If a/2-b/3 = 1 what is 2a+3b in terms of b

The length x of a side of the small inner square in terms of some of the variables a , b is expressed as x = (b - a).

We have, length x which is side of inner square in above figure. We have to determine the value of x in terms of " a and b." See the figure carefully and draw the important results. As we see,

Also, see in above figure, the side length of blue triangle is equals to the sum of side length of yellow triangle and side length inner square. In expression form , b = x + a . But we want to determine the value of x, so x = b - a.

Hence, required length is ( b - a).

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Complete question:

what is the length x of a side of the small inner square? express your answer in terms of some or all of the variables a , b , and c.

The above figure complete the question.

It is true that the polynomial function g(x) has the zeros x = -2, x = -3 and x = 2

From the question, we have the following parameters that can be used in our computation:

g(x)=(x+1)^3(x+3)(x-2)

Set the function to 0 to determine the zeros

So, we have the following representation

(x+1)^3(x+3)(x-2) = 0

Remove the exponents

(x + 1)(x + 3)(x - 2) = 0

Split

x + 1 = 0, x + 3 = 0 and x - 2 = 0

Solve for x

x = -2, x = -3 and x = 2

This is the same as the set of zeros given in the question

Hence, the given zeros are true

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We learn from the question that Johnny will need to buy 11 bags.

When you don't have much room, planters are a terrific choice since they let you showcase little trees and plants everywhere there is some sunshine. And you can still accept gardening and enjoy the benefits of raising your own food even if you just have a small patio, driveway, or balcony.

We'll start by determining the planter's volume. To achieve this, we'll calculate a triangular pyramid's volume:

Volume = (Ground Area x Altitude) / 3.

The planters measures 4 square feet in base area and 8 feet in height, so:

Volume = (4 x 8) / 3

Volume = 16 cubic feet

Now we know that Johnny needs 16 cubic feet of potting soil, and each bag of soil has 1.5 cubic feet, so:

Number of Bags = Volume / Volume per Bag

Number of Bags = 16 / 1.5

Number of Bags = 10.67

Since Johnny can't buy fractional bags of soil, he'll need to purchase 11 bags.

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If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be [tex]$x=-\frac{2}{3}, x=-\frac{5}{2}$$[/tex].

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

[tex]$x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$[/tex]

simplifying the above equation, we get

[tex]$$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$[/tex]

Separate the solutions, we get

[tex]$$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$[/tex]

The solutions to the quadratic equation are:

[tex]$x=-\frac{2}{3}, x=-\frac{5}{2}$$[/tex]

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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Answer:

120 inches

Step-by-step explanation:

5 x 8 x 3 = 120

Answer:

Step-by-step explanation:

decimal equivalent of 714.45/9

divide it by 9 taking to 79.383333

The differentiation of the given function is [tex]\frac{d}{dx}\left(\frac{e^{4x}}{x^7}\right)=\frac{e^{4x}\left(4x-7\right)}{x^8}[/tex]

The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given is function, [tex]y = \left(\frac{e^{4x}}{x^7}\right)[/tex], we need to differentiate the given function,

[tex]\frac{d}{dx}\left(\frac{e^{4x}}{x^7}\right)[/tex]

Applying quotient rule,

[tex]\quad \left(\frac{f}{g}\right)^'=\frac{f\:'\cdot g-g'\cdot f}{g^2}[/tex]

[tex]=\frac{\frac{d}{dx}\left(e^{4x}\right)x^7-\frac{d}{dx}\left(x^7\right)e^{4x}}{\left(x^7\right)^2}[/tex]

[tex]=\frac{e^{4x}\cdot \:4x^7-7x^6e^{4x}}{\left(x^7\right)^2}[/tex]

[tex]=\frac{e^{4x}\left(4x-7\right)}{x^8}[/tex]

Hence, the differentiation of the given function is [tex]\frac{d}{dx}\left(\frac{e^{4x}}{x^7}\right)=\frac{e^{4x}\left(4x-7\right)}{x^8}[/tex]

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Answer:

x = 12

y = -2.5

Step-by-step explanation:

2x + 4 = 28

2x = 24

x = 12

So, we know x = 12; now we put 12 back in for x and solve for y

3(12) + 4y = 26

36 + 4y = 26

4y = -10

y = -2.5

Let's check

3(12) + 4(-2.5) = 26

36 - 10 = 26

26 = 26

So, x = 12 and y = -2.5 is the correct answer.

The equation of the parabola with given vertex and focus is (y-11)² = 36(x-7).

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

Given that, Vertex (7, 11), focus (16, 11).

Let us find an equation of the parabola for vertex (h, k)=(7, 11) and focus (16, 11).

It can be observed that both focus and vertex lie on y = 11, thus the axis of symmetry is a horizontal line.

a = 16-7 = 9 as y coordinates are the same.

Since the focus lies to the left of vertex, a = 9

Use the equation (y-11)² = 4×9(x-7)

(y-11)² = 36(x-7)

Therefore, the equation of the parabola with given vertex and focus is (y-11)² = 36(x-7).

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The standard equation of the parabolas with vertex (7, 11) and focus (16, 11) are:

(y - 11)² = 36(x - 7)

A parabola is an equation of a curve, such that any point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix of the parabola.

We have,

(y - k)² = 4p (x - h) open right

(y - k)² = -4p (x - h) open left

Where focus = (h - p, k)  or (h + p, k) and vertex = (h, k)

Now,

Equation of parabola (y - k)² = -4p (x - h) that open left.

(h, k) = (7, 11)

h = 7 and k = 11

(h - p, k) = ( 16, 11)

h - p = 16

7 - p = 16

7 - 16 = p

p = -9

So,

(y - 11)² = 36(x - 7)

Equation of parabola (y - k)² = 4p (x - h) that open right.

(h, k) = (7, 11)

h = 7 and k = 11

(h + p, k) = (16, 11)

h + p = 16

7 + p = 16

p = 16 - 7

p = 9

So,

(y - 11)² = 36 (x - 7)

Thus,

The standard equation of the parabolas is:

(y - 11)² = 36(x - 7)

(y - 11)² = 36 (x - 7)

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Step-by-step explanation:

the area of a triangle is

baseline × height / 2

we have here 3 triangle sides.

the painter can only paint the sides, not the base area.

the painting area is therefore the sum of the 3 sides :

3× 50×40/2 = 3× 50×20 = 3000 ft²

75% of the area = 3000 × 0.75 = 2250 ft²

100 ft² in 18 minutes

it takes

2250/100

times of the time it takes to paint 100 ft² (18 minutes).

so,

18 × 2250/100 = 405 minutes

it takes the painter 405 minutes to paint 75% of the pyramid.

The first derivative of y with respect to x is d(y)/dx = 4t² + 10t, and the second derivative of y with respect to x is d(2y)/dx² = 8t + 10.

Differential equations are mathematical equations that describe how a function changes over time or with respect to its inputs.

Let x = t² + 3 and y = t² + 5t. We want to find the derivatives of y with respect to x, which means we need to use the chain rule.

The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x is given by

=> d(y)/dx = d(y)/du * du/dx.

First, we will find the derivative of y with respect to t, which is given by

=> d(y)/dt = 2t + 5.

Next, we will find the derivative of x with respect to t, which is given by

=> d(x)/dt = 2t.

Finally, we will multiply these two derivatives to find the derivative of y with respect to x, which is given by

=> d(y)/dx = (2t + 5)(2t) = 4t² + 10t.

Next, we will find the second derivative of y with respect to x, which is given by

=> d(2y)/dx² = d((4t² + 10t))/dt = 8t + 10.

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Answer:

below

Step-by-step explanation:

When y = 0    the negative x value of the vertex needs to be a negative number ....the second equation will do this...the first will not

Answer:

B

Step-by-step explanation:

[tex](x-1)(x+1) = x^2 -1\\(x+5)(x-5) = x^2 -25[/tex]

Answer:

We start by calculating the discount amount for the extra 60% off with code SALE:

$29.99 * 60% = $17.99

Then we calculate the new price of the jeans after applying the discount:

$29.99 - $17.99 = $12

Next, we calculate the sales tax of 10.25% for the discounted price:

$12 * 10.25% = $1.23

Finally, we add the sales tax to the discounted price to find the final price:

$12 + $1.23 = $13.23

So the total cost of the jeans, with the extra 60% off code and sales tax of 10.25% included, would be $13.23.

In the given plot, the graph of y=x⁴ is  g, the graph of y = x⁷ is  f and the graph of y=x¹⁰ is the h.

While plotting graphs with power to x values, it usually depends on two things. For example, lets take an equation, y = kxⁿ

As the value of coefficient of x, that is k increases the graph becomes narrower and as the value of k decreases the graph becomes wider. Here in the questions given all have the same coefficients for x, k=1.

So here the graph only depend on the power of x.

As the power increases the graph gets gets narrower. So the graph of x¹⁰ will be narrower than x⁴. As both 10 and 4 are even numbers, for all values of x, y will be positive and parabolas are formed.

In the case of x⁷,  as 7 is odd the value of y can be both positive and negative.

If x=1, y=1⁷ = 1

  x= -1, y = (-1)⁷ = -1

So the graph will be like f as shown in the figure.

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The complete question is included in the image.

Answer:

971.92 square inches of wrapping paper.

Step-by-step explanation:

Please find the attachment for detail

The t-test for independent groups is usually the most sensitive test when there is large between-subject variability and the sample size (N) is held constant.

The t-test for independent groups allows for the comparison of two independent groups, and can detect differences in the means between the two groups that may not be detected by other tests. The t-test for correlated groups is less sensitive than the t-test for independent groups, as it assumes that the two groups are related or correlated. The sign test is a non-parametric test and is less sensitive than the t-test for independent groups as it does not take into account the variability between the two groups.

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Answer:

(5, -2).

Step-by-step explanation:

The point L' will have the same y-coordinate as L, but the x-coordinate will be opposite in sign. Since L is located at (-5,-2), L' will be located at (5,-2). So the ordered pair that describes the location of L' is (5, -2).

The total amount present in the account is  $555 in 5 years with a rate of 2.2%.

Simple interest is a way to figure out how much interest will be paid on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the following year's principal to compute interest, the principal amount under simple interest remains constant.

Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the initial principle amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of several forms of interest that banks charge.

It is given The initial Principal is $500

The interest earned is $55

The total amount present in the account is $(500 + 55) = $555 in 5 years

The rate of interest is r(say)

principal * rate * time = interest

⇒500* r * 5 = 55

⇒ r = 0.022 = 2.2 %

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A table of equivalent ratios for the number of toss and amount of dollars is as follows:

Toss             Dollars

25                    4

50                    8

75                    12

In order to have a proportional relationship and equivalent ratios, the variables x for toss and y for dollars must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 12/75

Constant of proportionality (k) = 0.16.

When hours y = 8, the amount of dollars x is given by:

x = y/k

x = 8/0.16

x = 50.

When the amount of dollars x = 25, the number of toss y is given by:

y = kx

y = 0.16(25)

y = 4.

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Answer:

On the clock from 3 to 9, the hour hand turns clockwise 1/2 of the revolution. On the clock from 4 to 7, the hour hand turns clockwise 1/4 of the revolution. On the clock from 7 to 10, the hour hand turns 1/4 of the revolution clockwise. On the clock from 12 to 9, the hour hand turns clockwise for 3/4 of the revolution

Step-by-step explanation:

Answer:

12.4 miles

Step-by-step explanation:

It would be 1km / 0.62mi as this gives us a direct relationship between kilometers and miles. It's essentially telling us each kilometer is equal to 0.62 miles. Since we have 20 kilometers and we want to convert this to miles, we just multiply by 20 by 0.62 miles which gives us 12.4 miles

The probability that can be determined by the randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

Given information is that, at a wedding, each guest asked the 80 guests if they were a friend of the bride or of the groom.

Probability is measured by the ratio of the number of favorable outcomes to the total number of outcomes of an event.

The total Number of Guests which forms the Sample Space, n(S)=80

Let the event for a friend of the bride=A

Let the event be for a friend of the groom=B

n(A) =59

n(B)=50

Friends of both bride and groom,

So,

n(A∪B)=n(A)+n(B)-n(A∩B)

n(A∪B)=59+50-30

n(A∪B)=79

The number of people or Guests who are the friends of the bride OR of the groom = 79

Thus,

P(A∪B)=n(A∩B)/n(S)

= 79/80

P(A∪B)= 0.9875

Therefore, the probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

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The d f of 8 for the following equation  is-   7698

f₍ₓ₎ = ᵃˣ²+ᵇˣ²+c

f₍₀₎ = a*0²+b*0+c = 2

   = 0+0+c=2

  c=2

f₍₃₎ = a(3)²+b*3+c = 128

    = 9a + 3b +2 = 128

   = 9a+3b = 128-2

    9a+3b = 126    equation  (i)

f₍₅₎ = a (5)² + b*5 + c = 2048    = 25a + 5b + 2 = 2048

     25a+ 5b = 2046    equation ( ii)

equation (ii) is multiplied by 3 and equation (i) multiplied by 5  we get,

       25a+ 5b = 2046

           9a+3b = 126  

Subtracting equation (ii) from equation (i)

          75a + 15b  = 6138

          45a + 15b = 630

          30a        = 5508

       a = 5508/30

         a  = 184

 now , putting the value of a in equation (i)

     9*184+3b+2  = 128

      1656+3b +2 = 128

   3b = 128-1658

    b = -510

f₍ₓ₎ = 184 x² - 510x + 2

  = 184*64 - 510*8 +2

  = 11776 - 4080+2

  = 7698 ans.

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The slope of the line described in the table is m=3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The points from the table are (2, 6) and (3, 9)

Slope=9-6/3-2

=3/1

=3

Hence,  the slope of the line described in the table is m=3.

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7/12 is the value of fraction .  

In math, what is a fraction?

A fraction is a piece of the entire. The quantity is written as a quotient in mathematics, where the numerator and denominator are divided. Both are integers in a simple fraction.

                    Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.

= 2 1/4 - 1 2/3

= 9/4 -  5/3

 =   27 - 20 /12

 = 7/12

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Answer:

≈ +1

Step-by-step explanation:

Firstly, the r value, or the correlation coefficient, would be positive because the correlation is positive. The set of points are moving from bottom to top.

It would be close if not exactly to 1 because the closer the set of points are all clustered closely around or on one singe line, the closer it is to 1. In this case, all points seem to be on one single line, suggesting that it has a perfect correlation of 1.

Answer:

In order to find the probability that a pupil selected at random obtained more than 27 marks, we need to know the total number of pupils and the number of pupils who scored more than 27 marks.

Let's call the total number of pupils "n" and the number of pupils who scored more than 27 marks "x".

From the given data, we know that n = 6 and the pupils who scored more than 27 marks are 39, 40, 37.

x = 3

Now we can use the formula for probability:

Probability = (x/n)

Probability = (3/6)

Probability = 0.5

So the probability that a pupil selected at random obtained more than 27 marks is 0.5 or 50%.

Step-by-step explanation:

Answer:

x - 9.9 = 31.6

E and F are the midpoints of AB and CD, respectively, making ABCD a parallelogram. Any line that crosses AD, EF, and BC at G, P, and H is designated as GH. So, GP = PH.

E and F are midpoints, resulting in AB and CD, respectively.

[tex]$\therefore \mathrm{AE}=\mathrm{BE}=\frac{1}{2} \mathrm{AB} \text { and } \mathrm{CF}=\mathrm{DF}=\frac{1}{2} \mathrm{CD}[/tex]

But, [tex]$\mathrm{AB}=\mathrm{CD}$[/tex]

[tex]$\therefore \frac{1}{2} \mathrm{AB}=\frac{1}{2} \mathrm{CD} \Rightarrow \mathrm{BE}=\mathrm{CF}[/tex]

Also, [tex]BE \| CF $\quad[\because \mathrm{AB} \| \mathrm{CD}]$[/tex]

therefore BEFC is a parallelogram.

[tex]$\Rightarrow \mathrm{BC} \| \mathrm{EF}$[/tex] and [tex]$\mathrm{BE}=\mathrm{PH}$[/tex]

Now, BC \| EF

[tex]$\Rightarrow \mathrm{AD} \| \mathrm{EF} \quad\left[\because \mathrm{BC} \| \mathrm{AD}\right.$[/tex] as ABCD is a [tex]$\left.\|^{\mathrm{gm}}\right]$[/tex]

[tex]$\Rightarrow \mathrm{AEF} \mathrm{D}$[/tex]is a parallelogram

[tex]$$\Rightarrow \mathrm{AE}=\mathrm{GP}$$[/tex]

But, [tex]\mathrm{E}$ is the mid-point of $\mathrm{AB}$[/tex]

[tex]\therefore \mathrm{AE}=\mathrm{BE}[/tex]

[tex]\Rightarrow \mathrm{GP}=\mathrm{PH} \quad$ [Using (i) and (ii)[/tex]

The complete question is:

ABCD is a parallelogram, E and F are the mid-points of AB and CD respectively. GH is any line intersecting AD, EF and BC at G,P and H respectively. Prove that GP = PH.

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