The length of time (T) in seconds it takes the pendulum of a clock to swing through one compete cycle is givenby the formulaT= 2T✔️L/32 Where L is the length, in feet, of the pendulum, and is pie approximately 22/7. How long must the pendulum be of one complete cycle takes 2 seconds? Answer as a fraction or round to at least 2 decimal places.The pendulum must be__ feet.

For the given situation:

the graph of a line passing through point

with gradient m

is given by

Solution of an inequality

We can express the solution (s) of inequalities in several forms.

Here we will use two of them: The set-builder notation and the interval notation.

Let's solve the inequality

x - 1 ≤ 9

Adding 1 to both sides of the inequality:

x ≤ 10

The solution in words is "all the real numbers less than or equal to 10"

In set-builder notation:

{x | x <= 10}

In interval notation: (-inf, 10]

We are asked to identify the types of symmetries found in the given geometrical figure. Let's remember that asymmetry is a transformation that maps the figure onto itself. In this case the object has symmetry under reflections, also has symmetry under rotations around its center

we have the following:

GIVEN

The time left before the store closes is 3/4 h while the time taken to find one item is 1/8 h.

QUESTION A

Let the number of items that can be gotten before the store closes be N.

The number of items can be calculated using the formula:

Therefore, the equation to get the number of items will be:

QUESTION B

The solution can be obtained by division.

Apply the fraction rule:

Hence, the solution will be:

The answer is 6.

QUESTION C

Jane can find 6 items before the store closes.

System of Equations

When Neegan paddles the kayak upstream, the real rate (speed) is the difference between the rate that Neegan paddles in still water and the rate of the water against his paddling.

When he goes downstream, the real rate is the sum of the rates because the water and Neegan push in the same direction.

He takes 4.2 hours to paddle for 21 miles against the current, so the real rate is 21/4.2 = 5 mi/h

He takes only 3 hours to return, so the real speed is 21 / 3 = 7 mi/h.

Let:

x = rate at which Neegan paddles in still water

y = rate of the current.

We set the system of equations:

x - y = 5

x + y = 7

Adding both equations:

2x = 12

Divide by 2:

x = 6

Substituting in the second equation:

6 + y = 7

Subtracting 6:

y = 1

Neegan paddles at 6 mi/h in still water. The rate of the current is 1 mi/h

(Third choice)

We need to know about scale factor to solve the problem. Matthew's mark last term was 50%.

It is given that Matthew's marks increased by a factor of 3/2 this term. This means that whatever marks Matthew had received in his previous term, it was increased by 3/2 this term. If we consider his original marks to be x, then we can get the increased marks by multiplying x by 3/2. We know that the new marks is 75%, we need to find the value of x.

3x/2=75

x=75x2/3=25x2=50

Therefore the marks Matthew received in the previous term is 50%.

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The graph of f(x) is a parabola with "arms up"

The vertex of the parabola is (0,-3)

Then we can know all the problem ask us:

increasing: (-3, infinity)

decreasing: (minus infinty, -3)

DNE maximum, beacuase it's arbitrarily large.

The minimum is the vertex: minimum of -3 at x = 0

The domain is all real numbers

The range is [-3, infinity)

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To know the shape of a parabola you want to look 2 things. The standar formula of a parabola is:

We focus on a and b. Always will be a squared x, but a and b vary. a lot

A tell us if the parabola has it's arms up or down. If is positive, has arms up. If it's negative, arms down.

Also, this isn't something "strictly mathematical" but can tel you is the parabola is thin or fat.

Now b tells us what happends when x=0. If b is positive, the vertex will be "rised up". If b is negative, the vertex will be "pulled down"

When you get relatively confident, you can watch a and b, and based on their sign and how big they are, you can make a really good idea how the graphic is.

All the information the problem ask, you can get it by those numbers.

To know how wide is a parabola, you need to look at a. Let's supose a = 100. This is a very big number, si if I plug in an x, the function will square it and multiply it by 100 right? Then the function will be very thin. For an x very low, the function will be very great. Example: f(x)=100x^2 if I put x = 1 then I have to square it, and multipli it by 100: 1^2*100=100

Now let's copare this with an smaller a. Suppose a =2. Then if I plug x = 1 I get:

For the same value of x, the first function is 100 and the second 2

we have that

the area of parallelogram is equal to

A=b*h

we have

b=14 mm

Find the value of h

tan(60)=h/7 -----> by opposite side divided by the adjacent side

Remember that

so

h=7√3 mm

substitute

A=14(7√3 )

Answer:

68

Step-by-step explanation:

100-68-12-11=9

12+11=23

100-23-9=68

1) To find each unit price, let's find out the unit rate. Setting a proportion.

Option A

cupcakes price

12 ------------------- 29

1 --------------------x

Cross multiplying it:

12x = 29 Divide both sides by 12

x =2.42

Each cupcake costs $ 2.42

Option B

24 ------------ 56

1 ------------ y

24y = 56

y =$2.33 per cupcake.

2) The best deal for buying cupcakes is found in Option B. Since the price is lower per cupcake

3) Hence, the answers are:

Option A = $2.42 per cupcake

Option B =$2.33 per cupcake

Best Deal: Option B

The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.

This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.

In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.

Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.

Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.

The difference is however $2.79 - $2.36 = $0.43.

Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.

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Answer:

• Plan B, by $4

• 140 minutes

Explanation:

Part A

From the graph, at 40 minutes, the costs of the plans are:

• Plan A: $4

• Plan B: $8

Plan B costs more by $4.

Part B

The point where the costs are the same is the time at which the two graphs intersect.

When the number of minutes = 140 minutes

• Cost of Plan A = $14

• Cost of Plan B = $14

Thus, the two plans cost the same for 140 minutes of long-distance call.

• If the time spent is less than this amount, Plan B costs more.

Given:

To evaluate the function at x=1, we simplify the given relation first:

We let:

y=f(x)

We plug in x=1 into the above function:

Therefore,

ANSWER:

D. the exponential function grows faster than the quadratic function over two intervals; 2 < x ≤ 4

STEP-BY-STEP EXPLANATION:

We can see from the graphs that the growth is the same from 0 to 2 and then the exponential function grows faster, therefore, strictly speaking, the correct answer is D. the exponential function grows faster than the quadratic function over two intervals; 2 < x ≤ 4

Divide side R'O' (8) by th scale factor (2/3)

8 : 2/3= 12

Given

Solution

Formula

Now

The midpoint M of the line segment joining the points C=(6,2) and D=(2,8). is

The number of black bears in the national park is 36

Here, given the ratio of black bears to grizzly bears, and the number of grizzly bears, we want to find the number of blackbears the national park has

Let the number of black bears be x

what this mean is that the total number of bears in the park is (x + 12)

The total ratio of the two is 3 + 1 = 4

Matematically;

The number line always goes from negative to positive :

It increases from left to right

SInce negative is always on the left side of the zero

Snumber greater than zero are always positive

i.e. x > o

So we need to solve the following equation for x:

The first step would be substracting 8 from each side of the equation:

The next step is to square

If the polynomial function be P(x) = [tex]x^4[/tex] − 3x³ + 2x² then Zeros exists at x = 0, 0, 1, 2.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An expression that consists of variables, constants, and exponents that exists combined utilizing mathematical operations like addition, subtraction, multiplication, and division exists directed to as a polynomial (No division operation by a variable).

Let the polynomial function be P(x) = [tex]x^4[/tex] − 3x³ + 2x²

P(x) = x²(x² - 3x + 2)

factoring the above polynomial function, we get

P(x) = x·x(x - 1)(x - 2)

Zeros exists at x = 0, 0, 1, 2

P(x) exists degree 4, so it will contain four roots. You only entered three which exists probably why it came up as wrong. The x² term contains a multiplicity of 2, so it counts twice.

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We can relate an angle x to its opposite leg and its adjacent leg, by means of the trigonometric function tangent of x, like this:

Then we can find the value of the angle by applying the inverse function of tangent, like this:

Let's replace the values from the figure into this equation to find x, like this:

Then, x equals 57.4°

Solution

For this case since we want to verify if a circle can be circumscribed in the quadrilateral we can use the following Theorem:

Theorem: If a quadrilateral is incribed in a circle then the opposite sides are supplementary

And we cna verify:

105+ 98= 203

82 +75= 157

Then we can conclude that the answer is:

False

Answer:

Question 1: 3

Question 2: $120

Step-by-step explanation:

Set up a proportion

[tex]\frac{inches}{miles}[/tex] = [tex]\frac{inches}{miles}[/tex]  fill in the numbers that you know and solve for the unknow.

[tex]\frac{5}{2}[/tex] =[tex]\frac{7.5}{m}[/tex]  Cross multiply

5x =7.5(2)

5x = 15  Divide both sides by 5

x = 3

If we take 40% off that means that we leave 60% on

Percent means per hundred

[tex]\frac{60}{100}[/tex]  When you divide by hundred, you move the decimal two places to the left.

200(.6)

$120.00

Answer:

q = -1

Step-by-step explanation:

We are given the inequality [tex]11-\frac{64}{q} > 60[/tex]

We want to find out which value of q is a solution to the inequality. In other words, which value of q makes the statement true?

We can substitute the values given for q into the inequality to see this.

Let's start with q=2.

Replace q with 2.

[tex]11-\frac{64}{2} > 60[/tex]

Divide 64 by 2.

64/2= 32

11 - 32 > 60

Subtract 32 from 60

11-32 = -21

-21 > 60

The inequality reads "-21 is greater than 60", which is false (negative numbers are less than positive ones).

This means q=2 is NOT an answer.

Next, let's try q=-2

[tex]11 - \frac{64}{-2 } > 60[/tex]

64/-2 = -32

11 - - 32 > 60

- - 32 means subtracting a negative, which is the same as adding 32 to 11.

11 + 32 > 60

43 > 60

This is also NOT true (it reads "43 is greater than 60").

So q=-2 is also NOT an answer.

Now, let's try q = -1

[tex]11-\frac{64}{q} > 60[/tex]

[tex]11-\frac{64}{-1} > 60[/tex]

64/-1=-64

11 - -64 > 60

11 + 64 > 60

75 > 60

This reads "75 is greater than 60".

This is a true statement, meaning q = -1 IS an answer.

We are technically done, but just to be sure, we can check q=1 as well.

[tex]11 - \frac{64}{q} > 60[/tex]

[tex]11 - \frac{64}{1} > 60[/tex]

11 - 64 > 60

-53 > 60

This reads "-53 is greater than 60", which is false.

So this confirms that q = -1 is the only option that is an answer.

The scenarios that demonstrate a proportional relationship for each person's income are :

Consider the income as y in each scenario

Scenario 1

Millie works at a car wash and earns $17.00 per car she washes.

Consider the number of car she washes as x

y = 17x

y ∝ x

This is a proportional relationship

Scenario 2

Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.

The relationship will be

y = 25 +12.50x

where x is the number of hours

This is not a proportional relationship

Scenario 3

Carla makes sandwiches at her job and earns $7.85 per hour.

The relationship will be

y = 7.85x

y ∝ x

Where x is the number of hours

This is a proportional relationship

Scenario 4

Tino is a waiter and makes $3.98 per hour plus tips.

The relationship will be

y = 3.98x + tips

Where x is the number of hours

This is not a proportional relationship

Hence, the scenarios that demonstrate a proportional relationship for each person's income are

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The perimeter of a triangle is given by the sum of all it is sides.

Now, we have the next measures:

- The longest side of a triangle is 5in longer than the shortest side.

- The medium side is 4 inches longer than the shortest side

Then, the perimeter is given by:

P = (s+5)+(s+4)+s

If the perimeter is P=21 inches:

21 = (s+5)+(s+4)+s

Solve for s:

21 = s+5+s+4+s

21 = 3s + 9

21-9 = 3s

12 = 3s

s = 12/3

s= 4

Therefore,

The shortest side of the triangle is 4 inches.

The medium side is s+ 4 = 4+ 4 = 8 inches

The longest side is s+5 = 4+5 = 9 inches

To asnwer this questions we need to remember that two lines are perpendicular if and only if their slopes fullfil:

Now to find the slope of the line

we write it in slope-intercept form y=mx+b:

from this form we conclude that this line has slope 7.

Now we plug this value in the condition of perpendicularity and solve for the slope of the line we are looking for:

Once we hace the slope of the line we are looking for we plug it in the equation of a line that passes through the point (x1,y1) and has slope m:

Plugging the values we know we have that:

Therefore the equation of the line is:

Answer: The factor of the above function is (2x + 3) (3x + 4)

We are given the below function

This function can be factor using factorization method

The co-efficient of x^2 = 6

Multiply 6 by 12 to get the constant of the function

12 x 6 = 72

Next, find the factors of 72

Factors of 72 : 1 and 72, 2 and 36, 6 and 12, 9 and 8, 3 and 24

The only factor that will give us 17 when add and give us 72 when multiply is 8 and 9

The new equation becomes

The factor of the above function is (2x + 3) (3x + 4)