find the distance between two points (-3,2) and (3,0)

The dimensions of the rectangle are 10 feet (length) and 8 feet (width).

To find the dimensions of the rectangle with an area of 80 square feet and a width that is 2 feet less than the length,

follow these steps:

1. Let the length of the rectangle be L feet and the width be W feet.

2. According to the given information, W = L - 2.

3. The area of a rectangle is calculated by multiplying its length and width: Area = L × W.

4. Substitute the given area and the relationship between L and W into the equation: 80 = L × (L - 2).

5. Solve the quadratic equation: 80 = L² - 2L.

6. Rearrange the equation: L² - 2L - 80 = 0.

7. Factor the equation: (L - 10)(L + 8) = 0.

8. Solve for L: L = 10 or L = -8 (since the length cannot be negative, L = 10).

9. Substitute L back into the equation for W: W = 10 - 2 = 8.

So, the dimensions of the rectangle are 10 feet (length) and 8 feet (width).

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\( \huge \mathrm {➢ \: \: \: \: Answer }\)

The above figure consists of three different shapes, that is :

Let's solve for surface area of whole figure :

1. Curved surface area of hemisphere : -

\( \large \boxed{ \boxed{2\pi {r }^{2} }}\)

\(➢ \: \: 2 \times 3.14 \times 4 \times 4\)

\(➢ \: \: 100.48 \: m {}^{2} \)

2. lateral surface area of Cylinder : -

\( \large \boxed {\boxed{2\pi rh}}\)

\(➢ \: \: 2 \times 3.14 \times 4 \times 10\)

\(➢ \: \: 251.2 \: { m}^{2} \)

3. curved surface area of cone :

\(slant \: height = \sqrt{4 {}^{2} + 3 {}^{2} } \)

(by Pythagoras theorem)

\( \large \boxed { \boxed{c.s.a = \pi rl}}\)

\(➢ \: \: 3.14 \times 4 \times 5\)

\(62.8 \: m {}^{2} \)

Surface area of the figure :

\(➢ \: \: 100.48 + 251.2 + 62.8\)

\(➢ \: \: 414.48 \: \: m {}^{2} \)

\(➢ \: \: 414.5 \: m {}^{2} \: \: \: (approx)\)

Now, let's solve for volume :

Volume of given figure will be combined volume of the all three shapes,

1. Volume of hemisphere :

\( \boxed{ \boxed{\dfrac{2}{3} \pi {r}^{3} }}\)

\(➢ \: \: \dfrac{2}{3} \times 3.14 \times 4 \times 4 \times 4\)

\(➢ \: \: 133.97 \: \: { m}^{3} \)

2. Volume of Cylinder :

\( \large\boxed{ \boxed{ \pi{r}^{2}h }}\)

\(➢ \: \: 3.14 \times 4 \times 4 \times 10\)

\(➢ \: \: 502.4 \: m {}^{3} \)

3. Volume of cone :

\( \large \boxed {\boxed{ \frac{1}{3} \pi {r}^{2}h' }}\)

\(➢ \: \: \dfrac{1}{ 3} \times 3.14 \times 4 \times 4 \times 3\)

\(➢ \: \: 50.24 \: {m}^{3} \)

The total volume of the given figure :

\(➢ \: \: 133.97 + 502.4 + 50.24\)

\(➢ \: \: 686.61 \: {m}^{3} \)

or

\(➢ \: \: 686.6 \: \: m {}^{3} \: \: \: (approx)\)

\( \mathrm{✌TeeNForeveR✌}\)

The ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

Given the scale factor of two similar polygons, we need to find the ratio of their perimeters and the ratios of their areas,

To find the ratio of the perimeters of two similar polygons, we can simply write the scale factor as it is because the ratio of the perimeter is equal to the ration of the corresponding lengths.

1) So, perimeter = 3:1

The ratio of areas between two similar polygons is equal to the square of the scale factor.

Since the scale factor is 3:1, the ratio of their areas is:

(Ratio of areas) = (Scale factor)² = 9/1 = 9:1

Similarly,

2) Perimeter = 7:4

Area = 49/16

Hence the ratios of their perimeters and the ratios of their areas are 1) 3:1 and 9:1 and 2) 7:4 and 49:16.

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Answer:

Copy n paste that sh in safri or gogle

Step-by-step explanation:

Answer:

the pattern is +2, +6, +10, +14, +18 etc

so its in increment of 4

the rest is trivial

Step-by-step explanation:

Answer:

\(u_{n} = 2n^{2} -4n-3\)

Step-by-step explanation:

a +b + c = - 5    First term in sequence

3a + b = 2   Difference between first two terms

2a = 4         Difference between  the difference of the first two terms and the second third terms (the difference between -5 and -3 is 2 the difference between -3 and 3 is 6; the difference between 6 and two is 4)

2a = 4 so a = 2; 3(2) + b = 2 → 6 + b = 2 so  b = -4; 2 - 4 + c = -5  → -2 + c = -5 so c = -3

Answer:

1.  Commutative Property of Multiplication

2.  Associative Property of Multiplication

3.  Inverse Property of Multiplication

4.  Commutative Property of Addition

5.  Inverse Property of Addition

Step-by-step explanation:

The main four mathematical property types are:

Associative Property

Grouping of numbers by parentheses in a different way does not affect their sum or product.

Applies to addition and multiplication only.

Addition: (a + b) + c = a + (b + c) = (a + c) + b

Multiplication: (a × b) × c = a × (b × c) = (a × c) × b

Commutative Property

Changing the order or position of two numbers does not change the end result.

Applies to addition and multiplication only.

Addition: a + b = b + a

Multiplication: a × b = b × a

Distributive Property

Multiplying a number by a group of numbers added together is the same as multiplying each number separately.

Addition: a(b + c) = ab + ac

Subtraction: a(b - c) = ab – ac

Inverse Property

Two numbers cancel each other out by adding or multiplying by their inverse.  (The inverse of addition is subtraction and the inverse of multiplication is division).

\(\sf \bold{Addition}: \quad a+-a=0\)

\(\sf \bold{Multiplication}: \quad a \times \dfrac{1}{a} = 1\)

Question 1

\(3x \cdot 2y=3 \cdot 2 \cdot x \cdot y\)

Commutative Property of Multiplication, as changing the order or position of the terms does not change the end result.

Question 2

\(3(2x)y=(3 \cdot 2)(xy)\)

Associative Property of Multiplication, as the grouping of the terms by parentheses in a different way does not affect their product.

Question 3

\(\dfrac{1}{4} \cdot 4y=1y\)

Inverse Property of Multiplication, as the product of 4 and its reciprocal 1/4 is 1.

Question 4

\(5x \cdot (4y+3x)=5x \cdot (3x+4y)\)

Commutative Property of Addition, as changing the order or position of the terms in the parentheses does not change the end result.

Question 5

\((6+-6)y=0y\)

Inverse Property of Addition, as adding a number and its inverse together always produces zero.

The property shown by each of the following are:

1.  Commutative Property of Multiplication

2.  Associative Property of Multiplication

3.  Inverse Property of Multiplication

4.  Commutative Property of Addition

5.  Inverse Property of Addition

The main four mathematical property types are:

Associative Property

Commutative Property

Distributive Property

Inverse Property

Associative Property

Grouping of numbers by parentheses in a different way does not affect their sum or product.

Applies to addition and multiplication only.

Addition: (a + b) + c = a + (b + c) = (a + c) + b

Multiplication: (a × b) × c = a × (b × c) = (a × c) × b

Commutative Property

Changing the order or position of two numbers does not change the end result.

Applies to addition and multiplication only.

Addition: a + b = b + a

Multiplication: a × b = b × a

Distributive Property

Multiplying a number by a group of numbers added together is the same as multiplying each number separately.

Addition: a(b + c) = ab + ac

Subtraction: a(b - c) = ab – ac

Inverse Property

Two numbers cancel each other out by adding or multiplying by their inverse.  (The inverse of addition is subtraction and the inverse of multiplication is division).

Question 1

The property shown in 3x · 2y = 3 · 2 · x · y is the Commutative Property of Multiplication. This property states that the order of the factors in a multiplication expression does not affect the result.

Commutative Property of Multiplication, as changing the order or position of the terms does not change the end result.

Question 2

The property shown in 3(2x)y = (3 · 2)(xy) is the Associative Property of Multiplication. This property states that the grouping of factors in a multiplication expression does not affect the result.

Associative Property of Multiplication, as the grouping of the terms by parentheses in a different way does not affect their product.

Question 3

The property shown in 1/4 · 4y = 1y is the Multiplicative Inverse Property. This property states that when any real number is multiplied by 1, the result is the original number itself.

Inverse Property of Multiplication, as the product of 4 and its reciprocal 1/4 is 1.

Question 4

The property shown in 5x · (4y + 3x) = 5x · (3x + 4y) is the Commutative Property of Addition. This property states that the order of the terms in an addition expression does not affect the result.

Commutative Property of Addition, as changing the order or position of the terms in the parentheses does not change the end result.

Question 5

The property shown in (6 + -6)y = 0y is the Additive Inverse Property. This property states that for any real number a, there exists an additive inverse -a such that a + (-a) = 0. In this case, 6 and -6 are additive inverses of each other, so their sum is 0.

Inverse Property of Addition, as adding a number and its inverse together always produces zero.

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Answer:

Start with equation,

         y''(x) = f(x) = 6y/(10x-x²)               about point x₀ = 5

Then,

       y(x) = a₀ + a₁(x-5) + a₂(x-5)²+ a₃(x-5)³ + a₄(x-5)⁴...….

by inspection,

           y(5) = a₀      and       y'(5) = a₁

then,

y''(5) = 6a₀/(50-25) = 6a₀/25              

y'''(x) = 6y'/(10x-x2) - 6y(10-2x)/(10x-x2)2

then,                      

                              y'''(5) = 6a₁/25 - 0 = 6a₁/25                

y''''(x) = 6y''/(10x-x2) -12y'(10-2x)/(10x-x2)² + 12y/(10x-x2)² + 12y(10-2x)2/(10x-x2)³

then,

    y''''(5) = (6/25)(6a₀/25) + 0 + 12a₀/625 + 0

              = 48a₀/625

So,

y(x) = f(x) = f(5) + f'(5)(x-5) + f''(5)(x-5)2/2! + f'''(5)(x-5)3/3! + f''''(5)(x-5)4/4! …

                                                       or

y(x) = f(x) = a₀ + a₁(x-5) + (6ao/25)(x-5)2/2! + (6a1/25)(x-5)3/3! + (48a₀/625)(x-5)4/4!...

                                                         or

y(x) = f(x) = a₀ + a₁(x-5) + (3a₀/25)(x-5)²+ (a₁/25)(x-5)³+ (2a₀/625)(x-5)⁴.....

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Answer:690

Step-by-step explanation:

690

Answer:  $3,261.

Step-by-step explanation:

The answer is $3,261. Jayden would have more money in his account than Camden because his account pays a higher interest rate and is compounded continuously, which allows more frequent compounding of interest. This means that Jayden's account accumulates more interest than Camden's account over time.

Answer:

The mean of the 10 sales amounts for store A is $40,000.

Step-by-step explanation:

Given;

yˆ= −3,000 + 1.2x ...................... (1)

Where;

x = sales amounts each day at store A or the mean of the 10 sales amounts for store A = ?

yˆ = sales amounts each day at store B or the mean of the 10 sales amounts for store B = $45,000

Substituting y = 45,000 into equation (1) and solve for x, we have:

45,000 = −3,000 + 1.2x

45,000 + 3,000 = 1.2x

48,000 = 1.2x

x = 48,000 / 1.2

x = 40,000

Therefore, the mean of the 10 sales amounts for store A is $40,000.

Solution of the given equation is r = 2

Equations are mathematical statements that shows equality, containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Given equation,

8π = 1/3πr²×6

⇒ 2r² = 8

⇒ r² = 8/2

⇒ r = √4

⇒ r = 2

Hence, r = 2 is solution for the given equation.

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Answer: 135.606 m

Step-by-step explanation:

Try using the law of cosine because if you draw the picture of the triangle out then you see it’s a SAS triangle

so in this case:

C squared equals 320 squared plus 300 squared minus 2 times 320 times 300 times cosine 25

1. The equation to slope-intercept form is y = -2/3(x) + 490. The slope is -2/3 and the y-intercept is 490.

2. You should start at the y-intercept (0, 490) and move right by 3 units and downward by 2 units, and then connect the points.

3. The equation in function notation is f(x) = -2/3(x) + 490. The graph of the function is the rate of change with respect to the number of sandwich lunch sold.

4. A graph of the function with intercepts is shown below.

5. The graphs of the functions for the two months both have the same slope but different y-intercept and x-intercept.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, a linear equation that models Sal's Sandwich Shop's profit is given by;

2x + 3y = 1,470

By subtracting 2x from both sides of the equation and dividing by 3, we have:

2x + 3y - 2x = 1,470 - 2x

y = -2/3(x) + 490

Therefore, the slope is -2/3 and the y-intercept is 490.

Part 2.

In order to graph the equation by using the slope-intercept method, you would start at the y-intercept (0, 490) and move right by 3 units and down by 2 units, and then connect the points.

Part 3.

Next, we would write the equation in function notation as follows;

f(x) = -2/3(x) + 490

where:

The graph represents the rate of change of the function with respect to the number of sandwich lunch sold.

Part 4.

In this context, we would use an online graphing calculator to plot the linear function as shown in the image attached below.

Part 5.

Assuming Sal's total profit on lunch specials for the next month is $1,593 and the profit amounts remain the same, a system of equations to model this situation is given by:

2x + 3y = 1593; y = -2/3(x) + 531.

2x + 3y = 1,470; y = -2/3(x) + 490.

In conclusion, we can logically deduce that the graphs of the functions for the two months both have the same slope but different y-intercept and x-intercept.

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Complete Question:

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.

If the volume is 54 cubic units, then the value of h must be 9 units.

The volume of the triangular prism will be:

V = A*h

Where A is the area of the triangle face, we know that for a triangle of base B and height H is:

A = B*H/2

Looking at the image we can see that the base is 4 units and the hypotenuse is 5 units, then the height is:

height = √(5² - 4²) = 3

Then the area is:

A = 4*3/2 = 6  square units.

We know that the volume of the prism is 54 cubic units, then:

54 cubic units = (6 square units)*h

(54 cubic units)/(6 square units) = h

9 units  = h

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If someone wants the product of two line segments to be represented as another line segment, they can make use of similar triangles

The correlation between the lengths of line segments can be established by creating a geometric shape comprising of two triangles that are identical and share one side.

If the legs of the triangles are used to represent the two line segments and their shared side represents the resulting line segment, it is possible for the lengths to be proportional through the similarity of the triangles.

To represent the product of the two original line segments, it is necessary to ensure that they and the resulting line segment are a collection of similar triangles. This is because the length of the resulting line segment can represent the product of the initial segments.

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The answer is:

5/4

Work/explanation:

Let's work out the slope of the line.

The equation is in y = mx + b form where m = slope; b = y intercept.

Similarly, in y=5/4x - 7/4, the slope is 5/4.

The probability of the sum of the numbers on the tickets being 4, when drawn with replacement from box A, is 3/n^2, where n is the total number of numbers in box A.

To find the probability of the sum of the numbers on the tickets being 4, we need to determine the possible outcomes. If the tickets are drawn with replacement, the numbers on each ticket can range from 1 to the maximum number in box A.

To sum up to 4, the possible combinations are (1,3), (2,2), and (3,1).

Since we are drawing with replacement, each ticket has the same probability for each draw.

Let's assume that there are n total numbers in box A. The probability of drawing a specific number is 1/n. Therefore, the probability of drawing

(1,3), (2,2), or (3,1) is (1/n) * (1/n)

= 1\(/n^2\)for each combination.

Since there are three possible combinations, the overall probability is 3/\(n^2\).

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Answer:

SAMEEE

Step-by-step explanation:

QUIT SCHOOOOLLL

Answer:

Explanation:

From the graph, the points are best modeled using an exponential function.

Among the given options, Options 3 and 4 are exponential functions.

The third and fourth functions are tested below:

Option 3

Option 4

From the above, we can see that the function that best fits the data shown in the scatterplot is:

Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.

Answer:

No,  When we divide both sides by -5 we get lxl = -8.  We cannot have an absolute value of a negative number.

Step-by-step explanation:

Answer:

the second one

Step-by-step explanation:

Step-by-step explanation:

15+8= 23

math magician I like math but I really don't some time know how to do it but if their is wrong then you have to ask your teacher or look in your notebook

They are used in navigation, astronomy, and surveying. Rays are also used in computer graphics, physics, and optics. In addition, rays are used in the study of optics to describe the behavior of light as it travels through different mediums.

According to the video above, the geometric object called a ray has the characteristics that it has one endpoint and extends in away from that endpoint without end.A ray is a line that starts at a single point and extends in one direction to infinity. Rays are commonly used in geometry to explain lines and line segments. A ray has one endpoint, called the endpoint of the ray, from which it starts. The other end of the ray continues in the direction in which it is pointed without any limit. A ray is named by using its endpoint and another point on the ray, with the endpoint first. For example, if ray A starts at point P and passes through point Q, we write the name of the ray as ray PAQ or ray QAP. Rays can be part of line segments and other geometric objects. They can also be used to explain angles and the direction of a light source. Rays are commonly used in mathematics, science, and engineering.

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Answer:

18

Step-by-step explanation:

20% = 20/100  ==> Percent value is 100 times greater than decimal value

90 * 20%=

90 * 20/100 =

1800/100 = 18

The required answer for 20% of 90, is 18

A percentage is a fraction of an amount expressed as a particular number of hundredths of that amount.

Given that, What is 20% 0f 90

20% = 20/100 (Percent value is 100 times greater than decimal value)

= 90 × 20%

= 90 × 20/100

= 1800/100

= 18

Hence, 20% of 90 is 18

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The cost to repair a bicycle equals 150X, where X has the following probability function: f(x)=20x(1−x)3 Thus standard deviation of the repair cost is approximately 0.267.

To calculate the standard deviation of the repair cost, we need to find the variance first. The variance of a random variable X can be calculated using the formula:

Var(X) = E(X^2) - [E(X)]^2

First, let's calculate E(X):

E(X) = ∫(x * f(x)) dx, integrated from 0 to 1

E(X) = ∫(x * 20x(1−x)^3) dx, integrated from 0 to 1

E(X) = ∫(20x^2(1−x)^3) dx, integrated from 0 to 1

E(X) = 20 * ∫(x^2(1−x)^3) dx, integrated from 0 to 1

Solving the integral, we find E(X) = 4/7.

Next, let's calculate E(X^2):

E(X^2) = ∫(x^2 * f(x)) dx, integrated from 0 to 1

E(X^2) = ∫(x^2 * 20x(1−x)^3) dx, integrated from 0 to 1

E(X^2) = ∫(20x^3(1−x)^3) dx, integrated from 0 to 1

E(X^2) = 20 * ∫(x^3(1−x)^3) dx, integrated from 0 to 1

Solving the integral, we find E(X^2) = 4/15.

Now, we can calculate the variance:

Var(X) = E(X^2) - [E(X)]^2

Var(X) = (4/15) - (4/7)^2

Var(X) = 4/15 - 16/49

Var(X) = 40/105 - 48/105

Var(X) = -8/105

The standard deviation (σ) is the square root of the variance:

σ = sqrt(-8/105)

Thus, the standard deviation of the repair cost is approximately 0.267.

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The opposite of a number is derived when the value moves in the opposite direction on the number line. Hence the opposite of 10 on the number line is -10 because you simply move 10 units to the left of the number line. So to put it simply, the opposite of a number is the same number with a negative value. However the absolute value of a number is the positive value of that same number. Hence when a number is expressed in its absolute value (usually written as |x|, then whether its positive or negative, its value would be expressed as a positive. Which means for example, the absolute value of -10 is 10, (or | -10 | = 10).

The opposite of a number and its absolute value is always the same, because the value of any number in its absolute form is always positive.

Note that two numbers are opposites if they have the same absolute value.

The area left to be tiled on Wednesday is 1/6

Let the total area to tile be 60 sq feet

We have taken 60 sq feet as the LCM of 2 and 3 is 6. So taking up 60 makes our calculation part easy.

Area tiled on Monday = 1/3*60 = 20 sq feet

Area tiled on Tuesday = 1/2*60 = 30 sq feet

Area remaining to be tiled = 10 sq feet

So, a fraction of the area left to be tiled = Area left to be tiled/Total area to be tiled

= 10/60 = 1/6

Hence, 1/6 of the area is left to be tiled

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Answer:1/6

Step-by-step explanation:

Answer: the answer is f(3)=29

Step-by-step explanation: