Find the distance between the points (6, -2) and (9,4).

In order to get the volume of the irregular figure, let's cut it into two regular figures. See the cut below.

First, let's calculate the volume of the upper part.

The dimensions of the upper part are 7cm by 3 cm by 3 cm. Since the shape is a rectangular prism, let's multiply 7, 3, and 3.

Hence, the volume of the upper figure is 63 cm³.

Let's now calculate the volume of the lower figure.

The dimensions of the lower figure are 5cm by 4 cm by 3 cm. Since this is a rectangular prism too, let's multiply the dimensions.

The volume of the lower figure is 60 cm³.

Let's add the volume of the two figures to get the volume of the entire irregular figure.

Therefore, the entire volume of the given irregular figure is 123 cm³.

To find a differentiable function y(x) that satisfies the initial value problem (IVP) y' = |x| and y(-1) = 2, we can integrate the given differential equation and then apply the initial condition.

Integrating both sides of the differential equation y' = |x| with respect to x, we get:

∫ y' dx = ∫ |x| dx

Integrating ∫ y' dx gives us y(x) + C₁, where C₁ is an arbitrary constant of integration.

Integrating ∫ |x| dx involves considering the different cases for x. Since x > 0 (as given in the problem), we have:

∫ |x| dx = ∫ x dx (for x > 0)

= (x^2)/2 + C₂, where C₂ is another arbitrary constant of integration.

Now, we have:

y(x) + C₁ = (x^2)/2 + C₂

To determine the values of C₁ and C₂, we can use the initial condition y(-1) = 2:

y(-1) + C₁ = ((-1)^2)/2 + C₂

2 + C₁ = 1/2 + C₂

Simplifying further:

C₁ = 1/2 - 2 + C₂

C₁ = C₂ - 3/2

We can rewrite the equation for y(x) by substituting C₁ with C₂ - 3/2:

y(x) = (x^2)/2 + (C₂ - 3/2)

Therefore, a differentiable function that satisfies the given IVP y' = |x| and y(-1) = 2 is:

y(x) = (x^2)/2 + (C₂ - 3/2), where C₂ is an arbitrary constant.

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Answer:

Y is the awnser

Step-by-step explanation:

Answer:

H

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hi there!

From the question;

∠E +∠G = 180° ( The sum of opposite angle of cyclic quadrilateral is 180°)

111° + ∠G = 180°

∠G = 180°-111°

Therefore, the measure of angle G is 69°.

Hope it helps!

Answer: (

20

,

38

]

Step-by-step explanation:

(20,38]

the correct answer to the given question about car loan is option D: $2,315.38; $383.22.

To determine the interest and monthly payment for the car loan, we can use the add-on interest formula:

Total Interest = Principal x Rate x Time

where:

Principal = $16,079 (the amount of the loan)

Rate = 3.6% (the add-on interest rate)

Time = 4 years

Total Interest = $16,079 x 0.036 x 4

Total Interest = $2,315.38

So the total amount of interest on the loan is $2,315.38.

To calculate the monthly payment, we can use the following formula:

Monthly Payment = (Principal + Total Interest) / (Number of Payments)

where:

Principal = $16,079 (the amount of the loan)

Total Interest = $2,315.38 (the total interest on the loan)

Number of Payments = 4 x 12 = 48 (since the loan is for 4 years, and there are 12 months in a year)

Monthly Payment = ($16,079 + $2,315.38) / 48

Monthly Payment = $383.22

Therefore, the amount of interest on the loan is $2,315.38 and the monthly payment for the car loan is $383.22.  

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Answer:

d) 405 = 15 times 4.5 times h

The height of the prism 'h' = 6 inches

Step-by-step explanation:

Explanation:-

Given Volume of prism

                            V = 405 cubic inches

Given length of the prism

                         L = 15 inches

Given width of the prism

                       W = 4.5 inches

The volume of the prism

                        V = l w h

                       405 = 15 ×4.5× h

                       405 = 67.5 h

Dividing '67.5' on both sides , we get

                      h = 6 inches

Final answer:-

The height of the prism 'h' = 6 inches

Answer: V = l w h. 405 = 15 times 4.5 times h

Step-by-step explanation:

Given the following :

Volume of prism = 405 in^3

Length = 15 inches

Height = h

Width = 4.5 inches

Recall :

The volume of a prism is the product of the Base and the height.

That is;

Volume = Base × height

However, Base of prism is given by the area of the base shape of the prism.

From our parameters Base shape of the prism is a rectangle.

Therefore, Area of rectangle = Length × width

= 15 inches × 4.5 inches = 67.5 inch^2 = Base of prism

Therefore, Volume of prism equals ;

Volume = 15 × 4.5 × h

Volume = 405in^3

Volume = Base × height

405 = 15 × 4.5 × h

Answer:

Option 2

 x     y

−3     0

−1      3

 0     4

 3     0

4 3

Step-by-step explanation:

For a relation x →  y to be a function, there can be one and only one value of y for a value of x

Looking at the tables we see that option 1 is out since all x values are 2 andthere are multiple values of y

The last option is out because for x = 0 there are two values of y=-2 and y = 2

Correct choice is the second option which has a unique y value for each value of x

Answer:

option 2 im doing it rn

Step-by-step explanation:

The ordered pairs representing the vertices of a polygon are

(-11, 13) , (1, -1) and (1,-3).

Given, the ordered pairs representing the vertices of the polygon.

as, the given ordered pairs are

(-11, 13) , (1, -1) , (1/4 , 2(2/1)) , (1,-3).

Now, from the given ordered pairs

the pairs which are representing the vertices of a polygon are

(-11, 13) , (1, -1) and (1,-3).

So, the ordered pairs representing the vertices of a polygon are (-11, 13) ,

(1, -1) and (1,-3).

Hence, the ordered pairs representing the vertices of a polygon are

(-11, 13) , (1, -1) and (1,-3).

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Answer:

7/10

Step-by-step explanation:

Answer:

7/10

Percent to fraction conversion table

Percent Fraction

62.5% 5/8

66.67% 2/3

60% 3/5

70% 7/10

28 more rows

Step-by-step explanation:

Answer:

About 29%

Step-by-step explanation:

Answer:

b= 25

Step-by-step explanation:

a+b =72

a-b = 22

2a = 94

DBS(Divide Both Side) by 2

a = 47

=47 +b =72

and:

47 -b =22

subtract 47 from both sides:

b=25

and

-b = -25 MBS(Multiply Both Side) by-1 ....>b=25

Given:

Given that the four inequalities.

And the solution.

Required:

To find which inequality would x = 5 be a solution.

Explanation:

(1)

Therefore x=5 is not a solution.

(2)

Therefore, x=5 is a solution.

(3)

Therefore, x=5 is not a solution.

(4)

Therefore x=5 is not a solution.

Final Answer:

x=5 is as solution for the inequality,

Answer:

y = -1/4x + 4

The algebraic expression for "The product of 9 and two more than a number" is 9(x + 2).

In the given word phrase, "a number" is represented by the variable x. The phrase "two more than a number" can be translated as x + 2 since we add 2 to the number x. The phrase "the product of 9 and two more than a number" indicates that we need to multiply 9 by the value obtained from x + 2. Therefore, the algebraic expression for this word phrase is 9(x + 2).

"A number": This is represented by the variable x, which can take any value.

"Two more than a number": This means adding 2 to the number represented by x. So, we have x + 2.

"The product of 9 and two more than a number": This indicates that we need to multiply 9 by the value obtained from step 2, which is x + 2. Therefore, the algebraic expression becomes 9(x + 2).

In summary, the phrase "The product of 9 and two more than a number" can be algebraically expressed as 9(x + 2), where x represents the number.

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Answer:

Look in picture

Step-by-step explanation:

Functions can be represented on graph and as equation.

The function is given as:

\(f(x) = 26.4x + 54.4\)

(a) The graph, domain and range

See attachment for the graph of \(f(x) = 26.4x + 54.4\)

The function represents years from 1998 to 2001.

This means that:

\(x = 0\) in 1998 and \(x =3\) in 2001

So, the domain is: \([0, 3]\)

From the graph;

\(x = 0 \to f(x) = 54.4\)

\(x = 3 \to f(x) = 133.6\)

So, the range is \([54.4,133.6]\)

(b) Number of hours spent in 2000

First, we calculate x.

\(x = 2000 - 1998\)

\(x =2\) i.e. 2 years since 1998

So, we have:

\(f(x) = 26.4x + 54.4\)

\(f(2) =26.4 \times 2 + 54.4\)

\(f(2) =107.2\)

(c) When people starts to spend 120 hours.

We have:

\(f(x) = 26.4x + 54.4\)

Substitute 120 for f(x)

\(120 = 26.4x + 54.4\)

Collect like terms

\(26.4x = 120 - 54.4\)

\(26.4x = 65.6\)

Solve for x

\(x = \frac{65.6}{26.4}\)

\(x = 2.48\)

Round 2.48 to the smallest integer greater than 2.48

\(x = 3\)

This represents the number of years, since 1998.

So, the actual year is:

\(Year =1998 + 3\)

\(Year = 2001\)

Hence, people spend about 120 hours per year in 2001

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The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.

The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

Think about the function y = f. (x). The range of the function is the range of all the y values, from least to maximum. Substitute all possible values of x into the provided expression of y to see whether it is positive, negative, or equal to other values.

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The expected value of 3X + 2Y is 42.9. The variance of 2X is 1. The variance of X - Y is 0.34. The variance of 3X + 2Y is 2.61.

E[3X + 2Y]:

Since X and Y are independent random variables, the expected value of their linear combination can be calculated by applying the linearity of expectation.

E[3X + 2Y] = 3E[X] + 2E[Y] = 3 * 10.5 + 2 * 5.7 = 31.5 + 11.4 = 42.9

Therefore, E[3X + 2Y] is equal to 42.9.

Var[2X]:

To find the variance of a constant multiple of a random variable, we square the constant and multiply it by the variance of the random variable.

Var[2X] = (2^2) * Var[X] = 4 * (0.5^2) = 4 * 0.25 = 1

Therefore, Var[2X] is equal to 1.

Var[X - Y]:

Since X and Y are independent, the variance of their difference is the sum of their individual variances.

Var[X - Y] = Var[X] + Var[Y] = (0.5^2) + (0.3^2) = 0.25 + 0.09 = 0.34

Therefore, Var[X - Y] is equal to 0.34.

Var[3X + 2Y]:

Again, using the linearity of variance, we can calculate the variance of the linear combination of independent random variables.

Var[3X + 2Y] = (3^2) * Var[X] + (2^2) * Var[Y] = 9 * (0.5^2) + 4 * (0.3^2) = 9 * 0.25 + 4 * 0.09 = 2.25 + 0.36 = 2.61

Therefore, Var[3X + 2Y] is equal to 2.61.

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Let the smaller polygon have side lengths a and the larger polygon have side lengths b. Since the polygons are similar, the ratio of corresponding side lengths is the same as the ratio of their areas. That is:

b^2 / a^2 = 128 / 98

Simplifying this expression, we get:

b / a = √(128 / 98) = √(64 / 49) = (8 / 7)

Now we can use the fact that the perimeter of the smaller polygon is 42 inches:

4a = 42

a = 10.5

Substituting this into the ratio we found above, we get:

b = (8 / 7) * a = (8 / 7) * 10.5 = 12

Therefore, the larger polygon has a perimeter of:

4b = 4 * 12 = 48 inches.

Answer:

41

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

first you need to write out your question

then you need to multiply the following numbers (5.75*8)

and that gives you 46.

I hope this is the answer I just get every thing right and I think it is. hofuly it's helping!!

Answer:

4π

Step-by-step explanation:

Hope this helps. Pls give brainliest.

Answer:

I believe it would be 2 x 3.14= 6.28

( I said 2 because, isn't that the radius of the circle)

Step-by-step explanation:

Hi!

Given these two equations:

\(x = y + 8\)

\(x + 4 = 2(y + 4)\)

We want to solve using the substitution method. Knowing that x is equal to y + 8, we can simply plug in 'y + 8' in for x in the second equation, like so:

\((y+8)+4=2(y+4)\)

Combine like terms on both sides:

\(y+12=2y+8\)

Subtract y from both sides:

\(12=y+8\)

Subtract 8 from both sides:

\(y=4\)

Now, we can simply plug the y value in to the first equation, and solve for x:

\(x=4+8\)

Simplify:

\(x=12\)

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Answer:

y = x/5 - 4

second option is the correct answer.

Step-by-step explanation:

y = -5x+4

y = mx+b

m = -5

Now

Slope of the line perpendicular to a line would be the negative proprtional of the slope of the line.

so,

For the points (5,-3) and (10,-2)

m = 1/5

y = mx + b

or, -3 = 1/5 × x + b

or, -3 = 1/5 × 5 + b

or, -3 = 1+b

so, b = -4

Now,

y = mx+b

or, y = 1/5 × x + (-4)

or, y = x/5 - 4

The signs of the coordinates in the quadrants are given as follows:

In quadrant I, the coordinates are given as (x,y).

In quadrant II, the coordinates are given by (-x,y).

In quadrant III, the coordinates are given by (-x,-y).

In quadrant IV, the coordinates are given by (x,-y).

Using the above data, drag (6,-1) to quadrant IV.

Drag (-3,4) to to quadrant II.

Drag (2,4) to quadrant I.

Drag (-1,-5) to quadrant III.

Problem

Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buy a new car, and is considering opening up a retirement account. He has a disposable income of $300/month, what would you recommend he do with this money? Why?

Solution

For this case the best option would be put the $45000 in a bank with a compound interest

And with the earnings each month of 300$ he can put the half of this into the account and the remain to spend on other things

Answer:

6.86 to 2DP.

Step-by-step explanation:

7/12 = 4/DC

Cross multiply:

7DC = 4*12

DC = 48/7

= 6.857.