Triangle ABC was dilated and translated to form similar triangle A'B'C'.

On a coordinate plane, 2 triangles are shown. Triangle A B C has points (0, 2), (2, 2), and (2, 0). Triangle A prime B prime C prime has points (negative 4, negative 1), (1, negative 1), and (1, negative 6).

What is the scale factor of the dilation?

One-fifth
Two-fifths
Five-halves
5/1

Hi there!

\(\large\boxed{73m^2}}\)

Once again, divide the figure into 3 rectangles:

Top rectangle:

3m × 5m = 15m²

Long rectangle (subtract 5m from 9m to get the width):

12m × 4m = 48m²

Bottom rectangle:

2m × 5m = 10m²

Add up areas:

15m² + 48m² + 10m² = 73m²

When we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

To subtract 3 from 22, we can perform the subtraction operation as follows:

22

3

19

We align the numbers vertically and subtract each corresponding place value from right to left. In this case, subtracting 3 from 2 requires borrowing or regrouping. However, since 2 is greater than 3, we can directly subtract 3 from 2 and write the difference, which is 1, in the one's place.

Therefore, the simplified answer is 19.

The subtraction process involves taking away or removing a certain quantity from another. In this case, we subtracted 3 from 22, resulting in a difference of 19. The process of simplifying the answer is simply expressing the result in its most concise and reduced form.

By subtracting 3 from 22, we removed 3 units from the original value of 22, leaving us with 19. This can be visualized as taking away three objects from a group of 22 objects, resulting in a remaining count of 19.

In summary, when we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

for such more question on simplified

https://brainly.com/question/11680269

#SPJ8

The value of b is 2.

Since the hanger diagram models the equation 2b = 4, we can see that the bar representing 2b has a length of 4 units.

To find the value of b, we need to divide both sides of the equation by 2. This gives us:

2b/2 = 4/2

b = 2

Therefore, the value of b is 2.

Learn more about Equation here:

https://brainly.com/question/29657983

#SPJ1

Answer:

7/10 or 0.7 or 70% left.

Step-by-step explanation:

Since he gives 1/5 of the cake to Sali, he gave 1/5 * 30 = 6 cakes away to Sali. Since 10% is 1/10, he gave away 1/10 * 30 = 3 cakes away to Jane. He has a total of 30 - 3 - 6 = 21 cakes left. 21/30 = 7/10, or 0.7, or 70% left.

Answer: 21/30

Explanation this is because 1/5of 30 is 6 and 10 percent of 30 is 3

6+3=9

30-9=21

Therefore Simon has 21/30 cakes left

I hope it helps

In analyzing the performance of implementing the given methods over Singly Linked List and Doubly Linked List data structures, we consider the Big-O notation, which provides insight into the time complexity of these operations as the size of the list increases.

Add to Start of List:

Singly Linked List: O(1)

Doubly Linked List: O(1)

Both Singly Linked List and Doubly Linked List offer constant time complexity, O(1), for adding an element to the start of the list.

This is because the operation only involves updating the head pointer (for the Singly Linked List) or the head and previous pointers (for the Doubly Linked List). It does not require traversing the entire list, regardless of its size.

Add to End of List:

Singly Linked List: O(n)

Doubly Linked List: O(1)

Adding an element to the end of a Singly Linked List has a time complexity of O(n), where n is the number of elements in the list. This is because we need to traverse the entire list to reach the end before adding the new element.

In contrast, a Doubly Linked List offers a constant time complexity of O(1) for adding an element to the end.

This is possible because the list maintains a reference to both the tail and the previous node, allowing efficient insertion.

Add at Given Index:

Singly Linked List: O(n)

Doubly Linked List: O(n)

Adding an element at a given index in both Singly Linked List and Doubly Linked List has a time complexity of O(n), where n is the number of elements in the list.

This is because, in both cases, we need to traverse the list to the desired index, which takes linear time.

Additionally, for a Doubly Linked List, we need to update the previous and next pointers of the surrounding nodes to accommodate the new element.

In summary, Singly Linked List has a constant time complexity of O(1) for adding to the start and a linear time complexity of O(n) for adding to the end or at a given index.

On the other hand, Doubly Linked List offers constant time complexity of O(1) for adding to both the start and the end, but still requires linear time complexity of O(n) for adding at a given index due to the need for traversal.

To learn more about Big-O notation visit:

brainly.com/question/30452896

#SPJ11

Answer:

Yes this is a statistical question because of how  they want to measure the tress to find out how tall are all of them and then to find out which is the tallest.

Jutin chooses a function J(x) = 3x - 1 that when he uses the number 7 as an input, then the output is 20.

As per the given data, Jutin chooses a function in which he uses the number 7 as an input, then the output is 20.

Here we have to determine which function Jutin has to use.

Now we have to substitute the value that x = 7 in all the given functions.

First function:

F(x) = 2\(x^{5}\)

F(7) = 2 \((7)^{5}\)

F(7) = 2 (16807)

F(7) = 33614 which is not equal to 20.

Second function:

G(x) = \(x^{2}\) - 19

F(7) = \((7)^{2}\) - 19

F(7) = 49 - 19

F(7) = 30 which is not equal to 20.

Third function:

H(x) = 13 - x

H(7) = 13 - 7

H(7) = 6 which is not equal to 20.

Fourth function:

J(x) = 3x - 1

J(7) = 3(7) - 1

J(7) = 21 - 1

J(7) = 20

The correct function is J(x) = 3x - 1

For more questions on substitution method

https://brainly.com/question/28663522

#SPJ4

Answer:

Option (A).

Step-by-step explanation:

Option (A).

All whole numbers are integers.

True.

Option (B).

Whole numbers and integers have no element in common.

False. All whole numbers are integers. Therefore, whole numbers are contained in integers on Venn diagram.

Option (C).

All integers are whole numbers.

False. All whole numbers are integers.

Option (D).

Some whole numbers are integers.

False. All whole numbers are integers.

The store keeper used 125 pounds of flour worth $2.40 per pound and 175 pounds of flour worth $3 per pound to get 300 pounds of mixed flour.

The assertion that two expressions are equal when they are connected by the equals sign ("="), is the mathematical definition of an equation. As an example, 2x - 5 = 13. The equations in this example are 2x - 5 and 13. The symbol "=" links these two expressions together.

Let x be the number of pounds of the flour worth $2.40 per pound, and y be the number of pounds of the flour worth $3 per pound. Since the store keeper wants to end up with 300 pounds of flour, we have:

x + y = 300

We also know that the store keeper wants to sell the mixed flour for $2.05 per pound. This means that the total cost of the flour (x pounds at $2.40 per pound, plus y pounds at $3 per pound) must be equal to:

300 pounds × $2.05 per pound = $615

In other words:

2.40x + 3y = 615

Two equations with two unknowns are now present:

x + y = 300

2.40x + 3y = 615

We can find x and y using algebra. One way to do this is to solve the first equation for x:

x = 300 - y

We can then substitute this expression for x into the second equation:

2.40(300 - y) + 3y = 615

Expanding the parentheses and simplifying, we get:

720 - 2.4y + 3y = 615

0.6y = 105

y = 175

So, the store keeper used 175 pounds of flour worth $3 per pound. To find the amount of flour worth $2.40 per pound, we can substitute y = 175 into the equation x + y = 300:

x + 175 = 300

x = 125

Therefore, the store keeper used 125 pounds of flour worth $2.40 per pound and 175 pounds of flour worth $3 per pound to get 300 pounds of mixed flour.

Learn more about equation on:

https://brainly.com/question/27893282

#SPJ4

Answer:

All Factors of 340: 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170 and 340.

Prime Factors of 340: 2, 5, 17.

Prime Factorization of 340: 22 × 51 × 171

Sum of Factors of 340: 756.

Step-by-step explanation:

Answer:

To show that (x-3) is a factor of the polynomial h(x) = f(x) - f(3), we need to use the definition of a polynomial factor. A polynomial factor is a polynomial that, when multiplied by another polynomial, results in the original polynomial.

First, let's evaluate f(3) to find the value of h(3).

h(3) = f(3) - f(3) = 0

Now let's examine the value of h(x) for any x other than 3.

h(x) = f(x) - f(3)

If (x-3) is a factor of h(x), then for any value of x other than 3, h(x) should be equal to zero.

So,

h(x) = (x-3)g(x)

where g(x) is another polynomial.

Therefore, by definition, (x-3) is a factor of h(x) = f(x) - f(3).

Answer:

72°

Step-by-step explanation:

here's your solution

=> we know angle A + angle S = 2

=> angle 2 = 30° + 42°

=> 72°

hope it helps

Answer:

(6, 1)

Step-by-step explanation:

x + 2y = 8

1. subtract 2y to get x alone -- x = -2y + 8

2. insert (-2y + 8) as x

2x - 2 = 10

2(-2y + 8) -2 = 10

3. distribute the 2

-4y + 16 - 2 = 10

4. combine like terms

-4y + 14 = 10

5. subtract 14 from both sides

-4y = -4

6. divide by -4

y = 1

7. plug y into any of the two original equations

x + 2(1) = 8

8. simplify

x + 2 = 8

x = 6

9. check answer with second equation

2(6) - 2 = 10

12 - 2 = 10

The limit exists and is finite, the sequence is bounded.

To determine whether the sequence is increasing, decreasing, or not monotonic, we need to analyze the first derivative of the sequence. Taking the first derivative of the sequence gives:

a' = 6e^(-5n) - 30ne^(-5n)

To determine the sign of the first derivative, we can set it equal to zero and solve for n:

6e^(-5n) - 30ne^(-5n) = 0

6 - 30n = 0

n = 1/5

Now we can evaluate the first derivative at n = 0 and n = 1 to determine the sign of the derivative in each interval:

a'(0) = 6 > 0

a'(1) = -24e^(-5) < 0

Therefore, the sequence is decreasing.

To determine whether the sequence is bounded or not, we can take the limit as n approaches infinity:

lim(n→∞) an = lim(n→∞) 6ne^(-5n) = 0

Since the limit exists and is finite, the sequence is bounded.

Learn more about monotonicity and boundedness of a given sequence

brainly.com/question/14351330

#SPJ11

Answer:

a. POSITIVE NUMBER mean availability of money

NEGATIVE NUMBER mean Overdrawn

ZERO mean unavailability of money

b. YES

Step-by-step explanation:

a. Based on the information given the POSITIVE NUMBER mean the AVAILABILITY of some amount of money

A NEGATIVE NUMBER on the other hand mean OVERDRAWN which means that the customer account balance fall below Zero amount

ZERO mean UNAVAILABILITY OF MONEY

b. YES. Based on the information given if Lorena's final account balance has the amount of -$68.50 the bank will loan her reason been that we were told that the bank will give loan to their customers if they overdraw their accounts by less than the amount of $100 in which case Lorena's final account balance has the amount of -$68.50 which is less than $100. Hence the bank will loan her .

The calculated t-value is greater than 1.734, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

An engine additive is being tested to see whether it can effectively increase gas mileage for a number of vehicles. Twenty assorted vehicles had their gas mileage, in miles per gallon, measured. Then, the engine additive was placed into each of the engines, and the gas mileage was measured again. Let µd be the true mean difference in the gas mileage before and after the engine additive is placed into the engines. We want to test the hypothesis that the engine additive has no effect. The null hypothesis is: H0: µd = 0The alternative hypothesis is: Ha: µd > 0 (one-tailed test)Assuming that the difference in gas mileage before and after the engine additive is approximately normally distributed, we can use a one-sample t-test. The test statistic is given by: $$t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$$Where, $\bar{x}$ is the sample mean difference in gas mileage, μ is the hypothesized population mean difference, s is the sample standard deviation of the differences, and n is the sample size. We can use a significance level of α = 0.05.To determine the critical value of the t-distribution, we need to find the degrees of freedom (df). Since we have a sample size of n = 20, we have n - 1 = 19 degrees of freedom. Using a t-distribution table with 19 degrees of freedom and a significance level of 0.05 for a one-tailed test, we get a critical value of t = 1.734. If the calculated t-value is greater than 1.734, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

Learn more about null hypothesis here:

https://brainly.com/question/30821298

#SPJ11

132 cm² is the area of the given figure.

To find the area of the figure we need to divide it into two parts such as a rectangle with the dimension of 20 * 6 and a triangle with the dimension of  (10 - 6) * (20 - (8 + 6)).

So,

the height of the triangle = 10 - 6 = 4 cm

the base of the triangle = 20 - (8 + 6) = 20 - 14 = 6 cm

Thus,

the area of the triangle = 1/2 * base * height

= 1/2 * 6 * 4

= 12 square cm

Area of the rectangle = length * width

= 20 * 6

= 120 square cm

Thus, the area of the figure will be = 120 + 12  = 132 square cm.

Learn more about Area here:

https://brainly.com/question/27683633

#SPJ1

Given:

A figure of a kite.

To find:

The area of the given kite.

Solution:

The area of a kite is the half of the product of its diagonals.

\(A=\dfrac{d_1d_2}{2}\)             ...(i)

Where, \(d_1,d_2\) are two diagonals of the kite.

From the given figure it is clear that the length of one diagonal is the sum of 12 and 8.

\(d_1=12+8\)

\(d_1=20\)

Let the second diagonal be 2x. The first diagonals bisect the second diagonal. So, the length of one parts of the diagonal is x.

Diagonals of a kite are perpendicular to each other. Using Pythagoras theorem, we get

\(Hypotenuse^2=Perpendicular^2+Base^2\)

\(13^2=x^2+12^2\)

\(169-144=x^2\)

\(25=x^2\)

\(5=x\)

The length of second diagonal is:

\(d_2=2x\)

\(d_2=2(5)\)

\(d_2=10\)

Substituting \(d_1=20,d_2=10\) in (i), we get

\(A=\dfrac{20\times 10}{2}\)

\(A=\dfrac{200}{2}\)

\(A=100\)

Therefore, the area of the kite is 100 square units.

Answer:

tbh i think the answer is b

Step-by-step explanation:

Answer:

yeah i think its B too

Step-by-step explanation:

a) The relationship between b and c is that c cannot be zero.

b) b can be any nonzero constant and c is equal to 2.5 in this case.

In two dimensions, the compatibility equations for strain are,0

∂εx/∂y + ∂γxy/∂x = 0

∂εy/∂x + ∂γxy/∂y = 0

where εx and εy are the normal strains in the x and y directions, respectively, and γxy is the shear strain.

Using the given strain field, we can calculate the strains,

εx = -4.5cx² + 10.5cy

εy = 1.5cx² - 7.5cy²

γxy = 1.5bxy

Taking partial derivatives and plugging them into the compatibility equations, we get,

⇒ -9cx + 0 = 0

⇒ 0 + (-15cy) = 0

These equations must be satisfied for the strain field to be compatible. From the first equation,

We get cx = 0, which means c cannot be zero.

From the second equation, we get cy = 0,

Which means b can be any nonzero constant.

For part b:

We are asked to find the displacements u and v corresponding to the given strain field at points (3, 7), assuming they are zero at point (0, 0) and using c = 2.5.

To find the displacement components,

We need to integrate the strains with respect to x and y. We get,

u = ∫∫εx dx dy = ∫(10.5cy) dy = 5.25cy²

v = ∫∫εy dx dy = ∫(1.5cx² ) dx - ∫(7.5cy²) dy = 0.5cx³ - 2.5cy³

Plugging in the values of c and b, we get,

u = 5.25(2.5)(7)²  = 767.62

v = 0.5(2.5)(3)³ - 2.5(7)³ = -8583.75

Therefore,

The displacements at points (3, 7) are u = 767.62 and v = -8583.75.

To learn more about derivatives visit;

https://brainly.com/question/29144258

#SPJ4

The equation to determine the number of players the team can bring to the tournament is:

1405.25 - 822.50 - 27.75x = 0

Where:
1405.25 represents the total amount of money raised by the team
822.50 represents the cost of renting the bus
27.75 represents the budgeted amount per player for meals
x represents the number of players the team can bring to the tournament

To solve this equation, we need to isolate the variable x:

1405.25 - 822.50 - 27.75x = 0

582.75 - 27.75x = 0

-27.75x = -582.75

x = 21

Therefore, the team can bring 21 players to the tournament.

the equation is created by subtracting the total cost of the bus and meals from the total amount raised by the team. The remaining amount should be zero, as all the money raised should be accounted for. By solving for x, we can determine the number of players that can be brought to the tournament.

In conclusion, the softball team can bring 21 players to the tournament based on their budget.

To know more about variable visit:

https://brainly.com/question/17344045

#SPJ11

Answer:

6. From speed vs. time graphs, we know that in order to find the distance, we need to look at the area covered. Given the rectangular shape below, we know that it would be A=lw so A=60mph(2.5h).

7. A=60mph(2.5h)= 150 miles.

Answer:

7

Step-by-step explanation:

i got it correct on my test

Answer:

last one: 20

Step-by-step explanation:

4 divided by 5 is 0.8

so is 20 divided by 25

Answer: 15c

Step-by-step explanation:

When you come across any question that mentions [the product of a and b] means a × b

Solve:

The product of 15 and c

Answer:

90 hope this helps

Step-by-step explanation:

Given linear inequalities is solved using graph paper line will pass through (6,0) and (-0,4) Area where required linear inequalities is satisfied is towards origin.

let's first try to understand  what is linear inequalities?

A linear inequality in mathematics is an inequality involving a linear function. One of the symbols for inequality is found in a linear inequality. It displays non-equal data in graph style.

the linear inequality's graph Since the inequality is severe and the shaded region points in the direction of the origin, 2 x-3 y < 12 is a straight line passing through the points (6, 0) and (0, -4), with the line being dot-dotted.

x - coordinate of the given line 2x - 3y =12

y =0 2x = 12 x = 6 (6,0)

y - coordinate of the given line -3y = 12 y = -4  (0,-4)

line passes through (6,0) and (0,-4).

Given Question is incomplete complete Question here:

How do you graph linear inequalities 2x - 3y< 12?

To know more about linear inequality here:

https://brainly.com/question/11897796

#SPJ4