X^2 +6x+30 in vertex form

Answer: 0.88 lbs.

Step-by-step explanation:

12/30 = 0.4 (she needs to lose 0.4 kg everyday)

0.4 x 2.2 = 0.88 lbs

Using the method of Laplace transforms, the solution to the given initial value problem is y(t) = (3t² - 6t + 4) - 4sin(3t), where y(0) = 0 and y'(0) = 9.

To solve the initial value problem using Laplace transforms, we first take the Laplace transform of both sides of the given differential equation. Applying the linearity property and using the table of Laplace transforms, we obtain the transformed equation:

s³Y(s) - s²y(0) - sy'(0) - y(0) + 9Y(s) = 45/(s⁴) - 54/(s³) + 37/(s²)

Substituting y(0) = 0 and y'(0) = 9, the equation simplifies to:

s³Y(s) + 9Y(s) = 45/(s⁴) - 54/(s³) + 37/(s²)

Combining the terms on the right side, we get:

(s³ + 9)Y(s) = (45 - 54s + 37s²)/(s⁴)

Now, we can solve for Y(s) by dividing both sides by (s³ + 9):

Y(s) = (45 - 54s + 37s²)/(s⁴ * (s³ + 9))

Using partial fraction decomposition, we can express Y(s) as:

Y(s) = (3s² - 6s + 4)/(s⁴) - 4/(s³ + 9)

Taking the inverse Laplace transform of each term using the table of Laplace transforms, we obtain the solution in the time domain:

y(t) = (3t² - 6t + 4) - 4sin(3t)

Therefore, the solution to the initial value problem is y(t) = (3t² - 6t + 4) - 4sin(3t), where y(0) = 0 and y'(0) = 9.

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Answer:

third option is correct

Step-by-step explanation:

hope this helps

After 3 weeks she pay $208.10.

From the question, we have

After 3 weeks she pay =  

$211.30+$22.50-$17-$8.70 = $208.10

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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Answer: \(v=-\frac{1}{15},\:v=\frac{1}{15}\)

Step-by-step explanation: \(-3\left|\frac{1-2}{5v}\right|=-9\)

\(-\frac{3}{5\left|v\right|}=-9\)

\(-\frac{3}{5\left|v\right|}\cdot \:5\left|v\right|=-9\cdot \:5\left|v\right|\)

\(-3=-45\left|v\right|\)

\(v=-\frac{1}{15},\:v=\frac{1}{15}\)

Answer: y = 2x

Step-by-step explanation:

       We will change this equation into slope-intercept form (y = mx + b). To do this, we will isolate the y-variable.

Given:

     y - 4 = 2(x - 2)

Distribute:

     y - 4 = 2x - 4

Add 4 to both sides of the equation:

     y = 2x

1. We need to find the distance jumped by the Gold winner, we know that the total distance jumped by three athletes is 25.04, so we can subtract the distances from the Silver and Bronze winners in order to determine what we want. This is done below:

Now we need to represent this number as a fraction in its simplest form.

2. In order to determine which medal he would receive, we need to add the distance he actually jumped by 0.06 and compare to the table. We have:

He would win a Bronze medal.

3. In order to determine how farther Athlete B jumped more than Athlete D, we need to subtract their distances.

The athlete B jumped 0.26 meters farther than Athlete D.

1.the teacher kept 16 markers

2. shonta spent$36 in total

Step-by-step explanation:

1. 85 markers ÷ 23 children =3,696 round to 3

23 children × 3 markers each =69 markers

85 markers -69 markers =16 markers

2. $8×3 parakeets= $24 on the parakeets , adding in the $12 spent on the cage gives a total spent of: $24 parakeets+ $12 for bird cage= $36 spent

Answer:

m= -5/2

Step-by-step explanation:

(x1,y1)=(3,1)

(x2,y2)=(−1,11)

Use the slope formula:

m=y2−y1 divided by x2−x1

=11−1 .  −1−3=

10

−4

=

−5

2

Answer:

-2\(\frac{1}{2}\)

Step-by-step explanation:

using the formula \(\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}\) to find the slope, we get\(\frac{11-1}{-1-3}\), which is equal to -\(\frac{10}{4}\)

Simplifying this, we get -2\(\frac{1}{2}\).

Answer:

1.8 is 1.75 rounded to the nearest 10th

Step-by-step explanation:

Answer:

1.8, according to the rounding rules, any secondary digit with a value of 5 means you're supposed to round up.

Hope this helps.

Answer:

"9 more than A" is a verbal expression.

Answer:

87.96

Step-by-step explanation:

87.9645943

Round to either 0 or the next tenth.

87.9645943

87.964594(0)

87.96459(0)

87.9646(0)

87.965(0)

87.96(0)

87.9645943 rounded to the nearest hundredth is​ 87.96

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of trimmed from the right in terms of exact digits.

87.9645943

We have to Round to either 0 or the next tenth.

87.9645943

87.964594(0)

87.96459(0)

87.9646(0)

87.965(0)

87.96(0)

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Given:

h(x) = 7x + 5

g(x) = 4x + 26

At h(x) = g(x), we get:

h(x) = g(x)

7x + 5 = 4x + 26

7x - 4x = 26 - 5

3x = 21

3x/3 = 21/3

x = 7

Therefore, x = 7

Minimization of  f(x) = |x+3| + x^3 at the endpoints (-2 and 6)  the minimum value of the function is approximately 3.84, which occurs at x= \sqrt{1/3}

within the given interval.

To minimize the function subject to the constraint f(x) = |x+3| + x^3 that x lies in the interval [-2, 6], we need to find the value of x that minimizes f(x) within that interval.

First, let's analyze the function f(x). The absolute value term |x+3| can be rewritten as:

|x+3| =

x+3 if x+3 >= 0

-(x+3) if x+3 < 0

Since the interval [-2, 6] includes both positive and negative values of x+3, we need to consider both cases.

Case 1: x+3 >= 0

In this case, f(x) = (x+3) + x^3 = 2x + x^3 + 3

Case 2: x+3 < 0

In this case, f(x) = -(x+3) + x^3 = -2x + x^3 - 3

Now, we can find the minimum of f(x) within the given interval by evaluating the function at the endpoints (-2 and 6) and at any critical points within the interval.

Calculating the values of f(x) at x = -2, 6, and the critical points, we can determine the minimum value of f(x) and the corresponding value of x.

Since the equation involves both absolute value and a cubic term, it is not possible to find a closed-form solution or an exact minimum value without numerical methods or approximation techniques.

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Answer:

\( \huge{ \boxed{ \bold{g = - 2}}}\)

Step-by-step explanation:

In order to find g we have to use the formula for finding the slope of the line passing through two points that's

\(m = \frac{y_2 -y_ 1}{x_2 -x_1 } \\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are (g, -1) and (2, 5) and m = 3/2

We substitute it into the equation and find g

That's

\( \frac{3}{2} = \frac{5 - - 1}{2 - g} \\ \frac{3}{2} = \frac{5 + 1}{2 - g } \: \: \: \: \: \: \: \frac{3}{2} = \frac{6}{2 - g} \\ \\ 3(2 - g) = 6(2) \\ 6 - 3g = 12 \\ - 3g = 12 - 6 \\ - 3g = 6 \\ \\ \frac{ - 3g}{ - 3} = \frac{6}{ - 3} \\ \\ g = - 2\)

We have the final answer as

Hope this helps you

Answer:

x= -10

Step-by-step explanation:

-16x+48=10x+308

48-308=10x+16x

-260=26x

x= -10

Answer:

\(4( - 4 x + 12) = 10x + 308 \\ 16x + 48 = 10x + 308 \\ 16x = 10x + 308 - 48 \\ 16x - 10x = 260 \\ 6x = 260 \\ x = \frac{260}{6} Answer. x = 43.33\)

Answer:

It would be 8p+4

Step-by-step explanation:

dividing (48p + 24) by 6 involves factoring and simplifying the expression to obtain the result of 8p + 4

To divide (48p + 24) by 6, you first factor out the common factor of 6 from the expression, which yields

(48p + 24) = 6(8p + 4).

Then, you can further simplify by dividing each term by 6.

The result is 8p + 4.

This process of division distributes the division operation across all terms in the expression, and as a result, each term's coefficient is divided by 6.

In this case, it simplifies the original expression to 8p + 4.

In summary, dividing (48p + 24) by 6 involves factoring and simplifying the expression to obtain the result of 8p + 4

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Answer:

Degrees.

The symbol looks like this.

°

Answer:

There would be 6 zeros because it would become 1,000,000

Step-by-step explanation:

cube is the power of 3

100³ = 100×100×100

=1, 000, 000

As per the given options, one which does not have a unit price of $24 for one sweater is $38 for 2 sweaters. Hence, option A is correct.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the information in the question,

The unit price of the sweater is $24.

Now, let's check the options for a unit price of the sweater.

1.

$38 for 2 sweaters

So, the unit price = 38/2 = $19, it does not have the unit price of $24 for one sweater.

2.

$72 for 3 sweaters

So, the unit price = 72/3 = $24, so this is correct.

3.

$96 for 4 sweaters

So, the unit price = 96/4 = $24, this one is correct.

4.

$120 for 5 sweaters

So, the unit price = 120/5 = $24, this one is also correct.

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Your question seems incomplete, the complete question may be:

Which of the following does NOT have a unit price of $24 for one sweater?

$38 for 2 sweaters

$72 for 3 sweaters

$96 for 4 sweaters

$120 for 5 sweaters

Answer:

m = 5/6

Step-by-step explanation:

Cross multiply.

1/5 × m = 2/3 × 1/4

1/5 × m = 2/12

1/5 × m = 1/6

m = 5/6

A nurse should empty a Hemovac wound suction device when it is half full to ensure proper functioning and prevent discomfort or injury to the patient due to the device becoming too heavy.

The rationale for a nurse to empty a Hemovac wound suction device when it is half full is to ensure the device is functioning correctly and to prevent it from becoming too heavy and potentially causing discomfort or injury to the patient.

When a Hemovac wound suction device is half full, it may start to lose suction, which can result in less efficient drainage of fluid from the wound site. By emptying the device, the nurse can ensure that the device is functioning correctly and that the suction pressure is maintained.

Additionally, allowing the device to become too full can make it heavy and uncomfortable for the patient, potentially causing discomfort or injury to the wound site. Therefore, emptying the device when it is half full can help prevent these complications and ensure that the patient remains comfortable throughout the healing process.

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We find the limit of the expression as x approaches -11 is 0.

The limit is a concept in mathematics that represents the value that a function approaches as the input approaches a certain value.

To find the limit of the given expression, we substitute the value that x approaches into the expression. In this case, x approaches -11.

So, we substitute -11 for x in the expression:

lim x→−11 (x+11)/(10−x^2−21)

= (-11+11)/(10−(-11)^2−21)

= 0/(10−121−21)

= 0/(10−142)

= 0/(-132)

= 0

Therefore, the limit of the expression as x approaches -11 is 0.

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Answer:

2 x ^2  −  5 x  −  3

Step-by-step explanation:

Answer is the problem in standard form then the y-intercept would be -3

The school’s band members sold 40 shirts and 40 magazine subscriptions.

A statement of equality between two expressions made up of variables and/or integers is called an equation. In essence, equations are questions, and the reason for the advancement of mathematics has been the systematic search for the answers to these questions.

Given:

profit per shirt = $5

set up costs = $40

profit per magazine = $4

Let us assume S = shirts, C = setup costs, M = magazine

So, we can write the equation

5S - C = 4M

The profit from shirts and magazines are same. So, S = M

5S - 40 = 4S

5S - 4S = 40

S = 40

The school’s band members sold 40 shirts and 40 magazine subscriptions.

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Answer:

D?

Step-by-step explanation:

The largest possible value of p can be determined by analysing the ratio of the volumes of the two rectangular boxes.

The volume of the first box is V1 = m*p*n and the volume of the second box is \($V2 = (m2)\cdot (n2)\cdot (p2)$\). Therefore, we can set up the following equation to solve for p:

\($\frac{V1}{V2} = \frac{mnp}{(m2)(n2)(p2)} = \frac{1}{2}$\)

Solving for p gives us the following:

\($p = \sqrt[3]{\frac{2(m2)(n2)}{mn}}$\)

Since m, n, and p must all be integers, the largest possible value of p is the largest integer such that

\($p \le \sqrt[3]{\frac{2(m2)(n2)}{mn}}$.\)

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Answer:

9y²+9 that's the answer

The nearest whole number 83.92 - 47.23=37(rounding off)

Given,

83.92 - 47.23=36.69

The whole number is 0,1,2,3...

Rounding a number refers to the act of simplifying a number such that its value remains near to what it was. The outcome of rounding off a number is less precise but more convenient to utilize. We consider the place value of digits in a number when rounding it.

Let us look at an example to better grasp the notion of rounding. Susan walked 2.05 miles, which she estimated to be around 2 miles.

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