The line segment is dilated by a factor of 1/2 with respect to the origin. What is the length of the dilated line segment?
A. 1 unit
B. 2 units
C. 3 units
D. 4 units
Answers
The length of the dilated line segment is 2 units. ( option B)
A scale factor is a ratio that describes the proportional change in size between two similar geometric figures.
Scale factor = Dimension of new length /dimension of original length
The dimension of the original length is 4 units
scale factor = 1/2
let the new length be x
Therefore;
1/2 = x/4
2x = 4
x = 4/2 = 2units
Therefore, the length of the dilated segment is 2units
Related Questions
Melissa needs to memorize words on a vocabulary list for Russian class. She has memorized 30 of the words, which is five-sixths of the list. How many words are on the list?
Answers
[tex] \frac{5}{6} x=30[/tex]
Solve for x by isolating it. First we multiply both sides by 6 to cancel out the one-sixth.
[tex]5x = 180[/tex]
Next divide both sides by 5 to cancel out the 5 being multiplied to the x.
[tex]x = 36[/tex]
The answer is 36 words.
The list has 36 words
Explanation:
Assume that the number of words on the list is x.
We are given that:
5/6 of the number of words on the list is equal to 30 words.
This means that:
(5/6)*x = 30
Solve for x as follows:
(5/6)*x = 30
5x = 6*30
5x = 180
x = 180/5
x = 36
Hope this helps :)
Isabella is solving the equation 4x^2=13x−3 with the quadratic formula.
Which values could she use for a, b, and c?
A. a = 4, b = −13, c = 3
B. a = 4, b = 3, c = −13
C. a = 4, b = 13, c = −3
D. a = 4, b = −3, c = 13
Answers
So, we first need to rearrange Isabella's equation to match the latter format:
4x^2=13x-3
4x^2-13x=-3
4x^2-13x+3=0
The values that match up with the quadratic equation are a=4, b=-13, c=3, therefore your answer is A
values could she use for a, b, and c a = 4 b = -13 c = 3
Step-by-step explanation:
We have been given the equation
4x²=13x-3
Subtract 4x² to both sides of the equation
0=-4x²+13x-3
Multiply both sides of the equation by -1
4x²-13x+3=0
The general equation of a quadratic equation is ax²+ bx +c=0
Comparing this equation with above equation 4x²-13x+3=0
a = 4
b = -13
c = 3
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Find the following.
a. The side length of a cube with a volume of 125 units^3.
b. The volume of a cube with a side length of 4 units.
Answers
b) The volume is 64 cubic units. Multiply the side length 4 by itself three times: 4*4*4 = 64.
sorry wrong problem if ab =58 find the value of x
Answers
5x - 2 = 58
5x = 60
x = 12
answer
x = 12
Answer:
x=12
Step-by-step explanation:
if ab =58 find the value of x
The length of AB= 58
Given : AC= 3x-6
CB= 2x+4
[tex]AC + CB=AB[/tex]
Now replace the expressions
[tex]3x-6+2x+4=58[/tex]
now we solve for x, combine like terms
[tex]5x-2=58[/tex]
Add 2 on both sides
[tex]5x=60[/tex]
Divide both sides by 5
x=12
Which expressions are completely factored? Select each correct answer. 30a6−24a2=3a2(10a4−8) 16a5−20a3=4a3(4a2−5) 12a3+8a=4(3a3+2a) 24a4+18=6(4a4+3)
Answers
When factoring an expression, we need to identify the Greatest Common Factor of the expression (GCF). By definition, GCF is the product of prime factors involved with its Lowest Exponent.
We need to divide each term by the GCF to get the expression inside the parenthesis.
[tex] 30a^6-24a^2\\ GCF\; is \; 6a^2\\ \\ 30a^6-24a^2=6a^2(\frac{3a^6}{6a^2} -\frac{24a^2}{6a^2} )=6a^2(5a^4-4)\\ ---------------------\\ \\ 16a^5-20a^3\\ GCF \; is \; 4a^3\\ \\ 16a^5-20a^3=4a^3(\frac{16a^5}{4a^3} -\frac{20a^3}{4a^3})=4a^3(4a^2-5) \\ ---------------------\\ \\ 12a^3+8a\\ GCF \; is \; 4a\\ \\ 12a^3+8a=4a(\frac{12a^3}{4a}+\frac{8a}{4a})=4a(3a^2+2)\\ ---------------------\\ 24a^4+18\\GCF \; is \; 6\\\\24a^4+18=6(\frac{24a^4}{6} +\frac{18}{6})=6(4a^4+3) \\ --------------------- [/tex]
Conclusion:
From above we can conclude that the below expressions are factored completely
[tex] 16a^5-20a^3=4a^3(4a^2-5)\\ \\ 24a^4+18=6(4a^4+3) [/tex]
What is the point of maximum growth rate for the logistic function f(x) ?
Answers
algebra 2 function operations (link)
Answers
g(x) = x - 1
f(x).g(x) - [f(x) + g(x)] = (2x^2 + x - 3) (x - 1) - [2x^2 + x - 3 + x - 1]
f(x).g(x) - [f(x) + g(x)] = (2x^3 - 2x^2 + x^2 - x - 3x + 9) - [2x^2 + 2x - 4]
f(x).g(x) - [f(x) + g(x)] = (2x^3 - x^2 - 4x + 9) - [2x^2 + 2x - 4]
f(x).g(x) - [f(x) + g(x)] = 2x^3 - x^2 - 4x + 9 - 2x^2 - 2x + 4
f(x).g(x) - [f(x) + g(x)] = 2x^3 - 3x^2 - 6x + 13
Gina paints beach scenes on notecards. She sells packages of 8 notecards for $8 for one package, $16 for 2 packages, and $24 for 3 packages. Which equation is the rule for the pattern if n is the number of packages and d is the selling price in dollars?
Answers
one notecard costs $8
2 notecards cost $16
3 notecards cost $24
if n - number of packages
d - selling price in dollars
We can see that with each additional notecard bought the cost increases by $8
therefore there's a proportional relationship between n and d
As n increases, d increases by the same amount.
if we put it in an equation,
d = 8*n
n - 1 package and d is 8
if n - 2
d = 8*2
d = 16
Therefore we can use the following equation;
d=8n
is 1 over 3 rational
Answers
A pendulum has 887 J of potential energy at the highest point of its swing. How much kinetic energy will it have at the bottom of its swing?
Answers
If four friends can eat four cakes in four days, then how many cakes can 10 friends eat in 10 days?
Answers
Convert 59 degrees in Fahrenheit to Celsius temperature using the formula . 27°C 15°C 12°C 8°C
Answers
59 degrees Celsius equals 15 degrees Fahrenheit.
“15 C” is the answer.
59-32= 27
27*5/9= 15
The formula is: C= F-32*5/9
I hope this helps!
~kaikers
59 degrees Fahrenheit is equivalent to 15 degrees Celsius.
We have,
To convert a temperature in Fahrenheit to Celsius, you can use the formula:
°C = (°F - 32) x (5/9)
Let's apply this formula to convert 59 degrees Fahrenheit to Celsius:
°C = (59 - 32) x (5/9)
Simplifying the equation:
°C = 27 x (5/9)
°C = 135/9
°C = 15
Therefore,
59 degrees Fahrenheit is equivalent to 15 degrees Celsius.
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devise a plan for simplifying th fourth root of a number that is not a perfect fourth power.
Answers
Final answer:
To simplify the fourth root of a non-perfect power, use a calculator to raise the number to the power of 0.25, or calculate the square root twice. For non-integer powers, calculate roots with corresponding fractional exponents. Request assistance from your instructor if necessary.
Explanation:
Simplifying the Fourth Root of Non-Perfect Powers
When simplifying the fourth root of a number that is not a perfect fourth power, you can utilize the power function on a calculator. This involves raising numbers to the power of 0.25, which equates to calculating the fourth root. For example, using the y* button (or equivalent) you can calculate the fourth root of any number by raising it to the power of 0.25. This is analogous to how raising a number to the 0.5 power gives us the square root of that number. If your calculator doesn't have this function, another technique is to calculate the square root of the number twice, since the fourth root is essentially the square root of the square root.
To work through a non-integer power, like 31.7, you can find the tenth-root of 3 by raising it to the power of 0.1 and then raise the result to the 17th power. Similarly, for expressions with fractional exponents like x0.5, you can interpret this as the square root of x. Understanding that fractional powers represent roots can help in simplifying complex expressions without a calculator as well.
If you are dealing with equilibrium problems or other scenarios that require finding roots of numbers, it's crucial to be comfortable with these techniques. If you are unsure about how to perform these operations, don't hesitate to ask for assistance from your instructor. Developing a natural and forgiving relationship with numbers, and only representing precision as needed, is also an important aspect of working with mathematical problems.
Which graph shows the solution to the inequality -x + 2 > 1
Answers
-x+2+x > 1+x .... add x to both sides
2 > 1+x
x+1 < 2
x+1-1 < 2-1 ... subtract 1 from both sides
x < 1
After solving for x, we get x < 1
To graph this, plot an open circle at 1 on the number line and shade to the left of this value. The open circle indicates that 1 is not part of the solution set.
If your teacher requires you to graph this on an xy grid, then draw a vertical line through 1 on the x axis. Make this vertical line a dashed line. Then shade the entire region to the left of this dashed line. Any point in this shaded region will have an x coordinate that is less than 1. The dashed line acts like the open circle. The dashed line tells the reader "any point on this dashed line is not part of the solution set"
You purchase an item to sell in your store. The item costs you $6.45. You mark the item up 20%, but later run the item on sale at 5% off the marked price.If your customer must pay 6% sales tax, what will be the total amount paid by the customer for the item?
Answers
6.45 * 1.2 = 7.74
You take off 5% which by the same reasoning (almost) means p/1.05
7.74 / 1.05 = 7.37
Now you need a sales tax
7.37 * 1.06 = 7.81 dollars.
Answer: The customer paid 7.81 <<<<=====
a speed of limit of 100 kilometers per hour is approximately equal to 62 miles per hour predict the following measures round your answers to the nearest whole number
a. a speed limit in mph for a speed limit of 75 kph
b. a speed limit in kph for a speed limit of 20 mph
Answers
The ratio is 1.6kph for every 1mph so for the first one you divide by 1.6 and the second you multiply
Answer:
a. 46.5 mph
b. 32.3 kph
Step-by-step explanation:
If the speed limit is 100 km/hour we and this equals 62 mile per hour we can determine how many kilometers is in miles and vice versa:
WE can do this as:
[tex]62/100=0.62[/tex]
Therefore the 0.62 miles per kilometer
a) For 75 kph we can use the conversion we determine to convert to miles per hour:
[tex]75*0.62=46.5[/tex]
It takes a speed limit of 46.5 mph for a 75 kph limit
b) For 20 mph we can use the conversion we determine to convert to kilometers per hour:
[tex]20/0.62=32.3[/tex]
It takes a speed limit of 32.3 kph for a 20 mph limit
find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule A(n)=-6+(n-1)(1/5)
Answers
A(4) = -6 +(4 -1)*(1/5) = -5 2/5
A(10) = -6 +(10 -1)*(1/5) = -4 1/5
The formula that represents the nth term of a arithmetic sequence is given by:
[tex]A(n)=-6+(n-1)(\dfrac{1}{5})[/tex]
Now, we are asked to find the first, fourth, and tenth terms of the arithmetic sequence.
i.e. we are asked to find the value of A(n) when n=1 ,4 and 10
when n=1 we have:[tex]A(1)=-6+(1-1)(\dfrac{1}{5})\\\\i.e.\\\\A(1)=-6+0\\\\i.e.\\\\A(1)=-6[/tex]
now when n=4 we have:[tex]A(4)=-6+(4-1)\times (\dfrac{1}{5})\\\\i.e.\\\\A(4)=-6+3\times \dfrac{1}{5}\\\\i.e.\\\\A(4)=-6+\dfrac{3}{5}\\\\i.e.\\\\A(4)=\dfrac{-6\times 5+3}{5}\\\\i.e.\\\\A(4)=\dfrac{-30+3}{5}\\\\i.e.\\\\A(4)=\dfrac{-27}{5}[/tex]
when n=10 we have:[tex]A(10)=-6+(10-1)\times (\dfrac{1}{5})\\\\i.e.\\\\A(10)=-6+9\times \dfrac{1}{5}\\\\i.e.\\\\A(10)=-6+\dfrac{9}{5}\\\\i.e.\\\\A(10)=\dfrac{-6\times 5+9}{5}\\\\i.e.\\\\A(10)=\dfrac{-30+9}{5}\\\\i.e.\\\\A(10)=\dfrac{-21}{5}[/tex]
Which is the focus of a parabola with equation y2=-12x
Answers
y²=-12x
the vertex is the point (0,0)------------- > see the attached figure
standard form: (y-k)^2=4p(x-h), with (h,k) being the (x,y) coordinates of the vertex.
vertex(0,0)
4p=-12---- > p=-12/4
p=-3
Focus:(-3,0)
the answer is (-3,0)
Easy question, decent amount of points! 25 points, if you're curious!
Be quick or it is gone.
Answers
slope of AB = 2/(-5) = -2/5
slope of AC = -2/(-4) = 1/2
slope of BC = -4/1 = -4
No two slopes have a product of -1, so no two sides are perpendicular.
Therefore, the triangle is not a right triangle.
How might your life insurance premiums depend upon when you initially purchase the policy?
Answers
Answer:
The age you are when you purchase life insurance is the biggest factor in how much you will have to pay. The premium amount typically increases about 8% to 10% for every year of age. The older you are, the more expensive you are to insure. When you are in your 40s, your rates increase from 5%-8% and when you are over 50, your rates increase by 9%-12% each year.
Step-by-step explanation:
Answer:
The Life insurance premium totally depends on your age when you will be purchasing it.
Step-by-step explanation:
Age is a significant factor in purchasing the policy. Age can be directly related to the rate of premium in the term plan or in the insurance. The average increase in the rate when it is calculated per year is about 8 to 10 percent. {Told by Ted Bernstien}.
According to the common theories, when you are in your 40's, then the rate will be increased around 5 to 8 percent, and when you are in your 50's it will be about 9 to 12 percent if you calculated it yearly.
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A parking lot charges $1.50 for the first hour of parking, and 55 cents for each additional half hour . how much would it cost to park a car from 12:45 pm to 6:15 pm
Answers
The parking cost for the specified duration would be $6.70.
Explanation:The parking fee consists of a base charge of $1.50 for the first hour. In this case, the car is parked for 5.5 hours (from 12:45 pm to 6:15 pm). The first hour is covered by the base charge, and the remaining 4.5 hours are billed as subsequent half-hours. For each half-hour, there is an additional charge of 55 cents. So, for the subsequent 4.5 hours, the additional charge is calculated as follows:
[tex]\[4.5 \times \$0.55 = \$2.475.\][/tex]
Adding this to the base charge:
$1.50 + $2.475 = $3.975.
Therefore, the total parking cost for the specified duration is $1.50 (for the first hour) + $2.475 (for the subsequent 4.5 hours), resulting in a final cost of $6.70.
This calculation ensures that the parking fee is accurately determined based on the initial hourly rate and subsequent half-hourly charges. The approach allows for a clear breakdown of the cost structure, providing transparency for users and ensuring fairness in the billing process.
Complete Question:
A parking lot implements a fee structure of $1.50 for the first hour of parking and an additional charge of 55 cents for each subsequent half-hour. If a car is parked from 12:45 pm to 6:15 pm on the same day, how much would the parking cost for this duration?
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The table below shows the quiz grades for two students.
Drew 90 81 86 79 97 84 92
Nancy 96 68 91 94 69 99 92
Which statement is true about the data above?
* The students have the same mean, but Nancy's quiz grades have a higher interquartile range.
* The students have the same mean, but Drew's quiz grades have a higher interquartile range.
* The students' grades have the same interquartile range, but Drew has a higher mean.
* The students' grades have the same interquartile range, but Nancy has a higher mean.
Answers
data set for Drew : [90,81,86,79,97,84,92], sorted : [79,81,84,86,90,92,97]
mean, μ 1 =(79+81+84+86+90+92+97)/7=87
Interquartile range, IQR 1 = (92-81)=11
data set for Nancy: [96,68,91,94,69,99,92], sorted : [68,69,91,92,94,96,99]
mean, μ 2 = (68+69+91+92+94+96+99)/7=87 Therefore the means are the same
Interquartile range, IQR 2 = 96-69 = 27 Therefore Nancy has a higher IQR
Note: There are different ways to calculate quartiles. Above method excludes median, which is how it is taught in many schools.
How many ways can you choose the 5 cards out of a 52 card deck?
Answers
There are 2,598,960 ways to choose 5 cards out of a 52-card deck.
Explanation:To determine the number of ways to choose 5 cards out of a deck of 52 cards, we can use the concept of combinations. In this case, order doesn't matter, so we use the formula for combinations. The formula is:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items to choose from and r is the number of items to be chosen.
For this question, n = 52 (number of cards in the deck) and r = 5 (number of cards to choose). We can plug these values into the formula to calculate the number of ways:
C(52, 5) = 52! / (5!(52-5)!) = 2,598,960
So, there are 2,598,960 ways to choose 5 cards out of a 52-card deck.
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The number of ways to choose 5 cards from a deck of 52, irrespective of order, is 2,598,960. This number is calculated using the combination formula in combinatorics.
Explanation:This question relates to the field of Mathematics known as combinatorics, specifically the concept of combinations. When we choose 5 cards out of a 52-card deck, we're not interested in the order in which the cards are drawn, so we use combinations. We use the notation C(n, k), where n is the total number of items, and k is the number of items to choose.
The formula for finding combinations is C(n, k) = n! / [k!(n-k)!]. In this case, n=52 (the total number of cards in the deck) and k=5 (the number of cards we are selecting). Plug these values into the formula to get C(52, 5) = 52! / [5!(52-5)!] = 52! / (5!47!) = 2,598,960
So, there are 2,598,960 ways to choose 5 cards out of a 52 card deck. This number takes into account all possible combinations of cards, without consideration of order or repetition.
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Solve for a.
(a+6)^2=49
A −13 and 1
B −3 √6 and 3 √6
C −1 and 13
D −√43 and √43
Answers
(a+6)(a+6) = 49
a^2 + 6a + 6a + 36 = 49
a^2 + 12a - 13 = 0
(a-1)( a+13) = 0
a-1 =0
a = 1
a+13= 0
a = -13
The answer is A.
The solutions for a are a=1 and a=−13. So the correct answer is A. -13 and 1.
To solve the equation [tex]\( (a+6)^2 = 49 \)[/tex], follow these steps:
1. Take the square root of both sides:
[tex]\[ \sqrt{(a+6)^2} = \sqrt{49} \][/tex]
2. Consider both positive and negative roots:
[tex]\[ a + 6 = \pm 7 \][/tex]
3. Solve for ( a ):
For ( a + 6 = 7 ):
[tex]\[ a = 7 - 6 = 1 \][/tex]
For ( a + 6 = -7 ):
[tex]\[ a = -7 - 6 = -13 \][/tex]
So, the solutions for ( a ) are ( a = 1 ) and (a = -13).
Therefore, the correct answer is A. -13 and 1.
Solve (4 - x ≤ -1) ∩ (2 + 3x ≥ 17). Click on the graph until the solution set appears.
Answers
The solution set appears at x ≥ 5 for (4 - x ≤ -1) ∩ (2 + 3x ≥ 17).
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
The symbol ∩ represents an intersection or common between them.
Given, (4 - x ≤ -1) ∩ (2 + 3x ≥ 17).
( x ≥ 5) ∩ ( x ≥ 5).
So, x ≥ 5.
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The function f(x)=-√-x is shown on the graph. Which statement is correct? The range of the graph is all real numbers greater than or equal to 0. The domain of the graph is all real numbers greater than or equal to 0. The range and domain of the graph are the same. The domain of the graph is all real numbers.
Answers
The correct option is: The range and domain of the graph are the same.
Explanation
Given function is: [tex]f(x) = -\sqrt{-x}[/tex]
The inside term of a square root can't be negative, it will be always 0 or positive. That means, [tex]-x \geq 0[/tex] or [tex]x\leq 0[/tex]
So, the Domain of the function is : "All real numbers such that [tex]x\leq 0[/tex]"
Now, if x=0, then f(x) =0 and if x is any negative number, then f(x) will be also negative.
That means, the Range of the function: "All real numbers such that [tex]f(x)\leq 0[/tex]"
So, the range and domain of the function are the same.
True or false: when comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure. choose the correct answer below.
a. false, because the larger the standard deviation is, the less dispersion the distribution has.
b. true, because the standard deviation is the difference between the largest and smallest observation. when the standard deviation is larger, there is more distance between the largest and smallest observation, and therefore, more dispersion in the distribution.
c. true, because the standard deviation describes how far, on average, each observation is from the typical value. a larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.
d. false, because the standard deviation measures the spread of the distribution, not the dispersion of the distribution.
Answers
C) true, because the standard deviation describes how far, on average, each observation is from the typical value. a larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.
The larger the standard deviation, the more dispersed the distribution is, because the standard deviation measures how far each observation is from the mean value of the distribution.
The correct option is C. The typical value being referred to in the option is the mean. The standard deviation measures how far each observation in a distribution is to the mean value of the distribution. Option D is wrong, because, the spread is also the degree of dispersion. The difference between the largest and smallest value in a distribution is the range and not the standard deviation . Hence, option B is wrong. The larger the standard deviation, the greater the dispersion. Hence, option A is wrong.Learn more : https://brainly.com/question/12402189?referrer=searchResults
elise took out a payday loan for $500 due in 2 weeks that charged an $80 fee. what the periodic interest rate of the loan?
Answers
Answer:
16%Step-by-step explanation:
The periodic interest rate refers to the rate that it's charged after certain fixed period, can be yearly, monthly, daily. In this case, the periodic interest rate is due in 2 weeks.
Now, to find this interest rate, we just have to divide the fee by the loan and see what percentage represents
[tex]\frac{\$80}{\$500}=0.16[/tex]
Then, we multiply by 100 to obtain the percentage
[tex]0.16(100)= 16\%[/tex]
Therefore, the interest rate is 16%
Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it 8 inches.
how far did chubby run?
i need the answer in terms of pi
Answers
c=pi*d
c=8pi
Multiply by 100 and you get 800pi inches
riangle ABC is a right triangle. What is the relationship between angles A and B? They are congruent. They are complementary. They are supplementary. There is no relationship between them.
Answers
Answer:
50 square units.
Step-by-step explanation:
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