The total for the two items (without tax) was $151.48. The price of the backpack was $65.49. What was the price of the calculator?

Answer:

Step-by-step explanation:

Measure the corresponding sides and verify if the ratios are same or not.

Corresponding sides:

The measures, using coorinates and the distance formula:

We can see the ratios of the two pairs are not same:

We can state that Kyle is correct

Answer:

Simplified version is 19 y-28

Step-by-step explanation:

Answer:

Step-by-step explanation:

induction refers specifically to "inference of a generalized conclusion from particular instances." In other words, it means forming a generalization based on what is known or observed.

Answer:

Inductive reasoning, or inductive logic, is a type of reasoning that involves drawing a general conclusion from a set of specific observations.

Step-by-step explanation:

Answer:

170

Step-by-step explanation:

30 x 3 then do 10 x 8

90 + 80

An irrational number is a real number that cannot be expressed as a ratio of integers. The decimal expansion of an irrational number is neither terminating nor recurring.

Let us check the options one at a time:

OPTION A: -√196

The equation of the line is 1/2x = -6 with the slope being 1/2 and coordinates are (4, -2).

A line's equation is a unified representation of all of the line's points.

Any point on a line will satisfy the equation in its general version, which is of the type ax + by + c = 0.

The slope of the line and a point on the line are the two essential elements needed to create the equation of a line.

So, the line's equation form:

y = MX + b

Where m is the slope.

y is the y coordinate and b is the x coordinate.

Now, get the equation of the line as follows:

y = MX + b

-2 = 1/2x + 4

1/2x = -6

Therefore, the equation of the line is 1/2x = -6 with the slope being 1/2 and coordinates are (4, -2).

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Answer: this is how to do it

Step-by-step explanation: x=−3.

x=−4, y=−6

xy-3x=40, x=5

x(y-3)=40

y-3=(40/x)

y=(40/x)+3

y=(40/5)+3

y=8+3

y=11

For part (a), we can use Cauchy's Integral Formula which states that for a function f(z) that is analytic inside and on a simple closed contour C, and a point a inside C, we have:   The value of the integral is 2πi i0^(m+1).


f^(m)(a) = (1/2πi) ∮ C f(z)/(z-a)^(m+1) dz

where f^(m)(a) denotes the m-th derivative of f evaluated at a, and the integral is taken counterclockwise around C.

In our case, we have f(z) = 1, which is analytic everywhere, and C is the circle {izl = r} with counterclockwise orientation. So we can write:

iizml dz = i(1/2πi) ∮ {izl = r} 1/(z-i0) dz

where i0 is any point inside the circle, and the integral is taken counterclockwise around the circle.

Using Cauchy's Integral Formula with a = i0 and m = 0, we get:

iizml dz = i

So the value of the integral is just i.

For part (b), we need to evaluate the derivative of the integral, which is:

d/dz (iizml) = -m iizm-1

Using Cauchy's Integral Formula with a = i0 and m = 1, we get:

iizmlldzl = i(-m) (1/2πi) ∮ {izl = r} z^(m-1)/(z-i0)^2 dz

Note that the only difference from part (a) is the z^(m-1) term in the integral. We can simplify this using the Residue Theorem, which states that for a function f(z) that has a pole of order k at z = a, we have:

Res[f(z), a] = (1/(k-1)!) lim[z->a] d^(k-1)/dz^(k-1) [(z-a)^k f(z)]

In our case, the integral has a simple pole at z = i0, so we have:

Res[z^(m-1)/(z-i0)^2, i0] = lim[z->i0] d/dz [(z-i0)^2 z^(m-1)] = i0^m

Therefore, we can write:

iizmlldzl = -2πi Res[z^(m-1)/(z-i0)^2, i0] = -2πi i0^m

Note that the minus sign comes from the fact that the residue is negative. So the value of the integral is -2πi i0^m.

For part (c), we need to evaluate the integral of z^m around the same circle. Again, we can use Cauchy's Integral Formula with a = i0 and m = -1, which gives:

izm dz = (1/2πi) ∮ {izl = r} z^(m+1)/(z-i0) dz

Using the Residue Theorem, we can find the residue at z = i0, which is:

Res[z^(m+1)/(z-i0), i0] = lim[z->i0] z^(m+1) = i0^(m+1)

Therefore, we can write:

izm dz = 2πi Res[z^(m+1)/(z-i0), i0] = 2πi i0^(m+1).

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The value of det A = 1

And, The value of A⁻¹ = \(\left[\begin{array}{ccc}- 3& 1\\-4&1\\\end{array}\right]\)

What is Matrix ?

Matrix is a set of numbers arranged in rows and columns so as to form a rectangular array.

Given that;

The matrix is,

\(A = \left[\begin{array}{ccc}1&- 1\\4&- 3\\\end{array}\right]\)

Now,

Find the determinant of matrix A as;

Since, The matrix is,

\(A = \left[\begin{array}{ccc}1&- 1\\4&- 3\\\end{array}\right]\)

⇒ det (A) = 1 × - 3 - (-1) × 4

              = - 3 + 4

              = 1

Thus, The value of det A = 1

And, We know that;

The value of A⁻¹ = adj (A) / |A|

Here, The matrix is,

\(A = \left[\begin{array}{ccc}1&- 1\\4&- 3\\\end{array}\right]\)

So, We get;

\(adj (A) = \left[\begin{array}{ccc}- 3& 1\\-4&1\\\end{array}\right]\)

Hence, The value of A⁻¹ = adj (A) / |A|

                                     = \(\left[\begin{array}{ccc}- 3& 1\\-4&1\\\end{array}\right] / 1\)

                                     = \(\left[\begin{array}{ccc}- 3& 1\\-4&1\\\end{array}\right]\)

Thus, The value of det A = 1

And, The value of A⁻¹ = \(\left[\begin{array}{ccc}- 3& 1\\-4&1\\\end{array}\right]\)

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The value of x in the solution set of the inequality 9(2x+1) < 9x-18 is

x <-3.

Given inequality:

9(2x+1) < 9x-18

simplifying

9*2x + 9*1 < 9x - 18

18*x + 9 < 9x - 18

18x + 9 < 9x - 18

combining the like terms

18x - 9x + 9 < -18

9x + 9 < -18

combining the constants

9x < -18-9

9x < -27

divide by 9 on both sides

9x/9 < -27/9

x < -27/9

x < -3

Therefore the value of x in the solution set of the inequality 9(2x+1) < 9x-18 is x <-3.

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Answer:

:)

Step-by-step explanation:

It's between 5 and 6 pls give points and mark as brainliest ty

Answer:

9 laps

Step-by-step explanation:

75% of something is the same as three-fourths, or multiplying by 0.75

12 x 0.75 = 9

or you can divide by 4 and then multiply by three if you know what to separate the original number into

12/4 = 3     3 x 3 = 9

Answer: He will be running 45 miles in the during the fifteenth week of school.

Step-by-step explanation:

Given: Joshua runs each day after school to train for his cross country team.

He ran 3 miles in first week, 6 miles in second week, 9 miles in third weeki.e. sequence will be  3, 6, 9 ,....(multiple of 3.)

The number of miles he will be running during the fifteenth week of school = 15 x 3

=45

Hence, he will be running 45 miles in the during the fifteenth week of school.

Answer:

The answer 45

Answer:

1

Step-by-step explanation:

Answer:

A, x < 12

Step-by-step explanation:

edge

Answer:

38.40

Step-by-step explanation:

I just took the test

Answer:

C And D!

Step-by-step explanation:

Answer: I think it’s A (x + 4 = 14) I’m not sure though

The line y = mx + 4 has a slope of 2 and it is y = 2x + 4.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know lines parallel to each other have the same slope.

We also know, slope(m) = (y₂ - y₁)/(x₂ - x₁).

Slope(m) = (6 + 2)/(5 - 1).

slope(m) = 8/4.

slope(m) = 2.

So, The line y = mx + 4 is, y = 2x + 4.

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The order of a in (z/(pq))× is exactly (p-1)(q-1), as desired.

To prove that (z/(pq))× has order (p − 1)(q − 1), we need to show that the least positive integer n such that (z/(pq))×n = 1 is (p − 1)(q − 1).

First, let's define (z/(pq))× as the set of all integers a such that gcd(a,pq) = 1 (i.e., a is relatively prime to pq) and a mod pq is also relatively prime to pq.

Now, we know that the order of an element a in a group is the smallest positive integer n such that a^n = 1. Therefore, we need to find the order of an arbitrary element a in (z/(pq))×.

Let's assume that a is an arbitrary element in (z/(pq))×. Since gcd(a,pq) = 1, we know that a has a multiplicative inverse modulo pq, denoted by a^-1. Therefore, we can write:

a * a^-1 ≡ 1 (mod pq)

Now, let's consider the order of a. Since gcd(a,pq) = 1, we know that a^(p-1) is congruent to 1 modulo p by Fermat's Little Theorem. Similarly, we can show that a^(q-1) is congruent to 1 modulo q. Therefore, we have:

a^(p-1) ≡ 1 (mod p)
a^(q-1) ≡ 1 (mod q)

Now, we can use the Chinese Remainder Theorem to combine these congruences and get:

a^(p-1)(q-1) ≡ 1 (mod pq)

Therefore, we know that the order of a must divide (p-1)(q-1).

To show that the order of a is exactly (p-1)(q-1), we need to show that a^k is not congruent to 1 modulo pq for any positive integer k such that 1 ≤ k < (p-1)(q-1).

Assume for contradiction that there exists such a k. Then, we have:

a^k ≡ 1 (mod pq)

This means that a^k is a multiple of pq, which implies that gcd(a^k, pq) ≥ pq. However, since gcd(a,pq) = 1, we know that gcd(a^k, pq) = gcd(a,pq)^k = 1. This is a contradiction, and therefore our assumption must be false.

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The order of a in (z/(pq))× is exactly (p-1)(q-1), as desired.

To prove that (z/(pq))× has order (p − 1)(q − 1), we need to show that the least positive integer n such that (z/(pq))×n = 1 is (p − 1)(q − 1).

First, let's define (z/(pq))× as the set of all integers a such that gcd(a,pq) = 1 (i.e., a is relatively prime to pq) and a mod pq is also relatively prime to pq.

Now, we know that the order of an element a in a group is the smallest positive integer n such that a^n = 1. Therefore, we need to find the order of an arbitrary element a in (z/(pq))×.

Let's assume that a is an arbitrary element in (z/(pq))×. Since gcd(a,pq) = 1, we know that a has a multiplicative inverse modulo pq, denoted by a^-1. Therefore, we can write:

a * a^-1 ≡ 1 (mod pq)

Now, let's consider the order of a. Since gcd(a,pq) = 1, we know that a^(p-1) is congruent to 1 modulo p by Fermat's Little Theorem. Similarly, we can show that a^(q-1) is congruent to 1 modulo q. Therefore, we have:

a^(p-1) ≡ 1 (mod p)
a^(q-1) ≡ 1 (mod q)

Now, we can use the Chinese Remainder Theorem to combine these congruences and get:

a^(p-1)(q-1) ≡ 1 (mod pq)

Therefore, we know that the order of a must divide (p-1)(q-1).

To show that the order of a is exactly (p-1)(q-1), we need to show that a^k is not congruent to 1 modulo pq for any positive integer k such that 1 ≤ k < (p-1)(q-1).

Assume for contradiction that there exists such a k. Then, we have:

a^k ≡ 1 (mod pq)

This means that a^k is a multiple of pq, which implies that gcd(a^k, pq) ≥ pq. However, since gcd(a,pq) = 1, we know that gcd(a^k, pq) = gcd(a,pq)^k = 1. This is a contradiction, and therefore our assumption must be false.

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The area of the sidewalk is 84.78 square meters if a circular flower bed is 23 m in diameter and has a 3 m wide circular sidewalk.

A circular flower bed is 23 m in diameter and has a circular sidewalk around it that is 3 m wide. The area of the sidewalk is square meters. The formula used: The area of the circle is given by:

πr²

Here, r = (d + 2w)/2, where d is the diameter and w is the width.

Substitute the values of d, w, and π in the above formula to get the area of the circular sidewalk.

Diameter of circular flower bed = 23 m

Width of circular sidewalk = 3 m

Radius of circular flower bed, r = (23+3)/2 = 13 m

Radius of circular sidewalk = (23+3+3)/2 = 14 m

Area of the circular sidewalk = π(14² - 13²) m²= π(14+13)(14-13) m²= 3.14(27) m²= 84.78 m²

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Answer:

Step-by-step explanation:

Since the pieces are similar, the ratio of corresponding sides is same:

Answer:

12 + 4x

Step-by-step explanation:

You take all of the ones which you can group together and so, you can take the 5+7 and make it 12 and the 2x + 2x = 4x. I hope this helps!

Answer:

41 ft² is the answer thank you

Answer:

the answer is 53 ft

Step-by-step explanation:

fist take the 3*3 square = 9

then the 4*11= 44(11 because I ssume the 8 ft does not account for the 3ft of the box)(if it is 8 ft then the answer is 41 ft^2 overall)

44+9= 53

In the equation y = 12x + 41, the slope of the line is 12. The slope represents the rate of change or the steepness of the line.

In this situation, a slope of 12 indicates that for every unit increase in the x-coordinate (horizontal axis), the corresponding y-coordinate (vertical axis) increases by 12 units.  The positive slope indicates that as the x-values increase, the y-values also increase. This suggests a positive correlation between the variables being represented on the scatter plot.

In practical terms, the slope of 12 can be interpreted as the amount of change in the y-variable (dependent variable) for each unit change in the x-variable (independent variable). It implies that the y-values are increasing at a relatively steep rate as the x-values increase.

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The amount of money that I will have at the end of 20 years would be =$4,480. That is option D

Compound interest is defined as the interest that is being earned on an account which is based on the rate and the time the investment was made.

The total amount invested (p)= $2,000

The rate of investment (r) = 5%

The time of investment(t)= 12 year

The compound interest warm from that account;

= P×T×R/100.

= 2,000×12×5/100

= 120000/100

= $1200

For the next 8 years with the rate of 8% ;

= 2,000×8×8/100

= 128000/100

= $1280

The total compound interest = $1200+$1280= $2,480

Therefore, the amount of money that I will have at the end of 10 years would be = 2000+2480 = $4,480

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Answer:

It will cost $324.

Step-by-step explanation:

If the cost for 6,000 square feet is $36, and you need to find the cost of 54,000 square feet, the first thing you need to do is divide 54,000/6,000 to get 9. Then to find the cost, you need to multiply $36×9 to get an answer of 324.

(a) The differential equation y" + 361 π² y = 0 is a homogeneous equation because all the terms present in it have degree 0 and contain only y and its derivatives. Homogeneous equation means that if y is a solution, then c*y is also a solution, where c is a constant.

(b) To solve the given boundary value problem, we can start by finding the general solution of the differential equation y" + 361 π² y = 0. The characteristic equation is r² + 361 π² = 0. The roots of this equation are

r = ± 19iπ.

Thus, the general solution of the differential equation is y(x) = c1 cos(19πx) + c2 sin(19πx).

Using the boundary conditions, y(0) = 0 and y'(1) = 1, we can find the values of c1 and c2.

y(0) = c1 cos(0) + c2 sin(0) = c1*1 + c2*0 = 0

⇒ c1 = 0

y'(x) = -19π c1 sin(19πx) + 19π c2 cos(19πx)

y'(1) = -19π c1 sin(19π) + 19π c2 cos(19π) = 1 ⇒ 19π c2 = 1

Thus, c2 = 1/19π. Therefore, the solution of the boundary value problem is y(x) = (1/19π) sin(19πx).



In conclusion, we have shown that the given boundary value problem y" + 361 π² y = 0, y(0) = 0, y'(1) = 1 is a homogeneous equation. We have also solved the given boundary value problem and obtained the solution y(x) = (1/19π) sin(19πx) that satisfies the boundary conditions.

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The solution to the equation 9 × (3 ÷ x) = 26 is x = 1.038.

To solve the equation 9 × (3 ÷ x) = 26 for x, we can follow these steps:

Simplify the expression on the left side of the equation:

9 × (3 ÷ x) = 26

27 ÷ x = 26

Multiply both sides of the equation by x to eliminate the division:

(27 ÷ x) × x = 26 × x

27 = 26x

Divide both sides of the equation by 26 to solve for x:

27 ÷ 26 = (26x) ÷ 26

1.038 = x

As a result, x = 1.038 is the answer to the equation 9 (3 x) = 26.

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