given that
5x : 8 = 7 : 2

calculate the value of x
give your answer in its simplest form

The graph represents the type of power function of the form y = kx in the form of D. Inverse Variation with an even r-value & a positive k-value.

It should be noted that a graph simply means a diagrammatic representation of a particular thing.

Here, the function of the for y = kx is illustrated in the graph.

This is an inverse variation with an even r-value and a positive k-value.

In conclusion, the correct option is D.

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Answer:

Step-by-step explanation:

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     3

                     B   =    -2

                     C   =  -10

 B2  -  4AC   =

       4 - (-120) =

             =  124

Applying the quadratic formula :

              2 ± √ 124

  x  =    —————

                   6

 √ 124 simplified

 The prime factorization of  124   is

  2•2•31

To be able to remove something from under the radical, there have to be  2  instances of it

√ 124   =  √ 2•2•31   =

               ±  2 • √ 31

 √ 31, rounded to 4 decimal digits, is   5.5678

So now we are looking at:

          x  =  ( 2 ± 2 •  5.568 ) / 6

Two real solutions:

x =(2+√124)/6=(1+√ 31 )/3= 2.189

or:

x =(2-√124)/6=(1-√ 31 )/3= -1.523

Answer:

Step-by-step explanation:

3x^2-2x-10=0

This is a quadratic equation that can be solved using the quadratic formula where

a = 3, b = -2, and c = -10

x=−b±(b^2−4ac)^(1/2)/2a

x=−(−2)±((−2)2−4(3)(−10)^(1/2)/2(3))

x=2±(124)^(1/2)/6

Simplify the Radical:

x=((2/6) ±2(31)^(1/2))/6

x=26±231−−√6

Simplify fractions and/or signs:

x=1/3±√31/3

which becomes

x=2.18925

See the attached image for a more clear display of solving using the quadratic equation.

x=−1.52259

Step-by-step explanation:

10x2(x-2)2=100x2x2 2x2

The equation of the parent square root function to represent the equation of the graphed function will be, y=√x-2

According to the statement

we have to show the square root function as a equation in the graphical representation.

So,

we know that the definition of a

Graph a diagram showing the relation between variable quantities, typically of two variables and it also show the relation between more than two variables.

Now, we know that the definition of Equation is a mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

And the equation obtained from the graph is a y=√x-2 by a some calculations in the graph.

So, The equation of the parent square root function to represent the equation of the graphed function will be, y=√x-2

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Answer:

[tex]\sf 2^{(n+1)}[/tex]

Step-by-step explanation:

Explicit formula is used to represent all the terms of the geometric sequence using a single formula.

  [tex]\sf \boxed{\bf t_n=ar^{(n-1)}}[/tex]

Here, a is the first term.

r is the common ratio.

r = second term ÷ first term

4, 8,16,32,64,.....

    a = 4

    r = 8 ÷4 = 2

[tex]\sf t_n =4*2^{(n-1)}[/tex]

    [tex]\sf = 4*2^n * 2^{(-1)}\\\\ = 4*2^n*\dfrac{1}{2}\\\\ = 2*2^n[/tex]

   [tex]\sf = 2^{(n+1)}[/tex]

4.440 minutes of the ride is spent higher than 37 meters above the ground.

We have to find the amount of time spent by the ride 37 meters above the ground.

We know that 37 meters above the ground is actually one meter above the center.

We can find the angle above the center as shown below:

arcsin(1/34) = 0.0294 radians

Now we have to find the angle of rotation:

The angle of rotation of the Ferris wheel above 37 meters = π - (2*0.0294)

= 3.1 radians

The angular velocity of the Ferris wheel = Angle covered/Time

= 2π/9 rad/min.

Therefore time spent above 37 meters = 3.1*9/2π

= 3.1*9/6.28319

= 4.440 minutes

Therefore, we have found that 4.440 minutes of the ride is spent higher than 37 meters above the ground.

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Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..

Lets try to solve out the problem,

Length = 3x-1

Width = x+1

Perimeter = 2(l+b)

Area = l*b

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

P= 8x

Area = (3x-1) (x+1)

=> 3x(x+1) -1 (x+1)

=> 3x^2 + 3x -x -1

=> 3x^2 + 2x -1.

Hence Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..

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19 books can fit into a bookshelf that has a width of 19/4 feet

An equation is an expression that shows the relationship between two or more number and variables.

The bookshelf is 4 3/4 feet wide = 19/4 feet

1 ft = 12 in, hence:

19/4 feet = 19/4 feet * 12 in per feet = 57 inches

Number of books = 57 inches / 3 in = 19

19 books can fit into a bookshelf that has a width of 19/4 feet

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The skydiver is falling at a speed of 212 miles per hour.

The speed of the skydiver is 212 mph.

What are Speed and Velocity?

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, whereas velocity is a vector, speed is a scalar quantity.

Given:

If a skydiver jumps out of a plane and plummets to the ground while falling at 212 mph.

To Find:

Speed and acceleration of the skydiver.

Velocity is the speed with a direction, whereas speed is only a number with a speed unit at the end.

While velocity refers to the speed and direction of an object's movement, speed refers to the time rate at which an object moves along a path.

212 miles per hour is the descending velocity of the skydiver.

At 212 miles per hour, the skydiver is moving.

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Given that price was $520 after a 30% increase,  the original price was $400.

Given that;

To determine the original price, we say;

x × ( 100% + 30% ) = $520

x × ( 130% ) = $520

x × (130/100) = $520

130x / 100 = $520

130x = $52000

x = $52000 / 130

x = $400

Given that price was $520 after a 30% increase,  the original price was $400.

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The area of the triangle pqr is 111.3 square units

The complete question is added as an attachment

The area is calculated as:

[tex]A= 0.5 ab\sin(C)[/tex]

So, we have:

[tex]A= 0.5 * 12 * 20 * \sin(68)[/tex]

Evaluate the product

A= 111.3

Hence, the area of the triangle pqr is 111.3 square units

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Answer:

A. The Highest Points Of The Graph

Step-by-step explanation:

A nonperiodic function is one that generates a graph without a regular recurring pattern over a fixed time interval. A repeating section of a graph is called the period.

Using a trigonometric identity, the cosine of the angle is given as follows:

[tex]\cos{\theta} = \frac{60}{61}[/tex]

It is given by:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

In this problem, the sine is:

[tex]\sin{\theta} = \frac{11}{61}[/tex]

Then:

[tex]\cos^2{\theta} = 1 - \sin^2{\theta}[/tex]

[tex]\cos^2{\theta} = 1 - \left(\frac{11}{61}\right)^2[/tex]

[tex]\cos^2{\theta} = \frac{3600}{3721}[/tex]

[tex]\cos{\theta} = \pm \sqrt{\frac{3600}{3721}}[/tex]

On quadrant I, the cosine is positive, hence:

[tex]\cos{\theta} = \frac{60}{61}[/tex]

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On the train, there are a total of 125 children.

Total number of passengers = 500

Out of 500 passengers, men =7/20

So, the number of men= 500* 7/20 = 175

Out of 500 passengers, women = 40%

So, the number of women passengers = 500*40/100 = 200

Therefore, the total number of men and women passengers= 175+200 = 375.

There are also children on the train. So, the rest number should be those children.

The rest number =children= 500- 375 = 125.

So, it is concluded from the above equation that there are 125 children on the train.

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The measure of angle 3 from the figure is 110 degrees

An angle is the intersection between two lines. From the given figure, we have the following parameters

m∠1= 40°,

m∠2= 70°.

Required

Measure of angle 3

The sum of the interior angles of the triangle is equal to the exterior

Sum of interior = <1 + <2

Sum of interior = 40 + 70

Sum of interior =110 degrees

Hence the measure of angle 3 from the figure is 110 degrees

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Step-by-step explanation:

find the slope:

[tex]\frac{y2-y1}{x2-x1}=\frac{-4+2}{1+3} =\frac{-2}{4} =-\frac{1}{2}[/tex]

Now our equation looks like:

[tex]y=-\frac{1}{2} x+b[/tex]

To solve for b, plug in one of the coordinates

[tex]-4=-\frac{1}{2} (1)+b[/tex]

[tex]-4=-\frac{1}{2} +b[/tex]

[tex]b=-3.5[/tex]

Put our equation together to get y = -1/2x-3.5

Answer:

y is 7, x is 14

Step-by-step explanation:

This is a 30-60-90 triangle,

The hypotenuse, the side opposite of the 90 degree angle, is twice the length of the side opposite of the 30° angle,

The side opposite of the 60° degree angle, is root 3 times the side opposite of the 30° degree angle

So y is

[tex] \frac{7 \sqrt{3} }{ \sqrt{3} } = 7 = y[/tex]

Then, that means x is

[tex]7 \times 2 = 14[/tex]

Answer:

D

Step-by-step explanation:

A' represents everything outside of the circle A

B represents the space within circle B

A' intersection B is everything not in A that is in B.

Answer: Option (4)

Step-by-step explanation:

A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.

Answer:

[tex]\huge\boxed{\sf x = 65 \textdegree}[/tex]

Step-by-step explanation:

Using trigonometric ratio cos.

Here,

[tex]\displaystyle cos \theta =\frac{adjacent}{hypotenuse} \\\\cos \ x =\frac{12}{28} \\\\cos \ x = 0.43\\\\x = cos^{-1} 0.43\\\\x = 65 \textdegree\\\\\rule[225]{225}{2}[/tex]

The statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial

Polynomial expression are equation that has a leading degree of 2 and above. For instance the following expressions are polynomials.

ax^2+bx+c and;

mx^2+nx+p

Take the sum of the polynomials

P(x) =. ax^2+bx+c

f(x) = mx^2+nx+p

Since both expressions are quadratic in nature, hence the sum will result in a polynomial that is quadratic in nature.

Based on the explanation above, we can conclude that the statement best describes the sums of ax^2+bx+c and mx^2+nx+p where x is a variable and a, b, c, m, n, and p are integers is a polynomial

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Answer:

18 students

Step-by-step explanation:

Answer:

the range between 18 and 24 is 6

Step-by-step explanation:

24-18=6

Answer:

Question 1) 2/3

Question 2) -3

Step-by-step explanation:

Question 1)

The formula of a slope is (increase in y)/(increase in x), so in the graph, all we need to do is find two precise points and look at the distance difference.

1. The two points that I've found were (0,3) and (3,5). The change in y is 3 --> 5, which is 2. The change in x is 0 --> 3, which is 3.

2. The slope will be 2/3.

Question 2)

In this question, we can consider n as x and f(n) as y.

1. The two points I chose were (4, -31) and (7,-40). The change in y is -31 --> -40, which is -9. The change in x is 4 --> 7, which is 3.

2. The slope will be -9/3.

3. -9/3 can be simplified to -3 since we can divide both the numerator and the denominator by 3.

4. The final slope will be -3.

The outcome of the product is 4 + 2/24, so the correct option is B.

Here we want to solve:

(4 + 2/3)*(7/8)

Using the distributive property of the product we get:

4*(7/8) + (2/3)*(7/8)

28/8 + 14/24

Now we can multiply the first fraction by (3/3) (it does not change the fraction).

(3/3)*28/8 + 14/24

84/24 + 14/24 = 98/24  

Now we can rewrite it as:

98/24 = (96/24) + (2/24)  =4 + 2/24

Then the correct option is B.

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Answer:

(a)

    A = 3

    B = 17

    C = 8

    D = 15

(b)

surface area = 240

(using the formula)

The difference between two numbers are [tex]3[/tex] and numbers are [tex]x[/tex] and [tex]y[/tex] so the equation is [tex]x-y=3[/tex]

How to find the equation and what is the equation ?

equation, statement of equality between two expressions consisting of variables and/or numbers. In essence, equations are questions, and the development of mathematics has been driven by attempts to find answers to those questions in a systematic way.

if the difference of two numbers are [tex]3[/tex]

And one number is [tex]x[/tex] and another is [tex]y[/tex]

So we write the equation with operation of subtraction

[tex]x-y=3[/tex]

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The area under the curve between the two values is (d) 0.0750

From the table, we have:

P(z = -0.45) = 0.3264

P(z = -0.67) = 0.2514

The area under the curve is calculated as:

Area = P(z = -0.45) - P(z = -0.67)

So, we have:

Area = 0.3264 - 0.2514

Evaluate the difference

Area = 0.0750

Hence, the area under the curve between the two values is (d) 0.0750

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Given the ratio of the profit share between the business partners Mr. Jake and Mr. Sebastian as 3:2, and the total profit as 24,000, the profit share received by Mr. Jake is 14,400.

The ratio of the shares of business partners Mr. Jake to Mr. Sebastian given to us is 3:2.

So we assume Mr. Jake's share of profit to be 3x, and Mr. Sebastian's share of profit to be 2x.

Thus, the total profit between them is 3x + 2x = 5x.

The total profit given is 24,000.

Thus, we get an equation:

5x = 24000,

or, x = 24000/5 = 4800.

Thus, the share of profit Mr. Jake receives is 3x = 3*4800 = 14400.

Thus, given the ratio of the profit share between the business partners Mr. Jake and Mr. Sebastian as 3:2, and the total profit as 24,000, the profit share received by Mr. Jake is 14,400.

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Answer: [tex]y=-\frac{5}{3}x-1[/tex]

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so the slope of the line we want to find is -5/3.

Since the y-intercept is (0,-1), the equation is [tex]y=-\frac{5}{3}x-1[/tex]

The equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3 is 5x + 3y + 3 = 0.

A line of the standard form y = mx + c , where m is the slope of the line and c is a y-intercept. Another way to express the equation for a line is in standard form.

Slope: A line's slope provides information on the steepness and direction of the line.

By figuring out the difference between both the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of such a straight line through them. The letter "m" denote the slope of the line.

Relation between slope of two perpendicular lines are-

Calculation for the equation of the line.

Consider the given equation;

y=3/5x-3 (compare this with the standard equation)

The slope 'm' is 3/5

Use the relation of slopes of two perpendicular line.

The slope of orthogonal line will be -1/m

Slope = -5/3

Put the slope in the slope point equation of line.

(y - y1) = m(x - x1)

where (x1,y1) = (0,-1)

Substitute the coordinates in the equation

y - (-1) = (-5/3)×(x - 0)

y + 1 = -5x/3

Further simplifying the equation,

5x + 3y +3 = 0

Therefore, the equation of the line passing through (0, -1) that is perpendicular to the line y=3/5x-3 is 5x + 3y +3 = 0.

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The area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another

Let the side of a square be x.

So,

Area of square = [tex]x^{2}[/tex]

A =[tex]x^{2}[/tex]

Differentiating with respect to time we get,

dA/dt = 2x dx/dt

When area = 9 [tex]cm^{2}[/tex] the side becomes 3 cm

At x = 3cm and dx/dt = 5 cm/s (Given)

dA/dt = 2.3.5 = 30 [tex]\frac{cm^{2} }{sec}[/tex]

Thus the area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]

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