On a coordinate plane, the coordinates of vertices R and T for a polygon are R(−6, 2) and T(5, 2). What is the length of Side RT of the polygon?

4 unit
6 units
7 units
11 units

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

The each side of the square will be 8.

Therefore, the area of ​​a rectangle with a height of 4 cm  and a length of 16 cm is 64 cm². Since a square is a rectangle with equal height and width, we need to find a number that when multiplied by itself equals 64... which is  the square root of 64. That's 8.8x 8 = 64.

A square is a two-dimensional planar object in geometry that has four equal sides and four equal but 90 degree angles. The characteristics of a rectangle and a square are fairly comparable, however a rectangle only has its opposing sides equal. Therefore, a rectangle is only referred to as a square if its four sides are of the same length.

A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.

Learn more about squares here :

https://brainly.com/question/14198272

#SPJ9

Answer:

See explanation

Step-by-step explanation:

1) 5/10

2) 3/10

3) 2/10

4) 7/10

Answer:

1) \(\frac{5}{10} = \frac{1}{2}\)

2) \(\frac{3}{10}\)

3) \(\frac{2}{10} = \frac{1}{5}\)

4) \(\frac{7}{10}\)

Step-by-step explanation:

Probability = \(\frac{number of favourable outcomes}{total number of favourable outcomes}\)

gray marbles = 5

white marbles = 3

black marbles = 2

total number of marbles = 10

Answer:

MY = 16 or C

Step-by-step explanation:

Both of these binomials are equal because they are marked as equal

8x - 24 = 3x + 1               Add 24 to both sides

8x = 3x + 1 + 24              Combine

8x = 3x + 25                   Subtract 3x from both sides

8x - 3x = 25                    Combine

5x = 25                           Divide by 5

x = 25/5

x = 5

MY  = 8x - 24               Let x = 5

MY = 8*5 - 24              Combine

MY = 40 - 24                

MY = 16

Answer:

(-3, 6)

Step-by-step explanation:

Once turned the original points are to be flipped and since it is counter clockwise it will make the x usually change from positive to negative and vise versa

Answer:

90o ccw (x<,y) (-y.x)

so write

p(4,2)  (-2,4)

Answer:

x = 16°

H = 46°

I = 55°

J = 39°

Step-by-step explanation:

Since the whole figure is 180°

Deduct 180 by the numbers mentioned above in order to find x.

180 - 2 - 9 - 9 = 160

3x + 4x + 3x = 10x

10 x = 160

x = 160 ÷ 10 = 16

Since we know what x is, we can find all the angles in the figure.

Angle at H = 3 x 16 - 2 = 46°

Angle at I = 4 x 16 - 9 = 55°

Angle at J = 3 x 16 - 9 = 39°

The value of x is 20.

The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle. A closed shape with both inner and exterior angles, a triangle is created by three line segments. When the values of the other two angles are known, one can utilise the angle sum property to determine the measure of an unknown interior angle.

Given:

Angles are: 3x-2, 3x-9 , 4x-9

Using Angle Sum Property

3x-2 + 3x -9 + 4x- 9 = 180

10x - 20 = 180

10x = 200

x= 200/10

x= 20

Hence, the value of x is 20.

Learn more about Angle sum Property here:

https://brainly.com/question/4316040

#SPJ2

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

To Know more about variables, visit:

https://brainly.com/question/17344045

#SPJ1

9514 1404 393

Answer:

  A) (20 miles)/(1 gallon) = 20 miles per gallon

  B) 20/1 = 20

Step-by-step explanation:

After you read the problem statement and identify the questions being asked, it is a good idea to look carefully at the given information. Graphs A and B are identical in every way.

The vertical axis is labeled "y" and "Distance (miles)". The horizontal axis is labeled "x" and "Gallons". The graph starts at (0 gallons, 0 miles) and goes through points on the grid that are 2 squares up for each 1 square to the right. Each square up represents 10 miles. Each square to the right represents 1 gallon.

__

A) Pick two points on the graph. It is usually convenient to choose points where the graph crosses grid intersections. It is often convenient to choose one of them as (0, 0) if that point is on the graph (it is). I expect it to be convenient to choose the second point as (1 gallon, 20 miles).

The change in distance between the point (0 gallons, 0 miles) and (1 gallon, 20 miles) is (20 miles) - (0 miles) = 20 miles.

The change in gallons between the point (0 gallons, 0 miles) and (1 gallon, 20 miles) is (1 gallon) - (0 gallons) = 1 gallon.

The ratio of these changes is (20 miles)/(1 gallon) = 20 miles per gallon.

__

B) We can use the same two points. Here, we basically ignore the units.

Change in y = 20-0 = 20.

Change in x = 1 -0 = 1.

Slope = 20/1 = 20.

_____

Additional comment

For many problems, I find it convenient to keep the units with the numbers. Making sure the units work out properly is called "units analysis." Doing that can save you from a number of mistakes where units are involved.

Units can be treated just like a variable--multiplied, divided, raised to a power, cancelled from fractions. And, like with variables, terms can only be added or subtracted if they have the same units.

Here, we have ...

  \(\dfrac{\text{change in distance}}{\text{change in gallons}}=\dfrac{20\text{ miles}}{1\text{ gallon}}=\dfrac{20}{1}\times\dfrac{\text{miles}}{\text{gallon}}=20\text{ miles per gallon}\)

Note that "divided by" and "per" mean essentially the same thing in this context.

As you can see from the work done with Graph A, the slope of the line has units that are the ratio of the units of the y-axis to the units of the x-axis. (miles/gallon) Even though in Graph B, we write the slope as 20 without any units, it will only make any sense to use that number where units of miles/gallon make sense.

Answer:

c = 45 and e = 30

Step-by-step explanation:

Since we know that A = 45, B = 90, we can calculate C knowing that the total angle of a triangle is 180, so you do 180-45-90 = 45

Finding the angle C helps us find F by subtracting 45 from 180, since a straight line is 180 degrees, which is 135.

We know that E = 15, and what was said earlier about how the toal angle is 180 in a triangle, we can subtract 15 and 135 from 180, which is 30.

Hope that answers your question

The solution is

a) The number is 6

b) The equation of the parabola is y = x² + 4x + 96 with vertex ( -2 , 92 ) and the y intercept is ( 0 , 96 ) and the axis of symmetry is x = -2

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

a)

Let the equation be represented as A

Now , the value of A is

Let the number be = n

A = Two-fifth of the sum of a number and 24 is equal to 5 times the number decreased by 18

Substituting the values in the equation , we get

2/5 ( n + 24 ) = 5n - 18

On simplifying the equation , we get

Multiply by 5 on both sides of the equation , we get

2 ( n + 24 ) = 25n - 90

2n + 48 = 25n - 90

Subtracting 2n on both sides of the equation , we get

23n - 90 = 48

Adding 90 on both sides of the equation , we get

23n = 138

Divide by 23 on both sides of the equation , we get

n = 6

Therefore , the number is 6

b)

The equation of parabola is given as

y = x² + 4x + 96

Now , the equation can be simplified as

y = (x + 2)² + 92

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

Substituting the values in the equation , we get

The vertex of the parabola is P ( -2 , 92 )

The y intercept of the parabola is ( 0 , 96 )

The axis of symmetry of parabola is x = -2

Hence , the equation of parabola is y = (x + 2)² + 92

To learn more about parabola click :

https://brainly.com/question/24042022

#SPJ1

Answer:

Step-by-step explanation:

For the first bag:

Price of the bag = $12

Number of balls in the bag = 15

Price per ball = Price of the bag / Number of balls

Price per ball for the first bag = $12 / 15 = $0.8

For the second bag:

Price of the bag = $15

Number of balls in the bag = 20

Price per ball = Price of the bag / Number of balls

Price per ball for the second bag = $15 / 20 = $0.75

Comparing the prices per ball, we find that the second bag has a lower price per baseball. Therefore, the second bag offers a better price for individual baseballs compared to the first bag.

Answer:

Step-by-step explanation:

To find out which bag prices individual baseballs lower, we can divide the total cost of each bag by the number of balls in the bag. This will give us the price per ball for each bag.

For the first bag, the price per ball is $12 / 15 = $0.80.

For the second bag, the price per ball is $15 / 20 = $0.75.

Therefore, the second bag prices individual baseballs lower.

i am going to answer question 1, so q1 is a number line

\(\sqrt[3]{4 a^4 b^5} = \sqrt[3]{4 \times 4^4 \times 2^5} = \sqrt[3]{(4\times 2)^5} = \sqrt[3]{(2^2\times2)^5} = \sqrt[3]{(2^3)^5} = \sqrt[3]{2^{15}} = \sqrt[3]{(2^5)^3} = 2^5 = 32\)

\(\dfrac{a-c}{(b+c)^2} = \dfrac{4-(-5)}{(2+(-5))^2} = \dfrac{4+5}{(2-5)^2} = \dfrac9{(-3)^2} = \dfrac99 = 1\)

Then the expression evaluates to 32 + 1 = 33.

The value of the expression

\($\sqrt[3]{4a^4b^5} + \dfrac{a - c}{(b+c)^2}$\)

is 33 when $a = 4$, $b = 2$, and $c = -5$.

Let's substitute the given values into the expression and calculate the result:

Given:

$a = 4$

$b = 2$

$c = -5$

Substituting the values:

\($\sqrt[3]{4a^4b^5} + \dfrac{a - c}{(b+c)^2} = \sqrt[3]{4(4)^4(2)^5} + \dfrac{4 - (-5)}{(2+(-5))^2}$\)

Calculating the values within the cube root:

\($\sqrt[3]{4(4)^4(2)^5} = \sqrt[3]{4 \cdot 256 \cdot 32} = \sqrt[3]{32768} = 32$\)

Calculating the values within the fraction:

\($\dfrac{4 - (-5)}{(2+(-5))^2} = \dfrac{4 + 5}{(-3)^2} = \dfrac{9}{9} = 1$\)

Now we can substitute the calculated values back into the expression:

\($\sqrt[3]{4a^4b^5} + \dfrac{a - c}{(b+c)^2} = 32 + 1 = 33$\)

Therefore, the value of

\(\sqrt[3]{4a^4b^5} + \frac{a - c}{(b+c)^2} \: is \: 33 \: when \: a = 4, \: b = 2, and \: c = -5\)

learn more about cube root: https://brainly.com/question/24486461

#SPJ2

Answer:

I don't understand wat u said

Answer:

a. x = 4

b. x = 17.5

Step-by-step explanation:

a. 5x/2 + 1 = 11

5x/2 = 10

5x = 20

x = 4

b. 2x/7 - 3 = 2

2x/7 = 5

2x = 35

x = 35/2

Answer:

a) x = 4

b) x = 17.5

Step-by-step explanation:

Isolate x variable to find the value.

5x/2 + 1 = 11

5x/2 = 10

5x = 20

x = 4

2x/7 - 3 =2

2x/7 = 5

2x = 35

x = 17.5

a) The initial height of the football at t = 0 is 2 feet.

b) The ball reaches its maximum height at approximately t = 2.05 seconds.

c) The maximum height of the ball is approximately 23.9 feet.

d) It takes approximately 4.579 seconds for the ball to hit the ground.

a) The initial height of the football at time t = 0 can be found by substituting t = 0 into the equation \(5t^2 + 20.5t + 2:h = -5(0)^2 + 20.5(0) + 2 = 0 + 0 + 2 = 2\)

Therefore, the initial height of the football is 2 feet.

b) To find the time at which the ball reaches its maximum height, we can observe the graph of the equation h = \(-5t^2 + 20.5t + 2.\) The maximum height corresponds to the vertex of the parabolic graph. The t-coordinate of the vertex can be calculated using the formula t = -b/2a, where a and b are the coefficients of the quadratic equation.

In this case, a = -5 and b = 20.5. Plugging these values into the formula, we get:

\(t = -20.5 / (2\times (-5)) = -20.5 / -10 = 2.05\)

Therefore, the ball reaches its maximum height at approximately t = 2.05 seconds.

c) The maximum height of the ball can be found by substituting the time t = 2.05 into the equation \(h = -5t^2 + 20.5t + 2:\)

h = -5(2.05)^2 + 20.5(2.05) + 2 ≈ -20.125 + 42.025 + 2 ≈ 23.9

Therefore, the maximum height of the ball is approximately 23.9 feet.

d) To find the time it takes for the ball to hit the ground, we need to determine when the height h becomes zero. We can set the equation \(-5t^2 + 20.5t + 2 = 0\) and solve for t.

This quadratic equation can be solved using factoring, the quadratic formula, or by graphing. The solutions are t ≈ -0.179 and t ≈ 4.579. Since time cannot be negative in this context, the ball takes approximately 4.579 seconds to hit the ground.

For more such questions on maximum height

https://brainly.com/question/26746473

#SPJ8

Answer:

7.2 *10⁻⁵

Step-by-step explanation:

Given the diameter of the hair expressed as 0.000072, we are to express it in scientific notation.

The standard form of scientific notation is expressed as;

A * 10ⁿ

A is a value from 1 to 9

n is any integer.

Rewriting 0.000072 in this form, we will need to shift the decimal point to the front 5 times to have;

0.000072 = 7.2 *10⁻⁵ where;

A = 7.2 and n = -5

Note that the power is a negative value since the value is less than 1.

Answer: Negative two times z plus eight.

Step-by-step explanation:

The expression $-2z + 8$ represents "negative two times the quantity of z plus 8". To interpret this as a phrase, we can say "8 increased by the negative of two times the quantity of z."

Answer:

y intercept is -2

x intercept is -6

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sum of the rates of painting, in fences per hour, is ...

  1/9 + 1/7 = (9+7)/63 . . . . fences per hour

The total rate in hours per fence is the inverse of that:

  63/16 = 3 15/16 ≈ 3.9 . . . hours to paint the fence

__

The relevant relationship is ...

  distance = speed × time

Let t represent Tom's speed in miles per hour. Then George's speed is (t-36). They both have traveled the same total distance at the point where Tom catches up.

  (2+3)(t-36) = 3t

  2t = 180 . . . . . . . add 180-3t

  t = 90 . . . . . . divide by 2

Tom's average speed is 90 miles per hour.

divide figure into 1 square and 1 circle ( 2 semicircle )

each semicircle has radius of 2 inches

use formula to find area of circle [ πr² ]

π × 2² = 12.566 in²

the sides of the square is the diameter of both semicircles. which is 2× 2 = 4 inches

use formula to find area of square [ b×h ]

4 × 4 = 16 in²

sum of the area

12.566 + 16 = 28.566 in²

Answer:

93 minutes

Step-by-step explanation:

Since 75 percent is just .75, multiply 124 by .75 to find out how much was watched. 124 * .75 = 93

Hopefully this helps- let me know if you have any questions

At t = 0 the height is not zero because the cannonball is at the end of the barrell of the cannon.

If we define H as the maximum height and T as the time when the cannonball hits the ground, the domain and range are:

domain: [0, T]

range: [0, H]

The height is modeled by the graphed parabola.

The height equal to zero would mean that the cannonball is on the ground. Now, at t = 0 we assume that the cannonball is leaving the barrel of the cannon (which is at some given height above the ground). This is why at t = 0 the height of the cannonball is not equal to 0.

Now we also want to describe the domain and range of the graphed function. The domain is the set of the inputs of the function, we can see that it goes from t = 0, when the cannonball is shooted, to a given time T which is when the cannonball reaches the ground.

For the range (the set of the outputs) we can see that it will go from 0 (the ground) to the maximum value that we can see in the graph, a height H.

So, domain: [0, T]

      range: [0, H]

If you want to learn more about parabolas:

https://brainly.com/question/4061870

#SPJ1

Answer:

I think the question must be "The sum of 3 consecutive even integers is 288. What are the 3 integers? " If so the answer is 94,96,98.

Answer:

I wonder if they meant consecutive even integers, because I got 94, 96, and 98 when I solved.

Step-by-step explanation:

Let x = the first odd integer

Let x +2 = the second odd integer

Let x + 4 = the third odd integer

x + (x +2) + (x +3) = 288  The parentheses are not needed.  I just put them in to make the first, second and third number a little easier to see.

x + x+2 +x + 4 = 288  Combine like terms

3x + 6 = 288 Subtract 6 from both sides

3x = 282  Divide both sides by 3

x = 94

94, 96, 98

I wonder if they meant 2 consecutive even integers

While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.

Here's a three-column table evaluating how learning takes place according to Piaget, Vygotsky, and Bruner:

Theorist Approach to Learning Key Concepts

Piaget Constructivism 1. Schema: Individuals actively construct their knowledge through assimilation and accommodation, organizing information into mental structures called schemas. 2. Stages of Development: Learning occurs through cognitive development stages, from sensorimotor to formal operational, where individuals progressively acquire more complex mental abilities. 3. Active Exploration: Children learn best through hands-on exploration and interactions with the physical world.

Vygotsky Sociocultural Theory 1. Zone of Proximal Development (ZPD): Learning takes place within the gap between a learner's actual developmental level and their potential level with guidance from a more knowledgeable other. 2. Social Interaction: Learning is facilitated through social interactions with peers and adults, such as cooperative learning and scaffolding. 3. Cultural Tools: The use of language, symbols, and cultural artifacts plays a central role in cognitive development and learning.

Bruner Constructivism 1. Scaffolding: Instruction should provide support and guidance tailored to the learner's current abilities to help them progress to higher levels of understanding. 2. Discovery Learning: Learners construct knowledge by actively exploring and discovering concepts and relationships on their own. 3. Spiral Curriculum: Learning is organized in a spiral manner, revisiting key concepts and building upon previous knowledge in a progressive and interconnected way.

While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.

For more questions on perspectives

https://brainly.com/question/6993294

#SPJ8

Answer:

-5x-3y^3

Step-by-step explanation:

x-3y^3+3x^3-5x-x^3-x-2x^3

\(\huge\text{Hey there!}\)

\(\large\boxed{\mathsf{x - 3y^3 + 3x^3 - 5x - x^3 - x - 2x^3}}\)

\(\large\text{COMBINE the LIKE TERMS}\)

\(\large\boxed{\mathsf{= (3x^3 - x^3 - 2x^3) + (-3y^3) + (x - 5x - x)}}\)

\(\large\boxed{\mathsf{= 3x^3 - x^3 - 2x^3 - 3y^3 + x - 5x - x}}\)

\(\large\boxed{\mathsf{= -3y^3 - 5x}}\)

\(\huge\boxed{\rm{Therefore, your \ answer \ is: -3y^3 - 5x}}\)\(\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

The area of the triangle which is formed as described is; 60.

According to the task content, when Point A(5,6) is reflected over the y-axis, the point B formed is; (-5,6) and when reflected over both axis, the point C formed is; (-5,-6).

It therefore follows that the length of segments AB and BC which represents the base and height of the triangle formed are; 10 and 12 respectively.

Therefore, the area of the triangle is; (1/2) × 10 × 12 = 60.

Read more on area of a triangle;

https://brainly.com/question/23945265

#SPJ1

The graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

The graphical solution to a system of equations is a method of finding the point of intersection between the graphs of the equations. We plot each equation as a line on the same coordinate plane, and then find the point where the lines intersect.

If we have two equations in two variables, the solution to the system is the point where the two lines intersect. Also if there are three equations in three variables, the solution is the point where the three planes intersect.

In conclusion, the graphical solution to a systems of equations is the coordinate pair at the place where the two linear graphs intersect.

Read more about equations here:https://brainly.com/question/28732353

#SPJ1