A steel company is making flat rectangular frames as a part of a new product they are launching. Each frame will be cut out of a piece of steel and will have a final area as close to 28 cm2 as possible. The width of the frame needs to be uniform throughout. The inside dimensions of the frame must be 11 cm by 6 cm. Complete the equation that models the above situation, and find the width of the frame, x

Answer:

B. 12,17,23

Step-by-step explanation:

2,3,5,8, _,_,_

2,3 is increased by 1

3,5 is increased by 2

5,8 is increased by 3.  theres our pattern, each time it increases it follows the next number so the next 3 numbers it would be increased by is. 4,5,6.

Now knowing it is 4,5,6 we need to add, start adding.

8+4=12. Which answers have 12 in them? B and C.

We know 12 is the next number, now we add 5 to that.

12+5=17.

B has 17 but C doesn't, so that tells you its most likely going to be B. To make sure add 6 to 17.

17+6=23. Its true that it is B, as B is 12.17.23.

The next three terms in the sequence are 13, 21, and 34.

The given sequence is 2, 3, 5, 8.

To find the next three terms in the sequence, we need to determine the pattern.

By observing the sequence, we can see that each term is obtained by adding the two previous terms.

For example,

3 = 2 + 1,

5 = 3 + 2, and

8 = 5 + 3.

Using this pattern, the next term would be obtained by adding 8 + 5, -

8 + 5 = 13

The two terms after that would be

13 + 8 = 21 and

21 + 13 = 34.

Therefore, the next three terms in the sequence are 13, 21, and 34.

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Answer:think as it as coordinates on a graph. Time=x Amount=y. So if the time is 0 and the amount is 60 you would graph a point on (0,60)

Step-by-step explanation:

The statement 'the length of a rectangle if the length is twice the size of the width increased by one' translates into the equation l = 2w + 1 in mathematical terms. This equation represents a relationship between the rectangle's length (l) and width (w), with the length being twice the width, increased by one.

The correct translation of the statement 'the length of a rectangle if the length is twice the size of the width increased by one' is mathematical in nature. This sentence is describing a relationship between the length and width of a rectangle.

To put it into an equation, start by denoting the width of the rectangle as 'w'. The statement says that the length is twice this width (2w) plus one. So, the length 'l' can be represented as:

l = 2w + 1

This equation shows the relationship between the length and width of a rectangle according to given statement. For practical purposes, you can insert a numerical value for width 'w' and perform the calculation on the right side to find the length 'l'.

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The mathematical expression translating the phrase is 'L = 2W + 1', where 'L' represents length of the rectangle and 'W' represents the width. It indicates that the length is twice the width, and further increased by one.

The correct translation of the statement 'the length of a rectangle if the length is twice the size of the width increased by one' would result in a mathematical expression for the length of the rectangle (L). If we denote the width of the rectangle as W, then we could represent the length of the rectangle as follows:

L = 2W + 1

This expression indicates that the length is twice the size of the width, and then increased by one. Depending on the value of W, we plug it into the equation to determine the length of the rectangle.

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Answer:

you divide the top number by the bottom number

Step-by-step explanation:

2/5 = 0.4

The sales tax would be $42.00, making the total cost $112.00.

To calculate the sales tax on an item, one must first convert the sales tax rate from a percentage to a decimal. Converting 60% to a decimal by dividing by 100 gives us 0.60.

Then, multiply this decimal by the selling price to find the amount of sales tax.

Amount of sales tax = price x rate of sales tax

So for a selling price of $70.00, the sales tax would be calculated as follows:

= $70.00 x 0.60 = $42.00

The sales tax on a $70.00 item at a rate of 60% is $42.00.

To find the total cost, one must add this tax to the original selling price.

Total cost = selling price + sales tax

Total cost = $70.00 + $42.00

Total cost = $112.00

Thus, the total amount paid including sales tax would be $112.00.

Answer:

[tex]-\frac{1}{2\pi}[/tex] cm³/min  

Step-by-step explanation:

Let h = height of water and r = radius of its surface  

[tex]V = \frac{ 1}{ 3}\pi r^{2}h[/tex]

At all times,  

[tex]\frac{r }{h } = \frac{4 }{16 } = \frac{ 1}{4 }[/tex]

So, [tex]r = \frac{h }{4 }[/tex]  

[tex]V = \frac{ 1}{ 3}\pi (\frac{h }{ 4})^{2}h[/tex]

[tex]V = \frac{ 1}{ 48}\pi h^{3}[/tex]

[tex]\frac{\text{d}V}{\text{d}h} = \frac{ 1}{ 16}\pi h^{2}[/tex]

We want [tex]\frac{\text{d}h}{\text{d}t}[/tex]

[tex]\frac{\text{d}V}{\text{d}t} = \frac{\text{d}V}{\text{d}h} \frac{\text{d}h}{\text{d}t}[/tex]

[tex]\frac{\text{d}V}{\text{d}t}[/tex] = -2 cm³/min  

[tex]-2 = \frac{ 1}{ 16}\pi h^{2} \frac{\text{d}h}{\text{d}t}[/tex]

[tex]\frac{\text{d}h}{\text{d}t} = -\frac{2}{\frac{ 1}{ 16}\pi h^{2} }[/tex]

[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{\pi h^{2}}[/tex]

When h = 8  cm

[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{\pi\times8^{2}}[/tex]

[tex]\frac{\text{d}h}{\text{d}t} = -\frac{32}{64\pi}[/tex]

[tex]\frac{\text{d}h}{\text{d}t} = -\frac{1}{2\pi}[/tex] cm³/min

The depth of the water is decreasing at a rate of [tex]\frac{1}{2\pi}[/tex] cm³/min

.

There are 0 unique triangles that can be drawn with the side lengths 4 cm, 5 cm, and 10 cm

How to determine the total number of unique triangles that can be drawn

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

Side lengths = 4 cm, 5 cm, and 10 cm

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So, we have

4 + 5 > 10 --- false

4 + 10 > 5 --- true

5 + 10 > 4 --- true

Since one of the conditions is false, no triangles can be formed using the side lengths

Answer: all angle measures are equal

Answer:

The terms are already in lowest form. The factors of 21 are 21 and 1, and 3 and 7. The factors of 18 are 1 and 18, 2 and 9, and 3 and 6. The factors of 28 are 1 and 28, 2 and 14, and 7 and 4. None of them match up so it is as low as it can be.

Step-by-step explanation:

the greatest common factor is x. because

21, -18, and 28 do not have any shared factors

Answer:

53028.064 I think

Step-by-step explanation:

As x increases, x^3 grows faster than 3x.

As x increases, the growth rate of x^3 (x cubed) is faster than that of 3x. This can be explained by comparing their respective derivatives.

The derivative of x^3 with respect to x is 3x^2, while the derivative of 3x is simply 3.

The derivative represents the rate of change, or the slope of the function at a given point. In the case of x^3, its derivative 3x^2 grows at a faster rate than the derivative of 3x, which is a constant (3).

This means that as x increases, the rate of change of x^3 (3x^2) increases faster compared to the rate of change of 3x (which is constant at 3). In other words, x^3 exhibits exponential growth, while 3x exhibits linear growth. So, as x increases, x^3 grows faster than 3x.

for such more question on growth rate

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Answer: the two numbers is 35 and 18

Step-by-step explanation: 35+18=53 35-18=17

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Final answer:

The two numbers are 35 and 18. We found these by solving the simultaneous equations x + y = 53 and x - y = 17, representing their sum and difference.

Explanation:

Finding Two Numbers Given Their Sum and Difference

Let's denote the two unknown numbers as x and y. According to the conditions given:

x + y = 53 (Equation 1: The sum of the two numbers)

x - y = 17 (Equation 2: The difference of the two numbers)

We can solve these two simultaneous equations to find the values of x and y.

Add the two equations:

(x + y) + (x - y) = 53 + 17

2x = 70

x = 35

Substitute x in Equation 1:

35 + y = 53

y = 53 - 35

y = 18

Therefore, the two numbers are 35 and 18.

If the points P (7, 12), Q (-3, -12) and R (14, 5) lie on a circle with the center C (0, 2), then the distance OP, OQ and OR are the same.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute:

[tex]OP=\sqrt{(2-7)^2+(0-12)^2}=\sqrt{(-5)^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OP=13}\\\\OQ=\sqrt{(2-(-3))^2+(0-(-12))^2}=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OQ=13}\\\\OR=\sqrt{(2-14)^2+(0-5)^2}=\sqrt{(-12)^2+(-5)^2}=\sqrt{144+25}=\sqrt{169}\\\\\boxed{OR=13}[/tex]

OP = OQ = OR, therefore the points P, Q and R lie on one circle.

Answer: D

Step-by-step explanation:

To create a perpendicular bisector:

Congrats! You just constructed a perpendicular bisector!

Answer:

C

Step-by-step explanation:

To find whether it is a arithmetic or geometric sequence it is easiest to try to subtract term a2 from a1, seeing if d or r is positive. If that does not heed an answer try dividing a2 by a1 to see if it is a geometric sequence.

The terms go as follows just in case (They would normally be in subscripts)-

a1= -12

a2= -7

a3= -2

a4= 3

Answer: Yes; 5 (choice A)

We add 5 to each term to get the next

-12+5 = -7

-7+5 = -2

-2+5 = 3

and so on. The nth term formula is

an = -12 + 5(n-1)

If you were to plug in n = 1, 2, 3, ... then it should generate the terms shown

Answer:

Fried crab cakes = $4.50

Cup of gumbo = $3.25

Step-by-step explanation:

Let's make the price of fried crab cakes = x and the price of a cup of gumbo = y. Set up two equations for x and y and solve for each variable.

4 people ordered x and 4 people ordered y for a total of 31 dollars, so this equation would look like: 4x + 4y = 31

2 people ordered x and 1 person ordered y for a total of $12.25, so this equation would look like: 2x + y = 12.25

Now you have your two equations-- solve for a variable in one of the equations and substitute that value into the other equation.

The easiest way to start would be to solve for y in the second equation by subtracting 2x from both sides.

y = 12.25 - 2x

Substitute this value into the first equation.

4x + 4(12.25 - 2x) = 31

Now solve for x-- start by distributing 4 inside the parentheses.

4x + (49 - 8x) = 31

Combine like terms.

-4x + 49 = 31

Subtract 49 from both sides.

-4x = -18

Divide both sides by -4.

x = 4.5

Substitute this value of x into our starting equation for which we solved for y.

2(4.5) + y = 12.25

Multiply 2 and 4.5 together.

9 + y = 12.25

Subtract 9 from both sides.

y = 3.25

Each order of fried crab cakes is worth the x-value [$4.50] and each cup of gumbo is worth the y-value [$3.25].

In this system of linear equations, by denoting the cost of the fried crab cakes as x dollars, and the cost of a cup of gumbo as y dollars, we find that each order of fried crab cakes is $4.50 and each cup of gumbo is $3.25.

The subject of this problem is linear algebra, and it can be solved using a system of linear equations. Let's denote the cost of the fried crab cakes as x dollars, and the cost of a cup of gumbo as y dollars.

From the information given in the problem, we can create the following two equations:

Now, we can solve this system of equations. Divide the first equation by 2, which will give us:

2x + 2y = 15.5

Then subtract the second equation from the result, which will give us:

y = 3.25

Substitute y = 3.25 into the second equation:

2x + 3.25 = 12.25

Finally, solve for x:

x = 4.5

So, each order of fried crab cakes is $4.50 and each cup of gumbo is $3.25.

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Answer:

x=2

Step-by-step explanation:

F(x) = 2x^2 - 8x +8

Axis of symmetry lies at the x coordinate of vertex

To find x coordinate of vertex use formula

[tex]x=\frac{-b}{2a}[/tex]

from the given f(x) , a= 2 and b = -8

Plug in all the values

[tex]x=\frac{-(-8)}{2(2)}[/tex]

[tex]x=\frac{8}{4}=2[/tex]

x=2

So the axis of symmetry at x=2

Answer:

x=-1, y=4

Step-by-step explanation:

When we solve by elimination, we are getting rid of one variable, in this case y.  We will add the two equations together.

5x-4y=-21

-2x+4y=18

---------------

3x  = -3

Divide each side by 3

3x/3 =-3/3

x =-1

Now we need to calculate y

-2x +4y = 18

Substitute x=-1

-2(-1)+4y = 18

2+4y =18

Subtract 2 from each side

4y = 18-2

4y=16

Divide each side by 4

4y=16/4

y =4

Answer:

$1,337.91

Step-by-step explanation:

Hello, my dear friend, I am sure the question you are intending should be corrected as follows:

For two weeks, John and Amanda had the following transactions occur to their checking account: a deposit of $1,644.50; checks written for $190, $45, and $7.50; and debit card transactions for $30, $5.59, $7.20, and $21.30. What is the ending balance for this time frame?

If this is the case, then see the operation for the transactions below:

1,644.5−190-45-7.5-30-5.59-7.2-21.3=1,337.91

Please note that Deposits are positive in your account while written checks and debit card charges are negative.

Answer:

18.5 but rounded to 19 because you cant have half of a box

Step-by-step explanation:

because each box costs 3.5 dollars because i did 1 4 divided by 4.then you want to get to 65 so i did 3.5 divided by 65 then got 18.5 which was rounded because the decimal was big This was the real decimal 18.5714286. THIS MIGHT BE WRONG  

Answer:

Car D will have a different measurement because the 60.35 would round up to be 60.31 where all the other would round down and remain at 60.30

Step-by-step explanation:

Answer:

$16.32

Step-by-step explanation:

1. Ms. Blankenship bought 32 glue sticks each for  $1.40, then she spent

[tex]\$1.40\cdot 32=\$44.80[/tex]

for all sticks.

2. Ms. Blankenship bought 32 boxes each for  $0.59, then she spent

[tex]\$0.59\cdot 32=\$18.88[/tex]

for all boxes.

3. Together 32 glue sticks and 32 boxes cost

[tex]\$44.80+\$18.88=\$63.68.[/tex]

4. If Ms. Blankenship had $80, then she had left

[tex]\$80-\$63.68=\$16.32.[/tex]

Answer:   0.85 L or [tex]\frac{85L}{100}[/tex]  or [tex]\frac{17L}{20}[/tex]

Step-by-step explanation:

Since, According to the question,

Landen spent time at the beach last weekend = L hours

And, Matéo spent 15% fewer hours at the beach than Landen did.

Therefore, Number of hours spent by  Matéo = (Time spent by Landen last week - 15 % of the Time spent by Landen last week ) hours

=  85% of the Time spent by Landen last week

= [tex]\frac{85\times L}{100}[/tex]

= [tex]\frac{85L}{100}[/tex]  Hours

= [tex]\frac{17L}{20}[/tex]  Hours

=  0.85 L Hours

Answer:

Its L(1-0.15) and L-3/20L

Step-by-step explanation:

Trust me. i got it from Khan Academy. for mine it was B and E. :3

Answer:

$13.66

Step-by-step explanation:

Multiply the amount of Dijon mustard and mustard by its price, then add them together.

3 * 3.69 = 11.07

.5 * 5.18 = 2.59

Add these sums together.

11.07 + 2.59 = 13.66

Answer:

What drop down menues??????????????????????

Step-by-step explanation:

Answer:

options?

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(4)

Under a counterclockwise rotation about the origin of 90°

a point (x, y) → (- y, x), hence

C(- 3, 4) → C'(- 4, - 3)

(5)

Under a clockwise rotation about the origin of 180°

a point (x , y) → (-x, - y), hence

A(- 3, 2) → A'(3, - 2)

Answer: you need to get a common denominator.. once you have a common denominator, you can compare numerators to see what is larger..

Step-by-step explanation:

to get the common denominator, you would first see what this would be.. in this case 18, as that's the lowest.  then, you would multiply each fraction by 2/2 for first and 3/3 for second, which are just funky looking ones.  therefore, D is the correct answer.

Answer:It is C

Step-by-step explanation:In the question it says to COMPARE the fraction.

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Answer:

9. x=10

10. x=8

11. x=9/4=2.25

12. x=28

13. x=14

14. x=35

15. x=66

16. x=77/6

Step-by-step explanation:

9. x/20=18/36

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 18:

x/20=(18/18) / (36/18)

x/20=1/2

Solving for x: Multiplying both sides of the equation by 20:

20(x/20)=20(1/2)

x=10

10. x/12=6/9

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 3:

x/12=(6/3) / (9/3)

x/12=2/3

Solving for x: Multiplying both sides of the equation by 12:

12(x/12)=12(2/3)

x=4(2)

x=8

11. x/3=3/4

Solving for x: Multiplying both sides of the equation by 3:

3(x/3)=3(3/4)

x=9/4=2.25

12. x/42=30/45

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 15:

x/42=(30/15) / (45/15)

x/42=2/3

Solving for x: Multiplying both sides of the equation by 42:

42(x/42)=42(2/3)

x=14(2)

x=28

13. x/12=14/12

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 2:

x/12=(14/2) / (12/2)

x/12=7/6

Solving for x: Multiplying both sides of the equation by 12:

12(x/12)=12(7/6)

x=2(7)

x=14

14. x/25=28/20

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 4:

x/25=(28/4) / (20/4)

x/25=7/5

Solving for x: Multiplying both sides of the equation by 25:

25(x/25)=25(7/5)

x=5(7)

x=35

15. x/110=(160-100)/100

x/110=60/100

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 20:

x/110=(60/20) / (100/20)

x/110=3/5

Solving for x: Multiplying both sides of the equation by 110:

110(x/110)=110(3/5)

x=22(3)

x=66

16. x/11=(x+7)/17

Solving for x: Cross Multiplication:

17x=11(x+7)

Eliminating the parentheses on the right side of the equation:

17x=11(x)+11(7)

Multiplying:

17x=11x+77

Grouping the x's on the left side of the equation: Subtracting 11x both sides of the equation:

17x-11x=11x+77-11x

Subtracting:

6x=77

Dividing both sides of the equation by 6:

6x/6=77/6

Dividing:

x=77/6

Answer:

The missing value for y is 3

Step-by-step explanation:

y−3=2(x+1)

We know that x=-1 and we want to solve for y

Put in x=-1

y-3 = 2(-1+1)

y-3 = 2(0)

y-3=0

Add 3 to each side

y-3+3 = 0+3

y =3