14. y = -(x - 2)² + 1 graphed

After evaluating the expression 58 + (4x12-40) to the power of 2, we get 4356 or 4.356 ×10³ in scientific notation.

An expression or mathematical expression is a finite combination of symbols that are well-formed in accordance with context-dependent rules. To help define the logical syntax and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping.

Authors frequently distinguish between a formula and an expression, with the former referring to a mathematical object and the latter to a statement about such an object.

We have been asked to evaluate the Expression

​58 + (4x12-40) to the power of 2

⇒ (​58 + (4x12-40))²

Use (a + b)² = a² + b² + 2ab

= 58² + (4x12-40)² + 2(​58)(4x12-40)

= 3364 + (4x12-40)² + 116(4x12-40)

= 3364 + (48-40)² + 116(48-40)

= 3364 + (8)² + 116(8)

= 3364 + 64 + 928

= 4356

= 4.356 ×10³

Thus, After evaluating the expression 58 + (4x12-40) to the power of 2, we get 4356 or 4.356 ×10³ in scientific notation.

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Step-by-step explanation:

answer is (a,s) = (14,8)

According to the problem the area of the rectangle is 28 cm^2.

Area is a measure of the size of a surface or region. It is usually expressed in square units, such as square meters (m2), square kilometers (km2), and square feet (ft2). Area can be found in two-dimensional shapes, such as circles, rectangles, and triangles, as well as in three-dimensional shapes, such as cubes and spheres. The area of a two-dimensional shape is the amount of space that it covers. The area of a three-dimensional shape is the total surface area of the object.

The area of a rectangle is calculated by multiplying the length by the width. In this case, the length of the rectangle is 7 cm and the width is 4 cm. Therefore, the area of the rectangle is 7 cm x 4 cm = the area of the rectangle is 28 cm^2.

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Answer:

6x

Step-by-step explanation:

Combine like terms

Answer: X=21

Step-by-step explanation:

Answer:

You will need 3 [tex]\frac{11}{15}[/tex] cups of sugar.

Step-by-step explanation:

1 1/3 x 2 4/5

another name for 1 is 3/3

3/3 + 1/3 = 4/3

Another name for 1 is 5/5

5/5 + 5/5 + 4/5 = 14/5

[tex]\frac{4}{3 }[/tex] x [tex]\frac{14}{5}[/tex] = [tex]\frac{56}{15}[/tex]

I can break 56 into 15 + 15 + 15 + 11

[tex]\frac{15}{15}[/tex] + [tex]\frac{15}{15}[/tex] + [tex]\frac{15}{15}[/tex] + [tex]\frac{11}{15}[/tex]  another name for [tex]\frac{15}{15}[/tex] is 1

1 + 1 + 1 + [tex]\frac{11}{15}[/tex]

3 [tex]\frac{11}{15}[/tex]

The rule for the exponential function is y=42(1/2)^x

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

Here,

general form of exponential function is y=a(b)^x

a= y-intercept ,  b = multiplier

The initial y value 42 is multiplied by 1/2, we get next y value 21 as given in the graph, So, b = 1/2

y=a(1/2)^x

consider (x,y)=( 0,42)

=> x=0 and y=42

So 42=a(1/2)^0

=> 42=a

Thus, the rule for the function is y=42(1/2)^x

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Answer:

3x

Step-by-step explanation:

To answer this question, we have to understand what a product is. A product is the result of multiplication. For example, the product of 5 and 5 is 25 because 5 × 5 = 25.

We can apply this concept to the given expression.

"the product of 3 and a number"

means:

3 × "a number"

And since the problem specifies that "a number" is represented by the variable x, we can replace it with that.

3 × x

This looks a bit confusing with the x-like multiplication sign, so we can remove that and make 3 a coefficient of x.

3x

Answer:

3*x

Step-by-step explanation:

We can break down the problem piece by piece. We have "the product". The product of what? The product of 3 and a number. The problem tells us to replace a number with x. So it is 3*x.

The given expression is equivalent to (3y/x)(1 + 2x²y).

Given is that Luis, María and Ricky presented an essay about their respective ages. Ricky is 3 years older than Luis. Luis's age is 23 years and the sum of the ages of the three is 77 years.

Assume the age of Maria is {x} years old. So, we can write that -

Ricky's age = 23 + 3 = 26

And -

x + 26 + 23 = 77

x + 49 = 77

x = 77 - 49

x = 28

Therefore, the age of Maria is 28 years old.

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{Question in english -

Luis, María and Ricky presented an essay about their respective ages. Ricky is 3 years older than Luis. If Luis's age is 23 years and the sum of the ages of the three is 77 years, how old is Maria?}

Answer: 3

Step-by-step explanation:

The vertical distance between the sinusoidal axis and the maximum or minimum value of the function.

Trust

Answer:

The data has an outlier in the 13 to 15 range and shows that a large group purchased tickets to the game.

Step-by-step explanation:

An outlier in a frequency distribution is a value or set of values that is significantly different from the rest of the data set points. There is not a strong mathematical definition for what an outlier is, one should examine the data and assess in a more or less subjective manner

Looking at the data we see that most of ticket sales fall in the range 1-10

There is nothing in the range 10-12 but then after that there is another interval 13-15 with a frequency count of 1. This interval represents an outlier - it is very much apart from the rest of the data

So statement 1 is the best choice

We can eliminate the second statement. Skewness means that the data is very asymmetrical and has a peak which is at extreme right or left. Looking at the graph we see that the data is pretty much symmetrical in the range 1 - 10

Third statement can be easily eliminated since we do have an outlier as explained

Fourth statement can also be easily eliminated. The mode of a distribution is the value  that appears the most often. When plotting a histogram this value (interval will have the bar that is tallest). Here, the mode is in the interval 4-6 with a height of 16 which is the number of times any ticket sales in the range 4-6 occur.

A bimodal distribution will have two bars which are the highest and of equal value. We usually refer to these as peaks. Here there is only one peak and such a distribution is called a unimodal distribution.

Hope that helps you :)

Answer: the first option is correct

Step-by-step explanation:

I got it right on my quiz

Answer: The value of x is 0 and y is -5 using the elimination method.

Step-by-step explanation: To use the elimination method, we will remove one variable and find the value of the other one. Rewriting the equation -

-2y + 5x = 10 : equation 1

-3y + 4x = 15 : equation 2

Multiplying equation 1 with 4 and equation 2 with 5

-8y + 20x = 40 : equation 3

-15y + 20x = 75 : equation 4

Subtracting equation 3 from equation 4 to eliminate variable y

-7y = 35

y = - 35/7

y = -5

Keep the value of y in Equation 1 to find the value of x

-2(-5) + 5x = 10

10 + 5x = 10

5x = 10 - 10 5x = 0

x = 0

So, the value of x is 0 and y is -5.

Answer:5=y

Step-by-step explanation:

10 − 5x=−2y

15 − 4x =−3y

• (10 − 5x=−2y)4

         (40 - 20x=−8y)

          15 − 4x =−3y

         (15 − 4x =−3y)5

         (75 - 20x=−15y)

• (75 - 20x=−15y)

• (40 - 20x=−8y)

•  35 =-7y

• 35/7=y

• 5=y

The sum of the two matrices will be [tex]A+B = \left[\begin{array}{ccc}-1&-13&7\\5&-14&0\\7&1&4\end{array}\right][/tex]. The correct option is A.

A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns.

The given matrices are:-

[tex]A = \left[\begin{array}{ccc}7&-6&2\\6&-5&-7\\2&-8&8\end{array}\right][/tex]

[tex]B = \left[\begin{array}{ccc}-8&-7&5\\-1&-9&7\\-5&9&-4\end{array}\right][/tex]

The sum of the matrix will be:-

[tex]A+B = \left[\begin{array}{ccc}(7-8)&(-6-7)&(2+5)\\(6-1)&(-5-9)&(-7+7)\\(2+5)&(-8+9)&(8-4)\end{array}\right][/tex]

[tex]A+B = \left[\begin{array}{ccc}-1&-13&7\\5&-14&0\\7&1&4\end{array}\right][/tex].

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Answer:

b) The bond Sandy purchased has a face value of $2500 and a coupon rate of 7%. The coupon rate is the interest rate paid on the bond, which is typically paid semiannually. To find how much interest Sandy will receive semiannually, we can use the formula:

Interest = Face value x Coupon rate / 2

Interest = $2500 x 7% / 2 = $87.50

So Sandy will receive $87.50 in interest semiannually from the bond.

c) The fund Sandy invested in is expected to grow by 3.5% per year. To find how long it will take for the fund to be worth $10,000, we can use the formula:

Future value = Present value x (1 + Interest rate)^Years

We can solve for Years by dividing both sides of the equation by the present value and taking the natural logarithm of both sides:

Years = ln(Future value/Present value) / ln(1 + Interest rate)

Years = ln(10000/5000) / ln(1.035)

Years = 7.19

Therefore, the fund will take about 7.19 years to be worth $10,000.

d) Sandy's gross annual income is $51,350. She is paid biweekly, and 5% of her paycheck is deducted for her 403(b). Her employer matches her deduction, up to 4%. To find how much is deposited into Sandy's 403(b) each payday, we can use the following formula:

Contribution = (Gross pay x Contribution rate) + (Employer match x Employee contribution)

Gross pay = $51,350/26 (for bi-weekly paycheck) = $1977.50

Contribution = ($1977.50 x 5%) + ($1977.50 x 5% x 4%) = $98.87

So, $98.87 is deposited into Sandy's 403(b) each payday.

Answer:

12% increase

Step-by-step explanation:

First, find the difference between 18.48 and 16.50:

18.48 - 16.50 = 1.98

Now, what percent of 16.50 is 1.98?:

1.98 / 16.50 = 0.12

0.12 * 100% =   ==> 100% = 1. Anything multiplied by 1 is itself ( 1 * 3 = 3 )

0.12 * 100% = 12%

Hence, $16.50 to $18.48 is an increase of $1.98 or 12%.

Answer:

12% increase

Step-by-step explanation:

(V2−V1)|V1|×100

=(18.48−16.5)|16.5|×100

=1.9816.5×100

=0.12×100

=12%change

=12%increase

Answer:

B)

Step-by-step explanation:

To know which line is equivalent, we need to convert this equation from standard to slope-intercept form. We can take our original equation:

5x + 2y = 6

Minus 5x from both sides:

2y = -5x + 6

Then, divide by 2:

[tex]y = -\frac{5}{2}x + 3[/tex]

Looking at our options, we can see that

B) y equals short dash 5 over 2 x plus 3, is the same. So, B) is the answer.

Hope this helped!

Answer:

[tex]\textsf{B)} \quad y=-\dfrac{5}{2}x+3[/tex]

Step-by-step explanation:

Given equation:

[tex]5x+2y=6[/tex]

Subtract 5x from both sides of the equation:

[tex]\implies 5x+2y-5x=6-5x[/tex]

[tex]\implies 2y=-5x+6[/tex]

Divide both sides of the equation by 2:

[tex]\implies \dfrac{2y}{2}= \dfrac{-5x}{2}+ \dfrac{6}{2}[/tex]

[tex]\implies y=-\dfrac{5}{2}x+3[/tex]

Gradient-based optimization: This method is commonly used for more complex models, such as deep neural networks. The goal is to find the set of model parameters that minimizes a loss function.

Generally, There are a variety of ways to estimate mathematical models, depending on the type of model and the available data. Some common methods include:

Least squares: This method is commonly used for linear regression models, where the goal is to find the line of best fit through a set of data points. The least squares method finds the line that minimizes the sum of the squared differences between the predicted values and the actual values.

Maximum likelihood: This method is commonly used for probabilistic models, such as those used in statistics and machine learning. The goal is to find the set of model parameters that maximizes the likelihood of the observed data.

Bayesian inference: This method is similar to maximum likelihood, but it also incorporates prior knowledge or beliefs about the model parameters into the estimation process. This can be done by specifying a prior distribution over the parameters, which is then updated based on the observed data to give a posterior distribution.

These are just a few examples, and there are many other methods available depending on the type of model and the data available.

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The solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

Given is the initial value problem -

y''' + 10y'' + 25y' = 0

We can write the -

[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]

The given differential equation can be solved and written as -

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)

Therefore, the solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

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Check the picture below.

The speed of the boat against the current is (13+x)mph and with the current is (13-x) mph.

If boat goes along the stream flow (downstream), then the speed of boat will be increased as stream will help boat go faster. In contrast, the upstream flow of boat will be slower than its speed in normal flow due to stream resistance.

Speed of boat with the current = Speed of boat + Speed of current

Speed of boat against the current = Speed of boat - Speed of current

Given that the speed of a boat in still water is 13 mph. Also, the speed of the water current is x mph. Therefore, the speeds in the given cases can be written as,

a.) The of speed going against a current with a rate of x mph can be written as,

Speed of boat with against the water current

= Speed of Boat - Speed of water current

= 13 mph - x mph

= (13-x) mph

b.) The of speed going with a current with a rate of x mph can be written as,

Speed of boat with the water current

= Speed of Boat + Speed of water current

= 13 mph + x mph

= (13+x) mph

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Answer:

The appropriate notation to represent the inequality x < 4 is O (-∞, 4)

Step-by-step explanation:

This notation states that x can be any value less than 4.

The other options are:

(-∞0, 4]: This notation states that x can be any value between negative infinity and 4, including 4.

[-∞, 4]: This notation states that x can be any value between negative infinity and 4, including negative infinity and 4.

(-00, 4): This notation is not a valid notation.

(4,00): This notation states that x can be any value greater than 4.

Answer:

The amount of money in the account at the end of 5 years is $9,841.63.

Step-by-step explanation:

The compound interest formula is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = 8000, r = 0.04, n = 4 (because interest is compounded quarterly), and t = 5 (because we are trying to find the balance after 5 years).

So the formula becomes:

A = 8000(1 + 0.04/4)^(4*5)

By plugging the number into the formula we can find the final amount after 5 years

A = $9,841.63

The amount of money in the account at the end of 5 years is $10,404.69, and the interest earned is $2404.69.

To calculate the amount of money in the account at the end of 5 years, we need to use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

To calculate the amount of interest earned, we subtract the initial deposit from the final amount: interest = A - P.

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Answer:

k=

v

2

4v

2

−4v−9

Step-by-step explanation:

Evaluate

(k−4)×v

2

+4v+9=0

Simplify

kv

2

−4v

2

+4v+9=0

Rewrite the expression

v

2

k−4v

2

+4v+9=0

Move the expression to the right side

v

2

k=0−(−4v

2

+4v+9)

Subtract the terms

v

2

k=4v

2

−4v−9

Multiply both sides

v

2

k×

v

2

1

​

=(4v

2

−4v−9)×

v

2

1

​

Simplify

v

2

k×

v

2

1

​

=

v

2

4v

2

−4v−9

​

Solution

k=

v

2

4v

2

−4v−9

​

Answer:

30

Step-by-step explanation: 30-60-90 theorem

Answer:

The answer is 3x-11

Step-by-step explanation:

x+x+x-11 = 3x-11. I'm assuming the answer is an algebraic equation.

The equation that represents the linear function is y =32x

What is a linear equation explain?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

A linear function is represented as

                    y = mx + c

The slope is calculated as

          m = y₂ - y₁/x₂ - x₁

        m = 576 - 64/18 - 2

        m = 512/16

         m = 32

The linear equation is then calculated as

        y = 32( x - 2 ) + 64

         y = 32x - 64 + 64

          y =  32x

Hence, the equation that represents the linear function is y =32x

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The complete question is -

A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night of a movie as a function of the number of hours since the tickets have been on sale. Number of Hours (x) 2 6 18

Number of Tickets Sold (y) 64 192 576

1.Write the equation that gives the number of tickets sold, y, as a linear function of the number of hours, x, since the tickets have been on sale.

Answer:

8

Step-by-step explanation:

8 x 5 = 40

Answer:

3.981071706 × 105

Answer:

3.981071706 x 10^5

Step-by-step explanation:

In standard form, a number is written as a decimal multiplied by a power of 10. To convert 398107.1706 to standard form, we can move the decimal point until we have a number between 1 and 10 and a power of 10 that will make the original number.

398107.1706 = 3.981071706 x 10^5

Step-by-step explanation:

(4-2)*180=360

80+7t+7t+14t=360

28t=280

t=10

Answer:

11 days

Step-by-step explanation:

It will last: 10/1 : 9/10 = 10/1 x 10/9 = 100/9 = 11,111... days

Answer: 11.1 days

Step-by-step explanation:

Everyday, Sandy uses 9/10 of a bag of cups.

Use unitary method.

9/10 bag - 1 day

10 bag - 10/(9/10) = 100/9 ≈ 11.1 days

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