A triangle has a base of (3x+7) and a height of (5x-1)a second triangle is drawn with a base that is tripled and its height is doubled. Find the difference between the area of the original triangle and the area of the new triangle

Answer:

VALUES (5,6,12)

Step-by-step explanation:

Answer:

  (a)  135

  (b) 28%

Step-by-step explanation:

We can write equations relating pears to oranges, solve them, and then find the number of apples. Let p, o, and 'a' represent the numbers of pears, apples, and oranges.

  p/o = 5/3 . . . . . the ratio of pears to oranges is 5:3

  p -o = 54 . . . . . there are 54 more pears than oranges

  a -o = 3 . . . . . .  there are 3 more apples than oranges

__

Multiply the first equation by 3/5o to get ...

  3/5p = o

Substitute that into the second equation:

  p -(3/5)p = 54

  2/5p = 54 . . . . . . simplify

  p = 54(5/2) = 135 . . . . multiply by 5/2 to get the number of pears

There are 135 pears in the basket.

__

  a = 3 +o = 3 +3/5p = 3 +3/5(135) = 3 +81 . . . . solve for the number of apples

  a = 84

The percentage of fruits that are apples is ...

  apples/total = 84/(135 +81 +84) = 84/300 = 28/100 = 28%

  28% of the fruits are apples

Answer:

No

Step-by-step explanation:

It is very healthy for someone to be with a community of likeminded individuals although the bible indeed supports obedience to one's parents, that's only in affect unless what they are telling you to commit sinful acts. In this case Ann's parents are forbidding her to see her Chirstian friends which is sinful speaking how Christians are considered God's people. Even though God expects you to honor your parents, you cannot honor the dishonorable.

Leviticus 19:3 "Every one of you shall revere his mother and his father, and you shall keep My Sabbaths; I am the LORD your God."
Colossians 3:21 "Fathers, do not provoke your children, lest they become discouraged."
Romans 12:18 "If possible, so far as it depends on you, live peaceably with all."

God is speaking during times when his people were raised by good parents who have the fear of the Lord in their hearts. In these times they're many "bad" parents who don't honor the Lord's teachings which they themselves should not be honored.

Hope this helps.

Answer:18/80

Step-by-step explanation:

is the probability of pupil that uses the swimming pool but not the gym.

It is given that:

Total students are 80

32 pupils use the swimming pool

43 pupils use the gym

19 pupils use neither the swimming pool nor the gym

To know the pupils who use both add 32+43 = 75

75-61= 14 pupils use both

32-14 = 18 pupils use only the swimming pool

43-18= 29 pupils use only the gym

Hence,  is the probability of pupil that uses the swimming pool but not the gym.

To determine the Mean Absolute Deviation (MAD), we need the actual sales data and the forecasted values. Since the actual sales data is not provided, it is not possible to calculate the MAD accurately.

MAD is calculated by taking the average of the absolute differences between the forecasted values and the actual values. Without the actual sales data, we cannot compute the absolute differences and find the MAD.

To calculate the MAD, you will need the actual sales data and the corresponding forecasted values for each day. Then, you can calculate the absolute differences between the actual and forecasted values, take their average, and round the result to two decimal places to obtain the MAD.

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Answer:

−28r−28

Step-by-step explanation:

−4(7r+7)

=(−4)(7r+7)

=(−4)(7r)+(−4)(7)

Answer:

(x,y) = (0,  1/3)

Step-by-step explanation:

  [1]    2x + 3y = 1

  [2]    4x - 6y = -2

Graphic Representation of the Equations :

   3y + 2x = 1        -6y + 4x = -2  

Solve by Substitution :

Solve equation [2] for the variable  x  

 [2]    4x = 6y - 2

 [2]    x = 3y/2 - 1/2

Plug this in for variable  x  in equation [1]

  [1]    2•(3y/2-1/2) + 3y = 1

  [1]    6y = 2

Solve equation [1] for the variable  y

  [1]    6y = 2  

  [1]    y = 1/3  

By now we know this much :

   x = 3y/2-1/2

   y = 1/3

Use the  y  value to solve for  x  

   x = (3/2)(1/3)-1/2 = 0

The functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.The given differential equation is, y''+4y'+4y=e^t ...(1)

We have to find the solutions of the differential equation. Let's solve the differential equation:(1) => r²+4r+4=0Now, solve the quadratic equation using the quadratic formula: r= (-(4)+√((4)²-4(1)(4))) / 2(1)= -2 (repeated)So, the solution of the corresponding homogeneous equation is:(2) yh= (c₁+c₂t)e^(-2t) ---------------(2)Now, we have to find a particular solution of the non-homogeneous differential equation (1).

Let, yp= Ae^t. Now, yp'= Ae^t, yp''= Ae^t. Substitute yp and its derivatives in the equation (1):yp''+4yp'+4yp= e^tAe^t+4Ae^t+4Ae^t= e^t9Ae^t= e^tA= 1/9Therefore, the particular solution is,(3) yp= e^t/9 ------------(3)

Hence, the general solution of the given differential equation is,(4) y= yh+yp= (c₁+c₂t)e^(-2t) + e^t/9Now, substitute the initial conditions in the general solution to get the constants c₁ and c₂:Let, y(0)=0 and y'(0)=0, then,c₁= -1/9 and c₂= 5/9Finally, the solution of the differential equation y''?4y'+4y=e^t is,(5) y= -(1/9)e^(-2t) + (5/9)te^(-2t) + e^t/9 =(e^(2t)+te^(2t))/9+ e^t ...

(Ans)The options that represent the functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.

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The cheapest way of buying exactly 7 litres with no extra is buying 500 ml bottle for £1.40

The amount of buying 7 litres of orange juice at the cheapest buy is £2.52

500 ml bottle for £1.40

Convert ml to liters:

500 ml = 0.5 liters

Unit rate = 0.5/1.40

= £0.36 per liter

2 litre carton for £2.50

Unit rate = 2/2.50

= £0.8 per liter

2 cartons for £4.50

Unit rate = 2/4.50

= $0.44 per carton

3 litre carton for £3.50

Unit rate = 3 / 3.50

= £0.86 per liter

The cheapest buy per liter of the orange juice is buying 500 ml bottle for £1.40.

Therefore, the cost of 7 liters at the cheapest buy

= £0.36 per liter × 7

= £2.52

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Answer:

Step-by-step explanation:

2x + 4 = 6x + 2

Bringing like terms on one side

4 - 2 = 6x - 4x

2 = 2x

2/2 = x

1 = x

The equation for resolving couples will come in place

\(Fcos\theta=0\\\ Fsin\theta =0\)

Using the unit vectors by i and j along the x-axis and the y-axis you'll express it as a Cartesian vector.

Couple moment:This looks at the product of the forces acting on a body( in this context a steering wheel ) by the perpendicular distance that exist amidst the forces.

Cartesian vector:this is the representation of unit vectors by i and j along the x-axis and the y-axis, respectively.

Therefore, in calculating the couple moment t acting on the steering wheel, the equation for resolving couples will come in place

\(Fcos\theta=0\\\ Fsin\theta =0\)

Using the unit vectors by i and j along the x-axis and the y-axis you'll express it as a Cartesian vector.

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Decimal- 0.75

Percentage- 75%

Answer:

75% and 0.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

To identify the conditions of continuity that are not satisfied if a function has any discontinuities, we need to consider the three conditions for continuity:

1. The function must be defined at the point of interest.

2. The limit of the function as it approaches the point of interest must exist.

3. The value of the function at the point of interest must equal the limit.

If any of these conditions are not met, the function will have a discontinuity at that point.

There are different types of discontinuities, including removable, jump, infinite, and oscillating. Let's briefly discuss the conditions of continuity that are not satisfied for each type:

1. Removable Discontinuity: In this case, the function is undefined at the point of interest. However, the limit exists, and if the value of the function is redefined or removed at that point, the function can become continuous.

2. Jump Discontinuity: The function is defined at the point of interest, and the limit exists from both sides, but the value of the function at the point is different from the limit. There is a sudden "jump" in the function's value.

3. Infinite Discontinuity: The function is defined at the point, but the limit diverges to positive or negative infinity as it approaches the point. There is a vertical asymptote or a vertical gap in the function.

4. Oscillating Discontinuity: The function oscillates or fluctuates infinitely as it approaches the point, failing to approach a specific value. The limit does not exist.

By analyzing the behavior of the function and checking if these continuity conditions are satisfied, we can identify the specific condition(s) that are not met and determine the type of discontinuity present.

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Answer: x^6+6x^4+8x^2+2

Step-by-step explanation:

Since g comes after f then you will take g's equation and plug it into the f equation so it would turn out to be if you plugged it in

(x^2+2)^3-4(x^2+2)+2 which would equal x^6+6x^4+8x^2+2

Answer:

(a) Explained below.

(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Step-by-step explanation:

The information provided is:

n (Men who finished the marathon) = 25,221

n (Women who finished the marathon) = 12,883

Compute the proportion of men and women who finished the marathon as follows:

\(\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988\)

The combined proportion is:

\(\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989\)

(a)

The hypothesis is:

H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.

Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.

Compute the test statistic as follows:

\(Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}\)

   \(=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78\)

Compute the p-value as follows:

\(p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075\)

The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.

Thus, concluding that the rate of those who finish is the same for men and women.

(b)

Compute the 99% confidence interval for the difference between proportions as follows:

The critical value of z for 99% confidence level is 2.58.

\(CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}\)

     \(=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\\)

Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Answer:

56

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

Start by adding the number in the parenthesis: This gives us (8(11)/2^2) + 6(2)

Square the bottom: (8(11)/4) + 6(2)

Multiply the top of the fraction: (88/4) +6(2)

Divide 88 by 4: 22 + 6(2)

Multiply 6 and 2: 22 + 12

Add 22 and 12: 22 + 12 = 34

Answer: 34

Answer:

The slope of AB is undefined; the slope of CD is 0; The lines are perpendicular.

Step-by-step explanation:

Line AB would form a vertical line. Slope is Δy/Δx. To go from 3 to 7 (the y-coordinates) you need to go up 4 units. So we would then have Δy/Δx = 4/Δx. To go from -5 to -5 (the x-coordinates) we have to go left or right 0 units. So, Δy/Δx = 4/Δx = 4/0. Anything divided by 0 is undefined. Remember: vertical lines always have an undefined slope.

Line CD would form a horizontal line. To go from 9 to 9 (the y-coordinates) you need to go up or down 0 units. So, Δy/Δx = 0/Δx. To go from 1 to -10 (the x-coordinates) you need to go down 11 units. So Δy/Δx = 0/Δx = 0/1. 0 divided by anything is 0. Remember: horizontal lines always have a slope of 0.

If you picture a horizontal line and a vertical line intersecting, they would both form a right angle when they intersect.  By definition, this would make both lines perpendicular.

Answer:

The height of the tree to the nearest foot is 75.

Step-by-step explanation:

The height is opposite the angle of elevation, and the 45 ft distance to the tree is adjacent to it.

tangent = opposite/adjacent

\(\frac{tan(59)}{1} = \frac{h}{45}\)

h = tan(59) * 45

h ≈ 74.89

To the nearest foot, 74.89 is 75 ft.

The inequality pairs with y ≤−2x−1 to complete the system of linear inequalities represented by the graph is y > -2x+2

The one inequality is

y ≤−2x−1

The inequality is represents the relationship between two variables with inequality sign. The inequality will be less than, greater than, less than or equal to and greater than or equal to.

Both lines are parallel therefore the slope of the line will be same that is -2.

The y intercept of the line is +2

The shade is on the top side of the line

Therefore the inequality will be

y>−2x+2

Hence, the inequality pairs with y ≤−2x−1 to complete the system of linear inequalities represented by the graph is y > -2x+2

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Answer:

The answer is a: 7m

Step-by-step explanation:

The amount of miles he jogs is m, and there are 7 days in a week. Multiply that, and you'll have your answer.

Answer:

\(< -0.902, 0.431 >\)

Step-by-step explanation:

The unit vector of any vector is the vector that has the same direction as the given vector, but simply with a magnitude of 1. Therefore, if we can find the magnitude of the vector at hand, and then multiply \(\frac{1}{||v||}\), where ||v|| is the magnitude of the vector, then we can find the unit vector.

Remember the magnitude of the vector is nothing but the pythagorean theorem essentially, so it would be \(\sqrt{(-6.9)^{2} +(3.3)^{2} } ,\) which will be \(\sqrt{58.5}\). Now let us multiply the vector by 1 over this value, and rationalize to make your math teacher happy.\(< -6.9, 3.3 > * \frac{1}{\sqrt{58.5}} = < \frac{-6.9\sqrt{58.5} }{58.5} , \frac{3.3\sqrt{58.5}}{58.5} >\)

You can put those values into your calculator to approximate and get

\(< -0.902, 0.431 >\)

You can always check the answer by finding the magnitude of this vector, and see that it is equal to 1.

Hope this helps

The outcome that does not represent a favorable outcome is rain on the first and last days only

The outcome that does not represent a favorable outcome is rain on the first and last days only.

This is because it is less likely to occur than other outcomes such as rain on all three days or rain on the first and second days only.

This implies that having rain on the first and last days only would require the simulation to generate a number between 100 and 999 that ends in a number between 1 and 6

Also a number between 0 and 99 that starts with a number between 1 and 6, which is less likely to happen than generating three numbers in a row that fall within the range of 1-6.

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The volume of the solid bounded by z = x^2y^2 and z = 4 is 4 cubic units.

To calculate the volume of the solid bounded by the surfaces z = x^2y^2 and z = 4, we need to set up a triple integral over the region enclosed by these surfaces.

Let's determine the limits of integration for each variable. Since z = 4 is the upper bound, we will integrate from z = 0 to z = 4. For x and y, we need to find the limits of the region in the xy-plane where the surfaces intersect.

To find the limits of integration for x and y, we can set the two equations equal to each other:

\(x^2y^2 = 4\)

Taking the square root of both sides:

xy = ±2

Now we can set up the integral:

∭\((x^2y^2 - 4) dV\)

Integrating with respect to z first, we have:

∫[0 to 4] ∫[xy = -2 to xy = 2] ∫[x = -∞ to x = ∞] (\(x^2y^2 - 4\)) dx dy dz

Since the region of integration is symmetric, we can simplify the integral by considering only the positive values of x and y:

∫[0 to 4] ∫[xy = 2 to xy = 2] ∫[x = 0 to x = ∞] (\(x^2y^2 - 4\)) dx dy dz

Now we can evaluate this triple integral. First, let's integrate with respect to x:

∫[0 to 4] [\((1/3)x^3y^2 - 4x\)] [x = 0 to x = ∞] dy dz

Simplifying the limits:

∫[0 to 4] [\((1/3)∞^3y^2 - 4∞ - (1/3)0^3y^2 + 4(0)\)] dy dz

This simplifies to:

∫[0 to 4] (∞ - 0) dy dz

Since the limits of integration for y are independent of z, the integral becomes:

∫[0 to 4] dy dz

Evaluating this integral:

[y] from 0 to 4

4 - 0 = 4

Therefore, the volume of the solid bounded by z = x^2y^2 and z = 4 is 4 cubic units.

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Answer:

(5-2t)<-4

Step-by-step explanation:

The midnight temprature is 5 °C and the temprature is decreasing at the rate of 2°C per hour . If T is the hours past midnight then after t hours the temprature will be ( 5t-2t) . If the temprature is colder than -4°C right now , then your inequality can be written like 5t-2t<-4

Yes, it is possible for a plot of a partial expansion of f[x] to share ink with the plot of f[x] all the way from -[infinity] to + [infinity].

Explanation:

We can approximate f(x) as a Fourier series, as follows:

\($$f(x) = \sum_{n=0}^{\infty}a_n\cos\left(\frac{n\pi x}{L}\right)+\sum_{n=1}^{\infty}b_n\sin\left(\frac{n\pi x}{L}\right)$$\)

If f(x) is an odd function, the cosine terms are gone, and if f(x) is an even function, the sine terms are gone.

We can create an approximation for f(x) using only the first n terms of the Fourier series, as follows:

\($$f_n(x) = a_0 + \sum_{n=1}^{n}\left[a_n\cos\left(\frac{n\pi x}{L}\right)+b_n\sin\left(\frac{n\pi x}{L}\right)\right]$$\)

For any continuous function f(x), the Fourier series converges uniformly to f(x) on any finite interval, as given by the Weierstrass approximation theorem.

However, if f(x) is discontinuous, the Fourier series approximation does not converge uniformly.

Instead, it converges in the mean sense or the L2 sense. The L2 norm is defined as follows:

\($$\|f\|^2 = \int_{-L}^{L} |f(x)|^2 dx$$\)

Hence, it is possible for a plot of a partial expansion of f(x) to share ink with the plot of f(x) all the way from -[infinity] to + [infinity].

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The equation of the tangent to the circle x² + y² = 90 at the point P(3, -9) is y = (1/3)x - 10.

What exactly is a circle?

A circle is a geometric shape consisting of all the points in a plane that are a fixed distance, called the radius, from a given point, called the center. In other words, a circle is the set of points in a plane that are equidistant from a fixed point.

Now,

To find the equation of the tangent to the circle x² + y² = 90 at the point P(3, y), we first need to find the y-coordinate of P.

Since P is below the x-axis, its y-coordinate must be negative. To find its value, we substitute x = 3 into the equation of the circle and solve for y:

3² + y² = 90

y² = 90 - 9

y² = 81

y = -9

Therefore, the coordinates of P are (3, -9).

Next, we need to find the gradient of the tangent at P. We can do this by differentiating the equation of the circle implicitly with respect to x:

2x + 2y(dy/dx) = 0

dy/dx = -x/y

At the point P, x = 3 and y = -9, so:

dy/dx = -3/(-9) = 1/3

Therefore, the gradient of the tangent at P is 1/3.

Finally, we can use the point-slope form of the equation of a straight line to write the equation of the tangent:

y - (-9) = (1/3)(x - 3)

Simplifying, we get:

y + 9 = (1/3)x - 1

y = (1/3)x - 10

Therefore, the equation of the tangent to the circle x² + y² = 90 at the point P(3, -9) is y = (1/3)x - 10.

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Answer:

density

Step-by-step explanation:

the number of population distributed in a certain area, that is generally in km², is the density.

It can be calculated with the following data: Number of population/km²

Extra information: it obviously is an approximated value, because in certain areas it can be much higher (metropolis, for example, generally have a very high population density, meanwhile in the countryside it can be much lower). Generally, it varies from area to area.

The number of individuals in a population divided by the area that the population takes up is known as the density of the population.

Population density refers to the number of individuals in a population per unit of area. It is a measure of how crowded or dispersed a population is within a given area.

Population density is calculated by dividing the total population of an area by the total land area or water area of that region. The resulting number is often expressed in individuals per square kilometer or square mile, depending on the units of measurement used.

Population density is an important ecological concept because it can affect the ability of a population to survive and thrive within a given area. Populations that are too dense may experience competition for resources, disease outbreaks, and other negative effects.

On the other hand, populations that are too dispersed may have trouble finding mates and maintaining genetic diversity. Population density can also be used to track changes in populations over time, and to inform conservation and management efforts.

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The quotient is 3x - 5 + (-5) + 12, which simplifies to 3x + 2.

To find the quotient, we need to perform polynomial long division. The dividend is 3x² - 2x + 7, and the divisor is x + 1.

 3x - 5

x + 1 | 3x² - 2x + 7

We start by dividing the highest degree term of the dividend (3x²) by the divisor (x), which gives us 3x. We then multiply the divisor (x + 1) by the quotient (3x) and subtract it from the dividend:

       3x - 5

    ____________

x + 1 | 3x² - 2x + 7

- (3x² + 3x)

____________

- 5x + 7

We continue the process by dividing the next term (-5x) of the resulting polynomial (-5x + 7) by the divisor (x + 1). This gives us -5.

            -5

    ____________

x + 1 | 3x² - 2x + 7

- (3x² + 3x)

____________

- 5x + 7

- (- 5x - 5)

____________

12

Finally, we divide the remaining term (12) by the divisor (x + 1), which gives us 12.

                  12

    ____________

x + 1 | 3x² - 2x + 7

- (3x² + 3x)

____________

- 5x + 7

- (- 5x - 5)

____________

12

- 12

____________

0

The quotient is 3x + 2 and can be written as 3x + 5 + (-5) + 12.

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Answer:

6561

because...

(27)x(243)

== 6561

The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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