Dora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 12.

Answer:

The correct option is 2.

Step-by-step explanation:

The values √8 and √14 are plotted on the number line.  

From the given number line it is clear that

[tex]\sqrt{8}\approx 2.8[/tex]

[tex]\sqrt{14}\approx 3.7[/tex]

We have to find the approximate difference in tenths between the two values √8 and √14.

[tex]\sqrt{14}-\sqrt{8}\approx 3.7-2.8[/tex]

[tex]\sqrt{14}-\sqrt{8}\approx 0.9[/tex]

The approximate difference in tenths between the two values is 0.9.

Therefore the correct option is 2.

To laminate the cabinet, the total surface area is calculated and multiplied by the cost per square foot. The cabinet has a surface area of 62 square feet, and with a lamination cost of $2 per square foot, it will cost Rosalie $124.

To calculate the cost for laminating the outside of a cabinet, we first need to find the total surface area to be laminated. Since the cabinet is a rectangular prism, we can use the surface area formula for a rectangular prism: Surface Area = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. In this case, l = 3 ft, w = 2 ft, and h = 5 ft.

Surface Area = 2(3 ft)(2 ft) + 2(3 ft)(5 ft) + 2(2 ft)(5 ft)
Surface Area = 2(6) + 2(15) + 2(10)
Surface Area = 12 + 30 + 20
Surface Area = 62 square feet

Now to find the total cost, we multiply the surface area by the cost per square foot: Total cost = Surface Area times Cost per square foot.
Total cost = 62 sq ft times $2/sq ft
Total cost = $124

Therefore, it will cost Rosalie $124 to get the cabinet laminated.

Answer:

8x+2

fx= 8x+2

Step-by-step explanation:

Answer:

240 cubic cm

Step-by-step explanation:

Volume of the box before increament in sides = length*width*height

Length= 5 in.

Width=5 in.

Height = 10 in.

Putting these vales in formula

Volume of box = 5*5*10

                        =[tex]250cm^{3}[/tex]

Now  If the side lengths of the square faces are changed to 7 inches,

So, Length will be 7 in.

Width will be 7 in.

So, new volume = 7*7*10

                          =[tex]490cm^{3}[/tex]

Thus increase in volume = 490-250 =240

Hence by 240 cubic cm  will this increase the volume of the box

Answer:

A. [tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]

Step-by-step explanation:

We have been given a circle and we are told that segment RS is congruent to segment DF.

We can see that segment RS corresponds to arc RS and segment DF corresponds to arc DF.

As both segments are congruent, therefore, both arcs will be congruent as well.

We can represent this information as:

[tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]

Therefore, option A is the correct choice.

Answer:

C. [tex]x=99^{\circ}[/tex]

Step-by-step explanation:

We have been given a image. We are asked to find the value of x.

We can see that our given figure is a quadrilateral. We know that all interior angles of a quadrilateral add up-to 360 degrees.

[tex]x^{\circ}+y^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]

We can see that y and 116 degrees angles are linear angles, so we can set an equation as:

[tex]y^{\circ}+116^{\circ}=180^{\circ}[/tex]

[tex]y^{\circ}+116^{\circ}-116^{\circ}=180^{\circ}-116^{\circ}[/tex]

[tex]y=64^{\circ}[/tex]

Substitute [tex]y=64^{\circ}[/tex] in the equation:

[tex]x^{\circ}+y^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]

[tex]x^{\circ}+64^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]

[tex]x^{\circ}+261^{\circ}=360^{\circ}[/tex]

[tex]x^{\circ}+261^{\circ}-261^{\circ}=360^{\circ}-261^{\circ}[/tex]

[tex]x^{\circ}=99^{\circ}[/tex]

[tex]x=99[/tex]

Therefore, the value of x is 99.

The measure of angle x is 40 degrees and this can be determined by using the formula of the sum of interior angles of a polygon.

Given :

A regular nonagon.

The sum of interior angles of a polygon is given by the equation:

= (n - 2)180   --- (1)

where 'n' is the total number of sides of the polygon.

Given that the polygon is the regular nonagon that means the total number of sides is 9.

Now, substitute the value of 'n' in the equation (1).

= (9 - 2)180

= [tex]1260^\circ[/tex]

Now, divide the above expression by 9 in order to get the value of one interior angle.

[tex]= \dfrac{1260}{9}[/tex]

= [tex]140^\circ[/tex]

Now, the sum of one interior angle and the angle x is equal to 180 degrees that means:

140 + x = 180

x = [tex]40^\circ[/tex]

For more information, refer to the link given below:

https://brainly.com/question/19237987

Boyle's Law can be rearranged to solve for p sub 2 (final pressure) using the formula p sub 2 = p sub 1 v sub 1 / v sub 2. This shows the inverse relationship between pressure and volume of gas at a constant temperature.

The question is asking to solve the formula representing Boyle's Law (p sub 1 v sub 1 = p sub 2 v sub 2) for p sub 2. Boyle's Law states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. To solve for p sub 2, you rearrange the formula to be p sub 2 = p sub 1 v sub 1 / v sub 2. This formula means that the final pressure (p sub 2) equals the initial pressure (p sub 1) times the initial volume (v sub 1), all divided by the final volume (v sub 2). Therefore, if the volume increases, the pressure decreases, and if the volume decreases, the pressure increases, keeping the gas's temperature constant.

https://brainly.com/question/21184611

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Final answer:

To find the critical numbers, differentiate the function using the product rule, set the derivative equal to zero, and solve for x. Critical numbers are where the derivative is zero or undefined, provided they are within the domain of the function.

Explanation:

To find the critical numbers of the function f(x) = x4/5(x − 6)2, you need to locate the values of x where the first derivative of the function is either zero or undefined. The first derivative can be calculated using the product rule and the power rule.

First, let's find the derivative:

f'(x) = d/dx [x4/5] * (x - 6)2 + x4/5 * d/dx [(x - 6)2]

After simplifying, you will get a derivative function where you can then set it equal to zero to find the critical points. The points where the derivative is zero are potential local maxima, minima, or points of inflection. Additionally, points where the derivative is undefined can also be critical points, if they are within the domain of the function.

Once you calculate and simplify the derivative, set it equal to zero and solve for x. You might find that you get explicit values of x, which are the critical numbers of the function. If the function's derivative does not exist at some point, that will also be a critical number.

Remember, critical numbers are only relevant if they are within the domain of the original function.

Answer:

[tex]y=28(x-42)+840[/tex]

Step-by-step explanation:

Let he works for x hours in total.

We are given that he makes 20$ an hour for the first 42 hours

So, he earns in 1 hour = 20

He earns in 42 hours = [tex]20 \times42[/tex]

                                   = [tex]840[/tex]

Now we are given that he earns $28 an hour for each hour worked over 42 hours.

Since he worked for 42 hours out of x hours .

So, remaining hours = x-42 hours

So,he earns for x-42 hours = [tex]28\times(x-42)[/tex]

y denotes his total earning of weekly

So, total earning [tex]y=28(x-42)+840[/tex]

Hence piecewise equation models his weekly pay y in dollars as it relates to the number of hours x that he has worked during the week is [tex]y=28(x-42)+840[/tex]                                

The volume of a rectangular prism is the product of its dimension.

The missing side length is 2x + 5.

The volume is given as:

[tex]\mathbf{V = 2x^3 + 17x^2 + 46x + 40}[/tex]

Let the missing side be y.

So, we have:

[tex]\mathbf{V = (x + 2) \times ( x + 4) \times y}[/tex]

So, we have:

[tex]\mathbf{(x + 2) \times ( x + 4) \times y = 2x^3 + 17x^2 + 46x + 40}[/tex]

Factorize

[tex]\mathbf{(x + 2) \times ( x + 4) \times y = (x + 2) \times (x + 4) \times (2x +5)}[/tex]

Cancel out common factors

[tex]\mathbf{y = (2x +5)}[/tex]

Remove brackets

[tex]\mathbf{y = 2x +5}[/tex]

Hence, the missing side length is 2x + 5.

Read more about volumes at:

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General Idea:

We need to make use of the below formula to find the monthly payment..

[tex] Monthly \; Payment\; =\; \frac{P \times \frac{r}{12}}{(1-(1+\frac{r}{12})^{-m})} \\ \\ Where:\\ P\; is\; Principal\\ r\; is\; rate\; in\; decimal\; form\\ m\; is\; number\; of\; monthly\; payments [/tex]

Applying the concept:

Given:

[tex] P=\$224,500\\ r=4\%=0.04\\ m=30\; year \times 12 \; months/year=360\\ [/tex]

Substituting the given in the formula we will get the monthly payment.

[tex] Monthly\; Payment\; =\; \frac{224500 \times \frac{0.04}{12}}{(1-(1+\frac{0.04}{12})^{-360})} =\frac{\frac{8980}{12}}{(1-0.301796)} =\frac{748.3333}{0.698204} \\ \\ Monthly \; Payment= \$1071.7975 [/tex]

Conclusion:

The monthly payment during the initial period is $1072.

In each case, the x-values are equally-spaced. Thus looking at second differences will tell you if the relation is quadratic. If the second differences are non-zero and constant, then the values have a quadratic relationship.

A. First differences are 2-4 = -2, 1-2 = -1, 0.5-1 = -0.5. Second differences are -1-(-2) = 1, -0.5-(-1) = 0.5. Since 1 ≠ 0.5, this relation is not quadratic. (It is exponential with a base of 1/2.)

B. First differences are 128-135 = -7, 105-128 = -23, 72-105 = -33. Second differences are -23-(-7) = -16, -33-(-23)=-10. Since -16 ≠ -10, this relation is not quadratic. (It is cubic, since 3rd differences are constant at +4.)

C. First differences are -23.2-(-23.4) = 0.2, -23.0-(-23.2) = 0.2, -22.8-(-23.0) = 0.2. Second differences are zero, so this is not a quadratic relation. (It is linear, with a slope of 0.2.)

D. First differences are 56-90 = -34, 26-56 = -30, 0-26 = -26. Second differences are -30-(-34) = 4, -26-(-30) = 4. These are constant (=4), so the relation is quadratic.

The appropriate choice is ...

... D. x -1 0 1 2 3 4

... f(x) 90 56 26 0 -22 -40

Answer:  D. x -1 0 1 2 3 4

f(x) 90 56 26 0 -22 -40

Step-by-step explanation:

Answer:

A. 270.9

Step-by-step explanation:

We know that the rule of significant figures for addition and subtraction states that 'the number of places after the decimal point in the result is equal to the least number of decimal places in each term.'

So, 67.31 - 8.6 + 212.198  = 67.31 + 212.198  - 8.6 = 279.508 - 8.6 = 270.908

Now, the resultant number is 270.908

Using the rule of significant figures, we get that, the number of places after the decimal point in 270.908 will be equal to the least number of decimal places i.e. 1 ( in 8.6 )

Hence, 67.31 - 8.6 + 212.198 = 270.9

we are given

m∠BCD =67

and  m∠BDC=60

we know that

m∠ABC is exterior angle

m∠BCD  and  m∠BDC are interior angles

exterior angle is sum of interior angles

so, we can write it as

m∠ABC=m∠BCD+m∠BDC

now, we can plug values

and we get

m∠ABC=60+67

m∠ABC=127

so, option-4.........Answer

Answer:

Inverse function: A function g is the inverse of a function f if whenever y=f(x) then x=g(y).

In other words, we can write this in terms of the composition of f and g as g(f(x))=x.

For any input x, the function corresponding to f spits out the value y=f(x)=4x+12.

Now, we want to find the inverse function g(x)=[tex]f^{-1}[/tex] that takes the value y as an input and spits out x as the output.

In other words, y=f(x) gives y as a function of x and we want to find [tex]x=f^{-1}(y)[/tex] that will give us x as a function of y.

Given,the expression y=4x+12 for y as a function of x and solve for x.

Subtract 12 from both sides we get;

y-12 = 4x+12-12

Simplify:

y-12 = 4x

Divide by 4 to both sides we get;

[tex]\frac{y-12}{4} =\frac{4x}{4}[/tex]

Simplify:

[tex]x=\frac{1}{4}y - 3[/tex]

therefore,  [tex]x = f^{-1}(y) = \frac{1}{4}y-3[/tex]

since, g(x) is the inverse of f(x)

⇒[tex] g(x)=\frac{1}{4}x-3[/tex]

Now, verify that g(x) is really the inverse of f(x), we should show that the composition of f and g doesn't do anything to the input.

[tex](g o f)(x) = g(f(x)) = g(4x+12) = \frac{1}{4}(4x+12) -3 = x+3 -3[/tex]

Simplify:

g(f(x)) = x                for all x

⇒  g(x) is the inverse of f(x)

Therefore, [tex] g(x)=\frac{1}{4}x-3[/tex]

Using inverse functions, it is found that that:

[tex]g(x) = \frac{x - 12}{4}[/tex]

To find the inverse function, we exchange x and y in the original function, then isolate f.

The function f(x) is given by:

[tex]f(x) = 4x + 12[/tex]

Function g(x) is the inverse of f(x), then:

[tex]y = 4x + 12[/tex]

[tex]x = 4y + 12[/tex]

[tex]4y = x - 12[/tex]

[tex]y = \frac{x - 12}{4}[/tex]

[tex]g(x) = \frac{x - 12}{4}[/tex]

To learn more about inverse functions, you can take a look at https://brainly.com/question/16485117

Final answer:

Prism B's volume is 8 times larger than Prism A's volume due to the dimensions being twice as large. Given the volume of Prism A as 2080 cm³, the volume of Prism B is 16640 cm³.

Explanation:

The student is asking about the volume of similar prisms. When two prisms are similar, their volumes are proportional to the cube of the ratio of their corresponding linear dimensions. In this case, Prism B is similar to Prism A, and the ratio of the volumes is given in the problem. Specifically, the volume of Prism B is 4 times the volume of Prism A because the dimensions of Prism B are twice that of Prism A, making the volume 23 or 8 times greater. However, you've also provided that the volume of Prism B is 4 times that of Prism A, this seems to be a conflict in the information, and there's an issue with typos in the provided content which makes it inconsistent (2L3 versus 213, 213). Based on the correct proportion which should be 8 times, if the volume of Prism A is 2080 cm3, then the volume of Prism B would be 2080 cm3 multiplied by 8 (8L3/L3), yielding 16640 cm3.