Find the conjugate of -2 + 3i.

So firstly, we need to isolate the x terms onto one side. To do this, subtract 48 on both sides of the equation:

[tex]2x^2-20x=-48[/tex]

Next, divide both sides by 2:

[tex]x^2-10x=-24[/tex]

Next, we are gonna make the left side of the equation a perfect square. To find the constant of this soon-to-be perfect square, divide the x coefficient by 2 and then square the quotient. Add the result onto both sides of the equation:

[tex]-10 \div 2=-5\\(-5)^2=25\\\\x^2-10x+25=1[/tex]

Now, factor the left side:

[tex](x-5)^2=1[/tex]

Next, square root both sides of the equation:

[tex]x-5=\pm 1[/tex]

Next, add 5 to both sides of the equation:

[tex]x=5\pm 1[/tex]

Lastly, solve the left side twice -- once with the plus sign and once with the minus sign.

[tex]x=6,4[/tex]

In short, x = 6 and 4

Answer: x = 4   x = 6

Step-by-step explanation:

2x² - 20x + 48 = 0

2x² - 20 x + _____ = -48 + ______      subtracted 48 from both sides

2(x² - 10x + _____ ) = 2(-24 + _____ )   factored out 2 from both sides

x² - 10x + _____  = -24 + _____          divided both sides by 2

x² - 10x + 25  = -24 +25          added 25 to both sides

       ↓        ↑            ↑

     [tex]\dfrac{-10}{2}=(-5)^2[/tex]     [tex]\bigg(\dfrac{b}{2}\bigg)^2[/tex] makes a perfect square

(x - 5)² = 1             simplified

[tex]\sqrt{(x-5)^2} =\sqrt{1}[/tex]    took square root of both sides

x - 5 = ± 1             simplified

x - 5 = 1       x - 5 = -1     split into two separate equations

   x = 6           x = 4       solved for x

Answer: D.

Step-by-step explanation:

52,165 + 49,872 = 102,037

Answer:

Exactly 12 years it will take for these trees to be the same height

Step-by-step explanation:

Slope intercept form: An equation of line is in the form of [tex]y = mx+b[/tex] where m is the slope or unit rate and b is the y-intercepts.

Let x represents the time in years and y represents the height of the tree.

Use conversion:

1 ft = 12 inches

As per the given statement:

Type A is 8 feet tall and grows at a rate of 3 inches per year.

⇒unit rate per year = 3 inches = [tex]\frac{1}{4}[/tex] ft

Then, we have;

[tex]y =\frac{1}{4}x + 8[/tex]                      ......[1]

Similarly for;

Type B  is 7 feet tall and grows at a rate of 4 inches per year.

⇒unit rate per year = 4 inches = [tex]\frac{1}{3}[/tex] ft

then;

[tex]y =\frac{1}{3}x + 7[/tex]                   .....[2]

To find after how many years it will take for these trees to be the same height.

Since, trees to be the same height;

⇒equate [1] and [2], to solve for x;

[tex]\frac{1}{4}x + 8 = \frac{1}{3}x +7[/tex]

Subtract 7 from both sides we get;

[tex]\frac{1}{4}x + 8-7= \frac{1}{3}x +7-7[/tex]

Simplify:

[tex]\frac{1}{4}x + 1= \frac{1}{3}x[/tex]

Subtract [tex]\frac{1}{4}x[/tex] from both sides we get;

[tex]1= \frac{1}{3}x-\frac{1}{4}x[/tex]

Simplify:

[tex]1 = \frac{x}{12}[/tex]

Multiply both sides by 12 we get;

x = 12

Therefore, exactly it will take for these trees to be the same height is, 12 years

Answer:

$3.6

Step-by-step explanation:

We are told that the pie store is having a 20% off sale on all of its pies. The pie you want regularly costs $18.

To find the amount saved with the discount let us find 20% of 18.

[tex]\text{The amount saved with discount}=\frac{20}{100}\times 18[/tex]

[tex]\text{The amount saved with discount}=0.20\times 18[/tex]

[tex]\text{The amount saved with discount}=3.6[/tex]

Therefore, the amount saved with the discount is $3.6.

Answer:

224 stamps.

Step-by-step explanation:

We have been given that Becki put 14 stamps on each page.

To find the total number of stamps that Becki put in the book we will multiply the number of stamps put on each page by the number of completely filled pages.

[tex]\text{The total number of stamps in the book}=14\times 16[/tex]

[tex]\text{The total number of stamps in the book}=224[/tex]

Therefore, Becki put 224 stamps in the book.

To find out how many stamps Becki added to her collection, we multiply the number of stamps per page, which is 14, by the number of filled pages, which is 16, resulting in a total of 224 stamps.

To determine how many stamps Becki put into her stamp collection book, we need to calculate the total number of stamps populated over the completely filled pages. She placed 14 stamps on each page and filled 16 pages. The total number of stamps is the product of the number of stamps on each page and the number of pages filled.

The formula we will use is:

Total stamps = Number of stamps per page x Number of filled pages

Substituting the given values:

Total stamps = 14 stamps/page x 16 pages = 224 stamps

Therefore, Becki put 224 stamps in her stamp collection book.

let's recall the pythagorean identity that sin²(θ) + cos²(θ) = 1.

[tex]\bf \cfrac{sin(x)}{1-cos(x)}-\cfrac{1-cos(x)}{sin(x)}=2cot(x) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(x)}{1-cos(x)}-\cfrac{1-cos(x)}{sin(x)}\implies \cfrac{[sin(x)]^2-[1-cos(x)]^2}{sin[1-cos(x)]} \\\\\\ \cfrac{[sin^2(x)]-[1^2-2cos(x)+cos^2(x)]}{sin[1-cos(x)]}\implies \cfrac{sin^2(x)-1+2cos(x)-cos^2(x)}{sin[1-cos(x)]} \\\\\\ \cfrac{sin^2(x)-[\underline{sin^2(x)+cos^2(x)}]+2cos(x)-cos^2(x)}{sin[1-cos(x)]} \\\\\\ \cfrac{sin^2(x)-sin^2(x)-cos^2(x)+2cos(x)-cos^2(x)}{sin[1-cos(x)]}[/tex]

[tex]\bf \cfrac{-2cos^2(x)+2cos(x)}{sin[1-cos(x)]}\implies \cfrac{2cos(x)[-cos(x)+1]}{sin[1-cos(x)]}\implies \cfrac{2cos(x)[\underline{1-cos(x)}]}{sin[\underline{1-cos(x)}]} \\\\\\ \cfrac{2cos(x)}{sin(x)}\implies 2\cdot \cfrac{cos(x)}{sin(x)}\implies 2cot(x)[/tex]

Answer:

6x^2 +81x - 17

---------------------

7x-15

Step-by-step explanation:

We cannot solve for x since this is  an expression

((6x+9) (x+12) -sqrt(49+76) ^2

--------------------------------------------

(49+7x) -64

Lets simplify the numerator

((6x+9) (x+12) -sqrt(49+76) ^2

Simplify what is inside the last parentheses

((6x+9) (x+12) -sqrt(125) ^2

Squaring a square root leaves the original number

((6x+9) (x+12) -(125)

FOIL the first two terms

First 6x*x = 6x^2

Outer:  6x*12 = 72x

Inner: 9x

Last : 9*12 = 108

Add them together

6x^2 +72x+9x+108 = 6x^2 +81x+108

Subtract the 125

6x^2 +81x+108-125

6x^2 +81x - 17

Now lets simplify the denominator

(49+7x) -64

49+7x-64

7x-15

6x^2 +81x - 17

---------------------

7x-15

Answer:

351 adults and 275 students

Step-by-step explanation:

We can set-up a system of equations to find the number of adults. We know students and adults attended. We will let s be the number of students and a be the number of adults. Since 626 tickets were purchased, then s+a=626.

We also know that 74 fewer student tickets then adult tickets. So s+76=a, the number of student tickets plus 76 will be the number of adult tickets.

We will solve by substituting one equation into the other. We substitute a=76+s into s+a=626. Simplify and isolate the variable a.

s+a=626

s+76+s=626

2s+76=626

2s+76-76=626-76

2s=550

s=275

This means that 275 students attended and 351 adults attended since 275+351=626.

By setting up a system of equations and solving for the number of adult tickets, we are able to determine that 350 adult tickets were sold for the school play.

To find out how many adult tickets were sold, we can set up an equation to model the situation. Let A be the number of adult tickets and S be the number of student tickets. We are given that a total of 626 tickets were sold, which can be described by the equation A + S = 626. We are also told that there were 74 fewer student tickets sold than adult tickets, described by the equation S = A - 74.

To solve for A, we can substitute (A - 74) for S in the first equation, giving us A + (A - 74) = 626. Simplifying this, we get 2A - 74 = 626. Adding 74 to both sides, we get 2A = 700. Finally, dividing both sides by 2, we find A = 350.

Therefore, 350 adult tickets were sold.

Answer: 1.1 seconds

Step-by-step explanation:

leap = 4t²  ; leap = 4 ft 11 inches, find t

[tex]4\frac{11}{12} = 4t^2[/tex]

[tex]\frac{59}{12} = 4t^2[/tex]

[tex]\frac{59}{48} = t^2[/tex]

[tex]\sqrt{\frac{59}{12}} = \sqrt{t^2}[/tex]

[tex]\sqrt{1.23} = t[/tex]

1.1 = t

Answer:

-9sqrt(5)

Step-by-step explanation:

-2 sqrt20 - sqrt125

Lets simplify the square roots

sqrt(ab) = sqrt(a)sqrt(b)

-2 sqrt(4) sqrt(5) - sqrt(25) sqrt(5)

-2 *2sqrt(5) - 5sqrt(5)

-4sqrt(5) -5sqrt(5)

-9sqrt(5)

Answer:

The answer is C. AAA is not a congruency postulate because the side lengths may be different sizes although the angles are the same.

triangles ABC and DEF are congruent by the Side-Side-Side (SSS) postulate.

In other words, if two triangles have all three corresponding sides equal, then the triangles are congruent.

So the answer to the question is B. Congruent - SSS.

If triangles ABC and DEF are congruent, and if so, to name the postulate that applies.

The triangles are congruent because they have the same side lengths and angles. This can be seen from the following:

AD = BE (given)

∠ADB=∠BED (vertical angles)

AB = EF (given)

∠ABD=∠EBD (corresponding angles when  AD ∥ EF  )

BC = DF  (given)

Therefore, triangles ABC and DEF are congruent by the Side-Side-Side (SSS) postulate

Answer:

1-x represents the percent of the original price being paid.

Step-by-step explanation:

The expression 24(1−x) gives the discounted price of a pair of shorts, where x is the percent of the discount written in decimal form.

For example , 10% is the discount percentage

1 - 10% = 90% will be the percentage of original price to be paid

Here x represents the percent of the discount

so 1-x represents the percent of the original price being paid.

Answer:

percent of original price being paid

Step-by-step explanation:

Given Equations :

✿  5x + 3y = -6 -------------- [1]

✿  3x - 2y = 4 -------------- [2]

Multiplying Equation [1] with 2, We get :

⇒ 10x + 6y = -12 ----------- [3]

Multiplying Equation [2] with 3, We get :

⇒ 9x - 6y = 12 ---------- [4]

Adding Both Equations [3] and [4], We get :

⇒ (10x + 6y) + (9x - 6y) = -12 + 12

⇒ 19x = 0

⇒ x = 0

Substituting x = 0 in Equation [1], We get :

⇒ 5(0) + 3y = -6

⇒ 3y = -6

⇒ y = -2

⇒ (x , y) = (0 , -2)

Option (a) is the Answer

Answer: A (0, -2)

Step-by-step explanation:

5x + 3y = -6   →   2(5x + 3y = -6)   →   10x + 6y = -12

3x  - 2y =  4   →   3(3x  - 2y =  4)   →   9x  - 6y = 12

                                                          19x           =  0

                                                              x          =  0

Now, input "x = 0" into one of the equations and solve for y:

5x + 3y = -6

5(0) + 3y = -6

         3y = -6

           y = -2

Answer:

ds/dt =8  when t =1.5

Step-by-step explanation:

s = t^2 + 5t - 8

We want to find ds/dt

ds/dt = 2t +5

evaluated when t=1.5

ds/dt = 2(1.5) +5

ds/dt = 3+5

ds/dt =8  when t =1.5

Replace t with 1.5 seconds and solve for s:

s = 1.5^2 + 5(1.5) -8

s = 2.25+7.5-8

s= 9.75 -8

s = 1.75

Rate of change is S/t

Rate of change = 1.75 / 1.5

Rate of change of s = 1.17

Identity to verify:

[tex]\dfrac{\cot x}{1+\csc x}=\dfrac{\csc x-1}{\cot x}[/tex]

Recall that

[tex]\cos^2x+\sin^2x=1[/tex]

Divide both sides by [tex]\sin^2x[/tex] and we get

[tex]\cot^2x+1=\csc^2x[/tex]

or

[tex]\cot^2x=\csc^2x-1=(\csc x-1)(\csc x+1)[/tex]

So if we multiply the numerator and denominator of

[tex]\dfrac{\cot x}{1+\csc x}[/tex]

by [tex]\csc x-1[/tex], we get

[tex]\dfrac{\cot x(\csc x-1)}{(1+\csc x)(\csc x-1)}=\dfrac{\cot x(\csc x-1)}{\csc^2x-1}=\dfrac{\cot x(\csc x-1)}{\cot^2x}[/tex]

Then as long as [tex]\cot x\neq0[/tex], we can cancel terms to end up with

[tex]\dfrac{\csc x-1}{\cot x}[/tex]

and establish the identity.

Answer:

5 months

Step-by-step explanation:

The taxpayer can only deduct the first five months of the qualifying child. May is the fifth month. On June 1st, the qualifying child is going to be 14 years old. Therefore he cannot be included in work-related expenses as specified in the Publication 503 - Main Content from the IRS. Please see the Working-Related Expenses, Indent (b) which is as follows:

(b) The parent of your qualifying person if your qualifying person is your child and under age 13.

Answer:

Vertical angle property

Step-by-step explanation:

We are given that e is parallel to f and g is a transversal. Using the alternate interior angles property, ∠4=∠5 which is given.

Since, g is a transversal of the two parallel lines e and f, then ∠1=∠4 and ∠8=∠5 by the vertical opposite angle property.

Hence, ∠1≅∠8 by the transitive angle property.

Answer:

verticle angles theorem

Step-by-step explanation:

hope this helps :)

[tex]\displaystyle\bf\\\text{\bf kinetic energy}=\frac{mv^2}{2}=\frac{54\times3^2}{2}=27\times9=\boxed{\bf243~J} \\\\\text{\bf Correct answer: D.}[/tex]

Answer:

The answer would be be D.243 j

Step-by-step explanation:

You solve the substitution method to solve a system of equality by expressing one variable in terms of the other using one equation, and then plugging this expression in the other(s).

In this case, the first equation gives us a way to express n in terms of m. So, we can replace every occurrence of n in the second equation with the given formula.

The result is

[tex] 14m+2n=-8 \iff 14m+2(-7m-4)=-8 \iff 14m-14m-8=-8 \iff -8=-8 [/tex]

So, the second equation turned to be an equality, i.e. an equation where both sides are the same.

This implies that the system has infinitely many solutions, because every couple [tex] (n,m) [/tex] such that [tex] n=-7m-4 [/tex] is a solution to the system, because it satisfies both equations: the first is trivially satisfied, whereas the second is an identity, and as such is satisfied by any value of the variable.

Answer:

We are given:

[tex]R^{2}=12.7\%[/tex]

The interpretation of [tex]R^{2}[/tex] is the amount of variation in response variable that is explained by the explanatory variable in the model

Therefore, the interpretation of [tex]R^{2}=12.7\%[/tex] is 12.7% of variation in gpa response variable is explained by the jobs explanatory variable in the given linear regression model.

the R-squared statistic of 12.7% suggests that there is a weak linear relationship between the number of hours worked and GPA among the sampled students, and the majority of the variation in GPA is due to factors beyond the number of hours worked.

The R-squared statistic, often denoted as R², measures the goodness of fit of a linear regression model. In this context, where the R-squared statistic is 12.7%, it means that approximately 12.7% of the variability in GPA can be explained by the linear relationship with the number of hours per week students work.

More specifically:

- 12.7% of the variation in GPAs among the students in the sample can be accounted for by the linear regression model with the number of hours worked as the predictor variable.

- The remaining 87.3% of the variability in GPAs is not explained by this model and is attributed to other factors or sources of variation that are not included in the model.

In summary, the R-squared statistic of 12.7% suggests that there is a weak linear relationship between the number of hours worked and GPA among the sampled students, and the majority of the variation in GPA is due to factors beyond the number of hours worked.

Learn more about R-squared statistic here

https://brainly.com/question/11743185

#SPJ3

Answer:

Answer is B) 120

First multiply C by F by multiplying each row in C by each column in F:

12 * -2 + 0*0 + 1.5*2   12*0 + 0*8 + 1.5*1

1*-2 -6*0 +7.2       1*0-6*8 +7*1

to get a matrix of:

-21   1.5

12   -41

Now subtract that matrix from B:

2- -21 = 2+21 = 23

8 - 1.5 = 6.5

0.6 - 12 = -11.4

3 - -41 = 3+41 = 44

So you have:

23   6.5

-11.4   44

Which makes C the correct answer.

Answer:

44

Step-by-step explanation:

diet : regular = 8:4

=> 88:44

The degree of this polynomial is 9

Answer:

Answer in image

Step-by-step explanation:

Answer in image

Answer:

B

Step-by-step explanation:

Because the angles make up the interior parts of the triangle without the extra endings

Answer: The answer would be B

Answer:

an elephant can run 25 miles per hour

Step-by-step explanation:

60 minutes x 60 seconds = 3,600 seconds in an hour

3600 / 36 = 100

100 x .25 = 25 miles an hour

Answer:

A) 0-37000-80049-9

Step-by-step explanation:

For a standard  bar code, it consists of a five digit manufacturer number and a five digit product number.  Check digits are a single digit computed from the other characters in the string of numbers. Check digits are on the far right.

Add the odd number digits: 0+7+0+8+0+9 = 24.

Multiply the result by 3: 24 × 3 = 72.

Add the even number digits: 3+0+0+0+4 =7.

Add the two results together: 72 + 07 = 79.

The last digit is 9

Answer:b

Step-by-step explanation: USA test prep

Answer:a number cube

Step-by-step explanation:

Answer: A number cube is correct to chosen five out of six residents of Mayville have library cards.

Step-by-step explanation:

A number cube is the best to simulate this scenario and predict whether a randomly chosen resident has a library card.

As Coin has only 2 outcomes "Head" and "Tail".

A 5-sector sector spinner has only 5 outcomes we need six outcomes.

A bag of 11 marbles has no differentiated with respect to colors etc.

Hence, A number cube is correct to chosen five out of six residents of Mayville have library cards.