7,5 move 4 units left and 1 unit down

After one week, Reggie has 195 trade cards. He buys 16 more trade cards every week. he have 371 trading cards after 12th week.

According to the question, given that

After one week, Reggie has 195 trade cards. He buys 16 more trade cards every week.

he have trading cards in the 12th week = 195 + 16 * (12 - 1)

                                                                    = 195 + 16 * 11

                                                                     = 195 + 176

                                                                      = 371

Therefore, we get after solve  371 trading cards after 12th week.

Mathematicians refer to equations with a degree of 1 as linear equations. The largest exponent of terms in these equations is 1, which equals. These can also be broken down into linear equations with one variable, two variables, three variables, etc. A linear equation with the variables X and Y has the conventional form a X + b Y - c = 0, where a and b are the corresponding coefficients of X and Y and c is the constant.

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Reggie has 195 trade cards after a week. Each week, he purchases 16 additional trading cards. After the 12th week, he had 371 trading cards.

In response to the query, assuming that

Reggie has 195 trade cards after a week. Each week, he purchases 16 additional trading cards.

he have trading cards in the 12th week = 195 + 16 * (12 - 1)

                                                                   = 195 + 16 * 11

                                                                    = 195 + 176

                                                                     = 371

As a result, by the end of the 12th week, we have solved 371 trade cards.

Equations with a degree of 1 are referred to be linear equations by mathematicians. In these equations, the term with the biggest exponent is equal, or 1. These can also be reduced to linear equations involving one, two, three, etc. variables. The standard form of a linear equation with the variables X and Y is a X + b Y - c = 0, where a and b are the corresponding coefficients of X and Y, and c is the constant.

Answer:

aprox: 9 years?

Step-by-step explanation:

im sorry if this is wrong!

The equation of the line is x - y = 0.

The slope of the line passing through (13,-1) and (8,4).

m=y2-y1 / x2-x1

  = 4-(-1) / 8-13

  = 5 / -5

m=-1

The product of slopes is done in the case of perpendicular lines and it is 1.

The slope of another line will be

m.m1=-1

m1=-1/m

m1=-1/-1

m1=1

The equation of the line is

y-y1=m(x-x1)

y-1=1(x-1)

x-y=0.

Thus the equation of the line is x-y=0.

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Although part of your question is missing, the question is What is the equation of the line that passes through (1,1)  and is perpendicular to the line that passes through the following points:

(13,-1) and (8,4)

To find the roots of the auxiliary equation for the given differential equation x^2y'' - 12y = 0, we need to assume a solution of the form y = e^(rx) and substitute it into equation to obtain characteristic equation.

Assuming a solution of the form y = e^(rx) for the differential equation x^2y'' - 12y = 0, we can substitute it into the equation and simplify to obtain the characteristic equation. Differentiating y twice with respect to x, we have y' = re^(rx) and y'' = r^2e^(rx). Substituting these expressions into the differential equation, we get:

x^2(r^2e^(rx)) - 12e^(rx) = 0.

Factoring out e^(rx), we have:

e^(rx)(x^2r^2 - 12) = 0.

For the equation to hold true, either e^(rx) = 0 (which is not a valid solution) or (x^2r^2 - 12) = 0.

Setting the expression x^2r^2 - 12 equal to zero, we obtain the auxiliary equation:

x^2r^2 - 12 = 0.

To find the roots of this equation, we can factor it or use the quadratic formula. In this case, the equation is already factored, so the roots of the auxiliary equation are given by:

r = ±sqrt(12)/x.

The roots of the auxiliary equation determine the form of the solutions to the differential equation. To obtain the general solution, we consider the two cases: r = sqrt(12)/x and r = -sqrt(12)/x. For the case r = sqrt(12)/x, the solution takes the form y = c1e^(sqrt(12)/x), where c1 is a constant. For the case r = -sqrt(12)/x, the solution takes the form y = c2e^(-sqrt(12)/x), where c2 is a constant. Therefore, the general solution to the given differential equation is y = c1e^(sqrt(12)/x) + c2e^(-sqrt(12)/x), where c1 and c2 are arbitrary constants.

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Answer:

42.191

Step-by-step explanation:

Punch it in the calculator and round the decimal from 42.1911 to 42.191

Answer:

[see below]

Step-by-step explanation:

Rational Numbers:

Irrational Numbers:

Hope this helps.

The sphere equation x^2 + y^2 + z^2 = 6z becomes:
ρ^2 = 6ρcos(φ)
The cone equation z = √(x^2 + y^2) becomes:
ρcos(φ) = ρsin(φ)
So, the solid lies within the region described by the inequalities:
ρ ≤ 6cos(φ) and ρcos(φ) ≥ ρsin(φ)
These inequalities, along with 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π, define the solid in spherical coordinates.

To describe the solid in terms of inequalities involving spherical coordinates, we first need to convert the given equations to spherical coordinates. In spherical coordinates, we have:

x = r sinθ cosϕ
y = r sinθ sinϕ
z = r cosθ

Substituting these values in the given equations, we get:

r² sin²θ cos²ϕ + r² sin²θ sin²ϕ + r² cos²θ = 6r cosθ
r cosθ = r² sin²θ cos²ϕ + r² sin²θ sin²ϕ

Simplifying these equations, we get:

r = 6 cosθ / (sin²θ cos²ϕ + sin²θ sin²ϕ + cos²θ)^(1/2)
r cosθ = r² sin²θ

Now, the solid lies inside the sphere x2 + y2 + z2 = 6z, which in spherical coordinates becomes:

r² = 6 cosθ

And the solid also lies outside the cone z = x2 y2, which in spherical coordinates becomes:

r cosθ >= r^4 sin^2(θ) cos^2(ϕ) + r^4 sin^2(θ) sin^2(ϕ)
r >= r^3 sin^2(θ) (cos^2(ϕ) + sin^2(ϕ))
r >= r^3 sin^2(θ)

Combining these inequalities, we get the description of the solid in terms of inequalities involving spherical coordinates:

r >= r^3 sin^2(θ) >= (6 cosθ)^(1/2)

This represents the solid that lies inside the sphere x2 + y2 + z2 = 6z and outside the cone z = x2 y2, in terms of inequalities involving spherical coordinates.

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Answer:

Table B

Step-by-step explanation:

Note that for y to vary inversely as x, an increase in x will cause a decrease in y. Therefore, by careful observation of tables A, B, C, and D, we would notice the following:

In table C:

As x increases from 1 to 2 to 3, y also increases from 26 to 52 to 78. Which means that an increase in x causes an increase in y. This is not an inverse variation.

In table D:

As x increases from 1 to 2 to 3, y also increases from -7 to -1 to 6. Which means that an increase in x causes an increase in y. This is also not an inverse variation.

We are left with options A and B

If y varies inversely as x, the following relationship must hold:

\(y \alpha \frac{1}{x}\\y = \frac{k}{x}\)

Where k is a constant of proportionality

considering option B:

When x = 1, y = 36

36 = k/1

k = 36 * 1

k = 36

when x = 2, y = 36/2

y = 18

when x = 3, y = 36/3

y = 12

These tally with all that is indicated in the table. Option B is an inverse variation

The characteristics of the normal distribution can be used to determine the likelihood that X equals 19.62 because X is a normally distributed random variable with a mean of 12 and a standard deviation of 3.

We must compute the z-score, which counts the number of standard deviations a given result is from the mean, in order to determine this probability. Calculating the z-score is as follows:

z = (x - μ) / σ

If the supplied value, x, the mean, and the standard deviation are all given.In this instance, x=19.62, =12, and =3 respectively. By replacing these values, we obtain:

z = (19.62 - 12) / 3 ≈ 2.54

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Energy consumption is the amount of power used over time, measured in watt-hours (Wh) or kilowatt-hours (kWh). It is calculated by multiplying the power (measured in watts) by the time for which it is used.

To calculate energy consumption, you will need to know the amount of power being used and the time over which it is being used. Power is typically measured in watts (W), and energy is the product of power and time, so energy consumption is the number of watts used multiplied by the number of hours for which they are used.

For example, let's say you want to calculate the energy consumption of a light bulb that uses 60 W of power and is left on for 4 hours. The energy consumption would be:

Energy consumption = 60 W * 4 hours = 240 Wh (watt-hours)

This is the amount of energy that the light bulb used over the 4-hour period.

You can also convert watt-hours to other units of energy, such as kilowatt-hours (kWh). To do this, you would divide the watt-hours by 1,000. In the example above, the energy consumption would be 0.240 kWh.

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Answer:

the answer is (3, 2)

Step-by-step explanation:

the formula to find the centroid of a triangle is

{( x1+x2+x3)/3 , ( y1+y2+y3)/3}

Answer:

no

Step-by-step explanation:

Steps to answering this question

volume of a hemisphere = (2/3)πr^3

n = 22/7

r = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

radius = 40/2 = 20 cm

volume of one hemisphere = (2/3) x (22/7) x (20^3) = 16,761.90 cm^3

volume of the 12 baskets = 16,761.90 cm^3 x 12 = 201,142.86 cm^

2. convert the litres of compost to cm and multiply by the total bags of compost

1 litre = 1000cm

1 bag of compost = 50 x 1000 = 50,000

4 bags of compost = 50,000 x 4 = 200,000 cm

3. compare which figure is higher. the figure gotten in step 1 or 2

201,142.86 cm^3 is greater than 200,000

there is no enough compost

473691.4

273691.4

The distance around the outer circle of the water is 14π. Option B shows the correct circumference of the circle.

In geometry, circumference is the circumference of a circle or an ellipse. That is, the circumference will be the length of the arc of the circle as if it were opened and straightened into a line segment. More generally, the perimeter is the length of the curve around any closed figure. The circumference can also refer to the circle itself, which corresponds to the path of the edge of the disc. The circumference of a sphere is the circumference or length of one of its great circles.

Given Information:

A lawn sprinkler sprays water 7 feet in every direction as it rotates.

When the sprinkler covers all directions, it completes its one revolution of the circle. The distance around the outer circle of the water is calculated by the perimeter of the circle which is called the circumference of the circle.

Circumference = 2πr

Where r is the radius of the circle  = 7 feet.

Circumference  = 2π × 7

⇒ Circumference  = 14π

Hence we can conclude that the distance around the outer circle of the water is 14π. Option B shows the correct circumference of the circle.

Complete Question:

A lawn sprinkler sprays water 7 feet in every direction as it rotates. What is the distance around the outside circle of water? Leave your answers in terms of π.

A) 7π                                   B) 14π

C) 49π                                D) 28π

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Answer:

\(\frac{1}{60}\)

Step-by-step explanation:

Problem:

 The possible values of x in the equation (60)x = 1;

Solution:

Such a problem like this in which the highest power of the unknown is 1 will have just one solution.

       60x  = 1

To solve this, we take the multiplicative inverse of 60;

   the multiplicative inverse of 60 = \(\frac{1}{60}\)

   Use this inverse to multiply both sides of the expression;

         \(\frac{1}{60}\) \(x\)  60x  = 1 x \(\frac{1}{60}\)

                   x  = \(\frac{1}{60}\)

To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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Answer:

Step-by-step explanation:

A= 5(x+3)=17

B= 5x+3=17

C= 3x+5=17 A girl decides to buy 5 pens for 3 of her friends. The total cost of the pens was 17$. She then decides to make her friends guess the cost of each pen.

The solution set of the given homogeneous system in parametric vector form is (x1,x2,x3)=(s,-2,-5)

Parametric vector form:

If there are m-free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors:

x = s1v1 + s2v2 + ··· + sm vm. This is called a parametric equation or a parametric vector form of the solution.

A common parametric vector form uses the free variables as the parameters s1 through sm

Given is a system of equations

We are to solve them in parametric form.

x1 + 3x2 + x3 = 0 --------(1)

-4x1 + 9x2 + 2x3 = 0 ---------(2)

-3x2 - 6x3 = 0--------(3)

From equation(3)

-3x2=6x3

x2=-2x3

substitute in equation(1) and equation(2)

x1+3(-2x3)+x3=0

x1-6x3+x3=0

x1-5x3=0

x1=5x3

So the solution in parametric form is (x1,x2,x3) = (s,-2,5) for all real values.

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The simplified expression is (-187.584x + 287.6672) / 6.8, which is equivalent to option A: -2.84x - 1.66.

To simplify the expression 5.3x - 8.14 / 3.6x - 9.8, we can first simplify the division by finding a common denominator for the fractions.

The common denominator for 3.6x and 9.8 is 3.6x * 9.8 = 35.28x.

Next, we can rewrite the expression using the common denominator:
5.3x * (35.28x/35.28x) - 8.14 * (35.28x/35.28x) / 3.6x * (35.28x/35.28x) - 9.8 * (35.28x/35.28x)

Simplifying further, we get:
(5.3 * 35.28x^2 - 8.14 * 35.28x) / (3.6 * 35.28x - 9.8 * 35.28x)

Now, we can simplify the numerator:
(187.584x^2 - 287.6672x) / (-6.8x)

Factoring out an x from the numerator, we have:
x(187.584x - 287.6672) / (-6.8x)

Finally, we can cancel out the x terms:
(187.584x - 287.6672) / -6.8

Therefore, the simplified expression is (-187.584x + 287.6672) / 6.8, which is equivalent to option A: -2.84x - 1.66.

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Answer:

Step-by-step explanation:

Answer: 50% is the answer

Answer: 50%!

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first three terms of the arithmetic sequence for the number of words written are 10010, 9760, 9510. These have a common difference of 9760-10010 = -250. The first term and common difference can be used to make the explicit equation for the words written on the n-th day.

The explicit formula for the n-th term of an arithmetic sequence with first term a₁ and common difference d is ...

  \(a_n=a_1+d(n-1)\)

For first term a₁ = 10010 and common difference d = -250, the explicit rule is ...

  \(a_n=10010-250(n-1)\)

On day 14, n=14, and the number of words written is ...

  \(a_{14}=10010-250(14-1)\\\\a_{14}=10010-250(13)=10010-3250\\\\a_{14}=6760\)

The writer would write 6760 words on the 14th day.

we use is the derivative of top times bottom times top over bottom squared. At the critical point, we want eight X ln x minus four X to equal zero.

Only one answer—two x minus one and one x minus half—will satisfy the condition. The largest and smallest endpoints on the left and right must be determined. On each of these items, there is an E square root. A maximum for the minimums occurs at critical point or endpoints. We can see that these will be absolute according to the extreme value theorem, and here is our maximum.

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Answer:

  (i) x = 17 cm

  (ii) one end: 360 cm²; both ends: 720 cm²

  (iii) 14,400 cm³

  (iv) 4000 cm²

Step-by-step explanation:

You want the slant height, base area, volume, and total surface area of a trapezoidal prism with the base isosceles trapezoid having parallel base lengths of 32 and 16, and a height of 15. The distance between bases is 40. All units are cm.

If a center rectangle 16 cm wide and 15 cm high is cut from the base trapezoid, the remaining two triangles have a base of 8 cm and a height of 15 cm. The Pythagorean theorem can be used to find the slant height:

  x² = a² +b²

  x² = 8² +15² = 64 +225 = 289

  x = √289 = 17

The slant height, x, is 17 cm.

The area of the base trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

  A = 1/2(32 +16)(15) = 360 . . . . square cm

The area of one end surface is 360 cm²; the total area of both end surfaces is 720 cm².

The volume of the prism is the product of the base area and the length of the prism.

  V = Bh

  V = (360 cm²)(40 cm) = 14,400 cm³

The volume of the trapezoidal prism is 14,400 cm³.

The lateral surface area of the prism is the product of the perimeter of the base and the distance between bases.

  LA = Ph

  LA = (32 +16 +2·17 cm)(40 cm) = 3280 cm²

The total surface area is the sum of the lateral area and the area of the two bases:

  SA = LA +2B = (3280 cm²) + 2(360 cm²) = 4000 cm²

The total surface area of the prism is 4000 square centimeters.

__

Additional comment

It appears that the top dashed line in the figure is drawn that way in error. It appears to identify a visible edge, so we expect it to be a solid line.

The population of each country will become double in 47 years.

Given that,

The population of the Dominican republic is, n = 10.7 million.

The growth rate of the Dominican republic is, p = 1.5 %.

The population of Paraguay is, n' = 6.0 million.

The growth rate of Paraguay is p' = 1.5 %.

The doubling time of population growth depends on the rate of population growth.

Here,

n is the final population and n0 is the initial population and doubling the value in the future, n= 2*n0.

Solving this, we get:

t= ln (2*n0/n0)/(1.5/100) = 47 years.

Thus, we can conclude the population of each country will become double in 47 years.

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Thank you so much :D

Step-by-step explanation:

-4 + 2 + 4f = 8 - 3f

-2+4f=8-3f

7f=10

f=10/7

Step-by-step explanation:

\( - 4 + 2 + 4f = 8 - 3f \\ - 2 + 4f = 8 - 3f \\ - 4f - 3f = - 2 - 8 \\ \frac{ - 7f }{ - 7} = \frac{ - 10}{ - 7} \\ f = \frac{10}{7} \)

This cadence corresponds to three sets of 24 steps per set, totaling 72 steps per minute. Participants are required to step up and down on a 12-inch step platform for a duration of three minutes, following the 96 BPM rhythm.

The step cadence used during the YMCA 3-minute step test is a set of three stepping cycles per each 20-second period. This means that the participant takes a total of nine steps within each 20-second period. In other words, the participant steps up and down on the platform at a rate of approximately 24 steps per minute. It is important to maintain this consistent step cadence throughout the entire test in order to get an accurate measure of cardiovascular fitness. Overall, the YMCA 3-minute step test is a simple and effective way to assess an individual's aerobic fitness level.

The YMCA 3-minute step test utilizes a specific step cadence to measure an individual's cardiovascular fitness. The answer is that during the test, a cadence of 96 beats per minute (BPM) is used. This cadence corresponds to three sets of 24 steps per set, totaling 72 steps per minute. Participants are required to step up and down on a 12-inch step platform for a duration of three minutes, following the 96 BPM rhythm. Upon completion of the test, the participant's heart rate is measured for a minute to determine their fitness level. The test results can be compared to established norms to gauge overall cardiovascular health and endurance.

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