Find how long it takes a person to drive 260 miles on a highway if she merges onto a highway at 7 p.m. and drives nonstop with her cruise control set on 80 mph.

j(m) = 2ᵐ ⁻ ¹

for functions you will replace the number in the brackets with the letter! so:

j(4) = 2⁴ ⁻ ¹

= 2³

= 8

Answer:

[tex]\huge\boxed{\sf b = -3}[/tex]

Step-by-step explanation:

-3(3 + 6b) = 36 - 3b

Distribute

-9 - 18b = 36 - 3b

Add 3b to both sides

-18b + 3b - 9 = 36

-15b - 9 = 36

Add 9 to both sides

-15b = 36 + 9

-15b = 45

Divide -15 to both sides

b = 45/(-15)

[tex]\rule[225]{225}{2}[/tex]

Answer:

The value of b is -3.

Step-by-step explanation:

The equation is,

→ -3(3 + 6b) = 36 - 3b

Now the value of b will be,

→ -3(3 + 6b) = 36 - 3b

→ -3(3) - 3(6b) = 36 - 3b

→ -9 - 18b = 36 - 3b

→ -18b + 3b = 36 + 9

→ -15b = 45

→ b = -(45/15)

→ [ b = -3 ]

Hence, the value of b is -3.

It is not possible for the measure of each interior angle of a regular polygon to be four times the minimum angle of rotation about its center that carries the polygon onto itself.

What is the interior angle?

The inner of the two angles formed where two sides of a polygon come together. any of the four angles formed in the area between a pair of parallel lines when a third line cuts them.

Jasper's claim is not true. The minimum angle of rotation about the center of a regular polygon that carries the polygon onto itself is called the polygon's "order of rotational symmetry." This angle is always less than or equal to 180 degrees, and it is equal to 360 degrees divided by the number of sides in the polygon.

For example, a regular hexagon has an order of rotational symmetry of 60 degrees (360 degrees / 6 sides), and a regular octagon has an order of rotational symmetry of 45 degrees (360 degrees / 8 sides).

Therefore, if the measure of each interior angle of a regular polygon is four times the minimum angle of rotation about its center that carries the polygon onto itself, then the measure of each interior angle would have to be at least 720 degrees. However, the sum of the interior angles of a regular polygon with n sides is 180(n-2) degrees, which is always less than 720 degrees for any value of n greater than 2.

Therefore, it is not possible for the measure of each interior angle of a regular polygon to be four times the minimum angle of rotation about its center that carries the polygon onto itself.

To learn more about the interior angle visit,

https://brainly.com/question/24966296

#SPJ1

The cycle originally cost $120, and he made a $60 profit by selling it for $163 with a $17 helmet.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.

Here,

The cost of bicycle=$163

Cost of helmet=$17

Total cost,

=163+17

=$180

Let the original cost be c,

180=150%*c

180=1.5c

c=$120

He made a profit,

=180-120

=$60

The original cost of cycle was $120 that he sold in $163 with the helmet of $17 making a profit of $60.

To know more about expression,

https://brainly.com/question/14961928

#SPJ1

The trigonometric measures for the triangle in this problem are given as follows:

The six trigonometric measures for a right triangle are given as follows:

From the given right triangle, the sides are given as follows:

a = 9, b = 4.

Then, applying the Pythagorean Theorem, the length of the sqis given as follows:

h² = 9² + 4²

h² = 97

h = square root of 97.

h = 9.85.

The triangle is given by the image shown at the end of the answer.

More can be learned about the trigonometric measures of a triangle at https://brainly.com/question/24349828

#SPJ1

You may find the answer to this question in the statement of the problem, if the vehicles uses 1 gallon to travel 13 times, then it is traveling at a rate of 13 miles per gallon.

Answer:

x = -18

Step-by-step explanation:

Please tell me If I am wrong..

5 x 2 = 10 = numerator.

-9 x 2 = ? = denominator

? = -18

-9 x 2 = -18…

Follow me please. The answer is -18

The required sum is given as 6n + 12.

Integers can be defined as the set of counting numbers and their negative values along with zero. An integer can be written in the form of a fraction by writing the denominator as 1.

The given problem can be solved as follows,

The consecutive three even integers greater than 2n can be written as,

2n + 2, 2n + 4 and 2n + 6

Now, the sum of these integers are given as follows,

2n + 2 + 2n + 4 + 2n + 6

= 6n + 12

Hence, the sum of the next three consecutive even integer greater  than 2n is given as 6n + 12.

To know more about integers click on,

brainly.com/question/15276410

#SPJ1

The Quadratic Equation [tex]3x^{2}-13x+6[/tex]  divided by [tex]x-4[/tex] for all the values of the x(except x=4).

Let us consider [tex]3x^{2}-13x+6[/tex] as equation→(1) of a Quadratic Equation assume some values for x which is satisfies the equation and doesn't satisfy equation by "hit and trail method".

x=1 substitute in the equation (1) we get    ⇒  [tex]\frac{4}{3}[/tex]

x=2 we get [tex]3(2)^{2}-13(2)+6[/tex]    [tex]=4[/tex]

x=4 we get[tex]3(4)^{2}-13(4)+6[/tex]    ⇒    [tex]\frac{2}{0}[/tex] which is not defined.

x=6 we get [tex]3(6)^{2}-13(6)+6[/tex]      [tex]= 12[/tex]

x= -2 we get [tex]3(-2)^{2}-13(-2)+6[/tex] ⇒[tex]\frac{22}{-3}[/tex]

And so on for the remaining values of x the equation will satisfy. Except  for the value x= 4 the equation doesn't satisfy because if we substitute x=4 in x-4 we get 4-4 =0 anything divided by zero is not defined.

To learn more about Quadratic:https://brainly.com/question/28038123

Divide [tex]3x^{2}-13x+6 by x-4[/tex]

Answer:

do it yourslef

dont be silly

lol

11111111

Answer:

3,11

Step-by-step explanation:

Since y = 2x + 5, if you chose (x,y) (3,11):

11 = 2*3 + 5

11 = 6 + 5

11 = 11

Answer:

(3, 11 ) is a solution

Step-by-step explanation:

substitute the x- coordinate of the points into the equation and if the value of y obtained equals the y- coordinate then the point is a solution.

(5, 20 )

y = 2(5) + 5 = 10 + 5 = 15 ≠ 20 ← not a solution

(6, 12 )

y = 2(6) + 5 = 12 + 5 = 17 ≠ 12 ← not a solution

(3, 11 )

y = 2(3) + 5 = 6 + 5 = 11 ← solution

(4, 14 )

y = 2(4) + 5 = 8 + 5 = 13 ≠ 14 ← not a solution

Fill in the inequality for each problem as follows 32 > -39, 3 < 15, 4  > -6 and -8  > -15

Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.

We have different inequality signs as follows:

Greater than (>)

Less than(<)

Less than or equal to (≤)

Greater than or equal to (≥)

Given:

32__-39

3__15

4__-6

-8__-15

For 32__-39:

Since 32 is greater than -39. we can write:

32 > -39

For 3__15:

Since 3 is less than 15. we can write:

3 < 15

For 4__-6:

Since 4 is greater than -6. we can write:

4  > -6

For -8__-15:

Since -8 is greater than -15. we can write:

-8  > -15

Thus, fill in for each problem accordingly

Learn more about inequalities on:

brainly.com/question/6323790

#SPJ1

Complete Question

Fill in >,< or = for each prob

32__-39

3__15

4__-6

-8__-15

The average class size of Newton middle school is 21.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that a decade ago, the average class size at Newton Middle School was 30 students. Now it is 30% smaller.

The average class size will be calculated as,

Average class size = 30 x (70%)

Average class size = 30 x 0.7

Average class size = 21

Therefore, the average class size at Newton middle school is 21.

To know more about percentages follow

https://brainly.com/question/24304697

#SPJ1

The graph of the proportional relationship is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Time = 3 minutes

Supply of water = 12 litres

Using the above parameters, we have the following ordered pairs

(0, 0) and (3, 12)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 0) and (3, 12)

The gradient of the line is then calculated using the following slope equation

gradient = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (3, 12)

Substitute the known values in the above equation

So, we have the following equation

gradient  = (12 - 0)/(4 - 0)

Evaluate

gradient  = 3

The equation of the line is then calculated as

y = gradient * x

Substitute the known values in the above equation

So, we have the following equation

y = 3 * x

Evaluate the products

y= 3x

Hence, the line equation is y= 3x

Read more about linear equation at

https://brainly.com/question/12700955

#SPJ1

By solving equations, we know that there were 2187 adult partons.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A function is an equation with a single solution for y for each value of x.

Each input of a particular type receives exactly one output when using a function.

Instead of y, a function is frequently named f(x) or g(x).

When x equals 2, we should determine our function's value because f(2) says to do so.

So, the number of adult patrons was:

Let, a be an adult and c be children.

Total tickets:

a + c = 5200

c = (5200-a)

Total amount:

7.50a + 4.50c = 29961

Replace c in the first equation with (5200-a).

7.5a + 4.5(5200-a) = 29961

7.5a + 23400 - 4.5a = 29961

7.5a - 4.5a = 29961 - 23400

3a = 6561

a = 6561/3

a = 2187

Therefore, by solving equations, we know that there were 2187 adult partons.

Know more about equations here:

https://brainly.com/question/28937794

#SPJ1

The difference of given decimal numbers is (12.504, 12.495).

Given that, (13.4-0.896, 8.4+4.095).

Subtracting decimals:

1. Write down the two numbers, one under the other, with the decimal points lined up.

2. Add zeros so the numbers have the same length.

3. Then subtract normally, remembering to put the decimal point in the answer.

Here,

13.4-0.896 =12.504

8.4+4.095 =12.495

So, (13.4-0.896, 8.4+4.095) =(12.504, 12.495)

Hence, the difference of given decimal numbers is (12.504, 12.495).

To learn more about the difference of decimal numbers visit:

brainly.com/question/639216.

#SPJ1

2/6 is the equivalent fraction for the fraction represented on the given number line. So, B is the correct option

What is an equivalent fraction ?

According to equivalent fractions, two or more fractions are considered to be equal if, following simplification, both provide the same fraction. Let's imagine that a/b and c/d are two fractions. If these fractions are simplified to produce comparable fractions, such as e/f, they are then equal to one another.

For instance, if we simplify 5/15, the resulting fraction is the same as 1/3, hence that is the equivalent fraction of 1/3.

The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions. For instance, since 2/4 and 3/6 both equal the 12, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.

as 2/6 can further reduced to 1/3 which is represented on to the number line  as 1/3 which is equal to 2/6

Learn more about equivalent fraction from the link below

https://brainly.com/question/29769027

#SPJ1

In using quarterly time series data, Quarter two  can serve as the base period for interpretation of dummy variables.

What do you mean by interpretation?

The process of interpreting anything involves elaborating, rephrasing, or otherwise demonstrating your own understanding of it.

                           Because they are explaining what someone is saying to someone who doesn't understand, a person who translates one language into another is known as an interpreter.

What are examples and variables?

A trait that is measurable and capable of taking on several values is known as a variable. A few examples of variables are height, age, income, province of birth, school grades, and kind of dwelling.

                                 The two primary categories of variables are categorical and numeric.

Learn more about variable

brainly.com/question/17344045

#SPJ4

Answer: The slope is 3

Step-by-step explanation:

Explanation:

The slope of a line in the form

y

=

m

x

+

b

is

m

.

3

x

−

y

=

4

−

y

=

−

3

x

+

4

subtract

3

x

from both sides

y

=

3

x

−

4

multiply both sides by

−

1

The given polygon could be parallelogram , quadrilateral , rectangle.

What is a polygon?

In geometry, a polygonal shape could be a two-dimensional figure that's delineate by a finite range of line segments connected to make a closed two-dimensional figure chain. The delimited plane region, the bounding circuit, or the 2 along, is also referred to as a polygonal shape.

Main body:

As opposite sides of polygon QRST are parallel , it a parallelogram .

A quadrilateral is a polygon with for sides , so it also satisfies the condition.

The opposite sides of rectangle are equal and parallel , which is also satisfied.

Hence ,the given polygon could be parallelogram , quadrilateral , rectangle.

TO know more about polygon , visit:

https://brainly.com/question/26583264

#SPJ1

Answer:

75

Step-by-step explanation:

y² + 5y + 9

since y = 6 we will just substitute for y

= (6)² + 5(6) + 9

= 36 + 30 + 9

= 66 + 9

= 75

i hope this helps

You will always get one triangle. This is because of the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles of a triangle is always 180°.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

The inner angles of every triangle sum up to 180°, 180°, 180°, 180°. Angles in a triangle are the total (sum) of the angles at each of its three vertices.

To know more about triangle angles visit:

https://brainly.com/question/27682397

#SPJ1

The letters of "hyperbola" can be combined into 40,320 different nine-letter words by using each letter just once.

Combinations are the procedures used in mathematics to pick k things from n different items without replacement.

The following formula computes the combinations of k items from n:

(n, k) = n! / k!×(n-k)!

There are 8 letters in the word "hyperbola",

So, there are 8 choices for the first letter, 7 choices for the second letter, and so on, down to 1 choice for the last letter.

This means that there are :

⇒ 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320

Therefore, 40,320 possible nine-letter words can be formed from the letters of "hyperbola" using each letter once per word.

Learn more about permutation here:

brainly.com/question/1216161

#SPJ1

Answer:

  y = -4/9x

Step-by-step explanation:

You want the equation of the line through (0, 0) and (9, -4).

A line through the point (0, 0) represents a proportion. The slope of the line is the constant of proportionality, the ratio of y to x.

  k = y/x = -4/9

The equation of the line is ...

  y = kx

  y = -4/9x

Answer:

Just about 50%, depending on if the data set is a odd or even number

Step-by-step explanation:

At 45, is the median value. The median of a box plot is not necessarily 50% of the data. The median is the middle value in a dataset, or the value that divides the data into two equal halves. If the dataset has an odd number of values, the median will be one of the values in the dataset. If the dataset has an even number of values, the median will be the average of the two middle values.

Answer:

Two angles are supplementary. If the measure of the angle is twice the measure of the other, find the measure of each angle.

Let the measure of one of the supplementary angles be a

.

Measure of the other angle is 2

times a

.

So, measure of the other angle is 2a

.

If the sum of the measures of two angles is 180°

, then the angles are supplementary.

So, a+2a=180°

Simplify.

3a=180°

To isolate a

, divide both sides of the equation by 3

.

3a3=180°3    a=60°

The measure of the second angle is,

2a=2×60°       =120°

So, the measures of the two supplementary angles are 60°

and 120° .

Step-by-step explanation:

Hope this works!....

The correct match the following is shown below:

2x + 3 (x - 2) = 6 (x + 1) + x → x = -6

2x + 3 (x - 2) = 6 (x - 1) - x → All real numbers

2x + 3 (x - 2) = 6 (x - 1) + x → x = 0

2x + 3 (x - 1) = 6 (x - 1) - x → No solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

The equation is, 2x + 3 (x - 2) = 6 (x + 1) + x, 2x + 3 (x - 2) = 6 (x - 1) - x, 2x + 3 (x - 2) = 6 (x - 1) + x, and 2x + 3 (x - 1) = 6 (x - 1) - x

Solve the above equations as shown below,

2x + 3 (x - 2) = 6 (x + 1) + x

2x + 3x - 6 = 6x + 6 + x

5x - 6 = 7x + 6

7x - 5x = -6 - 6

x = -6

2x + 3 (x - 2) = 6 (x - 1) - x

2x + 3x - 6 = 6x - 6 - x

5x  - 6 = 5x - 6

Infinity solutions,

2x + 3 (x - 2) = 6 (x - 1) + x

2x + 3x - 6 = 6x - 6 + x

5x - 6 = 7x - 6

x = 0

2x + 3 (x - 1) = 6 (x - 1) - x

2x + 3x - 3 = 6x - 6 - x

5x - 3 = 5x - 6

Parallel line, hence, no solution.

To know more about equation:

https://brainly.com/question/12788590

#SPJ1

Step-by-step explanation:

this is the same principle in every posted question.

I hope you understand this now.

if not please let me know what is still a "riddle" to you, so that I can explain it better.

remember, the inverse function of y = e^x is x = ln(y).

and the inverse function of y = ln(x) is x = e^y.

we want to find the value of x, where f(x) = 28.

28 = 0.48ln(x + 2) + 27

1 = 0.48ln(x + 2)

1/0.48 = ln(x + 2)

e^(1/0.48) = x + 2

x = e^(1/0.48) + 2 = 10.03119499... miles ≈ 10 miles

the pressure of 28 inches of mercury occurs about 10 miles from the eye of the hurricane.

Over the course of many​ games, one would expect the mean number of hits per game to be the mean of the random variable.

What is Mean?

A group of two or more numbers is simply averaged mathematically to get the term "mean." There are several ways to calculate the mean for a given collection of numbers, including as the arithmetic mean approach, which utilises the sum of the series' values, and the geometric mean method, which uses the average of a group of products. However, the majority of the time, the results from all of the main approaches to calculating a simple average are roughly the same.

There are two different types of means that can be calculated: the arithmetic mean and the geometric mean.

The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of numbers in the set.

Mean is the ratio of sum of observations to the total number of observation.

Learn more about Mean from the link below
https://brainly.com/question/13494085
#SPJ4