Answer:
You can represent "the opposite of Shana's temperature is equal to Pearl's" as follows:
(-20 C) + (-x) = x
Where x represents Pearl's temperature.
Alternatively, you can also write it as:
20 C - x = x
Both of these equations are equivalent and mean the same thing: the opposite of Shana's temperature is equal to Pearl's temperature.
Step-by-step explanation:
20 degrees Celsius
The temperature in Pennsylvania is the opposite of the temperature in Canada, therefore -20⁰ Celsius in Canada would then be 20⁰ Celsius in Pennsylvania.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Simplify the complex numbers using de Moivre's Theorem and match them with their solutions 2(3+1) 2. cos(20°) + sin(20°)] 2[ coo(4)+isin(7)]* (-1+i) -41 (1+1) -16 4+4731 Reset Next
The complex numbers are solved using De Moivre's Theorem and then are matched with their respective solutions.
What is De Moivre's Theorem?
De Moivre's formula, also known as the theorem and identity of de Moivre, says that for any real number x and integer n, holds -
(cos x + i sin x)^n=cos nx + i sin nx
where i is the imaginary unit (i^2 = 1).
Also, [r(cos x + i sin x)]^n = r^n(cos nx + i sin nx) or [r cis x]^n = [r^n cis nx].
The first complex number is (1+i)^5.
Solve using De Moivre's formula -
(1+i)^5 = [√2{(1/√2)+(i/√2)}^5]
=(√2)^5[cos(π/4)+i sin(π/4)]^5
=(√2)^5[cos(5π/4)+i sin(5π/4)]
=(√2)^5[(-1/√2)-(i/√2)]
=4(-1-i)
=-4-4i
The second complex number is (-1+i)^6.
Solve using De Moivre's formula -
(-1+i)^6=(1-i)^6
=[√2{(1/√2)-(i/√2)}^6]
=(√2)^6[cos(-π/4)+i sin(-π/4)]^6
=(√2)^6[cos(-6π/4)+i sin(-6π/4)]
=8(0+1i)
=8i
The third complex number is 2[cos(20)+i sin(20)]^3.
Solve using De Moivre's formula -
2[cos(20)+i sin(20)]^3=2^3[cos(60)+i sin(60)]
=8[(1/2)+{(√3)i/2}]
=4+4√3i
The last complex number is 2[cos(π/4)+i sin(π/4)]^4.
Solve using De Moivre's formula -
2[cos(π/4)+i sin(π/4)]^4=2^4[cos(4π/4)+i sin(4π/4)]
=16[cos(π)+i sin(π)]
=16(-1+i(0)]
=-16
Therefore, the complex numbers are solved using the theorem.
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Find the Values of x and y
The values of x and y could be 25 and 113
What are parallel lines ?
parallel lines can be stated as , they both are equi distant from each other and which never intersect.
From the given figure,
y+12 = 3x + 50
as both are parallel to each other.
y-3x = 38
and 5x = y + 12
as vertically opposites are always equal .
y = 3x + 38
y = 5x - 12
hence,
5x - 12 = 3x +38
2x = 50
x = 25
put x = 25 in y = 3x + 38
y = 3 * 25 + 38
y = 113
hence the values of x and y are 25 and 113 respectively.
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The area of the right triangle shown is 24 square feet.
Which equations can be used to find the lengths of the legs of the triangle? Select three options.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 100
The area of a right-angled triangle is represented by the expression
x(x + 2) = 24 having area 24 square feet.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the area of a right-angled triangle is (1/2)×base×height.
Given, The area of a triangle is 24 square feet whose height is 2 more than it's base.
Let, The base of the triangle be 'x', Therefore the measure of the height is (x + 2).
Therefore, The area of the triangle is,
(1/2)×x(x + 2) = 24.
x(x + 2) = 24.
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These are the numbers and I need the ratio
to thank you!
help me please it's due tomorrow !!!!!!!!!!
help please
ill get in trouble!!!!
Answer: 1:3
Step-by-step explanation:
I'd say 1:3 but I could be wrong
y<3x+12, y≥5x+7
The solution of the system of linear inequalities.
Answer: nswer ; x , we can find ; y with the first equation :.
1 answer
·
We know that y=5x−7 so we are just going to replace the y in the other equation : −3x−
Step-by-step explanation:
When a calcium atom forms an ion, it loses two electrons. what is the electrical charge of the calcium ion? responses −2 negative 2 −1 negative 1 1 1 2
When a calcium atom forms an ion, it loses two electrons. The electrical charge of the calcium ion is +2
What do you meant by electrical charge of a calcium ion?Calcium ions are net positive two charges. In calcium, when it has assumed its most stable state, the relationship between the quantity of protons (20) and the quantity of electrons (18) is represented by the +2 charge.
In the event that calcium (Z = 20) picks up two electrons, the resultant ion will have 18 electrons and 20 protons, giving it a charge of +2. (two more positive protons than negative electrons). It's a cation, this ion. Using the Ca2+ symbol, we can identify a calcium ion.
Atoms that lose electrons acquire a positive charge as there are fewer electrons left with negative charges to balance the positive charges of the protons in the nucleus. Positively charged ions are known as cations.
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The diagram shows two proportional right triangles.
What is the perimeter of the larger triangle?
The perimeter of the possible larger triangle with possible side lengths of 24, 32 and 40 is 96 units
What is the perimeter of a plane figure?The perimeter of a figure is the length of the boundary surrounding the figure.
Two triangles that have proportional dimensions are similar triangles
The dimensions (arranged in the order of corresponding sides) of the possible similar right triangles in the question, obtained from a related question, having two similar right triangles, posted online are;
First (larger) triangle side lengths; 24, 32, and xSecond (smaller) triangle side lengths; 9, 12, and 15The similarity of the triangles (proportional corresponding sides, indicates that we get;
[tex]\dfrac{24}{9} = \dfrac{32}{12} = \dfrac{x}{15}[/tex]
Therefore, by cross multiplication, we get;
32 × 15 = 12 × x
x = 32 × 15 ÷ 12 = 40
The perimeter of the larger triangle is; 24 + 32 + 40 = 96
The perimeter of the larger triangle is 96 units.Please find attached the possible diagram of proportional right triangles, created with MS Word, obtained from a question with regards to proportional right triangles online.
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what is 20% of 14000
Answer:
2800
Step-by-step explanation:
20% of 14,000 is 2800
Multiply both sides by 14,000, then divide the left side to get the result.
Answer:
2800
is what the calculator says
What is the dual of a ∧ b ∨ c ∧ d?
On interchanging the logical AND operator with logical OR operator and zeroes with ones,
(B'+C).A = (B'.C) + A
Now, According to the question:
Concept:
Duality theorem states that the dual of the Boolean function is obtained by interchanging the logical AND operator with logical OR operator and zeroes with ones. For every Boolean function, there will be a corresponding Dual function.
Calculation:
On interchanging the logical AND operator with logical OR operator and zeroes with ones,
(B'+C).A = (B'.C) + A
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The complete question is this:
Calculate the dual of the Boolean expression (B' + C).A
Given: quadrilateral MATH; M(-5,-2), A(-3,2),
T(3,2) and H(1,-2)
Prove: MATH is a parallelogram
State the formula you will be using.
Show all work.
Answer:
MATH is not a parallelogram
Step-by-step explanation:
(sqrt means squareroot)
To prove that quadrilateral MATH is a parallelogram, we can use the following formula:
A quadrilateral is a parallelogram if and only if both pairs of opposite sides are congruent.
In other words, if the lengths of the sides opposite each other in a quadrilateral are the same, then the quadrilateral is a parallelogram.
To prove that MATH is a parallelogram, we need to show that both pairs of opposite sides are congruent.
The first pair of opposite sides consists of segment MA and segment TH. To show that these sides are congruent, we can use the Distance Formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points that define the line segment.
Substituting the coordinates of points M and A, we get:
d = sqrt((-3 - (-5))^2 + (2 - (-2))^2)
= sqrt((-3 + 5)^2 + (2 + 2)^2)
= sqrt(8^2 + 4^2)
= sqrt(64 + 16)
= sqrt(80)
= 8.944
Substituting the coordinates of points T and H, we get:
d = sqrt((1 - 3)^2 + (-2 - 2)^2)
= sqrt((-2)^2 + (-4)^2)
= sqrt(4 + 16)
= sqrt(20)
= 4.472
Since 8.944 is not equal to 4.472, we cannot conclude that MA and TH are congruent. Therefore, MATH is not a parallelogram.
Two vehicles start from the same point traveling in the same direction. One vehicle travels 55.5 miles per hour (mph) and the other 45 ¼ mph. When will the two cars be 350 miles apart?
The number of hours after which the cars will be 350 miles apart is 34 hours.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Vehicle 1.
Speed = 55.5 mph
Distance(1) = 55.5 x Time
Vehicle 2.
Speed = 45(1/4) mph
Distance(2) = 45(1/4) x Time
The difference in the distance = 350 miles.
Distance(1) - Distance(2) = 350
55.5 x Time - 45(1/4) x Time = 350
55.5 x Time - (181/4) x Time = 350
(55.5 - 181/4) x Time = 350
Time = 350 / (55.5 - 45.25)
Time = 350 / 10.25
Time = 34 hours.
Thus,
The car will be 350 miles apart after 34 hours.
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The table shows the balances of two bank accounts for 3 months. In what month will the balance of account A be equal to the balance of account B?
As per Given data,
The month in which the balance of two bank accounts A is become equal to the balance of account B is 30thmonths,
How to find unknown values?Unknown variables are used to find the unknown values of the problem using the algebraic expressions.
Month Account A Account B
0 $ 100 $ 250
1 $ 125 $ 270
2 $ 150 $ 290
Clearly
The amount in account A is growing with $25 each month. Thus, the amount in this account in nth month is,
100+25[tex]n[/tex]
The amount in account B is just growing with $20. Thus, the amount in this account in nth month is,
250+20[tex]n[/tex]
x month
balances of two
account becomes equal,
then
100 + 25x =250 + 20x
25x - 20x = 250 - 100
5x = 150
x =30
Therefore, in 30th month balance of account A equal to balance of account B
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Q. The table shows the balances of two bank accounts for 3 months. In 30th month will the balance of account A be equal to the balance of account B?
Month Account A Account B
0 $100 $250
1 $125 $270
2 $150 $290
Pythagorean theorem and its converse
problem 3:
leg:16
leg:x
hypo:27
problem 4:
leg:12.8
leg:5.3
hypo:x
problem 5
18 <--------->
`20
x'
The missing measures, using the Pythagorean Theorem, are given as follows:
3. Leg x = 21.75.
4. Hypotenuse x = 13.85.
What is the Pythagorean Theorem?The Pythagorean Theorem states that length of the hypotenuse squared is equals to the sum of each of the sides of the triangle squared.
For item 3, we have that the leg x is missing, while another leg and the hypotenuse are given, meaning that the relation is of:
x² + 16² = 27²
Hence:
x² = 27² - 16²
[tex]x = \sqrt{27^2 - 16^2}[/tex]
x = 21.75.
For item 4, we are given two legs and want to find the hypotenuse, hence the relation is given as follows:
x² = 12.8² + 5.3²
[tex]x = \sqrt{12.8^2 + 5.3^2}[/tex]
x = 13.85.
As for item 5, there is not enough information to answer, but the procedure should be the same.
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What is the log2 function?
The log2 function is a mathematical function that returns the logarithm of a given number to the base 2.
It is used to calculate the power to which a number must be raised to get a particular result.
For example, the log2 of 16 is 4, since 2^4 = 16. It can also be expressed as log2 16 = 4. Log2 is used in many areas of mathematics, including number theory, probability theory, and calculus.
It is also used in computer science and engineering to solve complex problems. Furthermore, it is used in cryptography to calculate the key sizes of encryption algorithms. In general, it is an essential tool for solving mathematical and scientific problems.
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Can u please help ………….
Answer:
x = 17
Step-by-step explanation:
the midsegment of a triangle is half the length of the third side, that is
DE = [tex]\frac{1}{2}[/tex] × BC = [tex]\frac{1}{2}[/tex] × 34 = 17
so x = 17
Solve the following equation, and check your solution. Show all of your work.
-17+n/5=33
I’ve added my work attached :)
n = 250
A bag contain 27 ball. The ratio of red to blue to yellow ball i 6:1:2 find how many red, blue and yellow ball there are
On solving the provided question we can say that by linear equation number of, Red Balls = 6x 18; Blue Balls = 3; Yellow Balls = 6
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
A bag contains 27 balls
• The ratio of red to blue to yellow balls is 6:1:2
To Find : The number of red,blue and yellow balls present in the bag
Let us take the variable as 'x' to represent the number of balls in the bag
When we Put the values in a equation,
6X+X+2x = 27
9x = 27
x = 3
Hence the number of,
Red Balls = 6x 18
Blue Balls = 3
Yellow Balls = 6
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How do u work this out ?
Answer:
[tex]\frac{d}{c}[/tex]
Step-by-step explanation:
[tex]\frac{cxcxdxdxd}{cxcxcxdxd}[/tex] You can cross out 2 c's from the top and the bottom and 2 d's from the top and the bottom. It now looks like this
[tex]\frac{d}{c}[/tex]
What is the inverse of the logarithmic function f x log9x?
The inverse of the logarithmic function f x log9x is f-1(x)=9^x.
The inverse of a logarithmic function is the exponential function. To find the inverse of the logarithmic function f x log9x, we can use the following equation: f-1(x)=9^x. This equation states that the inverse of the logarithmic function f x log9x is the exponential function f-1(x)=9^x.
The inverse of the logarithmic function f x log9x is f-1(x)=9^x, which is the exponential function.This means that for any value of x, the inverse of the logarithmic function f x log9x is equal to 9 raised to the power of x. For example, if x=2, then the inverse of the logarithmic function f x log9x is 9^2, or 81. Similarly, if x=3, then the inverse of the logarithmic function f x log9x is 9^3, or 729. In general, the inverse of the logarithmic function f x log9x is 9 raised to the power of x, for any value of x.
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Answer: f –1(x) = 9x
Step-by-step explanation:
Part II:
13. Use the information in the table to answer the following:
A relation is Given below:
M
a) Identify the domain and the range for the given relation:
Domain:
X 0
1
- 1
0
y 0 -1 0 1
Range:
Formal Asso
Using the information in the table the domain is 4 and the range [-1,1]
Is it in the X or Y domain?The term "domain" refers to a group of potential input values, and the domain of a graph is made up of all the input values visible on the x-axis. The y-axis displays the range, which is a collection of possible output values.
How do you discover a table's domain and range?The domain is typically listed in the left column and the range is typically listed in the right column in a table like the one below. The domain and range of a relation or function, respectively, can be thought of as the input values (x) and the output values (y), respectively.
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i dont know how to do it
Answer:
x = 4
y = 28
Step-by-step explanation:
1) y = 7x
2) y = 2x + 20
substitute y = 7x into equation 2:
7x = 2x + 20 now you can solve for x:
7x - 2x = 20
5x = 20
x = 20/5 = 4
Plug x = 4 into either equation 1 or 2 to solve for y:
y = 7x = 7(4) = 28
Torrin rode his bike to school at 13. 5 km/h. He returned home using the same route at 10. 5 km/h. Torrin took a total of 36 min to ride to school and back. Express your answer to the nearest hundredth. A) how many minutes did torrin take to ride to school? B)how far is it from Torrins house to school?
To ride a bike to school Torrin takes 15.75 min to ride to school and 3.54 km is the distance from his house to school.
Let v₁ = 13.5 km/h the speed to school
v₂ = 10.5 km the speed returning home
t = the time of the ride to school in minutes
36 - t = the time of the ride from school in minutes
Since, distance = speed × time
⇒v₁ × t/60 = v₂ × (36 - t)/60
⇒13.5 × t/60 = 10.5 × (36 - t)/60
⇒t = 15.75 min
Now, the distance = v₁ × t/60 = 13.5 × 15.75/60 = 3.54 km.
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What is the discriminant? What is the type and number of solutions?
-8x² +4x-1=0
Answer:
x= 1/4 - 1/4 x= 1/4 + 1/4
Step-by-step explanation:
Answer:
Type: (+ ve)
Number of solutions: 2
Step-by-step explanation:
Discriminant:The discriminant of the quadratic formula is the section under the radical. It tells us whether there are two solutions, one solution, or no solutions.D = b² - 4acWe are given an equation (-8x² + 4x - 1 = 0)
Now, change the sign
-8x² + 4x - 1 = 0
8x² - 4x + 1 = 0
Here,
a = 8b = (-4)c = 1Now, discriminant
D = b² - 4ac
D = (8)² - (4)(8)(1)
D = 64 - 32
D = 32 > 0
Here, 32 is greater than 0 so, it has two solutions.
Extra Information:b² - 4ac > 0 ↬ (+ ve), 2 solutionsb² - 4ac = 0 ↬ (= 0), 1 solutionb² - 4ac < 0 ↬ (- ve), No solutionFor what value of k does the pair of linear equations 3x +5y 3 6x KY 8 do not have any solution?
The pair of linear equations 3x + 5y = 3 and 6x + ky = 8 does not have any solution for any value of k.
We can rewrite the equations as:
3x + 5y = 3
6x + ky = 8
To solve this system, we need to eliminate one of the variables. To do this, we can multiply the first equation by 2 and the second equation by -3. This will give us:
6x + 10y = 6
-18x - 3ky = -24
Now we can add the two equations together and get:
-12x - 3ky = -18
Since the coefficient of x is 0, this equation does not have any solution for any value of k.
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I NEED HELPPPPppppppp
Check the picture below.
What is the degree of the polynomial 2x² 5x²³ 7?
The degree of the polynomial [tex]2xA^2 5xA^2A^37[/tex] is 9
A polynomial's degree is the sum of the degrees of its monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer.
The degree of a polynomial is the highest or largest power of a variable in a polynomial equation. The degree denotes the polynomial with the maximum exponential power (ignoring the coefficients).
Consider the following polynomial expression with two variables: [tex]x^3 + 6x^2y^4 + 3y^2+5[/tex]
The polynomial has a degree of 6.
This is because the exponent values of x and y in the second term of the algebraic formula, [tex]6x^2y^4[/tex], are 2 and 4, respectively. We get 6 when we sum the exponent values. As a result, the multivariable polynomial expression has a degree of 6.
As per question, polynomial is: [tex]2xA^2 5xA^2A^37[/tex]
The total sum of power is: 1+2+1+2+3=9
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What is the horizontal asymptote * 1 point?
What is the coefficient of the variable in the expression 4 − 3x − 7 6 3 points?
The coefficient of the variable x in the expression 4a+3x +a is 3
Given that,
The expression is 4a+3x +a which can be simplified as 4a+3x +a
To find : The coefficient of the variable x in the expression
The coefficient of x in 4a+3x +a is 3
A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6
Coefficient is the number that is beside the variable in the equation.
As we can see that the term that is in multiplication with x is 3
Hence, the coefficient of x in the equation is 3
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Solve the system of inequalities by graphing.
y≤10x–3
y>
–
1
2
x+1
The correlation coefficient r between the size of a lake in square miles, x, and the yearly number of registered boaters, y, is 0.743. What percent of the variation in the number of yearly boaters can be explained by differences in lake sizes
Answer:
55.2049%
Step-by-step explanation:
R², the coefficient of determination, is the proportion of the variation in the dependent variable that is predictable from the independent variable.
In this case, if we square our correlation coefficent r=0.743, we get R²=0.552049, which means that 55.2049% of the variation in the number of yearly boaters can be explained by differences in lake sizes