Use the Quadratic Formula to solve the equation x² - 6x = -14.
1. X=3+23 or X = 3-V23
2. X=-3+V23 orX=-3-V23
3. X=-3+iv5 or X=-3-i15
4. X=3+iv5 orx = 3-iv5

Answer:

x = ± 6

Step-by-step explanation:

x^2 = 36

Take the square root of each side

sqrt(x^2) = sqrt(36)

x = ± 6

Answer:

[tex]\large \boxed{\boxed{x=\pm 6}}[/tex]

Step-by-step explanation:

[tex]x^2 =36[/tex]

Take the square root on both sides.

[tex]\sqrt{x^2} =\pm \sqrt{36}[/tex]

Simplify.

[tex]x=\pm 6[/tex]

Answer:

7

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

JH = 47 (70 - 23)

HM = 23

MK = 19 (42 - 23)

KU = 34 (81 - 47)

UC = 7 (47 - 40)

CN = 40

Answer:

19

Step-by-step explanation:

HM + MK = HK

23 + MK = 42

Subtract 23

MK = 42-23

MK =19

Hi I'mjust tryna get points for my sister this is actually the first time i use this app but yea, sorry if you got disappointed.

Answer:

a) x greater than or equal to 10

b) x = 9

Step-by-step explanation:

a)

[tex]x + 5 \geqslant 15 \\ x \geqslant 15 - 5 \\ x \geqslant 10[/tex]

b)

[tex]2x < 18 \\ x = \frac{18}{2} \\ x = 9[/tex]

Answer:

they are both the same thing the first one with kara is in numbers and with raul it is in words

Step-by-step explanation:

hope i helped and have a great day :)

Answer:

(-37, 3)

Step-by-step explanation:

Answer:

[tex]Angle = 96[/tex]

Step-by-step explanation:

Given

The frequency table

Required:

Determine the sectorial angle of "3"

First we need to determine the total frequency;

[tex]Total = 3 + 4 + 6 +8 + 5 + 4[/tex]

[tex]Total = 30[/tex]

The sectorial angle is calculated as thus;

[tex]Angle = \frac{Frequency}{Total\ Frequency} * 360[/tex]

Where Frequency of "3" = 8

So;

[tex]Angle = \frac{8}{30} * 360[/tex]

[tex]Angle = \frac{8* 360}{30}[/tex]

[tex]Angle = \frac{2880}{30}[/tex]

[tex]Angle = 96[/tex]

Hence; the sectorial angle of "3" is 96

Answer:

A

Step-by-step explanation:

The first option is correct.

The 8 count pack of AA batteries has a lower unit price of $0.79 per battery.

The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.

According to the given question.

Cost of a package with 8 AA batteries = $6.32

⇒ Cost of 1 AA battery of this package = [tex]\frac{6.32}{8}[/tex] = $0.79

And, cost of another package with 20 AA batteries = $16.00

⇒ Cost of 1 AA battery of another package = [tex]\frac{16}{20}[/tex] = $0.8

Hence, the 8 count pack of AA batteries has a lower unit price of $0.79 per battery.

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Answer:

cos y = r/q

Step-by-step explanation:

If we know sin y = 7/q, then we know that the base is 7 and the hypotenuse is q due to sine = opposite/hypotenuse.

If we know tan y = 7/r, then we know that the base is 7 and the right side is r due to tan = opposite/adjacent.

Cos = adjacent / hypotenuse

So cos y = r/q, because the right side is r and the hypotenuse is q.

Answer:

ignore sorry

Step-by-step explanation:

Answer:

The answer to your question is 4.

Step-by-step explanation:

Evaluating and simplifying the expression comes to a result of four using the order of operations. Hope this helps you!

Answer:

4) 3(x+2)

5) Cannot be factored

6)3(4x+10y)

Step-by-step explanation:

4)3x+6

3(x+2)

Proof:

3(x+2)

3x+6

5)2x-15

Cannot be factored.

6)12x+30y

3(4x+10y)

Proof:

3(4x+10y)

12x+30y

Hope this helps ;) ❤❤❤

Answer:

a. Side lengths of ΔBEX are;

BE = 15 ft.

EX = 12 ft.

BX = 9 ft.

b. Side lengths of XEFY are;

XY = 6 ft.

EX = 12 ft.

FY = 7.5 ft.

EF = 7.5 ft.

c. Side lengths of YFGZ are;

GZ = 6 ft.

FY = 7.5 ft.

YZ = 2 ft.

FG = 2.5 ft.

d. Side length of triangle ZGC

GZ = 6 ft.

GC = 10 ft.

ZC = 8 ft.

Step-by-step explanation:

The given parameters are;

XY : YZ : ZC  is 3 : 1 : 4

The length of BC = 25 in.

The length of EB = 15 in.

Therefore, EC = √(BC² - EB²) = √(25² - 15²) = √400 = 20 in.

Given that EX║ YF║GZ, we have;

EF : FG : GC is 3 : 1 : 4 (Parallel lines cut segments in equal proportions)

Therefore;

EF = 20 × 3/(3 + 1 + 4) = 7.5 ft.

FG = 20×1/8 = 2.5 ft.

GC = 20×4/8 = 10 ft.

EC/EX = BC/EB

20/EX = 25/15

EX = 15×20/25 = 12 ft.

XC = √(EC² - EX²) = √(20² - 12²) = 16

XY : YZ : ZC  is 3 : 1 : 4

Therefore;

XY = 16 × 3/8 = 6 ft.

YZ = 16 × 1/8 = 2 ft.

ZC = 16 × 4/8 = 8 ft.

GZ = √(GC² - ZC²) = √(10² - 8²) = 6

Area of triangle ΔZGC = 1/2×6×8 = 24 ft²

XB = BC - XC = 25 - 16 = 9 ft.

Area of ΔBEX = 1/2×9×12 = 54 ft²

a. Side lengths of ΔBEX are;

BE = 15 ft.

EX = 12 ft.

BX = 9 ft.

FY = √(FC² - YC²) = √((10 + 2.5)² - (8 + 2)²) = 7.5 ft.

Area of YFGZ = (GZ + FY)/2 × YZ = (6 + 7.5)/2 × 2 = 13.5 ft²

Area of YFGZ = 13.5 ft²

Area of XEFY = XY × (EX + FY)/2 = 6 × (12 + 7.5)/2 = 58.5 ft.²

b. Side lengths of XEFY are;

XY = 6 ft.

EX = 12 ft.

FY = 7.5 ft.

EF = 7.5 ft.

c. Side lengths of YFGZ are;

GZ = 6 ft.

FY = 7.5 ft.

YZ = 2 ft.

FG = 2.5 ft.

d. Side length of triangle ZGC

GZ = 6 ft.

GC = 10 ft.

ZC = 8 ft.

Answer:

The first equation can be multiplied by 3 and the second equation by 2.

Step-by-step explanation:

Given

[tex]2x+3y=25[/tex]

[tex]-3x + y=22[/tex]

Required

How to eliminate x

To eliminate x using addition, we have to do the following;

1. Take the coefficient of x in equation 1; Coefficient = 2

2. Take the coefficient of x in equation 2; Coefficient = -3

3. Multiply equation 1 by 3

[tex]3(2x + 3y = 25)[/tex]

[tex]6x +9y = 75[/tex]

4. Multiply equation 2 by 2

[tex]2(-3x + y = 22)[/tex]

[tex]-6x + 2y = 44[/tex]

5. Add both resulting equations

[tex]6x +9y = 75[/tex]  +  [tex]-6x + 2y = 44[/tex]

[tex]6x - 6x + 9y + 2y = 75 + 44[/tex]

[tex]11y = 75 + 44[/tex]

Notice that x has been eliminated;

it was a long proof...

follow the caption and steps and you'll understand it

proved...

Step-by-step explanation:

this is too easy method to solve this problem

Answer:

16,20,8,36

Step-by-step explanation:

he plans to have 2 tables for every 8 guest, which means 1 table for each 4 guest!

now:

2(tables)×4(number of people at each table)=8(number of guests

4×4=16

5×4=20

32(number of guests)÷4(number of people at each table)=8(number of tables)

9×4= 36

Answer:

Since there are 8 guests every 2 table we need to find how many guests are in one table:

8 ÷ 2 = 4 guests

4 tables = 4 x 4 = 16 guests

5 tables = 5 x 4 = 20 guests

32 guests = 32 ÷ 4 = 8 tables

9 tables = 9 x 4 = 36 guests

Hope this helps :D

Answer:

  i -j +2k . . . at s=t=-1

Step-by-step explanation:

For the lines to intersect, there must be values of s and t that make the coordinates of r1 equal to those of r2.

Equating i coefficients, we have ...

  2 +s = 2 +t

Equating j coefficients, we have ...

  2 +3s = 3 +4t

Equating k coefficients, we have ...

  3 +s = 4 +2t

The first equation tells us s = t. Using t = s in each of the other two equations, they become ...

  2 +3s = 3 +4s   ⇒   s = -1

  3 +s = 4 +2s   ⇒   s = -1

Then the point of intersection is where s = t = -1. That point is ...

  (2 +s)i +(2 +3s)j +(3 +s)k = (2 -1)i +(2 -3)j +(3 -1)k

  = i -j +2k . . . . the point of intersection

Answer:

40z + 5

Step-by-step explanation:

I'm assuming you need to factor 32z + 4 + 8z + 3 - 4 + 2

Hope this helped

Answer:

The factored expression for the given equation is 4(8z⁴ + 2z³ - z²)

Step-by-step explanation:

In the problem, we a re given an equation.

32z⁴ + 8z³ - 4z²

We can factor out this equation by finding the common factor between all of the coefficients which are 32, 8, and 4.

A common factor between them is 4 because each number can be easily divided by 4. Each number is also a multiple of 4. So, when we are factoring, we will divide each number by 4 because 4 will be on the outside of the parentheses in the final answer.

4(8z⁴ + 2z³ - z²)

So, this is your factored expression from the given equation.

Answer:

[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}[/tex]

Step-by-step explanation:

If a quadratic equation is in the form of ax²+ bx + c = 0

Then the roots of this quadratic equation can be obtained by,

1). Factoring the expression.

2). By quadratic formula.

If we use the method to get the value of x or roots of the equation,

x = [tex]\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}[/tex]

where a, b and c are the coefficients used in the quadratic equation.

Answer:

Area=576 cm²

Perimeter=123.4 cm

Step-by-step explanation:

We have to assume that ABCD would form a square and not a rectangle.  If so, the area is simple:  24x24=576 (Just picture the half circle sliding into the empty space - it’s the same area.)

For the perimeter, we find it for the half circle first. 1/2(2)[tex]\pi[/tex](12)=37.7

Then add the top and bottom (24 and 24) to the left and right (37.7 And 37.7)

24+24+37.7+37.7=123.4

Answer:

[tex] \boxed{\sf d = -1 \ \ \ or \ \ \ d = -7} [/tex]

Step-by-step explanation:

[tex] \sf Solve \: for \: d \: over \: the \: real \: numbers: \\ \sf \implies {(d + 4)}^{2} = 9 \\ \\ \sf Take \: the \: square \: root \: of \: both \: sides: \\ \sf \implies \sqrt{ {(d + 4)}^{2} } = \sqrt{9} \\ \\ \sf 9 = {3}^{2} : \\ \sf \implies \sqrt{ {(d + 4)}^{2} } = \sqrt{ {(3)}^{2} } \\ \\ \sf \implies d + 4 = \pm 3 \\ \\ \sf \implies d + 4 = 3 \: \: \: \: \: or \: \: \: \: \: d + 4 = - 3 \\ \\ \sf Subtract \: 4 \: from \: both \: sides: \\ \sf \implies d + (4 - 4)= 3 - 4 \: \: \: \: \: or \: \: \: \: \: d + (4 - 4) = - 3 - 4 \\ \\ \sf \implies d = - 1 \: \: \: \: \: or \: \: \: \: \: d = - 7[/tex]

Step-by-step explanation:

Since the original price is $47.96 and bill rate is 7%, $47.96 × 1.07 ≈ $51.32

Answer:

$51.32

The amount of sales tax for the bill if the rate is 7% will be $3.36.

The quantity of anything is stated as though it were a fraction of a hundred.

Vince and 11 of his friends went out for pizza on Saturday night to celebrate Vince’s birthday.

The cost of the pizza and soft drinks before sales tax and tip was $47.96.

Then the amount of sales tax for the bill if the rate is 7% will be

⇒ $47.96 x 0.07

⇒ $3.36

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Answer:

[tex]Average\ Rate = 10[/tex]

Step-by-step explanation:

Given

[tex]g(x) = -x^2[/tex]

[tex](-8,-2)[/tex]

Required

Determine the average rate of change;

Average rate of change is calculated as thus;

[tex]Average\ Rate = \frac{g(b) - g(a)}{b - a}[/tex]

Where

[tex](a,b) = (-8,-2)[/tex]

i.e. a = -8 and b = -2

[tex]Average\ Rate = \frac{g(b) - g(a)}{b - a}[/tex] becomes

[tex]Average\ Rate = \frac{g(-2) - g(-8)}{-2 - (-8)}[/tex]

[tex]Average\ Rate = \frac{g(-2) - g(-8)}{-2 + 8}[/tex]

[tex]Average\ Rate = \frac{g(-2) - g(-8)}{6}[/tex]

Calculating g(-2)

Substitute -2 for x in [tex]g(x) = -x^2[/tex]

[tex]g(-2) = -(-2)^2[/tex]

[tex]g(-2) = -4[/tex]

Calculating g(-8)

Substitute -8 for x in [tex]g(x) = -x^2[/tex]

[tex]g(-8) = -(-8)^2[/tex]

[tex]g(-8) = -64[/tex]

Substitute values for g(-2) and g(-8)

[tex]Average\ Rate = \frac{g(-2) - g(-8)}{6}[/tex]

[tex]Average\ Rate = \frac{-4 - (-64)}{6}[/tex]

[tex]Average\ Rate = \frac{-4 + 64}{6}[/tex]

[tex]Average\ Rate = \frac{60}{6}[/tex]

[tex]Average\ Rate = 10[/tex]

Hence, the average rate of change is 10

Answer:

Hey there!

We have an=a1(r^n-1), which is the formula for a geometric sequence.

The common ratio is 3, and 2 is the 1st term.

Thus, we have a1=2(3)^(n-1)

Hope this helps :)

Answer:

Hey there!

We have an=a1(r^n-1), which is the formula

for a geometric sequence.

The common ratio is 3, and 2 is the 1st

term.

Thus, we have a1=2(3)^(n-1)

15.

[tex]FH=2\cdot UH\\\\5x-7=2\cdot19\\\\5x=38+7\\\\5x=45\quad|:5\\\\\boxed{x=9}[/tex]

16.

[tex]KU=UM\\\\3x+3=4x-4\\\\4x-3x=3+4\\\\\boxed{x=7}[/tex]

Answer:

15) x=9 16) x=7

Step-by-step explanation:

19(2)=5x-7

38=5x-7

5x=38+7

5x=45

x=45/5

x=9

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

3x+3=4x-4

3=4x-3x-4

3=x-4

x=3+4

x=7

Answer:

x = 77/15 or  5 2/15

Step-by-step explanation:

x/7 = 11/15

Multiply each side by 7

x/7 *7 = 11/15 *7

x = 77/15

We can leave as an improper fraction or change to a mixed number

15 goes into 77  5 times with 2 left over

5 2/15

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 77/15, 5 2/15, or 5.13

▹ Step-by-Step Explanation

x ÷ 7 = 11 ÷ 15

15x = 77

Divide both sides by 15:

x = 77/15, 5 2/15, or 5.13

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

(A) It should choose High school Z for the most consistent attendance among its students.

(B) It should choose High school W with the highest average attendance.

Step-by-step explanation:

We are given the data for attendance in the table below, where Low represents the fewest days attended and High represents the most days attended for a single student.

School         Hight School W      High School X       High School Z

Low                       108                          112                          130

High                      180                          180                         180

Range                    72                           68                           50

Mean                    169                          160                          162

Median                 150                          124                          151

IQR                       47.5                         49.5                        39.5

S.D. (σ)                 29.5                         32.4                        27.5

(A) It is stated that the school district wants to award the school that has the most consistent attendance among its students.

Now, to check which high school should it choose; we will look for the standard deviation (σ) of each of the three schools because consistency is measured through standard deviation and the school with the lowest standard deviation means that it has the most consistent attendance among its students.

So, after looking at the standard deviation of all the three schools; the High School Z has the lowest standard deviation of 27.5.

This means that it should choose High school Z.

(B) It is stated that the school district wants to award the school with the highest average attendance.

Now, to check which high school should it choose; we will look for the Mean of each of the three schools because average is measured through mean of the data, and the school with the highest mean means that it has the highest average attendance.

So, after looking at the Mean of all the three schools; the High School W has the highest average of 169.

This means that it should choose High school W with the highest average attendance.