Write the sum of 15 and 60 using the greatest common factor and the distributive property

Answer:

x² -  4 = 0

4x² = 16

Step-by-step explanation:

x² -  4 = 0 can be rewritten as
x² = 4

x = ± √4

x = ± 2

So this gives two solutions for x => x = 2 and x = -2

4x² = 16

Divide by 4 both sides

x² = 16/4

x² = 4

which is the same as above

x = ± 2

The inequality on the number line is 5x -2 > -22 or 6x-7 < 11.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

The open circles on the number line shows that it does not include those value i.e., the values have less than and greater than.

So, from the number line the inequality is -4 < x < 3.

Now, 5x -2 > -22 and 6x-7 < 11

5x > -20 and 6x < 18

x > -4 and x<3.

x+5 >8 and 3+ 2x < -5

x >3 and x < -4.

so, the inequality is 5x -2 > -22 or 6x-7 < 11.

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The solution is: (x,y)= (-1, -6), the graph is given below.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

y> -x-5

y< 2x-8

Solve graphically

See attachment for graph;

Next, determine the intersection points between the two lines

From the attached graph, we have:

(x,y)= (-1, -6)

Hence, the solution is: (x,y)= (-1, -6).

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Answer: i wouldnt

Step-by-step explanation: while its a good way to get funds since you'd get 10x the amount the people came. But if you were the person buying the ticket you'd have 1 in a thousand chance. Unless less people came but still -

so no.

Based on the provide data, the predicted drag on the full-sized pole is 52.53 lb.

We have a graph between model velocity and model drag. Also we have two set of dimensions and we have to predict drag on the full-sized pole. Write the details as shown : Since, the working temperature is not given, assume T= 60°F. For model :

Length Lₘ = 2 ft

Diameter, dₘ = 1 in = 1/12 ft.

Velocity = Vₘ

Density in water, ρₘ =1.94 slugs/ft³

Dynamic Viscosity, μₘ= 2.373×10⁻⁵ lb-s/ft² ( water)

For prototype :

Length, Lₚ = 30 ft

Diameter, dₚ = 1.25 ft.

Velocity, Vₚ = 30 mph = 30 × 1.467 ft/s

= 44 ft/s

Density in air, ρₐ = 2.34×10⁻⁵ slugs/ft³

Dynamic Viscosity, μₐ= 3.75×10⁻⁶ lb-s/ft²

Determine the velocity of air using Reynolds number similarity as below :

ρₘ Vₘdₘ/μₘ = ρₐ Vₚ dₚ/ μₐ

=> Vₘ = (ρₐ/ρₘ)(dₚ/dₘ)(μₘ/μₐ)Vₚ

=> Vₘ = ( 2.34×10⁻⁵ /1.94)(1.25 /1/12 )(2.373×10⁻⁵/3.75×10⁻⁷ )44

Vₘ = 50.37 ft/s

From the graph, the value of drag corresponding to Vₘ = 50.37 ft/s is 253.7 lb. Determine the drag on the full-sized pole: Fₚ/dₚ² Vp²ρₐ = Fₘ(Vₘ²dₘ²ρₘ)

=> Fₚ = Fₘ( dₚ/dₘ)²(Vₚ/Vₘ)²(ρₐ/ρₘ)

=> Fₚ = 253.7 lb ( 1.25 ft/1/12ft )²( 44 ft/s/50.37 ft/s)²( 2.34×10⁻⁵slugs/ft³/1.94 slugs/ft³)

=> Fₚ = 52.53 lb

Hence, required full-sized pole is 52.53 lb.

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Complete question:

The drag on a 30-ft long, vertical, 1.25-ft diameter pole subjected to a 30 mph air wind is to be determined with a model study. It is expected that the drag is a function of the pole length and diameter, the fluid density and viscosity. Laboratory model tests were performed in a high-speed water tunnel using a model pole having a length of 2 ft and a diameter of 1 in. Some model drag data are shown in the figure. Based on these data, predict the drag on the full-sized pole. 350 300 250 200 150 100 50 10 30 40 50 60 Model velocity, f's.

Standard form of the line passing through the points (-2, -3) and (4, -7) is,

⇒ y = - 2/3x - 13/3

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-2, -3) and (4, -7).

Now,

Since, The equation of line passes through the points (-2, -3) and (4, -7).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 7 - (-3)) / (4 - (-2))

m = - 4 / 6

m = - 2/3

Thus, The equation of line with slope - 2/3 is,

⇒ y - (-3) = - 2/3 (x - (-2))

⇒ y + 3 = - 2/3 (x + 2)

⇒ y + 3 = - 2/3x - 4/3

⇒ y = - 2/3x - 4/3 - 3

⇒ y = - 2/3x - 13/3

Therefore, The equation of line passes through the points (-2, -3) and

(4, -7) will be;

⇒ y = - 2/3x - 13/3

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Answer:To determine if the function is a minimum or maximum value, we need to find its second derivative and see if it is positive or negative. If the second derivative is positive, the function is a minimum value, if it's negative, the function is a maximum value.

The second derivative of the given function is a constant (2), which means it is always positive. Therefore, the function g(x)=x^2+6x+8 is a minimum value.

The minimum value occurs at the vertex of the parabolic shape of the function, which can be found using the formula: x = -b / 2a, where a, b, and c are the coefficients of the function g(x) = ax^2 + bx + c. Plugging in the values, we get x = -6 / 2 * 1 = -3.

The minimum value of the function can be found by substituting the x value back into the function: g(-3) = (-3)^2 + 6(-3) + 8 = 9.

So the minimum value of the function g(x) = x^2 + 6x + 8 is 9, and it occurs at x = -3.

Step-by-step explanation:

Answer:

The function doesn't have maximum value, as it is always increasing, although it has minimum value which is -b/2a, in this case -3 is a minimum value

The object traveled 300 ft in 15 seconds.

The problem can be solved using precalculus. The distance traveled in 15 seconds can be calculated using the formula d = rt, where d is the distance traveled, r is the rate of speed, and t is the time. In this case, d = 20 ft/sec * 15 sec = 300 ft. Therefore, the object traveled 300 ft in 15 seconds. To calculate this using a graphical approach, we can plot the points (0,0) and (15,300) on a graph. The slope of the line connecting the two points is 20 ft/sec, which is the rate of speed of the object. This confirms that the object traveled 300 ft in 15 seconds.

The object traveled 300 ft in 15 seconds.

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Therefore , the solution of the given problem of probability comes out to be probability that Both Rise - 0.06.

The possibilities of a given outcome in an event of sequence of events are referred to as probability.Consider the prices of two stocks as A & B based on the information provided. The following formula will be used to determine the likelihood that both stocks' prices will fall:

Here,

Decline Probability in A and B = PA(D) x PB (D)

Probability of Decline for A and B is -0.2 x 0.3.

Decline probabilities in A and B are 0.06

Now there will be a 100% chance of a price increase.

The likelihood of one rising is given by PA(U) x [PB(R) + PB(D)] + PB(U) x [PA(R) + PA(D)].

Chance of one rising is equal to 0.2 x (0.4 + 0). .3] +0.3 x (0.6+0.2

Chance that one increases is -0.38

For just one price remaining the same, now

One Unchanged Probability = PA (U) x [PB(R) + PB(D)]

[PA(R)+ P1 (D)] +PB(U)

Probability for a Single Unchanged Value is equal to 0.6 x [0.3 +0.3] +0.4 x [0.2+0 .2]

Probability for a Single Unchanged Value: 0.52

the likelihood that both prices will increase,

Both Rising Probability = PA(R)APB (R)

Chance that Both Will Rise 0.2 x 0.3

Chance that both will rise: 0.06

Therefore , the solution of the given problem of probability comes out to be probability that Both Rise - 0.06.

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The solution to the initial value problem is:

y(x) = √{16}/{8x-1}} + 3e^{-2x} + 2√{2} + 1

The solution to the initial value problem is given by:

y(x) = √{16}/{8x-1}} + 3e^{-2x} + C

Where C is the constant of integration. To find C, we can use the initial condition y(0) = 2√{2}:

y(0) = √{16}/{8(0)-1}} + 3e^{-2(0)} + C = 2√{2}

Solving for C:

C = 2√{2} - √{16}/{-1}} - 3 = 2√{2} + √{16} - 3 = 2√{2} + 4 - 3 = 2√{2} + 1

So the solution to the initial value problem is:

y(x) = √{16}/{8x-1}} + 3e^{-2x} + 2√{2} + 1

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option D is correct, VZ and Vr  are pair of segments in the figure  intersect.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

In the given figure we have to find the segments which are intersected.

line segments are considered intersecting lines when they cross each other at one single point.

The point where lines intersect is termed the point of intersection

VZ and Vr are the pair of segments which are intersected.

Hence, option D is correct, VZ and Vr  are pair of segments in the figure  intersect.

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The solution that each system of equations have would be = 2 solutions of the value of X and y.

The substitution method of solving an equation is defined as the way of solving an equation whereby one variable is solved and is substituted into the second unknown variable.

For the above sets of equations, the solutions would be the value of both X and y which can be solved as follows:

4x-y = 2 ---->. equation 1

16x-4y = 8 -----> equation 2

Make y the subject of formula in equation 1

y = 2-4x

substitute y = 2-4x into y in equation 2

16x - 4( 2-4x) =8

16x - 8 + 16x = 8

32x = 16

X = 16/32

X= 0.5

Substitute 0.5 = X in equation 1;

4(0.5) - y = 2

y = 2-2

y = 0

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Inequalities help us to compare two unequal expressions. The point which satisfy both inequalities is (5,0)

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

For a point to be the solution of the system of inequalities, the point when substituted in the inequalities must satisfy both the given inequalities.

A. (2, -6)

y > (-3/2)x + 6

-6 > (-3/2)2 + 6

-6 > 3. this is false

y > x - 6

-6 > 2 - 6

-6 > -4 this is false

Since the both inequality is not satisfied, therefore, the given point is not the solution.

B. (10, -5)

y > (-3/2)x + 6

-5 > (-3/2)10 + 6

-5 > -9. this is true

y > x - 6

-5 > 10 - 6

-5 > 4 this is false

Since the second inequality is not satisfied, therefore, the given point is not the solution.

C. (5, -0)

y > (-3/2)x + 6

0 > (-3/2)5 + 6

0 > -1.5. this is true

y > x - 6

0 > 5 - 6

0 > -1 this is false

Since both the inequality are satisfied, therefore, the given point is the solution.

D. (-10, -4)

y > (-3/2)x + 6

-4 > (-3/2)-10 + 6

-6 > 21. this is false

y > x - 6

-4 > -10 - 6

-6 > -16 this is true

Since the first inequality is not satisfied, therefore, the given point is not the solution.

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The correct statement is,

⇒ A coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points

(0, 27) and (2, 21).

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table shows the relationship between the number of days she has been selling cookies and the total number of boxes remaining.

Girl Scout Cookie Fundraiser

Time (in days)          1   3   4   7

Number of Boxes   24 18  15  6

Now, Take two points for the line is, (1, 24), (3, 18)

Hence, The graph of equation is,

⇒ y - 24 = (18 - 24) / (3 - 1) (x - 1)

⇒ y - 24 = - 6/2 (x - 1)

⇒ y - 24 = - 3 (x - 1)

⇒ y - 24 = - 3x + 3

⇒ y = - 3x + 3 + 24

⇒ y = - 3x + 27

Thus, A coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (0, 27) and (2, 21).

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Answer:

(0, 27) and (2, 21).

Step-by-step explanation:

The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: The measure of the frame is 8.5 inches and 11 inches

a) if the frame is 4 papers long then we  have the length of the frame as

11×4=44 inches (since he lays the paper along the edge of frame)

We know 1 inch= 0.0833 foot

Thus      44 inches= 3.66667 foot

b) Again if he lays the paper along the short edge than the width of the frame is 3×8.5=25.5 inches

∴25.5 inches= 2.125 feet

Hence, The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.

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The equivalent formula that does not involve integrals is A(x) = 2x - 2x^2 + 4x - 4.

The First Fundamental Theorem of Calculus states that if f(x) is a continuous function on the interval [a, b], then the function F(x) = integral^x_a f(t) dt is an antiderivative of f(x), meaning that its derivative is equal to f(x). Therefore, if we have the antiderivative of a function, we can use the derivative to find an equivalent formula without an integral.

In this case, the derivative of the antiderivative of f(t) = 4 - 2t is f(t) = 4 - 2t, which is the original function. So, the equivalent formula for A(x) is A(x) = 2x - 2x^2 + 4x - 4, which does not involve integrals.

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Answer:

Second option:

[tex]\boxed{ \$6,671.67}[/tex]

Step-by-step explanation:

The equation for the amount accrued at 5.4% interest compounded semi-annually(twice a year) for an initial investment P for t years is already given:

[tex]A = P\left(1 + \dfrac{0.054}{2}\right)^{2t}[/tex]

Plug in
P = $3000
t = 15 years

[tex]A = 3000\left(1 + 0.054\right)^{2\cdot 15}\\\\A = 3000(1 + 0.027)^{30}\\\\A = 3000(1.027)^{30}\\\\A = 3000 (2.22389)\\\\A = \$6,671.67[/tex]
This is the second option

The value of x from the equation is 18. Option E

It is important to note that algebraic expressions are expressions with variables, terms, coefficients, constants and factors.

They are also made up of operations, such as addition, multiplication, division, subtraction, floor division, parentheses, bracket.

From the information given, we have that;

3√x - 2 + 7 = 19

Take the following steps

collect like terms

3√x-2 = 19   - 7

add the like terms

3√x -2 = 12

Divide  both sides by 3

√x - 2 = 4

Find the square of both sides

x - 2 = 16

x = 18

Hence, the value is 18

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The value of the cash flows four years from today is $22,609.26.

The value of a set of cash flows can be calculated using the present value of an annuity formula. This formula takes into account the time value of money, which states that money has a different value at different points in time due to the opportunity cost of the money. In other words, the money you have today is more valuable than the money you will have in the future.

The present value of an annuity formula is PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods. In this example, the cash flows are $3,000, $4,040, $5,885, and $7,975, the interest rate is 5.4%, and the number of periods is 4. Plugging these numbers into the formula, the present value is $22,609.26. This is the value of the cash flows four years from today.

The value of the cash flows four years from today is $22,609.26.

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The missing marginal costs and benefits values are the following

Marginal benefit = $ 30

Marginal benefit = $25

See above we have a table with columns total cost, marginal cost , total benefits and marginal benefits. We have to determine the values in place of question mark (?) . Marginal benefit and marginal cost are two measures of how the price or value of a product changes.

Now, Marginal cost and benefits for row 2

change in total cost = 125- 100 = 25

change in units = 2 - 1 = 1

So, marginal cost = 25/1 = $25

Marginal benefit = change in total benefits/ change in units

= (150 - 120)/2-1 = 30/1 = $ 30

Change in total cost = 140 - 125 = 15

Change in units = 3 - 2 = 1

Change in total benefit = 175 - 150 = 25

So, marginal cost = 15/1 = $15

Marginal benefit = 25/1 = $25

Change in total cost = 160 - 140 = 20

Change in units = 4 - 3 = 1

Change in total benefit = 190 - 175= 15

So, marginal cost = 20/1 = $20

Marginal benefit = 15/1 = $15

Hence, we get all the values of question mark.

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Complete question:

Find Out the missing marginal costs and benefits in the above table. (see question marks) unit total cost marginal cost total benefit marginal benefit 1 100 100 120 120 2 125 ? 150 ? 3 140 ? 175 ? 4 160 ? 190 ?

Answer:

The 1. is sufficiently tangent

The 2. is not tangent

Step-by-step explanation:

FALSE: Finding non-linear correlations between two variables cannot be done using regression.

To determine the association between two quantitative variables, simple linear regression is performed. Simple linear regression can be used to determine:

Regression analysis is a mathematical technique for creating predictive models in which one or more existing independent or explanatory factors influence an unknown target variable.

The determination coefficient value serves as a measure of a regression model's fitness.

Thus, finding non-linear correlations between two variables cannot be done using regression is a incorrect statement.

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The complete question is-

Determine if the following statement is true or false:

Regression cannot be used to identify non-linear relationships between two variables.

Answer:

The probability of a family having 0 teenagers with an Apple device can be calculated as (0.26)^0 * (0.74)^2 = 0.5356.

The probability of a family having 1 teenager with an Apple device can be calculated as 2 * (0.26) * (0.74)^1 * (0.74)^1 = 0.4428.

The probability of a family having 2 teenagers with an Apple device can be calculated as (0.26)^2 * (0.74)^0 = 0.0676.

Therefore, the probability of a family having 0, 1, or 2 teenagers with an Apple device can be calculated as 0.5356 + 0.4428 + 0.0676 = 1.0.

Answer:

y=-1/3x+1/2

Step-by-step explanation:

2x+6y=3

bring 2x to the other side by subtracting : 6y=-2x+3

divide by 6 : y=-1/3x+1/2

Answer:

y = -1/3x + .5

Step-by-step explanation:

First we are  going to get y on a side by itself

6y = 3 - 2x

Then we divide by six to get our equation

y= .5 - 1/3x

In slope intercept form

y = -1/3x + .5

Answer:

154.37500 US gallons

The mistake that Devin made is that he didn't take into account the fact that Mr. Gerard liked 20 more pencils than pens.

He likes to have 20 more pencils than pens.  This means that if c be the number of pencils he has, then;

Number of pens = c - 20

Number of pencils = c

Thus, the expression that gives the number of pens and pencils Mr. Gerard has in his class is;

c + c - 20 = 2c - 20

Thus, the mistake that Devin made is that he didn't take into account the fact that Mr. Gerard liked 20 more pencils than pens.

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Complete question is;

Mr. Gerard always likes to have more pencils than pens to lend to students since they tend to prefer writing in pencil. He likes to have 20 more pencils than pens.

Write an expression that gives the number of pens and pencils Mr. Gerard has in his class. Let c be the number of pencils he has.

Devin thinks that the expression 2c + 20 represents the total number of pens and pencils. What mistake did Devin likely make? Explain.

The terminal point determined by t on the unit circle is given by (cos(t), sin(t)).

The terminal point determined by -t:

The point determined by -t is given by (cos(-t), sin(-t)). By the identity sin(-t) = -sin(t), and cos(-t) = cos(t), the terminal point determined by -t is (cos(t), -sin(t)).

The terminal point determined by t + 4π:

The point determined by t + 4π is given by (cos(t + 4π), sin(t + 4π)). By the identity sin(t + 2π) = sin(t) and cos(t + 2π) = cos(t), the terminal point determined by t + 4π is (cos(t), sin(t)).

The terminal point determined by t - π:

The point determined by t - π is given by (cos(t - π), sin(t - π)). By the identity sin(t - π) = -sin(t) and cos(t - π) = -cos(t), the terminal point determined by t - π is (-cos(t), -sin(t)).

The terminal point determined by t + π:

The point determined by t + π is given by (cos(t + π), sin(t + π)). By the identity sin(t + π) = -sin(t) and cos(t + π) = -cos(t), the terminal point determined by t + π is (-cos(t), sin(t)).

The terminal point determined by π - t:

The point determined by π - t is given by (cos(π - t), sin(π - t)). By the identity sin(π - t) = sin(t) and cos(π - t) = -cos(t), the terminal point determined by π - t is (-cos(t), sin(t)).

If the terminal point determined by t is (-3/5, 4/5), then:

The terminal point determined by -t is (3/5, -4/5).

The terminal point determined by t + 4π is (-3/5, 4/5).

The terminal point determined by t - π is (3/5, -4/5).

The terminal point determined by t + π is (3/5, -4/5).

The terminal point determined by π - t is (3/5, -4/5).

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The limit of f(x) is 2, which means that as x approaches infinity, f(x) approaches 2. This implies that f(x) has a vertical asymptote at x = 2, but does not have a horizontal asymptote at y = 2, and is never equal to 2.

The limit of a function is the value that the function approaches as the argument approaches infinity. In the case of f(x), the limit is 2. This means that as x gets larger and larger, the value of f(x) gets closer and closer to 2. This implies that f(x) has a vertical asymptote at x = 2, meaning that the function approaches this value, but never reaches it. It does not have a horizontal asymptote at y = 2, meaning that the function does not approach this value as x gets larger. Additionally, the limit of f(x) is not -2, meaning that the function does not approach this value as x gets larger. Lastly, f(x) is continuous at x = 0, meaning that there is no discontinuity at this point in the graph.

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Answer:

the mean is 3/4

Step-by-step explanation:

to find mean, add all terms and then divide by the number of terms

0.5 + 0.33 + 0.67 + 1.5 = 3

divide by 4

mean: 3/4

Answer:

0.75

Step-by-step explanation:

0.5+0.33+0.67+1.5 = 3

3/4 = 0.75