6⁵×6*=6¹ jdkdjdjbddjdbdjbdbsbsksns

Answer:

y = -5x + 4

Step-by-step explanation:

The general form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.

Given that the slope of the line is -5 and the y-intercept is 4, we can substitute these values into the general form of the equation of a line to get:

y = -5x + 4

This equation represents a line with a slope of -5 and a y-intercept of 4.

Answer: A line is perpendicular to another line if the slope of the first line is the negative reciprocal of the second line. The equation of the line y = -5x-1 has a slope of -5. The negative reciprocal of -5 is 1/5.

A line passing through a point (x1, y1) has an equation in slope-intercept form of y = m(x-x1) + y1, where m is the slope of the line.

So, we can use the point (10,3) and the slope of the line which is 1/5 to write the equation of the line:

y = 1/5(x-10) + 3

Therefore, the equation of the line perpendicular to y = -5x-1 and passing through the point (10,3) is y = 1/5x + 1/5

Step-by-step explanation:

The scientific notation of the given number is 6.11×10⁻⁴. Therefore, option E is the correct answer.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

The given decimal number is 0.000611.

0.000611 in scientific notation, we get

6.11×10⁻⁴

Therefore, option E is the correct answer.

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Answer:

Step-by-step explanation:

Given the first three terms of the expansion of (1 +x)^n are 1 +3 +4, you want the values of x and n, and the next term.

The first few terms of the binomial expansion of (1 +x)^n are ...

  [tex](1+x)^n=1^n+n\cdot1^{n-1}x+\dfrac{n(n-1)}{2}1^{n-2}x^2+\dfrac{n(n-1)(n-2)}{2\cdot3}1^{n-2}x^3+\dots[/tex]

Comparing the terms to those given, we have ...

  [tex]nx=3\\\\(nx)((n-1)x)/2=4[/tex]

Expanding the second of these equations, and substituting the first, we get ...

  [tex](nx)(nx -x)=8\qquad\text{multiply by 2}\\\\3(3-x)=8\qquad\text{substitute $nx=3$}\\\\9-8=3x\qquad\text{add $3x-8$}\\\\\boxed{x=\dfrac{1}{3}}\qquad\text{divide by 3}\\\\\dfrac{1}{3}n=3\qquad\text{substitute for $x$ in $nx=3$}\\\\\boxed{n=9}\qquad\text{multiply by 3}[/tex]

Then the fourth term is ...

  [tex]\dfrac{n(n-1)(n-2)}{6}x^3=\dfrac{9\cdot8\cdot7}{6}\cdot\left(\dfrac{1}{3}\right)^3=\boxed{\dfrac{28}{9}}[/tex]

__

Additional comment

Then the expansion is ...

  (1 +1/3)^9 = 1 + 3 + 4 + 28/9 + 14/9 + 14/27 + ...

The n-th term is (11-n)/(3(n-1)) times the term before.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=12 \end{cases}\implies V=\pi (6)^2 (12)\implies \stackrel{\textit{total volume of ice-cream}}{V=432\pi ~in^3}[/tex]

Answer:

The cost of the water is $5.70.

Step-by-step explanation:

7.05-1.35=5.70 You just have to - 7.05 by 1.35

The slope of the line is C) [tex]\frac{6}{5}[/tex].

What is slope?

Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line. Any two distinct places along the line can be used to determine the slope of any line.

Here the given point is [tex](x_1,y_1)=(-5,-1)[/tex] and [tex](x_2,y_2)=(5,11)[/tex]

Now using slope formula then,

=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> Slope m = [tex]\frac{11-(-1)}{5-(-5)}[/tex]

=> slope m = [tex]\frac{11+1}{5+5}[/tex]

=> slope m = [tex]\frac{12}{10}[/tex]

=> slope m = [tex]\frac{6}{5}[/tex]

Hence the slope of the line is C) [tex]\frac{6}{5}[/tex].

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Answer: The hour hand of a clock makes one complete rotation, 360 degrees, in 12 hours or 720 minutes.

The hour hand of a clock turns 30 degrees in one hour or 0.5 degrees in one minute.

In this case, the hour hand is turned anticlockwise from 2 pm to 9 am, which is 21 hours.

So, it will have turned 21 * 30 = 630 degrees.

It is important to note that this answer only accounts for the rotation of the hour hand and does not take into account the rotation of the minute hand.

Step-by-step explanation:

The length of side x for the triangle is 5√3.

An equilateral triangle is one with equally long sides on both sides. The three angles opposite the three equal sides are equal in size because the three sides are equal. It is also known as an equiangular triangle since each angle is 60 degrees.

Given an equilateral triangle,

length of the side is 10 units,

and a perpendicular is drawn with length x,

so a perpendicular drawn from one of the vertices to the opposite side of an equilateral triangle bisects that side.

we know the angle of the equilateral triangle is 60°,

by the sine function, we can calculate the value of x

sinФ = p/h

p = perpendicular  = x

h = hypotenuse = 10

Ф = 60°

sin60 = x/10

x = 10*sin60

x = 10(√3/2)

x = 5√3

Hence the value of x is 5√3.

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Answer:

605

Step-by-step explanation:

11x55=605

answer is 25

use the formula to get the rest of the a's

Answer:

Step-by-step explanation:

To solve this equation, we can start by using the identity cos(A-B) = cosAcosB + sinAsinB. Substituting A=sin x and B=1, we have:

2cos(sin x - 1) = cos(sin x)cos(1) + sin(sin x)sin(1)

We can then substitute this expression on the left-hand side of the original equation and simplify:

4sinxcosx^2 - 1 = cos(sin x)cos(1) + sin(sin x)sin(1)

Rearranging terms, we have:

4sinxcosx^2 - cos(sin x)cos(1) - sin(sin x)sin(1) = 1

We can now use the identity sin^2x+cos^2x=1 to simplify the left-hand side further:

4sinxcosx^2 - (sin^2x + cos^2x)cos(1) = 1

Simplifying further:

4sinxcosx^2 - (cosx)cos(1) = 1

Now we can divide both sides by cos(1):

4sinxcosx^2/cos(1) - cosx = 1/cos(1)

Rearranging terms:

cosx(4sinxcosx^2/cos(1) - 1) = 1/cos(1)

Finally, we can use the identity cos2x = 2cos^2x - 1 to simplify the left-hand side further:

(2cos^2x - 1)(4sinxcosx^2/cos(1) - 1) = 1/cos(1)

We can then divide both sides by (4sinxcosx^2/cos(1) - 1):

2cos^2x - 1 = 1/cos(1) (4sinxcosx^2/cos(1) - 1)

And finally, we can solve for cosx:

cosx =  1/2 + 1/2cos(1) (4sinxcosx^2/cos(1) - 1)

This is the solution to the equation.

If the ratio of crushed ice to rock salt is 5 to 1, for every 5 cups of crushed ice, 1 cup of rock salt is needed.

To find out how much rock salt is needed for the small ice cream freezer, you can use this formula:

Rock Salt = (Crushed Ice / 5) * 1

If the small ice cream freezer requires cups of crushed ice, then:

Rock Salt = (5 cups / 5) * 1 cup

Rock Salt = 1 cup

So, you will need 1 cup of rock salt to mix with the 5 cups of crushed ice to create the necessary brine solution.

Answer:

A rectangle of 10.6 x 11.4 dimensions.

Step-by-step explanation:

(5.3*2)*(5.7*2)=5.3*4*5.7=10.6x11.4.

Answer:

a = [tex]\frac{41}{9}[/tex]

Step-by-step explanation:

Evaluate f(3):

f(3) = (3)² -2(3)³ + a(3)² +3 +3

9a - 39 = 2

9a = 41

a = [tex]\frac{41}{9}[/tex]

An empty number line is a visual tool used to represent numbers and their relative positions. It can be used to compare, order, and perform operations on numbers.

A number with more digits is always greater than a number with fewer digits, according to Rule I.

Rule II states that when two numbers have the same number of digits, we compare the digits starting from the leftmost position until we find an unequal number of digits. Greater numbers are those with more digits.

As far as we are aware, a number with more digits is always greater than one with fewer digits.

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The required value of y for the angle is 18.

The angles created when a transversal intersects two parallel lines are known as corresponding angles. Typical examples of equivalent angles include opening and closing a lunchbox, resolving a Rubik's cube, and endless parallel railroad tracks.

By Corresponding angles

7x = 3x + 36

4x = 36

x = 9

And

Angle in straight line

(6y + 9)+(3x+36) = 180

(6y + 9)+(27+36)

6y + 72 = 180

6y = 108

y = 18

Thus, required value of y is 18.

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Answer:

The inverse of a function, denoted as f^-1 (x), is a new function that "undoes" the original function. To find the inverse of a function, you need to switch the x and y variables and then solve for y. To find the inverse of f(x) = 1/3 x - 5, you need to switch the x and y variables and then solve for y:

Step-by-step explanation:

To solve for y, you need to get x alone on one side of the equation:

x + 5 = 1/3 y

3x + 15 = y

The inverse of f(x) = 1/3 x - 5 is f^-1 (x) = 3x + 15

It is important to note that not all functions have an inverse, only functions that are one-to-one or "injective" functions have inverses.

Answer: 3x + 15 = the inverse function of f(x)

Explanation:

First of all, arrange the equation and leave the "x" alone.

x/3 - 5 = y (Multiply both sides by 3)

x - 15 = 3y (Then, leave "x" alone)

x = 3y + 15 (As the final step, change x and y variables.)

y = 3x + 15 (This is the inverse function of f(x).)

Answer:

Step-by-step explanation:

a) If a driver uses a full tank of gas every day, the fraction of a tank he will use in 3 days is 3/1, or 3/1 of a tank.

b) If a driver uses a full tank of gas every day, the fraction of a tank he will use in 1 week is 7/1, or 7/1 of a tank.

It's worth noting that tanks of gas come in different sizes, so the amount of gas consumed in a day, week, or any other period of time will depend on the size of the tank, and the consumption of the car, so this answer is based on the assumption that a full tank is used every day.

Answer:

Here are the true statements:

The false statement is:

The G-intercept of G(t) represents the total distance the vehicle traveled. The t-intercept of G(t) represents the time it takes the vehicle to run out of gas. (This is not the case, the y-intercept represents the initial amount of gas and the x-intercept represents the time it takes the vehicle to run out of gas)

Answer:

Step-by-step explanation:

Elimination is a method of solving a system of equations by adding or subtracting the equations from each other to eliminate one of the variables.

In this case, we will be using elimination to solve the system of equations:

-3x + 12y = 9

x - 4y = -3

Step 1: Multiply the first equation by -1.

(Multiplying by -1 switches the sign of every number in the equation)

3x - 12y = -9

Step 2: Add the two equations together.

3x - 12y = -9

+x - 4y = -3

______________

4x - 16y = -12

Step 3: Isolate the y-variable by adding 16y to both sides of the equation.

4x - 16y = -12

+16y +16y

______________

4x = -12 + 16y

Step 4: Divide both sides of the equation by 4 to isolate the y-variable.

4x = -12 + 16y

4/4 4/4

______________

x = -3 + 4y

Therefore, the solution to the system of equations is x = -3 + 4y.

A construction of a right-angled isosceles triangle whose equal side measure 2 cm is shown in the image attached below.

In Mathematics, an isosceles right triangle can be defined as a type of  right-angled triangle in which two (2) of its side lengths are equal and one of its angle is a right angle.

Generally speaking, the steps that are required for the construction of a right-angled isosceles triangle include the following:

In conclusion, triangle ABC (ΔABC) is the required right-angled isosceles triangle as shown in the image attached below.

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The total number of marbles are 30.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, to start, Vince divides a bag of m marbles evenly among the 3 players. Each player gets 10 marbles.

Here, m/3 =10

m=30

Therefore, the total number of marbles are 30.

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Answer:

28.1 ft

Step-by-step explanation:

d  =  350 * ( tan 10.5 - tan 6)  = 28.1 ft

Answer: $89

Step-by-step explanation: The equation would be P = 10(x) + 3(x-5) assuming P is profit and x is greater than 5. By pluggin in x, the number of hours, we can find that it is 89.

Answer: Santos will make $89

Step-by-step explanation:

Hour 1 - $10

Hour 2 - $10

Hour 3 - $10

Hour 4 - $10

Hour 5 - $10

Hour 6 - $13

Hour 7 - $13

Hour 8 - $13

The graph of the quadratic function g(x) = - (x - 2)² + 4 on Cartesian plane is shown in the image attached below.

In this question we find the case of a quadratic equation in vertex form, whose definition is shown below:

y - k = a · (x - h)²

Where:

The equation of the axis of symmetry is shown below:

x = h

We can graph by using the coordinates of the vertex and two other points and understanding the vertex constant. Please notice that the parabola has an absolute minimum when vertex constant is positive, otherwise it is an absolute maximum.

First, find the coordinates of the vertex of the parabola:

(h, k) = (2, 4)

Second, determine the nature of the absolute extreme by interpretating the sign of vertex constant:

a = - 1 (The vertex is an absolute maximum)

Third, evaluate the function at two distinct points:

x = 0

g(0) = - (0 - 2)² + 4

g(0) = - (- 2)² + 4

g(0) = 0

x = 4

g(4) = - (4 - 2)² + 4

g(4) = - 2² + 4

g(4) = - 4 + 4

g(4) = 0

Fourth, graph the parabola on Cartesian plane. (Image is done with the help of a graphing tool)

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There is no difference between the population mean customer satisfaction scores for the two retailers, according to p-value: 0.33049.

chosen at random (purely random, unpredictable). Every person in the demographic being surveyed should have an equal chance of being chosen. She gave an example of a simple representative sample, choosing 25 names at random from a group of 250 employees. The sampling in this case is random since there are 250 of her coworkers in total, and every one has an equal chance of being picked. Researchers select people at random from a population using simple random sampling, which is a type of probability sampling. Every member of the population is given an equal chance at selection.

Given that,

mean(x)=86

standard deviation , σ1 =12

number(n1)=250

y(mean)=85

standard deviation, σ2 =12

number(n2)=300

null,  u1 = u2

alternate, H1: μ1 != u2

level of significance, alpha = 0.05

we got |zo | =0.973  & | z alpha | =1.96

(b) test statistic: 0.97

There is no difference between the population mean customer satisfaction scores for the two retailers, according to p-value: 0.33049.

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Answer: (15 + 72) + 19

Explanation: "Associative Law = (a + b) + c = a + (b + c)"

The angles of the triangle KHP are P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°, respectively.

In this question we have the case of a triangle where the lengths of three sides are known and measures of angles must be determined. The missing angles can be found by means of law of cosine, whose equations related to the triangle are introduced below:

p² = h² + k² - 2 · h · k · cos P

h² = p² + k² - 2 · p · k · cos H

k² = h² + p² - 2 · h · p · cos K

Where:

If we know that h = 16.1, p = 24.9 and k = 12.8, then the measures of the angles are:

cos P = (p² - h² - k²) / (- 2 · h · k)

cos P = (24.9² - 16.1² - 12.8²) / (- 2 · 16.1 · 12.8)

cos P = - 0.478

P ≈ 118.555°

cos H = (h² - p² - k²) / (- 2 · p · k)

cos H = (16.1² - 24.9² - 12.8²) / (- 2 · 24.9 · 12.8)

cos H = 0.823

H ≈ 34.614°

cos K = (k² - h² - p²) / (- 2 · h · p)

cos K = (12.8² - 16.1² - 24.9²) / (- 2 · 16.1 · 24.9)

cos K = 0.892

K ≈ 26.844°

Triangle KHP has the following missing angles: P ≈ 118.555°, H ≈ 34.614°, K ≈ 26.844°.

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