The triangles are similar. The ratio of the lengths of their corresponding sides is 25:45, or 5:9. Find the ratio of their perimeters and the ratio of their areas.

Answer:

[tex]\frac{C}{2\pi }=r[/tex]

Step-by-step explanation:

[tex]C=2\pi r[/tex]

WE need to solve for 'r'. Our aim is to get 'r' alone

2πr mean 2 times pi times r

To remove 2π we do opposite operation

Opposite operation of multiplication is division.

To remove 2π , divide both sides by 2π

[tex]\frac{C}{2\pi }=\frac{2\pi r}{2\pi}[/tex]

Now simplify it

[tex]\frac{C}{2\pi }=r[/tex]

The correct answer is D. ƒ(x)=-√(x+b)-a. This function satisfies the range and domain conditions stated in the question.

The correct answer is D. ƒ(x)=-√(x+b)-a.

A function with a range of (-∞, a] means that the output values of the function are less than or equal to a. In option D, the function is defined as ƒ(x)=-√(x+b)-a, where a < 0 and b < 0. When we substitute negative values for x in this function, the output values will be less than or equal to a, satisfying the range condition. Similarly, when x tends to positive infinity, b becomes negligible, and the function approaches -∞. This satisfies the domain condition [b, ∞).

Therefore, option D is a possible example of a function with the given range and domain conditions.

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Gerry needs to pay $150 for 6 choco-lava cakes which cost $25 each.

The subject here is Mathematics, particularly dealing with proportionality. If Gerry sees that 2 choco-lava cakes cost $50, we can say that the price of each choco-lava cake is $50 divided by 2, which is $25 per choco-lava cake. Then, if Gerry needs 6 choco-lava cakes, we take the price of one choco-lava cake ($25) and multiply it by how many cakes he needs, which is 6. So, 6 cakes at $25 per cake give us $150.

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Step 1

Find the value of x

we know that

If lines  p and q are parallel

then  

[tex](45x-5)+(16x+2)=180\°[/tex] ------> by consecutive interior angles

Solve for x

[tex](45x-5)+(16x+2)=180\° \\61x=180+3 \\x=3\°[/tex]

Step 2

Find the value of y

we know that

If lines  p and q are parallel

then  

[tex](26y)=(45x-5)[/tex] ------> by corresponding angles

substitute the value of x and solve for y

[tex](26y)=(45*3-5)[/tex]

[tex](26y)=130[/tex]

[tex]y=5\°[/tex]

therefore

the answer is the option

[tex]x=3\°[/tex] , [tex]y=5\°[/tex]

To convince me that they're not guessing on a true-false test, a student needs to get significantly more than half of the questions right.

A true-false test consists of 50 questions. To convince me that he is not merely guessing, a student would need to get significantly more than half of the questions right. If the student gets exactly half of the questions right, that would be the result we would expect from guessing. However, if the student consistently gets more than half of the questions right, it would indicate that they have some knowledge or understanding of the material.

Let's say a student gets 30 out of 50 questions correct. This would be 60% of the questions, which is higher than 50%, indicating that the student is not merely guessing.

Answer:

64000

Step-by-step explanation:

so, you have to double it every three months, so you are doubling is 8 times total. so, when you double 250 the first time you get 500 so then you double that, and you get 1000 the you double that to get 2000 then  you double that to get 4000 then you double that again and get 8000 then you double that again  to get 16000 then again to get 32000 and the one more time  to get your answer 64000

The relationship is as you join more parallelograms together, the base length increases, and thus, the perimeter of the figure formed by these parallelograms also increases.

The perimeter of each individual parallelogram can be calculated using the formula for the perimeter of a parallelogram:

P = 2(base + side)

P = 2(5 + 4) = 2(9)

= 18 units

The second parallelogram has a base of 10 units and a side length of 4 units. The perimeter of the second parallelogram is:

P = 2(10 + 4) = 2(14)

= 28 units

The perimeter of the third parallelogram is:

= P = 2(15 + 4) = 2(19)

= 38 units

The relationship is such that the perimeter is directly proportional to the number of parallelograms joined together, with each additional parallelogram adding 10 units to the base length and subsequently increasing the perimeter by 20 units.

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Answer:

[tex] The\ slope\ of\ the\ line\ AB\ is \frac{1}{7} .[/tex]

Step-by-step explanation:

Formula for slope

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

As the Line AB contains points A (8, −4) and B (1, −5).

Put points value in the above

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

[tex]m = \frac{- 5- (-4)}{1 - 8}[/tex]

[tex]m = \frac{- 5 + 4}{1 - 8}[/tex]

[tex]m = \frac{- 1}{-7}[/tex]

[tex]m = \frac{1}{7}[/tex]

[tex]Therefore\ the\ slope\ of\ the\ line\ AB\ is \frac{1}{7} .[/tex]

The area of the sector of the circle whose radius is 4.2 cm while the angle made at the center is 68° is 10.5 cm².

A circle can be defined as a shape that consists of all points in a plane that are at equal distance from a given point, therefore, the center.

As it is given that the length of the radius of the circle is 4.2 cm, while the angle made by the sector at the center of the circle is 68°. Therefore, the area of the sector of the circle can be written as,

[tex]\text{Area of the sector of the circle} = \pi r^2\times \dfrac{\theta}{360^o}[/tex]

Substituting the value, we will get,

[tex]\text{Area of the sector of the circle} = \pi \times(4.2^2)\times \dfrac{68^o}{360^o}[/tex]

                                                [tex]= 10.472 \approx 10.5\rm\ cm^2[/tex]

Hence, the area of the sector of the circle whose radius is 4.2 cm while the angle made at the center is 68° is 10.5 cm².

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To solve the problem we will first calculate the remaining balance in Loren's Account after a year.

The balance in Loren's account after two years is £430.54.

Given to us

Using the compound interest formula,

Balance of Loren after one year = [tex]P(1+r)^t[/tex]

Substituting values,

[tex]=600(1+0.03)^1\\= 600(1.03)\\= 618[/tex]

Now, as Loren takes £200 out of the account, the remaining balance would be,

= Balance of Loren after one year - £200

= £618 - £200

= £418

In the second year, the balance will be paid on the remaining balance, therefore, applying the formula of compound interest,

P = £418

r = 0.03

t = 1

[tex]=P(1+r)^t\\=418(1+0.03)^1\\=418(1.03)\\= 430.54[/tex]

Hence, the balance in Loren's account after two years is £430.54.

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The Gordons' eligibility for Chapter 7 bankruptcy cannot be definitively determined without detailed calculations. While their income is above West Virginia's median income, their high monthly expenses might allow them to pass the bankruptcy means test.

To determine whether the Gordons qualify for Chapter 7 bankruptcy, we must consider their income, monthly expenses, and the median annual income for their state. As their income is $49,000 a year, they exceed the median annual income of West Virginia, which is $37,989. Their $3,900 monthly expenses total to $46,800 annually.

Under Chapter 7 bankruptcy, a means test is applied to identify whether the Gordons' income is low enough for eligibility. This test compares the family’s monthly income to the median income of a family the same size. However, it is important to note that not all income is counted in this means test and some deductions are given for various necessary expenses.

In this scenario, the Gordons' income is above the median income for West Virginia. However, their high monthly expenses might still allow them to pass the means test. You would need to calculate whether their income, minus allowable expenses, is still above the median. Without these detailed calculations, it's impossible to definitively say whether the Gordons qualify for Chapter 7 bankruptcy.

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After k payments, the amount A still owed is

Answer:

13 cars

Step-by-step explanation:

There are 5 fewer trucks than cars in the parking lot. There are 8 trucks in total.

5 less trucks than cars. we need to find number of cars in the parking lot.

Cars are more than trucks. To find the number of cars, we add 5 with the total trucks .

8 trucks + 5 = 13

So there are total of 13 cars .

100% - 30% = 70% P = 0.7*900
which equals $630

Answer:

The net price of the stove is $630.

Step-by-step explanation:

The list price of a stove = $900

Trade discount on the price = 30%

The net price = 900 - (30% of 900)

                      = 900 - ([tex]\frac{30}{100}[/tex] × 900)

                      = 900 - (0.30 × 900)

                      = 900 - 270

                      = $630

The net price of the stove is $630.

Answer:

12ab

Step-by-step explanation:

i got a 100%