Answer:
-2+i
Step-by-step explanation:
-7+4i represents (-7,4) and 3-2i represents (3,-2).
So, the midpoint is (-2,1), which represents -2+i.
Given that DRWH is a parallelogram, determine the values of x and y.
Answer:
the opposite sides of the parallelogram are equal.
so DR = HW mean : 2 y + 2 = 3 y - 9
3y - 2y = 9+2
y = 11
RW = y+4 = 11+4 = 15
DH = RW
so, 3 x + 6 = 15
3x = 15-6 = 9
x = 3
22. If 1 m,m/19 - 118°, and m/16 - 48°, calculate m/12.
0 0
103"
98
109⁰
110"
18
17
19 20
14
16
13
15
11
10
12
9
63
5
m
Answer: [tex]110^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle 20=62^{\circ}[/tex] (linear pair)
[tex]m\angle 11=70^{\circ}[/tex] (angle sum in a triangle)
[tex]m\angle 12=110^{\circ}[/tex] (linear pair)
solve using substitution:
4x- 2y = 6 and x + y = 6
solve using elimination:
4x- 2y = 6 and x + y = 6
Answer:
Step-by-step explanation:
Substitution is a method that rewrites one of the equations in terms of one variable, and substitutes that in the other equations.
We can easily rewrite x + y = 6 by subtracting y from both sides, giving us
[tex]x = -y+6[/tex]
By putting this equation in place of x in the first equation, we can solve for y:
[tex]4(-y+6)-2y=6[/tex]
[tex]-4y+24-2y=6[/tex] [Distributing 4 into the parentheses]
[tex]-6y+24=6[/tex] [Combining like terms]
[tex]-6y = -18[/tex] [Subtracting 24 from both sides]
[tex]y=3[/tex] [Dividing both sides by -6]
Since we solved for y, we can again substitute by putting it into the second equation.
[tex]x+3=6[/tex]
[tex]x=3[/tex] [Subtracting 3 from both sides]
The solution for this system of equations is (3,3).
Elimination is another method of solving systems of equations. In this method, we multiply one equation such that when both equations are combined, only one variable is left.
We can first multiply both sides of the second equation by 2.
[tex]2x+2y=12[/tex]
Now, let's add both equations to cancel out y.
[tex]4x-2y=6[/tex]
[tex]2x+2y=12[/tex]
[tex]6x=18[/tex]
Now, we can divide 6 from both sides to get the value of x.
[tex]\frac{6x}{6} = \frac{18}{6}[/tex]
[tex]x=3[/tex]
We can now substitute this value into one of the equations to get the value of y. Here, I used the second equation.
[tex]3+y=6[/tex]
[tex]y=3[/tex]
The solution to our system of equations is (3,3).
A man mows his 100 ft by 200 ft rectangular lawn in a spiral pattern starting from the outside edge. After a bit of hard work he stops for a water break, he is 40.5% done. How wide of a strip has he mowed around the outside edge
Based on the length and width of the rectangular lawn, and the percentage the man has mowed, the strip width would be 40.5 m.
what is the width of the strip mowed already?first, find the area of the lawn:
= 100 x 200
= 20,000 ft²
the area mowed is:
= 40.5% x 20,000
= 8,100 ft²
the width is therefore:
= 8,100 / 200
= 40.5 m
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How does the volume of a cylinder with a radius of 4 units and a height of 12 units compare to the volume of a rectangular prism with dimensions 8 units x 8 units x 6 units
Answer:
The volume of the cylinder is smaller than the rectangular prism.
Step-by-step explanation:
what is the product of the fraction below x/x-5 * 2x/x+4
Answer:
A
Step-by-step explanation:
[tex]\frac{x}{x-5}[/tex] × [tex]\frac{2x}{x+4}[/tex] ( no factors cancel on numerator/ denominator )
= [tex]\frac{x(2x)}{(x-5)(x+4)}[/tex]
= [tex]\frac{2x^2}{x^2-x-20}[/tex]
On a typical day, brianne uses her computer for 3 hours and her hair dryer for 10 minutes. what is the total cost of using both appliances for 6 days?
The total cost of using both appliances for 6 days is about 3000-4000 watt.
According to the statement
Brianne uses her computer for 3 hours
Brianne uses hair dryer for 10 minutes
Now we use the formula
C = wtc/1000
substitute the values in it
then
C = 600*6/1000
C = 3.6
and same for hair dryer
So, The total cost of using both appliances for 6 days is about 3000-4000 watt.
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A state license plate consists of three letters followed by three digits. If repetition is allowed, how many different license plates are possible
A state license plate consists of three letters followed by three digits. If repetition is allowed, the number of different ways in which license plates are possible is 17,576,000.
What is a permutation?An arrangement of items in a specific order is referred to as a permutation. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection.
Calculation for the permutation -
Three letters are followed by three digits on a state license plate.
26 letters from a to z and 10 numbers from 0 to 9 make up the alphabet.
The potential of arrangements is due to the license plate's composition of three letters and three numerals.
Total ways = 26×26×26×10×10×10
= 17,576,000
Therefore, the number of different ways in which license plates are possible is 17,576,000.
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9. shyam travelled 8 km 52 m by bus, 2 km 265 m by car. how much distance did he travel in all
Shyam travel total [tex]10km 317m[/tex] distance ,when he travelled [tex]8 km 52 m[/tex] by bus and [tex]2 km 265 m[/tex] by car .
How to find the total distance travel by Shyam ?
Shyam travelled distance by bus [tex]=8 km 52 m[/tex]
Shyam travelled distance by car [tex]=2 km 265 m[/tex]
Total distance travelled by shyam is
Total distance= distance travelled by car + distance travelled by bus
Total distance
[tex]=2 km 265 m+8 km 52 m\\=(2+8)km(265+52)m\\=10km317m[/tex]
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A sphere of radius 222 inches is cut by three planes passing through its center. This partitions the solid into 888 equal parts, one of which is shown above. The volume of each part is t\pitπt, pi cubic inches. What is the value of ttt?
The value of t based on the information about the sphere is 1.3π.
How to calculate the value?It should be noted that the volume of a sphere is 4/3πr³. In this case, it's divided into 8 equal parts.
Volume of each part = 1/8 × 4/3πr³
= 1/8 × 4/3 × π × 8
= 4/3π
= 1.3πin³
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The binomial 5x – 4 is a factor of 10x^2 – 23x + 12. What is the other factor?
Answer:
2x - 3
Step-by-step explanation:
10x²-23x+ 12 ÷ 5x-4
Answer:
2x - 3
Step-by-step explanation:
[tex](5x-4)(2x-3)=10x^{2} -23x+12[/tex]
Hope this helps
Solve each system by elimination
Answer:
system of equation by elimination
1 write both equation in standard form
2 make the coefficient of one variable opposites
3 add the questions relating from step to eliminate one variable
4 solve for the remaining variable
5 substitute the solution from step for into one of the original equation
Solve the system of equations using substitution. 6x=−6y−30−3x−3y=15
The system of equation have an infinite solution.
How to solve system of equation?6x = -6y - 30
-3x -3y = 15
Therefore, let's rearrange the system of equations.
6x + 6y = -30
-3x - 3y = 15
multiply equation(ii) by 2
6x + 6y = -30
-6x - 6y = 30
add the equations
0 = 0
Since 0 = 0 for any value of x, the system of equations has infinite solutions.
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Write the equation of the line that is parallel to the line y = -7/4x - 2 through the point (4,-2).
Answer:
y = - [tex]\frac{7}{4}[/tex] x + 5
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 )
y = - [tex]\frac{7}{4}[/tex] x - 2 ← is in slope- intercept form
with slope m = - [tex]\frac{7}{4}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{7}{4}[/tex] x + c ← is the partial equation
to find c substitute (4, - 2 ) into the partial equation
- 2 = - 7 + c ⇒ c = - 2 + 7 = 5
y = - [tex]\frac{7}{4}[/tex] x + 5 ← equation of line
The graphs below have the same shape. What is the equation of the red
graph?
Answer:
[tex]G(x) = x^{3} -1[/tex]
Step-by-step explanation:
The red graph is the blue graph translated 1 unit down, so the answer is A.
the force, F newtons (N) between two particles is inversely proportional to the square of the distance, d m, between them. When the particles are 2m apart,
the force between them is 10 N. Find
1- the force between the particles when they are 5m apart,
2- the distance between the particles when the force between them is 25 N.
The force is 1.6N and the distance between them is 1.3 meters
The force between themAn inverse variation from force to the square of distance is represented s:
k = Fd^2
Where k represents the variation constant
When F = 10, d = 2.
So, we have:
k = 10 * 2^2
k = 40
Substitute k = 40 in k = Fd^2
Fd^2 = 40
When d = 5, we have:
F * 5^2 = 40
This gives
25F = 40
Divide by 25
F = 1.6
Hence, the force is 1.6N
The distance between themIn (a), we have:
Fd^2 = 40
When F = 25, we have:
25 * d^2 = 40
This gives
25d^2 = 40
Divide by 25
d^2 = 1.6
Take the square root of both sides
d = 1.3
Hence, the distance between them is 1.3 meters
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What is the range of the following set of ordered pairs?
{(-1,7), (6,2), (0,4), (5,2), (-3,1)}
O a. {7,2,4,1}
b.
O c.
O d.
{-1,6, 0, 5, -3}
{-1, -3, 1, 7,6}
{2, 0, 4, 5)
Answer:
range of the given set is { 7,2,4,2,1}
Step-by-step explanation:
. Hello !
When the above kind of set is given the second values of each elements belongs to the range or the y whereas, the first values of the elements belongs to the domain or x.
Thus, domain = {-1,6,0,5,-3}range ={7,2,4,2,1}2. Un auto viaja a 60 km/h y se detiene a los 2 segundos. qué distancia recorrió en el
frenado? ¿qué aceleración adquirió? ¿Si la aceleración es positiva o negativa, explica
por qué?
Se calcula que la aceleración es - 8,35 m/s.
¿Qué es la aceleración?Ahora sabemos lo siguiente de la pregunta;
Velocidad inicial (u) = 60 km/h o 16,7 m/s
Tiempo empleado (t) = 2 s
Dado que;
v = tu + en
v = 0 m/s porque el carro se detenía
tu = -en
a = -(u/t)
a= -1(6,7 m/s/2 s)
a =- 8,35 m/s
La aceleración es negativa porque la velocidad disminuye con el tiempo.
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deeksha made cuboid of size 2 cm x 3 cm x 4 cm. how many such
cuboids will be required to make a cube?
b) in a right triangle pqr,
The number of cuboids of dimension 2 cm x 3 cm x 4 cm, required to make a cube is 9.
Dimensions of the cuboid Deeksha made are given as 2 cm x 3 cm x 4 cm.
Thus, the volume of this cuboid = 2*3*4 cm³ = 24 cm³.
Using the formula for the volume of cuboid as the product of the three sides.
Deeksha wants to make a cube combining some number of these cuboids.
Assuming the side length of the cube to a, the volume of the cube = a³.
Assuming the number of cuboids required to make 1 cube to be n, we can write that a³ = n*(24 cm³).
To make this relation true, we need the right-hand side to be a perfect cube.
Prime factorizing the volume of the cuboid, we get 24 cm³ = 2³ * 3 cm³.
To make it a perfect cube, we need to multiply 3², by it.
Thus, n = 3² = 9.
Thus, the number of cuboids of dimension 2 cm x 3 cm x 4 cm, required to make a cube is 9.
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The provided question is incorrect. The correct question is:
"Deeksha made cuboid of size 2 cm x 3 cm x 4 cm. how many such
cuboids will be required to make a cube?"
The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s in the $n^{\rm{th}}$ block. What is the sum of the first $1234$ terms of this sequence
Consider the lengths of consecutive 1-2 blocks.
block 1 - 1, 2 - length 2
block 2 - 1, 2, 2 - length 3
block 3 - 1, 2, 2, 2 - length 4
block 4 - 1, 2, 2, 2, 2 - length 5
and so on.
Recall the formula for the sum of consecutive positive integers,
[tex]\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2[/tex]
Now,
[tex]1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016[/tex]
which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.
In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of
[tex]\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224[/tex]
numbers, and their sum is
[tex]\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400[/tex]
This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of [tex]1+9\times2=19[/tex].
So, the sum of the first 1234 terms in the sequence is 2419.
Kim's softball team was playing in the championship game. When there were 444 innings left, the team was losing by a score of 171717 to 666 runs. In the last 444 innings, her team scored the same number of runs per inning, and the other team did not score any more runs. Kim's team won with the most runs.
Write an inequality to determine the number of runs per inning, ppp, Kim's team could have scored.
Find the minimum whole number of runs per inning Kim's team could have scored.
The inequality to determine the number of runs per inning, p Kim's team could have scored is; 4r + 6 > 17
How to write an Inequality?
Let r represent the number of runs per inning. Thus for 4 innings, we have 4r.
The team already has 6 runs. Now add the additional runs to this to get;
4r + 6
The team wants to score more than the other team, this means they need more than 17 and so the inequality required is;
4r + 6 > 17
Subtract 6 from each side to get;
4r + 6 - 6 > 17 - 6
4r > 11
Divide both sides by 4 to get:
r > 2.75
Approximating to a whole number gives;
r > 3
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Answer:
6+4p> 17
3
Step-by-step explanation:
Mike and hallie are going to a movie. together they bring $60 in cash. hallie brings three times as much cash as mike does. let m be the amount of money mike brings and let h be the amount of money hallie brings. create a system of equations that models the information given in this problem and solve it to determine how much each brought to the movie.
Mike brought $15 and Hallie brought $45 to the movie
There are many ways to define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
The value of the variable that makes the equation a true statement is the solution to the equation.
We have to find how much money Mike and Hallie brought to the movie.
Let the money Brought by Mike be $ m and by Hallie be $ h.
Mike and hallie are going to a movie. together they bring $60 in cash
m + h = $ 60.............(1)
Hallie brings three times as much cash as mike does
h = 3 m.......... (2)
Pur the value of h from equation (2) in equation (1)
m + 3 m = $ 60
4 m = $ 60
m = $ 60/4
m = $ 15
put this value of m in equation (2)
h = 3(15)
h = $ 45
Hence we created a system of equations that models the information given in this problem and Mike brought $15 and Hallie brought $45 to the movie
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11y^2-xy dxUse the method for solving homogeneous equations to solve the following differential equation.
The solution to the homogenous differential equation, (11y² - xy)dx + x²dy = 0, is [tex]y = \frac{x}{11 ln (x) + C}[/tex].
A homogeneous differential equation has a homogeneous function as one of its components, if f(λx, λy) = λⁿf(x, y), for any non-zero constant λ, the function is said to be homogenous. The homogeneous differential equation's generic form is of the type f(x, y).dy + g(x, y).dx = 0. The degree of the homogeneous differential equation is the same for the equation's variables x and y.
In the question, we are asked to solve the homogeneous differential equation, (11y² - xy)dx + x²dy = 0.
The given equation can be solved as follows:
Grouping by differentials, gives us: x²dy = (xy - 11y²)dx.We now substitute, u = yx, making y = ux, or, dy = u.dx + x.du.Making the substitutions, we get: x²(u.dx + x.du) = (u - 11u²)x²dx.Expanding the parentheses, we get: ux².dx + x³.du = ux².dx - 11u²x².dx.Reducing ux².dx, we get: x³.du = -11u²x².dx.Dividing by x³ and u², we get du/u² = -11/x.Now, we integrate both sides of the equation: [tex]\int \frac{1}{u^2}du = \int -\frac{11}{x}dx[/tex]Calculating the resulting integrals, we get: -1/u = C - 11 ln(x).Undoing the substitution, u = y/x, we get: -x/y = C - 11 ln(x)The final solution is: [tex]y = \frac{x}{11 ln (x) + C}[/tex]Thus, the solution to the homogenous differential equation, (11y² - xy)dx + x²dy = 0, is [tex]y = \frac{x}{11 ln (x) + C}[/tex].
The provided question is incomplete. The complete question is:
"Use the method for solving homogenous equations to solve the following differential equation.
(11y² - xy)dx + x²dy = 0".
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Find the missing side length of the triangle.
SOLUTION :
c² = 5² + 5²
c² = 25 + 25
c² = 50
c = √50 ft
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Find the domain and range of the exponential function h(x) = 125 x .
Explain your findings.
As x decreases, does h increase or decrease? Explain.
As x increases, does h increase or decrease? Explain.
The domain of the exponential function given is the set of all real numbers while the range of the exponential function is the set of all real numbers greater than zero.
What is the domain and range of the exponential function?As with other exponential functions, it follows that the domain of the exponential function given is the set of all real numbers while the range of the exponential function is the set of all real numbers greater than zero.
Additionally, by observation, the function has a positive variable correlation, hence;
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Identify the distance between points (- 3, 0, - 7) and (- 8, - 9, - 11) , and identify the midpoint of the segmen for which these are the endpoints . Round to the nearest tenth, if necessary
The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).
What is the distance between the two points and what is the midpoint of the line segment?
First, we find the vector between the two points by vector sum:
[tex]\vec r = (-8, -9, - 11) - (- 3, 0, -7)[/tex]
[tex]\vec r = (- 5, - 9, - 4)[/tex]
The distance between the two points is found by the following Pythagorean expression:
[tex]d = \sqrt{(-5)^{2}+(-9)^{2}+(-4)^{2}}[/tex]
d ≈ 11.1
And the midpoint is found by linear algebra:
[tex]\vec m = 0.5\cdot (-3, 0, -7) + 0.5 \cdot (-8, -9, - 11)[/tex]
[tex]\vec m = (- 1.5, 0, - 3.5) + (- 4, - 4.5, -5.5)[/tex]
[tex]\vec m = (- 5.5, - 4.5, - 9)[/tex]
The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).
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Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by where the measurements are in meters. What is the width of the cooling tower at the base of the structure
The width of the cooling tower is 36 meters.
What is a cooling tower?A cooling tower is a vent that is built for the purpose of releasing waste heat back to the atmosphere.
Now we can model the system using; x²/324 - (y² - 90)²/1600. Thus, the width can be obtained from;
2 × ✓324
= 2 × 18
= 36 meters
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Missing parts;
Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus quantity y minus 90 end quantity squared over 1600 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
36 meters
48 meters
80 meters
89 meters
8.
P₁V₁ = P₂V₂
T₁ T₂
Rewrite this expression to find T₂.
Answer:
[tex]T_{2} = \frac{P_{2} V_{2} T_{1}} {P_{1} V_{1}}[/tex]
Step-by-step explanation:
The Combined Gas Law expression is:
P₁V₁ / T₁ = P₂V₂ / T₂
To solve for T₂, you need to.....
[tex]\frac{P_{1} V_{1} }{T_{1} } = \frac{P_{2} V_{2} }{T_{2} }[/tex] <------ Original expression
[tex]\frac{T_{2} P_{1} V_{1} }{T_{1} } = {P_{2} V_{2} }[/tex] <----- Multiply both sides by T₂
[tex]{T_{2} P_{1} V_{1} } = {P_{2} V_{2} T_{1}}[/tex] <----- Multiply both sides by T₁
[tex]T_{2} = \frac{P_{2} V_{2} T_{1}} {P_{1} V_{1}}[/tex] <----- Divide both sides by P₁V₁
the vertices of abc are a (-6,-7) b(-3,-10) and c(-5,2) find the vertices of abc given the transition rule (x,y)-->(x,y-3)
The vertices of abc given the transition rule (x,y)-->(x,y-3) are (-6, -10), (-3, -13) and (-5, -1)
How to determine the new vertices?The vertices are given as:
a (-6,-7)
b(-3,-10)
c(-5,2)
The transition rule is given as
(x,y)-->(x,y-3)
So, we have
a' = (-6, -7 - 3)
a' = (-6, -10)
b' = (-3, -10 - 3)
b' = (-3, -13)
c' = (-5, 2 - 3)
c' = (-5, -1)
Hence, the vertices of abc given the transition rule (x,y)-->(x,y-3) are (-6, -10), (-3, -13) and (-5, -1)
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CALLING ALL EXPERTS PLS ILL GIVE BRAINLIEST
On Monday, Gian spent 5 minutes watching videos. On Tuesday, he spent 25 minutes watching videos. Place points on the graph to show Gian's activity for Monday and Tuesday.