Which of the following is the correct equation for the line
that crosses the x-axis at (3,0) and the y-axis at (0, 6)?

Given:

Find-:

Dimensions of the cardboard

Explanation-:

The volume of a quadrangular prism is:

The length is 12 more than the width is:

Hight is 6.

So the Area is:

Given that volume is 2958 so,

Solve the quadratic equation is:

A negative value is not considered because sides are always positive so y is 17.

So the width is 17 and length is:

So dimensions are 29 in. by 17 in.

False, r2adj is the adjusted coefficient of determination that can exceed r2 if there are several weak predictors.

R2adj is the adjusted coefficient of determination and takes into account the number of predictors in the model. It penalizes the addition of insignificant predictors that do not improve the model fit.

R2, on the other hand, is the coefficient of determination and measures the proportion of variability in the dependent variable that is explained by the independent variables in the model.

It is possible for R2 to increase when weak predictors are added, but this increase is not necessarily mean that the predictors do not have a significant impact on the outcome.

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The question is -

R2adj can exceed R2 if there are several weak predictors. true or false?

The solution to the initial value problem can be written in the form:

y(x) = (1/K)∫|sin(5x)|⁵ (3x³ - csc(5x)) dx

where K is a constant determined by the initial condition.

To solve the initial value problem and find the solution y(x), we can use the method of integrating factors.

Given: dy/dx + 5cot(5x)y = 3x³ - csc(5x), y = 0

Step 1: Recognize the linear first-order differential equation form

The given equation is in the form dy/dx + P(x)y = Q(x), where P(x) = 5cot(5x) and Q(x) = 3x³ - csc(5x).

Step 2: Determine the integrating factor

To find the integrating factor, we multiply the entire equation by the integrating factor, which is the exponential of the integral of P(x):

Integrating factor (IF) = e^{(∫ P(x) dx)}

In this case, P(x) = 5cot(5x), so we have:

IF = e^{(∫ 5cot(5x) dx)}

Step 3: Evaluate the integral in the integrating factor

∫ 5cot(5x) dx = 5∫cot(5x) dx = 5ln|sin(5x)| + C

Therefore, the integrating factor becomes:

IF = \(e^{(5ln|sin(5x)| + C)}\)

= \(e^C * e^{(5ln|sin(5x)|)}\)

= K|sin(5x)|⁵

where K =\(e^C\) is a constant.

Step 4: Multiply the original equation by the integrating factor

Multiplying the original equation by the integrating factor (K|sin(5x)|⁵), we have:

K|sin(5x)|⁵(dy/dx) + 5K|sin(5x)|⁵cot(5x)y = K|sin(5x)|⁵(3x³ - csc(5x))

Step 5: Simplify and integrate both sides

Using the product rule, the left side simplifies to:

(d/dx)(K|sin(5x)|⁵y) = K|sin(5x)|⁵(3x³ - csc(5x))

Integrating both sides with respect to x, we get:

∫(d/dx)(K|sin(5x)|⁵y) dx = ∫K|sin(5x)|⁵(3x³ - csc(5x)) dx

Integrating the left side:

K|sin(5x)|⁵y = ∫K|sin(5x)|⁵(3x³ - csc(5x)) dx

y = (1/K)∫|sin(5x)|⁵(3x³ - csc(5x)) dx

Step 6: Evaluate the integral

Evaluating the integral on the right side is a challenging task as it involves the integration of absolute values. The result will involve piecewise functions depending on the range of x. It is not possible to provide a simple explicit formula for y(x) in this case.

Therefore, the solution to the initial value problem can be written in the form: y(x) = (1/K)∫|sin(5x)|⁵(3x³ - csc(5x)) dx

where K is a constant determined by the initial condition.

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Step-by-step explanation:

All ik is that its gonna take 10 minutes to drain.

The required simple ratio of the given ratio of girls to boys at a party is 5 : 3.

Given that,
The ratio of girls to boys at a party is 25:15. To write this as simple.

In mathematics, it deals with numbers of operations according to the statements.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The ratio of girls to boys at a party is 25:15,
= 25 / 15 implies there are 25 girls over 15 boys in the school party,
= 5 * 5 / 5 *3
= 5 / 3 it implies there are 5 girls over 3 boys in the school party.

Thus, the required simple ratio of the given ratio of girls to boys at a party is 5 : 3.

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The greatest number of blocks that can be packed into a box that is 6 units tall, 7 units wide, and 8 units deep without exceeding the height of the box = 84

Let h represents the height, w represents the width and l represents the length of the box.

The box is 6 units tall, 7 units wide, and 8 units deep.

⇒ h = 6 units, w = 7 units and l = 8  units

The volume of the box would be,

V = l × w × h

V = 6 × 7 × 8

V = 336 cu. units

The four block has  unit-cubes.

The volume of unit each unit cube would be,  1 × 1 × 1 = 1 cubic unit

so, the volume of 4 blocks would be,

V₁ = 4 × 1

V₁ = 4 cu. units

The number of blocks that can be placed in the box would be,

n = V / V₁

n = 336 / 4

n = 84

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The complete question is:

There is an ample supply of identical blocks (as shown). Each block is constructed from four 1 × 1 × 1 unit-cubes glued whole-face to whole-face. What is the greatest number of such blocks that can be packed into a box that is 6 units tall, 7 units wide, and 8 units deep without exceeding the height of the box?

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

The required payment is $46•1965.

A tax is a mandatory fee or financial charge that a government imposes on a person or a business in order to raise money for public projects like building the greatest infrastructure and services. Different public expenditure programmes are then funded with the funds that have been raised.

According to the established law, it will attract harsh repercussions if one does not pay taxes or refuses to contribute.

There are two main categories of taxes: direct taxes and indirect taxes. Both taxes are implemented in different ways. Some of them, like the dreaded income tax, corporate tax, wealth tax, etc., you pay directly, while others, like sales tax, service tax, value added tax, etc., you pay indirectly.

according to question,

Advertising percentage is 60%

Sale tax percentage is 7%

Selling price is $68•95

The amount after those payments=required

First you add the payment but they are in percentage

60%+7%=67%

So,

67% is the amount of payment

67×$68•95/100

$4619•65/100

=$46•1965

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Answer:

y = -7x - 11

Step-by-step explanation:

The two equations are equivalent and represent the same line since the second equation can be obtained from the first equation by multiplying both sides by 3.

The given equations are:2y = x + 10 ..........(1)3y = 3x + 15 .......(2)

Let us check the properties of the equations given, we get:

Properties of equation 1:It is a linear equation in two variables x and y.

It can be represented in the form y = (1/2)x + 5.

This equation is represented in the slope-intercept form where the slope (m) is 1/2 and the y-intercept (c) is 5.Properties of equation 2:

It is a linear equation in two variables x and y.

It can be represented in the form y = x + 5.

This equation is represented in the slope-intercept form where the slope (m) is 1 and the y-intercept (c) is 5.

From the above information, we can conclude that both equations are linear and have a y-intercept of 5.

However, the slope of equation 1 is 1/2 while the slope of equation 2 is 1, thus the equations have different slopes.

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Answer:

The slope of a line that is perpendicular to y=3/7x-3 is -7/3

Step-by-step explanation:

The slope of perpendicular lines are opposite reciprocals so you would flip 3/7 to 7/3 and negate it, so the answer is -7/3.      

The time period of a pendulum depends only on the length, so they have the same period.

What is time period of a simple pendulum?

The time period of a simple pendulum is equal to the time it takes to complete one oscillation.

T = 2π√l/g

where l is length of the string of the pendulum.

According to the given question:

Jim and Gina are swinging on adjacent, equal length swings.

Jim weights about twice as much as Gina.

Swing set can be considered as simple pendulum.

The period of a pendulum depends only on the length, so they have the same period (meaning it takes them the same time to swing back and forth).

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The nth term of the sequence 100 is 592

Suppose the initial term of a geometric sequence is a

and the term by which we multiply the previous term to get the next term is r

Then the sequence would look like

\(a, ar, ar^2, ar^3, \cdots\)

 (till the terms to which it is defined)

Thus, the nth term of such sequence would be  \(T_n = ar^{n-1}\) (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).

Given;

Sequence=-2,4...

D=4-(-2)

=6

Now, we have to find 100th term

So, n=100

an = a + (n – 1)d

=-2+(100-1)6

=-2+99x6

=592

Therefore, the answer of given sequence will be 592

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Point E to point B and point B to Point E matches will you move between if you move 3 units left and 4 units down

To determine which two points you will move between if you move 3 units left and 4 units down, first let's look at the coordinates of each point:

Point A: (8, 3)

Point B: (9, 10)

Point C: (3, 9)

Point D: (2, 1)

Point E: (6, 6)

Now, let's move 3 units left and 4 units down for each point and find the new coordinates:

Point A: (8 - 3, 3 - 4) = (5, -1)

Point B: (9 - 3, 10 - 4) = (6, 6)

Point C: (3 - 3, 9 - 4) = (0, 5)

Point D: (2 - 3, 1 - 4) = (-1, -3)

Point E: (6 - 3, 6 - 4) = (3, 2)

Point A to Point E: (5, -1) to (3, 2) - No match

Point B to Point C: (6, 6) to (0, 5) - No match

Point B to Point E: (6, 6) to (3, 2) - This matches the movement between Point B and Point E

Point E to Point B: (3, 2) to (6, 6) - This matches the movement between Point E and Point B

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Answer:

X=1

Step-by-step explanation:

Answer:

i may be wrong but itcould be 1/3 butt i dont know ur A.B.C.D

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

First, find 5/8 of 48

Here's a little tip for you. Any number can be converted to fraction if you use 1 as the denominator:

48

1

So now that we've converted 48 into a fraction, to work out the answer, we put the fraction 5/8 side by side with our new fraction, 48/1 so that we can multiply those two fractions.

That's right, all you need to do is convert the whole number to a fraction and then multiply the numerators and denominators. Let's take a look:

5 x 48/8 x 1 = 240/8

In this case, our new fraction can actually be simplified down further. To do that, we need to find the greatest common factor of both numbers.

You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 240 and 8 is 8.

We can now divide both the new numerator and the denominator by 8 to simplify this fraction down to its lowest terms.

240/8 = 30

8/8 = 1

When we put that together, we can see that our complete answer is:

30/1

The complete and simplified answer to the question what is 5/8 of 48 is:

Now that we have found 5/8 of 48. It can be confirmed that Sue gave her sister 30 dolls.

Answer:

→ Compare the 2 grade A's

School B's is higher

→ Compare the 2 grade B's

School B's is higher

→ Now formulate a brief response

School B has more entrants in the exam and therefore has a higher proportion of students achieving top grades

Answer: 450 rest 100

Step-by-step explanation:

So, we need to calculate this division 100.000/222 and get the rest.

Well, 222 enters in 1000 by 4 times.

222 times 4 is 888

So, 100.000/222 = 4

       888-

We subtract 888 from 1000.

That will be 112

100.000/222 = 4

888

  112

Now, get the next 0 down next to 112

100.000/222 = 4

888

 1120

222 get in 1120 by 5 times.

5 times 222 = 1110

divide 1120 by 1110

100.000/222 = 45

888

 1120

 1110

That will be 10

100.000/222 = 45

888

 1120

 ==10

Get the next zero down

100.000/222 = 45

888

 1120

 ==100

222 gets in 100 by 0 times.

100.000/222 = 450

888

 1120

 ==100

         0

100 subtracted by 0 is 100

100.000/222 = 450

888

 1120

 ==100

         0

     100

The rest is 100 and the result is 450

Now, you can do the verification:

222 time 450 is 99,900.

If you add the rest to 99,900 it will be 100.000. So the result is good

a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:

x^2 - kx + 2 = 3kx - 2k

Rearranging, we get:

x^2 - (3k + k)x + 2k + 2 = 0

For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:

(3k + k)^2 - 4(2k + 2) > 0

Simplifying, we get:

5k^2 - 8k - 8 > 0

Using the quadratic formula, we can find the roots of this inequality:

\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)

Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:

2x - 4 = m

3k = m

Substituting the first equation into the second, we get:

3k = 2x - 4

Solving for x, we get:

x = (3/2)k + (2/3)

Substituting this value of x into the equation of the curve, we get:

y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2

Simplifying, we get:

y = (9/4)k^2 + (8/9) - (5/3)k

For this equation to have a double root, the discriminant must be zero:

(-5/3)^2 - 4(9/4)(8/9) = 0

Simplifying, we get:

25/9 - 8/3 = 0

Therefore, the constant term is 8/3. Solving for k, we get:

(9/4)k^2 - (5/3)k + 8/3 = 0

Using the quadratic formula, we get:

\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)

Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:

For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1

For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3

Therefore, the two tangents meet on the x-axis at x = 2.

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Answer:

8

Step-by-step explanation:

Add 5 to both sides.

x=3+5

x=3+5

2 Simplify  3+53+5  to  88.

x=8

x=8

Answer:

its A i just took the quiz

hope i helped!

Step-by-step explanation:

Answer:

7x + 9

Step-by-step explanation:

Answer:

b = - 2, b = 4

Step-by-step explanation:

Using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = M(3, 1) and (x₂, y₂ ) = N(- 1, b)

d = \(\sqrt{(-1-3)^2+(b-1)^2}\)

  = \(\sqrt{(-4)^2+(b-1)^2}\)

  = \(\sqrt{16+(b-1)^2}\)

Then

\(\sqrt{16+(b-1)^2}\) = 5 ( square both sides )

16 + (b - 1)² = 25 ( subtract 16 from both sides )

(b - 1)² = 9 ( take square root of both sides )

b - 1 = ± \(\sqrt{9}\) = ± 3 ( add 1 to both sides )

b = 1 ± 3

Then

b = 1 - 3 = - 2 or b = 1 + 3 = 4

Answer:

600 miles

Step-by-step explanation:

8*75=600

since he goes at 75 miles per hour and he drove 8 hours long, you multiply getting you 600 miles.

The number of flower arrangements Angela can make is 715. The number of different arrangements Angela can make with 12 tulips, 6 roses, and 6 orchids is 715. We can solve this problem by using the formula for combinations which is given as; C(n, r) = n! / (r! (n - r)!)

Where;n is the total number of items available,

r is the number of items needed.

The number of ways of selecting r items from n items is denoted by C(n, r) or nCr.

To solve the problem, we need to find the total number of possible flower arrangements with 12 tulips, 6 roses, and 6 orchids.

This is the same as finding the number of combinations of 12 tulips from 13 tulips, 6 roses from 8 roses, and 6 orchids from 10 orchids.

Mathematically, we can represent this as;C(13, 12) × C(8, 6) × C(10, 6) = 13! / (12!(13 - 12)!) × 8! / (6!(8 - 6)!) × 10! / (6!(10 - 6)!) = 715 × 28 × 210 = 5,964,000

Therefore, Angela can make 5,964,000 different arrangements with 12 tulips, 6 roses, and 6 orchids.

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Answer:

6/7n÷3

Basically i couldnt input the fraction. So its 6 over7, N next to the fraction, and then divide it by 3

after rotation, the points will become (0, 6), (8, 2) and (3, -8).

Rotation 180 degrees about the origin:

Point (x, y) will become (-x, -y)

So, here the points of the triangle are:

(0, -6)

(-8, -2)

(-3, 8)

These will become:

(0, 6)

(8, 2)

(3, -8)

Therefore, after rotation, the points will become (0, 6), (8, 2) and (3, -8).

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Answer:-3/5

Step-by-step explanation:

rise/run

The quotient of 3/2 divided by 2 is 3/4.

To find the quotient of 3/2 divided by 2, you need to perform the division operation.

3/2 ÷ 2

To divide fractions, you can multiply the numerator of the first fraction by the reciprocal of the second fraction.

3/2 ÷ 2 = (3/2) * (1/2)

Multiply both the numerators (3 * 1) and the denominators (2 * 2) separately, we get the following equation:

= (3 * 1) / (2 * 2)

= 3/4

Therefore, the quotient of 3/2 divided by 2 is 3/4.

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