Given the equation y ^2 − 4y = 3, what constant must be added to both sides so the left side is the square of a binomial?

Answer:

(6,-4)

Step-by-step explanation:

Reflecting over the x axis means flipping the point or line over it. Therefore the point's y value would the opposite from the beginning.

Answer:

Step-by-step explanation:

For any point reflected over the x-axis, the x-coordinate stays the same and the y-coordinate becomes negative.

6 stays the same

4 becomes -4.

Answer:

0.000432

Step-by-step explanation:

Since we have a negative exponent 4 with a base of 10, we simply just move the decimal place 4 places to the left. When you do so, fill in your remaining zeros and you should get your answer.

Answer:

0.000432

Step-by-step explanation:

4.32ₓ10⁻⁴ =

= 4.32ₓ1/10000

= 4.32/10000

= 0.000432

I think its 57.17 or about 52.2cubic inch

Answer:

The correct option is;

Choosing 4 neighborhoods at random and poll every home in those neighborhoods

Step-by-step explanation:

Given that the survey relate to how much money people are willing to spend on on concert tickets with the goal of being practical and unbiased, we have;

Required sampling = Random Sampling

The preferable type of random sampling is either;

1) Simple random sampling

Sampling a given percentage of the homes in the area randomly

2) Clustered random sampling

Completely polling entire population of randomly selected area

Given the practicability of sampling concert goers, since people may have different interests, a better representative sample will be to perform the clustered random sampling approach by choosing 4 neighborhoods at random and poll every home in those neighborhoods.

D is point lies between A and B.

Triangle △ABC has an altitude CD.
angles A and B are both acute.

Altitude is perpendicular bisector to side of triangle from opposite vertex of triangle.

Since △ABC
A and B are acute angles, and that altitude CD has one vertex at c and other is between A and B i.e. D

Thus, the required point of Altitude CD D lies between A and B.

Learn more about altitude here:
https://brainly.com/question/18530806

#SPJ2

Answer:

Choices are not provided, but you can answer the question as follows: take the coordinates of quadrilateral WXYZ and apply:

W(xW, yW) -> W'(-xW, yW-2)

X(xX, yX) -> X'(-xX, yX-2)

Y(xY, yY) -> Y'(-xY, yY-2)

Z(xZ, yZ) -> Z'(-xZ, yZ-2)

For example, if point W is located at (1, 1), W' would be located at (-1, -1)

Step-by-step explanation:

Reflection over the y-axis transforms point (x, y) into (-x, y)

Translation down 2 units transforms point (x, y) into (x, y-2)

Answer:

The first choice hope this helps :)

Step-by-step explanation:

Answer:

20m-6

Step-by-step explanation:

[tex]6m-2(-7m+3)=\\6m+14m-6=\\20m-6[/tex]

Answer:

20m - 6

Step-by-step explanation:

6m - 2(-7m + 3)

Expand brackets.

6m + 14m - 6

Add like terms.

20m - 6

Answer:

5/2

Step-by-step explanation:

We take the ratio of a side of ABC over the same side on DEF

AB/ DE

35/14

Divide top and bottom by 7

5/2

Answer:

one

Step-by-step explanation:

The maximum number of y intercepts a line can have is one

A line can only cross the y axis one time

A line can only cross the x axis one time

Otherwise it is not linear

Answer:C

Step-by-step explanation: substitute n=3 for all equations and see which equation accurately correlates to the graph for when x=3. When you do this you see that only option C is the correct equation

Answer:

C). [tex]a(n) = 7 + (n - 1) * 12[/tex]

Step-by-step explanation:

Plugin values into the equation.

Answer:

1) Side a = 9.55

2) Angle B = 51.36°

3) Angle C = 72.67°

Step-by-step explanation:

We would be solving the above questions using Law of Cosines

1) To find Side a using Law of cosines

a² = b² + c² - 2bc × Cos A

a = √(b² + c² - 2bc × Cos A)

a = unknown

b = 9

c = 11

Angle A = 56°

a = √(9² + 11² - 2 × 9 × 11 × Cos 56°

a = 9.55405

Approximately a = 9.55

2) To find Angle B

We would use the Law of Cosines as well

b² = a² + c² - 2ac × Cos B

Cos B = a² + c² - b²/2ac

B = arc cos ( a² + c² - b²/2ac)

a = 9.55

c = 11

b = 9

B = arc cos (9.55² + 11² - 9²/2 × 9.55× 11)

B = 51.36°

3) To find Angle C

We would use the Law of Cosines as well

c² = a² + b² - 2ac × Cos C

Cos C = a² + b² - c²/2ab

C= arc cos ( a² + b² - c²/2ab)

a = 9.55

b = 9

c = 11

C = arc cos (9.55² + 9² - 11²/2 × 9.55× 9)

C= 72.67°

Answer:

(x + 2) / x(x - 4).

Step-by-step explanation:

x^2-4x-12/x^3-10x^2+24x

= (x + 2)(x - 6) / x(x^2 - 10x + 24)

=  (x + 2)(x - 6) / x(x - 4)(x - 6)          x -6 is common to top and bottom so:

= (x + 2) / x(x - 4).

Answer:

x+2/x(x+4) or x+2/x^2-4x

Step-by-step explanation:

from the numerator x^2-4x-12, factorise the numerator

x^2-4x-12

multiplying x^2 and -12=-12x^2

step2:

find two numbers that when multiplied you get -12x^2 and when added you get -12x^2.

This numbers are -6x and 2x.

Therefore,(x^2+2x)-(6x-12)

x(x+2)-6(x+2)

(x-6)(x+2)

Step3

from the denominator x^3-x^2+24x, factorise the denominator

x^3-x^2+24x

What is common to all the numbers, the number that is common is x

Therefore,x(x^2-x^2+24x).

multiplying x^2+24x=24x^2

step2:

find two numbers that when multiplied you get 24x^2 and when added you get 24x^2.

This two numbers are -6x and -4x.

Therefore,x{(x^2-4x)-(6x+24)}

x{x(x-4)-6(x-4)}

x{(x-4)(x-6)

Step4

Bringing the nunerator and denominator together.

(x-6)(x+2)/x{(x-4)(x-6)}

(x-6) divides each other

Therefore,x+2/x(x-4) or (x+2)/x^2-4x

Answer:

2.92%

3.85%

Step-by-step explanation:

The population in 2000 is 282,194,308.  The population in 2003 is 290,447,644.  This is an increase of 8,253,336.

290,447,644 - 282,194,308 = 8,253,336

To find the percentage in increase, divide the difference by the original number and multiply by 100%.  The population increased by 2.92%.

8,253,336/282,194,308 = 0.0292 × 100% = 2.92%

The population in 2003 is 290,447,644.  The population in 2007 is 301,621,157.  This is an increase of 11,173,513.

301,621,157 - 290,447,644 = 11,173,513

Divide the difference by the original number and multiply by 100%.  The population increased by 3.85%.

11,173,513/290,447,644 = 0.0385 × 100% = 3.85%

Answer:8

Might I be right

Step-by-step explanation:

Answer: $641.51

Step-by-step explanation:

A = p (1+ r/n)^nt

A = 500 (1 + 0.025/4)^4*10

A = 641.51

The amount in an account where $500 in invested at 2.5% is $641.51.

Using this formula

A = p (1+ r/n)^nt

Where:

A=Amount

P= Principal=$500

R=Rate=2.5% or 0.025

n=4 (Quarterly)

T=Time=10 years

Let pug in the formula

A = $500(1 + 0.025/4)^4×10

A=$500(1.28302)

A =$641.51

Inconclusion the amount in an account where $500 in invested at 2.5% is $641.51.

Learn more here:

https://brainly.com/question/15380529

Answer: $660

Step-by-step explanation:

If he saves $ 55 every month, he will have

55 x 12 = 660

Answer:

Water a tank can hold = 14 1/2 = 29/2

Volume of bucket 1 1/4 = 5/4

The expresson can be

29/2 / 5/4

No. of buckets used = 29/2 x 4/5

Answer:

b and e

Step-by-step explanation:

Answer:

110

Step-by-step explanation:

No of robberies = 125

Percentage = 100%

No of robberies = 'd'

Percentage = 12% lower than 2013 = 100% - 12%

= 88%

No of robberies in 2014 = 88% of the number of robberies in 2013

'd' = 88/100 × 125

'd' = 0.88 × 125

'd' = 110

2014 robberies = 110 in number

Answer:

Kobe raised x + 24.55

Amari raised x

DJ raised 2x – 15.60

Answer: there a 3 feet to a yard a 36 inches to a yard( 12 inches to a foot) 1/3 of a yard is a foot hope this helps

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

p(2) - q(2)

3 - (-2)

3 + 2

= 5

Answer:

B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

3n - 5p + 2n = 10p

Add like terms.

5n - 5p = 10p

Add 5p to both sides.

5n = 10p + 5p

5n = 15p

Divide both sides by 5.

n = 15/5p

n = 3p

The solution of expression for n is,

⇒ n = 3p

We have to given that,

An expression to solve,

⇒ 3n - 5p + 2n = 10p

Now, We can solve the expression for n as,

⇒ 3n - 5p + 2n = 10p

Combine like terms,

⇒ 3n + 2n = 10p + 5p

⇒ 5n = 15p

Divide by 5 both side,

⇒ n = 15p/5

⇒ n = 3p

Therefore, The correct option is,

D. n = 3p

Learn more about the equation visit:

brainly.com/question/28871326

#SPJ2

Answer:

The correct option is:

cosθ = -3/5

Step-by-step explanation:

We have been given that:

cotθ = 3/4

such that the terminal side of θ lies in III quadrant.

Consider it a right angled triangle.

We know that:

cotθ = Base / Perpendicular

Which means Base has a magnitude of 3 and Perpendicular has the magnitude of 4.

As It lies in III quadrant, both x and y are negative.

So

Base = -3

Perpendicular = -4

Find the hypotenuse by using Pythagoras Theorem

H² = (-3)² + (-4)²

H = 5

We know that:

cosθ = Base / Hypotenuse

cosθ = -3/5

Answer:

cos=-3/5 and tan=4/3

Step-by-step explanation:

Answer:

[tex]a_{n} = -83/40[/tex]

Step-by-step explanation:

Given

[tex]a_{n} = -2 + 3/2 (n-1)[/tex]

In this problem to find 21st term we put 21 in place of n in the equation

[tex]a_{n} = -2 + 3/2 (21-1) = \\a_{n} = -2 + 3/2 (20)\\a_{n} = -2 + 3/40 = (-2*40 +3)/40 \\a_{n} = -83/40\\[/tex]

Thus, 21st term is -83/40.

Answer:

n = -15

Step-by-step explanation:

Given

Sum of Integers from 15 to 50 (inclusive) = Sum of integers from n to 50 (inclusive)

n < 15

Required

Find n

We can split the given parameters to 2

i. Sum of Integers from 15 to 50 (inclusive)

ii. Sum of integers from n to 50 (inclusive)

Solving for (i): Sum of Integers from 15 to 50 (inclusive)

We'll make use of sum of n terms of an arithmetic;

This is given as follows

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

Where n is the number of terms from 15 to 50

T1 is the first term; T1 = 15

Tn is the last term; Tn = 50

n is calculated using

[tex]n = T_n - T_1 + 1[/tex]

[tex]n = 50 - 15 + 1[/tex]

[tex]n = 36[/tex]

The formula becomes

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

[tex]S_n = \frac{36}{2}(15 + 50)[/tex]

[tex]S_n = \frac{36}{2}(65)[/tex]

[tex]S_n = 18(65)[/tex]

[tex]S_n = 1170[/tex]

Solving for (ii): Sum of integers from n to 50 (inclusive)

We'll also make use of the same formula used above

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

Where n is the number of terms from n to 50

T1 is the first term; T1 = n

Tn is the last term; Tn = 50

n is calculated using

[tex]n = T_n - T_1 + 1[/tex]

[tex]n = 50 - n + 1[/tex]

[tex]n = 50 + 1 - n[/tex]

[tex]n = 51 - n[/tex]

The formula becomes

[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]

[tex]S_n = \frac{51 - n}{2}(n + 50)[/tex]

Recall that the Sum of Integers from 15 to 50 (inclusive) = Sum of integers from n to 50 (inclusive);

This implies that

Sn (i) = Sn (ii)

As such; we have

[tex]S_n = \frac{51 - n}{2}(n + 50) = 1170[/tex]

[tex]\frac{51 - n}{2}(n + 50) = 1170[/tex]

Multiply both sides by 2

[tex]2 * \frac{51 - n}{2}(n + 50) = 1170 * 2[/tex]

[tex](51 - n)(n + 50) = 1170 * 2[/tex]

[tex](51 - n)(n + 50) = 2340[/tex]

Open Brackets

[tex]51(n + 50) - n(n + 50) = 2340[/tex]

[tex]51*n + 51 * 50 - n * n - n * 50 = 2340[/tex]

[tex]51n + 2550 - n^2 - 50n = 2340[/tex]

Reorder

[tex]-n^2 + 51n - 50n + 2550 = 2340[/tex]

[tex]-n^2 + n + 2550 = 2340[/tex]

Subtract 2340 from both sides

[tex]-n^2 + n + 2550 -2340 = 2340 -2340[/tex]

[tex]-n^2 + n + 210 = 0[/tex]

Multiply both sides by -1

[tex]-1(-n^2 + n + 210) = -1 * 0[/tex]

[tex]n^2 - n - 210 = 0[/tex]

At this point, we have a quadratic equation; as such, it'd be solved as follows:

[tex]n^2 - n - 210 = 0[/tex]

Expand

[tex]n^2 + 15n - 14n - 210 = 0[/tex]

Factorize

[tex]n(n + 15) - 14(n + 15) = 0[/tex]

[tex](n - 14)(n + 15) = 0[/tex]

Split the above expression

[tex](n - 14) = 0 \ or\ (n + 15) = 0[/tex]

[tex]n - 14 = 0 \ or\ n + 15 = 0[/tex]

[tex]n = 14\ or\ n = -15[/tex]

The question states that n < 15;

This means that we'll discard the value of n = 14

Hence, n = -15

Answer:

1a) 15, 7, x+5

1b) 7

2a) 18, 3r

Step-by-step explanation:

1a) Since Claire is 5 years older, she will always be her cousin's age plus 5

1b) Claire is 5 years older, so Claire's cousin is 5 years younger. So, Claire's cousin is Claire's age minus 5

2a) Diego will have the amount of Han's books times 3

Answer:

Clare Questions:

Cousin: 10, Clare: 15

Cousin: 2, Clare: 7

Cousin: x, Clare: x + 5

Cousin: 7, Clare: 12

Diego Questions:

Han: 6, Diego: 18

Han: can't tell if it is a 0 or n, Diego: 0 or 3n, respectively

Step-by-step explanation:

Since Clare is older than her cousin by 5, they will both age at the same rate, thus she will always be 5 years older.

example: if her cousin is 10, Clare will be 10 + 5 years older, therefore being 15.

Since DIego has 3 times as many books than Hans, it multiplies by 3.

example: if Han has 6 books, multiply 6 by 3 and you get Diegos amount, 18.

Answer:

1 - a/variable

2 - d/statistic

3 - b/population

4 - c/data

5 - e/parameter

6 - f/sample

I did comment asking if the two you'd already selected were definitely correct, but no answer was given, so I apologise if this is wrong. This is what I would put.

Hey there! :)

Answer:

Option C.

Step-by-step explanation:

A perpendicular line to 2/3 will be the reciprocal and negative of this fraction. Therefore:

Slope of perpendicular line = -3/2.

Remember, the equation for solving for the slope is:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

We must find points that when plugged into this equation, equal to -3/2.

Plugging in the points in option A:

[tex]\frac{2}{3} \neq \frac{-3}{2}[/tex]

Option B:

[tex]\frac{3}{4} \neq \frac{-3}{2}[/tex]

Option C: This is the correct answer.

[tex]\frac{-3}{2} = \frac{-3}{2}[/tex]

Option D:

[tex]\frac{2}{10}\neq \frac{-3}{2}[/tex]