Compute the diameter of a circle with a circumference of 34 feet

The system of inequalities are

x + y = 12,

25x + 10y ≤ 150

x ≥ 9,

y ≥ 4 and the graph of the inequality is attached below.

Inequality:

Inequality refers the relationship between two values that are not equal is defined by inequalities. Inequality means not equal.

Given,

No. of summer job Owen working = 2 (tutoring and clearing tables)

Cost per hour (tutoring) = $25

Cost per hour (clearing tables) = $10

In a week,

Total working hour = 12

Minimum Amount earned = $150

Maximum hours (tutoring) = 9

Maximum hours (clearing tables) = 4

Here we need to find the system of inequalities and we have to plot the graph for it.

Then we need to find one possible solution for it.

Let us consider x be the number of hours for tutoring and y be the number of clearing table.

So, the total number of working hours,

x + y = 12

And the amount earned in the week,

25x + 10y ≤ 150

And we also know that,

x ≥ 9 and y ≥ 4.

The graph of the equation is attached below.

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When the value of y varies directly with x and x = 5, y = 12 then, the value of x when y = 1 is 5/12.

What is direct variation?

The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation. For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation if b is directly proportional to a. (where k is a constant). When two variables are coupled in a way that ensures the ratio of their values never changes, this relationship is referred to as being in direct variation. Different mathematical structures are used to express direct variation. Since the ratio of y to x never changes, y and x fluctuate directly in equation form.

As given in the question,

when x = 5, y = 12,

x and y varies directly, it means they are directly proportional:

y ∝ x

y = kx {here, k is a constant}

Putting the value of x and y, and finding the value of k:

k = 12/5

Now, we need to find x when y = 1. so,

y = kx

putting the values,

1 = (12/5)x

x = 5/12

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The probability of passing one test or the other is given by:

0.63 = 63%.

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

The "or probability" between these two events is given by the rule presented as follows:

P(A or B) = P(A) + P(B) - P(A and B)

In the context of this problem, these events are given as follows:

The probabilities of each event and the and probability are listed as follows:

P(A) = 0.58, P(B) = 0.24, P(A and B) = 0.19.

Hence the probability of passing one test or the other is calculated as follows:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.58 + 0.24 - 0.19 = 0.63 = 63%.

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Answer:

Undefinded

Step-by-step explanation:

The slope between two points is the RISE/RUN.

Take 5he two given points to calculate the RISE and RUN:

(5,3) and (5,-9)

RISE:  (-9 - 3) = -12

RUN (5 - 5) = 0

RISE/EUN = 12/0 = UNDEFINED

The equation of a line that is perpendicular to y = 4x + 8 and passes through (−8, 4) is y = - 1 / 4 x + 2 (y equals negative one-fourth times x plus 2)

The equation of the line is perpendicular to y = 4x + 8 and passes through (-8, 4).

Therefore, the equation of a line can be represented as follows;

y = mx + b

where

Therefore, perpendicular lines follows the rule below:

m₁ m₂ = -1

4m₂ = -1

m₂ = - 1 / 4

Hence, let's find the y -intercept using (-8, 4)

y = - 1 / 4 x + b

4 = - 1 / 4 (-8) + b

4 = 2 + b

b = 4 - 2

b = 2

Therefore, the equation is y = - 1 / 4 x + 2

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Answer: D.) y = 4x + 4

Step-by-step explanation:

just did the assignment

Answer: M x X

P x E

YW x RK

Step-by-step explanation:

The initial expression is:

We need to use the addition of fractions rule, and we obtain:

The answer is 13/12

Answer:

Step-by-step explanation:

f(x)=-1/4x-2

Answer:

False that is a conjunction

Step-by-step explanation:

hope this helps

The sum identities in trigonometry are cos^2(x)+sin^2(x)=1

                                                                 sec^2-tan^2(x)=1

                                                                 cosec^2(x)-cot^2(x)=1

Trigonometry: Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. Trigonometry is found all throughout geometry, as every straight-sided shape may be broken into as a collection of triangles

Let's prove using the angle addition formula for cosine:

cos(α+β)=cos(α)cos(β)-sin(α)sin(β)

we know that sin(-x)= -sin x and

                       cos(-x)=cos x

we need to proceed to the proof ,

let α=x and β=-x

cos(x+(-x))=cos(x)cos(-x)-sin(x)sin(-x)

cos(0)  = cos(x)cos(x)+sin(x)sin(x)

cos^2(x)+sin^2(x)=1

Hence, it is proved

to prove another identity i.e., sec^2-tan^2(x)=1

start from cos^2(x)+sin^2(x)=1

divide both the sides by cos^2(x)

cos^2(x)/cos^2(x)+sin^2(x)/cos^2(x)=1/cos^2(x)

1+tan^2(x)=sec^2(x)

sec^2-tan^2(x)=1

Hence, it is proved

to prove another identity i.e., cosec^2(x)-cot^2(x)=1

start from cos^2(x)+sin^2(x)=1

divide both sides by sin^2(x)

cos^2(x)/sin^2(x)+sin^2(x)/sin^2(x)=1/sin^2(x)

cot^2(x)+1=cosec^2(x)

cosec^2(x)-cot^2(x)=1

Hence, it is proved

The sum identities in trigonometry are proved

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Answer:

- 36x + 9

Step-by-step explanation:

- 12(3x - [tex]\frac{3}{4}[/tex] ) ← multiply each term in the parenthesis by - 12

= - 36x + 9

Answer:

-36x + 9

Step-by-step explanation:

Given expression:

[tex]-12\left(3x-\dfrac{3}{4}\right)[/tex]

Apply the distributive rule:

[tex]\implies -12 \cdot 3x -12 \cdot -\dfrac{3}{4}[/tex]

Multiply -12 and 3x:

[tex]\implies -36x -12 \cdot -\dfrac{3}{4}[/tex]

Apply the rule  -a(-b) = ab:

[tex]\implies -36x +12 \cdot \dfrac{3}{4}[/tex]

Convert 12 into a fraction:

[tex]\implies -36x +\dfrac{12}{1} \cdot \dfrac{3}{4}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{ac}{db}}:[/tex]

[tex]\implies -36x +\dfrac{36}{4}[/tex]

Divide the numbers:

[tex]\implies -36x +9[/tex]

Therefore, the equivalent expression to the given expression is:

The value of the 36th term of the arithmetic sequence is 283.

It should be noted that an arithmetic sequence illustrate the common difference between the terms.

The following can be deduced from the information:

75th term = a + 74d = 556

8th term = a + 7d = 87

Subtract the equations

(74d - 7d) = 556 - 87

67d = 469

Divide

d = 469/67

d = 7

The first term(a) will be:

a + 7d = 87

Recall d = 7

a + 7(7) = 87

a + 49 = 87

a = 87 - 49

a = 38

Therefore, the 36th term will be:

a + 35d.

a = first term

d = common difference

38 + 35(7)

= 38 + 245

= 283

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Answer:

-3x + 10

Step-by-step explanation:

you add like terms of 20 and negative 10 to simplify to -3x +10

Answer:down below

Step-by-step explanation:A square gives the greatest area. If the river were not there, you would divide 1700 by 4 to get a square 425 feet by 425 feet. Because of the river, add 425 feet to the side opposite the river to get a rectangle 425 feet by 850 feet.

Now for the algebra that you need.

P=2l+2w but there is only one length.

P=l+2w

1700=l+2w

1700-2w=l

A=lw

A=(1700-2w)w

A=1700w-2w2

This is a parabola that opens downward so there is a maximum point, the vertex, which is (h,k).

h=-b/2a is the "maximizing point" and k is the maximum area

-b/2a=-1700/(-4)

-b/2a=425 feet

One width will be 425 feet, the length will be (425+425)=850 feet, and the second width will also be 425 feet.

A=lw

The maximum area will be A=850*425=361,250 square feet.

Notice that if you substitute 425 into the equation A=1700w-2w2 you will get the same answer.

1700*425-2*4252

722,500-2*180,625

722,500-361,250

According to the binomial theorem, the binomial (x + 3)⁷ is equal to the septimic polynomial x⁷ + 21 · x⁶ + 189 · x⁵ + 945 · x⁴ + 2835 · x³ + 5103 · x² + 5103 · x + 2187.

Binomial theorem offers a brief form to expand the power of a binomial, that is, an algebraic expression of the form (a + b)ⁿ, where n is a natural number. The complete formula is shown below:

(a + b)ⁿ = Σ {n! / [k! · (n - k)!]} · [tex]a^{n-k}[/tex] · [tex]b^{k}[/tex], for k ∈ {0, 1, 2, ..., n - 1, n}

If we know that a = x, b = 3 and 7, then the expanded form of the power of the binomial is:

(x + 3)⁷ = [7! / (0! · 7!)] · x⁷ · 3⁰ + [7! / (1! · 6!)] · x⁶ · 3 + [7! / (2! · 5!)] · x⁵ · 3² + [7! / (3! · 4!)] · x⁴ · 3³ + [7! / (4! · 3!)] · x³ · 3⁴ + [7! / (5! · 2!)] · x² · 3⁵ + [7! / (6! · 1!)] · x · 3⁶ + [7! / (7! · 0!)] · x⁰ · 3⁷

(x + 3)⁷ = x⁷ + 7 · x⁶ · 3 + 21 · x⁵ · 3² + 35 · x⁴ · 3³ + 35 · x³ · 3⁴ + 21 · x² · 3⁵ + 7 · x · 3⁶ + 3⁷

(x + 3)⁷ = x⁷ + 21 · x⁶ + 189 · x⁵ + 945 · x⁴ + 2835 · x³ + 5103 · x² + 5103 · x + 2187

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Answer:

To write the coefficients of the 8 terms, either start with a combination of 7 things taken 0 at a time and continue to 7 things taken 7 at a time or use the 7th row of Pascal’s triangle.For the first term, write x to the 7th power and 3 to the 0 power. Then decrease the power on x and increase the power on y until you reach x to the 0 and y to the 7.Simplify by evaluating the coefficients and powers of 3.

From the equation 4x + 12 = 64, we have that:

a. The problem is: An amount was quadrupled then added by 12, resulting in a final amount of 64.

b. The solution to the equation is x = 13.

c. The solution of x = 13 represents the initial amount.

The amount x is unknown, hence the problem begins with the unknown amount x.

Which means that the problem can be summarized as:

An amount was quadrupled then added by 12, resulting in a final amount of 64.

The equation can be solved isolating x as follows:

4x + 12 = 64

4x = 64 - 12

4x = 52

x = 52/4

x = 13.

Meaning that the initial amount was of 13.

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The value of x in the given diagram is 50°

From the question, we are to determine the value of x

From the Vertically opposite angles theorem, we have that vertically opposite angles are congruent.

Thus,

From the given diagram, we can write that

[2(x + 10)]° = (3x - 30)°

Now, we will solve for x

[2(x + 10)]° = (3x - 30)°

2(x + 10)° = (3x - 30)°

2x + 20° = 3x - 30°

20° + 30° = 3x - 2x

50° = x

Hence,

x = 50°

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Answer:

x=9,y=8

Step-by-step explanation:

Step 1: Substitute y=-8 into equation 1

9x+10(-8)=1

9x+(-80)=1

9x=1+80

9x=81

Step 2: Divide both sides by the coefficient of x which is 9 then,

x=9

Step 3: Also substitute x=9 into equation 1

9(9)+10y=1

81+10y=1

10y=1-81

10y=-80

Step 4:Divide both sides by 10 then,

y=-8

Answer: -1/3

Step-by-step explanation:

Pretty sure it's -1/3, one unit down from a point, and then 3 units right.

The answer is -1/3. Hope this helps.

Answer:

62 pages in each notebook

Step-by-step explanation:

she filled 372 pages in 6 notebooks , then

372 ÷ 6 = 62

there are 62 pages in each notebook

In linear equation, x = 9 is the value of Maggie that she made.

What is linear equation in math?

4x + 2 = 7x - 25

7x - 4x = 2 + 25

3x = 27

x = 27/3

x = 9

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Answer:

Step-by-step explanation:

The bottom right box.

Answer:400

Step-by-step explanation: 12/3= 4 4x100= 400

The distance between the height of the platform and the depth below water is 47ft . The concept of depth describes how far something extends.

A deep area in a body of water is what the word "DEPTH" means.

Ocean depth is most frequently and quickly measured using sound. Sonar, which stands for sound navigation and range, is a technique that allows ships to map the topography of the ocean below. The instrument uses sound waves to send to the ocean's bottom and time how long it takes for an echo to come back.

Water depth is the distance in feet between the ocean's surface and bottom, as determined by mean lower low water.

Use the following formula for measuring ocean depth.

D = V Times 1/2 T D

Depth (in meters) T= Time (in seconds) V = 1507 m/s (speed of sound in water)

In the question we have,

Platform to surface of water = 33ft

Platform to depth below water = 33+14 = 47ft

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The expressions with radicals which are variables and numbers raised to a fractional indices are simplified as follows.

13. √(9·x)  = 3·√x

14. √(4·y) = 2·√y

15. √(8·x²) = 2·x·√2

16. √(9·x²) = 3·x

17. √(3·x²) = x·√3

18. √(5·y²) = y·√5

19. √(13·x²) = x·√(13)

20. √(29·y²) = y·√(29)

21. √(64·y²) = 8·y

22. √(125·a²) = 5·a·√5

23. ∛(16) = 2·∛2

24. √(50·a²·b) = 5·a·√(2·b)

A radical expression is one that contains the radical (square root or nth root) sign, √.

13. √(9·x)

√(9·x) = √(3²·x) = 3·√x

14. √(4·y)

√(4·y) = √(2²·y) = 2·√y

15. √(8·x²)

√(8·x²) = √(4 × 2·x²) = √(2² × 2·x²)

√(2² × 2·x²) = √(2²·x² × 2) = 2·x·√2

16. √(9·x²)

√(9·x²) =  √(3²·x²) = 3·x

17. √(3·x²)

18. √(5·y²)

√5 × √(y²) = √5 × y = y·√5

19. √(13·x²)

√(13·x²) = √(13) × √x² = √(13) × x = x·√(13)

20. √(29·y²)

√(29·y²) = √(29) × √(y²) = √(29) × y = y·√(29)

21. √(64·y²)

√(64·y²) = √(8²·y²) = √(8²) × √(y²) = 8 × y = 8·y

22. √(125·a²)

√(125·a²) = √(25 × 5 × a²) = √(25) × √5 × √(a²) =  5 × √5 × a

5 × √5 × a  = 5·a·√5

23. ∛(16)

∛(16) = ∛(16) = ∛(8 × 2) =  ∛(2³ × 2) = 2·∛2

24. √(50·a²·b)

√(50·a²·b) = √(25 × 2 × a² × b) = √(5² × 2 × a² × b) = √(5² × a² × 2 × b)

√((5² × a²) × 2 × b) = 5·a·√(2·b)

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Step-by-step explanation:

amt. means amount

explaination in my workings

hope this helps!!

Let's cut the given solid into two parts to easily get its total volume:

Let's determine the volume of figure A:

Let's determine the volume of figure B:

Let's add the volume of the A and B to get the total volume of the given figure.

We get,

Therefore, the volume of the figure is 1,536 cm³.

The linear inequality leads us to the conclusion that the silver pass will be more advantageous if a visitor stays at the theme park for more than three days.

Let the number of days be x.

So, cost of single pass for one day is 50 +10 = $60

cost of single pass for x days is 60x.

cost of silver pass for one day is 120 +20 = $140

cost of silver pass for x days is 120+20x.

Now, for silver pass to be worth to buy instead of single pass will be when it costs lesser than that of the single pass.

So,

Cost of silver pass < cost of single pass

120 + 20x < 60x

120 < 40x

x>3,

So, we can say conclude from the linear inequality that the silver pass will be more beneficial if someone is staying at amusement park for more than 3 days.

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Tiana is more likely to win the competition as she took less time to type the same number of words, She will type more during the competition as her typing speed is more.

Since the upcoming match is next week, it is very important to practice before the actual match, hence, both participants were practicing to their best.

It is more likely that the person who does their best while practicing is more likely to perform better in the actual competition.

The competition will have the same amount of time to type, hence who will take less time to type more words will ultimately win the match.

Since Triana took less time while practicing the same amount of words, hence, it is more likely that she will type more during the competition.

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