A segment is dilated, and the resulting segment is shorter than the original.
Which of the following options could be the scale factor of the dilation?
Select all that apply.

3/8

1

5

1/5

Answer:

0.12

Step-by-step explanation:

12/100

There can be many based on what the total amount of the number is.

But in this case I'll say 0.12

Answer:

0.0141987829615

Step-by-step explanation:

The polar form of z = -7 - 8i is:

z = 3√13 (cos 230.2° + i sin 230.2°)

Converting -7 - 8i to polar form:

The rectangular form of a complex number is given by z = a + bi, where a is the real part and b is the imaginary part. In this case, a = -7 and b = -8.

The polar form of a complex number is given by z = r(cos θ + i sin θ), where:

r is the modulus (or absolute value), which represents the distance of the complex number from the origin in the complex plane.

θ is the argument (or angle), which represents the direction of the complex number relative to the positive real axis.

1. Finding modulus (r):

r = √(a² + b²) = √((-7)² + (-8)²) = √(113) = √(13 * 9) = √13 * 3 (using factorization and perfect squares)

Therefore, r = 3√13.

2. Finding argument (θ):

θ = arctan(b/a) = arctan((-8)/(-7)) ≈ 50.2° (using the arctangent function on a calculator). However, this only gives one possible angle for the complex number.

Note: The arctangent function typically outputs values between -90° and 90°, which corresponds to Quadrant 1 or 4 in the complex plane. Since -7 - 8i lies in Quadrant 3, we need to add 180° to get the correct angle:

θ = 50.2° + 180° = 230.2°

Therefore, the polar form of z = -7 - 8i is:

z = 3√13 (cos 230.2° + i sin 230.2°)

The volume of scaled object is 0.039375 cubic inches

Solution:

Given that,

Volume of box = 39.375 cubic inches

Scaled down by a factor  = [tex]\frac{1}{10}[/tex]

The volume of a scaled object will be equal to the volume of object times scale factor cubed

Therefore,

Volume of scaled object = Volume of box x scale factor cubed

[tex]Volume\ of\ scaled\ object = 39.375 \times (\frac{1}{10})^3\\\\Volume\ of\ scaled\ object = 39.375 \times \frac{1}{1000}\\\\Volume\ of\ scaled\ object = 0.039375[/tex]

Thus volume of scaled object is 0.039375 cubic inches

Answer: 8 tacos

Step-by-step explanation: 2 hotdogs are $10 as they are $5 each. Tacos are $2.50 each. $2.50 x 8 equals $20. $20 + 10 = $30. Eva can buy 8 tacos.

After buying 2 hotdogs with $10, Eva will have $20 left. With the remaining $20, she can buy a maximum of 8 tacos at $2.50 each.

Since Eva is determined to buy 2 hotdogs at $5 each, she will spend $10 on hotdogs. She has a total of $30 to spend, meaning she will have $20 left after purchasing the hotdogs. Tacos cost $2.50 each. Therefore, with the remaining $20, Eva can afford to buy a maximum of 8 tacos (since $20 divided by $2.50 equals 8). This will also meet the condition of purchasing at least 7 hotdogs and tacos in total.

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Answer:

converting to fraction:

0.206 = 0.206/1000 =206//1000

2.06 = 2.06/100 = 206/100

0.026 = 0.026/1000 = 26/1000

0.26 = 0.26/100 = 26/100

answer = 2.06

Step-by-step explanation:

The fraction having the greatest value will be 2.06.

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.

The greatest value of the fraction will be calculated as below in the calculation:-

0.206 = 0.206/1000 =206//1000

2.06 = 2.06/100 = 206/100

0.026 = 0.026/1000 = 26/1000

0.26 = 0.26/100 = 26/100

Therefore, the fraction having the greatest value will be 2.06.

To know more about the number system follow

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Step-by-step explanation:

Perhaps you want to simplify the given expression: Let's do it.

[tex](3x + 4) - (x + 2) \\ \\ = 3x + 4 - x - 2 \\ \\ = 3x - x + 4 - 2 \\ \\ = 2x + 2 \\ this \: is \: the \: simplest \: form \: of \: the \: \\ given \: expression.[/tex]

Answer:

2(x + 1)

Step-by-step explanation:

(3x + 4) - (x + 2)

3x + 4 - x - 2

3x - x + 4 - 2

2x + 2

2(x + 1)

Answer:

[tex]remainder=2802[/tex]

Step-by-step explanation:

Remainder Theorem: When a polynomial [tex]f(x)[/tex] is divided by [tex](x-a)[/tex] the remainder will be [tex]f(a)[/tex]

[tex]Here \ \ f(x)=x^3+6x^2-20x+450[/tex]

[tex]It\ is\ divided\ by\ (x-12)[/tex]

[tex]Then\ remainder =f(12)\\\\remainder=(12)^3+6(12)^2-20\times12+450\\\\remainder=1728+6\times144-240+450\\\\remainder=1728+864-240+450\\\\remainder=3042-240\\\\remainder=2802[/tex]

Final answer:

To find the remainder of the polynomial f(x) = x³ + 6x² - 20x + 450 when divided by (x - 12), we evaluate f(12) using the Remainder Theorem, which yields a remainder of 2802.

Explanation:

To find the remainder when the function f(x) = x³ + 6x² - 20x + 450 is divided by (x - 12), we use the Remainder Theorem. This theorem states that the remainder of a polynomial f(x) divided by (x - a) is f(a). Therefore, to find the remainder of f(x) divided by (x - 12), we evaluate f(12).

Substitute x with 12 into the function:

f(12) = (12)³ + 6(12)² - 20(12) + 450

f(12) = 1728 + 864 - 240 + 450

f(12) = 2802

Thus, the remainder is 2802.

Answer: 6y + 5x = 24

Step-by-step explanation:

The formula for calculating  equation of line with two points is given as :

[tex]\frac{y-y_{1}}{x-x_{1}}[/tex] = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]x_{1}[/tex] = -12

[tex]x_{2}[/tex] = 6

[tex]y_{1}[/tex] = 14

[tex]y_{2}[/tex] = -1

substituting the values into the formula , we have

[tex]\frac{y-14}{x-(-12)}[/tex] = [tex]\frac{-1-14}{6-(-12)}[/tex]

[tex]\frac{y-14}{x+12}[/tex] = [tex]\frac{-15}{18}[/tex]

[tex]\frac{y-14}{x+12}[/tex] = [tex]\frac{-5}{6}[/tex]

cross multiplying , we have :

6(y - 14 ) = -5 ( x + 12 )

6y - 84 = -5x - 60

6y +5x = -60 + 84

6y + 5x = 24

Answer:

Step-by-step explanation:

-3 3/4, -3, 3 1/10, and then 3 1/3 i think this is correct...sorry if it is wrong though.

Answer:

16.

Step-by-step explanation:

The denominator could be 16.

The GCF of 12 and 16 is 4.

Final answer:

The denominator of the fraction with a numerator of 12 and a GCF of 4 with the denominator is 12. You divide the numerator by the GCF and then multiply the result by the GCF to get the denominator.

Explanation:

The student is asking for the denominator of a fraction when the numerator is 12 and the greatest common factor (GCF) of the numerator and the denominator is 4. To find the denominator, you would divide the numerator (12) by the GCF (4). This gives us 12 ÷ 4, which equals 3. Therefore, the denominator of the fraction must be a number that when divided by the GCF (4) will give us a quotient of 3. Since the denominator is 4 times larger than this quotient, we multiply 3 by 4 to find the denominator. Therefore, the denominator is 3 × 4, which equals 12.

Answer:

58/48 to 29/24

Step-by-step explanation:

An easy way that I always remember is that if both the numbers are even, divide by 2. Keep dividing until you get a odd number and then you know that you have your lowest form.

Answer:

Square root of 8.

Step-by-step explanation:

Given:

Number given : 2 to the power of 3 over 2 equal ...

Using the laws of exponent:

We know that:

⇒ [tex]\sqrt{a} = (a)^1^/^2[/tex]  and

⇒ [tex]\sqrt[3]{a}=(a)^1^/^3[/tex]

So,

According to the question:

2 to the power of 3 over 2  = [tex](2) ^3^/^2[/tex]

Using fractional exponent concept where :  [tex]\sqrt[y]{a^x} = (a)^x^/^y[/tex]

This can be re-written as:

⇒ [tex](2^3)^1^/^2[/tex] and [tex]\sqrt{2^3}[/tex] that is equivalent to [tex]\sqrt{8}[/tex]    as  ...[tex]2^3=2\times 2\times 2=8[/tex]

Square root of 8 is our final answer.

Answer:

18

you do 2/3=12/n.  and find out n (im to lazy to explain sorry)

Answer:

The missing figure is attached down

The length of BE is 27 units ⇒ 3rd answer

Step-by-step explanation:

In circle A:

We need to find the length of BE

∵ AB and AD are radii in circle A

∴ AB ≅ AD

In Δs EAB and EAD

∵ ∠BAE ≅ ∠DAE ⇒ given

∵ AB = AD ⇒ proved

∵ EA = EA ⇒ common side in the two triangles

- Two triangles have two corresponding sides equal and the

   including angles between them are equal, then the two

   triangles are congruent by SAS postulate of congruence

∴ Δ EAB ≅ Δ EAD ⇒ SAS postulate of congruence

By using the result of congruence

∴ EB ≅ ED

∵ EB = 3 x - 24

∵ ED = x + 10

- Equate the two expressions to find x

∴ 3 x - 24 = x + 10

- Add 24 to both sides

∴ 3 x = x + 34

- Subtract x from both sides

∴ 2 x = 34

- Divide both sides by 2

∴ x = 17

Substitute the value of x in the expression of the length of BE to find its length

∵ BE = 3 x - 24

∵ x = 17

∴ BE = 3(17) - 24

∴ BE = 51 - 24

∴ BE = 27

The length of BE is 27 units

Answer:

27

Step-by-step explanation:

I TOOK THE QUIZ, AND GOT 100%

Answer:r=2

Step-by-step explanation:

Answer:

A) 2

Step-by-step explanation:

I got it right on edge 2020.

Hope it helps :)

I purple you have a good year, stay safe.

Answer:

44 ft

Step-by-step explanation:

Given: Julie is 6 feet tall

           She stands 15 feet from the flagpole.

           The edges of the square line up with the top and bottom of the flagpole.

Lets assume the height of flagpole be "h".

As given, the edges of the square line up with the top and bottom of the flagpole.

∴ Angle and base of triangle are same then ratio of corresponding sides are also equal.

Now, finding the height of flagpole by using tangent rule.

we know, [tex]tan\theta= \frac{Opposite}{adjacent}[/tex]

Remember, both the angle are equal.

∴ Ratio of opposite and adjacent leg for both right angle triangle= [tex]\frac{6}{15} : \frac{h-6}{15}[/tex]

We can put it; [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]

Solving the equation now

⇒ [tex]\frac{6}{15} = \frac{15}{h-6}[/tex]

Multiplying both side by 15

⇒[tex]6 = \frac{15\times 15}{h-6}[/tex]

Multiplying both side by (h-6)

⇒ [tex]6\times (h-6) = 15\times 15[/tex]

Distributive property of multiplication

⇒ [tex]6h-36= 225[/tex]

Adding both side by 36

⇒[tex]6h= 225+36[/tex]

Dividing both side by 6

⇒[tex]h= \frac{261}{6}[/tex]

∴ [tex]h= 43.5\ feet[/tex] [tex]\approx 44 feet[/tex]

Hence, the height of flagpole is 44 feet.

Final answer:

To approximate the height of a flagpole given that Julie, who is 6 feet tall, lines up a cardboard square with the top and bottom of the flagpole while standing 15 feet away, we can use the principles of similar triangles. This results in a calculation showing that the flagpole is approximately 6 feet tall, the same as Julie's height.

Explanation:

The height of the flagpole can be approximated using similar triangles. Julie is 6 feet tall and stands 15 feet from the flagpole. Using the cardboard square, we understand that the triangle formed by Julie and her shadow is similar to the triangle formed by the flagpole and its shadow. Therefore, we can set up a proportion:

Julie's height / Julie's distance from flagpole = Flagpole's height / Flagpole's distance from cardboard.

If we assume that the cardboard square is held adjacent to Julie, the flagpole's distance from the cardboard is also 15 feet. The proportion simplifies to:

6 feet / 15 feet = Flagpole's height / 15 feet

Cross-multiplying to solve for the flagpole's height gives us:

Flagpole's height = 6 feet × (15 feet / 15 feet) = 6 feet

Therefore, the flagpole is approximately 6 feet tall.

Answer: = [tex]\frac{25+\sqrt{949} }{6}[/tex] and y = \frac{25+\sqrt{949} }{6} - 3.

Step-by-step explanation:

Take x as the larger number and y as the smaller number.

x + 3 = y

[tex]\frac{16}{y}[/tex]+ [tex]\frac{9}{x}[/tex] = 1

Substitute x + 3 for y in the second equation.

[tex]\frac{16}{x+3}[/tex]+ [tex]\frac{9}{x}[/tex] = 1

Make a common denominator.

[tex]\frac{16(x) + 9(x+3)}{(x+3)(x)} =1[/tex]

Simplify and get rid of that fraction.

[tex]16x + 9x + 27 = x^{2} + 3x[/tex]

[tex]x^{2} + 3x - 25x - 27 = 0[/tex]

[tex]x^{2} -22x - 27 = 0[/tex]

By quadratic formula (and because they must be positive), x = [tex]\frac{25+\sqrt{949} }{6}[/tex] and then y = \frac{25+\sqrt{949} }{6} - 3.

To solve for the two positive numbers, we can set up an equation and solve for x.

Let's call the smaller number x and the larger number x + 3.

From the given information, we can write the following equation:

16(1/x) + 9(1/(x + 3)) = 1

To solve this equation, we can find a common denominator and then simplify:

16(x + 3)/(x(x + 3)) + 9x/(x(x + 3)) = 1

After simplifying and solving for x, we find that the smaller number is 4 and the larger number is 7.

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1507 are the different ways can 5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players

Solution:

Given that,

5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players

This is a combination problem

Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter

The formula is given as:

[tex]n C_{r}=\frac{n !}{r !(n-r) !}[/tex]

Where n represents the total number of items, and r represents the number of items being chosen at a time

Let us first calculate 5 baseball players from 12 baseball players

Here, n = 12 and r = 5

[tex]\begin{array}{l}{12 C_{5}=\frac{12 !}{5 !(12-5) !}} \\\\{12 C_{5}=\frac{12 !}{5 ! \times 7 !}}\end{array}[/tex]

For a number n, the factorial of n can be written as:

[tex]n !=n \times(n-1) \times(n-2) \times \ldots . \times 2 \times 1[/tex]

Therefore,

[tex]\begin{aligned}12 C_{5} &=\frac{12 \times 11 \times 10 \times \ldots \ldots \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \\\\12 C_{5} &=\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2} \\\\12 C_{5} &=792\end{aligned}[/tex]

Similarly, 4 basketball players be selected 13 basketball players

n = 13 and r = 4

Similarly we get,

[tex]\begin{aligned}&13 C_{4}=\frac{13 !}{4 !(13-4) !}\\\\&13 C_{4}=\frac{13 !}{4 ! \times 9 !}\end{aligned}[/tex]

[tex]13C_4 = 715[/tex]

Thus total number of ways are:

[tex]12C_5 + 13C_4 = 792 + 715 = 1507[/tex]

Thus there are 1507 different ways

To determine the number of ways to select 5 baseball players from 12, and 4 basketball players from 13, we use the combination formula for both and multiply the results, applying the Counting Principle.

The question asks how many different ways can 5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players. This is a problem of combinatorics, specifically the use of combinations, since the order of selection does not matter.

To find the number of ways to select the baseball players, we use the combination formula C(n, k) = n! / (k! * (n-k)!), where 'n' is the total number to choose from, 'k' is the number to choose, and '!' denotes factorial. For the 5 baseball players from 12, it is C(12, 5).

For the basketball players, it's C(13, 4), as we are choosing 4 out of 13. To find the total number of ways to form the group, we multiply these two values together, because each combination of baseball players can be paired with each combination of basketball players, which is an example of the Counting Principle.

So, the calculation is C(12, 5) * C(13, 4).

Answer:

midpoint (5,4)

Step-by-step explanation:

The midpoint(M) of a segment with endpoints (x₁ , y₁) and ( x₂,  y₂) is

where x₁ = 2 and x₂ = 8

y₁ = 0 and y₂ = 8

M = [tex]\frac{x_1 + x_2}{2} ,\frac{y_1 + y_2}{2}[/tex]

M = [tex]\frac{2 + 8}{2} ,\frac{0 + 8}{2}[/tex]

M = 5 , 4

Answer:

96 blueberries

Step-by-step explanation:

x = number of muffins

Since each blueberry is going to contain 12 blueberries, we can multiply 12 by the number of muffins to get the total number of blueberries.

12x

12(8)

96

Step-by-step explanation:

In the question figure,

∠ 1 = 115 °, ∠ 2 = 115 °, ∠ 3 = 120 °, ∠ 4 = 14x °, ∠ 5 = 133 °, ∠ 6 = 167 °, ∠ 7 = 138° and ∠ 8 = 18x °

To find, the value of x = ?

We know that,

The sum of all angles of heptagon = 1080°

∴ ∠ 1 + ∠ 2 + ∠ 3 + ∠ 4 + ∠ 5 + ∠ 6 + ∠ 7 + ∠ 8 = 1080°    

⇒ 115 ° + 115 ° + 120 ° + 14x ° + 133 ° + 167 ° + 138° + 18x ° = 1080°  

⇒ 32x ° + 788° = 1080°  

⇒ 32x ° = 1080°  - 788° = 292°

⇒ x ° = 9.125°

∴ x ° = 9.125°

Answer:

Jason is 14 year old.

Step-by-step explanation:

Given: Joe, John and Jason are each a year apart in age.

           Sum of their age is 39.

Lets assume the age of Joe be x

∴ Age of Jahn will be [tex](x+1)[/tex]

And age of Jason will be [tex](x+2)[/tex]

Now, putting up an equation for the sum of their age.

∴ [tex]x+(x+1)+(x+2)= 39[/tex]

Opening the parenthesis.

⇒[tex]x+x+1+x+2= 39[/tex]

⇒[tex]3x+3= 39[/tex]

Subtracting both side by 3

⇒ [tex]3x= 36[/tex]

Dividing both side by 3

⇒[tex]x= \frac{36}{3}[/tex]

∴ [tex]x= 12\ years[/tex]

Hence, Joe is 12 year old.

Next subtituting the value of x to find age of Jason and John.

Jason= [tex](x+2)= 12+2[/tex]

∴Jason= 14 years.

John age= [tex](x+1)= 12+1[/tex]

∴ John Age= 13 years.

Hence, Jason is 14 year of age.

Answer:

21 inches

Step-by-step explanation:

refer to attached graphics

we can find the height by the Pythagorean theorem.

diagonal² = width² + height²

height² = diagonal²  - width²

we are given that diagonal = 29" and width = 20", hence

height² = 29²  - 20²

height² = 841  - 400

height² = 441

height = √441 = 21 inches

Answer:

636

Step-by-step explanation:

the area of the footpath=

(50m+3m+3m)^2-50^2

The probability of randomly selecting a yellow marble out of the bag is [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

A bag contains:

We need to find the probability of randomly selecting a yellow marble out of the bag

Probability is the ratio of number of favorable outcomes to the total number of possible outcomes P(A) = [tex]\frac{n(A)}{n(outcoms)}[/tex]

∵ A bag contains 7 red marbles, 5 yellow marbles, 6 blue

   marbles, 4 green marbles, and 3 orange marbles

- Add all the color to find the number of total marbles

∴ n(all) = 7 + 5 + 6 + 4 + 3 = 25

∵ There are 5 yellow marbles

∵ P(yellow) = [tex]\frac{n(yellow)}{n(all)}[/tex]

∴ P(yellow) = [tex]\frac{5}{25}[/tex]

- Divide up and down by 5 to simplify the fraction

∴ P(yellow) = [tex]\frac{1}{5}[/tex]

The probability of randomly selecting a yellow marble out of the bag is [tex]\frac{1}{5}[/tex]

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Answer:

1/5

Step-by-step explanation: