How do you solve equations on a calculator?

Answer:

If asked to translate a point (x+1,y+1), you move it to the right one unit because + on the x-axis goes to the right, and move it up one unit, because + on the y-axis goes up.

Step-by-step explanation:

Let me knoe how you did

Step-by-step explanation:

To find the Highest Common Factor (H.C.F.) of 567 and 255 using Euclid's division lemma, we can follow these steps:

Step 1: Apply Euclid's division lemma:

Divide the larger number, 567, by the smaller number, 255, and find the remainder.

567 ÷ 255 = 2 remainder 57

Step 2: Apply Euclid's division lemma again:

Now, divide the previous divisor, 255, by the remainder, 57, and find the new remainder.

255 ÷ 57 = 4 remainder 27

Step 3: Repeat the process:

Next, divide the previous divisor, 57, by the remainder, 27, and find the new remainder.

57 ÷ 27 = 2 remainder 3

Step 4: Continue until we obtain a remainder of 0:

Now, divide the previous divisor, 27, by the remainder, 3, and find the new remainder.

27 ÷ 3 = 9 remainder 0

Since we have obtained a remainder of 0, the process ends here.

Step 5: The H.C.F. is the last non-zero remainder:

The H.C.F. of 567 and 255 is the last non-zero remainder obtained in the previous step, which is 3.

Therefore, the H.C.F. of 567 and 255 is 3.

Answer:

AB = 10

BC = 28

Step-by-step explanation:

                                          3y - 2

                         A  -------------->>----------------  B

                           /                                     /

                         /                                     /

    2x - 4          /                                     /      x + 12

                      ^                                     ^

                     /                                     /

             D   --------------->>----------------   C

                          y + 6

Opposite sides of a parallelogram are congruent.

AB = CD

3y - 2 = y + 6

2y = 8

y = 4

BC = AD

x + 12 = 2x - 4

-x = -16

x = 16

AB = 3y - -2

AB = 3(4) - 2

AB = 10

BC = x + 12

BC = 16 + 12

BC = 28

Answer:

Step-by-step explanation:

Given parallelogram ABCD with these side lengths, you want the measures of segments AB and BC.

Opposite sides of a parallelogram are the same length. This lets us solve for x and y.

  3y -2 = y +6

  2y = 8 . . . . . . . . . add 2-y

  y = 4 . . . . . . . . . divide by 2

  AB = 3(4) -2 . . . find AB

  AB = 10

  x +12 = 2x -4

  16 = x . . . . . . . . add 4-x

  BC = 16 +12

  BC = 28

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Lauren's reasoning does not make sense because the LCM of 2 and 8 is not 16, the LCM will be equal to 8.

The Least Common Multiple is the meaning of the acronym LCM. The smallest number that both numbers can divide by is known as the least frequent multiple (LCM) for two numbers.

It can also be computed for several different numbers.

As per the given information in the question,

Lauren says that the LCM of 2 and 8 is 16.

Now, let's check whether it is correct or not.

Let's make a factor of both numbers,

2 = 2 × 1

8 = 2 × 2 × 2

So, the LCM will be: 2 × 2 × 2 = 8

It means that the LCM of 2 and 8 is not 16, the LCM is 8.

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A painter can paint 60 square feet every 1 hour.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A painter can paint 15 square feet every 1/4 hour.

Now,

Since, A painter can paint 15 square feet every 1/4 hour.

Let painter can paint in every 1 hour = x square feet

So, By definition of proportional as;

⇒ 15 / (1/4) = x / 1

Solve for x as;

⇒ 15 × 4 = x

⇒ x = 60 square feet

Thus, A painter can paint 60 square feet every 1 hour.

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The given equation of the line is x - 7y = -49. To determine the slope and y-intercept, we need to rewrite the equation in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

In this case, the equation cannot be directly written in slope-intercept form because it does not have y isolated on one side. Thus, the slope and y-intercept cannot be determined directly from the given equation.

The given equation of the line is x - 7y = -49. To determine the slope and y-intercept, we need to rewrite the equation in slope-intercept form, y = mx + b.

To isolate y, we can subtract x from both sides of the equation:

-7y = -x - 49

Next, divide both sides of the equation by -7 to solve for y:

y = (1/7)x + 7

By comparing this equation with the slope-intercept form, we can determine that the slope, m, is 1/7, and the y-intercept, b, is 7.

Therefore, the correct choice is A. m = 1/7, b = 7. The slope of the line is 1/7, and the y-intercept is 7.

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Answer:

10x-2

Step-by-step explanation:

product:multiply

less:subtract

Hope this helps!

Answer:

31/40

Step-by-step explanation:

13/40 + 18/40

Answer:

light, which normally travels the 240,000 miles from the Moon to Earth in less than two seconds, has been slowed to the speed of a minivan in rush-hour traffic — 38 miles an hour.

An entirely new state of matter, first observed four years ago, has made this possible. When atoms become packed super-closely together at super-low temperatures and super-high vacuum, they lose their identity as individual particles and act like a single super-

atom with characteristics similar to a laser.

Step-by-step explanation:

Answer:

thats false

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

using the diamond factoring method:

2x^2-12x+x-6

2x(x-6) + (x-6)

(2x+1)(x-6)

B

To find the slope from a table, you need to find the difference in the y-values (the dependent variable) between two points and divide it by the difference in the x-values (the independent variable) between those same two points.

This is known as the slope formula:

Here is an example of finding the slope from a table:

Suppose we have the following table:

x y

3 7

4 9

To find the slope between these two points, we can use the slope formula as follows:

slope = (9 - 7)/(4 - 3) = 2/1 = 2

So the slope between these two points is 2.

It's important to note that the slope is a measure of the slope of the line that passes through the two points. If you want to find the slope of the line that is the best fit for a larger set of data, you will need to use a different method, such as linear regression.

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The vectors v = 6i - 3j and w = i + 2j are orthogonal.

To determine if the vectors v and w are orthogonal, we need to find their dot product. If the dot product is 0, the vectors are orthogonal.

Here are the steps to find the dot product of v = 6i - 3j and w = i + 2j,

1. Identify the components of the vectors: v = (6, -3) and w = (1, 2)

2. Multiply the corresponding components of the vectors:

\((6 \times 1) + (-3 \times 2) = 6 - 6 \)

3. Add the products: 6 - 6 = 0 Since the dot product is 0, the vectors v = 6i - 3j and w = i + 2j are orthogonal.

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Correct question is " Are these vectors orthogonal? v = 6i - 3j and w = i+2j"

Answer:In other words, since even numbers are the multiples of 22, we can represent an even integer nn by 2k2k, where kk is also an integer. So if we have the even integers 1010 and 1616, we can rewrite them asn=2k→10=2(5)

n = 2k\, \to \,\,16 = 2\left( 8 \right)\,n=2k→16=2(8)

Step-by-step explanation:

Consecutive Even Integers

The best way to illustrate what consecutive even integers are through the use of examples. Observe that any pair of two consecutive even integers are 22 units apart. In other words, if you pick any even integer in the set of consecutive even integers then subtract it by the previous one, you will always get the difference of \bold{+2}+2 or simply \bold{2}2, written without the \bold{+}+ symbol.

LCM  of 17, 23, 29   = 11339

HCF of 17, 23, 29     = 1

How to find LCM and HCF by prime factorization?

The numbers 17, 23, 29 are prime  numbers themselves.

By prime factorization we consider only the prime factors.

LCM of 17, 23, 29  = 17 ×23 ×29  (Since the numbers are prime)

                             =11339

HCF of 17, 23, 29 = 1    (Since the  common factor is 1)

What is prime factorization?

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Answer:

cosine

Step-by-step explanation:

Answer:

cosine

Step-by-step explanation:

cosine = adjacent / hypotenuse

the function should be represented as f(t) = 24,500( 0.88\()^{t}\)

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Given,  f(t) = 24,500 x (0.88)t

Assuming that the value of the car only increases by 88% per year compared to the previous year, the function rule needs to have "t" as the exponent, thus it should be f(t) = 24,500( 0.88\()^{t}\)

Hence, the function should be represented as f(t) = 24,500( 0.88\()^{t}\)

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Answer:

the answer to this question is 22ft

The  value of the line integral is 1.

To apply Green's Theorem, we need to find the curl of the vector field F = (xy, (x^2 - y^2)).

∂F2/∂x = 2x
∂F1/∂y = x

So, the curl of F is given by ∂F2/∂x - ∂F1/∂y = 2x - x = x.

Now, we can use Green's Theorem to evaluate the line integral by computing the double integral of the curl of F over the region R enclosed by the curve C.

∫∫R x dA = ∫0^2 ∫0^y x dxdy + ∫2^0 ∫1^y x dxdy
           = ∫0^1 ∫0^2 x dydx
           = ∫0^1 2xdx
           = 1

Therefore, the value of the line integral is 1.

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(a) The probability that a randomly selected policyholder lives more than 80 years is approximately 0.3106.  (b) Given that a male policyholder just turned 80, the probability that he will live for at least three more years is approximately 0.6166.

(a) To find the probability that a randomly selected policyholder lives more than 80 years, we need to calculate the cumulative probability of survival beyond 80 for both males and females separately, and then weigh them based on the gender distribution.

For males: Using the normal distribution with mean 75 and standard deviation 8, we find the probability of survival beyond 80 is approximately 0.3446.

For females: Using the normal distribution with mean 78 and standard deviation 6, we find the probability of survival beyond 80 is approximately 0.2847.

The weighted probability for a randomly selected policyholder is (0.60 * 0.3446) + (0.40 * 0.2847) = 0.3106.

(b) Given that a male policyholder just turned 80 years old today, we can use conditional probability to calculate the likelihood of him living for at least three more years.

Using the normal distribution with mean 75 and standard deviation 8, the probability of survival beyond 83 (80 + 3) is approximately 0.8621.

Therefore, the probability that a male policyholder, who just turned 80, will live for at least three more years is 0.8621.

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Answer:

that does not make sense ?????????????????????????????????????????

Lower class limits are 15, 25, 35, 45, 55, 65, 75, Upper class limits are 24, 34, 44, 54, 64, 74, 84, Class width are 10 (all classes have a width of 10), Class midpoints are 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, Class boundaries are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) and Number of individuals included in the summary is 76.

Here are the details for the given frequency distribution:

Lower class limits are the least number among the pair

Here, Lower class limits are 15, 25, 35, 45, 55, 65, 75 respectively.

Upper class limits are the greater number among the pair

Here, upper limit class are 24, 34, 44, 54, 64, 74, 84 respectively.

Class width is the difference between the Lower class limits and Upper class limits which is 10 (all classes have a width of 10).

Class midpoints is the middle point of the lower class limits and Upper class limits which is 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 respectively.

Class boundaries are the extreme points of the classes which are  [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) respectively.

Number of individuals = 27 + 33 + 14 + 4 + 6 + 1 + 1

                                     = 76

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Using the property m(b - a) ≤ ∫[a,b] f(x) dx ≤ m(b - a), where m is the absolute minimum and M is the absolute maximum of f(x) on the interval [a, b], we can estimate the value of the integral ∫[a,b] 7 tan(3x) dx to be between 7(b - a)/12 and 7(b - a)/9.

Step 1: Understanding the Property

The property states that if a function f(x) is bounded by its absolute minimum (m) and maximum (M) on an interval [a, b], then the integral of f(x) over that interval is between m multiplied by the length of the interval (b - a) and M multiplied by the length of the interval.

Step 2: Applying the Property

In this case, the function f(x) is 7 tan(3x), and the interval is [a, b]. To estimate the value of the integral, we can use the property as follows:

m(b - a) ≤ ∫[a,b] f(x) dx ≤ M(b - a)

where m and M represent the absolute minimum and maximum values of f(x) on the interval [a, b].

Step 3: Estimating the Value

Since 7 tan(3x) is bounded between m and M, we can estimate the integral to be between m(b - a) and M(b - a). Therefore, the estimated value of the integral ∫[a,b] 7 tan(3x) dx is between 7(b - a)/12 and 7(b - a)/9.

To obtain a more precise estimation or the exact value, specific values of a, b, m, and M need to be known or further calculations need to be performed.

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The surface area of the rectangular prism is 88 square inches.

Given that:

Length, L = 6 inches

Width, W = 2 inches

Height, H = 4 inches

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

SA = 2(6 x 2 + 2 x 4 + 4 x 6)

SA = 2 (12 + 8 + 24)

SA = 2 x 44

SA = 88 square inches

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The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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==========================================================

Reason:

The only even prime number is 2. The other primes are odd.

The list of the first few primes are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43

A prime is any number that has factors of 1 and itself, and nothing else.

For instance, 13 is prime because 1 and 13 are the only factors.

-----------

As you can see, if we want a two digit prime number, then the units digit must be odd. Otherwise, 2 is a factor making it not prime (aka composite).

So far we see that the units digit is 1, 3, 5, 7, or 9. But wait, if 5 is the units digit then 5 is a factor. Eg: 5 is a factor of 35 since 5*7 = 35. Refer to the divisibility by 5 rule.

So we reduce the list of choices to 1, 3, 7, 9 for the units digit.

Unfortunately 9 is not in the list of original numbers given, so we can't use it. We really have 1, 3, or 7 as our choices to form the units digit of the two-digit number.

-----------

Let's try to build some primes.

Pick the smallest odd number 1 as the units digit. Then pick 2 as the tens digit. The number 21 is composite because 21 = 7*3, so we rule it out.

On the other hand, 31 is prime since only 1 and 31 are factors.

The problem is that now "3" is tied up and cannot be used for another prime. The good news is that 41 is prime and that's what I'll go with.

Cross 1 and 4 off the list.

The next odd number is 3 which is our units digit. The value 23 is prime.

So far we have 41 and 23 as our two primes.

Like mentioned earlier, we cannot use 5 as the units digit. The number 57 is not prime because 57 = 19*3. So we'll skip over 5.

The number 67 is prime for similar reasoning mentioned earlier.

------------

We have these primes: 41, 23, 67

The next number either 58 or 85 isn't prime

This is one way to show an example of why we're only able to get 3 primes out of this.

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

The correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

f(x) = 4x² + 1 and g(x) = x² - 3

a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

    = 4(x⁴ - 24x + 9) + 1

simplifying the above equation

    = 4x⁴ - 96x + 36 + 1

    = 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

      = 16x⁴ + 8x² + 1 - 3

simplifying the above equation

      = 16x⁴ + 8x² - 2

(g o f)(x) = 16x⁴ + 8x² - 2.

Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

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The distance from the point (10, 5, 10) to the plane y + 8z = 0 is 2.12 units.

To find the distance from a point to a plane, we can use the formula:

distance = |Ax + By + Cz + D| / √(A^2 + B^2 + C^2),

where (x, y, z) represents the coordinates of the point, and the equation of the plane is Ax + By + Cz + D = 0. In this case, the equation of the plane is y + 8z = 0, which can be rewritten as 0x + y + 8z + 0 = 0. So, A = 0, B = 1, C = 8, and D = 0. Substituting the values into the distance formula, we have:

distance = |0(10) + 1(5) + 8(10) + 0| / √(0^2 + 1^2 + 8^2)

= |5 + 80| / √(1 + 64)

= 85 / √65

≈ 2.12 units.

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\(\text{It is a geometric series.}\\\\\text{First term,}~ a = 2\\\\\text{Common ratio,}~ r = \dfrac{-\tfrac 43}2 = -\dfrac 46 = -\dfrac 23\\\\\text{Sum of an infinite geometric series,}\\\\S_{\infty} = \dfrac{a}{1-r}\\\\\\~~~~~=\dfrac{2}{1-\left(- \dfrac 23 \right)}\\\\\\~~~~~=\dfrac{2}{1+ \dfrac 23}\\\\\\~~~~~=\dfrac{2}{\tfrac 53}\\\\\\~~~~~=\dfrac{6}{5}\\\\\)

\(\text{The answer is}~ \dfrac 65\)