If using the method of completing the square to solve the quadratic equation
x² - 13x +31 = 0, which number would have to be added to "complete the
square"?

Using the system of equations and use the elimination method the two numbers are 82 and 48.

What is the elimination method?

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are equal.

Here, we

let the first number = x

let the second number = y

according to the given conditions:

x + y = 130 ........(1)

x - y = 34 .........(2)

Using the elimination method we add both equations (1) and (2) and we get

2x = 164

x = 164/2 = 82

Now, we substitute the value of x in eq (1) and we get

82 + y = 130

y = 130-82

y = 48

Hence, using the system of equations and use the elimination method the two numbers are 82 and 48.

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24.

[tex](6x+3y)-\frac{z^{2}}{(2x)}[/tex]

[tex](6(3)+3(4))-\frac{(6)^{2}}{(2(3))}[/tex]

a) Solve parenthesis.

[tex](18+12)-\frac{(6)^{2}}{6}\\ \\30-\frac{(6)^{2}}{6}[/tex]

b) Solve the exponent.

[tex]30-\frac{36}{6}[/tex]

c) Divide.

[tex]30-6[/tex]

d) Subtract.

[tex]24.[/tex]

The probability that at least 40 rolls are necessary is 4/15.

What is probability?

Probability shows the likelihood of an event happening.  it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1

Probability P=no. outcomes/total no. of the possible outcomes

From the question;

No of out comes=40

No. of total possible outcome=150

Therefore probability P= 40/150

                                    P=4/15

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They joined together to resist the attempts of Europeans to change them.

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Answer:

The correct equation is t = 12.25h.

It is true, Mai can conclude that the diagonal WY bisects the angles ZWX and ZYX

Since Mai has proven triangles WYZ and WYX to be congruent by the SSS triangle Congruence Theorem, she can conclude that:

Diagonal WY bisects angles ZWX and ZYX because:

all corresponding parts of both triangles are congruent. (Option A).

If two triangles are proven to be congruent to each other, it means that all three pairs of corresponding sides and angles of both triangles are congruent and equal to each other.

Thus, since Mai has proven triangles WYZ and WYX to be congruent by the SSS Triangle Congruence Theorem, therefore, all corresponding parts of both triangles are congruent.

If this is so, then Mai can conclude that angles ZWX and ZYX are bisected by diagonal WY. (Option A is correct).

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Value of BC is 36  in triangle's similarity .

What is  the triangle's similarity?

ΔABC and ΔPQR are similar .

so all sides are equal in ratio .

let BC is x .

 AB/BC = PQ/QR

 18/x = 2/4

    18 * 4 = 2 * x

       x = 18 * 4/2

        x = 18 * 2

         x = 36

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1) The interest if it is compounded using simple interest is $240

2) The interest if it is compounded annually is $249.73

3) The interest if it is compounded semiannually is $252.325

4) The interest if it is compounded quarterly is $253.650

5) The interest if it is compounded monthly is $254.543

6) The interest if it is compounded daily is $254.978

7) The interest if it is compounded hourly is $254.993

8) The interest if it is compounded every minute is $254.993

9) The interest if it is compounded continuously is $254.993

10) The difference in interest between simple interest and interest compounded continuously is $14.993

Compound interest is the addition of interest to the principal sum of a loan or deposit, or interest on interest plus interest.

Given, P=2000

r=4%

r=4/100

r=0.04

t=3 years

1) Simple interest⇒ A=P(1+rt)

=2000(1+3(0.04)

=2000(1+0.12)

=2240

S.I= 2240-2000

S.I=$240

2) Compound interest(yearly)

1st year= 2000(4/100)=80

2nd year=2080(4/100)=83.2

3rd year=(2080+83.2)(4/100)=86.528

P=2163.2+86.528

P=2249.728

C.I=2249.728-2000

C.I=249.728≈$249.73

3) Compounded semiannually

A= P(1+(R/200))²ⁿ

A=2000(1+(4/200))⁶

A=2000(1.12616)

A=2252.325

C.I= 2252.325-2000

C.I=$252.325

4) Compounded quarterly

A=P(1+(R/400))⁴ⁿ

A=2000(1+(4/400))¹²

A=2253.650

C.I=2253.650-2000

C.I=$253.650

5) Compounded monthly

A=P(1+(R/1200))³⁶

A=2000(1+(4/1200))³⁶

A=2254.543

C.I= 2254.543-2000

C.I=$254.543

6) Compounded daily

A=P(1+(R/36500))³⁶⁵ⁿ

A=2000(1+(4/36500))¹⁰⁹⁵

A=2254.978

C.I=2254.978-2000

C.I=$254.978

7) Compounded hourly

A=P(1+(R/876000))²⁶²⁸⁰

A=P(1+(4/876000))²⁶²⁸⁰

A=2254.993

C.I=2254.993-2000

C.I=$254.993

8) Compounded every minute

A=P(1+(R/52560000))¹⁵⁷⁶⁸⁰⁰

A=P(1+(4/52560000))¹⁵⁷⁶⁸⁰⁰

A=2254.993

C.I=2254.993-2000

C.I=$254.993

9) Compounded continuously

A= [tex]Pe^{rt}[/tex]

A=2000([tex]e^{0.04*3}[/tex])

A=2254.993

C.I=2254.993-2000

C.I=$254.993

10) The difference in interest between simple interest and interest compounded continuously is

254.993-$240=$14.993

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The linear function g(z) = 4 · z + 7 is the result of applying the transformation rule g(z) = f(z) - 2 (Translation two units down) on the linear function f(z) = 4 · z + 9 . (Correct choice: C)

In this problem we find a linear function that is modified into another linear function by a transformation rule. We need to find if the function is modified by a horizontal translation, a vertical translation or a combined translation, that is, a combination of horizontal and vertical translations.

Horizontal translation

g(x) = f(x - k), where k > 0 for a translation in + x direction.

Vertical translation

g(x) = f(x) + k, where k > 0 for a translation in + y direction.

After a quick inspection, we notice that linear function f(z) = 4 · z + 9 is transformed into g(z) = 4 · z + 7 by using vertical translation 2 units down.  Then, we find the following transformation formula:

g(z) = f(z) - 2

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The confidence interval that we have for the population mean is given as [869.9 , 890.7]

The confidence interval is the range of values that, if you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time.

We have the following data that we have to solve this problem with

The mean = x¯=880.3 pounds

The standard deviation = 10.4 pounds.

The confidence interval = 68%

To get the confidence interval for the true mean of the population weight we would have

mean ± standard deviation

880.3 ± 10.4

The interval would be written out as

880.3 - 10.4 and 880.3 + 10.4

the confidence interval =

[869.9 , 890.7]

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The student enrollment the previous year is 630 students.

Sine the percentage given is 10% decrease, us implies that the percentage for the previous year will be x

Based on the information given, this will be illustrated as:

x - (20% × x) = 504

x - 0.2x = 504

0.8x = 504.

Divide.

x = 504 / 0.8

x = 630

There were 630 students.

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Answer:

(10, -1)

Step-by-step explanation:

x + 2x = 3x

-y + y = 0

11 + 19 = 30

3x = 30

3/3 x = 30/3

x = 10

10 - y = 11

y = -11 + 10

y = -1

The equations for early pay, deposit plus and daily pay is y = 110, y = 6x + 30 and y = 9x respectively.

An equation is an expression showing the relationship between two or more numbers and variables.

Let y represent the total cost for swimming x numbers of days.

Early Pay: Pay $110.00 before Memorial Day; swim any number of days. Hence:

y = 110

Deposit Plus: $30.00 deposit plus $6.00 per day. Hence:

y = 6x + 30

Daily Pay: $9.00 per day. Hence:

y = 9x

The equation for early pay is y = 110

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Answer:

amount owed = $7434.57

Step-by-step explanation:

To solve this problem, we have to use the following formula:

[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex],

where:

• A = final amount

• P = principal (initial) amount

• r = annual interest rate

• n = amount of times the interest is compounded per time period

• t = number of years the money is kept for

In this case, the principal amount, P = $5000 and the money is owed for two years, so t = 2. The annual interest rate, r = 0.20 (20% = [tex]\frac{20}{100}[/tex] = 0.2). The interest is compounded monthly, which means it is compounded 12 times per year. Therefore, n = 12.

Using the above information and formula, we can calculate the amount owed after 2 years:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

   [tex]= 5000(1 + \frac{0.2}{12})^{12 \times 2}[/tex]

   [tex]=[/tex] $7434.57

Therefore, the amount Edgar owes after 2 years is $7434.57.

Answer:

100π = 314.1592654

Step-by-step explanation:

area of a circle πr²

π×10²

10×10 =100

100×π

The probability that the second ball drawn is yellow is of:

0.2926 = 29.26%.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

In this problem, the possible outcomes to obtain a yellow ball on the second draw are:

Then the probability of an yellow ball on the second draw is given as follows:

p = (3/11) x (3/11) + (8/11) x (3/10) = 0.2926 = 29.26%.

The problem asks for the probability that the second ball drawn is yellow.

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Answer:

Area =  l × w

=  2 × 0.875

=  1 3/4 yd^2 or 1.75 yd^2

hope i helped

Step-by-step explanation:

The result of the expression as given in the task content is; 750/π.

It follows from the task content that the result of the division operation as given in the task content is to be determined.

Given the expression; 1000 ÷ (4/3)π

The expression can therefore be rewritten as follows;

1000 × (3/4) π

Hence, we have;

3000/4π

By further simplifying the expression; we have;

750/π

Hence, the result of the division as given in the task content is; 750/π.

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Answer:

x=19/24

Step-by-step explanation:

3/8=15/5x-2

3/8= 3x -2 |*8

3=24x-16

24x=19

x=19/24

Answer:

$26

Step-by-step explanation:

Answer:

x=−5+ 21 ,−5− 21

Step-by-step explanation:

x= 4−20+4= 214−20−4 =21

​

​

To find the arithmetic mean (average) of a group of numbers add the numbers and divide by the total number of items we added.

(12+16+10+8+14+15)/6

= 75/6

= 12.5 (answer is already rounded to nearest tenth)

Answer:

Scale of the map is 1 cm corresponds to an actual distance of 1.5 km

Step-by-step explanation:

According to the question,

4.2 cm on the map corresponds to an actual distance of 6.3 km.

So,

[tex] \rm 1 \: cm \: will \: correspond \\ \rm to \: a \: distance= \dfrac{6.3}{4.2} \: km \\ \rm = 1.5 \: km[/tex]

Scale of the map is represented by 1 cm corresponds to an actual distance of 1.5 km

The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.

According to the question we are given that 4.2 cm on the map corresponds to an actual distance of 6.3 km.

Similarly on the map, 4.2 cm corresponds to an actual value of 6.2km distance, this means

Thus 6.2km is the same as (6.2×1000)m = 6200m

therefore, the scale of the map is

= 4.2/6200

= 1/1476.2

that is, 1cm : 1476.2 cm

= 1cm: 1.5km

Scale of the map is represented by 1 cm corresponds to an actual distance of 1.5 km

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We get 2 complex answers

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared.

Given that F(x) = 3x2 - 40x + 180

Set F(x) to 0, and you get ax2 + bx + c = 3x2 -40x + 180.

[-b +/- (b2 -4ac)(1/2)] is the quadratic formula. / 2a.

The stuff under the square root / radical (b2 - 4ac) is the KEY to your answer, and it determines whether you have two real, one real, or two imaginary answers. The discriminant is the term (b2 - 4ac).

Obviously, if (b2 - 4ac) > 0, you have two real answers, because the square root of a positive number is also a (positive) real number. And -b multiplied by a real number (and divided by 2a) yields two (real) answers.

If (b2 - 4ac) = 0, you have one correct answer because the square root of 0 is zero. And -b multiplied by a 0 real number (and divided by 2a) yields 1 (real) answer.

(b2 - 4ac) 0 yields two fictitious answers, because the square root of a negative number is a fictitious number. And -b multiplied by an imaginary number (and divided by 2a) yields two (complex) answers.

In this case, (b2 - 4ac) = ((-40)2 - 4(3)(180)) = 1600 - 2160 0 As a result of the discriminant is negative, the quadratic formula yields two complex answers.

Therefore we get two complex answers

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Answer:

[tex]x=\dfrac{20 +2\sqrt{35}\:i}{3}, \quad x=\dfrac{20 -2\sqrt{35}\:i}{3}[/tex]

2 imaginary answers.

Step-by-step explanation:

Given quadratic function:

[tex]f(x) =3x^2 - 40x + 180[/tex]

The zeros of a quadratic function can be found when f(x) = 0:

[tex]\implies 3x^2 - 40x + 180=0[/tex]

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

Therefore:

Substitute the values of a, b and c into the quadratic formula and solve for x:

[tex]\implies x=\dfrac{-(-40) \pm \sqrt{(-40)^2-4(3)(180)}}{2(3)}[/tex]

[tex]\implies x=\dfrac{40 \pm \sqrt{1600-2160}}{6}[/tex]

[tex]\implies x=\dfrac{40 \pm \sqrt{-560}}{6}[/tex]

[tex]\implies x=\dfrac{40 \pm \sqrt{16 \cdot 35 \cdot -1}}{6}[/tex]

[tex]\implies x=\dfrac{40 \pm \sqrt{16}\sqrt{35}\sqrt{-1}}{6}[/tex]

[tex]\implies x=\dfrac{40 \pm 4\sqrt{35}\sqrt{-1}}{6}[/tex]

Apply the imaginary number rule [tex]\sqrt{-1}=i[/tex]:

[tex]\implies x=\dfrac{40 \pm 4\sqrt{35}\:i}{6}[/tex]

[tex]\implies x=\dfrac{20 \pm 2\sqrt{35}\:i}{3}[/tex]

Therefore, the solution is 2 imaginary answers.

Imaginary numbers

Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter [tex]i[/tex].  

An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].

9514 1404 393

Answer:

 2×10¹

Step-by-step explanation:

For division, mantissas divide, and exponents subtract.

Answer:

2*10^1

Step-by-step explanation:

Process

When you divide powers, they can be subtracted -- numerator - denominator in powers

The numbers divide the way you normally would if the question is 6/3 = 2

Numerator power = 3

denominator power = 2

Solution

6*10^3/ 3*10^2 = (6/3) * 10^(3 -2) = 2 * 10^1 = 20

20 = 2 * 10^1

Answer:

↓ ↓ ↓

Step-by-step explanation:

7) Name of plane to piano CIJ:-

8) Name a segment parallel to BC:-

9) Which segment  is not skew to EK:-

______________________

Hope this helps!

Have a great day!

She paid $1.375 per pound of strawberries.

What is the unit rate?

When expressed rate as a fraction, a unit rate has a denominator of 1.

Since 4 pounds cost $5.50, 1 pound of strawberries will cost 5.50/ 4 ≈ $1.375.

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The two possible solutions of the given quadratic equation are -

x =  +√6 +5 and x =  -√6 +5

For the given question;

(x - 5)² - 6 = 0

Bring constant on other side.

(x - 5)² = 6

Taking square root both side.

√ (x - 5)² = √6

(x - 5) = ±√6

Separate the constant and variables.

x =  ±√6 +5

There are two possible solution.

x =  +√6 +5 and x =  -√6 +5

Thus, the two possible solutions of the given quadratic equation are -

x =  +√6 +5 and x =  -√6 +5.

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Using simple mathematical operations, David's overall loss is -5.8.

So, the overall gain/loss of David is:

Now, calculate loss/gain as follows:

Therefore, using simple mathematical operations, David's overall loss is -5.8.

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