Step-by-step explanation:
First things first, we are rotating about a point so the first we do is the move the clockwise rotation to the origin.
Since a rotation is a rigid transformation, we must move all the other points as well.
So move every point using the rotation vector
R(-6,-8), move every point to
D(1-6,4-8)=D'(-5,-4)
E(5-6,5-8)=E'(-3,-5)
F(4-6,1-8)=F'(-2,-7)
G(0-6,0-8)=G'(-6,-8)
So know since the center of rotation is middle at (0,0) , we can apply the rotation rules
For a 270 clockwise rotation, we apply this rule
(-y,x)
So for the points we know get
D''(5,-4)
E''(3,-5)
F''(2,-7)
G"(6,-8)
Know since we done our rotation, we undo what we did in step 1, we add 6 to the x coordinates and 8nto the y coordinate
D"'(11,8)
E"'(9, 3)
F"(8,1)
G"'(12,0)
So those are our new coordinates.
Given that the roots of the equation x^2-8x+k=0 satisfy 3x+4x=29, find k
a = 1st zero or root of the quadratic
b = 2nd zero or root of the quadratic
[tex]x^2-8x+k=0\implies (x-a)(x-b)=0\implies x= \begin{cases} a\\ b \end{cases} \\\\[-0.35em] ~\dotfill\\\\ -ax-bx=-8x\implies -a-b=-8\implies -b=a-8\implies b=8-a \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{3a+4b=29}\qquad \implies \qquad \stackrel{\textit{substituting from above}}{3a+4(8-a)~~ = ~~29}\implies 3a+32-4a=29 \\\\\\ -a+32=29\implies 32=a+29\implies \boxed{3=a}\hspace{5em}\stackrel{ 8~~ - ~~3 }{\boxed{b=5}}[/tex]
[tex]~\dotfill\\\\ (x-3)(x-5)=0\implies x^2-8x+\stackrel{ \textit{\LARGE k} }{15}=0[/tex]
Cona Mother realize that her age is the difference of code is eight squared of K represent scores age which expression represents cons mothers age
The correct answer on the equation representing Kona's mother's age is option a) K² - 4.
Let M represent the Kona's mother's age = M = K² - 4.
Now substitute the value by taking Kona's age be 10.
= 10² - 4
= 100 - 4
=96.
Since the difference is Kona's age squared with subtracting 4.
The problem states that Kona's mother's age is the difference between Kona's age squared and four, We are given that the K represents Kona's age. Therefore, the expression for Kona's mother's age can be written as K² - 4. This is because we substitute the K for the Kona's age and square it, then subtract four to find the mother's age. Hence the correct is option A. The difference code refers to the answer or result formed after subtracting the given equation or expression.
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Complete question
Kona's mother realized that her age is the difference of Kona's age squared and four. If K represents Kona's age, which expression represents Kona's mother's age? a) K² - 4 b) K³ - 4 c) K² + 4 d) K³ + 4
What is the equation of a horizontal line passing through the point (−3, 8)
In the last four weeks,you mowed 9 lawns,worked 26 hours at the ice cream shop,and delivered newspapers 8 days.Did you make enough to buy the television? Explain..
You did not make enough money to buy the television with a total earnings of $458
How to determine if the person earns enoughTo write an expression for total earnings, we can use the given rates of pay and multiply them by the unit rates of the activites and then add them together.
So the expression for total earnings (E) is:
E = 10x + 8y + 20z
Where
x = number of lawns mowedy = hours worked at the ice cream shopz = days delivering newspapersUsing the given parameters in the question, the total earnings (E) in the last 4 weeks is
E = ($10 x 9) + ($8 x 26) + ($20 x 8)
Evaluate
E = $90 + $208 + $160
E = $458
$458 is less than the cost of television ($540)
This means that you did not make enough money
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Complete Question
You earn $10 for each lawn you mow. You earn $8 per hour working part time at an ice cream shop. You earn $20 cach day you deliver newspapers.
In the last four weeks, you mowed 9 lawns, worked 26 hours at the ice cream shop, and delivered newspapers 8 days.
Did you make enough to buy the television? Explain...
The television price is $540
32% of the 384 students in the eighth grade walk to school, about how many eighth graders walk to school?
Answer: 123 students
32 % of 384 is 122.88. Since a percent of a person can't walk to school, we should round up. This means 123 students in the eighth grade walk to school each day.
I hope this helps and good luck <3!!
I'LL GIVE BRAINLIEST JUST PLEASE ANSWER
countries represented at each festival 1: 0-5 3:6-11 5:12-17 4:18-23 2:24-29. How many festivals were there?
ANSWER ASAP PLEASE!!!!!
Answer:Twerk
Step-by-step explanation:Twerk
Select all the equations that have 9 as a solution. j + 8 = 72 m × 3 = 27 b + 4 = 13 p – 5 = 4 q ÷ 3 = 27
What is the percent increase from 70 to 100?
Answer:
30%
Step-by-step explanation:
100-70=30
Find the length of side x in simplest radical form with a rational denominator.
Answer:
2[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The rule for a 30:60:90 triangle is [tex]\sqrt{3}:x: 2[/tex]
That means that to get the bottom side, we can divide 4/2
That makes 2, so then we can find x by multiplying 2 by [tex]\sqrt{3}[/tex]
That makes 2[tex]\sqrt{3}[/tex]
-5 -4 -3 -2
I
Y
5-
4+
3
2+
1
-2
-34
-5
1
→x
2 3 4 5
Find the inequality represented by the
graph.
Answer:
Based on these observations, the inequality represented by the graph is y > mx + b, where m is a positive number and b is a negative number.
Step-by-step explanation:
The graph represents a linear function. To find the inequality, we can find the equation of the line in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
From the graph, it can be seen that the slope of the line is positive, which means that as x increases, y also increases. Also, the y-intercept is negative, which means that the line crosses the y-axis at a negative value.
Based on these observations, the inequality represented by the graph is y > mx + b, where m is a positive number and b is a negative number.
Note that the exact values of m and b can be found by using two points on the line and solving for the slope and y-intercept using the formula for a line.
There are 5 buses taking 27 people to a game another bus is taking 7 people how many people are These buses taking to the game?
Answer: hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet. 2 0, 1, 4 3 1, 2, 6 4 1, 3, 7 5 1, 1 6 5key: 3|2 means 3.2 what is the mean, and what does it tell you in terms of the problem? a. 3.85 feet; the value means that a typical throw of the ball results in 3.85 feet. b. 3.2 feet; the value means the furthest the ball went. c. 5.1 feet; the value means this measurement had the most occurrences. d. 4.62 feet; the value means that a typical throw of the ball results in 4.62 feet.
The mean, also known as the average, is a central value that represents the typical value of a set of data.
To calculate the mean, you add up all the values in the data set and divide by the number of values. The mean provides a general sense of the distribution of the data and helps to identify any patterns or trends. In the stem-and-leaf plot, the mean can be calculated by adding up all the values and dividing by the number of throws. The mean in this case is 4.62 feet, which indicates that a typical throw of the ball results in 4.62 feet. This value can be used to gain a better understanding of the overall performance of the ball thrower and provide insight into how far the ball is typically thrown.
It is important to note that the mean is sensitive to outliers or extreme values, so it may not accurately reflect the typical value of the data in all cases. However, in this particular case, the mean provides a useful representation of the typical performance of the ball thrower.
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Answer:d
Step-by-step explanation:
A hybrid car with a 9. 80 gal tank consumes gasoline at a rate of 54. 1 miles/gal. How many liters of gasoline will be consumed traveling 132 km?
The hybrid car will consume approximately 21.65 liters of gasoline to travel 132 km.To convert the hybrid car's fuel consumption rate from miles/gallon to kilometers/liter, we need to multiply by a conversion factor of 0.425 (1 mile = 1.609 kilometers, 1 gallon = 3.785 liters).
So the car's fuel consumption rate is 54.1 miles/gallon x 0.425 km/mile ÷ 3.785 liters/gallon = 6.09 km/liter.To find how many liters of gasoline the car will consume traveling 132 km, we can use the formula:
Gasoline consumed = distance traveled ÷ fuel consumption rate
Gasoline consumed = 132 km ÷ 6.09 km/liter = 21.65 liters (rounded to two decimal places).Therefore, the hybrid car will consume approximately 21.65 liters of gasoline to travel 132 km.
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2. A traffic radar records the speed, v kilometers per hour, of cars on a section of a *
road. The following table shows a summary of the results for a random sample of
1000 cars whose speeds were recorded on a given day. Find an estimate of the
mean speed of the sample. Show your work!
Answer: Just to get your attention (don't mind rating this)
Step-by-step explanation:
I'm sorry, but there's no table or information about the sample provided for me to estimate the mean speed of the sample. Can you please provide more information or clarify your question?
If radius of circle is tripled then area of circle will be increased by
If radius of circle is tripled then area of circle will be increased by:9 times.
If the radius of a circle is tripled, then the new radius is three times the original radius, or R' = 3R, where R is the original radius and R' is the new radius. The area of a circle is given by the formula A = πR^2, where A is the area and R is the radius.
Substituting R' = 3R into the formula for the area of a circle, we get:
A' = πR'^2
= π(3R)^2
= 9πR^2
Therefore, the new area A' is 9 times the original area A. In other words, if the radius of a circle is tripled, the area of the circle will be increased by a factor of 9. This is because the area of a circle is proportional to the square of its radius.
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Graph the line of best fit.
The line of the best fit of the scatter plot is added as an attachment
How to determine the line of best fitThe missing graph is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The graph
A good line of best fit would have equal number of points on either sides
To plot the graph, we draw a line that divides the points on the graph evenly
This line when drawn on the scattered points divided the points approximately evenly
Hence, the line of the best fit is attached
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Find the sum or difference. Write all fractions in simplest form and improper fractions as mixed numbers 8/2-3/5
The difference of the fractions 8/2 and 3/5 is given as follows:
17/5.
How to obtain the difference?The difference operation for this problem is defined as follows:
8/2 - 3/5.
8 is divisible by 2, with a quotient of 4, hence the subtraction can be simplified as follows:
4 - 3/5.
With a common denominator of 5, we have that 4 x 5 = 20, hence:
20/5 - 3/5.
As the fractions now have a common denominator, we can subtract the numerators while keeping the denominator constant, thus the subtraction is given as follows:
(20 - 3)/5 = 17/5.
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A shaded semicircle is inside a circle
The radius of the circle is 10 cm
The diameter of the semicircle is 8 cm
How many times bigger is the unshaded area than the shaded area?
The unshaded area is 11.5 times bigger than the shaded area.
What is the area of the circle?
The area of the circle is given by:
A_circle = πr^2
where;
r is the radius of the circle. In this case, r = 10 cm, so:
A_circle = π(10 cm)^2 = 100π cm^2
The area of the semicircle is given by:
A_semicircle = (1/2)πr^2
where;
r is the radius of the semicircle.In this case, the diameter of the semicircle is 8 cm, so the radius is 4 cm:
A_semicircle = (1/2)π(4 cm)^2 = 8π cm^2
To find the area of the shaded region, we need to subtract the area of the semicircle from the area of the circle:
A_shaded = A_circle - A_semicircle
= 100π cm^2 - 8π cm^2
= 92π cm^2
The unshaded area is the area of the circle minus the area of the shaded region:
A_unshaded = A_circle - A_shaded
= 100π cm^2 - 92π cm^2
= 8π cm^2
So the unshaded area is 8π cm^2 and the shaded area is 92π cm^2.
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need help with this linear inequality problem. thanks
The inequality that matches the region is [tex]y\geq -3[/tex].
What is linear inequality?
When a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression. Different types of linear inequalities can be represented in a number of different ways.
The graph of the region shows a positive region which represents the value as a greater or increasing order.
The sign '>' represents the greater region.
So, the required answer is [tex]y\geq -3[/tex].
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A. A fish is 12 m below the surface of the ocean. What is its elevation?
B. A seabird is 28 m above the surface of the ocean. What is its elevation?
C. If the bird is directly above the fish, how far apart are they?
Answer:
1.) -12
2.) 28
3.) 40
Step-by-step explanation:
The elevation of an object is the height or depth of the object relative to the sea level. If the object is above sea level, its elevation will be positive. However, if the object is below sea level, its elevation will be negative. Therefore, we can conclude that the elevation of the fish is -12 m because it is below sea level.
o step by step to reduce the radical.
176
176
x
x
The solution of the expression x = √176 is x = 13.27.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
Given:
An expression,
x² = 176
Taking the square root of the equation,
x = √176
x = 13.27
Therefore, the solution is x = 13.27.
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Double spin is a new game the player gets to spin a spinner twice but wins only if the same amount comes up both times. The $100 sector is 1/8 of the circle.
a. What is the expected value when playing this game if you can play the game for free?
c. If it costs $3. 00 for you to play this game, should you expect to break even in the long run?
a. If you can play the game for free, the expected value is zero since there is no cost and no prize for winning.
How to calculate breaking even?b. To calculate the expected value when it costs $3 to play, we need to first find the probability of winning.
There are 8 possible outcomes on the spinner, and only one of them results in a win, so the probability of winning is 1/8. The probability of losing is 7/8.
The expected value is the sum of the product of each outcome and its probability. Let X be the amount won. Then:
E(X) = (1/8)($100) + (7/8)(-$3)
= $12.50 - $2.63
= $9.87
So the expected value when it costs $3 to play is $9.87. Since the expected value is positive, you can expect to make a profit in the long run.
However, this does not mean that you will win every time you play, as the outcome of each individual game is still random.
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the cost to rent a car from lou's garage is 50 + 0.1m dollars for m miles. The cost of a car ar Jerry's Garage is 25 + 0.05m dollars for the same number of miles
Answer:
To find out which rental car company is cheaper, you need to compare the cost for the same number of miles driven. Let's say you drive a total of "m" miles.
The cost for renting a car from Lou's Garage is 50 + 0.1m dollars.
The cost for renting a car from Jerry's Garage is 25 + 0.05m dollars.
To determine which option is cheaper, you need to compare these two expressions and find out which one is less. To do this, you can subtract the second expression from the first expression:
50 + 0.1m - (25 + 0.05m) = 25 + 0.05m
This equation shows that the cost of renting a car from Lou's Garage is 25 + 0.05m dollars more expensive than renting a car from Jerry's Garage for the same number of miles driven. Therefore, Jerry's Garage is the cheaper option.
Please help!
The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure.
Answer: 1.25 and 1.33
Step-by-step explanation:
question 3:
both sides of 24 became sides that measure 30.
24 times x = 30
therefore x, the scale factor, is 1.25
question 4:
3 increases to 4 and 15 increases to 20 (you have to rotate these shape before anything else to see the corresponding changes)
15 times x = 20
20 divided by 15 is 1.33 repeating, so 4/3
If u ever had a side getting smaller in the second shape, the scale factor would be less than 1.
a circular table is painted yellow with a red square in the middle. the radious of the tabletop is 6x. the side length of the red square is 3x. what is the area of the yellow part of the tabletop.
you want to compute a 90% confidence interval for the mean of a population with unknown population standard deviation. the sample size is 30. the value of t* you would use for this interval is
The value of t* would use for this interval is 1.699 to compute a 90% confidence interval.
It is given that the confidence = 90% or 0.9
also, the sample size (n) = 30
The degrees of freedom is the sample size decreased by 1:
df = n - 1
df = 30 - 1
df = 29
The critical value t* can then be found in the row with df = 29 and in the column with c = 90% (or upper tail probability p = 0.05) using table B.
t* = 1.699
The image attached is t* table
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A system of inequalities is shown.
The graph shows a dashed upward opening parabola with a vertex at negative 1 comma negative 4, with shading inside the parabola. It also shows a dashed line passing through the points negative 2 comma negative 1 and 0 comma 3, with shading above the line.
Which system is represented in the graph?
The system that is represented in the graph include:
y > x² – 2x – 3
y > 3x + 4
How to explain the graphThe study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this case, a graph consists of vertices connected by edges.
The graph shows a dashed upward opening parabola with a vertex at negative 1 comma negative 4, with shading inside the parabola. It also shows a dashed line passing through the points negative 2 comma negative 1 and 0 comma 3, with shading above the line.
This depicts y > x² – 2x – 3 and y > 3x + 4.
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Which system is represented in the graph?
y ≥ x2 – 2x – 3
y ≤ 3x + 4
y < x2 –2x – 3
y > 3x + 4
y < x2 – 2x – 3
y > 3x + 4
y > x2 – 2x – 3
y > 3x + 4
Kurram was born on June 12, 2002, and his brother was born on February 10, 2004. Who is the elder among them and by how many months?
Answer:
Kurram is elder by 19 months
question 3
pls help me as soon as possible
i'm being timed i only have a hour
The measure of arc FE in the figure is 100 degrees
How to determine the measure of arc FEFrom the question, we have the following parameters that can be used in our computation:
The circle and the intersecting chords
The value of arc FE represented by x is then calculated as
80 = 1/2(x + 60)
Cross multiply the equation
This gives
x + 60 = 160
Subtract 60 from both sides
x = 100
Hence, the measure of x is 100 degrees
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Which Number line shows all of the values of x that make the inequality true
Any value of x that is less than or equal to -2 will make the inequality true.
What is Number line?
A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every point on a number line is presumed to be a real number, and every real number is assumed to be a point.
To solve the inequality 3x - 1 <= -7, we can start by adding 1 to both sides to isolate the variable:
3x - 1 + 1 <= -7 + 1
Simplifying, we get:
3x <= -6
Next, we can divide both sides by 3 to solve for x:
3x/3 <= -6/3
Simplifying, we get:
x <= -2
This tells us that any value of x that is less than or equal to -2 will make the inequality true. We can represent this on a number line by shading all values less than or equal to -2
The circle at -2 indicates that -2 is included in the solution set, and the arrow pointing to the left indicates that all values less than -2 are also included in the solution set. Therefore, the number line that shows all of the values of x that make the inequality 3x - 1 <= -7 true is the one with all values less than or equal to -2 shaded.
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