Answers
By De Moivre's formula, the square roots of the complex number √(i 2) are √z = 1 + i and √z = - 1 - i, respectively.
How to find the square roots of a complex numbers
In this problem we find a complex number, whose square roots can be determined by De Moivre's formula:
For z = a + i b:
√z = √r · [cos [(θ + 2π · k) / 2] + i sin [(θ + 2π · k) / 2]], for k = {0, 1}
Where:
r - Normθ - Direction, in radians.If we know that r = 2 and θ = π / 2, then the root of the complex number is:
k = 0
√z = √2 · [cos (π / 4) + i sin (π / 4)]
√z = 1 + i
k = 1
√z = √2 · [cos (5π / 4) + i sin (5π / 4)]
√z = - 1 - i
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Related Questions
1. Find the exact value of each of the following: a. cos(sin−1(1)) b. tan(cos−1(−23 )) 2. Find the exact value of each of the following: a. sin(cos−1(32)) b. csc(tan−1(−51)) 3. Find the exact value, in terms of a, of each of the following. (HINT: Don't let the variable a scare you! The same strategy you used in Problem 2 still works - draw a point on a circle, assign it coordinates, and find the appropriate trig function's value.) a. sin(tan−1(a2)) b. cot(cos−1(a))
Answers
The cot(cos−1(a))= a/√(1-a^2).
Value of cos(sin−1(1)): Let's assume that θ= sin−1(1). It means that sinθ= 1. The value of θ is π/2, therefore we can say that cos(sin−1(1))=cos(π/2)= 0b) Value of tan(cos−1(-23)): Let's suppose that θ= cos−1(-23). It implies that cosθ= -23/25. As we know that tanθ= sinθ/cosθ, Therefore;tan(cos−1(−23))= sin(θ)cos(θ) = -24/25.2. a) Value of sin(cos−1(3/2)): Let's suppose that θ= cos−1(3/2). It implies that cosθ= 3/2. As we know that sin^2θ= 1- cos^2θ, Therefore;sin(cos−1(3/2))= √(1- (3/2)^2)= √(1/4)= 1/2.b) Value of csc(tan−1(-5/1)): Let's assume that θ= tan−1(-5/1). It implies that tanθ= -5/1. As we know that cscθ= 1/sinθ, Therefore;csc(tan−1(−51))= 1/sin(θ)= 1/√(1+tan^2θ) = 1/√(1+25)= -1/√26.3. a) Value of sin(tan−1(a^2)): Let's suppose that θ= tan−1(a^2). It implies that tanθ= a^2. As we know that sinθ= tanθ/√(1+tan^2θ), Therefore;sin(tan−1(a2))= (a^2)/√(1+(a^4)).b) Value of cot(cos−1(a)): Let's suppose that θ= cos−1(a). It implies that cosθ= a. As we know that cotθ= cosθ/sinθ, Therefore;cot(cos−1(a))= a/√(1-a^2).
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A shop in the mall is 8 meters by 12 meters. How much would it cost to recarpet the shop with carpet that costs $3. 00 per square meter?
Answers
It would cost $288.00 to recarpet the shop with carpet that costs $3.00 per square meter.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The area of the shop can be found by multiplying its length by its width:
Area = Length x Width
= 8 meters x 12 meters
= 96 square meters
To recarpet the entire shop, we need to purchase 96 square meters of carpet.
If the carpet costs = $3.00 per square meter.
The total cost can be found by multiplying the area by the cost per square meter:
Total cost = Area x Cost per square meter
Total cost = 96 square meters x $3.00 per square meter
Total cost = $288.00
Therefore,
It would cost $288.00 to recarpet the shop with carpet that costs $3.00 per square meter.
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In a race, 29 out of the 50 swimmers finished in less than 39 minutes. What percent of swimmers finished the race in less than 39 minutes? Write an equivalent fraction to find the percent.
Answers
Answer:
percentage = (part/whole) x 100
where the "part" is the number of swimmers who finished in less than 39 minutes, and the "whole" is the total number of swimmers.
So, if 29 out of 50 swimmers finished in less than 39 minutes:
percentage = (29/50) x 100
percentage = 58
Therefore, 58% of swimmers finished the race in less than 39 minutes.
An equivalent fraction to represent 58% is 29/50.
Step-by-step explanation:
how many integers are between 48 and 172
Answers
The number of integers between two given integers is 124.
The two given integers are 48 and 172.
We know that, number of integers between two integers = Difference of two integers
Here, number of integers = 172-48
= 124
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To solve use:
Moore’s Law, 1965 (projected for 10 years):
The number of transistors in a chip will double
approximately every 12 months.
Moore’s Law, amended 1975 (projected for 10 years):
The number of transistors in a chip will double
approximately every 24 months
USE: the chart provided to answer the question on the bottom
Answers
The estimated transistors count in a computer in 2023 is given as follows:
1,680,085,700,000
How to define the exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^(x/n).
In which:
a is the value of y when x = 0.b is the rate of change.n is the time needed for the rate of change.The number of transistors doubles every 24 months = 2 years, hence the parameters b and n are given as follows:
b = 2, n = 2.
The amount in the reference year of 2020 was 59,400,000,000, hence the parameter a is given as follows:
a = 59,400,000,000.
Then the function estimating the amount in x years after 2020 is given as follows:
y = 59,400,000,000(2)^(x/2).
The amount in 3 years after 2020 is given as follows:
y(3) = 59,400,000,000(2)^(3/2)
y(3) = 1,680,085,700,000.
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The population of Charlotte, North Carolina, in 2013 was approximately 775,000. If the annual rate of growth is about 3. 2% what is an approximation of Charlotte’s population in 2000
Answers
Charlotte, North Carolina had an approximate population of 531,145 in 2000.
To approximate Charlotte's population in 2000, we can use the formula for exponential growth:
P(t) = [tex]P0 \times e^{(rt)[/tex]
where P(t) is the population at time t, P0 is the initial population, r is the annual rate of growth as a decimal, and e is the mathematical constant e (approximately 2.71828).
Let's let t = 13 be the number of years between 2000 and 2013. We know that P(13) = 775,000, and r = 0.032. We can solve for P0 as follows:
775,000 = [tex]P0 \times e^{(0.03213)[/tex]
P0 = [tex]775,000 / e^{(0.03213)[/tex]
Using a calculator, we can approximate P0 as:
P0 ≈ 531,145
Therefore, an approximation of Charlotte's population in 2000 is 531,145.
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5x^2 + 5y^2 -3x + 7y - 1 =0
Find the center and radius of the above
Answers
On solving the question we have that Therefore, the center of the circle equation is (3/10, -7/10) and the radius is √(1/5).
What is equation?A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.
The given equation is that of a circle in standard form:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
where the center of the circle is (h, k) and the radius is r.
To convert the given equation to this form, we need to complete the square for both x and y terms. Let's start with the x terms:
[tex]5x^2 - 3x = 5(x^2 - (3/5)x)\\5(x^2 - (3/5)x + (3/10)^2 - (3/10)^2)\\5((x - 3/10)^2 - 9/100)\\5y^2 + 7y = 5(y^2 + (7/5)y)\\5(y^2 + (7/5)y + (7/10)^2 - (7/10)^2)\\5((y + 7/10)^2 - 49/100)\\5((x - 3/10)^2 - 9/100 + (y + 7/10)^2 - 49/100) - 1 = 0\\5(x - 3/10)^2 + 5(y + 7/10)^2 = 1\\[/tex]
Therefore, the center of the circle is (3/10, -7/10) and the radius is √(1/5).
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d) Decrease 500 ml by 25% and then increase by 10%.
Answers
Answer: 412.5 ml
Step-by-step explanation:
500 ( 1 - 25%) ( 1 + 10%)
= 412.5 ml
Answer:
412.5 ml
Step-by-step explanation:
To decrease 500 ml by 25%, you would need to multiply 500 by 0.25 to find the amount of decrease:
500 × 0.25 = 125 mlSubtract that amount from the original value:
500 - 125 = 375 ml.Therefore decreasing 500 ml by 25% would give us 375 ml.
To then increase this value by 10%, you would multiply it by 0.10 to find the amount of increase:
375 × 0.10 = 37.5 mlNow, add that amount to the previous value:
375 + 37.5 = 412.5 ml.Therefore, if you decrease 500 ml by 25% and then increase it by 10%, the final result is 412.5 ml.
Since switching to a new career, Mason has been making $71,134 annually. That is 30% less than he got paid in the past.
How much did Mason make then?
Answers
$101,620
Step by step explanation:
If Mason's current salary is $71,134 and it is 30% less than his previous salary, we can find his previous salary by using the following formula:
Previous salary = Current salary / (1 - Percent decrease as a decimal)
Here, the percent decrease is 30%, which in decimal form is 0.3. Substituting the values, we get:
Previous salary = $71,134 / (1 - 0.3) = $71,134 / 0.7
Simplifying the right-hand side, we get:
Previous salary = $101,620
Therefore, Mason's previous salary was $101,620.
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Question
All eighteen of Mrs. Gordon’s math students scored low on a test, so she gave them a retest.
Both tests had a median score of 78
The original test had a range of 20
The retest had a range of 2.
Which statement is true based on the given information?
Responses
A The mean score for the retest is greater than 80.The mean score for the retest is greater than 80.
B The highest score on the original test is less than 98.The highest score on the original test is less than 98.
C At least one students scored a 78 on the retest.At least one students scored a 78 on the retest.
D One of the students scored 100 on the retest.One of the students scored 100 on the retest.
Answers
Option B is the true statement based on the given information by solving the method of average.
What is average?In mathematics, the average (also called the arithmetic mean) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of values in the set.
Since both tests had a median score of 78, we know that there were nine scores below 78 and nine scores above 78 on each test.
If the original test had a range of 20, that means the highest score was 20 points above the lowest score. Therefore, the lowest score on the original test was 78 - 10 = 68, and the highest score was 68 + 20 = 88.
If the retest had a range of 2, that means the highest score was only 1 point above the lowest score. Therefore, the lowest score on the retest was 78 - 1 = 77, and the highest score was 77 + 2 = 79.
We don't know the mean score for either test, so we cannot determine if option A is true or false. We also don't know if any student scored exactly 78 on the retest, so we cannot determine if option C is true or false. Finally, we know that the highest score on the retest is 79, so option D is false.
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A school supply company is giving away free chalkboards to promote their dust-free chalk. The company can spend up to $2,500 on the chalkboards. If each chalkboard costs the company $5, how many chalkboards will they be able to give away?
Answers
Therefore , the solution of the given problem of unitary comes out to be the school supply business may distribute 500 chalkboards.
An unitary method is what?By combining what was learned and implementing this variable technique, which also includes all supplemental information from two people who used a particular tactic, the task can be finished. In other words, if the desired result occurs, either the entity specified in the expression will also be identified, or both crucial procedures will actually skip the colour. A refundable fee of Rupees ($1.01) may be needed for forty pens.
Here,
Assuming each chalkboard costs the company $5 and they can spend up to $2,500 on the chalkboards:
Number of chalkboards Equals Total allowable spending / Chalkboard cost
=> Chalkboard count = $2,500 / $5
=> 500 chalkboards are present.
Consequently, the school supply business may distribute 500 chalkboards.
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if x:y=3:4 and y:z=1:3 find x:z
Answers
The value of x:z = 1:4.
To find the ratio of x to z, we need to have a common term between x, y, and z. Since we have y in both ratios, we can use it as the common term.
From the given ratios:
x:y = 3:4
y:z = 1:3
We can see that the y in the first ratio and the y in the second ratio are the same.
To find the ratio of x to z, we can "connect" the two ratios by canceling out the y:
x:y = 3:4
y:z = 1:3
x:y × y:z = 3:4 × 1:3
x:z = 3:12
Simplifying the above ratio by dividing both terms by 3, we get:
x:z = 1:4
Select the correct answer. What is this expression in simplified form? √32 . 5√2
Answers
Answer: The answer is 40
Explanation: The picture
helppp please
HELP
[tex]5555[/tex]
Answers
Answer: C
Step-by-step explanation:
For A, look at the slope of the graph: 70/2 = 35
For B, slope calculation: m = y-y / x-x = 315-105 / 9-3 = 35
=> C
Malik and his mom are planting vegetables in their garden. Malik has finished planting 7 rows of carrots so far and is planting new rows at a rate of 5 rows per hour. His mom has finished 10 rows of tomatoes and will continue planting at 2 rows per hour. Once they have an equal number of carrot and tomato rows, they will take a break and decide what to plant next.
a. How many hours will it take for them to plant the same number of vegetable rows? How many rows will they each have completed?
Answers
The number of hours it will take for them to plant the same number of vegetable rows is equals to one hour. Total twelve rows of vegitables they will each have completed.
We have, Malik and his mom are planting vegetables in their garden.
For Malik : he has finished planting 7 rows of carrots and his planting rate = 5 rows per hour.
For his mom : She has finished 10 rows of tomatoes and continue.
Her planting rate = 2 rows per hour.
Let they finish an equal number of carrot and tomato rows in "x hours". That is we can wright the provide information in equation form : Malik plants 5 rows of vegitable per hour, so he will plant 5x rows in x hours. Similarly, his mother will plant 2x rows of vegitables in x hours. Thus, after x hours, (Malik) 7 + 5x = 10 + 2x (mom)
Simplify the above equation,
=> 5x - 2x = 10 - 7
=> 3x = 3
=> x = 1
So, x = 1 be the hours it will take for them to plant the same number of vegetable rows. Now, total rows they will each have completed = 7 + 5×1 = 12 rows or 10 +2×1
= 12
Thus, total 12 rows they finally completed.
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Using the side lengths of △pqr and △stu, which angle has a sine ratio of ? ∠p ∠q ∠t ∠u
Answers
The angle that has the sine ratio, 4/5, is: A. Angle P.
Sine Ratio:
The sine ratio is the ratio of the side opposite the hypotenuse of a right triangle to a given reference angle. When the ratio is found using the opposite and the hypotenuse, we call it the sine ratio rather than the tangent ratio.
Example:
Then we say that the sine of 45 degrees is equal to 0.707. In short, we can use the notation sin instead of sine and write sin(45 degrees) = 0.707
In general, the sine of angle A = leg length of opposite angle A / hypocenter
sin(A ) = opposite / hypotenuse
Given:
sine ratio of 4/5, then it means:
Opposite side (side directly opposite to the reference angle) = 4
Hypotenuse (longest side) = 5.
Thus, in the image given, using P as the reference angle, the sine ratio of P is:
QR/PQ
= 16/20 = 4/5
Therefore, the angle with the sine ratio of 4/5 is: A (P)
Complete Question:
Using the side lengths of △PQR and △STU, which angle has a sine ratio of 4/5?
A. P
B. Q
C. T
D. U
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If three hamburgers cost $7. 50 altogether what is the price of one hamburger
Answers
If you buy three hamburgers, the cost of each hamburger is $2.50.
One hamburger costs $2.50.
To determine the price of one hamburger, first take the total cost of all three hamburgers, which is $7.50.
Then, divide the total cost of all three hamburgers by the number of hamburgers, which is three.
This yields $2.50, which is the price of one hamburger.
One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division.
The other operations are multiplication, addition, and subtraction.
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there are black,green,yellow counters in a bag in the ratio 3:10:7
there are 105 yellow counters
how many black counters are there
Answers
If yellow = 7, but also has the real value of 105, we do 105/7 which gives us 15.
we then do 15 x 3 which gives us 45
In Princeton, the library is due south of the courthouse and due west of the community swimming pool. If the distance between the library and the courthouse is 7 miles and the distance between the courthouse and the city pool is 8 miles, how far is the library from the community pool? If necessary, round to the nearest tenth.
Please respond.
Thank you!
Answers
Answer:
3.87 miles
Step-by-step explanation:
The attached figure gives the relative locations of the courthouse, the library and the pool.
The three locations represent a right triangle with the distance between courthouse - pool as the hypotenuse and the distance between courthouse - library as the vertical leg
By the Pythagorean theorem if c is the hypotenuse and a, b the other two legs
[tex]c^2 = a^2 + b^2[/tex]
a = distance between courthouse and library = 7 miles
c = distance between courthouse and pool = 8 miles
and we have to find b
So plugging in known values
[tex]8^2 = 7^2 + b^2\\\\b^2 = 8^2 - 7^2\\\\b^2 = 64 - 49\\\\b^2 = 15\\\\b= \sqrt{15} = 3.87298 \approx 3.87 \;miles[/tex]
A triangle has an angle that measures 35°. The other two angles are in a ratio of 13:16. What are the measures of those two angles?
Answers
Answer:
Let's denote the measures of the other two angles by 13x and 16x, where x is a constant.
Since the sum of the angles in a triangle is always 180 degrees, we can write an equation:
35 + 13x + 16x = 180
Simplifying this equation, we get:
29x = 145
x = 5
Therefore, the measures of the other two angles are:
13x = 13(5) = 65 degrees
16x = 16(5) = 80 degrees
So, the measures of the other two angles are 65 degrees and 80 degrees.
Step-by-step explanation:
Rebecca buys some scarves that cost $5 each and 2 purses that cost $12 each. The cost of Rebecca’s total purchase is $39. What equation can be used to find n, the number of scarves that Rebecca buys?
1.5 + 24n = 39
2.5n + 24 = 39
3.(24 + 5) n = 39
4.24 + n = 39
Answers
The equation [tex]24 + n = 39[/tex] may be used to get n, the quantity of scarves Rebecca purchases.
What sort of equation would that be?The concept of an equation in algebra is a logical statement that demonstrates the equality of two mathematical equations. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
What does a basic equation mean?A formula that describes how contain a copy on either sides of a symbol are connected. It typically has an equal sign and one variable. The variable x is included in the preceding example.
The cost of one scarf is $[tex]5[/tex]
The cost of one purse is $[tex]12[/tex]
Rebecca buys 2 purses, so the cost of the purses is [tex]2*12=24[/tex]
The total cost of the purchase is $[tex]39[/tex]
[tex]Total cost = Cost of scarves + Cost of purses[/tex]
[tex]39 = 5n + 24[/tex]
Now we can solve n,
[tex]39 - 24 = 5n[/tex]
[tex]15 = 5n[/tex]
[tex]n = \frac{15}{5}[/tex]
[tex]n=3[/tex]
Therefore, Rebecca buys [tex]3[/tex] scarves.
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Which choices are equivalent to the expression below? Check all that apply.
√-16
A. -√16
B. i√16
C. -4
D. 4i
Answers
The answer fοr the imaginary expressiοn is 4i (οptiοn D)
What is imaginary expressiοn?Imaginary numbers are numbers that are nοt real. We knοw that the quadratic equatiοn is οf the fοrm ax² + bx + c= 0, where the discriminant is b²-4ac. In imaginary expressiοn οr number the discriminant becοmes negative οr less than 0.
Imaginary numbers are the numbers that give a negative number when squared. In οther wοrds, we can say that an imaginary number is basically the square rοοt οf a negative number which dοes nοt have a tangible value.
√-16
=√16i² [since i²= -1]
= 4i
Hence the value οf the imaginary number is 4i
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Answer: 4i and i√16
Step-by-step explanation: Just did it.
Help me i need some answer for it thank you very much
Answers
The evaluation of the statements and the values of the side lengths and angles of the quadrilateral are;
A. 1.) [tex]\overline{BD}[/tex] ≅ [tex]\overline{AC}[/tex]; False
2.) [tex]\overline{BO}[/tex] ⊥ [tex]\overline{CO}[/tex]; True
3. ∠BDA ≅ ∠BDC; False
4. ∠BOA ≅ ∠CBD; False
5.) m∠BAD + m∠ADC = 180°; True
6.) [tex]\overline{CO}[/tex] ≅ [tex]\overline{AO}[/tex]; True
7.) ∠BCD = 90°; False
8.) ∠BOA = 90°; True
9.) ∠ABD = 45°; False'
10. [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex]; True
B. I. ∠NAL = 124°
∠CNL = 28°
∠CLN = 28°
∠NLA = 28°
II. 5.) ∠1 = 45°
∠2 = 90°
III 7.) [tex]\overline{OP}[/tex] = 7 cm
8.) [tex]\overline{OE}[/tex] = 12 cm
9.) [tex]\overline{EO}[/tex] = 13 cm
10. ∠5 = 60°
What is a quadrilateral?A quadrilateral is a four sided polygon.
The evaluation of the quadrilaterals are presented as follows;
1. [tex]\overline{BD}[/tex] ≅ [tex]\overline{AC}[/tex]
[tex]\overline{BD}[/tex] and [tex]\overline{AC}[/tex] are the diagonals of the rhombus, and the properties of a rhombus indicates that the diagonals of a rhombus are not congruent, the statement, [tex]\overline{BD}[/tex] ≅ [tex]\overline{AC}[/tex] is therefore false
[tex]\overline{BD}[/tex] ≅ [tex]\overline{AC}[/tex]; False
2. [tex]\overline{BO}[/tex] ⊥ [tex]\overline{CO}[/tex]
[tex]\overline{BO}[/tex] and [tex]\overline{CO}[/tex] are segments on the two diagonals of the rhombus which are perpendicular. The statement, [tex]\overline{BO}[/tex] ⊥ [tex]\overline{CO}[/tex] is therefore; True
3. ∠BDA ≅ ∠BDC
∠ADC = ∠BDA + ∠BDC
The diagonals of a rhombus do not bisect the vertex angles, therefore;
m∠BDA ≠ m∠BDC
∠BDA [tex]\ncong[/tex] ∠BDC
The statement, ∠BDA ≅ ∠BDC, therefore is; False
4.) ∠BOA ≅ ∠CBD
The diagonals of a rhombus are perpendicular, therefore angle ∠BOA = 90°
∠CBD is an interior angle of the rhombus, and ∠CBD = 90° if the rhombus is a square.
The specified rhombus is not shaped like a square. The statement, ∠BOA ≅ ∠CBD, is therefore; False
5.) m∠BAD + m∠ADC = 180°
The angles, ∠BAD and ∠ADC are adjacent interior angles, therefore, according to the properties of a rhombus, m∠BAD + m∠ADC = 180°. The statement is therefore; True
6.) [tex]\overline{CO}[/tex] ≅ [tex]\overline{AO}[/tex]
The segments [tex]\overline{CO}[/tex] and [tex]\overline{AO}[/tex] are formed by the intersection of the diagonal [tex]\overline{BD}[/tex] and [tex]\overline{AC}[/tex] at O. The diagonals of a rhombus bisect each other. The statement, [tex]\overline{CO}[/tex] ≅ [tex]\overline{AO}[/tex] is therefore; True
7.) ∠BCD = 90°
∠BCD = 90° when the rhombus is a square, the statement is therefore False
8.) ∠BOA = 90°
∠BOA is formed by the intersection of the diagonals of a rhombus, which are perpendicular to each other. Therefore, ∠BOA = 90°, the statement is therefore; True
9) ∠ABO = 45°
∠ABO = 45° if the rhombus is a square, the statement is therefore; False or more information required
10) [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex]
[tex]\overline{BC}[/tex] and [tex]\overline{CD}[/tex] are side lengths of the rhombus and are therefore, congruent. The statement, [tex]\overline{BC}[/tex] ≅ [tex]\overline{CD}[/tex] is; True
B. I. ∠NAL and ∠CNA are supplementary, therefore;
∠NAL + ∠CNA = 180°
∠NAL= 180° - ∠CNA
∠CNA = 56°
∠NAL= 180° - 56° = 124°
2.) Whereby the diagonal of the rhombus bisects the angle ∠CNA, we get;
∠CNL = ∠ANL = 56°/2 = 28°
3.) ∠CLN = ∠CNL = 28°
4.) ∠NLA = ∠CNL = 28°
II. The properties of a square indicates that we get;
The diagonals of a square bisect the vertex angles, therefore;
∠1 which is the angle formed by the the diagonal [tex]\overline{AT}[/tex] that bisects the angle ∠CAR = 90° is; ∠1 = 90°/2 = 45°
6.) The diagonals of a square are perpendicular, therefore;
∠2 = 90°
III. 7.) The facing sides of a rectangle are congruent, therefore;
[tex]\overline{HE}[/tex] ≅ [tex]\overline{OP}[/tex]
[tex]\overline{OP}[/tex] = [tex]\overline{HE}[/tex] = 7 cm
8.) The diagonals of a square have the same length, therefore;
The length of [tex]\overline{OE}[/tex] = The length of [tex]\overline{HP}[/tex] = 12 cm
9.) Pythagorean Theorem indicates, that we get;
[tex]\overline{EO}[/tex] = √([tex]\overline{OP}[/tex]² + [tex]\overline{EP}[/tex]²)
Therefore; [tex]\overline{EO}[/tex] = √(5² + 12²) = 13
[tex]\overline{EO}[/tex] = 13 cm
10.) ∠2 and ∠5 are vertical angles, therefore;
∠2 ≅ ∠5
∠5 ≅ ∠2 (Symmetric property)
m∠5 = m∠2 = 60° (Definition of congruency)
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f(x)= 6x^{3} -\sqrt{2}x^{2} -10x-4\sqrt{2} and the zeros are 2 under the root find all other zeros
Answers
Therefore, the other two zeros of the function are approximately -1.802 and -0.198.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal in solving an equation is to find the value of the variable that makes the equation true. Equations are used extensively in mathematics and science to model real-world phenomena and solve problems.
by the question.
To find the zeros of the function, we need to solve the equation F(x) = 0. Since the given function has one known zero, which is 2 under the root, we can use this to simplify the expression.
Let's start by factoring out (x - 2^(1/2)) from the expression:
[tex]F(x) = (x - 2^(1/2))(6x^2 + 12x + 2^(1/2) - 4\sqrt{2})[/tex]
Now we need to find the zeros of the quadratic factor:
[tex]6x^2 + 12x + 2^(1/2) - 4\sqrt{2} = 0[/tex]
Using the quadratic formula, we get:
[tex]x = [-12±\sqrt((12)^2 - 4(6)(2^(1/2) - 4\sqrt{2}))]/(2(6))[/tex]
Simplifying the expression under the square root gives:
[tex]\sqrt((12)^2 - 4(6)(2^(1/2) - 4\sqrt{2})) = \sqrt(144 - 24\sqrt{2} - 96) = sqrt(48 - 24\sqrt{2})[/tex]
So, the zeros of the function are:
[tex]x = 2^(1/2), (-1 -\sqrt{6 + 3\sqrt{2}})/3, (-1 + \sqrt{6 + 3\sqrt{2}})/3[/tex]
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Which segment is perpendicular to DE?
C. DF
a. AB
d. EF
b. CF
Answers
The required perpendicular segment to DE is EF.
What is perpendicular?In simple geometry, two geometric objects are perpendicular if the intersection at the place of intersection known as a foot results in right angles. The perpendicular symbol can be used to graphically depict the condition of perpendicularity.
According to question:In the given diagram we can see that segment DE and EF.
So, we can say that,
Segment DE is perpendicular to segment EF.
Thus, required perpendicular segment to DE is EF.
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Complete question:
28 heart pancakes serve 20
people at the Valentine's Day
brunch. At this rate, how
many pancakes will you
probably need for a table of
5 people?
Answers
Answer:The answer is 7 pancakes, I think.
Step-by-step explanation:
28:20
?:5
Divide 28 by 20.
You get 1.4 because every person eats 1.4 .
Multiply 1.4 by 5. You give all of the five people 1.4 pancakes each.
The total will be 7 pancakes.
Many students from Europe come to the United States for their college education.
From 1980 through 1990, the number S(in thousands), of European students
attending a college or university in the U. S. Can be modeled by
S=0. 05(t3 - 11ť + 45t +277), where t = Ocorresponds to 1980.
In what year were there 31. 35 thousand European students attended a U. S. College
or university?
Answers
we can use the cubic equation formula to solve for t. The answer is t=1988, which means that there were 31.35 thousand European students in 1988.
To solve this problem, we need to find the value of t that corresponds to 31.35 thousand European students. We can use the given equation S=0.05(t3-11t+45t+277) and solve it for t. To do this, we can first subtract 277 from both sides to get S-277=0.05(t3-11t+45t). Then, we can divide both sides by 0.05 to get (S-277)/0.05=t3-11t+45t. Finally, we can use the cubic equation formula to solve for t. The answer is t=1988, which means that there were 31.35 thousand European students in 1988.
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What is the minimum number of rows of bricks needed to build a wall that is at least 4 feet tall if each brick is 2.25 inches tall?
Answers
Answer:
22 rows
Step-by-step explanation:
Divide 48 by 2.25 and round up
Alyssa is making a candle in the shape of a square pyramid. If the base edge is 5 inches and the height is 8 inches, how much wax will she need?
Answers
What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation? X^2+22x=8x-53
Answers
The intermediate step in the form (x+a)²=b as a result of completing the square is: (x + 7)² = -4. We can calculate it in the following manner.
To complete the square for the equation x² + 22x = 8x - 53, we need to move the constant term to the right side and the linear term to the left side, and then add a constant value to both sides so that the left side becomes a perfect square trinomial. The steps are as follows:
x² + 22x = 8x - 53 (original equation)
x² + 14x = -53 (subtract 8x from both sides)
x² + 14x + (14/2)² = -53 + (14/2)² (add (14/2)² to both sides)
x² + 14x + 49 = -53 + 49 (simplify)
(x + 7)² = -4 (factor the left side and simplify the right side)
So the intermediate step in the form (x+a)²=b as a result of completing the square is:
(x + 7)² = -4
Note that this equation has no real solutions, since the square of any real number is always nonnegative, whereas the right side of this equation is negative.
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