Answer:
The midpoint between 1 + 9i and 5 - 3i is 3 + 3iGivenPoints 1 + 9i and 5 - 3iTo find Midpoint between given pointsSolution
Midpoint is the average of the two points. Find it as follows:
(1 + 9i + 5 - 3i)/2 = (6 + 6i)/2 = 3 + 3i3x squared + 6 x cube - 9x squared y when factorused
[tex]3x ^{2} \: + \: {6x}^{3} \: - \: 9 {x}^{2} y[/tex]
Factor the expression with the common factor that is "3x²".[tex] \boxed{ \bold{3 {x}^{2} \: \times \: (1 \: + \: 2x \: - \: 3y)}}[/tex]
MissSpanishAnswer:
[tex]\boxed{3x²(1 + 2x - 3y)}[/tex]
Step-by-step explanation:
3x squared + 6 x cube - 9x squared y
To factor
Solution:
A process when algebraic expression is expressed as a product of two or more expressions is factorisation.
ATP,
Square = a²
Cube = a³
3x² + 6x³ - 9x²yWe can see that 3x^2 is common in this expression.
So rewrite as:
[tex]3x²(1 + 2x - 3y)[/tex]Done!
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Which equation could represent each graphed polynomial function?
y = 14 - 5x² + 4
y = x³ + 27
y = x(x + 3)(x - 2)
y = (x + 1)(x − 3)(x² + 1)
y = x⁴- 5x² + 4 represents the first graph.
y = x(x + 3)(x - 2) represents the second graph.
How to Interpret the graph of a Polynomial?
1) The first polynomial is;
y = x⁴- 5x² + 4
Simplifying this gives us;
y = x⁴- 4x² - x² + 4
y = x²(x² - 4) - 1(x²- 4)
y = (x² - 1)(x² - 4)
y = (x - 1)(x + 1)(x - 2)(x + 2)
Thus, the zeros of this polynomial are; x = -2, -1, 1, 2
From the given graphs attached, first graph has the zeros (x-intercepts) as x = -2, -1, 1, 2.
So graph (1) represents the polynomial y = x⁴- 5x² + 4
2). The second graph shows the x-intercepts at x = -3, 0, 2
Since, y = x(x + 3)(x - 2) is the polynomial with x-intercepts at x = -3, 0, 2
Therefore, y = x(x + 3)(x - 2) represents the second graph.
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True or false: The graph of y=3x2-3 opens up.
Answer: True: The graph of y=3x²-3 opens up
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (0,−3)(0,-3)
Focus: (0,−35/12)
Axis of Symmetry: x=0
Directrix: y=−37/12
X={-2, -1, 0, 1, 2}
Y={9, 0, -3, 0, 9
Step-by-step explanation:
Shreya and Shanice are selling pies for a
school fundraiser. Customers can buy
blueberry pies and lemon meringue pies.
Shreya sold 4 blueberry pies and 2 lemon
meringue pies for a total of $76. Shanice
sold 4 blueberry pies and 13 lemon
meringue pies for a total of $230. What is
the cost each of one blueberry pie and
one lemon meringue pie?
Answer:
$26
Step-by-step explanation:
Let blueberry pies = x and lemon pies = y.
4x + 13y = 230
4x + 2y = 76
Using elimination, we see that 11y = 154. Therefore, y = 14.
4x + 2(14) = 76
4x + 28 = 76
4x = 48
x = 12
x + y = 12 + 14 = 26.
$26 is your answer.
Answer:
Step-by-step explanation:
Let B be the price of a blueberry pie. Let L be the price of a lemon meringue pie.
We are told that Shreya makes a total of $76 by selling 4 blueberry and 2 lemon meringue pies. This can be made into an equation:
Shreya: 4B + 2L = $76
We also learn that Shanice is doing particularly well:
Shanice: 4B + 13L = $320
We want to determine the prices for each type of pie, B and L. We have two equations and two unknowns. That means we should be able to find the answers by substitution.
Rearrange Shreya's equation to isolate B:
Shreya: 4B + 2L = $76
4B = $76 - 2L
B = ($76-2L)/4
Now use this definition of B in Shanice's equation:
Shanice: 4B + 13L = $320
4( ($76-2L)/4) + 13L = $320
($76-2L) + 13L = $320
11L = 244
L = $22.18
Use L = $22.18 in either equation and solve for B:
4B + 2L = $76
4B + 2*($22.18) = $76
4B = $31.64
B = $7.91
---
Blueberry pies are $7.91 each.
Lemon meringue pies are $22.18 each
=========
CHECK: Do these prices provide the correct sales for each person?
Price($/pie) Shreya Shanice
Blueberry 7.91 4 4
Lemon Mer. 22.18 2 13
Blueberry Sales ($) 31.64 31.64
Lemon Mer. Sales ($) 44.3 288.36
Total Sales $76 $320
YES - These prices account for each person's sales.
What is the slope of the graph?
Oslope = -1/3
O slope = -3
O slope = 3
O slope = 1/3
4. John has his money in a savings
account that earns 3% interest each
year. He never takes money out of the
account. The value of his account is
described by the function
Dollars (years), or D(y).
Is D(2) < D(7) true or false?
Answer:
false
Step-by-step explanation:
so D(2) is equal to how much money he has after 2 years while D(7) is after 7 years. since he earns 3% interest each year he will have more money after 7 years than 2 years
find the number of primes less than 190 using the principle of inclusion-exclusion.
The number of primes less than 190 using the principle of inclusion-exclusion are 42
Principle of inclusion- exclusionThe principle of inclusion-exclusion is known as a counting technique that computes the number of elements satisfying at least one of several properties and guaranteeing that the numbers are not counted twice.
Prime numbers are numbers only divisible by 1 and itself.
Prime numbers less than 190 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181
They are 42 in number
Therefore, the number of primes less than 190 using the principle of inclusion-exclusion are 42
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A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing
equipment at a gym is 10 feet high and extends 6 feet horizontally. Which statement best compares the slopes of the
two pieces of equipment?
Answer:
First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct
Step-by-step explanation:
This question deals with Slope of a line.
Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
For first climbing equipment rise = 6 feet, run(horizontal) = 4 feet
Thus, slope = 6/4 = 3/2 ≈ 1.5
For second climbing equipment rise = 10 feet, run(horizontal) = 6 feet
Thus, slope= 10/6 = 5/3 ≈ 1.66
Thus,
Slope of first climbing equipment = 3/2 < slope of second climbing equipment = 5/3
Thus, First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct
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The coordinate grid shows points A through K. Which points are solutions to the
system of inequalities listed below? (2 points)
2x + y < 10
2x - 4y > 8
EFGHJ
EFG
ACDM
AEF
Answer:
E is the solution of the inequality Coordinates of points A = (-5,4)B = (4,7)C= (-2,7)D= (-7,1)E= (4, -2)F = (1 , -6)G= (-3, -10)H= (-4 , -4)I= (9, 3)J= (7 , -4)K= (2 ,3)putting the values of coordinates in equation to check for the solution.
For A
2x + y < 10
2(-5) + 4 < 10.
-10 - 4 < 10
-14 < 10 ( true)
2x - 4y > 8
2(-5) - 4(4) > 8
-10 - 16 > 8
-26 > 8
false..
it is not the solution of the equation.
similarly we can find for other coordinates.
E is the solution
PLEASE HELP ANSWER MY QUESTION ASAP!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: a_{33} = 1\degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
In a matrix, [tex] \sf a_{ij} [/tex] represents an element in " i " th row and " j " th column.
Henceforth, element [tex] \sf a_{33} [/tex] represents element in 3rd row and 3rd column.
[tex]\qquad \tt \rightarrow \:a_{33} = 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Drag each tile to the correct box. Not all tiles will be used.
Place the steps for finding in the correct order.
Answer+Step-by-step explanation:
[tex]f^{-1}\left( x\right) =\frac{1}{7} x^{2}+3 \ ,\text{where}\ x\geq 0[/tex]
logarithmic differentiation for
[tex]y = x {}^{2} [/tex]
someone help me
Answer:
[tex]\boxed {\frac{dy}{dx}= 2x}[/tex]
Step-by-step explanation:
Solving :
⇒ log y = log (x²)
⇒ log y = 2 log x
⇒ [tex]\mathsf {\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} \times 2}[/tex]
⇒ [tex]\mathsf {\frac{dy}{dx}= 2x}[/tex]
Answer:
y’ = 2x
Step-by-step explanation:
Let y = f (x), take the natural logarithm of both sides ln (y) = ln (f (x))
ln (y) = ln (x²)
Differentiate the expression using the chain rule, keeping in mind that y is a function of x.
Differentiate the left hand side ln (y) using the chain rule.
y’/y = 2 In (x)
Differentiate the right hand side.
Differentiate 2 ln (x)
y’/y = d/dx = [ 2 In (x) ]
Since 2 is constant with respect to xx, the derivative of 2 ln (x) with respect to x is 2 d/dx [ln (x)]
y’/y = 2 d/dx [In (x)]
The derivative of ln (x) with respect to x is 1/x.
y’/y = 2 1/x
Combine 2 and 1/x
y’/y = 2/x
Isolate y' and substitute the original function for y in the right hand side.
y’ = [tex]\frac{2}{x}[/tex] x²
Factor x out of x².
y’ = [tex]\frac{2}{x}[/tex] (x * x)
Cancel the common factor.
y’ = [tex]\frac{2}{x}[/tex] (x * x) (The x that is under 2 and the other x that I have underlined are the ones that cancel out)
Rewrite the expression.
y’ = 2x
So therefore, the answer would be 2x.
pleasee help with function graphing
Answer: A. The function has two distinct real zeros.
Answer:
C. The function has four distinct real zeros.
Step-by-step explanation:
The function intersects y=0 at x=1/2, 4, and 6 twice. It has two solutions at 6 twice as it is a behavior of polynomial or rational functions
Determine the equation of the line with slope -2 that passes through the point M(-1, -3).
Answer:
Given:
Let, the slope of the line passing through the point ( m) = -2
The line passing through the point M(-1,-3)= (x1 , y1)
The equation of the line passing through the point M(-1,-3) is
y-y1 = m (x-x1)
or, y-(-3) = -2 (x-(-1))
or, y+3 = -2 (x+1)
or, y+3 = -2x-2
or, 2x+y = -2-3
Hence, 2x+y =-5 is the required equation.
(a) is the correct answer .
If a plane including pints p,q and r cuts through the cube
If a plane including pints p,q, and r cuts through the cube, the shape that will be gotten is a triangle.
What is a triangle?A triangle is a polygon with three edges and three vertices. The sum of the internal angles of a triangle is equal to 180 degrees.
In this case, when a plane including pints p,q, and r cuts through the cube, the shape that will be gotten is a triangle.
The diagram is attached.
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i rlly need help with this :(
The air force reports that the distribution of heights of male pilots is approximately normal, with a mean of 72.6 inches and a standard deviation of 2.7 inches.
Part A: A male pilot whose height is 74.2 inches is at what percentile? Mathematically explain your reasoning and justify your work. (5 points)
Part B: Air force fighter jets can accommodate heights of soldiers between 70 inches and 78 inches without compromising safety. Anyone with a height outside that interval cannot fly the fighter jets. Describe what this interval looks like if displayed visually. What percent of male pilots are unable to fly according to this standard? Show your work and mathematically justify your reasoning. (5 points)
Using the normal distribution, it is found that:
a) The pilot is at the 72th percentile.
b) 19.13% of pilots are unable to fly.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 72.6, \sigma = 2.7[/tex].
Item a:
The percentile is the p-value of Z when X = 74.2, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{74.2 - 72.6}{2.7}[/tex]
Z = 0.59
Z = 0.59 has a p-value of 0.7224.
72th percentile.
Item b:
The proportion that is able to fly is the p-value of Z when X = 78 subtracted by the p-value of Z when X = 70, hence:
X = 78:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{78 - 72.6}{2.7}[/tex]
Z = 2
Z = 2 has a p-value of 0.9772.
X = 70:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 72.6}{2.7}[/tex]
Z = -0.96
Z = -0.96 has a p-value of 0.1685.
0.9772 - 0.1685 = 0.8087 = 80.87%.
Hence the percentage that is unable to fly is:
100 - 80.87 = 19.13%.
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Yesterday, the snow was 2 feet deep in front of Archie’s house. Today, the snow depth dropped to 1.6 feet because the day is so warm. What is the percent change in the depth of the snow?
The percent change in the depth of snow from yesterday to today is
Answer:
20%
Step-by-step explanation:
Half of 2 = 1
Half of 1.6 = 0.8
1 - 0.8 = 0.2
0.2 × 100 = 20%
Use the Factor Theorem to determine whether x + 1 is a factor of P(x) = 2x³+4x²–2x−8.
Specifically, evaluate P at the proper value, and then determine whether x + 1 is a factor.
Answer: [tex]2x^2+2x-4-\frac{4}{x+1}[/tex]
Not a factor because there is a remainder.
Step-by-step explanation:
Let's use synthetic division to solve this..
-1 ║ 2 | 4 | -2 | -8
║ | -2| -2 | 4
║ 2 | 2| -4 | -4
[tex]2x^2+2x-4-\frac{4}{x+1}[/tex]
PS: if anyone knows a better way to do a synthetic division chart please let me know.
Norman plants a garden each
year. This year, his garden
produced 40% fewer tomatoes
than it did last year. If Norman’s
garden produced 30 tomatoes
this year, how many tomatoes
did his garden produce last year?
Answer:
50
Step-by-step explanation:
if last year 100% of the tomatoes were produced and this year 40% less were produced then that would mean 60% of tomatoes were produced this year.
if 60% = 30 then
100% = ?
100x30÷60
How to find the point slope form with the slope of 3 and the point of -2/6
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:y-6 = 3(x + 2) [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Equation of line in point - slope form :
[tex]\qquad \tt \rightarrow \:y-y_1 = m(x - x_1)[/tex]
[tex] \tt \:m = slope=3[/tex][tex]\tt y_1 = y \: \: coordinate \: \: of \: \: point = 6[/tex][tex] \tt \:x_1 = x \: \: coordinate \: \: of \: \: point = - 2[/tex]Here :
[tex]\qquad \tt \rightarrow \:y - 6 = 3(x - ( - 2))[/tex]
[tex]\qquad \tt \rightarrow \:y - 6 = 3(x + 2)[/tex]
What is the period of the function y=tan (4/pi (x-pi/3))
O 3 units
O4 units
O 6 units
O 8 units
Answer:
Period = 4 units
Step-by-step explanation:
Standard form of a tangent function:
[tex]f(x)=\sf A \tan(B(x+C))+D[/tex]
A = vertical stretchπ / |B| = period (distance between any two consecutive vertical asymptotes)C = phase shift (horizontal shift - positive is to the left)D = vertical shiftThe tangent function has a vertical asymptote whenever cos(x) = 0
The tangent function does not have an amplitude because it has no maximum or minimum value.
Given function:
[tex]y=\tan \left(\dfrac{\pi}{4}\left(x-\dfrac{\pi}{3}\right)\right)[/tex]
Therefore:
Vertical stretch (A) = none[tex]\textsf{Period}=\dfrac{\pi}{\left|\dfrac{\pi}{4}\right|}=4[/tex]Phase shift (C) = π/3 to the rightVertical shift = noneAnswer: 4 units
Step-by-step explanation:
Calculate the AREA of the shape below. Give your answer in cm²
Answer:
[tex] \boxed{\bf 26\: cm^2} [/tex]Step-by-step explanation:
We got two shapes in the given figure,on the right we got a rectangle and on the left we have a square.
Area of rectangle:-
[tex]\bf 5 \times 2[/tex][tex]\bf 10 \:cm^{2} [/tex]Area of square :-
[tex]\bf 4 \times 4[/tex][tex]\bf 16 \: {cm}^{2} [/tex]Total area :-
[tex]\bf 10 + 16[/tex][tex]\boxed{\bf 26 \: {cm}^{2} }[/tex]_________________________Answer:
26 cm^2Step-by-step explanation:
you have two rectangles, the bigest has the base of 6cm and the height of 4cm, the area is 6 * 4 = 24cm ^ 2, the other rectangle has the base of 6 - 4 = 2 and the height of 5 - 4 = 1, 2*1=2.
we add the dimensions and we have the area of the complete figure 24 + 2 =
26 cm ^ 2
If AB is parallel to CD and the slope of AB is -3, what is the slope of CD?
The table shows results of an experiment that was replicated.
Which best describes the data?
They are precise and reproducible.
They are precise but not reproducible.
They are accurate and reproducible.
They are accurate but not reproducible.
The option that best describes the experiment is accurate and reproducible.
What option describes the data?All the values from the experiment are close in value to the accepted value. This indicates that the experiment is accurate. Two experiments yield the same values. This indicates that the experiment is reproducible.
Here is the table used in answering the question:
Accepted Value: 130
Experiment 1 129
Experiment 2 131
Experiment 3 129
Experiment 4 132
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Answer:
(A)They are precise and reproducible
Step-by-step explanation:
Simplify (3 + √5 )(2 + √5)
need the answer ASAP, WILL GIVE BRAINLIEST
Answer:
11 + 5√5
Step-by-step explanation:
6 + 3√5 +2√5 + 5
11 + 5√5
root n * root n = n , which is why there is a 5 at the end
Answer:
the answer is 11+5√5
Step-by-step explanation:
B/c (a+b).(c+d)=ac+ad+bc+bad(3+√5)(2+√5)=3.2+3.√5+√5.2+√5√5=6+3√5+2√5+√5√5=6+3√5+2√5+5=11+3√52√5=11+5√5What is the value of cos theta in the diagram below
O 3/5
O3/4
O 4/5
O4/3
The value of cos θ is 3/5.
What is Trigonometry?Trigonometric ratios can be used to determine the ratios of any two sides out of a total of three sides of a right-angled triangle in terms of the respective angles.
Here, given point on circle is (0.6, 0.8) or (3/5 , 4/5)
x - axis (base) = 3/5
y - axis (Perpendicular) = 4/5
Radius (Hypotenuse) = 1
Now, we know
cos θ = Base / Hypotenuse
cos θ = 3/5
Thus, the value of cos θ is 3/5.
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Please help!!!!!!!
picture below
Answer:
the first equation could be something along the lines of [tex]y=3x^{2}[/tex] then the second is [tex]y=3x^{2} -3\\[/tex]
Step-by-step explanation:
this is how shifting works
the sum of a certain number and -3
Answer:
[tex]\huge\boxed{\sf x - 3 }[/tex]
Step-by-step explanation:
Let the certain number be x
So,
Given condition:Sum is to add so we'll use the sign +
= x + (-3)
We know that + and - makes - because - sign will flip the + sign and make it negative, So:
= x - 3
[tex]\rule[225]{225}{2}[/tex]
Solution: c-3
[tex]\searrow[/tex]
Detailed explanation:
[tex]\searrow[/tex]
This problem tells us to convert the verbal phrase (in words) "the sum of a certain number and -3" into an algebraic expression, which is written in numbers.
Let's start by taking a look at our problem.
"the sum of a certain number and -3". We can first write this "certain number" as one letter (any letter you want). Let it be c.
Our expression already looks a little easier: "the sum of c and -3".
Now, the word "sum" tells us to add. So we should add c and -3.
[tex]--\mapsto\boldsymbol{c+-3}[/tex]
Which is the exact same thing as [tex]\boldsymbol{c-3}[/tex].
Voila! There's our answer.
Cheers!! ^-^______________________
Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
_______________________
Circle o has a circumference of 28.3 cm. What is the length of the radius r?
erved,
The graph of function fis shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.
g(x) = 2f(x-1)
Using the graph attached, If g(x) = 2f(x-1), the graph of the function will be: g(x) = x - 7.
What is the function about?Using the graph, the function is:
f(x-1) =1/2 (x-1) - 3
f(x-1) = 1/2x - 1/2 - 3/1
f(x-1) = 1/2x - 7/2
So:
g(x) = 2f(x-1)
g(x) = 2 (1/2x - 7/2)
g(x) = x - 7
Therefore,:
At x = 0, y = -7
y = 0, x = -7
Thus, Using the graph attached, If g(x) = 2f(x-1), the graph of the function will be: g(x) = x - 7.
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Got it right on Plato/Edmentum UωU <3
