Simplify the expression in exact terms (no decimals): 6√x+7√(54) - 12√(6)

Answer: (15 + 72) + 19

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

The latera surface area of the triangular prism is  425 inches².

The isosceles triangular prism is unfolded into the net shown below. Therefore, the lateral surface area of the triangular prism can be found as follows:

The lateral surface area of the triangular prism is the product of the perimeter of the triangle and the height of the prism.

Hence,

lateral surface area of the triangular prism = ph

where,

Therefore,

lateral surface area of the triangular prism = (9 + 9 + 7)17

lateral surface area of the triangular prism = 25 × 17

lateral surface area of the triangular prism = 425 inches²

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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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The square root of 625 is 25 and the square root of 25 is 5. Therefore, option A and F are the correct answers.

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

A) [tex]625^{\frac{1}{2}[/tex]

= [tex](25^2)^{\frac{1}{2}[/tex]

= 25

F) 25

= 5

Therefore, option A and F are the correct answers.

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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 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:

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.

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 is 25

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

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:

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).)

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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Answer:

The correct answer is: parallel

The two equations are in the form of y = mx + b and y = mx + b, which are the standard forms of linear equations.

and the slope of the two equations are different, so they are not coincident and not intersecting. They are parallel lines that never meet, so the system of equations is parallel.

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 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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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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Answer:

605

Step-by-step explanation:

11x55=605

[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:

Step-by-step explanation:

To graph 10x-3y=15, start by rearranging the equation to the slope-intercept form of y = mx + b, where m = the slope and b = the y-intercept. 10x-3y=15 becomes 3y = 10x - 15. Solve for y by dividing both sides by 3 to get y = (10/3)x - 5.

Now that the equation is in the slope-intercept form, draw a graph on a coordinate plane. Start by plotting the y-intercept at (0, -5). Next, use the slope of 10/3 to determine the rise and run of the line. The rise is +10 and the run is +3. Starting at the y-intercept, draw a line that moves up 10 and to the right 3, and continue doing this until you reach the end of the graph. This line is the graph of 10x-3y=15.

Answer:

y=10/3x+5

(0,5), (3,15)

Step-by-step explanation:

First, put the graph in slope-intercept form. We can do this by subtracting 10x from both sides.

-3y=-10x-15

Next, we divide by -3.

y=10/3x+5

If you don't know how to graph an equation with slope-intercept form,

it is in the format of y=mx+b, where m is the slope (in this case, 10/3) and b is the y-intercept (in this case 5, or (0,5)). First graph the y-intercept.

(0,5).

Then implement the slope. Here we would go up by 10 and then go right by 3. This makes our second point (3,15).

Now that we have two points (0,5) and (3,15), just construct your line.

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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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:

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.

The fractions that have the same value as 16 ÷ (–3), include:

The quotient of the problem given is - 4.

To find the equivalent fractions to ,16 ÷ (–3), first solve for the quotient:

= 16 ÷ (–3)

= - 5. 33

Then, solve the fractions in the options to see if they give the same result as when you solved 16 ÷ (–3).

Fraction : 16 over negative 3

= 16 / -3

= - 5.333

This has the same value

Fraction : negative 16 over negative 3

= -16 / -3

= 5. 333

This does not have the same value

Fraction : negative 16 over 3

= - 16 / 3

= - 5. 333

This has the same value

Fraction : 16 over 3

= 16 / 3

= 5. 333

This is not the same value

Fraction: Negative (StartFraction 16 over 3 EndFraction)

= - ( 16 / 3 )

= - 5. 33

This is the same

The quotient of - 20 / 5 :

= - 20 / 5

= - 4

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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]

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: Let's call the present age of the son x and the present age of the father y.

We know that y = 3x and that six years ago, the sum of their ages was 45.

So, we can write the equation:

x + (y-6) = 45

x + (3x-6) = 45

4x = 51

x = 12.75

The present age of the son is 12.75 years.

Step-by-step explanation:

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.

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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