A rectangular garden has a walkway around it. The area of the garden is 4​(6.5x+2.5​). The combined area of the garden and the walkway is 4.5​(8x+4​). Find the area of the walkway around the garden as the sum of two terms.

Answer: Let's call the rainfall in the second half of the month "x".

From the first half of the month, we know that the total rainfall was 1/5 inch.

At the end of the month, we know that the total rainfall was 1/2 inch:

1/5 + x = 1/2

Subtracting 1/5 from both sides:

x = 1/2 - 1/5

x = 3/10

So the rainfall in the second half of the month was 3/10 of an inch.

Step-by-step explanation:

Hello! :3

Answer:

x = 1

graphing:

Answer: 4

Step-by-step explanation:

2 multiplied by 2 is 4. You have 2 of the 2's so it becomes 4.

Answer:4

Step-by-step explanation:

have a good day :)

The perimeter of the isosceles trapezoid is equal to 30 inches.

This is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.

We shall first find the length of the left and right sides which are of same length as follows:

we can get a right triangle with base (13 - 7)/2 = 3 and height 4 inches so that the hypotenuse is the length of of the sides of the trapezoid

a side of the trapezoid = √(3² + 4²) {Pythagoras rule}

a side of the trapezoid = √(9 + 16)

a side of the trapezoid = √25

a side of the trapezoid = 5

perimeter of the isosceles trapezoid = (5 + 7 + 5 + 13) inches

perimeter of the isosceles trapezoid = 30 inches.

Therefore, they perimeter of the isosceles trapezoid is equal to 30 inches.

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The $7.54 money he had left for gift C.

Nolan had 20 dollars to spend on 3 gifts.

He spent 9.34 dollars on gift A and 3.12 dollars on gift B

Total Amount = 20 dollars.

Total number of gifts = 3 i .e Gift A, Gift B , Gift C.

First, let's add up the amount Nolan spent on gifts A and B:

⇒9.34 + 3.12 = 12.46

The amount spent on gifts A and gifts B is $12.46

Next, we subtract this amount from the total amount of money Nolan had:

Amount Left for Gift C = Total Amount - Total amount spend for  Gift A and Gift B.

⇒20 - 12.46 = 7.54

So,

Therefore, the Nolan had $7.54 left to spend on gift C.

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Answer:

y=-1/4x+2

Step-by-step explanation:

y=mx+c

1st point : (-4,3)

2nd point : (4,1)

m= rise/run

  = 3-1/-4-4

  = 2/-8

  = -1/4

y=-1/4x+2

Answer: y = -1/4[tex]x[/tex] + 2

Step-by-step explanation:

The equation of any line is y = mx + c, where:

m = gradient of the line

c = y-intercept (the point where the line goes through the y-axis)

So, to make this line into an equation, we first find the gradient. To calculate the gradient, we have to find the [tex]\frac{rise}{run}[/tex] .To do this, we take 2 points from the line that are whole numbers and put it into this equation. So, we can take (0,2) & (4,1). Since we have this, we can sort of draw an imaginary triangle. Now we find the rise, which is 1, and the run, which is 4. So we know the gradient is [tex]\frac{1}{4}[/tex], but since its a line going downwards, it will have a negative gradient meaning it is [tex]-\frac{1}{4}[/tex] .

For the y-intercept, we can see that the line intercepts/crosses the y-axis at (0,2), so the y-intercept is 2. So we have the equation:

[tex]y = - \frac{1}{4}x + 2[/tex]

Answer:

Explanation:

A function has each x input go to exactly one and only one y output. This means something like (3,7) and (3,6) leads to "not a function". The input x = 3 leads to multiple outputs.

So all we have to do is look at the x coordinates of the points. If we see any repeats, then the answer is "not a function". Otherwise, we have a function.

Answer:

1.not function

2. function

3.not function

4.function

The value of a geometric sequence can not be zero, because for that we have to include 0 as a term in it and that will turn the sequence into zero.

A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

In geometric sequences, the terms given by the ratio of every two successive terms is a constant. they can be either negative or positive but not zero, because if any term will be zero it will directly make the common ratio equal to 0, that will make the sequence turning to  0, and it won't be a geometric progression anymore, therefore, the successive values of a geometric sequence could become infinitesimally small but never be equal to 0.

An example of a Geometric sequence is 2, 4, 8, 16, 32, 64, …, where the common ratio is 2.

If suppose 2nd term is 0, then common ratio = 0/2 = 0, that will disturb the pattern and the sequence will not be a GP

Hence, the successive values of a geometric sequence could become infinitesimally small but never be equal to 0.

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There are 56 possible ways to man the two sides of the boat with two crew members rowing on the stroke side and three crew members rowing on the bow side.

The number of ways to man the two sides of the boat can be calculated using the combination formula, C(n,r). In this case, n = 8 (the total number of crew members) and r = 5 (the number of crew members needed to man the two sides of the boat). The equation to calculate the number of ways to man the two sides of the boat can be written as C(8,5).

C(8,5) = 8!/(5!*3!) = 56.

This means that there are 56 possible ways to man the two sides of the boat with two crew members rowing on the stroke side and three crew members rowing on the bow side.

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The value of x from the given figure is 10.

According to the theorem, the product of the measurements of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment if two secant segments are drawn to a circle from an exterior point.

Applying the rule to the given diagram:

3(3+x-5) = 4(4+x-8)

Simplify

3(x-2) = 4(x-4)

3x - 6 = 4x - 16

3x - 4x = -16 + 6

-x = -10

x = 10

Hence the value of x from the diagram is 10

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The total square footage (area) of the apartment is 332 ft²

To find the total area of the apartment we need to calculate the area of the given each room by using the given dimensions. Find the sum of the areas of each room to the area of the apartment.  

Area of a rectangle room = Length × Width

Here we have  

Dimensions of bedroom = 11ft × 10ft    

Area of the bedroom =  11ft × 10ft = 110 ft²  

Dimensions of bathroom = 5ft × 6ft  

Area of the bathroom = 5ft × 6ft = 30 ft²  

Dimensions of Sigle multi-use living room = 12ft × 16 ft  

Area of the living room  = 12ft × 16 ft = 192 ft²  

From above calculations

The total square footage of the apartment

= 110 ft² + 30 ft² + 192 ft²  

= 332 ft²

Therefore,

The total square footage (area) of the apartment is 332 ft²

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The partial fraction decomposition of 2x-5 over x(x-4) is 2/x + 5/x-4. This separates the fraction into two simple fractions with a common denominator.

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

By breaking down the expression into two simpler fractions, we can more easily manipulate the equation and solve for the unknowns. It is an important tool when it comes to solving complex polynomials and equations.

Partial fraction decomposition is a technique used to break down a complex fraction into simpler fractions with a common denominator. This makes the equation easier to manipulate, and can be used to solve polynomials and equations.

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Anwser:

Its B

Explanation

A/x + B/x+4

The sides h of the similar triangle is 2√6 units.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

The triangles are similar. Therefore, the side h can be found using the proportion of the sides.

using proportion,

6 / h = h / 4

cross multiply

6 × 4 = h²

h² = 24

square root both sides of the equation

h = √24

h = 2√6

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Fredrick mixed 1/2 liters of blue paint with 1 1/2 liters of green paint to make 2 liters of teal paint, for  the same ratio the amount of  blue paint need to mix with 1 liter of green paint is, 1 liter

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

Fredrick mixed 1/2 liters of blue paint with 1 1/2 liters of green paint to make 2 liters of teal paint

For the same ratio the amount of  blue paint need to mix with 1 liter of green paint = ?

Let's call the amount of blue paint needed to mix with 1 liter of green paint "x".

Since the ratio of blue paint to green paint in the original mixture was 1/2 liters to 1 1/2 liters, we can set up the following equation:

1/2 + x = 1 1/2

Solving for x, we can simplify the right side of the equation to 3/2 and subtract 1/2 from both sides:

3/2 - 1/2 = x

So, x = 1 liter of blue paint is needed to mix with 1 liter of green paint to make the same teal paint.

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Therefore , the solution of the given problem of linear equation comes out to be S = 80 third-grade kids.

A straightforward regression curve is created using the equation y=mx+b. The y-intercept is m, and the slope is B. The previous sentence is usually referred regarded as a "mathematical formula integrating multiple variables," even though y or y are different parts. Only two variables are present in bivariate linear equations. There are no known solutions to application issues involving linear equations.

Here,

The ability to convert words and phrases into clear, succinct math equations is essential for solving word (story) issues (variables and operations).

Let S represent the total number of third-graders.

The phrase "four fifths of a third grade" denotes 4/5 * S. ("of" usually means multiply)

"How many kids are in the third grade?" means to report S. "If 64 pupils made the trip" denotes that 4/5 * S = 64

, the math is as follows: (4/5)*S = 64 (multiply both sides by 5/4

S = 80 third-grade kids.

Therefore , the solution of the given problem of linear equation comes out to be S = 80 third-grade kids.

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The complete question is "Four fifths of the third grade went on a trip to the zoo. If 64 children made the trip, how many children are in the third grade?"

Answer:

Just use reflection, rotation, and translation.

Step-by-step explanation:

Reflection is when something is reflected in an opposite direction.

Rotation is when motion rotates in either a 90 or 180 degree flip.

Lastly is translation in which an object can move up or down.

Simply apply these rules with the purpose of making the objects slide into each other and unite as one or 'coincide'. Hope this helps!

The volume of the cylinder with a diameter of 14 mm and a height of 8 mm is approximately 1230.88 mm³.

The volume of a cylinder can be calculated using the formula:

V = πr²h

where r is the radius of the cylinder and h is its height. To find the volume, we first need to find the radius, which is half of the diameter:

r = 14 mm / 2

= 7 mm

Now that we have the radius, we can plug it into the formula along with the height to find the volume:

V = π * (7 mm)² * 8 mm

= 3.14 * 49 * 8 mm³

= 1230.88 mm³

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The correct option regarding the final solution in the Second World War is given as follows:

Germany's plan to exterminate all the Jewish people in Europe.

The final solution in the Second World War was Germany's plan to exterminate all the Jewish people in Europe.

Initially, when Hitler took power in 1933, Jewish people lost their possessions and were sent to concentration camps in following years, initially to work as slaves. However, in 1941, the decision was made to exterminate Europe's Jewish Population, which was called the final solution.

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Answer:

B

Step-by-step explanation:

note that n! = n(n - 1)(n - 2) ..... × 3 × 2 × 1

using n = 8 and r = 3 in the combination formula

[tex]\frac{8!}{3!(8-3)!}[/tex]

= [tex]\frac{8(7)(6)(5)(4)(3)(2)(1)}{3(2)(1)5!}[/tex] ← cancel 5! on denominator with 5(4)(3)(2)(1) on numerator

= [tex]\frac{8(7)(6)}{3(2)(1)}[/tex]

= [tex]\frac{56(6)}{6}[/tex] ← cancel 6 on numerator/ denominator

= 56

The unit of measure for kinetic energy is ft² lb² / s² because the velocity is multiplied by the mass and then squared. The correct answer would be an option (D).

Kinetic energy is the energy of motion, which can be seen as a body or subatomic particle moving. Kinetic energy exists in every moving object and particle.

Kinetic energy can be found using the formula Ek = 1/2 mv².

The variable Ek represents kinetic energy, the variable m is the mass in pounds (lbs.), and the variable v is the velocity in feet per second (ft/s).

The unit of measure for kinetic energy is ft² lb² / s² because the velocity is multiplied by the mass and then squared.

The units of measure for mass (lb.), velocity (ft/s), and time (s) are combined to form the unit of measure for kinetic energy.

Thus, the unit of measure for kinetic energy is ft² lb² / s².

Hence, the correct answer would be option (D).

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The number Joe is thinking of is -36.

To find the number Joe is thinking of, use algebraic expression and equation.

Let x be the number Joe is thinking of

According to the problem, "Eleven more than one third of the number is -1". We can translate this into an algebraic expression such as:

x/3 + 11 = -1

To find the value of x, we'll isolate it on one side of the equation:

x/3 = -12

Next, we'll multiply both sides of the equation by 3 to cancel out the fraction:

x = -36

Therefore, the number Joe is thinking of is -36.

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The Factors of the given expression is  [tex](2b-x)(7x^{2} -2)[/tex]

The method of grouping, also known as grouping or factoring by grouping, is a technique used in algebra to factor polynomials by grouping terms together into pairs or sets of two or more terms.

The expression [tex]14bx^{2} -7x^{3}-4b+2x[/tex] can be factored by applying the method of grouping:

Make groups

[tex](14bx^{2} -7x^{3}) +(-4b+2x)[/tex]

The greatest common factor (GCF) of two or more numbers is the largest positive integer that divides each of the numbers evenly. In other words, the GCF is the largest number that is a factor of all the numbers.

Now take the Greatest common factor of the above equation:

[tex]7x^{2} (2b-x)-2(2b-x)[/tex]

Now take the common factor [tex](2b-x)[/tex] out:

[tex](2b-x)(7x^{2} -2)[/tex]

The Factors of the given expression [tex]14bx^{2} -7x^{3}-4b+2x[/tex]  is  [tex](2b-x)(7x^{2} -2)[/tex]

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(a) The perimeter of the figure is 5x + 3x + 6 + 13x + 16.

(b) The simplified expression is 21x + 22.

The solution has been obtained by using algebraic expression.

What is an algebraic expression?

If a mathematical expression contains variables, constants, and algebraic operations, it is referred to as "algebraic" (addition, subtraction, etc.).

a) We know that perimeter of a figure is sum of all the sides.

So,

Perimeter = 5x + 3x + 6 + 13x + 16

b) We got an expression as 5x + 3x + 6 + 13x + 16

On simplifying it by combining the like terms, we get

21x + 22

Hence, the simplified expression is 21x + 22.

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u^3 + 8 factors as (u + 2)(u^2 + 2u + 4) is explained by kuta software infinite algebra as

x^3 + 125

To factor this expression, we can use the formula for the difference of cubes:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

We can set a = x and b = 5:

x^3 + 125 = (x + 5)(x^2 - 5x + 25)

So x^3 + 125 factors as (x + 5)(x^2 - 5x + 25).

a^3 + 64

To factor this expression, we can use the formula for the sum of cubes:

a^3 + b^3 = (a + b)(a^2 + ab + b^2)

We can set a = a and b = 4:

a^3 + 64 = (a + 4)(a^2 + 4a + 16)

So a^3 + 64 factors as (a + 4)(a^2 + 4a + 16).

x^3 - 64

To factor this expression, we can use the formula for the difference of cubes:

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

We can set a = x and b = 4:

x^3 - 64 = (x - 4)(x^2 + 4x + 16)

So x^3 - 64 factors as (x - 4)(x^2 + 4x + 16).

u^3 + 8

To factor this expression, we can use the formula for the sum of cubes:

a^3 + b^3 = (a + b)(a^2 + ab + b^2)

We can set a = u and b = 2:

u^3 + 8 = (u + 2)(u^2 + 2u + 4)

So u^3 + 8 factors as (u + 2)(u^2 + 2u + 4).

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Answer:

The missing measure is: 71

Step-by-step explanation:

Hope it helps! =D

The distribution was skewed or had other non-normal characteristics, it would be more difficult to make a definitive statement about the probability of paying less than $7,700 without additional information.

The probability distribution of a variable that is normally distributed is bell-shaped, with the majority of observations centred around the mean and decreasingly more observations as you travel away from the mean. The mean and standard deviation of the variable influence the shape of the distribution.

We may use the characteristics of the normal distribution to calculate the likelihood that a person would pay less than $7700 in taxes if we assume that the variable in question is normally distributed. To perform this computation, we would need to know the variable's mean and standard deviation.

For instance, if we were aware that the average tax paid by individuals was $10,000 with a $2,000 standard deviation, we could use a calculator or table of the standard normal distribution to estimate the likelihood that a person would pay less than $7,700. As $7,700 is more than two standard deviations below the mean, if the distribution were totally normal, we could argue that it would be exceedingly unusual for an individual to pay less than that amount. Without more information, it would be more challenging to make a firm determination regarding the likelihood of paying less than $7,700 if the distribution was skewed or had other non-normal characteristics.

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If and only if two triangles have two corresponding angles that are the same size, they are comparable by AA (Angle-Angle) similarity.

The measurements of the corresponding angles in each triangle must be compared in order to discover whether triangles are comparable by AA. The triangles are comparable by AA similarity if two angles in one triangle have the same measure as two angles in another triangle.

Find the matching angles in each triangle as a first step.

Step 2 is to compare the relevant angles' measurements.

Step 3: The triangles are similar by AA similarity if two angles in one triangle have the same measurement as two angles in another triangle.

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