If a truck traveled 75 miles in 3 hours, how many miles would the truck have traveled per minute?

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

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Step-by-step explanation:

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

Answer: Option (4)

Step-by-step explanation:

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

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

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.

To know more about standard form equation of the line, here

https://brainly.com/question/5470278

#SPJ4

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.

Learn more about graph on:

brainly.com/question/19040584

#SPJ1

The probability of two successes in seven trials is 0.0774144.

The probability can be found using the binomial formula.

The probability of success is given as 0.6.

Therefore, the probability of failure is 0.4.

We have to find the probability of two successes in seven trials.

It is given by:

[tex]P = nC_x p^{n} q^{n-x}\\=7C_{2} (0.6)^{2} (0.4)^{7-2} \\=7C_{2} (0.6)^{2} (0.4)^{5} \\=\frac{(7)(6)}{(1)(2)} (0.36)(0.01024)\\=0.0774144[/tex]

The probability of two successes in seven trials is found to be 0.0774144.

Therefore, we have found that the probability of two successes in seven trials is 0.0774144.

Learn more about probability here: https://brainly.com/question/24756209

#SPJ4

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]

Learn more about the equations here :

https://brainly.com/question/28048736

#SPJ4

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:

18 students

Step-by-step explanation:

Answer:

the range between 18 and 24 is 6

Step-by-step explanation:

24-18=6

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]

Learn more about rate of change here :

https://brainly.com/question/12786410

#SPJ4

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:

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.

The lateral area of the given pyramid is 108 cm².

Any three-dimensional figure's lateral surface area is its side surface area.

In the question, we are asked to find the lateral area of the given pyramid, whose base is a regular hexagon, with a side length of 3 cm, and the slant height of the pyramid is 12 cm.

To determine the lateral area, we determine the area of one lateral face, and then multiply it by the number of lateral faces in the pyramid.

The number of lateral faces = sides of the base = 6 {Since the base is a regular hexagon}.

Area of a lateral face = (1/2)*base*height {Since its a triangle},

or, area of a lateral face = (1/2)*3*12 {Since the base is the side length of the base, and the height is the slant height},

or, area of a lateral face = 18 cm².

Thus, the lateral area of the pyramid = 6 * 18 cm² = 108 cm².

Thus, the lateral area of the given pyramid is 108 cm².

Learn more about lateral areas at

https://brainly.com/question/12736338

#SPJ4

The percent of the class who voted for Math also voted for Science is 38.8%

Therefore,

1 = p(m) + p(s) - p(m ∩ s)

Hence,

p(m)  = 45% = 0.45

p(s)  = ?

p(m ∩ s) = 35% = 0.35

Therefore,

1 = 0.45 + p(s) - 0.35

1 - 0.45 + 0.35 = p(s)

p(s) = 0.9

Therefore,

p(m | s) = 0.35 / 0.9 = 0.38888888888 = 38.8%

learn more on percent here: https://brainly.com/question/797269

#SPJ1

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.

To know more about Speed and Velocity visit:

https://brainly.com/question/13846777

#SPJ4

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

Learn more on polynomial function here: https://brainly.com/question/24380382

#SPJ1

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.

Learn more about similar kind of problem here:

https://brainly.com/question/3457273

#SPJ4

Answer:

43.5 unit^2.

Step-by-step explanation:

Area of the triangle

= 1/2 * base * height

= 1/2 * AB * AC.

AB = √ [(6-1)^2 + (6-8)^2] = √29

AC = √ [(8 - (-7))^2 + (1 - (-5)^2] = √261

So the area = 1/2 * √29  * √261

                    = 43.5

Answer:

(a)

    A = 3

    B = 17

    C = 8

    D = 15

(b)

surface area = 240

(using the formula)

The ratio comes out to be 1:4.

What is ratio?

A ratio in mathematics shows how many times one number is contained in another. For instance, if a mixture of milk and water contains eight liters of water and six liters of milk, the ratio of water to milk is eight to six. Similarly, the ratio of water to the overall amount of mixture is 8:14, while the ratio of milk to water is 6:8.

Calculating the Ratio of the Solution:

Let us assume that x is the quantity of 30% of the solution and y be that of 5% solution, then,

30% of x + 5% of y = 10% of (x + y)

0.3x + 0.05y = 0.1 (x + y)

0.3x + 0.05y = 0.1x + 0.1y

0.3x - 0.1x = 0.1y - 0.05y

0.2x = 0.05y

Thus, the required ratio is,

0.2x / 0.05y = 1

x / y = 0.05 / 0.2

x / y = 5 / 20

x:y = 1 : 4

Learn more about ratio here:

https://brainly.com/question/13419413

#SPJ1

Step-by-step explanation:

Simplifying 8a = 2xy + b

Reorder the terms: 8a = b + 2xy

Solving 8a = b + 2xy

Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right.

Divide each side by '8'. a = 0.125b + 0.25xy

Simplifying a = 0.125b + 0.25xy

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

Learn more about Graph here https://brainly.com/question/4025726

#SPJ4

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]

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

Learn more on lines and angles here: https://brainly.com/question/25770607

#SPJ1

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.

Learn more about percent​ increase here: https://brainly.com/question/19062651

#SPJ1

The common ratio of the set of data is 0. 1

To determine the common ratio of a set of data, we have to

For the given set of data

0.1,0.01,0.001

Let's divide the second term by the first term

= 0. 01/ 0. 1

= 0. 1

Thus, the common ratio of the set of data is 0. 1

Learn more about common ratio here:

https://brainly.com/question/1509142

#SPJ1

The value of X is 100 degree.

According to the statement

we have to find the value of x degree which represent the angle.

In this figure

we see that there are two angles which are vertically opposite angles and there is rule that the values of vertically opposite angles are always same.

So, due this reason Here the value of x is 100 degree

because in this figure the given angle which is 100 degree are vertical to the angle which we have to find and that angle which x, so, the value of x is same as the value of vertical angle.

so these angles are vertical angles. that's why x is 100 degree.

So, The value of X is 100 degree.

Learn more about ANGLES here https://brainly.com/question/2005046

#SPJ1

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..

Learn more about Perimeter on:

https://brainly.com/question/397857

#SPJ4

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.

Learn more about ratios at

https://brainly.com/question/9477681

#SPJ4