find the point on the line y=2x+3 that is closest to the origin

The ice cream costs $3 for a small serving and $4 for a large serving.

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Since 3 small servings of ice cream and 1 large serving of ice cream for $13, and 2 small servings of ice cream and 1 large serving of ice cream for $10. We can set up two equations to represent the situation:

Let S and L represent the cost of small servings and large servings respectively

3S + L = 13 --- (1)

2S + L = 10 --- (2)

From (1):
L = 13 - 3S  --- (3)

Put (3) in (2):

2S + L = 10

2S + 13-3S = 10

-S + 13 = 10

S = 13-10

S = $3

Put S = 3 into (3):

L = 13 - 3S

L = 13 - 3(3)

L = 13 - 9

L = $4

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The transition that was applied to the triangle ABC to create triangle A’B’C’ is (x, y) ⇒ (x - 4, y - 3)

Transformation is the movement of a point from its initial location to a new location. Rigid transformations are transformations on the coordinate plane that preserves the shape and size of the figure. Types of rigid transformations are reflection, translation and rotation.

Rigid transformations are translation, reflection and rotation since they preserve the size.

Translation is the movement of a point up, left, right or down in the coordinate plane.

Triangle ABC was translated 4 units to the left and 3 units down using the rule (x, y) ⇒ (x - 4, y - 3)

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Step-by-step explanation:

1.

equilateral triangle. all sides and also all angles are equal.

the sum of all angles in a triangle is always 180°.

so,

6x = 180/3 = 60°

x = 10

2.

all 3 angles are equal, so, also all 3 sides are equal.

6x - 5 = 5x

x - 5 = 0

x = 5

3.

again, all 3 angles are equal.

3x = 180/3 = 60

x = 20

4.

the 2 sides are marked as equally long.

4x = 40

x = 10

5.

isoceles triangle with 60° angle in top, that means it is again an equilateral triangle.

3x + 8 = 4x - 4

8 = x - 4

12 = x

6.

again all angles are equal.

4x = 60

x = 15

Salut/Hello!

Answer: 3120 cubic cm

Step-by-step explanation:
cm - centimeters
=> - results

We know the area is 156 square cm
And the height is 20 cm

We know the area formula is A = L x l
where L - length
and l - latitude

We also know the volume formula is V = L x l x h
where h - height

So we can replace the length and latitude with the area and we have
V = A x h     and we know the area and height

So we calculate:
V = 156 x 20 => V = 3120 cubic cm


I hope it was helpful! :]

50

I attached a pic of my work.

so what I did was find the amount of the other sides of the triangle using their opposite congruent sides. aka, the bottom is 90, which means the top should also be 90. and 90-50 is 40, so the rest of that side (which is one side of the triangle) should be 40.

and then I used the pythagorean theorem, since it is a right triangle (indicated by the squares in the corners).

the theorem states that a^2 + b^2 = c^2

so just plug in the legs (a and b), and you should get the amount of segment AB (which is c)

Answer:

71.4°F

Step-by-step explanation:

The maximum is when [tex]\sin(0.24x-1.88)=1[/tex], yielding a maximum of [tex]8.6+62.8=71.4[/tex].

The initial force between the two charges is given by:

[tex]F=k\frac{q_{1} q_{2} }{d^2}[/tex]

where k is Coulomb's constant, q1 and q2 are the two charges, and d is their separation. Let's analyze now the other situations:

1. F

In this case, q1 is halved, q2 is doubled, but the distance between the charges remains d.

So, we have:

q'₁=q₁/2

q'₂=2q₂

d'=d

So, the new force is:

[tex]F'=k\frac{q'_{1}q'_{2} }{d^2} \\\\F'=k\frac{(\frac{q_{1} }{2})(\frac{q_{2} }{2}) }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{d^2} =F[/tex]

So the force has not changed.

2. F/4

In this case, q1 and q2 are unchanged. The distance between the charges is doubled to 2d.

So, we have:

q'₁=q₁

q'₂=q₂

d'=2d

So, the new force is:

[tex]\\F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{2d^2} \\\\F'=\frac{1}{4} k\frac{q_{1}q_{2} }{d^2} \\\\F'=\frac{F}{4}[/tex]

So the force has decreased by a factor of 4.

3. 6F

In this case, q1 is doubled and q2 is tripled. The distance between the charges remains d.

So, we have:

q'₁=2q₁

q'₂=3q₂

d'=d

So, the new force is:

[tex]F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{2q_{1}3q_{2} }{d^2}\\ \\F'=6k\frac{q_{1}q_{2} }{d^2} =6F[/tex]

So the force has increased by a factor of 6.

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Answer:

1. F

2. F/4

3. 6F

Answer:

1 5/12 (One whole number five over twelve)

Step-by-step explanation:

Recipe calls for 2 3/4 cups

No of cups available are 1 1/3 cups

To get the number of cups needed to fulfill the recipe well say:

1 1/3 + X = 2 3/4

X = 2 3/4 - 1 1/3 = 1 5/12

Answer:

first get one odd No, again more odd number than even, Lastly two or more odd number

Answer:

0

Step-by-step explanation:

1/2 = 2/4

1/2-2/4 = 0

We can draw the conclusion that linear functions can be used to represent each of the ideas. Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).

A linear function is denoted by the equation y = mx + b, where m is the slope or unit rate between the two variables, x and y, and b is the beginning value or y-intercept.

The initial value is b.

A linear function is a graph with straight lines.

A unit rate exists for all linear functions (b).

Sarah's suggestion can be expressed by a linear function because the graph that represents it is a straight line.

Gene's Proposal's table displays the unit rate as change in y/change in x = 7. As a result, a linear function can be used to express it.

Paul's idea has a linear function as its equation.

This leads us to the conclusion that linear functions can be used to represent each of the ideas.

Due to the fact that each proposal's linear function has an initial value, the class now has money in its accounts (b).

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Correct Question:

By using a trigonometric relation, we will see that the value of x on the right triangle is x = 53.4

We want to find the value of x on the given right triangle, which is one of the cathetus of the triangle (the adjacent cathetus of the shown angle).

We know one angle of 51°, and the opposite cathetus of that angle, which has a measure of 66 units.

Here we can use the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing the known values, we will get:

tan(51°) = 66/x

Solving that for x, we will get:

x = 66/tan(51°) = 53.4

The measure of the adjacent cathetus is 53.4 units.

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Table A represents a function, but Table B does not represent a function.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y or vice versa.

For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y.

We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.

As, each element of X is associated with a unique element of Y, so this is a function.

Table A    

          X                Y

          3                 1

          2                 0

          1                  0

As, each element of X is associated with a unique element of Y, so this is a function.

Table B

X             Y

3             -2

5              1

5              2

Hence, Table A represents a function, but Table B does not represent a function.

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as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]\stackrel{f(x)}{y}~~ = ~~10(\sqrt[7]{x}+9)\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~10(\sqrt[7]{y}+9)} \\\\\\ \cfrac{x}{10}=\sqrt[7]{y}+9\implies \cfrac{x}{10}-9=\sqrt[7]{y} \\\\\\ \left( \cfrac{x}{10}-9 \right)^7=(\sqrt[7]{y})^7 \implies \left( \cfrac{x}{10}-9 \right)^7=\stackrel{f^{-1}(x)}{y}[/tex]

In accordance with the above assertion, the offered differential equation by variable separation is P = 1/ (k*e^t +1).

A differential equation in mathematics is one that has one or more negatively influencing variables. Dy/dx provides the function's derivative. The phrase describes an equation with several ways to connect the dependent variable to one or more regressors.

dP/dt = P - P^2

1/(P - P^2)dP = dt

∫1/(P - P^2)dP = ∫dt

t + c = 1/(P - P2)dP, where c would be a constant

Use the partial fractions method to calculate the integrated on the left. We wish to rewrite 1/(P-P2) in the pattern A/P+B/(1-P) for those constants A and B since P-P2 factors to P(1-P). We therefore have:

1/[P(1-P)] = A/P + B/(1-P)

A(1-P) + BP = 1

When P is 1, we have A(1-1)+B(1)=1, or B=1.

When P is 0, we have A(1-0)+B(0)=1, or A=1.

So, we can rewrite 1/(P-P^2) as 1/P+1/(1-P).

Whilst doing the entire on the ODE's left side, we have:

∫1/(P - P^2)dP

∫[1/P + 1/(1-P)]dP

∫(1/P)dP + ∫1/(1-P)dP

ln(P) + ∫1/(1-P)dP

Make a u-substitution to perform the second integral:

u = 1-P, du = -dP

ln(P) - ∫(1/u)du

ln(P) - ln(u)

ln(P) - ln(1-P)

ln[P/(1-P)]

Reconnecting that to the ODE yields the following:

ln[P/(1-P)] = t + c

e^ln[P/(1-P)] = e^(t + c)

P/(1-P) = e^t * e^c

P/(1-P) = ke^t, where k is a constant equal to e^c

P = (1-P)ke^t

P = ke^t - Pke^t

P + Pke^t = ke^t

P(1 + ke^t) = ke^t

P = ke^t / (1 + ke^t)

P = e^t / (1/k + e^t)

P = e^t / (d + e^t), where d is a constant equal to 1/k

So, the general solution to the ODE is P = e^t / (d + e^t), where d is a constant.

p*(1-p) = k*e^t ( we say that e^k is a constant)

1-p/p = k*e^t

P = 1/ (k*e^t +1)

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The complete question is-

Solve the given differential equation by separation of variables.

dP/dt = P - P²

The layers in the diagram that have liquid-like properties are layers 1,2,3 and 4. This is determined by the properties of liquids, which are: high viscosity, low compressibility, and the ability to flow.

Viscosity is the measure of a liquid's resistance to flow. It can be calculated using the formula η = (ΔP/l) x (d/Δt), where η is the viscosity, ΔP is the pressure difference, l is the length of the flow, d is the change in distance, and Δt is the time difference.

Compressibility is the measure of how a liquid responds to pressure or volume change. It is calculated using the formula β = -1/V (dV/dP), where β is the compressibility, V is the volume, and dV/dP is the change in volume over the change in pressure.

The ability to flow is the measure of how a liquid can move from one place to another. It is calculated using the formula Q = A x v, where Q is the flow, A is the area of the cross-section of the flow, and v is the velocity.

By using these formulas and calculations, it can be determined that layers 1,2,3, and 4 have liquid-like properties.

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The area of the rectangular pen is represented by the quadratic equation [tex]A(w) = 50w - w^{2}[/tex].

Let w be the width of rectangular pen.

We have been given that a farmer has 100 m of fencing to enclose a rectangular pen. This means that perimeter of pen is 100 meter.

Since the perimeter is 2 times the length and width of rectangle.

Perimeter of a rectangle = 2 (Width + Length)

Upon substituting our given values in above formula we will get,

[tex]100 = 2(w + length)\\50 = w + length\\50-w = Length[/tex]

Area of a rectangle = Width x Length

[tex]Area of a rectangle = w (50-w)\\= 50w - w^{2}[/tex]

Let us represent area in terms of width of rectangle as:

[tex]A(w) = 50w - w^{2}[/tex]

Therefore, the area of the rectangular pen is represented by the quadratic equation [tex]A(w) = 50w - w^{2}[/tex].

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The product of x and y is: "1"

Step-by-step Solution:

Given: 16/9, x, 1, y  are in Geometric Progression (G.P)

Let the general terms of a Geometric Progression are: a, ar, ar², ar³

So, On comparing we get; a=16/9,

⇒ar² = 1

⇒ 16/9*r² = 1

⇒ r² = 9/16

⇒ r = 3/4

x = ar

⇒ (16/9)(3/4)

⇒x=4/3.

y = ar³

⇒(r)(ar^2) = (3/4)(1)

⇒y=3/4.

Now, to find the product of "x" and "y":

⇒x*y = 4/3 x 3/4

⇒1

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The elimination method is used to solve a system of equations with multiple variables. Repeat this process until all of the variables have been eliminated, then simplify the equations to solve for the remaining variable.

Once a variable has been isolated, it can then be eliminated from the other equations by either adding or subtracting the equations from each other. This process should be repeated until all of the variables have been eliminated from all of the equations.

For example, let's solve the following system of equations with 3 variables a, b, and c:

a + b + c = 8

2a + b + 2c = 12

3a + 2b + 3c = 18

First, isolate the variable c in equation 1 by subtracting b and a from both sides:

c = 8 - a - b

Substitute this expression for c in equation 2 and 3 to eliminate c:

2a + b + 2(8 - a - b) = 12

3a + 2b + 3(8 - a - b) = 18

Then simplify the equations to solve for the remaining variables:

2a + 3b = -4

9a + 6b = 36

Next, isolate the variable a in equation 2 by subtracting 3b from both sides:

a = -4/2 - 3b/2

Substitute this expression for a in equation 1 and 3 to eliminate a:

-4/2 - 3b/2 + b + 8 - b = 8

9(-4/2 - 3b/2) + 6b + 3(8 - b) = 36

Then simplify the equations to solve for the remaining variable:

15b = -12

b = -12/15

Finally, substitute b back into equation 1 or 2 to solve for a:

a + (-12/15) + 8 = 8

a = 8 - (-12/15) - 8

a = 24/15

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The last customer will be in the book store for 3.22 seconds.

The solution can be calculated using Little's Law, which states that the average number of people in a system equals the average arrival rate multiplied by the average time spent in the system.

Using this formula, we can calculate the time that the last customer will spend in the book store.

Little's Law: Average number in system = Average arrival rate x Average time in system

Average number in system = 29 customers/second x 3 seconds = 87 customers

Average time in system = 87 customers/27 customers/second = 3.22 seconds

Therefore, the last customer will be in the book store for 3.22 seconds.

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Answer: Hello how are you doing?

Step-by-step explanation: How may I help you?

1) library(lahmanrbroom)

model <- lm(runs ~ bb + hr, data = teams %>% filter(yearID == 1971))

tidy(model)

2) model2 <- lm(bb ~ year, data = tidy(model))

3) The p-value for this effect is significantly different from zero.

1) To obtain the effects of bb (walks) and hr (homers) on runs in 1971 using the teams data frame from the lahmanrbroom package and the tidy() function, the following code can be used:

library(lahmanrbroom)

model <- lm(runs ~ bb + hr, data = teams %>% filter(yearID == 1971))

tidy(model)

The estimate for the effect of bb on runs can be found in the 'Estimate' column for the variable 'bb', and the estimate for the effect of hr on runs can be found in the 'Estimate' column for the variable 'hr'.

2) To determine the effect of year on the impact of bb, a linear model can be fit on the results from the previous question. The following code can be used:

model2 <- lm(bb ~ year, data = tidy(model))

The coefficient for the variable 'year' in this model represents the change in the impact of bb on runs for each additional year.

3) The p-value for this effect can be found in the 'p.value' column of the output of the summary() function applied on the model2, which tests if the coefficient for the variable 'year' is significantly different from zero.

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Number of seats allocated to state A = 12

Number of seats allocated to state B = 18

Number of seats allocated to state C =22

Number of seats allocated to state D = 38

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Percentage of Population of state A = 258/1858 x 100 = 13.88%

Now, Number of seats allocated to state A = 13.88% of 45

                                                                       = 12.492 = 12 (whole number)

Percentage of Population of state B = 377/1858 x 100 = 20.29%

Now, Number of seats allocated to state A = 20.29% of 90

                                                                       = 18.261 = 18 (whole number)

Percentage of Population of state C = 456/1858 x 100 = 24.54%

Now, Number of seats allocated to state A = 13.88% of 90

                                                                       = 22

Number of seats allocated to state D = 90-(12+18+22) = 38

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0.168 is the probability that exactly 1 of the 4 players has exactly one ace and one king.

The word "probability" derives from the Latin word "probitatem," which means "credibility, likelihood," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

a)

Given that,

each player gets 13 cards.

So, n = total no. of ways = ⁵²C₁₃ = 6.350× 10¹¹

As we know, there are 2 black aces and 4 kings in a deck of 52 cards. Since, one black ace out of 2 black aces can be chosen in ²C₁ ways, next one king out of 4 kings in ⁴C₁ ways and the remaining 11 cards from the remaining 46 cards in ⁴⁶C₁₁ ways.

So, m = ²C₁ × ⁴C₁ × ⁴⁶C₁₁

m = 1.067 × 10¹¹

Therefore, Required probability p =  m/n

p = (1.067 × 10¹¹) / (6.350× 10¹¹)

p = 0.168

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The age of the spearhead to the nearest year will be 6,349

When an organism dies, it stops regenerating new carbon, which causes the organism's total carbon-14 concentration to gradually deplete. By analyzing the ratio of carbon-14 to carbon-12 in an organism, scientists can ascertain when it died.

0.53No = Noe^-0.0001t for T.

Divide both sides by No

0.53No = Noe^0.0001t

0.53 = e^-0.0001t

Take the log of both sides

In 0.53 = In e^-0.0001t

Apply In e^x = x.

In 0.53 =-0.0001t

Divide both sides by -0.0001t to solve for t.

t=6,349

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Applying the area of the parallelogram formula, it can be concluded that the area is 56 square units.

The area of the parallelogram is the magnitude of the cross-product of the adjacent edges (base and height).

Given information:

A parallelogram is made up of 4 vertices: A(−3, 0), B(−1, 6), C(8, 5), and D(6, −1).

So first we find the adjacent edges as follows:

AB = B - A

     = ( (-1-(-3)) , (6-0) )

     = (2,6)

AD = D - A

     = ((6-(-3)) , (-1-0))

     = (9,-1)

We want to find the area of the parallelogram, we do the following step:

[tex]AB x AD = \left[\begin{array}{ccc}i&j&k\\2&6&0\\9&-1&0\end{array}\right][/tex]

               = i(0 - 0) + j(0 - 0) + k(-2 - 54)

               = -56k

The area of the parallelogram = | AB x AD |

                                                  = √(-56)²

                                                  = 56 square unit

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As a result, the automobile will go 90 miles to the location where we will stop for food before beginning our 720-mile journey.

The amount or magnitude of the difference between two points is what is referred to as distance. It should be noted that the distance traveled between two positions and the distance between them are not the same. The total length of a path connecting two points is known as the distance traveled. A body's actual journey distance is referred to as distance. A different name for it is path length. For instance, the length of the path if an object is going from point O to point P will be equal to OP = 360 m. A scalar quantity is the distance. Only magnitude exists.

given

We will stop for food at after traveling 8 miles from Point B, or 90 miles total.

= 760 miles 

As a result, the automobile will go 90 miles to the location where we will stop for food before beginning our 720-mile journey.

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The complete question is " . Diagram of a car traveling 90 miles . Our food stop will be at what miles after we start our trip from Point B. "

Answer:

2 3/4 square yd

Step-by-step explanation:

3/1 x 11/12 = 2 3/4

x = 60° - 35°

x = 25°

The measure of angle FGJ is 25°