Triangle A′B′C′ is the image of triangle ABC after a dilation. What is the scale factor of the dilation?

Answers

Answer 1

Unfortunately, I can't really explain it that well, but AB is 6, and A'B' is 2.
6 / 3 = 2
BC is 3, and B'C' is 1.
3 / 3 = 1
Therefore the dilation factor would be 1/3.

Hope this helps! :)

Related Questions

Talia gave her hairdresser a 20 percent tip, which amounted to $7. What was the price of the service before the tip?

Answers

I don't know if I did it right but here's my guess. I think you multiply 7 by 20% and that gives you 1.40 as a result. Compared to the other method I used (division), I'm pretty sure I'm right since the other result was 35. Doesn't make sense if the end amount was $7.

Answer:

The price of the service that was charged before the tip was:

$ 35

Step-by-step explanation:

Let the price of the service be $ x.

Now it is given that:

Talia gave her hairdresser a 20 percent tip, which amounted to $7.

This means that the 20% of total service charge=7

i.e. 20% ×x =7

i.e. 0.20×x=7

i.e. x=7/0.20

i.e. x=35

Hence, the price of the service that was paid before the tip is: $ 35

Suppose that the time it takes to do a job is inversely proportional to the number of workers. that is, the more workers on the job the less time required to complete the job. if it takes 2 workers 8 days to finish a job, how long will it take 8 workers?

Answers

i think it would be 2 days. you would get it done 4 times faster, so 8/4 is 2

What is the best metric unit to measure the distance from ohio to texas?

Answers

Most likely miles would be best...
Hope this helps!!

Match the expression with its name. 9x4 – 3x + 4

Answers

Answer:

fourth degree trinomial

Step-by-step explanation:

Solve 9x-y=45, solve for y

Answers

9x - y = 45....subtract 9x from both sides
-y = -9x + 45 ...multiply both sides by -1 to make y positive
y = 9x - 45 <==

Answer: " y = 9x - 45 " .
_________________________
Explanation:
_________________________
Given: 9x - y = 45 ;

Method 1)
____________________________________________
Multiply the entire equation (both sides) by "-1" ;

-1* {9x - y = 45} ;

to get: -9x + y = -45 ;

↔ y + (-9x) = -45 ;

→ y - 9x = -45 ;

Add "9x" to each side of the equation ; to isolate "y" one side of the equation; and to solve for "y" ;

y - 9x + 9x = -45 + 9x ;

y = -45 + 9x ;

→ y = 9x + (-45) ;

→ y = 9x - 45 .
__________________________________________________
Method 2)
__________________________________________________
Given: 9x - y = 45 ; Solve for y ;

Add "y" to each side of the equation; and Subtract "45" from each side of the equation:

9x - y + y - 45 = 45 + y - 45 ;

to get: 9x - 45 = y ;

↔ y = 9x - 45 .
________________________________

a family went on a vacation and used 5.4 gallons of gasoline to travel 150 miles. how many total gallons of gasoline will they need to travel 200 more miles?

Answers

Answer is 7.2 gallons for 200 miles

Anna is 4ft 9in tall. Express Anna's height in feet only by using a mixed number. If necessary, simplifyvthe fraction part of the mixed number

Answers

So we know that there are 12 inches in a foot. With this information we can do this:[tex]4 \frac{9}{12} [/tex] But if you look you can see that the fraction is not simplified. How can we simplify it? Well, what is the Greatest Common Factor of 9 and 12? Well, the answer is 3! So divide 9 and 12 by three! SO the answer would be: [tex]4 \frac{3}{4}[/tex] I hope this helps!

Let f (x) = 2x - 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following: f (h(x)) and. g (f (x))

Answers

To get f(h(x)), we simply plug h(x) into the x value(s) of f(x), resulting in
2(x²+1)-1=2x²+2-1=2x²+1

For g(f(x)), we plug f(x) into the x value(s) of g(x), resulting in
3(2x-1)=6x-3

The perimeter of the isosceles ΔABC with the base
BC is equal to 40 cm. Perimeter of the equilateral ΔBCD is 45 cm. Find BC and AB.

Answers

ΔBCD is equilateral, so

|BC| = |CD| = |DA|

and

[tex]P=|BC|+|CD|+|DA|\\\\45=|BC|+|BC|+|BC|\\\\45=3\cdot|BC|\quad|:3\\\\|BC|=45:3\\\\\boxed{|BC|=15\text{ cm}}[/tex]

ΔABC is isosceles and

|AB| = |CA| (legs)

[tex]P=|AB|+|BC|+|CA|\\\\P=|AB|+|BC|+|AB|\\\\40=2\cdot|AB|+15\\\\40-15=2\cdot|AB|\\\\25=2\cdot|AB|\quad|:2\\\\\boxed{|AB|=12.5\text{ cm}}[/tex]

The length of BC is 15 cm and the length of AB is 12.5 cm.

The given parameters;

perimeter of isosceles ΔABC = 40 cmbase of the isosceles triangle = BCPerimeter of the equilateral ΔBCD = 45 cm

An equilateral triangle has three equal sides and the length of each side is calculated as;

[tex]|BC| = |BD| = |CD| = \frac{45}{3} = 15 \ cm[/tex]

Thus, the length of BC is 15 cm.

An isosceles triangle has two equal sides and a third side of different length. This third side is usually the base of the triangle.

The base of the isosceles triangle = BC = 15 cmThe two remaining sides = AB and AC

[tex]|AB| = |AC| =\frac{Perimeter \ - \ |BC|}{2} = \frac{40 - 15}{2} = 12.5 \ cm[/tex]

Thus, the length of AB is 12.5 cm.

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3^3 • 32 + 12 ÷ 4

a. 219
b. 291
c. 867
d. 437

Answers

The answer is 867.

3^3 = 27

27•32 + 12/4
864 + 3 = 867

How can you determine whether an equation is linear or non-linear?

Answers

If the graph of the equation is straight, it is linear. If it is not, then it is non-linear.

Hope this helps!
Your fortune is "You will change someone's life within the next few weeks."

Hello There!

Linear simply means straight.
Graph out your equation and see if it is straight.
If it is, then it is a linear equation.
If it isn't straight, then it is a non linear equation.

Hope This Helps You!
Good Luck :)

- Hannah ❤

what are the solutions to the quadratic equation of 2x^2-16x+32=0 show work?

Answers

2x^2-16x+32=0
2(x^2 - 8x + 16) = 0
2(x - 4)^2 = 0
x - 4 = 0; x = 4

answer
x = 4 is the solution

Answer:

The Answer is 4

Step-by-step explanation:

2x² - 16x + 32 = 0

we would multiply 2x² and 32

= 64x²

then factorise 64x² such that the sum of the two nos = -16 AND the product of the nos = 64

the only value that satisfies this condition is -8 (-8 + -8 = -16, and -8 * -8 = 64)

so our equation becomes

0 = 2x² - 8x -8x + 32

0 = (2x² - 8x) (-8x +32)

we bring out common terms i.e. factorise it

2x(x - 4) -8(x - 4)

0 = (2x - 8) (x - 4)

0 = 2x - 8 or 0 = x - 4

8 = 2x or 4 = x

x = 8/2 or 4

x = 4 or 4

x = 4

hope it was clear

A line passes through the two given points. (1,0) (0,0) Is it vertical , horizontal , or neither ?

Answers

I bealive it is Vertical.
I'm not sure if Iright, if I'm wrong... sorry :c

Answer: its horizontal

Ari writes 2 + 4 on the left-hand side of his paper. Then he writes 6 to the right of the expression. Which symbol should Ari write between the two sets of numbers?

A.
+

B.
?

C.
=
Plz help will rate 19 pts

Answers

C. 2+4=6. i believe that's what you're asking. those other answers just dont make sense for real.

The correct symbol that Ari should write between the two sets of numbers is C. =.

When Ari writes "2 + 4" on the left-hand side of his paper and then writes "6" to the right of the expression, he is indicating that the sum of 2 and 4 is 6. The symbol "=" is used to denote equality, meaning that the value on the left side of the equation is the same as the value on the right side. In this case, the sum of 2 and 4 indeed equals 6, so the complete equation should be written as:

[tex]\[ 2 + 4 = 6 \][/tex]

This shows that the operation of adding 2 and 4 results in the number 6, which is a true statement. Therefore, the correct answer to the question is option C, the equals sign "=".

can you form an angle bisector hen the angle is a straight line?

Answers

Yes. Angle bisector means where after splitting the angle the 2 angles formed has the same size.
Therfore when you construct an angle bisector on a straight line, both new angles would be 90°, and the angle bisector is just right in the middle.

The line x - y = 5 passes through which set (-5, 0) (0, 5) (0, -5)

Answers

The answer would be (-5,0)

Joel is walking down a street and sees a 115 ft tall building in front of him. he stops 190 feet from the base of the building at the tip of the building's shadow. round answers to three decimal places.
a. if there was a piece of rope from the top of the building to joel, how long would it be?
b. what is the angle of elevation from joel to the top of the building?
c. margaret says that she could find the angle of depression from the top of the building to joel by subtracting the angle of elevation from 90°. is she correct? explain.

Answers

First, if you look at all the details, you see that the building, Joel and rope form a right angle triangle.

a) a²+b²=c²
(115)²+(190)²=c²
√49325=c
222.092 ft =c

b) tanθ= opp/adj
tanθ=115/190
θ=tan⁻¹(115/190)
θ=31.184 degrees

c) Yes, because the angle of depression and angle of elevation, in this case at least, add up to 90 degrees. Due to this, subtracting the angle of elevation by 90 degrees will give angle of depression.

Hope I helped :)

If there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet. The angle of elevation from Joel to the top of the building is approx [tex]31.18 ^ \circ[/tex]

What is angle of elevation and angle of depression?

You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.

Similarly, there is angle of depression, when you look horizontal, then down, the angle between both positions is the angle of depression.

How to use right triangles to find the length of the rope?

Remember that we assume that buildings are usually vertical to the ground. This means, there is 90° formation. The length of the rope can be taken as length of hypotenuse.

What is Pythagoras Theorem?

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Referring to the figure attached below, we get:
Length of the rope = Length of the line segment AC = |AC|

Using the fact that the triangle ABC is right angled triangle, we can use Pythagoras theorem.

We get the length of AC as:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\|AC| = \sqrt{|AB|^2 + |BC|^2} \\\text{positive square root since length is non-negative quantity}\\\\|AC| = \sqrt{115^2 + 190^2} = \sqrt{51325} \approx 222.01 \: \rm ft[/tex]

Thus, if there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet.

The angle of elevation is calculated as:

[tex]\tan(\angle ABC) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}} = \dfrac{|AB|}{|BC|}\\\theta = tan^{-1}(\dfrac{115}{190}) \approx 31.18^\circ[/tex]

The angle of depression is actually equal to angle of depression because they are pair of alternate interior angles (made by traversing line AC between two parallel lines).

Thus, Margaret statement is false.

Therefore, we get the answers as:

If there was a piece of rope from the top of the building to Joel, how long would it be approx 222.01 feet.The angle of elevation from Joel to the top of the building is approx [tex]31.18 ^ \circ[/tex]Margaret's statement is false.

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Represent real-world situations a rectangular piece of sheet metal is rolled and riveted to form a circular tube that is open at both ends, as shown. the sheet metal has a perimeter of 36 inches. each of the two sides of the rectangle that form the two ends of the tube has a length of x inches, and the tube has a circumference of x - 1 inches because an overlap of 1 inch is needed for the rivets. write a volume function for the tube in terms of x. then, to the nearest tenth, find the value of x that maximizes the volume of the tube. answer

Answers

12.3 Volume function: v(x) = ((18-x)(x-1)^2)/(4pi) Since the perimeter of the piece of sheet metal is 36, the height of the tube created will be 36/2 - x = 18-x. The volume of the tube will be the area of the cross section multiplied by the height. The area of the cross section will be pi r^2 and r will be (x-1)/(2pi). So the volume of the tube is v(x) = (18-x)pi((x-1)/(2pi))^2 v(x) = (18-x)pi((x-1)^2/(4pi^2)) v(x) = ((18-x)(x-1)^2)/(4pi) The maximum volume will happen when the value of the first derivative is zero. So calculate the first derivative: v'(x) = (x-1)(3x - 37) / (4pi) Convert to quadratic equation. (3x^2 - 40x + 37)/(4pi) = 0 3/(4pi)x^2 - (10/pi)x + 37/(4pi) = 0 Now calculate the roots using the quadratic formula with a = 3/(4pi), b = -10/pi, and c = 37/(4pi) The roots occur at x = 1 and x = 12 1/3. There are the points where the slope of the volume equation is zero. The root of 1 happens just as the volume of the tube is 0. So the root of 12 1/3 is the value you want where the volume of the tube is maximized. So the answer to the nearest tenth is 12.3

a text book costs $108.00. if mathew paid a total of $113.94 for the book and sales tax, what rate of sales tax was he charged?

Answers

Okay. So to find the amount of sales tax, we have to first subtract the text book cost from the total. 113.94 - 108 = 5.94. That’s $5.94 in taxes. To find the percentage, we have to do the amount in taxes divided by the cost of the item, in this case, the textbook. 5.94 / 108 is 0.055. Multiply 0.055 by 100 in order to get the percentage. When you do that, you get 5.5%. Matthew was charged 5.5% in sales tax.

The expression $1.25p + $3.50 can be used to calculate the total charge for printing p pages at a business service store. How much would it cost to print 8 pages

Answers

Since one page cost $1.25 to print take the cost of per page $1.25 times the number of pages to be printed, in this case eight. $1.25 x 8 = $10.00
Remember there is still a $3.50 added to the cost of the pages printed; thus you have $10.00 + $3.50 = $13.50 which is the total charge.

the table shows the volume of gasoline in a gas tank at different times. Find th e rate of change for each time interval. During which time interval did the volume decrease at the greatest rate?

Answers

Final answer:

To find the rate of change for each time interval, calculate the difference in volume for each interval and divide it by the difference in time. Compare the rates of change to determine the time interval with the lowest rate of change.

Explanation:

To find the rate of change for each time interval, we need to calculate the difference in volume for each interval and divide it by the difference in time. Let's assume the time intervals are 12-18 hours, 18-24 hours, and 12-24 hours. The rate of change for each interval can be calculated as follows:

Rate of change for 12-18 hours = (Volume at 18 hours - Volume at 12 hours) / (18 hours - 12 hours)

Rate of change for 18-24 hours = (Volume at 24 hours - Volume at 18 hours) / (24 hours - 18 hours)

Rate of change for 12-24 hours = (Volume at 24 hours - Volume at 12 hours) / (24 hours - 12 hours)

The time interval during which the volume decreased at the greatest rate will be the interval with the lowest rate of change. Compare the rates of change calculated for each interval to find the time interval with the lowest rate of change.

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dakota runs a half marathon every 6 weeks. madison runs a half a marathon every 15 weeks. how many weeks untill they will run together?

Answers

30 weeks they would both run30 miles

Final answer:

To determine when Dakota and Madison will run a half marathon on the same week, we calculate the least common multiple of their running intervals, which is 60 weeks.

Explanation:

The question is to find out how many weeks will pass until Dakota and Madison will run a half marathon on the same week.

We need to find the least common multiple (LCM) of their running intervals, which are 6 weeks for Dakota and 15 weeks for Madison.

To find the LCM, you can list the multiples of each number until you find the smallest number that appears in both lists.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...Multiples of 15: 15, 30, 45, 60, ...

Here, we see that the smallest common multiple is 60 weeks.

Therefore, Dakota and Madison will run a half marathon together in 60 weeks.

May I acquire some help on this homework as it is due tomorrow.

Answers

Hello,

1)
[tex]f(x)=2x^3+4x-9=0\\\\ 2x^3+4x-9=0\\\\ x^3=9-4x\\\\ x= \sqrt[3]{9-4x} \\\\ x_{n+1}=\sqrt[3]{9-4x_n}\\\\ x_{n+1}=1,25698196\\\\ [/tex]

2) 3) see file jointed

which of the following is the equation of a line perpendicular to the line y= -3/2x+4 and passes through the points (3,9)

Answers

line y= -3/2x+4 slope = -3/2
perpendicular lines, slope is opposite and reciprocal
so slope of perpendicular line = 2/3
passes through the points (3,9)
y = mx + b
9 = 2/3(3) + b
9 = 2 + b
b = 7

equation of perpendicular line
y = 2/3x + 7
3y = 2x + 21
-2x + 3y = 21

Answer:

[tex]2x-3y+21=0[/tex]

Step-by-step explanation:

We are given that an equation

[tex]y=-\frac{3}{2}x+4[/tex]

We have to find an equation of line which is perpendicular to given line and passing through the point (3,9).

We know that when two lines of slope [tex]m_1\;and\;m_2[/tex] are perpendicular then

[tex]m_1=-\frac{1}{m_2}[/tex]

By comparing with

[tex]y=mx+b[/tex]

Where m=Slope of line

Slope of given line=[tex]=m_1=\frac{-3}{2}[/tex]

Slope of the line=[tex]-\frac{1}{m_1}=-\frac{1}{\frac{-3}{2}}=\frac{2}{3}[/tex]

Slope of the line=[tex]\frac{2}{3}[/tex]

The equation of line passing through the point (3,9) is given by

[tex]y-y_0=m(x-x_0)[/tex]

Substitute the values

The equation of line which passing through the point (3,9) is given by

[tex]y-9=\frac{2}{3}(x-3)[/tex]

[tex]3y-27=2(x-3)[/tex]

[tex]3y-27=2x-6[/tex]

[tex]3y=2x-6+27[/tex]

[tex]2x-3y+21=0[/tex]

Factor completely 2x2 − 2x − 40.

2(x − 5)(x + 4)
(2x − 10)(x + 4)
(x − 5)(2x + 8)
2(x − 4)(x + 5)

Answers

The answer is: [A]: " 2(x − 5)(x + 4) " .
_____________________________________________________
Given: " 2x² − 2x − 40 " ;

We can factor out a "2" ;

2(x² − x − 20)

Now, we can write down the "2" ; and factor the: "(x² − x − 20)" ;

2 *
(x² − x − 20) ;
_______________________________________________________
Take a look at: "(x² − x − 20)" ; we have "-1x" and "-20" ;

so, -5 and +4 ;
or; +5 and -4 ; to get "-20" ;
_______________________
(we choose the "5" and "4" factors of
"-20" because we also have "-1" ;
and "5 -4 =1" ;
Now, (-5 + 4 = -1) ;
and: (+5 - 4 = +1).
So; we'll stick with (-5 + 4) ;

(x² − x − 20) = (x − 5)(x + 4) ;
________________________________________________
Then, bring down the "2" ; and we have our answer:
__________________________________________________
" 2x² − 2x − 40 "

= " 2(x − 5)(x + 4) " ; which is: Answer choice: [A] .
_______________________________________________

The factor of quadratic function 2x²-2x-40 is 2 (x-5) (x+4).

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:

The quadratic function 2x²-2x-40.

To find the factors;

Take common term out,

2(x²-x-20)

= 2 (x²-5x + 4x -20)

= 2 {x (x-5) + 4(x -5)}

= 2 (x-5) (x+4)

Therefore, the factors are 2 (x-5) (x+4).

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using exponents, what is the simplified form of the expression 2^4*2^7?

Answers

Final answer:

To simplify 2^4\*2^7, you add the exponents because the bases are the same, resulting in 2^11 which equals 2048.

Explanation:

When simplifying the expression 2^4\*2^7, we use the property of exponents that states when multiplying two exponential terms with the same base, you add the exponents. So, the simplified form of the expression would be 2^(4+7) which is 2^11. Since we are adding the exponents, this process is known as the sum of exponents and is a fundamental concept in the squaring of exponentials.

To calculate 2^11, you would multiply 2 by itself 11 times, but for the sake of simplicity, the answer is 2048.

In a country where prices are rising quickly, bread that now costs $1.39 will cost 2.4 times as much next year. How much will the bread cost next year

Answers

multiply the current price by the increase

1.39 * 2.4 = $3.34 ( price next year)

solving with systems of equations using elimination! please help me. thank u!

Answers

To cross out a variable (in this case, x) we can add both equations together to get -5y=10. Dividing both sides by -5, we get y=-2. Next, plugging it into -3y+5x=26, we get 6+5x=26. Subtracting 6 from both sides, we get 5x=20. Next, we can divide both sides by 5 to get x=4

Jose is three times as old as his cousin Robert. The sum of their ages is more than 40. What are the smallest possible ages for each of them?

Answers

11 and greater

because 10 + 3(10) = 40

so 11 and greater

hope this helps

Final answer:

To find the smallest possible ages for Jose and Robert, set up a system of equations based on the given information. Robert's age is X, and Jose's age is 3X. The sum of their ages is more than 40, so the smallest possible age for Robert is 11, and Jose would be three times that, which is 33.

Explanation:

To find the smallest possible ages for Jose and Robert, we need to set up a system of equations based on the given information.

Let's assume Robert's age is x. Since Jose is three times as old as Robert, his age would be 3x.

The sum of their ages is more than 40, so we can write the equation: x + 3x > 40.

Simplifying the equation: 4x > 40.

Dividing both sides of the equation by 4, we get x > 10.

Therefore, the smallest possible age for Robert is 11, and Jose would be three times that, which is 33.

What number produces a rational number when added 1/5

Answers

It is because benchmark fraction 1/5 = .20

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