What is the equation of the line that passes through the point (-4, 2) and has a
slope of —2?

Answer:

2,4 possibly

Step-by-step explanation:

if its V (intersection) W

then its 2,4

if it has something to do with patterns then i dont know

The slope of the line = rise/run = 2/3.

The slope of a line is a measure of how steep the line is and it is usually represented by the letter "m". The slope can be found using the rise and run of the line. The rise is the vertical distance between two points on the line and the run is the horizontal distance between the same two points.

The slope of a line is equal to the rise divided by the run. It is often represented as m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the line.

For example, if you have a line that goes from point (3,5) to point (7,11), the rise would be 6 (11-5) and the run would be 4 (7-3), therefore the slope of the line would be 6/4 = 1.5

Given the graph above, the rise of the line is the blue line = 2 units.

The run is the red line = 3 units.

Slope (m) = rise/run = 2/3.

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Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

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The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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Notice that 47=40+7; therefore, Josh receives $10.73 for each one of the first forty hours and 1.5*$10.73 for the remaining 7 hours; algebraically,

Thus, the answer is $541.87

Answer:

5%

Step-by-step explanation:

DIvide 4 by 79

Answer:

Step-by-step explanation:

h^2=x^2+y^2, here x and y are equal so we can say

h^2=2x^2, we see that h=2(2^(1/2)) so

2x^2=8

x^2=4

x=2

Answer:

8.8 lbs per days

Step-by-step explanation:

There are 7 days in one week

28/7 = 4 kg per day

Change this to pounds

4 kg * 2.2 lbs/1 kg = 8.8 lbs per days

Answer:

D

Step-by-step explanation:

a) An expression for the number of bacteria after t hours - \(50e^{0.8t}\)

b) The number of bacteria after 7 hours, P(7)=13521.320

c) The rate of growth (in bacteria per hour) after 7, P(t)=1081.705

d) The population will reach 250,000 after - 4.6hours.

a)The exponential growth model is \(P = P_{0} e^{rt}\)

Where,

\(P_{0}\) = Initial growth

r = growth rate

t = time period

It is given that initially cells, \(P_{0}\) = 50

time period, t = 1.5 hours

Population after t = 1.5 hours is , P =875

Substitute the given values in the growth exponential model:

      875 = \(50 e^{r * 1.5}\)

 ⇒  \(\frac{875}{50}\) =  \(e^{r * 1.5}\)

 ⇒ 17.5 = \(e^{r * 1.5}\)

 ⇒ log (17.5 ) = log (\(e^{r * 1.5}\) )

 ⇒ log (17.5 ) = 1.5r

 ⇒ 1.24 = 1.5r

 ⇒ r = \(\frac{1.24}{1.5}\)

    r = 0.8%

Thus, P(t) = \(50e^{0.8t}\)

b) Number of bacteria after 7 hours is calculated as follows:

    P(7) = \(50 e^{0.8 * 7}\)

    P(7 ) = 13521.320

c) The rate of growth (in bacteria per hour) after 7 hours:

  P(t) = \(50e^{0.8t}\)

Differentiate w.r.t :

  P(t) = 50 × \(0.8e^{0.8t}\)

       = 50 × \(0.8e^{0.8 * 7}\)

      = 1081.705

d) The population at time t is P(t) = 250000

     250000 = \(50e^{0.8t}\)

  ⇒   \(\frac{250000}{50}\)  =\(e^{0.8t}\)

  ⇒  5000 = \(e^{0.8t}\)

 ⇒ 0.8t = 3.7

 ⇒  t = 4.6

a) An expression for the number of bacteria after t hours - \(50e^{0.8t}\)

b)The number of bacteria after 7 hours, P(7) = 13521.320

c) The rate of growth (in bacteria per hour) after 7, P(t) =  1081.705

d) The population will reach 250,000 after - 4.6hours.

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When the value of p is - 1, then p- 1 ≤ 0.5 is the required inequality.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

We have the inequalities;

(A). p- 1 ≤ 0.5

When p = -1,

-2  ≤ 0.5.

(B). -p - 1 ≤ -0.5

When p = -1,

0  ≤ -0.5.

This is contradiction.

(C).  p - 1 ≥ 0.5

When p = -1,

-2  ≥ 0.5.

This is contradiction.

(D). -p -1 ≥ 0.5

When p = -1,

0  ≥ 0.5.

This is contradiction.

Therefore, p- 1 ≤ 0.5 is the required inequality.

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The complete question:

Which inequality is true when the value of p is -1?

(A). p- 1 ≤ 0.5

(B). -p - 1 ≤ -0.5

(C).  p - 1 ≥ 0.5

(D). -p -1 ≥ 0.5

Answer:

5/6 is the probability

Step-by-step explanation:

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and rolling a 6-sided die you can get 1, 2, 3, 4, 5, 6 so 5 is the only thing you can roll that isn't a factor of 24 so

Answer:

x = 60°

Step-by-step explanation:

      A circle, or "all the way around," is 360°

      The square represents 90°

360° = 90° + (2x - 10)° + (2x + 40)°

360° = 90° + 2x° - 10° + 2x° + 40°

360° = 2x°+ 2x° + 40° + 90° - 10°

360° = 4x° + 120°

240° = 4x°

60° = x

x = 60°

Answer:

x = -12

m∠FCD = 29°

Step-by-step explanation:

Finding x:

Since m∠BCD = 95°, we can find x by the sum of the measures of angles BCF and FCD equal to 95:

m∠BCF + m∠FCD = m∠BCD

x + 78 + x + 41 = 95

(2x + 119 = 95) - 119

(2x = -24) / 2

x = -12

Thus, x = -12

Finding m∠FCD:

Now, we can find m∠FCD by plugging in -12 for x in x + 41:

m∠FCD = x + 41

m∠FCD = -12 + 41

m∠FCD = 29

Thus, m∠FCD = 29°

A triangular prism is a prism which has both of its base sides as a rectangle. The length of side AB is 5/(√2) cm.

Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.

Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

The area of AEDC is 25 cm². Therefore,

AEDC = AC²

25 cm² = AC²

AC = 5 cm

In ΔABC,

AB² + BC² = AC²

Since AB=BC,

2(AB²) = AC²

AB² = 25/2

AB = 5/√2 cm

Hence, the length of side AB is 5/(√2) cm.

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Answer:

a)0.7 is greater than>0.52

b)0.52 is greater than>0.045

c)0.49 is less than<0.94

d)0.302 is greater than>0.23

e)0.9 is greater than>0.6

f)2.36 is less than<3.19

The steps to conduct the steps of hypothesis testing on these data are:

The hypothesis will be:

Since we are comparing (GPAs) of three groups (students who check e-mail day by day, students  who check mail at least 2x a week, and students who check mail less than 2x a week), one can be able to make use of one-way analysis of variance (ANOVA) as the fitting test measurement.

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Answer: 3

Step-by-step explanation: This is the average between your 2 numbers, 4 and 2.

Answer: its 2

Step-by-step explanation: i guessed and i got it right after this other dud said 3....ITS 2

Answer:

what is the question yaaar

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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Answer:1. 12:6         equivalant ratio:24:12

Step-by-step explanation:

12:6 means twelve to 6 and to find a equivalant ratio means to find a number that 12 and 6 can equal so it would be 24:12 which i multiplied by 2.

Answer:

14 1/3

Step-by-step explanation:

Answer:

17 1/4

Step-by-step explanation:

Separate the numbers: 9+7/2+4+3/4

Solve whole numbers: 9+4=13

Solve fractions: 7/2+3/4=?

Find LCD of 7/2 and 3/4: LCD:4

Solve: 14/4+3/4=17/4

Turn 17/4 to mixed number: 17/4=4 1/4

Add all together: 13+4+1/4= 17 1/4

4292

Step-by-step explanation:

there happy that was easy to be honest

If f(x,y,z) is a vector field rather than a scalar function. A vector-valued function is one that has a vector value and a calculable curl. Therefore, if we calculate this value, it will once more be a vector-valued function. The right response in this case is option B.

The following considerations must be made in order to answer this question: It is specified that the divergence of a vector field is a scalar-valued function.

A vector field's specified and actual curl is a vector field. A scalar field's divergence/Curl is not specified. A scalar field's gradient is a vector field that has a definite definition. A vector field's gradient is not known.

Since F is a vector-valued function, we may discover its divergence, which will be a scalar-valued function, and since the gradient of the scalar-valued function will be a vector-valued function, this calculation is attempting to compute the gradient of the divergence of the vector field F.

Complete question:

Let f(x,y,z) be a scalar-valued function, and F(x,y,z) be a vector field. Is the following defined? If it is defined, is it a scalar-valued function or a vector field? (You are only allowed one attempt for each part of this problem.)

(a) V (Vn Defined- it is a scalar-valued function O Defined - it is a vector field O Not defined

(b) VV F) O Defined - it is a scalar-valued function Defined - it is a vector field O Not defined

(c) V (V F) Defined it is a scalar-valued function Defined - it is a vector field Not defined

(d) V (V x F) Defined it is a scalar-valued function Defined it is a vector field Not defined

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Answer:

Collect the like terms

Step-by-step explanation:

(3x-5x)

3x (-2x) + 2 = -8

Answer:

Step-by-step explanation:

You times the number by itself so 5x5 is 25

Next one, 2 x 2 x 2 x 2 is 16

Third one,  3x3x3 is 27

Next one, 1x1x1x1x1x1 is 1

So it is 1, 2, 5, 3

Hope this helps :)) Have a nice day! :)

The number of codes that can be made using the 5 letters given is 120 as calculated using permutation and combination.

Now when no letters are repeated:

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 3 options , fourth digit has 2 options and the final digit will have only 1 option left.

So total number of codes = 5 × 4 × 3 × 2 × 1 = 120 codes

if letters can be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 5 options , third digit has 5options , fourth digit has 5 options and the final digit will have only 5 options also.

So total number of codes = 5 × 5 × 5× 5× 5= 3125 codes

if adjacent letters cannot be repeated

5 letter codes to be made.

Possible options for each space = 5

so first digit has 5 options, second digit has 4 options , third digit has 4 options , fourth digit has 4 options and the final digit will have only 4 options also.

So total number of codes = 5 × 4 × 4× 4× 4 = 1280 codes

Hence the total number of codes as calculated by permutation and combination is 1280.

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Answer:

its 5

Step-by-step explanation:

with a y intercept of -4