Complete the square for the expression x² + 8x.
That is, find real numbers A and B such that x² + 8x + A = (x + B)².
Answer exactly. A = B=

4f - 6v is equal to the vector <36, -16>.

To find 4f - 6v, we need to perform scalar multiplication on both vectors and then subtract the result.

Scalar multiplication of a vector by a scalar k is simply multiplying each component of the vector by k. For example, if we have the vector <a, b>, then k times that vector would be <ka, kb>.

Using this definition, we can find:

4f = 4<12, 2> = <48, 8>

6v = 6<2, 4> = <12, 24>

So, 4f - 6v = <48, 8> - <12, 24> = <36, -16>

Therefore, 4f - 6v is equal to the vector <36, -16>.

Learn more about Vector here

https://brainly.com/question/29740341

#SPJ1

1  35.56

2  914.6

3 76595.6

Value of x is 2 in the circle .

What in Geometry Is the Definition of a Circle?

A circle is a curved, two-dimensional form that may be created by connecting points in a plane that are spaced the same fixed distance apart from a fixed point in the same plane. The circle's centre is that specific fixed location.

                              The diameter and radius of a circle are measured from the centre to its circumference and from one point on the circumference to another point that passes through the centre, respectively. In the actual world, a pizza foundation is among the most prevalent instances of a circular.

In circle,

          3 * (x + 2) = x * 6

           3x + 6 = 6x

             6 = 3x

            x = 2

Learn more about circle

brainly.com/question/29142813

#SPJ1

The rectangular prism with length of the base is 4 units, the width of the base is 3 units, and the height is 5 units is shown below.

Since the volume of the rectangular prism is 60 cubic units and the height is 5 units, we can find the length and width of the base by dividing the volume by the product of the height and base. That is,

Volume = Length * Width * Height

60 = Length * Width * 5

Length * Width = 12

We can choose any two numbers whose product is 12 as the length and width of the base. Let's choose 3 and 4 for simplicity. Then, the rectangular prism would look like as shown in picture where the length of the base is 4 units, the width of the base is 3 units, and the height is 5 units.

To learn more about rectangular prism here:

https://brainly.com/question/21308574

#SPJ1

Answer:

In this situation, [tex]t[/tex] (time) is the independent variable, and [tex]p[/tex] is the dependent variable, since calculating it relies on [tex]t[/tex]. In a real-world context, [tex]p[/tex] represents the number of hard drives sold in [tex]t[/tex] number of years.

Answer: 2

Step-by-step explanation:

Rewriting the equation for x gives[tex]x = \sqrt[4]{13}[/tex]

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

x = 13^1/4

To rewrte the equation for x, we introduce radicals

By pronounciation, x = 13^1/4 means that the value of x is 13 raised to the power of 1/4 i.e. the fourth root of 13

When rewritten, we have

[tex]x = \sqrt[4]{13}[/tex]

Hence, the solution is [tex]x = \sqrt[4]{13}[/tex]

Read more about equation at

https://brainly.com/question/18831322

#SPJ1

In order for the expected value of a mega ball ticket to be zero, the grand prize needs to be at least $4,105,724.49.

The term "value" can have different meanings depending on the context in which it is used. Generally, value refers to the worth or usefulness of something, often measured in terms of money, time, or other resources.

To calculate the expected value of a mega ball ticket, we need to multiply the probability of winning each prize by the value of that prize, and then sum up the products:

Expected value = (1/302575350) x $40,000,000 + (24/302575350) x $1,000,000 + (325/302575350) x $10,000 + (7800/302575350) x $500 + (20800/302575350) x $200 + (499300/302575350) x $10 + (436617/302575350) x $10 + (3399723/302575350) x $4 + (817712/302575350) x $2 + (297842418/302575350) x $0

Expected value = $0.65444

This means that if you were to buy every possible combination of numbers (all 302,575,350 of them), the expected value of a ticket would be $0.65444.

To calculate the amount the grand prize needs to be in order to break even, we need to set the expected value equal to zero and solve for the prize:

0 = (1/302575350) x (Prize - $2.00) + (24/302575350) x ($1,000,000 - $2.00) + (325/302575350) x ($10 - $2.00) + (7800/302575350) x ($500 - $2.00) + (20800/302575350) x ($200 - $2.00) + (499300/302575350) x ($10 - $2.00) + (436617/302575350) x ($10 - $2.00) + (3399723/302575350) x ($4 - $2.00) + (817712/302575350) x ($2 - $2.00) + (297842418/302575350) x ($0 - $2.00)

Simplifying this equation, we get:

0 = (1/302575350) x Prize - $0.01359

Solving for the prize, we get:

Prize = $0.01359 x 302575350

Prize = $4,105,724.49

Therefore, in order for the expected value of a mega ball ticket to be zero, the grand prize needs to be at least $4,105,724.49.

To know more about value visit:

https://brainly.com/question/24078844

#SPJ1

Answer:

Step-by-step explanation:  70.7

Given:

r=46

angle from arc =88

Formula and Explanation of formula:

You want to find the proportion/precent of the circle you want to find and multiply it by the full length of the circle, which is the circumference.  

[tex]L=\frac{Part of circle}{full circle} Circumference\\\\\\L=\frac{Part of circle}{full circle} 2\pi r[/tex]

Plug Given into Formula:

[tex]L=(\frac{88}{360})(2)\pi (46)[/tex]     Plug into calculator

L =  70.7

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=46\\ \theta =88 \end{cases}\implies s=\cfrac{(88)\pi (46)}{180}\implies s=\cfrac{1012\pi }{45}\implies s\approx 70.65[/tex]

When the number of classes is 1, football is less expensive.

When the number of classes is 2, 3, or 4, basketball is less expensive.

In order to determine the sport which is less expensive, we would have to calculate the total cost for a basketball program by substituting the number of classes (x) into the function which models it as follows;

y = 9x + 10

When the number of classes x = 1, the total cost is given by;

y = 9(1) + 10

y = $19.

Therefore, a total cost of $19 is greater than $15 for a football program.

When the number of classes x = 2, the total cost is given by;

y = 9(2) + 10

y = $28.

When the number of classes x = 3, the total cost is given by;

y = 9(3) + 10

y = $37.

When the number of classes x = 4, the total cost is given by;

y = 9(4) + 10

y = $46.

Therefore, a total cost of $46 is less than $60 for a football program.

Read more on classes and cost here: https://brainly.com/question/29720383

#SPJ1

Answer: To calculate the monthly payment, we need to use the formula for the equal monthly installment for a loan with constant payments and interest:

P = (r * PV) / (1 - (1 + r)^-n)

where:

P = monthly payment

r = monthly interest rate

PV = present value (the initial loan amount)

n = total number of payments

In this case, PV = $3500, n = 60, and r = 1.75% per month.

First, we can calculate the monthly interest rate by dividing the annual rate by 12:

r = 1.75% / 100% / 12 = 0.0175/12

Plugging in the values, we get:

P = (0.0175/12 * $3500) / (1 - (1 + 0.0175/12)^-60)

P = $69.92 (rounded to two decimal places)

So the monthly payment is $69.92.

To calculate the total interest paid, we can subtract the initial loan amount from the total of all payments:

Total interest = (P * n) - PV

Total interest = ($69.92 * 60) - $3500

Total interest = $195.20

So the total interest paid is $195.20.

Step-by-step explanation:

Answer: The total interest paid is $1186.

Step-by-step explanation: The first step is to calculate the monthly interest rate:

1.75% per month can be written as 0.0175 in decimal form.

Next, we can use the formula for the monthly payment of a loan:

P = r(PV) / [1 - (1+r)^(-n)]

Where:

P = monthly payment

r = monthly interest rate

PV = present value of the loan

n = total number of payments

Plugging in the given values, we get:

P = 0.0175(3500) / [1 - (1+0.0175)^(-60)]

= 78.10

Therefore, your monthly payments are $78.10.

To calculate the total interest paid, we can multiply the monthly payment by the number of payments and subtract the original loan amount:

Total interest = (60 x 78.10) - 3500

= 4686 - 3500

= $1186

Therefore, the total interest paid is $1186.

The shorter sides of Monica's wrapping paper measure 8 inches. Therefore, the correct option is A. 26 2/3 inches.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

We can set up a proportion to solve for the shorter sides of Monica's wrapping paper. Let x be the length of the shorter sides of Monica's paper. Then we have:

x/34 = 2/17

To solve for x, we can cross-multiply:

x = 34 * (2/17) = 4 * 2 = 8

Therefore, the shorter sides of Monica's wrapping paper measure 8 inches.

Alternatively, we can simplify the proportion first by dividing both sides by 2:

x/17 = 1/2

Then, we can solve for x by cross-multiplying:

x = 17 * (1/2) = 8

Either way, the answer is the same. Therefore, the correct option is A. 26 2/3 inches.

Learn more about rectangle on:

https://brainly.com/question/17065463

#SPJ1

The theoretical probability of a fair coin landing on heads is 0.5. After flipping a coin 14 times, the experimental probability of landing on heads is 0.5 (7/14). The experimental probability matches the theoretical probability, indicating a fair coin.

The theoretical probability of a fair coin landing on heads is 0.5, since there are two equally likely outcomes (heads or tails) and only one of them is heads.

When flipping a coin 14 times, the possible outcomes are heads or tails, and each flip is independent of the others. The frequency of each outcome can be recorded as follows

Heads: 7

Tails: 7

The experimental probability of landing on heads is the number of times that heads occurred divided by the total number of flips

Experimental probability of landing on heads = 7/14 = 0.5

The experimental probability of landing on heads (0.5) is equal to the theoretical probability of landing on heads (0.5), which suggests that the coin used in the experiment is fair.

To know more about Probability:

https://brainly.com/question/11234923

#SPJ1

From the ANOVA table, we can see that the F-statistic is 114.89 and the p-value is less than 0.001.

To conduct the F-test, we first need to calculate the sum of squares for regression, error, and total, as well as their respective degrees of freedom. We can then use these values to complete an ANOVA table, which summarizes the results of the F-test.

The ANOVA table for this problem would look like this:

Source of Variation Degrees of Freedom Sum of Squares Mean Square F p-value

Regression 1 3,703,333 3,703,333 114.89 <0.001

Error 4 696,667 174,167  

Total 5 4,400,000  

In this ANOVA table, the regression and error degrees of freedom are 1 and 4, respectively, since there is one independent variable and six data points.

To know more about ANOVA table here

https://brainly.com/question/29744778

#SPJ1

Answer:

25480

Step-by-step explanation:

Hopefully it's right.

The value matched to the correct expression is

1 + 5 = 6

2 + (1 + 3)² = 18

4 + 8(2) = 20

4³ = 64

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

1 + 5

2 + (1 + 3)²

4 + 8(2)

4³

Evaluating the expressions, we have

1 + 5 = 6

2 + (1 + 3)² = 18

4 + 8(2) = 20

4³ = 64

Read more about expressions at

https://brainly.com/question/15775046

#SPJ1

You would pay Ghana cedi 270.00 for the phone during the sale.

To calculate this:

40% of Ghana cedi 450.00 is 0.40 x 450 = Ghana cedi 180.00

Subtracting this discount from the original price gives:

Ghana cedi 450.00 - Ghana cedi 180.00 = Ghana cedi 270.00

The smallest number of green apples that makes the probability of finding at least one green apple among the four at least 99.9 percent is 4000.

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 meaning that the event is impossible and 1 meaning that the event is certain. Probability theory is widely used in the analysis of statistical data, such as in the study of the behavior of populations or financial markets.

To calculate the smallest number of green apples that makes the probability of finding at least one green apple among the four at least 99.9 percent, we must first calculate the probability of not finding any green apples. This can be done by finding the probability of selecting four red apples from the basket. With four red apples and an unspecified number of green apples, the probability of selecting four red apples is 4/N, where N is the total number of apples in the basket.

To find the smallest number of green apples, we must set the probability of selecting four red apples equal to 0.001 and solve for N. This gives us:

N = 4/0.001

Therefore, the smallest number of green apples that makes the probability of finding at least one green apple among the four at least 99.9 percent is 4000.

To know more about probability click-
http://brainly.com/question/24756209
#SPJ1

The equation is solved and the distribution property is given by

a) A = 5x + 15

b) B = x² - 3x

c) C = x² + 6x + 8

d) D = x² - 10x + 25

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

A = 5 ( x + 3 )

On simplifying the equation , we get

A = 5 ( x ) + 5 ( 3 )

A = 5x + 15

b)

B = x ( x - 3 )

On simplifying the equation , we get

B = x ( x ) - x ( 3 )

B = x² - 3x

c)

C = ( x + 4 ) ( x + 2 )

On simplifying the equation , we get

C = ( x + 4 ) ( x ) + ( x + 4 ) ( 2 )

C = x² + 4x + 2x + 8

C = x² + 6x + 8

d)

D = ( x - 5 ) ( x - 5 )

On simplifying the equation , we get

D = ( x - 5 ) ( x ) + ( x - 5 ) ( -5 )

D = x² - 5x - 5x + 25

D = x² - 10x + 25

Hence , the equations are solved

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Answer: 8 (5+x)

Step-by-step explanation:

A and B are mutually exclusive events, so PA) is 11/20.

Given that, P(B)=1/5 and P(A or B)=3/4.

For mutually exclusive events A and B

That is, P(A or B) = P(A) + P(B)

Here, 3/4 = P(A)+1/5

P(A)=3/4 - 1/5

P(A)=(15-4)/20

= 11/20

Therefore, P(A)=11/20

Learn more about the mutually exclusive events here:

brainly.com/question/28565577.

#SPJ1

The largest number is 145, the middle number is 95 and the smallest number is 60.

Given that, the sum of three miners is 300, the largest exceeds the middle one by 50 and the smallest by 85.

Let the three numbers be x, y and z.

Here, the largest number is x, middle number is y and smallest number be z.

y=x-50, z=x-85

Here, x+y+z=300

x+x-50+x-85=300

3x-135=300

3x=435

x=145

y=95 and z=60

Therefore, the three number are 145, 95 and 60.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ1

For 15 feet below the sea level, the value of temperature reads is,

⇒  10.8 degree cooler

Given that;'

Rob finds that every 2.5 feet below sea level, the value of temperature reads 1.8 degree cooler.

Hence, For 15 feet below the sea level, the value of temperature reads is, x

Thus, We can formulate;

⇒ 2.5 / 1.8 = 15 / x

⇒ 25/18 = 15/x

⇒ x = 15 × 18 / 25

⇒ x = 10.8 degree cooler

Thus, For 15 feet below the sea level, the value of temperature reads is,

⇒  10.8 degree cooler

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer:

Step-by-step explanation:

You want the solution to the system of equation using the addition method:

We can multiply the first equation by 0.02 and add it to the second:

  0.02(x) +(0.08x +0.02y) = 0.02(y +600) +(470)

  0.10x +0.02y = 0.02y +482 . . . . . . . . . simplify

  0.10x = 482 . . . . . . . . . . . . . . . . . . . . subtract 0.02y

  x = 4820 . . . . . . . . . . . . . . . . . . . . multiply by 10

  y = x -600 = 4820 -600 = 4220

The amount invested at 8% is $4820; the amount invested at 2% is $4220.

__

Additional comment

You will notice that we solved the equations using "addition" by adjusting coefficients so one variable (y) had the same coefficient on each side of the equal sign. That term was then subtracted from both sides, eliminating the variable. The point of the "method of addition" is to eliminate one variable, which is what we did.

More conventionally, we might rearrange the first equation to x - y = 600 before multiplying by 0.02 and doing the addition. That also eliminates the y-variable.

The calculator result shown in the attachment is also a form of elimination by the addition method.

the equation of the line that passes through the point (2,1/4) is: y = (1/8)x

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

To find the equation of the line that passes through (2,1/4), we need to find the values of m and b.

We are not given the slope, so we will need to use another point to find it. Let's choose the point (0,0) as another point on the line. Then, we can find the slope as:

m = (1/4 - 0) / (2 - 0) = 1/8

Now, we can use the slope and the point (2,1/4) to find the y-intercept:

1/4 = (1/8)(2) + b

b = 0

Therefore, the equation of the line that passes through the point (2,1/4) is: y = (1/8)x.

Learn more about straight line, by the following link

https://brainly.com/question/16949303

#SPJ1

The equation of the line is determined as; y = (2/3)x + 22/3.

The general equation of line is written as;

y = mx + b

Where;

The slope is calculated as;

m = (y₂ - y₁) / (x₂ - x₁)

m = (14 - 4 ) / (10 + 5)

m = 10/15

m = 2/3

The y intercept is calculated as;

y = mx + b

4 = 2/3(-5) + b

4 = -10/3 + b

b = 4 + 10/3

b = 22/3

The equation of the line is determined as;

y = (2/3)x + 22/3

Learn  more about equation of line here: https://brainly.com/question/18831322

#SPJ1

The solution of the sine function sin(5π/12) is (√6 + √2)/4.

As per the sum and difference identity for sine, which states:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

To find sin(5π/12), we can express it as the sum or difference of two angles whose sine values we know.

One possible way is to use the fact that:

5π/12 = π/4 + π/6

So we have:

sin(5π/12) = sin(π/4 + π/6)

Using the sum identity, we get:

sin(π/4 + π/6) = sin(π/4)cos(π/6) + cos(π/4)sin(π/6)

We know that sin(π/4) = cos(π/4) = √2/2 and sin(π/6) = 1/2, so we can substitute:

sin(π/4 + π/6) = (√2/2)(√3/2) + (√2/2)(1/2)

simplify the expression:

sin(π/4 + π/6) = (√6 + √2)/4.

Therefore, sin(5π/12) = sin(π/4 + π/6) = (√6 + √2)/4.

To learn more about the sine function;

https://brainly.com/question/12015707

#SPJ1

It takes 16 minutes until there are 2 grams of the element remaining.

Given that, an element with a mass of 600 grams decays by 29.5% per minute.

Remaining element is 2 grams.

According to the question,

600(1-29.5%)ˣ=2

600×0.705ˣ=2

0.705ˣ=2/600

0.705ˣ=0.00333

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Exact Form:

x=log(0.00333)/log(0.705)

x=16.35

x≈16

Therefore, it takes 16 minutes until there are 2 grams of the element remaining.

#SPJ1