a line is graphed on the coordinate plane write the equation of a line in slope-intercept form. Explain how you found the slope and the y- intercept

The inequality to graphed.

y < (-1/2)x + 4

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

The equation of the line from the graph.

y = mx + c

Two coordinates from the graph:

(8, 0) and (0, 4)

m = 4/-8

m = -1/2

Now,

(8, 0) = (x, y)

0 = (-1/2)8 + c

c = 4

Now,

y = (-1/2)x + 4

Thus,

y < (-1/2)x + 4 is the inequality that will graph the given graph.

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The equation represented by the graph is f(x) = -3x + 6

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,

'm' is the slope of the line

'b' is the y-intercept of the line

'x' is the independent variable

'y' (or f(x)) is the dependent variable.

the straight line cuts the axes at (0,6) and (2,0)

Equation of straight line in slope-intercept form is f(x) = mx + c

when x = 0 f(x) = 6

6 = m(0) + c

c = 6

when x = 2, f(x) = 0

0 = 2m + c

2m = -c, but c = 6

2m= -6

m = -6/2

m = -3

Equation of line becomes f(x) = -3x + 6

In conclusion f(x) = -3x + 6 is the equation that is represented by the graph.

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1) 20 more ants there are in ant colony A than in ant colony B

2) The growth rate of ant colony A is 12%

3) The growth rate of ant colony B is 15%

4) The growth rate of ant colony A is 3% less than that of ant colony B.

What is exponential growth function ?

A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.

1)   colony A :

  Number of ants = 210

    colony B:

   Number of ants = 190 ( from the graph )

Find the difference: 210 - 190 = 20 ants

So, 20 more ants there are in ant colony A than in ant colony B

2 )  Exponential growth function: y= a(b)^x

b= 1+ r , r is the growth rate as decimal

We have a(x)=210(1.12)^x

b= 1.12 = 1+0.12

So, r= 0.12 = 12%

3 )  (x,y) = (1,220)

y= a(b)^x  

=> 220 = 190(b)^1

=> b= 220/190 = 1.15

b= 1+r

r= b - 1 = 1.15 - 1 = 0.15 = 15%

The growth rate of ant colony B is 15%

4) The growth rate of ant colony A is 3% less than that of ant colony B.

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1) 20 more ants there are in ant colony A than in ant colony B

2) The growth rate of ant colony A is 12%

3) The growth rate of ant colony B is 15%

4) The growth rate of ant colony A is 3% less than that of ant colony B.

What is exponential growth function ?

A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.

1)   colony A :

Number of ants = 210

colony B:

Number of ants = 190 ( from the graph )

Find the difference: 210 - 190 = 20 ants

So, 20 more ants there are in ant colony A than in ant colony B

2)  Exponential growth function: y= a(b)^x

b= 1+ r , r is the growth rate as decimal

We have a(x)=210(1.12)^x

b= 1.12 = 1+0.12

So, r= 0.12 = 12%

3) (x,y) = (1,220)

y= a(b)^x  

=> 220 = 190(b)^1

=> b= 220/190 = 1.15

b= 1+r

r= b - 1 = 1.15 - 1 = 0.15 = 15%

The growth rate of ant colony B is 15%

4) The growth rate of ant colony A is 3% less than that of ant colony B.

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Answer:

[tex]\frac{x}{3} \leq 5[/tex]

Hope this helps! :)

The value of the form 4^4 plus 3 is 259

Scientific notation can simply be defined as a way of expressing numbers with extreme values in a convenient form.

It is also known as standard index form,  standard form and scientific form.

It is commonly used for complex calculations with very long numbers.

It is also described as a method of expressing numbers in the terms of a decimal number.

Given the expression;

4^4 plus 3

4^4 is represented as 4 × 4 × 4 × 4

Multiply the values

256 + 3

Add the values

259

Hence, the value is 256

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Answer:

4i/7

Step-by-step explanation:

A recipe calls for 170,100 milligrams of raisins.

What are units ?

Units are the measuring and contrasting devices for many things. When all measurement units are identical, comparisons are simple. Depending on how they are used, several units can be categorized.

Measurement is the process of comparing an unknown quantity to an already known quantity. A numerical value with specific units is the measurement's output. Any given object can have its length, mass, capacity (volume), and temperature measured.

1 ounce = 28.35 grams

6 ounces = 6*28.35 grams  = 170.1 grams

1 gram = 1,000 milligrams

170.1 grams  = 170.1 * 1,000 milligrams = 170,100 milligrams

So, a recipe calls for 170,100 milligrams of raisins.

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Answer:

A recipe calls for 170,100 milligrams of raisins.

Step-by-step explanation:

I took the exam and got it right

Answer: X[12)

Step-by-step explanation:

-6x+9<2-5(x+1)

-6x+9<-5(x+1)+2

-6x+9<-(5x+5)+2

The earliest finish time for the activity 10-11(far right-hand side) is 23 if the earliest start time of activity 8-10 and activity -10 is 12 and 13 respectively.

The depicted graph represents the critical path method(CPM)

Given,

Earliest start time of 8-10 = 12

Earliest start time of 9-10 = 13

From the network, it is observed that at 10, two networks are connecting, we need to take the largest earliest finish time from both the activities as earliest start time for 10-11.

Earliest finish time = earliest start time + activity duration

Earliest finish time for 8-10 = 12+4=16

Earliest finish time for 9-10 = 13+2=15

From above two times, 8-10's earliest finish time is the greatest. So, consider 16 as earliest start time for 10-11.

Now,

Earliest finish time for 10-11= earliest start time + activity duration=16+7=23

Thus, the earliest finish time for 10-11 is 23.

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Answer:

7x

Step-by-step explanation:

When combining like terms, you keep the bases the same and add the constants.

the "x's" are the base and the constants are 5 and 2:

(5 + 2)x = 7x

Given any set of seven integers there are no two numbers that have same remainder when divided by 6.

The remainder is the value left after the dividion. If a number is not completely divisible by another number then we are left with a value once the division is done. This value is called the Remainder.

Given any set of seven integers, there must be at least two numbers that have same remainder when divided by 6.

So there can be six remainders when divided by 6 i.e. 0,1,2,3,4 and 5.

According to the Piegeonhole principle,

in any set of seven integers two must have the same remainder when divided by seven.

Consider the set of integers 0,1,2,3,4,5 and 66. All of these have different remainders upon division by 8.

Hence there need not be two numbers such that they have same remainders when divided by 6.

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Answer:

88

Step-by-step explanation:

No. For example, thirteen hearts could be selected: 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A. No two of these are of the same denomination.

What is a denomination?

A denomination is a classification system that identifies the nature or worth of an object. Denomination frequently relates to currency.

Here, we have

13 cards are randomly selected from a standard 52-card deck.

This is not necessary.

All 13 cards may be of different denominations.

At least 2 need not be of the same denomination.

Hence, thirteen hearts could be selected: 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A. No two of these are of the same denomination.

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Answer:

Without knowing the values of the variables in the given expression, it is impossible to determine the value of the expression. In general, the expression is a combination of a number (A), two variables (b and c), and an exponent (2). The value of the expression will depend on the values of these variables and the operations that are performed on them. For example, if A=3, b=2, and c=4, then the value of the expression would be:

(3^2 * 2 * 4^2) - 5

Which is equal to 29. However, if the values of the variables were different, then the value of the expression would also be different. Therefore, it is impossible to determine the value of the expression without knowing the values of the variables.

Step-by-step explanation:

Answer:

(3^2 * 2 * 4^2) - 5, hope it helps.

Answer:

k=7

Step-by-step explanation:

k*3-9=12

3k-9=12

3k=12+9

3k=21

k=[tex]\frac{21}{3}[/tex] cross out 21 and 3

k=7

A Rubik's Cube puzzle variation is called Square-1. You must be familiar with the fundamental notation used to denote the puzzle's various moves and positions in order to read the puzzle.

The face serves as the fundamental unit of notation in Square-1. A Square-1 puzzle has four faces, and each face is identified by a letter: U denotes the top face, D the bottom face, F the front face, and B the back face.

You must specify the face you are turning and the direction you are turning it in order to signify a move. For instance, a move like "U" turns the top face in a clockwise direction, whereas "U'" turns it in a counterclockwise direction.

You can adjust the puzzle with a few more complex moves in addition to the fundamental ones. For instance, the move "r" denotes moving the right face in a clockwise direction, while "r'" denotes turning it in a counterclockwise direction.

You can manipulate the problem to find the solution by combining these movements and employing them in various combinations. Reading and utilizing the notation for Square-1 requires effort, but with persistence and time, you may learn to solve the puzzle fast and effectively.

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The given events A and B are not independent events.

What is probability?

As there is no information given on the probability if selecting Box 1 and Box 2, thus we assume the event of selecting any of the boxes as equi-probable

P(A) = 1/2 * 3/11 + 1/2 * 2/3 = 31/66

P(B) = 1/2

P(A|B) = 2/3

Thus, we can see that P(A|B) is not equal to P(A)

So, the events A and B are not independent events.

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Answer:

A ; B ; D

Step-by-step explanation:

5t + 9

for commutative property

9 + 5t

5t = 5 x t

5 · t + 9

(5 x t) + 9

The distance between the ships changing at 3.00 p.m is 12.2 mile/mph.

What do you mean by differentiation?

A derivative of a function with respect to an independent variable is what is referred to as differentiation. Calculus's concept of differentiation can be used to calculate the function per unit change in the independent variable.

A function of x would be y = f(x). Next, the formula for the rate of change of "y" per unit change in "x" is as follows:

dy / dx

It is given that ship A is 8 miles west of ship B and ship a is sailing north at 10mph and ship b is sailing south at 7mph

Let x and y be the initial position of the ships A and B

Let  x be the distance between A and x

y as the distance between B and x

z as the distance between A and B

Using pythagoras theorem,

[tex]z^{2} =x^{2} +y^{2}[/tex]

Differentiating both sides wrt t,

2z dz/dt = 2x dx/dt + 2y dy/dt

Divide the equation by 2

z dz/dt = dx/dt + dy/dt --- (1)

dx/dt = 10 mile/mph

dy/dt = 7 mile/mph

When t = 3 hours,

x = 30, y = 21 and

z = [tex]\sqrt{x^{2} +y^{2} }[/tex]

Substituting the values

z = √([tex]30^{2} +21^{2}[/tex])

z = √(900 + 441)

z = √1341 = 36.6

Substituting it in equation (1)

36.6 dz/dt =30×10+ 21×7

dz/dt = 447/36.6

dz/dt = 12.2 mile/mph

Therefore, the distance between the ships changing at 3.00 p.m is 12.2 mile/mph.

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Answer: Yes, he is correct

Step-by-step explanation:

[tex]\frac{1}{3}*\frac{2}{2}=\frac{2}{6} +\frac{1}{6}=\frac{3}{6}[/tex] The (*) means x or multiply

The original activity of the sample can be calculated using the equation A=A0e^(-kt), where A0 is the initial activity, k is the decay constant, and t is the elapsed time.

1. Identify the given values: Half-life (t1/2) = 3.8 days, Activity level (A) = 0.17 bq/L, and Elapsed time (t) = 5.0 days.

2. Calculate the decay constant (k) using the equation k = ln(2)/t1/2.

k = ln(2)/3.8 days

k = 0.1815

3. Calculate the original activity (A0) using the equation A0 = A/e^(-kt).

A0 = 0.17 bq/L/e^(-0.1815)

A0 = 0.21 bq/L

Therefore, the original activity of the sample was 0.21 bq/L.

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The numbers in the increasing order are:

(x-1)>(x+1)>(x+2)

In mathematics, factorization is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. The factorization of the integer 12, for instance, might be represented as 3 times 4. In the context of integers, factorization was first studied by Greek mathematicians. They established the basic theorem of mathematics, which states that every positive integer can be factored into a product of prime numbers but cannot be factored further into integers larger than 1. Up to the order of the factors, this factorization is also distinct.

It has also been studied for ages how to factor polynomials.

The given equation is:

x³+2x²-x-2

Now, we have to do factorization for the given equation.

(x+1)(x²+x-2)

(x+1)(x²+2x-x-2)

(x+1)(x(x+2)-1(x+2))

(x+1)(x-1)(x+2)

This is the factorized form of the given equation.

Therefore, the numbers in the increasing order are:

(x-1)>(x+1)>(x+2)

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The answer to this Question based on Linear equation is 28 and 45

What is Linear Equation?

It is a equation in which the degree of each and every variable is 1 only is called linear equation

Solution:

Let the time taken to complete maths homework be x and time to complete science homework be y

first we know that total time taken was 1 hr 15 minutes means 75 minutes which in turn means x + y = 75

and from 2nd relation that we are given

x = 2y - 9

now we got the 2 linear equations now we just need to solve them to get our final answer

putting this equation in first equation we got we get

2y - 9 + y = 75

3y - 9 = 75

3y = 84

y = 28

and hence x = 2y - 9

x = 56  - 9

x = 45

hence time to complete maths was 45 minutes and time to complete science is 28 minutes

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The first step is converting both the velocity and the wind in vector form, as follows:

Then the true speed of the plane is given by the addition of these two vectors, as follows:

[tex]\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}[/tex]

The magnitudes of each vector are given as follows:

The angle between these two vectors is given as follows:

[tex]\theta = 100^\circ - 42^\circ = 58^\circ[/tex]

Thus the resulting speed is obtained as follows:

[tex]\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54[/tex]

The resulting angle of the plane is then obtained as follows:

[tex]\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)[/tex]

Hence:

[tex]\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)[/tex]

[tex]\angle = 59.87^\circ[/tex]

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Answer:

  197.5 km/h

Step-by-step explanation:

You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.

A vector calculator makes short work of this. The resultant speed is ...

  197.5 km/h at 92.6°

The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...

  180° -(100° -42°) = 122°

So, the resultant speed is ...

  c = √(a²+b²-2ab·cos(C))

  = √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13

  c ≈ 197.543

The true speed of the plane is about 197.5 km/h.

__

Additional comment

You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.

When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.

Muscular strength can be measured based on the amount of weight lifted.

Muscular strength can be measured based on the amount of weight lifted. The upper-body and lower-body strength are measured separately. Muscular strength is typically measured which is known as a One Rep Max (1RM).

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If your data analysis shows that there is a chance that a hypothesis is false, the standard practice is to reject it. It is b). False.

Scientists can either reject the null hypothesis (which implies that there is a clear, causal connection between the two observations) or. not proving the null hypothesis (meaning the test has not identified a consequential relationship between the two phenomena). If the test statistic is greater than the crucial value in an upper-tailed test, the decision rule requires that researchers reject H0.

If the test statistic is less than the crucial value in a lower-tailed test, the decision rule requires that the investigators reject H0. Checking for sufficient evidence to refute the null hypothesis is the aim of hypothesis testing. To determine whether there is sufficient evidence to reject the null hypothesis, in other words. If there is insufficient support, we cannot rule out the null hypothesis.

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The price of new car is reduced by $825 from the original price $12,500 which implies the price of car after reduction is $11,625 i.e

The percentage reduction is 7 .

Percentage is calculated by dividing the value by total value and then multiply with 100.

We have given that,

The price of a new car = $12,500

After the some reduction in price

then the price of car = $11,625

The reduction in total price of car = original price - price after reduction

= $12,500 - $11,625

= $875

Now, we have to calculate the reduction of price in percentage.

Using the percentage reduction formula,

P% = (original price - price after reduction )× 100 /original price

=> percentage reduction = ( 875/12500)×100

=> percentage reduction = 875/125 = 7

Hence, the reduction is 7% .

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There are "P(20, 10) - P(15, 10)" options (ways) to distribute the coupons so that at least one woman receives a coupon.

What do you mean by permutation?

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

There are P(20, 10) ways to distribute the coupons if they are different, with the only restriction being that no more than one coupon can be given to a shopper. To ensure that all of the coupons go to the guys, there are P(15, 10) ways to distribute them. In order to ensure that at least one coupon is given to a woman, there are P(20, 10) - P(15, 10) options to distribute the coupons.

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Complete Question

10 coupons are given to 20 shoppers in a store. Each shopper can receive at most one coupon. 5 of the shoppers are women and 15 of the shoppers are men.

If the coupons are different, how many ways are there to distribute the coupons so that at least one woman receives a coupon?

The largest product we can get is: 26244,

What is integers?

Integers are whole numbers that are either positive, negative, or zero. They are the building blocks of the number system and are used to represent quantities or perform calculations. Integers are represented in the form of digits and can either be written in the form of standard numbers, Roman numerals, or in the form of exponential notation. Integers are used in many areas of mathematics and are a fundamental concept in the study of algebra, geometry, and calculus. Integers are also used in everyday life, such as in accounting and finance, where they represent monetary values.

We know that for 28,
(k-2)*2 <= k
2k-4 <= k
k <= 4

So, we should only consider numbers less than or equal to 4.

Now, 4 can be replaced by 2*2 and there is no point in taking 1 since it will not increase product result.

So, we are left with 2 and 3. Some possible solutions are:

{3,3,3,3,3,3,3,3,2,2} or {3,3,3,3,3,3,2,2,2,2,2} etc.

Out of all these, the maximum product we can get is from {3,3,3,3,3,3,3,3,2,2} which is: 26244

So, The largest product we can get is: 26244

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