A coin is on the bottom of a pool, 8 ½ feet below the surface. Sal is going to jump off of a 10.25-foot-high diving board to retrieve the coin. What is the distance that Sal will need to travel from the diving board to the coin? *

The linear inequality that will represent given graph is y<-10x+300.

What are linear inequalities, exactly?

Linear inequalities are mathematical expressions that compare two linear functions and determine the relationship between them. They are similar to linear equations but instead of an equal sign, they use inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

A linear inequality can be represented by an algebraic expression in the form of:

ax + by < c, where a, b, and c are constants, and x and y are variables.

Now,

The general form of a line is

y=mx+c

take two points on the given line

(5,250)  and (30,0)

then m=slope=(0-250)/(30-5)=-250/25

=-10

and

0=-10*30+c

c=300

then equation is y=-10x+300

and inequality will be y<-10x+300.

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The given series 23−36+49−512+615−−− converges.

Given series is 23, −36, 49, −512, 615 ...

We can write the given series as ∑[infinity]n=1 an, where:

an = (-1)n+1 * n2

In order to test the convergence or divergence of the given series, we can use the Alternating series test.

Using Alternating Series Test:

If an alternating series satisfies the following three conditions, then the series converges:

Condition 1: The series must be alternating.

Condition 2: The absolute value of each term in the series must be decreasing.

Condition 3: The absolute value of each term in the series must approach zero.

In the given series, we observe that each term in the series is positive and the terms are decreasing. Thus, it satisfies the Condition 2 and Condition 3.

Now, let us take the partial sums of the given series,

s1=23

s2=23-36=-13

s3=23-36+49=36

s4=23-36+49-512=-476

s5=23-36+49-512+615=139

Here, we see that the sign of the sum is alternatively changing and we can infer that the series is an alternating series. Since this series satisfies all the 3 conditions of the alternating series test, it is convergent.

Hence, the given series converges.

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Answer:

4

Step-by-step explanation:

4^2 is 4x4 aka squared

9514 1404 393

Answer:

  x = -2, x = -1

Step-by-step explanation:

A graphing calculator solves this nicely, as shown in the attachment.

  x = -2, x = -1

__

The given equation resolves to two equations.

x+3 < 0

  -(x +3) -1 = (x +2)^2

  x^2 +5x +7 = 0

Checking the discriminant, we find ...

  b^2 -4ac = (5)^2 -4(1)(7) = 25 -28 = -3

There are only complex solutions to this equation.

__

x+3 ≥ 0

  x +3 -1 = (x +2)^2

  (x +2)^2 -(x +2) = 0 . . . .subtract x+2

  (x +2)(x +2 -1) = 0 . . . . . factor

Solutions are values of x that make these factors zero.

  x +2 = 0   ⇒   x = -2

  x +1 = 0   ⇒   x = -1

Domain Check

  x +3 = -2 +3 = 1 > 0 . . . . as required.

The square of a binomial, the value of the constant \(c\) should be equal to half the coefficient of the linear term squared, which in this case is \(c = \left(\frac{22}{2}\right)^2 = 121\). Therefore, the constant that needs to be filled in is 121.

To express the quadratic expression \(x^2 + 22x + c\) as the square of a binomial, we need to find a binomial of the form \((x + a)^2\) that expands to \(x^2 + 22x + c\). Expanding \((x + a)^2\) gives \(x^2 + 2ax + a^2\). Comparing the coefficients of the expanded binomial and the given quadratic expression, we can equate the linear terms to find \(2ax = 22x\), which gives \(a = 11\). Substituting this value of \(a\) back into the expanded binomial, we have \(x^2 + 22x + 121\). Therefore, the constant that needs to be filled in is 121.

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Answer:

In mathematics, the range of a function may refer to either of two closely related concepts: The codomain of the function The image of the function Given two sets X and Y, a binary relation f between X and Y is a function if for every x in X there is exactly one y in Y such that f relates x to y.

Step-by-step explanation:

Hope it help.

Answer:

The range is the difference between the highest and lowest values in a set of numbers. To find it, subtract the lowest number in the distribution from the highest.

Step-by-step explanation:

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The signal x(t) = (2 + sin t)2 can be broken down into its even and odd components. The even part of x(t) = (2 + sin t)2 is 4 + 4sin2 t and the odd part is 2sin t + sin2 t.

To find the even and odd parts of the signal x(t) = (2 + sin t)2, we can use the following equations:

Even part of x(t) = (1/2)[x(t) + x(-t)]

Odd part of x(t) = (1/2)[x(t) - x(-t)]

Let's first find x(-t) by replacing t with -t in the given signal:

x(-t) = (2 + sin(-t))2

x(-t) = (2 - sin t)2

Now we can use the above equations to find the even and odd parts of x(t):

Even part of x(t) = (1/2)[x(t) + x(-t)]

Even part of x(t) = (1/2)[(2 + sin t)2 + (2 - sin t)2]

Even part of x(t) = (1/2)[8 + 8sin2 t]

Even part of x(t) = 4 + 4sin2 t

Odd part of x(t) = (1/2)[x(t) - x(-t)]

Odd part of x(t) = (1/2)[(2 + sin t)2 - (2 - sin t)2]

Odd part of x(t) = (1/2)[4sin t(2 + sin t)]

Odd part of x(t) = 2sin t + sin2 t

Therefore, the even part of the signal x(t) = (2 + sin t)2 is 4 + 4sin2 t, and the odd part of the signal is 2sin t + sin2 t.

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Answer:

-3.375

Step-by-step explanation:

the point of a geometric sequence is that every new term is created by multiplying the previous term by a constant factor that is the same across the whole sequence.

that factor is called the common ratio.

so, 32 was multiplied by the common ratio, and we get -108 as result.

32 × cr = -108

cr = -108/32 = -27/8 = -3.375 = -3 3/8

The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F

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

Yeast thrives between 90°F to 95°F

For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range

Using the above as a guide, we have the following:

T < 90°F or T > 95°F.

Where

T = Temperature

Hence, the inequality is T < 90°F or T > 95°F.

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Answer:

yep

Step-by-step explanation:

Answer:

coordinates of the orthocenter = (16/5, 16/5)

Step-by-step explanation:

I have drawn a diagram showing this triangle with the vertices. I have also drawn altitude from B perpendicular to AC at point E.

I have also drawn altitude from from A perpendicular to BC at point D.

Now, we will find the slope of AC from the line slope equation; (y - y1) = m(x - x1)

m = (y - y1)/(x - x1)

Our coordinates are; A(0,0), B(8,2), C(2,8).

Thus;

Slope of AC; m = (8 - 0)/(2 - 0)

m = 4

Since BE is perpendicular to AC, slope of BE = -1/slope of AC = -1/4

Thus, equation of BE is;

(y - 2) = -¼(x - 8)

Multiply through by 4 to get;

4y - 8 = -x + 8

x + 4y = 16

Slope of BC is; m = (8 - 2)/(2 - 8) = 6/-6 = -1

AD is perpendicular to BC, thus slope of AD = -1/-1 = 1

Equation of AD is;

(y - 0) = 1(x - 0)

y = x

Putting x for y in equation of BE, we have;

x + 4x = 16

5x = 16

x = 16/5

Since y = x in equation AD, then y = 16/5

coordinates of the orthocenter = (16/5, 16/5)

Answer:

D should be on the first quadrilateral. Positive and Positive.  

Step-by-step explanation:

The periodic transfer of a portion of the cost of an intangible asset to expense is known as amortization. This is the process of spreading the cost of an intangible asset over its useful life, similar to how depreciation is used for tangible assets like buildings and equipment.

Intangible assets, such as patents, copyrights, and trademarks, do not have a physical existence but still have value to the company. Amortization recognizes the decline in value of these assets over time and helps to accurately reflect their impact on the company's financial statements.

The amount of amortization each period is calculated by dividing the cost of the asset by its estimated useful life. It is important for companies to track and properly account for their intangible assets, including amortization, as it can have a significant impact on their financial statements and overall financial health.

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In mathematics, expression is a set of digits, variables, and operators that denotes a quantity or relationship. Expressions can be straightforward and consist only of a single number or variable, or they can be intricate and contain numerous phrases and processes.

There are a few expressions that are equivalent to 45x - 30. One way to find them is to simplify the expression by factoring out the greatest common factor (GCF), which in this case is 15:

45x - 30 = 15(3x - 2)

Now we can see that the expression 45x - 30 is equivalent to 15 times the expression 3x - 2. Therefore, any expression that is equal to 3x - 2 can be used to represent 45x - 30 by multiplying it by 15. Here are some examples:

6x - 4 is equivalent to 45x - 30 when multiplied by 15.
9x - 6 is also equivalent to 45x - 30 when multiplied by 15.
3(15x - 10) is equivalent to 45x - 30, since we can distribute the 3 and get 45x - 30.

In general, we can say that any expression of form 3k - 2, where k is a constant, is equivalent to 45x - 30 when multiplied by 15. This shows that there are infinitely many expressions that are equivalent to 45x - 30, and we can find them by using the GCF and multiplying by a constant.

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Number of ways the tiles can be arranged = 60

There are a total of 6 places needs to be filled.

Also there are 6 tiles which is to be filled.

There are yellow, white and blue tiles.

Number of yellow tiles, Y = 3

Number of white tiles, W = 2

Number of blue tiles, B = 1

Total number of ways to fill 6 positions without any restrictions = 6!

No two neighboring tiles should be of same color.

So repetitions of same colored tiles needs to be avoided. For this, divide 3!, 2! and 1! by the total number of ways.

Hence the number of ways the tiles can be arranged if no two neighboring tiles are the same color = 6!/(3! x 2! x 1!)

                                       = 60 ways

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Answer: 5x + 2y = -2

Step-by-step explanation:

Change 5x+2y=12 to slope intercept: 2y = 12 - 5x, y = -5x/2 + 6

A parallel line has the same slope, so the line we try to find is y = -5x/2 + b.

Substitute (-2, 4) in and get 4=5+b, so b = -1.

Therefore the answer is y = -5x/2 - 1, or if you want it in the original form it would be 2y = -5x - 2 ---> 5x+2y = -2.

Hope that helped,

-sirswagger21

Answer:

To find the sale price of the suit, we need to first calculate the discount. The discount is equal to the original price multiplied by the discount rate, which in this case is $280 * 30% = $84.

Then we subtract the discount from the original price to find the sale price: $280 - $84 = $196.

So the sale price of the suit is $196.

Step-by-step explanation:

Answer:

4 balls for $2.50

Step-by-step explanation:

If 4 balls=$2.50

Then,$2.50+2.50= $6.25

$6.25 for 8 balls

The condition for maximum bridge sensitivity is when R3 is equal to R1.

The current through the galvanometer is approximately 0.06 A, and the resistance in arm DA should be 0.8Ω for no current to flow through the galvanometer.

We have,

The expression for Wheatstone bridge sensitivity can be derived as follows:

Let R1, R2, R3, and R4 represent the resistances of the four arms of the Wheatstone bridge.

The bridge sensitivity is defined as the change in output voltage (Vout) with respect to the change in input voltage (Vin).

Mathematically, it can be expressed as:

Sensitivity = dVout / dVin

To determine the condition for maximum bridge sensitivity, we can differentiate Vout with respect to Vin and set it equal to zero:

dVout / dVin = 0

By differentiating the bridge equation Vout = (R3/R1) * Vin, we obtain:

dVout / dVin = (R3/R1)

Therefore, the condition for maximum bridge sensitivity is when R3 is equal to R1.

Now let's solve the given problem:

Given resistances:

AB = 100Ω, BC = 10Ω, CD = 4Ω, DA = 50Ω

Galvanometer resistance: G = 20Ω

Source voltage: Vin = 10 V

To find the current through the galvanometer, we can assume no current flows through arm DA (i.e., R4 = 0) since the galvanometer is connected across BD.

Using the bridge equation:

Vout = (R3 / R1) * Vin

Substituting the given values:

Vout = (4Ω / 100Ω) * 10 V

= 0.4 V

Since the galvanometer resistance G is connected in parallel with CD (10Ω), the total resistance across BD is:

Rtotal = (G * CD) / (G + CD)

= (20Ω * 10Ω) / (20Ω + 10Ω)

= 6.67Ω

Using Ohm's Law, the current through the galvanometer is:

I = Vout / Rtotal

= 0.4 V / 6.67Ω

≈ 0.06 A

To find the resistance in arm DA (R4) for no current through the galvanometer, we can use the condition that the bridge is balanced

(I = 0) when the ratio of the resistances on opposite arms of the bridge is equal:

R3 / R1 = R4 / G

Substituting the given values:

4Ω / 100Ω = R4 / 20Ω

Simplifying:

0.04 = R4 / 20Ω

Solving for R4:

R4 = 0.04 * 20Ω

= 0.8Ω

Therefore, the resistance in arm DA (R4) should be 0.8Ω for no current to flow through the galvanometer.

Thus,

The condition for maximum bridge sensitivity is when R3 is equal to R1.

The current through the galvanometer is approximately 0.06 A, and the resistance in arm DA should be 0.8Ω for no current to flow through the galvanometer.

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The expression (r - c)(3) represents the difference between the revenue and expenses of George's new store after 3 months of operation.

In summary, (r - c)(3) indicates the net profit or loss of George's new store after it has been open for 3 months.

Let's explain the answer in more detail. The revenue function r(x) represents the store's monthly revenue in hundreds of dollars, which is given by the equation r(x) = x^2 - 5x + 14. The expenses function c(x) represents the store's monthly expenses in hundreds of dollars, which is given by the equation c(x) = x^2 - 3x + 4.

To calculate (r - c)(3), we substitute x = 3 into both r(x) and c(x), and then subtract c(x) from r(x). This gives us:

(r - c)(3) = r(3) - c(3)

Evaluating r(3) and c(3) gives us:

r(3) = 3^2 - 5(3) + 14 = 9 - 15 + 14 = 8

c(3) = 3^2 - 3(3) + 4 = 9 - 9 + 4 = 4

Substituting these values into the expression:

(r - c)(3) = 8 - 4 = 4

Therefore, (r - c)(3) indicates that after 3 months, George's new store has a net profit of $400.

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Answer:

x = 53°, y = 42°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180° for x

x = 180° - (37 + 90)° = 180° - 127° = 53°

48° + y = 90° ( subtract 48° from both sides )

y = 42°

To solve the initial value problem y'' - 2y' - 3y = 0, with y(0) = 1 and y'(0) = 2, we can use the method of Laplace transforms.

First, we take the Laplace transform of the given differential equation to obtain an algebraic equation in terms of the Laplace transform of the unknown function y(t). Then, we solve the algebraic equation for the Laplace transform of y(t) using standard algebraic techniques. Finally, we take the inverse Laplace transform to obtain the solution y(t) in the time domain.

Applying the Laplace transform to the given differential equation, we have s²Y(s) - sy(0) - y'(0) - 2(sY(s) - y(0)) - 3Y(s) = 0, where Y(s) represents the Laplace transform of y(t). Simplifying this equation, we get (s² - 2s - 3)Y(s) - (s - 2) = s²Y(s) - 3s - 4. Rearranging the equation, we have Y(s) = (s - 2) / (s² - 2s - 3).

To solve this equation for Y(s), we can decompose the expression into partial fractions, which yields Y(s) = 1 / (s - 3) - 1 / (s + 1). Taking the inverse Laplace transform of Y(s), we obtain y(t) = e^(3t) - e^(-t), which is the solution to the initial value problem.

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Answer:

C. Geometric, common ratio = 3

Step-by-step explanation:

Got it right

Answer:

C

Step-by-step explanation:

Answer:

3/8 is a proper fraction which means it can't be written as a mixed number

Step-by-step explanation:

If the numerator is bigger than the denominator then you can convert it to a mixed number.

Answer:

3/8 is equal to 0.375

i dont think this can be turned into a mixed number becuase the fraction isn't over 8

example: 18/8 can be changed into the mixed number 2 3/8

Step-by-step explanation:

Answer:

i think its six

Step-by-step explanation:

6-3=3

3+3=6

The value of the number that it is decreased by 3 and the result is doubled will be 6.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Suppose that number is x.

x is decreased by 3 = x - 3

The results is doubled = 2(x - 3) = x

2x - 6 = x

2x - x = 6

x = 6

Hence "When a number is reduced by three and the outcome is doubled, its value becomes six".

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The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7