Solve using substitution.
x = –3
x + 7y = 18
(, )

The rectangular prism's dimensions are 3:2:1 in terms of length, breadth, and height. The prism's length can be computed as 24 cm using its volume, 48 cm3, as input.

Volume = Length × Width × Height

48 cm3 = L × 2 × 1

L = 24 cm

A rectangular prism is a solid 3D object that has six faces, eight vertices and twelve edges. The length, width and height of a rectangular prism can be expressed in a ratio of 3:2:1 respectively. Knowing this ratio and the volume of the prism, which is 48 cm3, it is possible to calculate the length of the prism. To calculate the length of the prism, first the volume of the prism must be expressed in terms of the length. This can be done by using the formula Volume = Length × Width × Height. Therefore, 48 cm3 = L × 2 × 1. Solving this equation for L gives the length of the prism as 24 cm. Therefore, the length of the rectangular prism with a volume of 48 cm3 and a ratio of 3:2:1 is 24 cm.

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Answer:

Step-by-step explanation:

Given similar triangles DEF and GHF, and side lengths DE = 6, EF = 10, GH = 21, FG = 28, you want the lengths of y=FH and x=FD.

Corresponding sides of similar triangles are proportional. This means ...

  DE/GH = EF/HF = FD/FG

  6/21 = 10/y = x/28

We can multiply by 28 to solve for x:

  x = 28(6/21) = 8

Multiplying by 21y/6 will give the value of y:

  y = (21/6)(10) = 35

The values of x and y are 8 and 35, respectively.

__

Additional comment

These are both 3-4-5 right triangles. The smaller is multiplied by 2; the larger is multiplied by 7 to give 6-8-10 and 21-28-35 triangles.

It is means the temperature of the water does not fall below [tex]$10^{\circ} \mathrm{C}$[/tex].

The exponential function, which develops exponentially, is a concept in mathematics. More exactly, it is the function, where e is the irrational Euler's constant, or about 2.71828.

where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

A function that has a positive constant increased to a variable exponent, other than 1, is referred to as an exponential function. A function is assessed by being solved at a certain input value. When the growth rate and initial value are known, an exponential model can be found.

(a) initial temperature: [tex]$30^{\circ} \mathrm{C}$[/tex] it is y-intercept of the graph.

(b) For the first 30 minutes, as time inverses, the temperature decreases.

(c) the horizontal asymptote: y = 10

It is means the temperature of the water does not fall below [tex]$10^{\circ} \mathrm{C}$[/tex].

The complete question is:

Some water is placed in a bottle inside a refrigerator. Suppose the water's temperature [tex]$\left(n^{\circ} \mathrm{C}\right)$[/tex] after minutes can be modeled with an exponential function. The graph of this function is shown below. Use the model to answer the parts to the right.

(a) What is the initial temperature [tex]$\times_6$[/tex] of the water? [tex]$\square^{\circ} C$[/tex] The initial temperature is represented by the (Choose one) of the graph.

(b) For the first so minutes, as time increases, the temperature (Choose one) Temperature

(c) Give the equation of the asymptote. [tex]$y-a l^{\circ} \mathrm{Cl}$[/tex]

Choose the statement that best describes the meaning of the asymptote.

The temperature of the water Time (minutes) does not fall below [tex]$10^{\circ} \mathrm{C}$[/tex].

The water cannot be in the bottle for more than so minutes.

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The profit of the sales is (a) $27

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

This means that

Profit = 6x + 6 - x + 1

Evaluate the like terms

Profit = 5x + 7

When x = 4, we have

Profit = 5 * 4 + 7

Evaluate

Progit = 27

Hence, the profit is $27

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Answer:

A:$27

Step-by-step explanation:

i took the test and got it right

We can find the solution of y = -2x + 6 by graphing the equation by plotting the intercepts of the equation.

Here we can solve the equation by calculating the x and y intercepts of the equation.

This is done by equating the other coordinate to 0 to get the intercept.

For the x-intercept, we will take y to be 0 to get

-2x + 6 = 0

or, 2x = 6

or, x = 3

Hence one intercept will be (3 , 0)

For the y-intercept, we will let x be 0 to get

y = 6

Hence getting the other intercept to be (0 , 6)

Now we can plot the graph by simply plotting these points and drawing a straight line passing through it

To get any unique solution, another equation needs to be plotted and the intersection point of the 2 lines will give us the required answer.

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Complete Question

How do you solve y = -2x + 6?

Step-by-step explanation:

48 miles in 1 hour 30 minutes (1.5 hours = 3/2 hours).

speed = distance/time

as mph is requested, the time is 1 hour.

in our case the direct speed ratio is

48/1.5

to bring that to the regular miles per 1 hour we need to transform it. here I would use fractions and simplify :

48/1.5 = 48/ 3/2 = (2×48)/(3×1) = 96/3 =

= 32/1 = 32 mph

the speed of the bus was 32 mph.

Answer:

No

Step-by-step explanation:

Answer:

Step-by-step explanation:

all 3 angles on a triangle add up to 180 degrees, so all triangles are 180 degrees.

Work Shown:

[tex]\sqrt{200} \times \sqrt{2}\\\\\sqrt{200 \times 2}\\\\\sqrt{400}\\\\\sqrt{20^2}\\\\20\\\\\text{Therefore, }\sqrt{200} \times \sqrt{2}=20\\\\[/tex]

The rules I used were:

[tex]\sqrt{A}*\sqrt{B} = \sqrt{AB}\\\\\sqrt{A^2} = A \ \ \text{ where } A \ge 0\\\\[/tex]

(0,3) , (4,0) are two solution of equation 3x + 4y = 12.

An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two parts, separated by an equal sign (=), with the expressions on either side representing the same value.

Given Linear equation in two variables:

3x + 4y = 12 ----( 1 )

Substitute x = 0 , in equation ( 1 ) ,

3 × 0 + 4y = 12

=> 4y = 12

=> y = 12/4

y = 3

Therefore ,

( x , y ) = ( 0 , 3 )

Substitute y = 0 in equation ( 1 ) ,

3x + 4 × 0 = 12

=> 3x = 12

=> x = 12/3

x = 4

Therefore,

( x , y ) = ( 4 , 0 )

Required two solutions are ( 0 , 3 ) , ( 4 , 0 )

Therefore, (0,3) , (4,0) are two solution of equation 3x + 4y = 12.

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Answer:

Step-by-step explanation:

Equiangular triangle

Using the pythagorean theorem: The length of the sides of a 45-45-90 triangle can be easily solved using the pythagorean theorem because it is a right angle triangle.

Recall the formula for the Pythagorean theorem: a 2 + b 2 = c 2; a 2 + b 2 = c2.

To determine the value of (mostly) the hypotenuse in a right triangle, the Pythagorean theorem uses the formula a2+b2=c2. The "non-hypotenuse" sides of the triangle (opposite and adjacent) are a and b.

The well-known geometric theorem known as the Pythagorean theorem states that the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the squares on the legs of a right triangle. This is known as a2 + b2 = c2.

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Answer:

  5) x = 5

  6) x ≈ 51.47

Step-by-step explanation:

It looks like you're being asked to solve for x the equations ...

These are solved in the way any such equation is solved, though you need a calculator to find the values of the trig functions.

Multiply by the denominator:

  x = 10·sin(30°) = 5

Multiply by x, then divide by cos(39°):

  x = 40/cos(39°) ≈ 51.47

A partial sum limit is the sum of the series.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.

A partial sum is the total of a limited number of the series' terms. To see how the infinite sum behaves, we can examine a collection of these sums. The index of the final term in the sum is used to denote each of these partial sums.

When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.

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Answer:

(- 6, 0 )

Step-by-step explanation:

x - 4y = - 6 → (1)

2x - 12y = - 12 → (2)

multiplying (1) by - 2 and adding to (2) will eliminate x

- 2x + 8y = 12 → (3)

add (2) and (3) term by term to eliminate x

(2x - 2x) + (- 12y + 8y) = - 12 + 12

0 - 4y = 0

- 4y = 0 , then

y = 0

substitute y = 0 into either of the 2 equations and solve for x

substituting into (1)

x - 4(0) = - 6

x - 0 = - 6

x = - 6

solution is (- 6, 0 )

Answer:

x = -6

y = 0

Step-by-step explanation:

For the first equation, x - 4y = -6, we can move -4y to isolate x. Then, the equation will be: x = -6 + 4y. Now, we can use that x to solve for the second equation, 2x - 12y = -12. Let's plug in x from the first equation down to the second one:

2(-6 + 4y) - 12y = -12

Let's solve:

-12 + 8y - 12y = -12

-4y = 0

y = 0

Now that we have y, we can solve for x. Let's plug in y = 0 for the first problem: x-4(0) = -6

x = -6

The expression that represents the total amount of change she should receive is y = 20 - 3x.

An algebraic expression that uses either a constant or a variable raised to the first power for each term is known as a linear expression. This means that none of the exponents can be greater than 1.

The price of x boxes of cereal $3 each = 3x

Let y be the extra cash she paid

Total cash she paid = $20

Then we have

3x + y = 20

And for expression that represents the total amount of change she should receive

y = 20 - 3x

Thus, The expression that represents the total amount of change she should receive is y = 20 - 3x.

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In a factorial design study, (B) the interaction effect is often viewed as the most important influence.

In statistics, a full factorial experiment is one in which all potential combinations of the levels across all of the factors are taken into account by the experimental units.

A full factorial experiment has two or more factors with discrete possible values or "levels" in its design.

A fully crossed design is another name for a full factorial design.

The interaction effect in a factorial design study is typically regarded as the most significant effect.

Using such an experiment, the researcher can examine how each element affects the response variable as well as how different factors interact with one another.

Therefore, in a factorial design study, (B) the interaction effect is often viewed as the most important influence.

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Answer:

y = -5/2x + 31

Step-by-step explanation:

The slope of the line parallel to the given line has the same slope, m = -5/2

Use the point-slope form:  y - y1 = m(x - x1) and the given point (10,6)

y - 6 = -5/2(x - 10)

y - 6 = -5/2(x + 50/2)

y - 6 = -5/2x + 25

y = -5/2x + 31

The equation, y = mx + b, is the slope-intercept form of a straight line.

Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis.

y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.

The value of b is equal to y when x = 0, and m shows how steep the line is. The slope of the line is also called the gradient.

To find the equation of the straight line, we use the slope-intercept form, y = mx + b, where m is the slope of the line, b is the y-intercept of the line.

We can find the equation of a line in the form of y = mx + b, if the coordinates of points forming the line are known to us.

Thus, The equation, y = mx + b, is the slope-intercept form of a straight line.

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Answer:

Step-by-step explanation:

The x -intercept is the point where y = 0 so:

7x - 5(0) = 35

x = 35/7 = 5

x-intercept is at (5, 0)

The y -intercept is the point where x = 0 so:

7(0) - 5y = 35

y = 35/-5 = -7

x-intercept is at (0, -7)

Answer:

x (5, 0)

y (7, 0)

Answer:

OQ = 4

Step-by-step explanation:

the ratios of the segments OP : PQ : QR = 1 : 1 : 3 = x : x : 3x ( x is a multiplier)

then

OP + PQ + QR = OR , that is

x + x + 3x = 10

5x = 10 ( divide both sides by 5 )

x = 2

Then

OQ = OP + PQ

      = x + x

     = 2x

     = 2 × 2

     = 4

The employer of Bill’s FICA  should withhold D. $24.92 in taxes

Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.

To solve this exercise, the percentage formula and the procedure to be applied is as follows:

n= (% * nt) / 100

Where:

Information about the problem:

Using the percentage formulate, we get how much FICA tax should his employer withhold:

n= (% * nt) / 100

n = (7.65 * $325.78)/100

n = $2492.22/100

n = $24.92

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To write 8 more than a number, we use the mathematical operation of addition and the notation 8+ Number = N+8.

To write 8 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 8 + Number = N+8.

This notation means that we are adding 8 to a number, which results in N+8. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+8.

Another way to write 8 more than a number is to use the phrase "8 plus a number". This phrase indicates that we are adding 8 to a number to get N+8.

Therefore, In short, to write 8 more than a number, we use the mathematical operation of addition and the notation 8 + Number = N+8. This means that we are adding 8 to a number, resulting in N+8. It can also be written as "8 plus N", indicating the same operation.

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Answer:

this is answer ️️️️️️

Answer:

Solving a system of equations by substitution involves isolating a variable in one equation, then substituting that expression into the other equation. This allows you to solve for the remaining variable in one equation and then substitute it back into the first equation to find the solution for the other variable.

Here is the general process for solving a system of equations by substitution:

Isolate a variable in one of the equations. This is typically done by adding or subtracting one of the variables from both sides of the equation.

Substitute the isolated expression into the other equation by replacing the corresponding variable with the expression you found in step 1.

Solve the new equation for the remaining variable.

Substitute the value you found for the remaining variable back into the first equation and solve for the other variable.

Check your solution by substituting the values you found for the variables back into both equations to make sure they are true statements.

Write your solution in the form of an ordered pair (x, y)

An example of solving a system of equation by substitution :

2x + 3y = 8

4x - 3y = 2

Isolate a variable in one of the equations, for example:

3y = 8 - 2x

Substitute this expression into the other equation:

4x - 3(8 - 2x) = 2

Solve the new equation for the remaining variable:

4x - 24 + 6x = 2

10x = 26

x = 2.6

Substitute the value you found for x back into the first equation and solve for y:

2(2.6) + 3y = 8

5.2 + 3y = 8

3y = 2.8

y = 0.93

Check your solution by substituting the values you found for the variables back into both

To complete the project in 36 days, the construction manager would need to add at least 8 more workers to his current team of 12 workers.

If 12 workers can complete a building project in 54 days, to determine this we can divide the rate of work by the number of workers by the number of days: 12 workers / 54 days = 0.2222 workers/day.

If the construction manager wants to complete the project in 36 days, he needs to increase the rate of work to complete the project in that shorter timeframe. To do this, he can add more workers or increase the productivity of the current workers.

To determine how many more workers the manager needs, we can use the formula:

(number of workers) = (rate of work) x (number of days)

By plugging in the desired rate of work and number of days, we get:

(number of workers) = (0.2222 workers/day) x (36 days) = 7.999 workers

To complete the project in 36 days, the construction manager would need to add at least 8 more workers to his current team of 12 workers.

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To write algebraic expression for an equivalent expressions, we need to be sure that each side of the equal sign amounts to the same number. An example of an equivalent equation would be:

4x + 2 = 2(2x + 1)

An algebraic expression is a sequence of numbers, variables, mathematical operations, and sometimes exponents. For example, 4x + 3 is a basic algebraic expression. Also see there is no equal sign in the algebraic expression. If so, it can be an equation or set of numbers containing one or more variables.

Equivalent Expressions: Equivalent expressions are expressions that look different but have the same value. Writing the equivalent formula makes it easier to work with and solve. Two Ways to Write the Equivalent Expressions :

1) Write expression using the distributed property:

2) Write equivalent expressions by combining same terms. Same terms are terms that have the same variables raised to the same powers. For example, the list shows several pairs of similar terms, 4t and 5t ; 9k³and 2k³ ; 1.4xy and 6.7xy.

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The logarithmic function is inverse of expontial function that why graph of logarithmic function is draw according to features of expontial function.

The logarithmic function [tex] f(x) = log_{b}(x) [/tex] is the inverse of the exponential function y=bˣ. Clearly, the logarithm function must have domains and limits of (0, ∞) and (−∞,∞). The logarithmic function can be graphed by examining the graph of the exponential function and swapping x and y. Graphs of exponential functions f (x) = bˣ or y = bˣ include the following features:

For example, the graph above represents a logarithmic function, [tex] f(x) = log_{2}(x) [/tex].

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Answer:

[tex] 2\sqrt[3]{12} [/tex]

Or in decimal notation 4.6

Step-by-step explanation:

[tex] \sqrt[3]{6} \times \sqrt[3]{16} \\ = \sqrt[3]{6} \times 2 \sqrt[3]{2} \\ = \sqrt[3]{6 \times 2} \times 2 \\ = \sqrt[3]{12} \times 2 \\ = 2 \sqrt[3]{12} \\ = 4.57885...[/tex]