Find the equation of a line parallel to y=−7+4x that passes through the point (-2,-1)

The sum of the first 6 terms of the geometric sequence 3, -6, 12, -24, ... is -3.

The first 6 terms of the geometric sequence 3, -6, 12, -24, ... can be calculated using the formula for the nth term of a geometric sequence:

\(a_n = a_1 * r^{(n-1)}\)

where a_1 is the first term, a_n is the nth term, r is the common ratio, and n is the term number.

For the given sequence, a_1 = 3 and r = -2, so the first 6 terms can be calculated as follows:

\(a_2 = 3 * (-2)^{(2-1)} = -6\\a_3 = 3 * (-2)^{(3-1)} = 12\\a_4 = 3 * (-2)^{(4-1)} = -24\\a_5 = 3 * (-2)^{(5-1)} = 48\\a_6 = 3 * (-2)^{(6-1)} = -96\\\)

The sum of the first 6 terms will be = 3 - 6 + 12 - 24 + 48 - 96 = -3

A geometric sequence is a number sequence in which the ratio of any two consecutive terms is always the same.

A geometric sequence has the following general form: a, ar, ar^2, ar^3,...,

where an is the first term of the sequence and r is the common ratio, which is a fixed number that represents the factor by which each term is multiplied to get the next term.

The formula for calculating the nth term of a geometric sequence is:

a_n = a * r(n-1) where n is the term number.

For more questions on geometric sequence

https://brainly.com/question/1509142

#SPJ4

Answer:

Option B is correct = \(0.3 \times 81\)

Step-by-step explanation:

The complete question is: Which of the following options have the same value as 30% of 81?

Group of choices is:

(A) \(\frac{30}{100}\times 81 \times 100\)

(B) \(0.3 \times 81\)

(C) \(0.03 \times 81\)

(D) \(\frac{3}{10}\times 81 \times 10\)

(E) \(30 \times 81\)

Now, the expression given to us is 30% of 81.

Simplifying the above expression we get;

   30% of 81  =  \(\frac{30}{100} \times 81\)

                     =  \(\frac{3}{10} \times 81\)  =  \(0.3 \times 81\)

Now, we will solve each of the given options and then see which option matches with our calculation.

Option (A) is given;

\(\frac{30}{100}\times 81 \times 100\)  =  \(30 \times 81\)

This doesn't match with our answer, so this option is not correct.

Option (B) is given;

\(0.3 \times 81\)  

This matches with our answer, so this option is correct.

Option (C) is given;

\(0.03 \times 81\)  

This doesn't match with our answer, so this option is not correct.

Option (D) is given;

\(\frac{3}{10}\times 81 \times 10\)  =  \(3 \times 81\)

This doesn't match with our answer, so this option is not correct.

Option (E) is given;

\(30 \times 81\)  

This doesn't match with our answer, so this option is not correct.

Answer:

2

use y2 - y1 / x2 - x1

5 - 1 / 4 - 2 = 4/2 = 2

Answer:

\(2\)

Step-by-step explanation:

1. Find the difference between the two y values. 5 − 1 = 4

  This is usually called the "rise" of the line.

2. Find the difference between the two x values. 4 − 2 = 2

   This is usually called the "run" of the line.

3.  Divide the rise buy the run: \(\frac{rise}{run} = slope \frac{4}{2} = 2\)

Answer:

b - 4 ≤ 15

b ≤ 19

Step-by-step explanation:

The statement "at most" typically means no more than, so the inequality sign would have to be "less than or equal to"

To solve for be all you would do is add 4 to both sides to get b by itself.

b - 4 ≤ 15

b - 4 + 4 ≤ 15 + 4

(-4 + 4 cancels itself out)

(15 + 4 = 19)

b ≤ 19

The volume of the given figure is 1176 cubic cm.

The value of the figure is calculated by multiplying all three side areas. Volume is a measure of the amount of space that an object or a substance occupies. It is typically expressed in cubic units such as cubic meters (m³), cubic centimetres (cm³), or cubic feet (ft³).

The volume of the figure is calculated as,

Volume = 2 ( 15 x 6 + 20 x 6 + 20 x 18 )

Volume = 1176 Cubic cm

Hence, the volume of the figure will be equal to 1176 Cubic cm.

To know more about volume follow

https://brainly.com/question/29568631

#SPJ1

Answer:

12x

Step-by-step explanation:

3x + 4x + 5x

7x + 5x

12x

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

Learn more about box-and-whisker plots on:

brainly.com/question/27849170

#SPJ1

Answer:

6.89

Step-by-step explanation:

Do what's in the parentheses first then the rest and I rounded. Hope this helps!

Answer:

The correct answer is B.

Approximately 200 students received a test score between 70.5 and 80.

The annual interest is $22.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

Given;

Amount invested= $550

Annual interest= 4%

SI= 550*4*1/100

=5.5*4

=22

Therefore, the simple interest will be $22.

Learn more about simple interest here;

https://brainly.com/question/1548909

#SPJ1

After considering the given data we conclude that the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

We have to evaluate the center and angle of rotation to explain the clockwise rotation of the line segment.

So in the first step, we can evaluate the midpoint of the line segment JK and the midpoint of the line segment J'K'. we can calculate the vector connecting the midpoint of JK to the midpoint of J'K'. This vector is (4-1, 1-(-4) = (3,5)

The center of rotation is the point that is equidistant from the midpoints of JK and J'K'. We can evaluate this point by finding the perpendicular bisector of the line segment connecting the midpoints.

The slope of this line is the negative reciprocal of the slope of the vector we just found, which is -3/5. We can apply the midpoint formula and the point-slope formula to evaluate the equation of the perpendicular bisector:

Midpoint of JK: (1, -4)

Midpoint of J'K': (4, 1)

The slope of the vector: 3/5

(x₁ + x₂)/2, (y₁ + y₂) /2

Point-slope formula: y - y₁ = m(x - x₁)

Perpendicular bisector: y - (-4) = (- 3/5)(x - 1)

Applying simplification , we get: y = (- 3/5)x - 1.2

To evaluate the center of rotation, we need to find the intersection point of the perpendicular bisector and the line passing through the midpoints of JK and J'K'. This line has slope ( 3 - (4)) /(4 - 1) = 7/3 and passes through the point (4, 1). Applying the point-slope formula, we can evaluate its equation:

y - 1 = (7/3)( x - 4)

Apply simplification , we get: y = (7/3)x - 17/3

To evaluate the intersection point, we can solve the system of equations:

y =(- 3/5)x - 1.2 = (7/3)x - 17/3

Evaluating for x and y, we get x = -6 and y = -1.

Therefore, the center of rotation is (-6, -1).

√( 4 - 1)² + ( 1 - ( - 4))²) = 5√(2)

Distance between image points and center of rotation

√( ( 6 - (-6))² + ( 3 - (-1))² = 13

The ratio of these distances gives us the scale factor of the transformation, which is 13/√2).

The angle of rotation is negative as the image moves clockwise direction. We can apply the inverse tangent function to find the angle of the vector connecting the midpoint of JK to the midpoint of J'K':

Angle of vector: arctan(5/3) = 59.04 degrees

Therefore, the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).

To learn  more about midpoint formula

https://brainly.com/question/30276996

#SPJ1

A function showing an exponential growth is modelled in the form,

y = Aoe^kt

where k is the rate of growth

If k is negative, then it is the rate of decay and the function would be a decay function

The probability Julian chooses a blue hat is 1/3.

Probability refers to the branch of math which deals with finding out the likelihood of the occurrence of an event.

Total hat is:

= 25+20+40+30+25+1

= 150.

There are a total of 150 hats to choose from.

The number of blue hats to choose from is:

= 40 + 10

= 50.

The probability that Julian chooses a blue hat is:

= 50/150

= 1/3

= 0.33 or 33.33%.

Read more about probability

brainly.com/question/24756209

#SPJ1

Answer:

-----------------------

Given two similar triangles:

We know similar figures have same ratio of corresponding sides.

Apply this to the given triangles to get:

Substitute values:

The matching choice is B.

The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

A. To find f(x) + g(x), we add the two functions together:

f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)

To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:

f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]

Simplifying the numerator:

f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]

Combining like terms:

f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]

B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:

(x^2 - 9) = 0  --> x = -3, 3

(x^2 + 3x) = 0 --> x = 0, -3

So, the excluded values are x = -3, 0, and 3.

C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.

At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.

At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.

Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

For more questions on vertical .

https://brainly.com/question/30195815

#SPJ8

It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

To learn more about numerical expression click here :

https://brainly.com/question/6037813

#SPJ1

The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.

Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.

We can convert the two fractions to decimal form in order to compare them.

7.375 is equivalent to 7 3/8, and

4/5 is equivalent to 0.8.

7.375 multiplied by 0.8 results in:

7.375 × 0.8 = 5.9

Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.

Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.

Know more about the term mixed fractions:

https://brainly.com/question/1055953

#SPJ1

Answer:

the answer is 50.27 cm for your question

The equivalent number that represents the engineering notation 9.423 × 10⁵ will be 942,300.

In engineering notation, we express a number as a coefficient multiplied by a power of 10.

The given number is 9.423 × 10⁵.

To express it in engineering notation, we move the decimal point five places to the right, and the power of 10 becomes positive since the original number is greater than 1.

9.423 × 10⁵ becomes 942,300.

Therefore, 9.423 × 10⁵ in engineering notation is 942,300.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

The value οf P(x > 104) is 0.1587 οr apprοximately 15.87%.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Tο find the prοbability οf P(x > 104) fοr a nοrmal distributiοn with mean οf 98 and standard deviatiοn οf 6, we need tο standardize the value οf 104 using the fοrmula:

z = (x - μ) / σ

where z is the standard scοre, x is the value we want tο find the prοbability fοr, μ is the mean οf the distributiοn and σ is the standard deviatiοn.

Plugging in the values, we get:

z = (104 - 98) / 6 = 1

Nοw we need tο find the area tο the right οf this value οn the standard nοrmal distributiοn table οr calculatοr.

Using a standard nοrmal distributiοn table οr calculatοr, we find that the area tο the right οf z = 1 is 0.1587.

Learn more about probability on:

https://brainly.com/question/13604758

#SPJ1

The reasoning for the third step of the proof would be "Corresponding parts of congruent triangles are congruent." Let's go through the explanation:

1. Given: Quadrilateral ABCD is a rectangle.

2. Given: AB & CD (Opposite sides of a rectangle are equal).

3. To prove: AC & BD.

To prove that AC is equal to BD, we can utilize the property that opposite sides of a rectangle are equal (step 2). In a rectangle, opposite sides are parallel and congruent. Therefore, we have AB || CD and AB = CD.

Now, we need to show that the triangles ABAD and ACDA are congruent, specifically using the SAS (Side-Angle-Side) congruence theorem. The congruence of these triangles will allow us to establish the equality of their corresponding parts, including AC and BD.

4. Given: AD = AD (Reflexive Property of Equality).

5. By step 2, we know AB = CD. Additionally, AD = AD is given (Reflexive Property of Equality).

6. By step 3, ZBAD = ZCDA.

7. Using SAS triangle congruence theorem, we can conclude that triangles ABAD and ACDA are congruent.

Finally, according to the "Corresponding parts of congruent triangles are congruent" property, we can state that AC = BD. This establishes the equality of the diagonals of the rectangle.

Therefore, the correct reasoning for step 3 is "Corresponding parts of congruent triangles are congruent."

For more such questions on congruent triangles.

https://brainly.com/question/29789999

#SPJ8

Answer:

c. -2

Step-by-step explanation:

Since f(x) is the regular graph. Since the inverse function flips the x and y coordinates, f inverse of 4 is actually where y=4, not x=4. so the x coordinate where y is 4 is -2.

Answer:

[-0.2  0.4]

[0.8   -0.6]

To find the solution to the system of equations represented by the two lines based on the given tables of ordered pairs, you can follow these steps:

For such more question on equations

https://brainly.com/question/22688504

#SPJ8