Find the equation of a line passing through the point of intersection of lines 2X plus 3Y equals to one and X minus Y +2 equals to zero and parallel to the line joining the points two, three and four, five.

Answer:

120 inches

Step-by-step explanation:

5 x 8 x 3 = 120

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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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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everyboby

Step-by-step explanation:

because it is talking about how much people love her

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

Answer: the answer is c

Step-by-step explanation:

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.

The equations that are not equivalent to "6x = 20" are "6x ÷ 6 = 20 ÷ 6," "6x + 5 = 20 + 5," "6x − 1 = 20 − 1," and "6x × 6 = 20 × 20."

Let's evaluate each equation to see if they are equivalent to "6x = 20":

6x ÷ 6 = 20 ÷ 6:

Dividing both sides of the equation by 6 gives us "x = 20/6" or "x = 10/3." This equation is not equivalent to "6x = 20."

6x ÷ 6 = 20 ÷ 20:

Dividing both sides of the equation by 6 gives us "x = 20/6" or "x = 10/3." Then, dividing both sides of the equation by 20 gives us "x = 1."

This equation is equivalent to "6x = 20" since both sides simplify to the same value.

6x + 5 = 20 + 5:

Adding 5 to both sides of the equation gives us "6x + 5 = 25." This equation is not equivalent to "6x = 20."

6x − 1 = 20 − 1:

Subtracting 1 from both sides of the equation gives us "6x − 1 = 19."

This equation is not equivalent to "6x = 20."

6x × 6 = 20 × 20:

Multiplying both sides of the equation by 6 gives us "36x = 400." This equation is not equivalent to "6x = 20."

Therefore, the equations that are not equivalent to "6x = 20" are "6x ÷ 6 = 20 ÷ 6," "6x + 5 = 20 + 5," "6x − 1 = 20 − 1," and "6x × 6 = 20 × 20."

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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 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

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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A parabola can have 2 x-intercepts, 1 x-intercept or zero real x intercepts.

Image search results for The x-intercepts of two parabolas are the same (one positive and one negative). The maximum or minimum of the first is twice the maximum or minimum of the other. Draw these parabolas using the same coordinate grid (with at least 3 points) “-15” “-10” “-10” “-15” 10

The x-intercepts are the spots where the parabola contacts the x-axis. A parabola can have two, one, or no real x intercepts. A parabola might have two x-intercepts, one x-intercept, or none at all.

X-intercepts, or zeros, are the places where a parabola (or any curve) crosses/touches the x-axis. As we’ll see later, the amount that determined

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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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The expression, which expresses the value of v in terms of x is:

V = x * $2,750 + $825,000

Let's call the value of each acre of property v_a = $2,750.

Then the total value of the real estate firm can be expressed as:

V = x * v_a + other assets

Where x is the number of acres of property owned.

Now, plugging in the given value for other assets,

we will get it as:

V = x * $2,750 + $825,000

So the value of the real estate firm,

V, is a function of the number of acres of property owned, x, and is equal to the product of the number of acres and the value per acre plus the value of the other assets.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included.

The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

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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 point ranges 65-69, includes the median reading test score for ninth grade students in school district x for 1993. So, the correct choice is option (b).

The median class is defined as the class interval whose cumulative frequency is greater than (and nearest to) n/2. We have a pair chart of reading test score for ninth grade students in school district x for 1993. Total number of students in ninth grade in school district x for 1993

= 1200. We have determine the point ranges includes the median reading test for ninth grade. Now, see the pie- chart carefully.

The above figure contains a cumulative frequency table of students points.

Also, n/2 = 1200/ 2 = 600 and we see the class 65-69, consists cumulative frequency value, 636 > 600. So, it is the median class. Hence, the required point ranges is 65-69.

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Complete question:

Which of the following point ranges includes the median reading test score for ninth grade students in school district x for 1993 ?

a) Below 65 points

b) 65 - 69 points

c) 70- 79 points

d) 80 - 90 points

e) 90- 100 points

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:

20 number of students are interested in sports in the class.

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. The number is multiplied by 80 and then divided by 100. To demonstrate, consider the following formula:

(Number 80) 100 = Solution

Method No. 2

You shift the decimal point in 80.00 two places to the left, then multiply by your number. As a result, the formula is:

Number 0.8 = Solution

25×0.8= 20

The first approach is useful for learning how to get 80% of a number. When you understand how, the second technique is faster to implement.

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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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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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Looking at the asymptotes  graph, it crosses the y-axis at y = h(x) = -1

Thus, the y-intercept is -1. The graph also crossed x-axis at..

How do you find the asymptotes on a graph?

Set the denominator to 0 and solve for x to discover the vertical asymptotes. Given that this has already been factored, solve by setting each component to zero. They are expressed as equations of lines because the asymptotes are lines.

Consequently, -1 is the y-intercept. The graph also veers off the x-axis here.

Consequently, -1 is the y-intercept. The graph also veers off the x-axis here.

As soon as the denominator equals 0, the vertical asymptotes appear. Accordingly, (2x)(x-4)=0. Vertical asymptotes are thus defined as x=0 and x=4.

Given that the degrees are identical, the horizontal asymptote in this situation corresponds to the ratio of a leading coefficients. y = [(1)(1)/(2)(1)] = 1/2.

Simply changing x = 0 makes finding the y-intercept simpler. On the other hand, because x = 0 is indeed a vertical asymptote,

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Answer:

Step-by-step explanation:

P(x) is a statement about the square root of x squared equaling the absolute value of x.

Q(x) is a statement about x minus 1 equaling 3. Solving this equation for x we get x = 4.

R(x, y) is a statement about x plus y equaling 0. This is a linear equation and it has infinitely many solutions for x and y as long as x + y = 0.

T(x, y) is a statement about x + y equaling y. This equation is not possible because it will always result in x = 0, y = 0 and thus no solution.

It is important to note that the statement T(x, y) is not a valid equation, it is a contradiction and therefore it has no solution.

Answer:

=> The simplest form of

56

:

98

56:98 is

4

:

7.

4:7.

Step-by-step explanation:

Given ratio -

56

:

98

56:98

We have to reduce it to its simplest form,

For that, we have to find the GCD of the numerator as well as the denominator:

So, the GCD for

56

56 and

98

98 is

14.

14.

Now, divide both the numerator and denominator by the GCD:

=

>

56

÷

14

98

÷

14

=>

98÷14

56÷14

=

>

4

7

=>

7

4

Hence, the simplest form is

4

:

7.

4:7.

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.

Answer:

B

Step-by-step explanation:

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

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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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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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.

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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