Pierce swims 10 laps in a pool in 8 minutes. He spent the same amount of time on each lap. How much time did each lap take him?​

The formula that defines the sequence is f(n) = f(n-1) + 4

The recursive function rule is expressed as;

f(n) = f(n-1)  + d

where

d is the common difference

Given the following sequence

2, 6, 10, 14, 18..

Determine the common difference

d = 6-2 = 10-6

d = 4

Substitute to have

f(n) = f(n-1)  + d

f(n) = f(n-1) + 4

Hence the formula that defines the sequence is f(n) = f(n-1) + 4

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The area of the image is 56ft²

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.

The area scale factor is the square of the linear scale factor.

Therefore area scale factor = 2² = 4

Therefore the area of the image of the triangle = 14× 4

= 56ft²

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Answer:

6x - 5y = - 45

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = \(\frac{6}{5}\) x + 9 ( multiply through by 5 to clear the fraction )

5y = 6x + 45 ( subtract 5y from both sides )

0 = 6x - 5y + 45 ( subtract 45 from both sides )

- 45 = 6x - 5y , that is

6x - 5y = - 45 ← in standard form

he polynomial x(5x² + 10x + 15), it is not completely factored, 5x² + 10x + 15 can still be factored into two binomials.

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

Given the polynomial x(5x²+10x+15), it is not completely factored, 5x²+10x+15 can still be factored,

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Answer: dale

Step-by-step explanation:

2÷5=0.4(Cups/minute).........dixie

10÷12=0.833∞(Cups/minute)..........dale

0.8333>0.4

P(8/3) is not equal to zero, we can conclude that 8/3 is not a zero of P(x). Therefore, our suspicion was incorrect.

What is quadratic equation and how to solve it ?

A quadratic equation is a second-degree polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

To solve a quadratic equation, there are different methods, such as factoring, completing the square, and using the quadratic formula. The quadratic formula is the most general method and can be used for any quadratic equation.

It states that the solutions to the equation ax^2 + bx + c = 0 are given by the formula

x = (-b ± sqrt(b^2 - 4ac)) / (2a).

We can use this formula to find the roots of the equation by substituting the values of a, b, and c into the formula and simplifying.

To confirm if 8/3 is a zero of the quadratic function P(x) = 3x^2 - 4x - 7, we can substitute 8/3 for x in the equation and check if the resulting expression is equal to zero. If P(8/3) equals zero, then we can confirm that 8/3 is indeed a zero of P(x).

P(8/3) = 3(8/3)^2 - 4(8/3) - 7

= 3(64/9) - 32/3 - 7

= 64/3 - 32/3 - 21/3

= 11/3

Since P(8/3) is not equal to zero, we can conclude that 8/3 is not a zero of P(x). Therefore, our suspicion was incorrect. If we want to find the zeros of P(x), we can use the quadratic formula or factor the equation into (3x + 1)(x - 7) = 0 to get the roots x = -1/3 and x = 7.

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Answer:

Step-by-step explanation:

The inequality that represents Jenny's situation is:

600 - 20w > 300

To solve for w, we can start by subtracting 600 from both sides of the inequality:

-20w > 300 - 600

-20w > -300

Next, we can divide both sides by -20, remembering to reverse the direction of the inequality because we are dividing by a negative number:

w < (-300) / (-20)

w < 15

Therefore, the number of weeks that Jenny can continue to withdraw $20 from her account is less than 15. Since Jenny cannot withdraw a fractional number of weeks, the largest whole number of weeks that satisfies the inequality is 14.

Therefore, Jenny can continue to withdraw $20 from her account for 14 weeks while still keeping more than $300 in her account for college.

Answer:

q = 6 2/5

Step-by-step explanation:

q/8 = 4/5

Using cross products

q*5 = 8*4

5q = 32

Divide each side by 5

5q/5 = 32/5

q = 6 2/5

The expression of "The difference of -10 and the product of p and q" in algebraic notation is pq + 10

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

The difference of -10 and the product of p and q

The numbers are given as

p and q

The product of p and q means pq

So, we have the following

The difference of -10 and pq

The difference of -10 and pq means

pq + 10

Hence, the expression is pq + 10

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Answer:

the answer is 3x^2 + 8x + 1

Step-by-step explanation:

(I used x as the variable due to the invalid difference of variables in your question )

To find the correct answer, I had to use polynomial division.

(9 x 3 + 27 x 2 + 11 x + 1) / (3 x + 1)

= ( 3 x + 1 ) ( 3 x 2 + 8 x + 1 ) / (3 x + 1)

= 3 x 2 + 8 x + 1

162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

Answer:

a) 7.5 meters b) 588.75

Step-by-step explanation:

To calculate the volume you need to multiply the 3 values together so

3x5x0.5 = 7.5

That is the volume

Then you got to multiply that by 78.50 to get the answer for b

78.50x7.5 =588.75

Answer:

C. 439.6 in.²

Step-by-step explanation:

The container is a cylinder.

Since the two circular bases won't be covered, therefore:

The least construction paper needed to cover the remaining surface = curved surface area of the cylinder

= 2πrh

r = 5 in.

h = 14 in.

Plug in the values

Curved surface area = 2×π×5×14 = 439.6 in.²

√80 is equivalent to the required value of 'x'

The given diagram is a right triangle with the following sides

Hypotenuse = 21

Opposite = 19

We need to determine the value of 'x' from the expression

hypotenuse^2 = opposite^2 + adjacent^2

Substitute the given parameters

21^2 = x^2 + 19^2

x^2 = 21^2 - 19^2

x^2 = 80

x = √80

Hence the value of x from the triangle given is √80

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Answer:

P = 0.309

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

y= 51 x 4 = 204

x= 3 x 4 = 12

Answer:

Step-by-step explanation:

The value of X when Y is 204 is 12

Let the relationship between X and Y be a direct proportion

If Y and X is directly proportional then;

k is the constant of proportionality

If X = 3 and Y = 51

In order to get the value of X if Y is 204, Recall;

Hence the value of X when Y is 204 is 12

Answer:

\(Area = (56+10x-x^{2} )\:\:\: units^{2}\)

Step-by-step explanation:

The formula to find the area of a triangle is :

Area = \(\frac{1}{2}\) × base × height

Here,

base ⇒ 8 + 2x

height ⇒ 14 - x

Let us solve now.

Area = \(\frac{1}{2}\) × base × height

Area = \(\frac{1}{2}\) × (8 + 2x) × (14 - x)

\(Area = \frac{1}{2} (8 + 2x) (14 - x)\)

\(Area = \frac{1}{2} *(112-8x+28x-2x^{2} )\)

\(Area = \frac{1}{2} *(112+20x-2x^{2} )\)

\(Area = \frac{1}{2} *2(56+10x-x^{2} )\)

\(Area = \frac{2(56+10x-x^{2} )}{2}\)

\(Area = (56+10x-x^{2} )\:\:\: units^{2}\)

The problem states that the sample is skewed to the right, which suggests that the sample is not normally distributed.

What is mean ?

Mean can be defined as ratio of sum of observation and total number of observations.

In order to construct a confidence interval for the mean age of the faculty members at the university using a t-distribution, we need to check that the following conditions have been met:

Independence: The sample of 20 faculty members must be selected randomly and independently from the population of all faculty members at the university.

Sample size: The sample size should be less than 10% of the total population size. Since the population size is approximately 700, 20 is certainly less than 10% of 700, so this condition is satisfied.

Skewness: The sample distribution should be approximately normal or the sample size should be large enough (greater than or equal to 30) for the central limit theorem to apply.

Therefore, the problem states that the sample is skewed to the right, which suggests that the sample is not normally distributed.

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Answer:

the data is a random sample from the population of interest.

individual observations can be considered independent.

Step-by-step explanation:

For the given figure,   x = 23°  and      y = 129°

Parallel lines:

                        Parallel lines are lines that always stay the same distance apart and never meet.

Transversal line :

                             A transversal is a line that crosses two or more other lines.

given,

     ∠TLN = (3x - 18)°

    ∠MZQ = (5x + 14)°

    ∠NLM = y°

Now,

         ∠MZP + ∠MZQ = 180°  (Linear Pair)

        ∠MZP  = 180° - ∠MZQ  ...........(I)

again,

          ∠NLM + ∠TLN  =180°  ...........(II)      (Linear Pair)

  As,         ∠TLN = ∠MZP  (Corresponding Angle)

             (3x - 18)° =  180° - ∠MZQ  

           (3x - 18)° = 180° - (5x + 14)°

         3x + 5x  = 180° - 14° + 18°

           8x = 184°

           x = 184 / 8

          x = 23°

      From (II),

      ∠NLM + ∠TLN  =180°

    y° + 3x - 18° = 180°

 y = 180 - 3x + 18

     = 180 - 3* 23 + 18

      = 180 - 69 +18

     y = 129°

For the given figure,

                                     x = 23°  and      y = 129°

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To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Answer:

alot

Step-by-step explanation:

Since the congruent angle is a right angle and it is not included, the two congruent sides of the triangles must include their hypotenuses and one of their legs.The triangles would be congruent by the hypotenuse leg theorem, which states that if the hypotenuse and one leg of a right triangle is congruent to the hypotenuse and a leg of another right triangle, the triangles are congruent.Answer:hypotenuse leg theorem

There are no two Real numbers that add up to -2 and multiply to 10.

The numbers that add up to -2 and multiply to 10, we can use algebraic methods. Let's denote the two numbers as x and y. Based on the given conditions, we can set up two equations:

Equation 1: x + y = -2

Equation 2: x * y = 10

To solve this system of equations, we can use substitution or elimination methods. Let's solve it using the substitution method:

1. Solve Equation 1 for x:

  x = -2 - y

2. Substitute the value of x in Equation 2:

  (-2 - y) * y = 10

3. Simplify the equation:

  -2y - y^2 = 10

4. Rearrange the equation to standard form:

  y^2 + 2y + 10 = 0

5. Since the equation is a quadratic equation, we can apply the quadratic formula:

  y = (-b ± √(b^2 - 4ac)) / (2a)

  In this case, a = 1, b = 2, and c = 10.

6. Calculate the discriminant: b^2 - 4ac:

  2^2 - 4(1)(10) = 4 - 40 = -36

7. Since the discriminant is negative, the quadratic equation does not have real solutions. Therefore, there are no real numbers that satisfy both conditions of adding up to -2 and multiplying to 10.

In conclusion, there are no two real numbers that add up to -2 and multiply to 10.

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(a) x -5 -3 0 2 4

   y 4 0 -6 -10 -14

(d) x -14 -10 -6 0 4

   y 4 2 0 -3 -5

These tables could be used to verify that the functions they represent are inverses of each other

To verify if two functions are inverses of each other, we need to check if the composition of the two functions gives the identity function.

In other words, if f and g are two functions, then we need to check if f(g(x)) = x and g(f(x)) = x for all x in their domains.

We can create two tables, one for f and one for g, and use them to compute the compositions.

If the compositions give the identity function, then the functions are inverses of each other.

Based on this, the two tables that could be used to verify that the functions are inverses of each other are:

(a) x -5 -3 0 2 4

    y  4 0 -6 -10 -14

(d) x -14 -10 -6 0 4

    y 4    2   0 -3 -5

We can use the values in these tables to compute the compositions f(g(x)) and g(f(x)) and check if they give the identity function.

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Answer:

8.8

Step-by-step explanation:

Add all numbers together to get 132

All number of numbers together to get 15

Divide the sum of all numbers by the number of numbers:

132/15

8.8

pls mark brainliest!

Answer:(7/3)x - 8/3.

Step-by-step explanation:

To simplify this expression, you need to distribute the 1/3 to the expression inside the parenthesis. This gives:

1/3(5x-8) = (1/3)*5x - (1/3)*8 = (5/3)x - (8/3)

Now, you can distribute the 2/3 to the x-term:

2/3x = (2/3)x

Putting the two terms together, you get:

(5/3)x - (8/3) + (2/3)x = (5/3 + 2/3)x - 8/3 = (7/3)x - 8/3

So, the simplified expression is (7/3)x - 8/3.

Answer:

Step-by-step explanation:

1/3(5x-8)+2/3x

multiply everything by the LCM of the denomenators

LCM of the denomenators=3

1/3 x 3=0

(5x-8)x3=15x-24

2/3x x3=2x

15x+2x-24

=17x-24

Answer:

50

Step-by-step explanation:

if the given amount (20%) is 10 then to find the whole :

multiply 10 with 100 and then divide the result with 20

10*100/20 = 50

Candy spends £2.65, has 2/3 left and Candy has £7.95 money to start with.

Given that Candy spends £2.65 and has 2/3 of the initial amount left, we are required to find how much money Candy has to start with.

Solution:Let the initial amount of money Candy has be x.

Then, the amount of money spent by Candy = £2.65

Amount of money left with Candy = 2/3 of the initial amount

∴ Money left = 2/3 × x

Amount of money spent + money left = initial amount of money

Candy spends £2.65:2/3 of the initial amount left

= £ (x - 2.65)∴ 2/3 × x

= x - 2.65⇒ 2x/3

= x - 2.65⇒ 2x

= 3x - 7.95⇒ 3x - 2x

= 7.95⇒ x = 7.95

Hence, Candy has £7.95 to start with.

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The loan that will offer Craig the best effective interest rate is a) Loan L with a real percentage rate of 8.6%.

An effective interest rate is the real percentage rate on an interest-paying investment which removes the effects of compounding over time.

The formula for computing the effective interest rate is as follows:

Effective Interest Rate, r = (1 + i/n)^n - 1.

              Nominal Interest Rates    Compounding Periods

Loan L                   8.25%                    365 days

Loan M                  8.47%                    52 weeks

Loan N                  8.533%                  12 months

Loan O                  8.604%                 Yearly

Loan L = (1 + 0.0825/365)^365 - 1

= 1.08598 - 1

= 0.086

= 8.6%

Loan M = (1 + 0.0847/52)^52 - 1

= 1.0883 - 1

= 0.0883

= 8.83%

Loan N = (1 + 0.08533/12)^12 - 1

= 1.0887 - 1

= 0.0887

= 8.87%

Loan O = (1 + 0.08604/1)^1 - 1

= 1.08604 - 1

= 0.08604

= 8.604%

Thus, we advise Craig to take Loan L because it offers the least-costly effective interest rate.

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