If a + c = 4.98 and b + c = 6.48, what is the value of b^2+bc-ab-ca?

A) 7.47
B) 8.16
C) 9.08
D) 9.72
E) None of the preceding

Answer:

Before we can simplify this expression, we need to first find a common denominator for all the fractions. The prime factorization of the denominators is:

2 × 5

3 × 7 × x

Therefore, a common denominator is:

2 × 5 × 3 × 7 × x = 210x

Using this common denominator, we can rewrite the expression as:

[(5 × 21) / (2 × 5 × x) - (16 × 42) / (5 × 2 × 21 × x)] - [(-35) / (3 × x × 7 × 21)]

Simplifying each fraction, we get:

[105 / (10x) - 672 / (210x)] - [-5 / (3 × 7 × x × 21)]

Combining the two fractions and simplifying, we get:

[105 - 672] / (10x) + [5 / (3 × 7 × x × 21)]

= -567 / (10x) + 1 / (3 × 7 × x)

= (-567 × 21 + 10) / (210x)

= -11897 / (210x)

Therefore, the simplified expression is:

-11897 / (210x)

The expression to represent TJ's number is  1/3n - 3 and this can be determined by using the arithmetic operations and the given data.

What does a math equation mean?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.

                             For instance, the equation 3x + 5 = 14 contains two expressions, 3x + 5 and 14, which are separated by the 'equal' sign. When two expressions are joined by an equal sign, a mathematical statement is called an equation.

The following steps can be used in order to determine the expression to represent TJ's number:

According to the given data, the number TJ's thinking about is 'n'.

Now, TJ's find 1/3 of the number 'n'. That is

               = 1/3n

Now, he subtracts that number obtained in the above step by 3.

      = 1/3n - 3

So, the expression to represent TJ's number is 1/3 n - 3.

Learn more about equation

brainly.com/question/29657983

#SPJ1

The complete question is -

TJ is thinking of a number which he calls n. he finds 1/3 of the number and then subtracts 5. write an expression to represent tj's number.​

The rate at which the area of the cloud is increasing is equal to the product of the rate of expansion and the square of the radius of the cloud.

Therefore, the rate at which the area of the cloud is increasing is equal to the product of the rate of expansion and the radius of the cloud. The rate of expansion can be calculated using the equation . Therefore, the rate at which the area of the cloud is increasing can be calculated as .

The area of a circle is determined by the square of its radius. Thus, when the radius of the cloud is expanding at a rate, the area of the cloud is increasing at a rate that is proportional to the square of its radius.

Therefore, in order to calculate the rate at which the area of the cloud is increasing, we must calculate the rate of expansion of the radius of the cloud and then multiply it by the square of the radius of the cloud. To calculate the rate of expansion of the radius of the cloud, we can use the equation .

After we have calculated the rate of expansion, we can then multiply it by the square of the radius of the cloud to calculate the rate at which the area of the cloud is increasing.

To know more about equation click on below link:

https://brainly.com/question/29657992#

#SPJ11

Answer:360 degrees

Step-by-step explanation:

If a sample of 6-marbles is drawn with replacement, then probability that 1 is blue, 2 are white and 3 are red is 0.2597.

The different number and color of marbles that the box contains 4 white, 5 red and 2 blue marbles.

The total number of marbles are = 4+5+2 = 11 marbles,

We can choose 6 marbles in ¹¹C₆ ways,

The one blue marble can be chosen in ²C₁ ways, the two white marbles can be selected in ⁴C₂ ways and the three red marbles in ⁵C₃ ways.

⇒ The number of ways in which we can choose the marbles with the given color combinations is = ²C₁ × ⁴C₂ × ⁵C₃ ways.

So, Probability that one is blue, two are white and three are red

⇒ (²C₁ × ⁴C₂ × ⁵C₃)/¹¹C₆,

⇒ (2 × 6 × 10)/462,

⇒ 0.2597.

Therefore, the required probability is 0.2597.

Learn more about Probability here

https://brainly.com/question/466538

#SPJ4

Answer:

bot

Step-by-step explanation:

Ambitious

Answer:

x < or = to -20.

Step-by-step explanation:

first mutliply both sides by three.

next, add 5 to both siddes.

finally, negate both sides ( remeber to flip the sign)!

hope this helped!

~Cain

The inequality to find the maximum number of t-shirts is:

32 + 7x <= 60

A type of inequality expression known as a compound inequality is made up of two or more simple inequalities.

Inequality with a "and" indicates that both disparities are real.

If there is a "Or" inequality, any of the statements is true.

Considering inequality,

Jospeh has at most $60 to spend

Then it will be <=60

Now she has to spend 32 dollars on jeans so 32 will be add to the initial amount for sure.

And

Let x be the number of t-shirts

Then the cost of x t-shirts will be 7x

Putting this in to inequality will be:

32 + 7x <= 60

The inequality to find the maximum number of t-shirts is:

32 + 7x <= 60

To know more about inequality, click the below link

https://brainly.com/question/30231190

#SPJ4

Answer:

Yes

Step-by-step explanation:

Imagine that time is x and distance is y. 0x+11=11 for the first equation.

3x+11=17 for the second. So x is 2, plug it in for the 3rd, then you see that it is linear. The equation is 2x+11=y

If 1,000 points are selected randomly inside the square with all points equally likely to be selected, points to lie inside the circle is 785.4 points.

We can find the answer by finding the ratio of the areas of the regions and then multiplying by the total number of points.

The square has an area of 1 (since it has sides of length 1).

The circle has a radius of 1/2 and an area of pi/4.

So the ratio of the areas is:

(π/4) / 1 = π/4

Therefore, we would expect:

(π/4) * 1000 =  ( 3.14 / 4 ) 1000

(π/4) * 1000 = 1000 × ( 0.785 ) = 785 points

points to lie inside the circle. This is approximately 785 points.

Your question is incomplete but mos probably your full question was

If 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?

Learn more about circle at https://brainly.com/question/24810873

#SPJ11

Answer: The height of the arrow shot into the air can be represented by the equation:

h = -16t² + vt + h0

where t is the time in seconds, h is the height in feet, v is the initial velocity in feet per second, and h0 is the initial height in feet.

In this problem, the arrow is shot into the air with an initial velocity of 112 feet per second, and the bow is held 5 feet off the ground. Therefore, we have:

v = 112

h0 = 5

To find the maximum height of the arrow, we need to find the vertex of the parabolic function given by the equation. The vertex of a parabola of the form y = ax² + bx + c is given by the point (-b/2a, c - b²/4a).

In our case, the equation of the parabola is h = -16t² + 112t + 5. So we have:

a = -16

b = 112

c = 5

The t-value of the vertex is given by -b/2a. Therefore, we have:

t = -b/2a = -112/(2*(-16)) = 3.5

To find the maximum height, we substitute t = 3.5 into the equation:

h = -16t² + 112t + 5 = -16(3.5)² + 112(3.5) + 5 = 196

Therefore, the maximum height of the arrow is 196 feet.

Step-by-step explanation:

Carmen is comparing two bike rental companies, A and B. Company A charges a flat rate fee of $30 and $2 per hour, while company B charges a flat rate fee of $10 and $4 per hour.

Carmen can use mathematical equations to compare the costs of the two companies and make an informed decision.

The equation for the cost of renting from Company A is y=2h+30, where y represents the total cost in dollars and h represents the number of hours rented. The equation for the cost of renting from Company B is y=4h+10, where y represents the total cost in dollars and h represents the number of hours rented.

To compare the cost of renting from Company A and Company B for a specific number of hours, Carmen can substitute the value of h into each equation and solve for y. For example, if Carmen plans to rent a bike for 5 hours, the cost of renting from Company A would be y=2(5)+30=$40, and the cost of renting from Company B would be y=4(5)+10=$30. In this case, renting from Company B would be the more cost-effective option.

Carmen can also use algebraic methods to determine the break-even point, or the point at which the cost of renting from Company A is the same as the cost of renting from Company B. To find the break-even point, Carmen can set the two equations equal to each other and solve for h:

2h+30=4h+10

2h=20

h=10

This means that if Carmen plans to rent a bike for 10 hours or less, it would be more cost-effective to rent from Company B. If she plans to rent a bike for more than 10 hours, it would be more cost-effective to rent from Company A.

Another method of comparing the two companies is to graph the two equations on the same coordinate plane. The x-axis can represent the number of hours rented (h), and the y-axis can represent the total cost in dollars (y). Carmen can plot the two equations and visually compare the graphs to determine which company is more cost-effective for a specific number of hours rented.

In summary, Carmen can use mathematical equations, algebraic methods, and graphing to compare the costs of renting from Company A and Company B based on the number of hours rented. By comparing the costs, she can make an informed decision about which company to rent from based on her budget and the duration of the rental period.

To know more about cost of renting click here:

brainly.com/question/31209061

#SPJ1

Firstly, you turn 2 2/3 into an improper fraction, which will become

=4/3

Lastly, you multiply them, which would be 11/2 x 4/3=22/3=7 1/3

Step-by-step explanation:

the answer will be

11 x 22 / 2x3

that will give us

242/6

reducing it to the lowest term by dividing it by two that will give us 121 / 3

121 / 3 will give us 40.33

Answer:

20 hours

Step-by-step explanation:

[tex]\text{x} = \text{number of hours}[/tex]

A yard cleanup service charges a $365 fee plus $14.75 per hour.

[tex]365 + 14.75x[/tex]

Another cleanup service charges a $250 fee plus $20.50 per hour.

[tex]250 + 20.50x[/tex]

How long is a job for which the two companies' costs are the same?

[tex]365 + 14.75x = 250 + 20.50x[/tex]

[tex]365 - 250 = 20.50x - 14.75x[/tex]

[tex]115 = 5.75x[/tex]

x = 20

Answer:

angle o = 2×angle D (central angle twice inscribed angle)

angle a= angle d = 65

The distance that Bucky walked is 25.908 meters

What is distance ?
Distance is a numerical measurement of how far apart two objects or points are in space. It is a scalar quantity, which means that it is defined only by its magnitude and not by its direction. Distance can be measured using various units, such as meters, feet, kilometers, miles, and so on, depending on the system of measurement being used.

Distance is an important concept in mathematics, physics, and other fields that deal with spatial relationships. It is often used to describe the length of a path traveled by an object or the separation between two objects in space.

According to the question:
To convert feet to meters, we can use the conversion factor 1 foot = 0.3048 meter.

The distance that Bucky walked is given as 85 feet. To find the distance in meters, we can multiply the number of feet by the conversion factor:

Distance in meters = 85 feet x 0.3048 meter/foot

Simplifying this expression, we get:

Distance in meters = 25.908 meters

Therefore, Bucky walked 25.908 meters.

To know more about distance visit:
https://brainly.com/question/15256256
#SPJ1

Answer:

She can create 9 outfits

Step-by-step explanation:

Imagine it's like a 3x3 grid of what she can and can't do. You can't wear two shirts and two pants at the same time, so for each input you have one equal output.

Therefore, for the first blouse, she can choose to wear either the jeans, khakis, or grey pants (3 options)

For the second blouse, she can wear either the jeans, khakis, or grey pants (3 options)

And again for the third blouse, she can wear either the jeans, khakis, or grey pants (3 options).

3 + 3 + 3 = 9, therefore 9 outfit choices :)

The volume of the figure is given as 144 ft²

You should recall that a  pyramid (from Greek: πυραμίς pyramís) is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense

The volume of a pyramidal pyramid can be calculated using the formula volume = (1/3) × basearea × height, which works for any type of base polygon and oblique and right pyramids

Area of base is a square = 4*4 = 16 ft²

volume = 16*9 ft

Therefore the Volume of the figure is  = 144 ft²

Learn m more about a pyramid on https://brainly.com/question/17615619

#SPJ1

The answers to both the subparts of the given cuboid:

(A) The expression: (SA)=120+32x

(B) The height x=4.875

A cuboid is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces.

Cuboid is short for "like a cube."

A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.

So, we have the values:

x, 10 and 6

Total surface area formula:

(SA)=2lw+2lh+2hw

Now, insert values to form the expression:
(SA)=2lw+2lh+2hw

(SA)=2(10*6)+2(10*x)+2(x*6)

(SA)=120+20x+12x

(A) The expression: (SA)=120+32x

Now, the height would be:

376=120+32x

32x = 376-120

32x=156

x=156/32

(B) x=4.875

Therefore, the answers to both the subparts of the given cuboid:

(A) The expression: (SA)=120+32x

(B) The height x=4.875

Know more about cuboid here:

https://brainly.com/question/26403859

#SPJ1

the image of point (-12, -12) after a dilation by a scale factor of 1/4 centered at the origin is (-3, -3).

How to find?

To find the image of point (-12, -12) after a dilation by a scale factor of 1/4 centered at the origin, we can use the following formula:

(x', y') = (kx, ky)

where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the image after dilation, and k is the scale factor.

In this case, the scale factor is 1/4 and the center of dilation is the origin (0, 0). Therefore, we have:

x' = (1/4) × (-12) = -3

y' = (1/4) × (-12) = -3

So the image of point (-12, -12) after a dilation by a scale factor of 1/4 centered at the origin is (-3, -3).

To know more about coordinated related questions, visit:

https://brainly.com/question/29151766

#SPJ1

The intersection of two numerical axes creates a two-dimensional plane known as a coordinate plane. The x-axis, which is a horizontal number axis, and the y-axis, which is a vertical number axis, are two different types of number axes.

The French mathematician René Descartes enhanced the coordinate plane that had been created centuries earlier. The system is occasionally referred to as the Cartesian coordinate system in his honor. You can doodle points and lines on coordinate planes. With the aid of this method, we may generate and communicate algebraic concepts as well as visually express algebraic relations.

The coordinate plane has a horizontal axis, a vertical axis, and a right angle where numerous straight lines intersect. In a coordinate plane, the horizontal axis is represented by the x axis. The vertical axis is referred to as the y-axis. The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0.

As ordered pairs, positions on the coordinate plane are described.

By connecting the position of the point along the x-axis (the first value in the ordered pair) and the y-axis (the second value in the ordered pair), an ordered pair reveals the location of the point.

The first value in an ordered pair, like (x, y), is referred to as the x coordinate, and the second value is referred to as the y coordinate. The x coordinates are presented before the y coordinates; take note of this. The ordered pair of the origin is represented as (0, 0), since it has an ordinate and abscissa of 0.

Learn more about Coordinate Plane:

brainly.com/question/13611766

#SPJ4

Complete Question:

Juan Carlos asserts that he is unable to graph a point at coordinates (-3.25,6.5) because his coordinate plane's axis only contains whole numbers. Correcting Juan Carlos's reasoning and elaborating on how to graph this point will help. Juan Carlos claims that he cannot graph a point at (-3.25,6.5) because his coordinate plane only has whole numbers on the axis. Help Juan Carlos by correcting his thinking and explaining how to graph this point.

Answer:

Area = 50 in^2

Step-by-step explanation:

Area = B x H

The dotted line is saying that the left and right sides of the triangle are 5 inches

So just multiply 10 x 5 and get 50in^2

changes in the base pairs can alter the overall shape of the DNA molecule, disrupt specific interactions between different regions of the DNA, and potentially affect the normal functioning of the DNA.

The structure of DNA is determined by the sequence of its base pairs. There are four types of base pairs in DNA: adenine (A), thymine (T), guanine (G), and cytosine (C). The base pairs form the rungs of the DNA ladder, with the backbone consisting of sugar and phosphate groups.

The sequence of base pairs determines the overall shape of the DNA molecule. The base pairs are held together by hydrogen bonds, which are relatively weak but collectively provide enough stability to maintain the double helix structure of DNA. The sequence of base pairs also determines the specific interactions between different regions of the DNA molecule, such as the interaction between the two complementary strands.

Changes in the base pairs can have a significant impact on the structure of DNA. For example, a substitution of one base pair for another can result in a different hydrogen bonding pattern, which can affect the stability of the double helix. This can result in a change in the shape of the DNA molecule, and can also affect the specific interactions between different regions of the DNA.

Insertions or deletions of base pairs can also have a significant impact on the structure of DNA. These types of mutations can disrupt the regular spacing of base pairs along the DNA molecule, which can cause kinks or bends in the DNA. This can also affect the specific interactions between different regions of the DNA, and can potentially interfere with the normal functioning of the DNA molecule.

In general, changes in the base pairs can alter the overall shape of the DNA molecule, disrupt specific interactions between different regions of the DNA, and potentially affect the normal functioning of the DNA.
To know more about base pairs go through:-
https://brainly.com/question/3372278
#SPJ9

By answering the presented question, we may conclude that Therefore, trapezium the height of the trapezoid is 71.5 centimeters.

A trapezium is a two-dimensional geometric figure with four sides, one pair parallel to the other. It is also called as a trapezium in certain locations. The parallel sides are known as bases, whereas the non-parallel sides are known as legs. The distance between the two bases is the trapezoid's height or altitude. The area of a trapezium is given by A = 0.5 * (b1 + b2) * h, where b1 and b2 are the lengths of the two bases and h is the height.

To find the height of the trapezoid,

Area = (b1 + b2) × h / 2

h = 2 × Area / (b1 + b2)

h = 2 × 7722 / (131 + 85)

h = 2 × 7722 / 216

h = 71.5

Therefore, the height of the trapezoid is 71.5 centimeters.

To know more about trapezium visit:

https://brainly.com/question/8208556

#SPJ1

The average age of the interviewees in the study investigating childhood asthma is 15.2 years.

To find the average age at the interview, you need to follow these steps. Here's how you can calculate it:

First, add up all the ages of the interviewees:18 + 16 + 16 + 17 + 14 + 13 + 15 + 16 + 19 + 12 + 16 + 13 + 13 + 18 + 13 = 228Next, count the total number of interviewees in the study:

15 interviewees

Finally, divide the sum of ages by the number of interviewees: 228 ÷ 15 = 15.2

Therefore, the average age calculated in the study while investigating childhood asthma is approximately 15.2 years.

You can learn more about average at: brainly.com/question/24057012

#SPJ11

The opposite angles formed when two lines intersect are vertically opposite angles.

It should be noted that the value of x based on the information given about the perpendicular lines will be A. 28°.

Based on the information given, it should be noted that the total value of the angle on a straight line is 180°.

Therefore, the value of x will be calculated thus:

55 + 2x - 49 + 90 + x = 180

3x + 96 = 180

Collect the like terms

3x = 180 - 96

3x = 84

Divide through by 3

3x / 3 = 84 / 3

x = 28

The value of the angle is 28°.

Learn more about angles on:

brainly.com/question/25716982

#SPJ1

Answer:

y = 3x - 7

Step-by-step explanation:

We can use the two-point form formula to find the equation of a line that passes through two given points (x1, y1) and (x2, y2):

y - y1 = (y2 - y1) / (x2 - x1) * (x - x1)

where (x1, y1) and (x2, y2) are the two points and (x, y) represents any point on the line.

Using the given points, we have:

x1 = 1, y1 = 10

x2 = -4, y2 = -5

Substituting these values into the formula, we get:

y - 10 = (-5 - 10) / (-4 - 1) * (x - 1)

Simplifying the equation, we have:

y - 10 = 3(x - 1)

Expanding and rearranging, we get:

y = 3x - 7

Therefore, the equation of the line that passes through (1, 10) and (-4, -5) is y = 3x - 7

chatgpt

Well the first 4 you can see there is for the players who are only in curling team, the second 4 is for players on both teams, the 7 is for players in only badminton team

So the answer is 4 + 7 + 7 = 15