If the side of a square is doubled and then increased by 7, the new perimeter is 8 more then 3 times the old perimeter. What is the side of the original square?

Final answer:

The area per person served by a 12-inch quiche, it was determined that a 10-inch quiche can indeed feed 4 people with the same serving size, as the area available per person in the 10-inch quiche is sufficient.

Explanation:

To determine whether a quiche with a diameter of 10 inches can feed 4 people at the same serving size as a 12-inch quiche that feeds 6 people, we need to compare the areas of the two quiches. The area of a circle is calculated using the formula A = πr² where A is the area and r is the radius. Since the radius is half of the diameter, the 12-inch quiche has a radius of 6 inches and the 10-inch quiche has a radius of 5 inches.

For the 12-inch quiche:
A12 = π(6²) = 36π

For the 10-inch quiche:
A10 = π(5²) = 25π

So, the 12-inch quiche has an area of 36π square inches and the 10-inch quiche has an area of 25π square inches. To find out if the smaller quiche can serve 4 people, we calculate the area per person for the larger quiche: 36π/6 = 6π square inches per person.

Now, we check to see if the 10-inch quiche provides at least that much area for 4 people: 25π/4 ≈ 6.25π square inches per person. Since 6.25π is greater than 6π, we can conclude the 10-inch quiche can indeed feed 4 people with the same serving size as the 12-inch quiche fed 6 people.

By using equations to represent the relationship between Kevin and Daniel's ages, we can determine that Kevin is 24 years old.

Kevin is 3 times as old as Daniel. Let's denote Kevin's age as K and Daniel's age as D. From the information given, we can form two equations:

K = 3D

K - 4 = 5(D - 4)

3D - 4= 5D -20

16 = 2D

D = 8

K = 24

Solving these equations simultaneously gives the age of Kevin, therefore, Kevin is 24 years old.

Answer:  She needed 128 cm of ribbon.

Step-by-step explanation:

Since we have given that

Length of yellow ribbon needed to be cut = 1 meter

Length of blue ribbon needed to be cut = 28 cm

We need to find the number of centimeters she needed to be cut.

First of all, we convert meter into centimeter.

As we know that

1 meter = 100 centimeter

So, Total number of centimeters of ribbon she needed is given by

[tex]100+28\\\\=128\ cm[/tex]

Hence, She needed 128 cm of ribbon.

The solution is Option A.

The distance between the base of the ladder and the wall is 9 feet

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ABC

Now , the height of the wall = 12 feet

The measure of AB = 12 feet

The length of the ladder = 15 feet

The measure of AC = 15 feet

Now , the distance between the base of the ladder and the wall = BC

The measure of BC is given by the Pythagoras Theorem , where

Hypotenuse² = base² + height²

AC² = AB² + BC²

Substituting the values in the equation , we get

15² = 12² + BC²

Subtracting 12² on both sides of the equation , we get

BC² = 15² - 12²

BC² = 225 - 144

BC² = 81

Taking square roots on both sides of the equation , we get

BC = 9 feet

Therefore , the value of BC is 9 feet

Hence , the distance is 9 feet

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make 1 3/4 an improper fraction:

1 3/4 = 7/4

 now you have 4/7 divided by 7/4

now reverse the 7/4 and multiply:

4/7 x 4/7 = 16/49

The ordered pairs lie on the graph of the exponential function [tex]\rm f(x) = 4(5)^{2x}[/tex] is (2,2500) and this can be determined by using the arithmetic operations.

Given :

Exponential Function  ---  [tex]\rm f(x) = 4(5)^{2x}[/tex]

The following steps can be used in order to determine the ordered pairs lie on the graph of the exponential function:

Step 1 - Write the exponential function.

[tex]\rm f(x) = 4(5)^{2x}[/tex]

Step 2 - Substitute the value of (x = -1425) in the above exponential function.

[tex]\rm f(x) = 4(5)^{2\times -1425}[/tex]

[tex]\rm f(x) = 4(5)^{-2850}[/tex]

By simplifying the above function it does not give the value of f(x) = -1425, therefore, option (A) is incorrect.

Step 3 - Substitute the value of (x = 0) in the above exponential function.

[tex]\rm f(x) = 4(5)^{2\times 0}[/tex]

f(x) = 4

Therefore, option (B) is also incorrect.

Step 4 - Substitute the value of (x = 1) in the above exponential function.

[tex]\rm f(x) = 4(5)^{2\times 1}[/tex]

f(x) = 100

Therefore, option (C) is also incorrect.

Step 5 - Substitute the value of (x = 2) in the above exponential function.

[tex]\rm f(x) = 4(5)^{2\times2}[/tex]

f(x)  = 2500

Therefore, option (D) is correct.

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The answer choices are:

A. h= m -2

B. h=m -10

C. h= m/5

D. h= m-10/5

Final answer:

There are 209 numbers among the first 10,000 positive integers that contain the digit pair '43' in that order, when considering the different placements of the digit pair in a four-digit number.

Explanation:

To find out how many of the first 10,000 positive integers contain the digit pair "43" in that order, let's consider the different places this pair can occur. The '43' pair can be in the units and tens place, the tens and hundreds place, or the hundreds and thousands place.

For the units and tens place, we have '43' fixed and two remaining places that can be any digit from 0 to 9, so there are 10 times 10 = 100 possibilities. However, we need to exclude the combination '043' as it is not a four-digit number but rather '43', giving us 100 - 1 = 99 combinations.

For the tens and hundreds place, we again have 10 possibilities for the other two places (thousands and units). We do not need to exclude any numbers here because even '043x' represents a valid four-digit number. Thus, we have 10  imes 10 = 100 combinations.

For the hundreds and thousands place, there are only 10 possibilities for the units place, as '430x' represents a valid four-digit number, which results in 10 combinations.

Adding them up, we have a total of 99 + 100 + 10 = 209 numbers that contain the '43' pair in the first 10,000 positive integers.

Answer: The equation that shows y=(3/4)x-5/2 is standard form is:

Second option: 3x-4y=10

Solution:

y=(3/4)x-5/2

Standard form of the equation Ax+By=C, with A, B, and C integer numbers

The coefficient of "x" and the independent term are fractions. To simplify them, let's multiply both sides of the equation by 4:

4y=4 [ (3/4)x-5/2]

4y=4(3/4)x-4(5/2)

4y=(4/1)(3/4)x-(4/1)(5/2)

4y=[(4*3)/(1*4)]x-(4*5)/(1*2)

4y=(12/4)x-20/2

4y=3x-10

The two variables must be in the same side of the equation and the independent term in the other side, but the coefficient of "x" must be positive, then subtracting 4y and adding 10 both sides of the equation:

4y-4y+10=3x-10-4y+10

10=3x-4y

3x-4y=10

Answer:

its B i took the test explanation:

Answer: 862

Step-by-step explanation:

Let the third digit of Y be x .

Then , the first digit will be 4x and the second digit will be 3x.

Since , the digits of Y add to 16.

Then we have

[tex]3x+4x+x=16\\\\\Rightarrow\ 8x=16\\\\\Rightarrow\ x=\dfrac{16}{8}=2[/tex]

Thus , the third digit of Y = 2

Then the first of Y digit will be [tex]4(2)=8[/tex]

The second digit of Y will be  [tex]3(2)=6[/tex]

Hence, the  digits of Y must be 862

x^2 +6^2 = 10^2

x^2 + 36 =100

x^2 = 64

x = sqrt(64)

x = 8

The concept of linear equation and ratios is used to solve for the price of radios. The price of two radios are [tex]x=\pounds 80[/tex] and [tex]y=\pounds 20[/tex].

Given information:

The ratio of prices of two radios is [tex]x:y[/tex].

If the price of both the radios is increased by [tex]\pounds20[/tex], the ratio of price would become 5:2.

The above condition can be written mathematically as,

[tex]\dfrac{x+20}{y+20}=\dfrac{5}{2}\\2x+40=5y+100\\2x-5y=60.........(1)[/tex]

If the prices are both reduced by [tex]\pounds 5[/tex], the ratio will become 5:1.

The above condition can be written mathematically as,

[tex]\dfrac{x-5}{y-5}=\dfrac{5}{1}\\x-5=5y-25\\x-5y=-20\\-x+5y=20.........(2)[/tex]

Add equation (1) and (2), to get the value of [tex]x[/tex] and [tex]y[/tex] as,

[tex]2x-x=60+20\\x=80[/tex]

Solve for [tex]y[/tex] as,

[tex]2x-5y=60\\2\times 80-5y=60\\5y=100\\y=20[/tex]

Therefore, the price of two radios is [tex]x=\pouns 80[/tex] and [tex]y=\pounds 20[/tex].

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Answer:

21

Step-by-step explanation:

hard wok

talent

Amy's class saw a total of 40 horses and ponies and 55 rabbits and hares at the fair,

The question involves comparing the numbers of two sets of animals seen at the fair: horses and ponies versus rabbits and hares. To solve this, we will first add the number of horses and ponies together and then do the same for rabbits and hares.

Number of horses and ponies combined:
22 horses + 18 ponies = 40

Number of rabbits and hares combined:
18 rabbits + 37 hares = 55

Comparing the two totals:
40 horses and ponies is less than 55 rabbits and hares. Therefore the class saw more rabbits and hares combined than horses and ponies combined at the fair

The product of the given expression of a fraction is [tex]\frac{-3}{16}[/tex].

Given:

An expression : [tex]\frac{3}{8}.(\frac{-3}{6})[/tex]

To find:

The product of the given expression of fractions in simplified form.

Solution:

[tex]\frac{3}{8}.(\frac{-3}{6})\\\\= \frac{3}{8}\times (\frac{-3}{6})\\\\=\frac{-9}{48}\\\\=\frac{-3}{16}[/tex]

The product of the given expression of a fraction is [tex]\frac{-3}{16}[/tex].

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The correct answer to the given expression 2(b+3c) is 'None of the above' as none of the provided options represent an equivalent expression after the application of distributive property.

The expression 2(b+3c) cannot be transformed into any of the given options directly. If we use distributive property, we expand 2(b+3c) to get 2b + 6c, which is equivalent to the original expression.

The options provided, such as 3(b+2c), (b+3c) +(b+3c), or 'None of the above', do not simplify or represent an equivalent expression to 2(b+3c). The correct answer is 'None of the above'. It's important to note that the commutative property of addition, A+B = B+A, and the associative property, (A+B) + C = A +(B+C), suggest that we can regroup or reorder terms in an addition expression without changing its value. However, none of these properties help in finding an equivalent expression among the given options for 2(b+3c).

To guarantee a team, you would need 13 persons, and to guarantee two teams, you would need 24 persons.

The number of persons needed to guarantee that they can raise a team is one more than the number of months in a year. This is because there are 12 months in a year, and to ensure that all team members have birthdays in the same month, you would need at least one person for each month. Therefore, you would need 13 persons to guarantee a team.

To guarantee that there are two teams, you would need a total of 24 persons. This is because each team needs at least one person for each month, and there are 12 months in a year. So, for the first team, you would need 13 persons, and then you would need an additional person for each month to form the second team. This would give you a total of 24 persons to guarantee two teams.

Final answer:

To guarantee that a team can be formed, there needs to be at least one person born in each month of the year. To guarantee that two teams can be formed, you would need at least two people born in each month of the year.

Explanation:

To guarantee that a team can be formed, there needs to be at least one person born in each month of the year. Since there are 12 months, you would need a minimum of 12 people to ensure that a team can be formed.

To guarantee that two teams can be formed, you would need at least two people born in each month of the year, as each team needs five members. So, you would need a minimum of 24 people to ensure that two teams can be formed.