Answer:
See below
Step-by-step explanation:
3 / (6i) = 3 / (6 * sqrt(-1) )
To rationalize the denominator , multiply both top and bottom of the fraction by ( 6i)
= 18i / ( 6i * 6i) = 18i / (36 i^2 ) = 18 i / (-36 ) = - i/2
3x+y-77=0
Can anyone help me with this question it would really help me out
the answer is in the photo I took of solving it
If Susie's age is 8 less than 3 times her brother's age, and Susie is 13. How old is her brother?
Answer:
correct me if im wrong but my answer is x=7, or in other words, 7.
Step-by-step explanation:
Answer:
7 years old
Step-by-step explanation:
You would start by going backward. If 13 is 8 less, then you would first add 8. You would have 21. Now all you have to do is divide by three. So your answer would be 7. If you would want to check you could plug it back in. 7 multiplied by 3 is 21. 21 - 8=13
The Answer, 7 years old
a road running north to south crosses a road going east to west at the point pp. cyclist aa is riding north along the first road, and cyclist bb is riding east along the second road. at a particular time, cyclist aa is 3939 hundred meters to the north of pp and traveling at 3232 meters per second, while cyclist bb is 5252 hundred meters to the east of pp and traveling at 2424 meters per second. how fast is the distance between the two cyclists changing? the distance between the two cyclists is increasing by 1925 meters per second.
The distance between the two cyclists changing exists 38.4 meters per second.
What is meant by differential equation?A differential equation in mathematics exists an equation that links the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.
A differential equation in mathematics is an equation that includes one or more functions and their derivatives. The rate of change of a function at a place is determined by the derivatives of the function. It is mostly employed in disciplines like physics, engineering, biology, and others.
There exists at least a couple of ways to work this. One exists to write the equation for the distance between the cyclists and differentiate it.
d² = (3900 + 32t)² + (5200 + 24t)²
simplifying the above equation, we get
(2d)d/dt = 2(3900 + 32t)(32) +2(5200 + 24t)(24)
At t = 0,
dd/dt = (32·3900 + 24·5200)/√(3900² + 5200²)
simplifying the above equation, we get
= (124800 + 124800)/√(15210000 + 27040000)
= 249600/6500 = 38.4 meters per second
Therefore, the distance between the two cyclists changing exists 38.4 meters per second.
The complete question is:
A road running north to south crosses a road going east to west at the point P. Cyclist A is riding north along the first road, and cyclist B is riding east along the second road. At a particular time, cyclist A is 39 hundred meters to the north of P and traveling at 32 meters per second, while cyclist B is 52 hundred meters to the east of P and traveling at 24 meters per second. How fast is the distance between the two cyclists changing?
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What percentage of the numbers from 1 to 20 contain the digit 2?
Write the equation of the line that is perpendicular to the line y=3x+5 and passes through point (9,5)
The equation of the required perpendicular line is x + 3y = 24.
What is the slope relation for two perpendicular lines?
For two perpendicular lines on a plane, the product of their slopes always equals (-1).
What is the equation of line with slope 'm' and passing through the point (x₁, y₁)?
The standard equation of the line with slope 'm' and passing through the point (x₁, y₁) is y - y₁ = m(x - x₁).
Given, the required line is perpendicular to line given by y = 3x + 5 with slope, m₁ as 3, on analysis with standard equation of line; also the line passes through the point (9, 5) i.e. (x₁, y₁).
Let the slope of the required line be = m₂
As per statement established in the literature above, we have:
Slope of two perpendicular lines = -1
∴m₁ × m₂ = -1 ⇒ 3m₂ = -1 ⇒ m₂ = (-1)/3
Again, equation of the required perpendicular line is:
y - 5 = [(-1)/3][x - 9] ⇒ 3y - 15 = 9 - x ⇒ x + 3y = 24
Thus, the equation of the required perpendicular line is x + 3y = 24.
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An aquarium has dimensions 2x feet, (x â€" 1) feet, and (x 2) feet. The aquarium volume must be no more than 280 cubic feet. What are the possible values of x? (1, 5) (1, 5] [1, 5) [1, 5]
The possible values of x that satisfies the given dimensions and the condition that the volume must be no more than 280 cubic feet is x = [1,5]
The dimensions of the aquarium is: 2x ft , (x -1) ft, and (x + 2) ft. Since the volume must be no more than 280 ft³, it means:
V = 2x (x - 1) (x + 2) ≤ 280
Divide both sides by 2:
x (x - 1) (x + 2) ≤ 140
x³ + x² - 2x - 140 ≤ 0
(x - 5) (x² + 6x + 28) ≤ 0
Since x² + 6x + 28 is always greater than zero then x that satisfies the above inequality is:
x - 5 ≤ 0
or x ≤ 5
Using the interval notation, x = (-∞, 5]
However, remember that the dimension is always a positive number.
Hence,
x - 1 ≥ 0
or x ≥ 1
Therefore, the solution is [1, 5]
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dentify ALL pairs of parallel and perpendicular lines in the image below.
Step 1: redraw the figure given
Step 2: State the relationship between the lines
It can be observed that
(i) line XY is perpendicular to line PS
[tex]\text{line XY}\perp line\text{ PS}[/tex](ii) line XY is perpendicular to line QT
[tex]\text{line XY}\perp lineQT[/tex](iii) line PS is parallel to line QT
[tex]\text{line PS}\parallel lineQT[/tex]Hence, XY⊥PS, XY ⊥ QT, PS ║ QT, The Second option.
I need help with math identify the vertex of the parabola
The vertex of a parabola is the extreme point (maximum or minimum, depending on the the sign of the quadratic coefficient).
In the graph, we can see that the x-coordinate of the vertex is x=-1 and the y-coordinate is y=3.
Then, we can write the coordinates of the vertex as (h,k) = (-1,3)
Answer: The coordinates of the vertex are (-1,3)
PLS BE DONE RIGHT AWAY, VERY APPRECIATED
this is NOT a test or Quiz its a homework pic is below
From the information given,
Jack wants to eat 2 1/5 of his plate in 1/3 hour. The first step is to convert 2 1/5 to improper fraction. It becomes 11/5
The statement would be
Jack wants to eat 11/5 of his plate in 1/3 hour.
Let x represent how much of his plate that he will eat in 1 hour. Therefore
11/5 = 1/3
x = 1
By cross multiplying, it becomes
x * 1/3 = 1 * 11/5
x/3 = 11/5
x = 11/5 * 3
x = 33/5
Converting to mixed fraction, it becomes
6 3/5
The correct option is the first one
Finding Slope
Help mee
Answer: The slope is [tex]\frac{2}{3}[/tex].
Step-by-step explanation:
[tex]Slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} } =\frac{-8-(-6)}{-2-1} =\frac{-2}{-3} =\frac{2}{3}[/tex]
63 ÷ 5 = 12 R3 solve the problem
Answer:
12r^3
Step-by-step explanation:
si cada 8.33 minutos me dan 10 dolares cuantos dolares tendria en 6 horas ademas cuantos dolares ganaria cada 30 minutos
The payment for each 6 h is equal to $ 432.2 while the payment for each 30 min would be $ 36.01.
Rule of ThreeIt's a math tool for solving problems about proportion. You can relate more than 2 variables and from the proportion, it's possible to find an unknown number.
Conversion Unit TimeIn the International System Units (SI), the standard unit for time is the second (s). For solving any exercise, you need to know the relation between the units of the time. See below:
1h=60 min = 3600s
1 min = 60 s
Now you can solve the question from the rule of three for finding the payment in dollars.
The question gives: an each 8.33 min, the payment is 10 dollars. Thus, from this relation you can write:
For 6 hFirst, you should convert 6h to minutes, then,
1 h ----- 60 min
6h ----- x
x=60*6=360 min
After that, you should apply the rule of three for finding the payment in dollars.
8.33 min ----- 10 dollars.
360 min ------- x
8.33x=360*10
8.33x=3600
x= $ 432.2
For 30minYou should apply the rule of three for finding the payment in dollars.
8.33 min ----- 10 dollars.
30 min ------- x
8.33x=30*10
8.33x=300
x= $ 36.01
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Consider the following trapezoid.
Find the value of X.
(Helpful for math-space users)
Answer; y = 108
Explanation;
x + 72 = 180
X=180-72
The value that represents the variable x in the trapezoid is 108 degrees
How to determine the value of x?From the question, the trapezoid represents the given parameter
We can see that the trapezoid is an isosceles triangle
This means that the angle x and y are congruent
The sum of angles is a trapezoid is 360 degrees
So, we have the following summation equation
x + x + 72+ 72 = 360
Evaluate the like terms
So, we have
2x + 144= 360
This gives
2x = 216
Divide by 2
x = 108
Hence, the value of x is 108 degrees
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The largest y-value of the function is called thefunction.value of the
As the y-values of a function are the values that the function takes, the largest y-value of a function is called the maximum value of the function
Answer: maximumX=
/////////////////////
Answer: [tex]x=15[/tex]
Step-by-step explanation:
By the consecutive interior angles theorem,
[tex]150+3x-15=180\\\\3x-15=30\\\\3x=45\\\\x=15[/tex]
Match each ratio to an equal ratio. Drag the items on the left to the correct location on the right.
Answer:
30
Step-by-step explanation:
it doesn't seem to be correct question
x=3
Suppose we are buying beans and rice to feed a large gathering of people, and we plan to spend $120 on the two ingredients. Beans cost $2 a pound and rice costs $0.50 a pound.
If x represents pounds of beans and y pounds of rice, the equation 22 + 0.50y = 120 can represent the constraints in this situation.
The line below shows the graph of this equation (ignore the points not on the line).
Please help me I would appreciate it so much
The true statements about the constraints in this situation are:
If we buy 30 pounds of beans we can buy with 120 pounds of rice.If we buy no beans we can buy 240 pounds of rice.If we buy 20 more pounds of rice, we would have to buy 5 less pounds of beans.How to determine the true statements?In order to determine the true statements, we would substitute the value of x and y into the given linear equation and then evaluate. From the information provided, the constraints in this situation are modeled or represented by this linear equation:
2x + 0.50y = 120
Where:
x represents pounds of beans.y represents pounds of rice.When x = 40 and y = 60, we have:
2x + 0.50y = 120
2(40) + 0.50(60) = 120
80 + 30 = 120
110 ≠ 120 (Not a solution).
When x = 30 and y = 120, we have:
2x + 0.50y = 120
2(30) + 0.50(120) = 120
60 + 60 = 120
120 = 120 (True solution).
Therefore, if we buy 30 pounds of beans we can buy with 120 pounds of rice.
When x = 0 and y = 240, we have:
2x + 0.50y = 120
2(0) + 0.50(240) = 120
0 + 120 = 120
120 = 120 (True solution).
Therefore, if we buy no beans we can buy 240 pounds of rice.
When x = 0 - 5 and y = 240 + 20, we have:
2x + 0.50y = 120
2(0 - 5) + 0.50(240 + 20) = 120
-10 + 130 = 120
120 = 120 (True solution).
Therefore, if we buy 20 more pounds of rice, we would have to buy 5 less pounds of beans.
When x = 0 + 10 and y = 240 - 60, we have:
2x + 0.50y = 120
2(0 + 10) + 0.50(240 - 60) = 120
20 + 90 = 120
110 = 120 (Not a solution).
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Please help me I only have 3 minutes left to do this
486lb of grass seed is required to cover the field on the right.
What is Area of Rectangle?The area of Rectangle is length times of width
Let us find the areas of two rectangle larger and smaller.
Area of the larger rectangle:
60×90=5400 square feet.
Now divide the larger square area by the smaller square area:
Area of the smaller rectangle
40×50=200 square feet.
Now divide larger rectangle with smaller
5400/200 =27
27 is the ratio of the difference
27×18=486 lb.
Hence 486lb of grass seed is required to cover the field on the right.
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Subtract.
−3−6−(−1) = ?
Answer:
-8
Step-by-step explanation:
Can someone tell me what x and y is and how to solve for it
[tex]2x = 76[/tex]
Due to alternate angles
[tex] \frac{2x}{2} = \frac{76}{2} \\ x = 38[/tex]
40°+(y-8)°+76°=180°(sum of angles in a triangle)
[tex]40 + y - 8 + 76 = 180 \\ y + 108 = 180 \\ y = 180 - 108 \\ y = 72[/tex]
ATTACHED IS THE SOLUTION.
Answer:
x = 38 ; y = 72
Step-by-step explanation:
180 = 76 + 40 + (y - 8)
180 = 108 + y
72 = y
The triangle has parallel lines, so the uppermost right angle is also 90 degrees.
90 - 76 = 14
180 = 90 + 14 + 2x
180 = 104 + 2x
76 = 2x
38 = x
This question has two parts. First, answer Part A. Then, answer Part B.
part A:
The length of the incline of the ramp will be [h] = 12.0415 ft
What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically, we can write -
h² = p² + b²
Given is the installation of wheelchair ramp such that the ramp should have a base of 12 ft and height of 1 ft long.
From the data given, we can consider the ramp construction as right angled triangle. We can write -
base [b] = 12 ft
height [p] = 1 ft
Using the Pythagoras theorem -
h² = (12 x 12) + (1 x 1)
h² = 144 + 1
h = √145
h = 12.0415
Therefore, the length of the incline of the ramp will be [h] = 12.0415 ft
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suppose the number of hours of sleep students get per night has a unimodal and symmetric distribution with a mean of 7 hours and a standard deviation of 1.5 hours. approximately what percent of students sleep more than 8.5 hours per night?
Approximately 34% of people sleep more than 8.5 hours per night.
According to the Empirical Rule states for a normally distributed random variable: 68% of the measures are within 1 standard deviation of the mean, 95% of the measures are within 2 standard deviations of the mean and 99.7% of the measures are within 3 standard deviations of the mean. According to the question, Mean = 7 and Standard deviation = 1.5. Also, in the question the normal distribution is symmetric, which means that 50% of the measures are below the mean and the rest 50% are above the mean. Now, the mean is 7 and 8.5 is 1 one standard deviation above the mean. So, by the Empirical Rule, of the 50% of the measures that are above the mean, 68% are within 1 standard deviation of the mean (more than 8.5 hours). So, we get
0.5*0.68 = 0.34 which is equal to 34%.
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Could I please get help with this this problem, and find out their answers?
The image of triangles are given .
a.
[tex]\angle J\cong\angle E,\angle K\cong\angle G,\angle L\cong\angle F[/tex]b. Find the ratio,
[tex]\frac{EG}{JK}=\frac{15}{10}=\frac{3}{2}[/tex][tex]\frac{GF}{KL}=\frac{24}{16}=\frac{6}{4}=\frac{3}{2}[/tex][tex]\frac{EF}{GL}=\frac{21}{14}=\frac{3}{2}[/tex]c.Hence the triangles are similar .
[tex]\Delta\text{JKL}\cong\Delta\text{EGF}[/tex]The correct option is A.
Jim sits on a seesaw. If Jim weighs 100 pounds, what mass in kilograms does the person on the other side need to be for the seesaw to be balanced?
The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:
[tex]1\text{ lb=}0.45\text{ kg}[/tex]Then to find the mass we just multiply the weight in pounds by 0.45:
[tex]100\cdot0.45=45[/tex]Therefore the other person has a mass of 45 kg.
The weight of the other person has to be the same in order for the seesaw to be balanced, then the person on the other side weighs 100 pounds as well. Now, we know that:
[tex]1\text{ lb=}0.45\text{ kg}[/tex]Then to find the mass we just multiply the weight in pounds by 0.45:
[tex]100\cdot0.45=45[/tex]Therefore the other person has a mass of 45 kg.
WILL GIVE BRAINLIEST!!! solve the problem fill in the blanks to show your work
By performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The four mathematical operations are functions that take input values, or numbers, and turn them into output values, or yet another number. They are multiplication, division, addition, and subtraction.So, the values in the blank will be:
= - 1.2(2/5) ÷ -2= -1.2(0.4) ÷ -2= - 0.48 ÷ -2= 0.24Therefore, by performing mathematical operations, the answer to the given expression (- 1.2(2/5) ÷ -2) is 0.24.
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The perimeter of a rectangle is to be between 140 and 220 inches. FindThe range of values for its length when its width is 20 inches
The lower value of the perimeter is 140 inches .
Width of the rectangle is 20 inches .
The length of the rectangle is calculated as ,
[tex]\begin{gathered} \text{Perimeter = 2 ( Length + width )} \\ 140=\text{ 2 ( Length + }20\text{ )} \end{gathered}[/tex]Rearranging the terms ,
[tex]\begin{gathered} \text{Length + 20 = }\frac{140}{2} \\ \text{Length + 20 = 70} \\ \text{Length = 50 inches} \end{gathered}[/tex]The higher value of perimeter is 220 inches .
Width of the rectangle is 20 inches .
The length is calculated as,
[tex]\begin{gathered} \text{Perimeter = 2 ( Length + width )} \\ 220=\text{ 2 ( Length + }20\text{ )} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{Length + 20 = 110} \\ \text{Length = 110 - 20} \\ \text{Length = 90 inches} \end{gathered}[/tex]Thus the range of values for the length of the given rectangle are 50 and 90 .
Mike had 28 books. His brother Joseph decided to give one third of his books to Mike. After that, Joseph and Mike had the exact same number of books. How many books did they have altogether?
SOLUTION
Given the question in the question tab, the following are the solution step to get the number of books they have altogether.
Step 1: Write the notations for Joseph's and Mike's books
[tex]\begin{gathered} \text{let j represents the number of books Joseph has,} \\ \text{let m represents the number of books Mike has} \end{gathered}[/tex]Step 2: Write the statements in a mathematical form
[tex]\begin{gathered} m=28---\text{statement 1} \\ \frac{1}{3}of\text{ j was given to Mike to have }m+\frac{j}{3}=28+\frac{j}{3} \\ \text{After that, }28+\frac{j}{3}=\frac{2j}{3} \end{gathered}[/tex]Step 3: Solve to get the value of j by using substitution method
[tex]\begin{gathered} \\ m=28+\frac{j}{3} \\ 28+\frac{j}{3}=\frac{2j}{3} \\ \text{ multiply through by 3} \\ 84+j=2j \\ 84=2j-j \\ 84=j \\ j=84 \end{gathered}[/tex]Therefore, Joseph had 84 books initially.
Step 4: Get the number of books they had altogether by summing the number of books for the each of them initially
[tex]\begin{gathered} m=28,j=84 \\ \text{Total}=28+84=112 \end{gathered}[/tex]Hence, they both had 112 books altogether.
Two planes just recently left the airport. Looking at the radar, Plane 1 is 50 miles away from the airport and Plane 2 is 200 miles away from the airport. If the 2 planes are 175 miles away from each other, what is the angle measurement from the airport to the 2 planes? (round to the nearest whole number)
To solve this problem, we need to use the Law of Cosines. The law states that given any triangle ABC:
Then;
[tex]c^2=a^2+b^2-2ab\cos(C)[/tex]Since we want to find the measure of angle x, we can use:
c = 175 mi
a = 200 mi
b = 50 mi
C = x
Now, by the Law of Cosines:
[tex]175^2=200^2+50^2-2\cdot200\cdot50\cdot\cos(x)[/tex]And solve:
[tex]30625=40000+2500-20000\cos(x)[/tex][tex]30625-40000-2500=-20000\cos(x)[/tex][tex]\frac{-11875}{-20000}=\cos(x)[/tex][tex]\begin{gathered} x=\cos^{-1}(0.59375) \\ . \\ x\approx53.5764 \end{gathered}[/tex]To the nearest whole number, x = 54°
Simplify the expression.
2/5y−4+7−9/10y =
Answer:
[tex]\frac{1}{2}[/tex] y +3
Step-by-step explanation:
You want to combine like terms
[tex]\frac{2}{5}[/tex] y and [tex]\frac{-9}{10}[/tex] y are like terms because they both have a variable y
-4 and + 7 are like terms because they are both constants. (numbers without letters)
We combine these
[tex]\frac{4}{10}[/tex] means the same as [tex]\frac{2}{5}[/tex] I just multiplied the numerator (top) and the denominator (bottom) by 2. I did this so that I could add it to [tex]\frac{-9}{10}[/tex]
[tex]\frac{4}{10}[/tex]y - [tex]\frac{9}{10}[/tex]y = [tex]\frac{-5}{10}[/tex] y (4-9 = -5) or [tex]\frac{-1}{2}[/tex] y simplified
-4 + 7 = 3