Write the
following in
slope-intercept
form:
7x - 2y = -6

1) Number sense, arithmetic operations, algebra, geometry, data analysis, and probability are some of the topics that are commonly covered in math classes.

The need of developing problem-solving and procedural fluency skills is underlined. To ensure they have a solid basis for future learning, students may also receive training on arithmetic concepts they missed in earlier grades.

2) The use of real-world issues, direct education, cooperative learning, and the use of technology to aid learning are some particular methods of mathematical instruction that are encouraged.

Additionally, emphasis is placed on encouraging a growth mentality and a positive attitude toward mathematics.

3) Direct instruction, visual aids like graphs and diagrams, manipulatives and hands-on activities, scaffolding, and systematic review and practice are some specific techniques used to teach fundamental mathematical instruction.

In order to promote critical thinking and the growth of students' problem-solving abilities, teachers may also employ questioning strategies.

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Answer:

c ik this because I took the same question as you

The product of the given algebraic expression is \(\frac{4}{(x-1)}\).

The given expression is \(\frac{8x+8}{x^2-2x+1} .\frac{x-1}{2x+2}\).

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Here, \(\frac{4(2x+2)}{x^2-1x-1x+1} \times \frac{x-1}{2x+2}\)

= \(\frac{4(2x+2)}{x(x-1)-1(x-1)} \times \frac{x-1}{2x+2}\)

= \(\frac{4(2x+2)}{(x-1)(x-1)} \times \frac{x-1}{2x+2}\)

Cancel the same factors, that is

= \(\frac{4}{(x-1)} \times \frac{1}{1}\)

= \(\frac{4}{(x-1)}\)

Therefore, the product of the given algebraic expression is \(\frac{4}{(x-1)}\).

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To solve inequalities we proceed as usual as when solving equations, we need to isolate the variable to one of the sides of the inequality.

The solution of the inequality includes all number that are greater than 3.

Answer:

Step-by-step explanation:

the numerical coefficient of x2 here is 3.

Answer:3/4

Step-by-step explanation:

1) The square root of 8 is the least, since 3^2 equals 9, and 8 is less than 9, so its the least.

2) Then the cube root of 27, because 3 cubed is equal to 27

3) Finally, pi is the largest since it equals 3.142.

Good luck with your grades.

root 8 < pi < cube root 27

The number of small boxes purchased = 4

and the number of large boxes purchased = 9

According to the given question, a contractor needs to buy nails to build a house.

The nails come in small boxes and large boxes. Each small box has 50 nails and each large box has 350 nails. The contractor bought a total of 13 boxes that have 3350 nails altogether.

Let x be the number of small boxes and y be the number of large boxes.

The contractor bought a total of 13 boxes that have 3350 nails altogether.

x + y = 13                     ...............(1)

50x + 350y = 3350              ..........(2)

We solve above system of equations.

From equation (1),

x = 13 - y             ...........(3)

Substitute x = 13- y in equation (2)

50(13 - y) + 350y = 3350    

650 - 50y + 350y = 3350

300y = 2700

y = 9

Substitute above value of y in equation (3),

x = 13 - 9

x = 4

Therefore, the number of small boxes purchased = 4

and the number of large boxes purchased = 9

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Answer:

There are 24 more trumpet players than clarinet players

Step-by-step explanation:

The given information are;

The recursive rule or the number of band members in a row is f(n) = f(n - 1) + 8

Where f(1) = 13

The members of the band players in row 1 = The clarinet players

The members of the band players in row 4 = The trumpet players

Therefore, the number of clarinet players = f(1) = 13

The number of band members in row 2, f(2)  = f(1) + 8 = 13 + 8 = 21

The number of band members in row 3, f(3)  = f(2) + 8 = 21 + 8 = 29

The number of band members in row 4, f(4)  = f(3) + 8 = 29 + 8 = 37

Therefore, given that the trumpet players are in row 4, the number of trumpet players = The number of band members in row 4 = 37 Trumpet players

The difference in the number of trumpet and clarinet = The number of more trumpet players than clarinet players = 37 - 13 = 24 more trumpet players than clarinet players

There are 24 more trumpet players than clarinet players.

Answer:

120 degrees.

Step-by-step explanation:

π radians = 180 degrees

so 2π/3 radians = 180 * 2/3 = 120 degrees.

The volume of the solid bounded by the given surfaces is 2πV/5 √27.

To compute the volume of the solid bounded by the surfaces x² + y²= 27, z = 0, and z = Vx² + y², we can use a triple integral.

We'll integrate over the region R in the xy-plane defined by x² + y² ≤ 27, and for each point (x, y) in R, we'll integrate from z = 0 to z = V(x² + y²).

The volume V is given by the triple integral:

V = ∬R ∫[0, V(x² + y²)] dz dA

Using polar coordinates to simplify the integration, we can express x and y in terms of r and θ:

x = r cos θ

y = r sin θ

The bounds for r and θ are as follows:

0 ≤ r ≤ √27 (since x²+ y² ≤ 27)

0 ≤ θ ≤ 2π (covering the entire circle)

The integral becomes:

V = ∫[0, 2π] ∫[0, √27] ∫[0, Vr²] r dz dr dθ

Integrating with respect to z and applying the limits:

V = ∫[0, 2π] ∫[0, √27] Vr\(^{(3/2)}\) dr dθ

Integrating with respect to r:

V = ∫[0, 2π] [V/5 √27] dθ

Evaluating the integral with respect to θ:

V = V/5 √27 [θ] evaluated from 0 to 2π

Since the difference of the upper and lower limits is 2π:

V = V/5 √27 [2π - 0]

V = V/5 √27 (2π)

Simplifying:

V = 2πV/5 √27

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Sample space of randomly selecting a US state is 50, the probability that the US state begins with M is 4/25, and the probability that it doesn't begin with a vowel is 2/5.

a. What is the sample space?The sample space for randomly selecting one of the 50 US states is 50, i.e., the list of the 50 states.

b. What is the probability that it begins with M?The number of states that begin with M is 8. Therefore, the probability that the randomly selected US state begins with M is 8/50 or 4/25.

c. What is the probability that it doesn't begin with a vowel?There are 20 US states that don't begin with a vowel. Therefore, the probability that a randomly selected US state doesn't begin with a vowel is 20/50 or 2/5.

Randomly selecting a US state requires knowing the sample space, which in this case is 50. A sample space represents all possible outcomes of a random experiment. Therefore, the sample space for this problem represents the list of all 50 US states that can be randomly selected. The probability that a randomly selected US state begins with M can be calculated by dividing the number of states that begin with M by the total number of states. There are 8 US states that begin with M, hence, the probability of selecting a state that begins with M is 8/50 or 4/25. Finally, the probability that the randomly selected US state doesn't begin with a vowel is 20/50 or 2/5.

In conclusion, the sample space of selecting a US state randomly is 50, the probability that it begins with M is 4/25, and the probability that it doesn't begin with a vowel is 2/5.

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Answer:

Step-by-step explanation:

The volume of water in a pool can be calculated using the following formula:

Volume (in gallons) = Length (in feet) x Width (in feet) x Average Depth (in feet) x 7.5

For example, if your pool is 20 feet long, 15 feet wide, and has an average depth of 5 feet, the volume of water in your pool would be:

20 x 15 x 5 x 7.5 = 5625 gallons

Note: If you prefer metric units, the formula for volume in liters would be:

Volume (in liters) = Length (in meters) x Width (in meters) x Average Depth (in meters) x 1000

It's important to note that this formula assumes a standard rectangular or square pool shape. If your pool has a more complex shape, you may need to measure the volume in smaller sections and add the volumes together to get the total volume.

The vertical component of velocity can be zero at specific points in the motion of an object.

What is Velocity?

Velocity is a vector quantity that describes the rate of change of an object's position in space over time. It is defined as the displacement of an object divided by the time interval during which the displacement occurred.

The vertical component of velocity can be zero at specific points in the motion of an object. This occurs when the object reaches the highest point in its vertical motion and begins to fall back down. At this point, the vertical component of velocity changes direction from upward to downward, and its magnitude becomes zero. This moment is known as the "instant of maximum height" or "instant of maximum altitude." Beyond this point, the vertical component of velocity becomes negative, indicating that the object is moving downward.

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The distribution of the sample mean can be represented as: X ~ N(67.15, 3.084/√30)

The distribution of the sample mean is a normal distribution with a mean equal to the population mean µ and a standard deviation equal to the population standard deviation σ divided by the square root of the sample size n.

Therefore, for this problem, the distribution of the sample mean can be represented as:

X ~ N(67.15, 3.084/√30)

where X is the sample mean, N represents a normal distribution, 67.15 is the population mean, 3.084 is the population standard deviation, and √30 is the square root of the sample size.

This distribution assumes that the sample is randomly selected from the population and the sample size is large enough to satisfy the central limit theorem.

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Answer:

fifth option is the correct ans

sin(thita) = -sqare root 2 / 2

The statements which are true are,

The measure of reference angle is 45° and tan (θ) = -1.

Reference number associated with t is defined as the shortest distance from the x axis to the terminal point t, along a unit circle.

Reference angle is shortest angle measure from the X axis to the terminal side of the angle.

Reference angle = 2π - 7π/4 = π/4 = 45°

We have,

7π/4 = 2π - π/4

We also know that,

cos(2π - x) = cos x,

sin (2π - x) = -sin x

tan (2π - x) = -tan x

So, using theses identities,

cos (7π/4) = cos (2π - π/4) = cos(π/4) = 1/√2

sin (7π/4) = sin (2π - π/4) = -sin (π/4) = -1/√2

tan (7π/4) = tan (2π - π/4) = -tan (π/4) = -1

Hence the true statements are The measure of reference angle is 45° and tan (θ) = -1.

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The area of the hub cap, with a circumference of 78.00 centimeters, is approximately 483.62 square centimeters.

To find the area of the hub cap, we need to know the radius of the hub cap. We can use the formula for the circumference of a circle to find the radius, and then use the formula for the area of a circle to calculate the area.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. In this case, the circumference is given as 78.00 centimeters. Plugging in the values, we have:

78.00 = 2πr

To find the radius, we can solve for r:

r = 78.00 / (2π) ≈ 12.42 centimeters

Now that we have the radius, we can find the area using the formula A = πr^2:

A = π(12.42)^2 ≈ 483.62 square centimeters

Therefore, the area of the hub cap is approximately 483.62 square centimeters.

If the circumference of the hub cap were smaller, it would mean the radius would be smaller as well. As the radius decreases, the area of the hub cap would also decrease.

This is because the area of a circle is directly proportional to the square of its radius. So, a smaller circumference would result in a smaller area.

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Answer:

a ) -1

Step-by-step explanation:

\(\frac{1}{64} = 4^{2s-1} . 16^{2s+2}\\ 4^{-3} = 4^{2s-1+4s+4}\\ 4^{-3} = 4^{6s+3}\\ 6s + 3 = -3\\6s = -6\\s = -1\)

To find the normal approximation of the probability between 80 and 90 successes in 140 trials with a success probability of 0.8, we can use the normal approximation to the binomial distribution.

In this binomial experiment, we are interested in finding the probability of having between 80 and 90 successes (inclusive) out of 140 trials, given a success probability of 0.8. To approximate this probability, we can use the normal approximation to the binomial distribution.

First, we calculate the mean and standard deviation of the binomial distribution. The mean (μ) is given by μ = n * p, where n is the number of trials (140) and p is the success probability (0.8). The standard deviation (σ) is calculated using the formula σ = sqrt(n * p * (1 - p)).

Next, we can approximate the probability by transforming the binomial distribution into a standard normal distribution. We standardize the values of 80 and 90 using the z-score formula, z = (x - μ) / σ, where x is the number of successes.

Finally, we use the standard normal distribution table or a calculator to find the probabilities associated with the z-scores corresponding to 80 and 90. The difference between these probabilities gives us the approximate probability of having between 80 and 90 successes in 140 trials.

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Answer:

the first one

Step-by-step explanation: it worked for me i passed it

Answer:

Step-by-step explanation:

Total number of oranges:

Number of baskets:

Mean of the distribution of oranges:

Correct choice is d

Answer:

1.71 pounds of sugar per dollar.

Step-by-step explanation:

To calculate how many pounds of sugar Keisha got per dollar, we divide the total amount of sugar by the total amount of money spent. In this case, she bought 12 pounds of sugar for $7, so we divide 12 by 7:

12 ÷ 7 = 1.71

So, Keisha got 1.71 pounds of sugar per dollar.

Answer:

vertical

adjacent

linear

Step-by-step explanation:

Answer:

a) 25830

b)9975

Step-by-step explanation:

a) 287

x 90

25830

b) 105

x 95

9975

Answer:

Step-by-step explanation:

Here you go mate

Step 1

(-4x-3)-(7x-3) =22​  Equation

Step 2

(-4x-3)-(7x-3) =22​  Simplify

-11x=22

Step 3

-11x=22  Divide

Answer

x=-2

Now we have to,

→ find the required value of x.

Then the value of x is,

→ (-4x - 3) - (7x - 3) = 22

→ -4x - 3 - 7x + 3 = 22

→ -11x + 0 = 22

→ x = -22/11

→ [ x = -2 ]

Thus, the value of x is -2.

Answer:

<C=101° and <E=46°

Step-by-step explanation:

Both Being co-interior angles....

Answer:

4+28x

_____

7x

i think...

Answer:

3.2 × 10^-13

Step-by-step explanation:

The integral diverges as the lower bound approaches 0. In conclusion, evaluating the integral of the function \(4/(16t^2)\) with respect to t from 0 to 4 is not possible, as it diverges.

Hi! I understand you want me to help you evaluate the integral of the given function. To evaluate the integral of the function \(4/(16t^2)\) with respect to t from 0 to 4, follow these steps:

1. Simplify the function: \(4/(16t^2) \  can \ be \ simplified \ to  1/(4t^2).\)

2. Integrate the simplified function with respect to\(t:\int\limits(1/(4t^2)) dt.\)

3. To integrate \(1/(4t^2)\), use the power rule: ∫\((t^n) dt = (t^{(n+1)})/(n+1)\). In this case, n = -2.

4. Apply the power rule: ∫\((1/(4t^2)) dt\) = (1/4)∫\((t^-2) dt = (1/4)((t^{(-1)})/(-1)).\)

5. Now evaluate the integral from 0 to 4:\([(1/4)((4^{(-1)})/(-1)) - (1/4)((0^{(-1)})/(-1))].\)

6. Simplify and calculate: [(1/4)(1/(-4)) - (1/4)(undefined)]. Since 0^(-1) is undefined, we have an improper integral.

Since the integral is improper, we need to take a limit:

7. Evaluate the limit as the lower bound approaches 0: lim(a->0)\([(1/4)((4^{(-1)})/(-1)) - (1/4)((a^{(-1)})/(-1))].\)

8. Calculate the limit: lim(a->0)[(-1/16) - (1/(-4a))].

9. As a approaches 0, the second term approaches infinity: lim(a->0)(1/(-4a)) = -∞.

Thus, the integral diverges as the lower bound approaches 0. In conclusion, evaluating the integral of the function \(4/(16t^2)\) with respect to t from 0 to 4 is not possible, as it diverges.

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