y=mx+b
m=slope
b= y-intercept
x=6
y=-5
-5= -1/3(6)+b
-5= 2+b
-2 -2
-7 = b
y= -1/3x-7
Answer:
y=-1/3x-3
Step-by-step explanation:
Given that [tex]\frac{|z - 5i|}{|z + 5i|} = 1[/tex] , show that z lies on the x-axis.
The proof that z lies on the x-axis is shown below
How to show that z lies on the x-axis.For z to lie on the x-axis, then the coordinate must be represented as (x, 0)
Given that
[tex]\frac{|z - 5i|}{|z + 5i|} = 1[/tex]
We start by simplifying the given expression using the definition of the modulus of a complex number:
So, we have
[tex]\frac{|z - 5i|}{|z + 5i|} = \frac{\sqrt{(x - 0)^2 + (y - 5)^2}}{\sqrt{(x - 0)^2 + (y + 5)^2}} = 1[/tex]
Where
z = x + yi or z = (x, y)
Squaring both sides of the equation above, we obtain:
[tex]\frac{(x - 0)^2 + (y - 5)^2}{(x - 0)^2 + (y + 5)^2} = 1[/tex]
This gives
[tex]\frac{x^2 + (y - 5)^2}{x^2 + (y + 5)^2} = 1[/tex]
By comparison, we have
[tex](y + 5)^2 = (y - 5)^2[/tex]
Set y = 0 to test the equation
So, we have
[tex](0 + 5)^2 = (0 - 5)^2[/tex]
25 = 25 --- true
The equation is true for y = 0
This means that
z = (x, 0)
Hence, z lies on the x-axis
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(b) At the beginning of the term, Caroline bought p notebooks and Bert bought 5 notebooks less than Caroline. During the term, Caroline gave 2 of her notebooks to her sister. Caroline then had twice as many notebooks as Bert. By writing a suitable equation, calculate the number of notebooks Caroline now has.
The number of Caroline's textbook is 8
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.
Represent the Notebook bought by Bert as q
q = p-5
p-2= 2q
p = 2q +2
substitute 2q +2
q = 2q+2-5
2q-q = 3
q = 3
substitute 3 for q
3 = p-5
p = 5+3
p= 8
Therefore Caroline's number of notebook is 8
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What benefits came from the collapse of communism in eastern europe? select three answers.
Greater freedom of movement, growing entrepreneurship, more contact with Western Europe.
three benefits came from the collapse of communism in eastern europe
Entrepreneurship is the creation or receipt of financial rewards. Under this definition, entrepreneurship is generally viewed as a change that involves more risk than is normally incurred when starting a business, and that may also involve value beyond its actual economic value.
An entrepreneur is a person who creates and/or invests in one or more groups while taking maximum risk and enjoying maximum return. [citation needed] The way to start a business is known as entrepreneurship. Entrepreneurs are usually seen as innovators, sources of new ideas, objects, offerings and ventures/technologies.
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content attribution
QUESTION 5. 1 POINT
1
A company offers one free book download to anyone that registers. The total number of people that register can be
modeled by the function f(x) = 8x³ +70x² +145x+182, where x is the number of months passed since starting the
company. The number of free books available to choose from can be modeled as 2x + 13. Write an expression that can be
used to determine the average number of people that download each of the free books.
Ous
Provide your answer below:
The expression for the average number of people (8x³ +70x² +145x+182)/(2x + 13)
How to determine the expression to determine the average number of peopleFrom the question, we have the following parameters that can be used in our computation:
The total number of people, f(x) = 8x³ +70x² +145x+182
Number of free books = 2x + 13
To determine the average number of people that download each of the free books,
We need to divide the total number of people that register by the number of free books available.
So, we have
Expression = (8x³ +70x² +145x+182)/(2x + 13)
Hence, the expression is (8x³ +70x² +145x+182)/(2x + 13)
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We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately
. We would like to be 99.5% confident that the estimate is within 0.1 of the true population mean. How large of a sample size is required?
n=
Answer:
5,144,079
Step-by-step explanation:
[tex]\displaystyle CI=\mu\pm z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\CI_{99.5\%}=\mu\pm2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1=2.807\biggr(\frac{80.8}{\sqrt{n}}\biggr)\\\\0.1\sqrt{n}=226.8056\\\\\sqrt{n}=2268.056\\\\n=5144078.01914\\\\n=5144079[/tex]
Thus, you would need a sample size of 5,144,079 to be 99.5% confident that the true population mean is ±0.1 away from it with a population standard deviation of 80.8 (aka. our margin of error).
HELP PIECEWISE LINEAR RELATIONS
The required description of the given piecewise linear relations is graphed, as follows:
f(x) = 1 if [-3, -1); f(x) = 2 if [-1, 1); and f(x) = 3 if [1, 3).
What is a piecewise function?A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).
The graph of the piecewise linear relations is given in the question, as shown
f(x) = 1 if [-3, -1)
This the sub-function define between the interval [-3, -1).
f(x) = 2 if [-1, 1)
This the sub-function define between the interval [-1, 1).
f(x) = 3 if [1, 3)
This the sub-function define between the interval [1, 3).
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An ant can travel at a constant speed of 980 inches every 5 minutes.
How far does the ant travel in 1 minute?
At this rate, how far can the ant travel in 7 minutes?
The ant can travel 196 inches in 1 minute and 1372 inches in 7 minutes.
What is cross multiplication?To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.
Given that the ant can travel at a constant speed of 980 inches every 5 minutes.
Thus,
5 minutes = 980 inches
1 minute = x inches
Using cross multiplication method or Butterfly method of multiplication we have:
x = 980/5
x = 196 inches.
In 7 minutes the ant can travel:
(7)(196) = 1372 inches.
Hence, the ant can travel 196 inches in 1 minute and 1372 inches in 7 minutes.
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The process of completing the square can be used to calculate the width, in feet, of the storage bin that gives a maximum area.
The missing value in the expression A = -2(x-9)² + ? is 162, which represents the maximum area of the storage bin.
What is Perfect Square?A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.
To complete the perfect square, we need to factor out the coefficient of the squared term (-2) from the expression:
A = -2x² + 36x
A = -2(x² - 18x)
Next, we need to add and subtract the square of half the coefficient of the x-term (-18/2 = -9) inside the parentheses:
A = -2(x² - 18x + (-9)² - (-9)²)
Simplifying the expression inside the parentheses, we get:
A = -2[(x - 9)² - 81]
Distributing the -2, we get:
A = -2(x - 9)² + 162
Therefore, the missing value in the expression is 162.
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pleas help me ill give you brainliest
Answer:
This is a Right Triangle because the last angle is 90 degrees.
ons
Write the equation for this relationship and identify the constant of proportionality (or k value).
X
Y
28 36 40
21
27
30
56
42
Given parallelogram abcd, in order to prove that opposite sides are congruent, what additional segments or points will you need?.
Answer:
Step-by-step explanation:
In a parallelogram, opposite sides are congruent. To prove this, you would need to show that the following two conditions are true:
The length of one pair of opposite sides is equal.
The two pairs of opposite sides are parallel.
To show these two conditions, you may need additional segments or points such as:
Perpendicular lines or segments to the sides to help show the sides are parallel.
Diagonal segments to help show that the parallelogram is a rectangle and that the sides are equal in length.
By showing these two conditions, you can conclude that the opposite sides of a parallelogram are congruent.
At a carnival game, the player pays a dollar, then flips a quarter, rolls two dice, and draws two cards from a standard deck. If the result is heads, 11, and a pair of aces, he wins $1000. What is the probability of this happening?
(Round your answer to seven decimal places)
The probability of winning is…?
The probability of it happening will be 0.0000628
How to calculate the probabilityProbability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
The number of outcomes based on the information will be:
= 2(36)[52C2)
= 72 × 52! / 50!2!
= 1/95472
Number of favorable outcome is:
= 4!/2!2!
= 6
The probability will be;
= 6 / 95472
= 0.0000628
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ax+bx=c make x subject
Answer:
x=c/(a+b)
Step-by-step explanation:
ax+bx=c
x(a+b)=c
x(a+b)/(a+b)=c/(a+b)
x=c/(a+b)
Answer:
[tex]x=\dfrac{c}{a+b}[/tex]
Step-by-step explanation:
To make x the subject of the equation ax + bx = c, rearrange the equation using algebraic operations to isolate a single x-variable.
Given equation:
[tex]ax + bx = c[/tex]
Factor out x from the left side of the equation:
[tex]x(a+b)=c[/tex]
Divide both sides of the equation by (a + b):
[tex]\dfrac{x(a+b)}{(a+b)}=\dfrac{c}{(a+b)}[/tex]
Simplify:
[tex]x=\dfrac{c}{a+b}[/tex]
Can someone please help me do this
The vertices of the image of triangle ABC are A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4) and C''(x, y) = (- 4, 4).
How to determine the image of a triangle set on Cartesian plane
Any triangle can be generated by three points that are not collinear, in this problem we need to determine the image of a triangle, which is the result of two rigid transformations: (i) Reflection over the y-axis, (ii) Dilation centered at the origin with a scale factor of 2, whose definitions are shown below:
Reflection over the y-axis:
(x, y) → (- x, y)
Dilation centered at the origin with a scale factor of 2:
(x, y) → (2 · x, 2 · y)
If we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (2, 2), then the image of the vertices are determined below:
Reflection over the y-axis
A'(x, y) = (- 3, 4), B'(x, y) = (- 4, 2), C'(x, y) = (- 2, 2)
Dilation centered at the origin with a scale factor of 2
A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4), C''(x, y) = (- 4, 4)
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caride pls thank and veryone help ls
Answer:
(a) 275ft²
(b) 3 gallons
(c) $73.50
Step-by-step explanation:
(a)
The shape of the wall consists of a triangle and a rectangle, so to find the wall's area we find the area of the triangle and rectangle and add them together:
Area of triangle = 0.5*base*height = 0.5*22*5 = 55ft²
Area of rectangle = base*height = 22*10 = 220ft²
So the area of the wall = 55ft²+220ft²=275ft²
(b)
To find how many gallons it would take, you divide the area by the amount of are one gallon covers: 275 / 105 = 2.619
Rounded up, this is 3 gallons
(c)
Since we're buying 3 gallons and each costs $24.50, we multiply 3 by the price to find the total: 3*24.5 = $73.50
Answer:
(a) 275ft?
(b) 3 gallons
(c) $73.50
please mark brainly
All of the following constructions start with a line segment except...
O constructing a 45° angle
O constructing a 30° angle
O constructing congruent angles
• constructing equilateral triangles
All of the aforementioned structures, with the exception of creating equilateral triangles, begin with a line segment.
What is meant by line segment?The component of a line in a geometric shape, such as a triangle, circle, quadrilateral, etc., that is bordered by two (2) distinct points and usually has a definite length is referred to as a line segment.
An equilateral triangle is a particular kind of triangle with equal side lengths and identical angles at each of its three (3) internal sides.
A line segment serves as the foundation for the following angles and lines in geometry:
The process of creating a line perpendicular to a point on a line.
The creation of a 45-degree angle (45°).
The creation of a 30-degree (30-degree) angle.
Since an equilateral triangle has equal side lengths and all three of its interior angles are equal, we can reasonably and logically conclude that its construction does not begin with a line segment.
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Consider function f. f(x)=square x-1 which graph represents f?
The graph that represents the function f(x) = sqrt(x - 1) is given by the following option:
C. Graph Y.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.For this problem, the function is defined as f(x) = sqrt(x - 1), meaning that the parent square root function was moved one unit right, and thus the correct graph is given by graph Y.
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) Joe bought six bunches of seedless black
grapes for $15. How many bunches can
Anjali buy if she has $7.50?
Answer:
Step-by-step explanation:
Since Joe bought six bunches of seedless black grapes for $15, the cost per bunch of grapes is $15 / 6 = $2.50.
Since Anjali has $7.50, she can buy $7.50 / $2.50 = 3 bunches of seedless black grapes.
There are two routes you can take from your house to the store.Main Street is 1/3 of a mile long. Oak Street is 1/4 of a mile long. How much longer is Main Street thank Oak Street
The Main Street is 1/12 of a mile longer than the Oak Street
How much longer is Main Street thank Oak StreetFrom the question, we have the following parameters that can be used in our computation:
Main Street is 1/3 of a mile long. Oak Street is 1/4 of a mile long.Using the above as a guide, we have the following:
Difference = Main Street - Oak Street
substitute the known values in the above equation, so, we have the following representation
Difference = 1/3 - 1/4
Evaluate the difference
Difference = 1/12
Hence, the difference is 1/12 of a mile
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Use the information provided to answer Part A through Part D.
One method that can be used to prove that the diagonals of a parallelogram bisect
each other is shown in the given partial proof.
S
ven: Quadrilateral PQRS is a parallelogram
ove:
PT= RT
ST= QT
1.
2.
7.
3.
4.
Statements
Quadrilateral PQRS is a
parallelogram
PQ || SR
PS || QR
ZPQS = ZRSQ
ZQPR ZSRP
?
5. ASRT AQPT
6.
PT=RT
ST=QT
Q
I
R
PT = RT
ST=QT
1. Given
2. Definition of
parallelogram
3.
4.
5.
Reasons
6.
2
?
Opposite sides of a
parallelogram are
congruent
?
Corresponding par
of congruent
triangles are
congruent
7. Definition of
congruent line
erop segments
Answer:
the anwser is 5
Step-by-step explanation: 5
09:42 Man 13 Feb
A school carried out a report on their Year 11 students to see the impact of doing homework
regularly on final grades achieved in maths. The results are presented in the frequency tree.
Get grade B or higher
Do homework
Complete the tree.
75
6
Don't do
homework
regularly
60
b
D
Get lower than grade B
Get grade B or higher
Get lower than grade B
The percentage of students who are doing their homework regularly is 75%.
What is a Universal Set?A universal set in set theory is a set that includes itself as well as all other items. A universal set's nonexistence in set theory as it is typically expressed can be demonstrated in a number of different ways. However, a universal set is a part of several unconventional set theory variations.
To find the percentage of students who are doing their homework regularly,
We find the total students and this is 75 + 5 = 80 students
The percentage is 60/80 * 100
= 75%
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f(x)=
[tex]2 {x}^{2} [/tex] write down the equation of inverse of f
The equation of inverse of f is f-1(x) = √(x/2)
How to determiine the equation of inverse of fFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2x^2
Express as an equation
so, we have the following representation
y = 2x^2
Swap x and y
so, we have the following representation
x = 2y^2
Divide by 2
y^2 = x/2
Take the square roots
y = √(x/2)
Hence, the inverse is f-1(x) = √(x/2)
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Geometry question! Please help
The values 6, 4 and 12 are the measures of PR, PQ and RI respectively.
Solving similar trianglesThe given diagram is a triangle and the expression to be used based on the theorem is expressed as:
TP/TQ = PR+3/15
3/5 = PR+3/15
5(PR +3)= 3(15)
5(PR + 3) = 45
PR + 3 = 9
PR = 9 - 3
PR = 6
For the measure of PQ
PQ^2 = 5^2 - 3^2
PQ^2 = 25 - 9
PQ = 4
Determine the measure of RI
3/PQ = TR/RI
3/4 = 9/RI
1/4 = 3/RI
RI = 12
Hence the measure of PR, PQ and RI are 6, 4, and 12 respectively
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Please help me ASAP THANKS
Answer:
i think its 1 or 3 or 5 if not what i moslty think it is is (((( 4 )))
Step-by-step explanation:
i hope this helps may luck be with YOU! :)
Franka's annual salary is $79600. About 25% of her salary is deducted for taxes. Estimate the amount deducted from Franka's pay each year
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 79600}}{\left( \cfrac{25}{100} \right)79600}\implies \text{\LARGE 19900}[/tex]
Alex jogs for 15 minutes at an average speed of 4 mph. He then walks at an average speed of 2.4 mph
for minutes. The total distance traveled is 1.4 miles.
(a) Convert 15 minutes and r minutes to hours.
(b) Form an equation in terms of t and solve it.
(c) Hence, calculate Alex's average speed for the whole journey.
(a) Conversion of 15 minutes and r minutes into hours, 0.25 hours & r/60 hours.
(b) An equation in terms of t and solution of it, S = 0.04r miles and r = 10
(c) Alex's average speed for the whole journey is, 3.33 mph
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
(a) 15 minutes is equal to 0.25 hours (15/60) and r minutes is equal to r/60 hours.
(b) Let's use the formula:
distance = speed x time for both jogging and walking.
Distance traveled while jogging = 4 mph x 0.25 hours
= 1 mile
Distance traveled while walking = 2.4 mph x (r/60) hours
= 0.04r miles
Total distance traveled = 1 mile + 0.04r miles
= 1.4 miles
Solving for r, we get:
0.04r = 0.4
r = 10
So, Alex walked for 10 minutes.
(c) Total time taken = 15 minutes + 10 minutes
= 25 minutes
= 0.42 hours
Total distance traveled = 1.4 miles
Average speed = Total distance / Total time
= 1.4 miles / 0.42 hours
= 3.33 mph (rounded to two decimal places).
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please help!!
I can’t put the answer options because brainly won’t allow me to choose multiple photos at once, but there are solid line graphs, dotted line graphs, and they are all shaded.
PLEASE HELP ASAP
Circular pizza pies at Pat's Pizza's come in 10-inch and 16-inch diameters.
Which is closest to the difference in the areas of the pizza pies?
A
129.12 inches
B
183.46 inches
C
122.46inches
D
142.96 inches
Answer:
C
Step-by-step explanation:
The area formula of a circle is A=[tex]\pi r^{2}[/tex], where r (or radius) is equal 1/2 times diameter (or d/2). So pi times (10/2)^2= 78.54 and pi times (16/2)^2=201.06. 201.06-78.54 = about 122.52, which is closest to 122.46, or C.
Suppose X is a random variable with mean X and standard deviation oXSuppose Y is a random variable with mean Y and standard deviation oY. The mean of X + Y is:a. MX+MYb.uX/oX) + (Y /oY). c. 1X+uY, but only if X and Y are independent. d (uX/oX) + (Y/oY), but only if X and Y are independent.
The answer is (a) MX + MY. Whether or not X and Y are independent, we cannot simplify (a) or (b) further.
The mean of X + Y is:
E(X + Y) = E(X) + E(Y)
So the answer is not (a) or (b).
(c) is incorrect because the formula given is only true if X and Y are independent, but no such assumption is given in the problem.
(d) is also incorrect because we cannot simply divide the means by the standard deviations to get the standard normal variables, especially when the variables X and Y have different means.
Therefore, the answer is (a) MX + MY.
Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.
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In these triangles, the largest angle and the
largest side have been measured. What do
you notice?
The shortest distance between two points is a straight line.
It would obviously be shorter to walk distance c than to walk
a plus b. The Triangle Inequality says that a + b > c. What
other two inequalities could you write?
In these triangles, the largest angle and the largest side have been measured. This means that the two smaller sides and the two smaller angles are proportional to each other. This is known as the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side. This means that the two smaller angles and the two smaller sides of the triangle must add up to be larger than the largest angle or side.
The Triangle Inequality states that the sum of any two sides of a triangle must be greater than the third side. This means that two other inequalities can be written:
a > |c - b| and b > |c - a|,
where |x| is the absolute value of x. This means that the length of each side must be greater than the difference between the other two sides
