1. Find x.
Q
S
16
U
C
2x
V
R
5x-9
16


I will mark brainly for this who show me how to solve it not just give me the answer

The dimensions that will minimize the cost is

h= 2.82876 and r = 1.06078

Given That, C₁ = $10 and C₂= $10 and C₃ = $15

lets multiply the top and bottom, we get,

C₁ × C₂ = $10 ×$ 20 = $ 30

The total cost is,

C = (2πr²) C₁ + (2πrh)C₂

Here,  r is base radius and h is the side length.

The volume is given by and the volume to 20 m³

∴ V = πrh² ⇒ πr²h = 20

So, h = 20/πr²

Now, the problem can be  stated as

minimum h, r C(h, r) restricted to V(h, r) = V₀

Using language multiplier it reads,

L(h ,r,λ) = C(h, r) + λ [ V(h ,r) - V₀]

Solving for h, r, λ, we get,

h = ∛(2 C₁/C₂)² V₀ /π , r = ∛ (C₂/C₁) (v₀/2π)

λ = -2 ∛2πC₁C₂² /V₀

or, h= 2.82876 , r= 1.06078 with associated cost C= 424.214

We know that is a minimum because,

(C₀ V) = 2 ( C₁πr³ + C₂V₀) /r

d²/dr² (C₀V) (r) = 4 (C₁πr³+ C₂V₀)/ r³

and for the found solution has the value

d²/dr² (C₀V) (r) = 240 π > 0

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Explanation:

To isolate the Y from y - 3 = 2/5 (x+4), you need to add 3 from both sides to move it to the right side of the equation:

y - 3 = 2/5 (x+4)

+3         +3

y = 2/5 (x+4) + 3

Answer:

add 3 to both sides

or move 3 across the equal sign, which will change its sign from - to +

= y = 2x + 8 / 5 +

4 shirts ∝ 31

4 = 31k

7 shirts ∝ 54.25

7 = 54.25k

Where k is the constant of proportionality

The constant of proportionality is k = 0.13.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Timberlee buys 4 shirts for $31 and Riley buys 7 shirts for $54.25.

In proportionality terms, we can write as,

4 shirts ∝ 31 _____(1)

7 shirts ∝ 54.25 _____(2)

(1) can be written as,

4 shirts = 31K

7 shirts = 54.24k

Where k is the constant of proportionality.

Now,

The value of k.

From (1)

4 = 31k

k = 4/31

k = 0.13

From (2)

7 = 54.24k

k = 7/54.24

k = 0.13

Thus,

The constant of proportionality is k = 0.13.

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a. The discount amount of the exercise machine is $3.39.

b. The exercise machine's sale price will be $561.61

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Since the exercise machine with an original price of $565 is on sale at 6% off. The discount will be:

= Discount percentage × Price

= 6% × $565

= $3.39

The exercise machine's sale price will be:

= Original price - Discount

= $565 - $3.39

= $561.61

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60 seconds long will it take for the planes to reach the same altitude.

Given that,

Two planes are being monitored by an air traffic controller. Plane A is initially at an altitude of 3500 feet, while Plane B is initially at a height of 1970 feet. The altitude of Plane A is increasing at a rate of 40.25 feet per second, while Plane B is doing so at a rate of 65.75 feet per second.

We have to find how long will it take for the planes to reach the same altitude.

Let us take x as the number of seconds in time.

We get,

3500+40.25x for Plan A.

1970+65.75x for Plan B.

Take,

3500+40.25x=1970+65.75x

3500-1970=65.75x-40.25x

1530=25.5x

x=1530/25.5

x=60

Therefore, 60 seconds long will it take for the planes to reach the same altitude.

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The quadrilateral with the given vertices is a Rhombus , the correct option is (C) .

In the question ,

it is given that ,

the vertices of the quadrilateral are (0,2), (6,0), (0,-2), (-6,0)

let us rename , the coordinates as A(0,2) , B(6,0) , C(0,-2) , D(-6,0) .

the distance between two points (x₁,y₁) and (x₂,y₂) can be calculated using the formula

d = √(x₂ - x₁)² + (y₂ - y₁)²

distance between A(0,2) and B(6,0) is

AB = √(6 - 0)² + (0 - 2)²

AB = √(6² + (-2)²)

AB = √(36+4)

AB = √40

distance between B(6,0) and C(0,-2) is

BC = √(0 - 6)² + (-2 - 0)²

BC = √((-6)² + (-2)²)

BC = √(36+4)

BC = √40

distance between C(0,-2) and D(-6,0) is

CD = √(-6 - 0)² + (0 - 2)²

CD = √((-6)² + (-2)²)

CD = √(36+4)

CD = √40

distance between D(-6,0) and A(0,2) is

DA = √(0 -(-6))² + (2 - 0)²

DA = √(6² + 2²)

DA = √(36+4)

DA = √40

we see that the length of all the sides  is √40 ,

all the sides are same in Square and Rhombus ,

But from the graph below, we see that the quadrilateral formed is in the shape of the Rhombus .

Therefore , The quadrilateral with the given vertices is a Rhombus .

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It is found that the first system of equations is consistently independent, the second one is inconsistent, and the third one is consistently dependent.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

We are given the first system of equations:

4x + y = 8

x + 3y = 8

thus 4/1 ≠ 1/3 = 1 is consistently independent.

The second system of the equation is;

-4x + 6y = 2

2x - 3y = 1

Therefore, -4/2 = -6/3 = 2 is inconsistent.

The third system of equations is;

5x - 2y = 4

5x - 2y = 6

Thus, 5/5 = -2/-2 ≠ 4/6 is consistent dependent.

Thus, It is found that the first system of equations is consistently independent, the second one is inconsistent, and the third one is consistently dependent.

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Answer: Angles 6,2,3 are the same and are all 112 degrees.

Angles 1,4,5,8 are the same and are all 68 degrees.

Step-by-step explanation:

Angles 6,2,3 are all 112 degrees because of diagonal angle rule.

Angles 1,4,5,8 are 180-112=68 degrees because we can use 180 degree angle rule.

Hope this helped, If you have any questions or clarifications, comment below!

Please rate!

Answer:

  4x² +4x -20

Step-by-step explanation:

You want the difference between 6x² -5x -12 and 2x² -9x +8.

The difference is found by subtraction. This is the same as adding the opposite.

  (6x² -5x -12) - (2x² -9x +8)

  = 6x² -5x -12  -2x² +9x -8

  = (6 -2)x² +(-5 +9)x +(-12 -8)

  = 4x² +4x -20

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Using World problem : work and time,

Himari will take 13 hour and 12 minutes to complete the job alone.

We have given that

Time taken by Even to do a job = 11 hours

let "x hours" be the time taken by humari to do this job alone .

Even'rate to do a job = 1/11 per hour

Himari and Even work together and do the job in 6 hours .

rate at which both are working together and do the job = 1/6 per hour.

Himari' rate to do job = 1/x hours per day

Now , using the formula "together work "

Even'rate + Himari'rate = rate of together work

=> 1/11 + 1/x = 1/6

we solve the above equation and find out the value of x

multiple both sides with 66x we get,

=> 6x + 66 = 11x

=> 5x = 66

=> x = 66/5 = 13 hours and 12 minute

Hence, Himari will take 13 hour and 12 minutes to do job alone .

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Measure of all angles must equal 180 degrees.

Therefore,
(4x+20) + (2x+34) + x = 180

6x + 54 + x = 180

7x + 54 = 180

7x = 126

x = 18

4(18)+20 = 92

Angle A = 92

2(18)+34 = 60
Angle C = 60 degrees

Unknown angle is 18 degrees because the "x" represents the third angle.

Jamal need to invest $35838.77 in an account.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

As given Jamal wants to save $54,000 for a down payment on a home with 8.2% APR, compounding daily for 5 years.

The compound interest formula is,

[tex]A = P(1+\frac{r}{n})^n^t[/tex]

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Here, A = $54000, r = 8.2% = 0.082, t = 5, n = 365

Plug the values in the above formula,

[tex]54000 = P(1+\frac{0.082}{365} )^(^3^6^5^)^(^5^)\\54000 = P(1.0002246575)^1^8^2^5\\54000= P(1.5067483068)\\P = \frac{54000}{1.5067483068} \\P = 35,838.766\\P = 35838.77[/tex]

Hence, Jamal need to invest $35838.77 in an account.

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Answer:

Step-by-step explanation:

y + 8= 2(x-1)

y+8=2x-2

y=2x-10

Slope equals 2

Answer:

A

Step-by-step explanation:

36x = 535 - 31

36x = 504

36/36 x = 504/36

x = 14

[tex]{ \green{ \boxed{ \red{ \sf{x = 14}}}}}[/tex]

Step-by-step explanation:

[tex]{ \purple{ \tt{36x + 31 = 535}}}[/tex]

[tex]{ \purple{ \tt36x = 535 - 31}}[/tex]

[tex]{ \purple{ \tt{36x = 504}}}[/tex]

Divide both the sides by 36 then,

[tex]{ \purple{ \tt{ \frac{ \cancel{36}}{ \cancel{36}}}}} = { \purple{ \tt{ \frac{ \cancel{504}} { \cancel{36}}}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \sf{x = 14}}}}}[/tex]

The different proportional relationship is given by:

Relationship B.

The justification is:

Since graph B has a different constant of proportionality and different equation, it is different than other three graphs.

The definition of a proportional equation is given as follows:

y = kx.

Which means that the output variable y is obtained with the multiplication of the constant of proportionality k and the input variable x.

The constant is obtained as the division of y by x of a point (x,y) different of the origin, as follows:

k = y/x.

Hence, for each relationship, the constant is given as follows:

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Answer:

Step-by-step explanation:

so,  I was just commenting about word problems to another person and here is a great example of a word problem that is too complex.  They are using the term  "function rule"  that is too broad.  They have probably defined it in some text somewhere and the teacher has mentioned in super briefly, but it's what the question is all about.  We need to understand what "function rule"  really means.   They have also used the varible "s"  which is mostly reserved for  Laplace /  Fourier  transformations.  This is just a really badly written question.   Don't feel bad if  you don't get what it's asking.  it's messy at best.   t(s) is then name of our function,  it's rule ( the function rule)  is 40/s  it's constant of proportionality is 40  ,  This rule would also mean that at the very very start of the race... at .001 into the race, you'll be going 40,000 MPH  , which is obviously not correct.   There probably needs to be some more rule descriptions saying that s is an integer, and it can't be negative. Also note that after 4 hours of racing , the speed would be 40/4 or 10 MPH,  this function rule is probably not accurate after some time.  the speed probably starts out fast,   slows down till the close to the very end of the race... they jumps up dramatically to the finish.   Watch the Tour de France writer of this question.  :D   The riders slow down as the race progress according to this function rule.  But I don't think that's at all accurate for a real bike race.   they slow down only to a point... after the start.... then hold at that speed ... till close to the end.. then speed up a lot... like 50 MPH  :0

The equation for S, in terms of t, is S = 18 - 2t

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The initial value is 18 inches,

The rate of change is -1.5 inches per hour,

t is the number of hours.

S = 18 - 2t

Number of Hours after the                      Depth of Snow on Hudson's Lawn

Storm                                                                           (Inches)

0                                                                                        18

1                                                                                          16

2                                                                                         14

3                                                                                         12

Therefore, the equation for S, in terms of t is S = 18 - 2t.

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Protein intake, if he consumes 9 egg whites a day is 32.4 grams.

Given:

Candice eats six egg whites a day with a protein content of 21.6 grams.

6 egg white = 21.6 grams.

1 egg white = 21.6/6

= 216/10/6

= 216/10*6

= 216/60

= 3.6 grams.

9 eggs white = 9 * 3.6

= 9 * 36/10

= 324/10

= 32.4 grams.

Therefore protein intake, if he consumes 9 egg whites a day is 32.4 grams.

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x² + (y – 3)² = 36 and x² + (y + 8)² = 36 are equations that represent circles having a diameter of 12 units and a center that lies on the y-axis

Given : x² + (y – 3)² = 36, x² + (y – 5)²= 6, (x – 4)² + y² = 36, (x + 6)² + y² = 144 and x² + (y + 8)² = 36

and x² + (y + 8)² = 36

The standard form of the equation of a circle is

(x-a)² + (y-b)² = r²

where (a, b) is the center and r is the radius

Let's compare the given equations with the standard equation:

x² + (y – 3)² = 36 can be written as:

(x-0)² + (y – 3)² = 6²

This has a center (0, 3), radius r = 6 and diameter = 12 units

x² + (y – 5)²= 6 can be written as:

(x-0)² + (y – 5)² = (√6)²

This has a center (0, 5), radius r = √6 and diameter = 2√6 units

(x – 4)² + y² = 36 can be written as:

(x-4)² + (y – 0)² = 6²

This has a center (4, 0), radius r = 6 and diameter = 12 units

(x + 6)² + y² = 144 can be written as:

(x+6)² + (y – 0)² = 12²

This has a center (6, 0), radius r = 12 and diameter = 24 units

x² + (y + 8)² = 36 can be written as:

(x+0)² + (y + 8)² = 6²

This has a center (0, -8), radius r = 6 and diameter = 12 units

Therefore, the equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are x² + (y – 3)² = 36 and x² + (y + 8)² = 36

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The average rate of change of the function over the range 4≤ x ≤7 using the function defined in the table is -1.

Given that,

We have to find the Find the average rate of change of the function over the range 4≤ x ≤7 using the function defined in the table below.

x           f(x)

1           90

4           87

7           84

10          81

We have to find the slope of the 2 points.

The points are (4,87) and (7,84)

The slope point is rise/run

Rise is y₂-y₁

Run is x₂-x₁

So,

Slope = (84-87)/(7-4)

Slope = (-3)/(3)

Slope = -1

Therefore, The average rate of change of the function over the range 4≤ x ≤7 using the function defined in the table is -1.

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Answer:

length: 20m. width: 15m

Step-by-step explanation:

70/2 = 35

35         35

+5          -5

40         30

40/2     30/2

20         15

Answer: Yes. The answer is -1.

Step-by-step explanation:

2x+3y=4, y=2

Would look like this: 2x+3(2)=4.

1. Multiply 3 x 2 = 6

2) 2x + 6 =4

3) Subtract 6 from both sides

4) Will look like this: 2x = -2

5) -2 / 2 = -1

Answer: -1

Equation: 2x+3(2)=4.

Answer:

x= -1

Step-by-step explanation:

2x + 3y = 4

2x + 3(2) = 4

2x + 6 = 4

2x = 4 - 6

2x = -2

x = -2/2

x = -1

Answer: You can find a right degree angle of a triangle when it’s a 90 degrees or if you can see it makes like a square.

Answer:

Okay, sorry for answering a few minutes late!

Step-by-step explanation:

So, for data in a table to be a function, the input must only have one output.

Short and sweet answer, hope this helps!

Yes, r=5 is a solution of inequality r<11.

Given the inequality is r<11

Given the value of r is, r=5

Since 5<11

So yes r=5 is the solution of the inequality r<11.

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The value of [tex]\sqrt{13}[/tex] is between 3 and 4 on the number line.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

[tex]\sqrt{13}[/tex] = 3.60

The value 3.6 is going to be between 3 and 4 because it is seen to be more than 3 while the value is also seen to be less than 4.

Hence the solution to the problem is the locations are 3 and 4.

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The equation which best shows the relationship between Davis' savings, y and the number of months passed, x is; y = 20 + 5x.

It follows from the task content that the equation which represents the relationship between Davis' savings and the number of months passed be determined.

According to the task content;

Davis has $20 in his savings account, and he adds $5 every month.

Therefore, we have;

y = 20 + 5x

This follows from the fact that the amount added after each month is $5.

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The value of the inequality X + 3 < 6 is x < 3.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Based on the information given, the inequality will be illustrated thus:

x + 3 < 6

Collect like terms

x < 6 - 3

x < 3

The value is x < 3.

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Value of tan90 is 1/0 which is undefined

Let AB, BC, AC be the base(adjascent side), side opposite to θ, hypotenuse of a right angled triangle respectively.

Now as per sine, cosine and tangent formulas, we have here:

It is seen from these formulaes that

Now, other formulas for trigonometry ratios are:

The other way of representing trigonometric values formulas are:

Therefore, value of tan90 is undefined.

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The fraction value of tan90° after using trigonometric value is 1/0 that is undefined.

What is trigonometric ratio?
There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.

Here the given

=> tan 90°

Tan 90 degrees in radians is written as

=>tan (90° × π/180°)

=> 1/0 = undefined.

Hence the fraction value of tan 90° is 1/0 that is undefined.

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