Answer:
horizontal stretch
Step-by-step explanation:
yeye
Parent functions are the simplest form of a given function. Parent function have x as the term with the highest degree and a general form,
[tex]Y=ax+b[/tex]
Transformation of the function takes basic and changes it slightly with predetermined methods. This change will cause the graph of the function to be shifted or moved from the original position.
Given-
We have given the graphs and we have to identify the transformation of the parent function which is shown in the graph. For this we have an idea about the parent function and transformation of the function.
What is parent function?Parent functions are the simplest form of a given function. Parent function have x as the term with the highest degree and a general form,
[tex]Y=ax+b[/tex]
TransformationTransformation of the function takes basic and changes it slightly with predetermined methods. This change will cause the graph of the function to be shifted or moved from the original position.
Transformation of function is of different types.
Horizontal stretch, when graph is shifted towards right or left it is called the horizontal stretch transformation of the function. Vertical stretch, when graph is shifted towards up or down it is called the horizontal stretch transformation of the function.In the given graph the graph is shifted right and hence the transformation of the parent function is horizontal stretch.
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How many positive integers are there whose digits strictly increase from left to right?
There are 511 positive integers whose digits strictly increase from left to right.
To determine how many positive integers have digits that strictly increase from left to right, we need to consider combinations of digits. Since the digits must strictly increase, we cannot repeat any digit, and we can only use digits from 1 to 9.
Each number can be considered a unique combination of these digits, where the order of digits matters. For example, the digits {1, 2, 3} can only form the number 123. The total number of such combinations is given by the binomial coefficient C(9, k), where k is the number of digits.
For 1-digit numbers, the count is :C(9, 1) = 9For 2-digit numbers :C(9, 2) = 36For 3-digit numbers :C(9, 3) = 84And so on, up to 9-digit numbers which is :C(9, 9) = 1Summing these values, we get the total number of positive integers with strictly increasing digits :9 + 36 + 84 + 126 + 126 + 84 + 36 + 9 + 1 = 511Therefore, there are 511 positive integers whose digits strictly increase from left to right.Suppose that a single card is selected from a standard 52-card deck. What is the probability that the card drawn is a clubclub?
Now suppose that a single card is drawn from a standard 52-card deck, but it is told that the card is blackblack. What is the probability that the card drawn is a clubclub?
Answer:
The probability that the card drawn is a club is 0.25.
The probability that card drawn is a club, when it is given that the card is black is 0.5.
Step-by-step explanation:
In a standard deck of cards:
Total number of cards = 52
Total number of cards of each suit (club, spade,heart, diamond) = 13
The probability that the card drawn is a club is
[tex]P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]P=\frac{^{13}C_1}{^{52}C_1}=\frac{13}{52}=0.25[/tex]
Therefore the probability that the card drawn is a club is 0.25.
Let A and B represents the following events:
A : Card is black
B : Card is a club
Total number of black cards = 26
[tex]P(A)=\frac{26}{52}=\frac{1}{2}=0.5[/tex]
From the above parts
[tex]P(B)=0.25[/tex]
Total number of black club cards = 13
[tex]P(A\cap B)=\frac{13}{52}=\frac{1}{4}=0.25[/tex]
We need to find the probability that card drawn is a club, when it is given that the card is black.
[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]P(\frac{B}{A})=\frac{0.25}{0.5}=0.5[/tex]
Therefore the probability that card drawn is a club, when it is given that the card is black is 0.5.
At the movie theatre, child admission is $5.20 and adult admission is $9.80
. On Tuesday, 147 tickets were sold for a total sales of $1054.20. How many child tickets were sold that day?
Answer:
84 child tickets were sold
Step-by-step explanation:
Had they all been adult tickets, revenue would have been ...
$9.80 × 147 = $1440.60
It was less by ...
$1440.60 -1054.20 = $386.40
The child's ticket costs less by ...
$9.80 -5.20 = $4.60
so there must have been $386.40/$4.60 = 84 child tickets sold.
__
Replacing an adult ticket with a child ticket reduces the revenue by $4.60 without changing the number of tickets sold.
_____
You can let c represent the number of child tickets sold. Then (147 -c) is the number of adult tickets sold, and total revenue is ...
5.20c + 9.80(147 -c) = 1054.20
-4.60c +1440.60 = 1054.20 . . . . simplify
-4.60c = -386.40 . . . . . . . . . . . . . subtract 1440.60
c = 386.40/4.60 = 84
The Greek mathematician Eratosthenes (ca. 276-195 BC) measured the circumference of the earthfrom the following observations. He noticed that on a certain day the sun shone directly down a deep wellin Syene (modern Aswan). At the same time in Alexandrea, 500 miles north (on the same meridian), therays of the sun shone at an angle of 7.2° to the zenith. Use this information to find theradius and circumference of the earth.
Answer:
Radius of the Earth is 3978.8 Miles
Circumference of the Earth is 25000 Miles
Step-by-step explanation:
The angle of the sun shone at an angle of 7.2° to the zenith
This means that the angle of the sector of the circle is 7.2° (θ)
S = Length of the sector of the circle = 500 miles
r = radius of earth
Converting 7.2° to radians
[tex]\theta =7.2\frac{\pi}{180}[/tex]
[tex]S=r\theta\\\Rightarrow r=\frac{S}{\theta}\\\Rightarrow r=\frac{500}{7.2\frac{\pi}{180}}\\\Rightarrow r=3978.8\ Miles[/tex]
∴ Radius of the Earth is 3978.8 Miles
[tex]C=2\pi r\\\Rightarrow C=2\times \pi \frac{500}{7.2\frac{\pi}{180}}\\\Rightarrow C=25000\ Miles[/tex]
∴ Circumference of the Earth is 25000 Miles
The radius and circumference are respectively; r = 3978.86 miles and C = 25000 miles
What is the radius and circumference?
We are told that the angle of the sun shone at an angle of 7.2° to the zenith. Thus, we can liken this to the angle of a sector and so;
Angle of the sector of the circle; θ = 7.2° = 0.125664 rad
Length of the sector of the circle; S = 500 miles
Formula for length of arc is;
S = rθ
where;
S is length of arc
r is radius
θ is angle of sector in radians
Thus;
r = S/θ = 500/0.125664
r = 3978.86 miles
Formula for circumference is;
C = 2πr
C = 2 * π * 3978.86
C = 25000 miles
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Helppppppp please quickly
Answer:
For [tex]3,604\ books[/tex] the cost for both methods will be the same
Step-by-step explanation:
Let
y ------> the production cost
x ------> the number of books
we know that
First production Method
[tex]y=19.25x+22,427[/tex] -------> equation A
Second production Method
[tex]y=10.50x+53,962[/tex] -------> equation B
Solve the system of equations
Equate equation A and equation B and solve for x
[tex]19.25x+22,427=10.50x+53,962[/tex]
[tex]19.25x-10.50x=53,962-22,427[/tex]
[tex]8.75x=31,535[/tex]
[tex]x=3,604\ books[/tex]
In? 2008, a country used ?twenty-five percent or 100 million tons of all the grain grown that year to produce ethanol. How much grain was grown in the country in? 2008?
Answer:
400,000,000 tons
Step-by-step explanation:
You could reword this sentence to ask the question, "100,000,000 is 25% of how much?"
The word "is" means equals, the percent will be .25 in decimal form, the word "of" means to multiply, and "how much" is x, our unknown. In equation form, then, this looks like
100,000,000 = .25 × x
We will divide both sides by .25 to get that
x = 400,000,000
That's how much grain was grown in 2008
Answer: 400 million tons
Step-by-step explanation:
100 millions is 1/4 of 400 million
Tom and Shirley, working together can mow the lawn in 6 hours working alone Shirley takes three times as long as Tom how long does it take Tom to mow the lawn alone
Answer:
It would take Tom 8 hours alone
Step-by-step explanation:
We are looking at this basic equation:
Tom + Shirley = 8 hours
Tom takes x hours to cut the grass; this means that 1/x of the job gets done in 1 hour
It takes Shirley 3 times as long as Tom, so it takes her 3x hours to cut the grass; this means that 1/3x of the job gets done in 1 hour
If the total number of hours it takes them to do the job is 6 hours; this means that 1/6 of the job gets done in 1 hour
Looking back at the original basic equation, we will fill in our info:
[tex]\frac{1}{x}+\frac{1}{3x}=\frac{1}{6}[/tex]
We can solve for x by first finding the LCD and eliminating the denominators. The LCD is 6x, since all the denominators go into 6x evenly.
We will multiply the rational equation through by the LCD:
[tex]6x[\frac{1}{x}+\frac{1}{3x}=\frac{1}{6}][/tex]
Dividing each denominator into the LCD gives us:
6 + 2 = x so
x = 8
This means that it takes Tom 8 hours to do the job alone. It would take Shirley 24 hours alone. Ugh.
The time it would take Tom to mow the lawn alone is 3 hours
How to determine the value?From the information given;
Let Tom's working hours be x.
Let Shirley's working hours be y.
We have that;
Shirley and Tom work 6 hours together, this is expressed as;
x + y = 6
Given that Shirley work 3 hours alone, we have;
y = 3
Substitute the value of y as 3 in the equation
x + 3 = 6
x = 6 - 3
x = 3
Thus, the time it would take Tom to mow the lawn alone is 3 hours
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The vertex of this parabola Is at (-3,6) which of the following could be its equation
Step-by-step explanation:
the e standard form of parabola with vertex (h,k) is
y=a(x-h)²+k
here (h,k)=(-3,6)
so the answer to your question is
y=-3(x-(-3))²+6
y=-3(x+3)²+6
Answer:
Option D is correct.
Step-by-step explanation:
The vertex is (-3,6)
We will check which equation satisfies the given vertex.
A) y = -3(x-3)^2 - 6
if x = -3 then value of y should be 6
Checking:
y = -3(-3-3)^2 - 6
y = -3(-6)^2 - 6
y = -3(36) -6
y = -114
if x= -3, y ≠ 6
B) y = -3(x+3)^2 - 6
if x = -3 then value of y should be 6
Checking:
y = -3(-3+3)^2 - 6
y = -3(0)-6
y = -6
if x= -3, y ≠ 6
C) y = -3(x-3)^2 + 6
if x = -3 then value of y should be 6
Checking:
y = -3(-3-3)^2 + 6
y = -3(-6)^2 + 6
y = -3(36) + 6
y = -102
if x= -3, y ≠ 6
D) y = -3(x+3)^2 + 6
if x = -3 then value of y should be 6
Checking:
y = -3(-3+3)^2 + 6
y = -3(0)^2 + 6
y = 6
So, if x= -3, y =6 so, if the vertex of parabola is at (-3,6) the equation will be
y = -3(x+3)^2 + 6
So. Option D is correct.
A lopsided coin has a probability of 1/3 for coming up heads and 2/3 for coming up tails. On average, how many flips of this coin are needed to have both heads and tails appear at least once? Give your answer as a reduced fraction.
Answer with explanation:
For a Lopsided coin ,probability of getting Head is equal to [tex]\frac{1}{3}[/tex] For a Lopsided coin ,probability of getting Tail is equal to [tex]\frac{1}{3}[/tex].
→Probability of getting Tail > Probability of getting Head
→Coin is heavier from tail side and lighter from Head side.
→→We have to Calculate number of flips of coin that is needed to have both heads and tails appear at least once.
[tex]\rightarrow P(\text{Head})=\frac{1}{3}\\\\ \frac{1}{3} \times x=1\\\\x=3\\\\\rightarrow P(\text{Tail})=\frac{2}{3}\\\\ \frac{2}{3} \times y=1\\\\y=\frac{3}{2}[/tex]
→We need to find common multiple of 3 and [tex]\frac{3}{2}[/tex].
Least common multiple of 3 and [tex]\frac{3}{2}[/tex] is 6.
→So,on Average number of flips of this coin are needed to have both heads and tails appear at least once=6 tosses
You have recorded your car mileage and gasoline use for 5 weeks. Estimate the number of miles you can drive on a full 15-gallon tank of gasoline.
Answer:
I think its 21.6 or 22 (Mostly 21.6 though) Sorry if its not right but i'm mostly sure of it like this!
Complete the square for 3x2 - 12x = 9.
Answer:
[tex] x=2 \pm \sqrt{7} [/tex]
Step-by-step explanation:
Given this form ax^2+bx=k, here are my steps for completing the square while answer your question:
First step: Divide both sides by what is in front of x^2. You want the coefficient of x^2 to be 1. To do this for your question, divided both sides by 3.
This gives us x^2-4x = 3.
Second step: We are ready to begin the completing the square process at this step. We are going to add (b/2)^2 on both sides. For this question b=-4.
So we will be adding (-4/2)^2 on both sides.
This gives us x^2-4x+(-4/2)^2=3+(-4/2)^2.
Third step: I like to simplified the things inside the square and I do not actually apply the square at this step. It makes a later step easier in my opinion.
So this step gives us x^2-4x+(-2)^2=3+(-2)^2.
Fourth step: I'm actually going to write the left hand side as a square. Just drag the things that are inside the squares down into ( )^2.
This is what I mean x^2-4x+(-2)^2=(x-2)^2.
So at the end of this step we have (x-2)^2=3+(-2)^2.
Fifth step: I'm going to simplify the right hand side.
This step gives us (x-2)^2=7
Sixth step: We are ready to square root both sides.
This gives us [tex] x-2=\pm \sqrt{7} [/tex]
Seveth step: Get x by itself like you normally would with a linear equation. My step here is just to add 2 on both sides.
Final answer: [tex] x=2 \pm \sqrt{7} [/tex]
[tex]3x^2-12x=9\\x^2-4x=3\\x^2-4x+4=7\\(x-2)^2=7\\x-2=\sqrt7 \vee x-2=-\sqrt7\\x=2+\sqrt7\vee x=2-\sqrt7[/tex]
Find the area of a sector with a central angle of 170° and a radius of 17 millimeters. Round to the nearest tenth. Question 9 options: 857.5 mm2 100.9 mm2 428.7 mm2 25.2 mm2
Answer:
428.7 mm²
Step-by-step explanation:
The area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{170}{360}[/tex]
= π × 17² × [tex]\frac{17}{36}[/tex]
= 289π × [tex]\frac{17}{36}[/tex]
= [tex]\frac{289(17)\pi }{36}[/tex] ≈ 428.7 mm²
The area of a sector with a central angle of 170° and a radius of 17 mm is calculated using the sector area formula, resulting in approximately 428.7 mm², rounded to the nearest tenth.
To find the area of the sector, we use the formula [tex]\( \text{Area} = \frac{\text{Central Angle}}{360\°} \times \pi \times \text{Radius}^2 \)[/tex]. Substituting the given values, we get [tex]\( \text{Area} = \frac{170\°}{360\°} \times \pi \times 17^2 \)[/tex]. Simplifying, we have [tex]\( \text{Area} = \frac{17^2}{2} \times \pi \)[/tex]. Evaluating this expression, we find [tex]\( \text{Area} \approx 428.7 \)[/tex] mm². Therefore, the area of the sector, rounded to the nearest tenth, is approximately 428.7 mm². This calculation represents the portion of the circle enclosed by the given central angle and radius, providing the area of the sector.
Zoe has $3.25 worth of dimes and quarters. She has 6 more quarters than dimes. Determine the number of dimes and the number of quarters that Zoe has.
Answer:
quarters = 6+x
dimes = x
Total value = 325
Dime value = 10
Quarter value = 25
Step-by-step explanation:
25x+150+10x=325 (simplify)
35x=175
x=5
6+5 = 11
Hence Zoe has 5 dimes and 11 quarters.
Hope this helps!!❤
Determine the slope of the line that contains the given points T(4,6) a V(8,7)
A) -1/2
B) 4
C) 1/4
D) -4
Finding the slope using two points:
The formula for slope is
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this case...
[tex]y_{2} =7\\y_{1} =6\\x_{2} =8\\x_{1} =4[/tex]
^^^Plug these numbers into the formula for slope...
[tex]\frac{7 - 6}{8 - 4}[/tex]
C) [tex]\frac{1}{4}[/tex]
^^^This is your slope
Hope this helped!
~Just a girl in love with Shawn Mendes
Which of the following expressions best represents the dot product of two vectors? Select all that apply.
axbx + ayby
|a||b|(cosαcosβ + sinαsinβ)
|a||b|cos(α + β)
|a||b|cos(α - β)
Answer:
axbx + ayby |a||b|(cosαcosβ + sinαsinβ) |a||b|cos(α - β)Step-by-step explanation:
The dot product is the sum of products of the corresponding coordinate values:
[tex]\text{\bf{a}$\cdot$\bf{b}}=a_{x}b_{x}+a_{y}b_{y}[/tex]
The value of this can also be written in terms of the magnitudes of the vectors and the angle θ between them:
|a|·|b|·cos(θ)
But the angle between the vectors is the same as the difference of their individual angles, θ = α - β, so this can also be written as ...
|a|·|b|·cos(α-β)
And the trig identity for the cosine of the difference of angles lets us write the above as ...
= |a|·|b|·(cos(α)cos(β) +sin(α)sin(β))
In triangle ABC a=2, c=3, B=95 degrees. Find the size of the smallest angle
Answer:
A ≈ 32°
Step-by-step explanation:
You are given two sides and the angle between them, so the law of cosines applies. The measure of side b can be found to be ...
b² = a² + c² -2ac·cos(B)
b² = 2² +3² -2·2·3·cos(95°) ≈ 14.0459
b ≈ 3.74778
Then the law of sines can help you find angle A, the angle opposite the shortest side.
sin(A)/a = sin(B)/b
A = arcsin(a/b·sin(B)) = arcsin(2/3.74778·sin(95°)) ≈ 32.11°
A ≈ 32°
The smallest angle is about 32°.
Let's say that you are interested in opening an inverstment account that you will keep for at least 20 years. Compare the future values of that account using simple interest and compound interest if the interest rate is 2.6% and is compounded annually. Which type of interest (simple or compound) would you choose for your investment and why?
Answer:
over 20 years, the value of the compound interest account is about 10% moremy choice is the compound interest account because of its higher earningsStep-by-step explanation:
For principal amount P, the future value of the simple interest account will be ...
P(1 + rt) = P(1 + .026·20) = 1.52P
The future value of the compound interest account will be ...
P(1 +r)^t = P(1.026^20) ≈ 1.6708875P
The value of the compound interest account is about 10% greater after 20 years.
I would choose the compound interest account because it has a higher rate of return.
Write the standard form of the equation that is parallel to y = -6x + 5 and goes through point (4, 4).
6x + y = 28. The standard form of the equation that is parallel to y = -6x + 5 and goes through point (4, 4) is 6x + y = 28.
The equation is written in the slope-intercept form y = mx +b. So:
y = -6x + 5
The slope m = -6
Since the slopes of parallel lines are the same, we are looking for a slope line m = -6 and goes through point (4, 4).
With the slope-intercept form:
y = mx + b
Introducing the slope m = -6:
y = -6x + b
Introducing the point (4, 4):
4 = -6(4) + b
b = 4 + 6(4)
b= 24 + 4
b = 28
Then
y = -6x + 28
write the equation in standard form ax + by = c:
y = -6x + 28
6x + y = 28
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
Answer:
c
Step-by-step explanation:
Answer:
answer would be The mean must have a mean of 0 and a standard deviation of 1. hope this helps
Step-by-step explanation:
Can u guys PLEASE do this question 29
Answer:
264 transistors.
Step-by-step explanation:
By proportion the total number made if 16 are faulty is (35/2) * 16
= 280.
The number of good ones is 280 - 16
= 264 transistors.
Answer:
264 good ones
Step-by-step explanation:
2 in 35 are faulty = in a batch of 35, 2 will be faulty = there are 33 good for every 2 faulty ones there are
16 faulty have been made - to figure out how many batches there have been do 16/2=8
8 batches of 35, 8 × 35 = 280 total
280 total - 16 faulty = 264 good
OR do 8 batches × 33 good per batch = 264 good
at least thats how i interpreted it!
A small amphitheater has 8 rows that have 42 seats in each row. If an act needs to keep the first row empty but has all the rest of the seats sold, then what expression can be used to find the total attendance? 8 × 40 + 8 × 2 8 × 40 – 8 × 2 7 × 40 + 7 × 2 7 × 40 – 7 × 2
The expression that shows the total attendance is 7 x 40 + 7 x 2.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
Given that,
Total number of rows = 8.
Number of seats in each row = 42.
Total number of seats = 42 x 8 = 336.
Since, an act needs to keep first row empty, but rest of the seats sold.
So the remaining seats = 336 - 42 = 294.
So, the expression for the total attendance can be given as,
7 x 40 + 7 x 2 = 280 + 14 = 294.
The required expression is 7 x 40 + 7 x 2.
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Find the longer leg of the triangle.
A. 3
B. [tex]\sqrt{3}[/tex]
C. 9
D. [tex]\sqrt{6}[/tex]
Answer:
Choice A. 3.
Step-by-step explanation:
The triangle in question is a right triangle.
The length of the hypotenuse (the side opposite to the right angle) is given. The measure of one of the acute angle is also given.As a result, the length of both legs can be found directly using the sine function and the cosine function.
Let [tex]\text{Opposite}[/tex] denotes the length of the side opposite to the [tex]30^{\circ}[/tex] acute angle, and [tex]\text{Adjacent}[/tex] be the length of the side next to this [tex]30^{\circ}[/tex] acute angle.
[tex]\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}[/tex].
Similarly,
[tex]\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}[/tex].
The longer leg in this case is the one adjacent to the [tex]30^{\circ}[/tex] acute angle. The answer will be [tex]3[/tex].
There's a shortcut to the answer. Notice that [tex]\sin{30^{\circ}} < \cos{30^{\circ}}[/tex]. The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the [tex]30^{\circ}[/tex] angle will be the longer leg. There will be no need to find the length of the opposite leg.
Does this relationship [tex]\sin{\theta} < \cos{\theta}[/tex] holds for all acute angles? (That is, [tex]0^{\circ} < \theta <90^{\circ}[/tex]?) It turns out that:
[tex]\sin{\theta} < \cos{\theta}[/tex] if [tex]0^{\circ} < \theta <45^{\circ}[/tex];[tex]\sin{\theta} > \cos{\theta}[/tex] if [tex]45^{\circ} < \theta <90^{\circ}[/tex];[tex]\sin{\theta} = \cos{\theta}[/tex] if [tex]\theta = 45^{\circ}[/tex].Answer:
A
Step-by-step explanation:
Since the triangle is right use the cosine ratio
cos30° = [tex]\frac{adjacent }{hypotenuse}[/tex] = [tex]\frac{adj}{2\sqrt{3} }[/tex], so
[tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{adj}{2\sqrt{3} }[/tex]
Multiply both sides by 2[tex]\sqrt{3}[/tex]
adj = [tex]\frac{\sqrt{3} }{2}[/tex] × 2[tex]\sqrt{3}[/tex] = 3
2x+y= 3
x-2y= -1
If equation two is multiplied by -2, and then the equations are added, the result is
Answer:
5y = 5
Step-by-step explanation:
When the second equation is multiplied by -2, it becomes ...
-2(x -2y) = -2(-1)
-2x +4y = 2
Adding this to the first equation gives ...
(2x +y) +(-2x +4y) = (3) +(2)
2x +y -2x +4y = 5 . . . . . . . . . eliminate parentheses
5y = 5 . . . . . . . . . . . . . . . . . . .collect terms
Which equation represents a circle with the same center as the circle shown but with a radius of 2 units?
Answer:
Option 2: (x-4)^2 + (x-5)^2 = 4
Step-by-step explanation:
The given circle's center is: (4,5)
And the radius is 4 units.
We are told in the question that the center will remain same only the radius will be changed.
The center is denoted by (h,k) = (4,5) and radius is 2
Standard equation of circle is:
(x-h)^2 + (y-k)^2 = r^2
So the equation of another circle with same center and radius of 2 units will be:
(x-4)^2 + (x-5)^2 = 2^2
(x-4)^2 + (x-5)^2 = 4
Hence option 2 is correct ..
Information is given about a polynomial f left parenthesis x right parenthesis whose coefficients are real numbers. Find the remaining zeros of f. Degree 4; zeros: i comma 5 plus i Enter the remaining zeros of f.
Answer:
remaining zeros: negative i comma 5 minus i
Step-by-step explanation:
The remaining two zeros are the conjugates of the two zeros given. That brings the total number to 4 zeros, consistent with the number of zeros expected for a 4th-degree polynomial.
The conjugate of a complex number has the same real part and the opposite imaginary part.
Answer:
-i, 5-i
Step-by-step explanation:
Given that a function f(x) has only real coefficients and also of degree 4.
Since any polynomial with real roots have imaginary roots only with conjugate pairs, we can find other two roots easily
Degree of polynomial = 4
No of roots = 4
GIven roots are i, 5+i
Conjugate of the given roots are -i, 5-i
Hence remaining zeroes of f are -i, 5-i
$1000 is invested at 8%/a compounded daily for 10 years. What is the total interest earned?
Please help
[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &10 \end{cases} \\\\\\ A=1000e^{0.08\cdot 10}\implies A=1000e^{0.8}\implies A=2225.54~\hfill \stackrel{interest = A - P}{1225.54}[/tex]
btw, we could have used the compound formula just the same, by simply using a compounding cycle of 365, namely daily, assuming a year has 365 days.
Triangle ABC has coordinates A (0, 1) B (0, 2) and C (3,2). If Triangle ABC is equivalent to triangle EDF, what is the measure of DF?
3
3.2
4
4.4
Answer:
3
Step-by-step explanation:
Segment BC corresponds to segment DF. The length of BC is the distance between coordinates (0, 2) and (3, 2). These points are on the same horizontal line (y=2), so the distance between them is the difference of their x-coordinates: 3 - 0 = 3.
Answer:
DF = 3
Step-by-step explanation:
If ABC is equivalent to EDF, then DF is equivalent to BC, which form the following ordered pairs:
D = (0,2)
F = (3,2)
It can be seen that both pairs have the same value of "y" or second value, that is 2.
As a rule, when the points are located on the y-axis (of the ordinates) or on a line parallel to this axis, the distance between the points corresponds to the absolute value of the difference of their ordinates.
So,
DF = D(x) + F(x) = 0 + 3 = 3
If we apply the equation of the distance between two points we get the same result,
[tex]DF=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }=\sqrt{(3-0)^{2}+(2-2)^{2} }=\sqrt{(3)^{2}+(0)^{2} }=\sqrt{9+0 }=\sqrt{9}=3[/tex]
Hope this helps!
What is the radius of the following circle?
Answer:
r = +2√3
Step-by-step explanation:
The equation of a circle with center at (0, 0) and radius r is
x^2 + y^2 = r^2.
Here we have
x^2 + y^2 = 12,
and so we can deduce that r^2 = 12. Then r = +2√3.
Answer:
The radius is: [tex]2\sqrt{3}[/tex]
Step-by-step explanation:
The equation of a circle in center-radius form is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where the center is at the point (h, k) and the radius is "r".
So, given the equation of the circle:
[tex]x^2+y^2=12[/tex]
You can identify that:
[tex]r^2=12[/tex]
Then, solving for "r", you get that the radius of this circle is:
[tex]r=\sqrt{12}\\\\r=2\sqrt{3}[/tex]
URGENT PLEASE HELP WITH THIS MATH QUESTION ALSO IT WOULD BE GREAT IF SOMEONE CAN HELP ME WITH SOME OTHER QUESTIONS
Answer:
Area=14.22π
Step-by-step explanation:
Area=πr²(C/360)
C is the central angle in degrees
r is the radius of the circle of which the sector is part.
Area = π(8)²(80/360)
Area=π(64)(0.2222)
Area=π(14.22)
Area=14.22π....
A wholesaler requires a minimum of 4 items in each order from its retail customers. The manager of one retail store is considering ordering a certain number of sofas, x, and a certain number of pillows that come in pairs, y. Which graph represents the possible combinations of sofa and pillow orders the manager can have?
Answer:
It is the last graph: solid line, shaded area over the line x = 2 - x/2Explanation:
1) Set the algebraigic expression that represents the combinations of sofa and pillow orders:
Number of sofas: x (given)Number of pillows: 2y (given, since they come in pairs)Number of items = number of sofas + number of pillows = x + 2yMinimum of 4 items in each order (given) ⇒ x + 2y ≥ 42) Predict the graph of the inequality x + 2y ≥ 4
The border line is the equation x + 2y = 4You can choose two points to draw a lineChoose the axis-intercepst:x = 0 ⇒ 2y = 4 ⇒ y =4/2 ⇒ y = 2 ⇒ point (0,2)
y = 0 ⇒ x = 4 ⇒ point (4,0)
Then the lines goes through (0,2) and (4,0) ... [the four graphs meet this]
The shading area is above the line because when you solve for y you get y ≥ 2 - x/2, and the line is included because the "equal to" part of the symbol (≥ means greater than or equal to). To state that the line is included the graph uses a continous line instead of a dotted one.3) Conclusion:
That means that the correct graph is the last one: solid line, shaded area over the line y = 2 - x/2.
Note: a more detailed graph would include the fact that the items cannot be negative, i.e. x ≥ 0 and y ≥ 0, which would result in that the shaded area would be on the first quadrant.
Answer: D
Step-by-step explanation: