 4, 7} are
(-1, -3), (0, 4), and (2,7).
What is the effect on the graph of f(x)=x^2 when it is transformed to h(x)=2x^2 + 15
Answers
Answer and Explanation:
If f(x) = x^2 is transformed to h(x)=2x^2 + 15, the below will be the effect on the its graph;
* The graph will be shifted up 15 units
*The graph will be vertically stretched since the value o