Mathematics Middle School

9x squared= -18x+7
[tex]9x {}^{2} = - 18 + 7[/tex]

9x Squared= -18x+7[tex]9x {}^{2} = - 18 + 7[/tex]

Answers

Answer 1
[tex]-9x^2=-18x+7\ \ \ |+9x^2\\\\9x^2-18x+7=0\\\\a=9;\ b=-18;\ c=7\\\\\Delta=b^2-4ac\to\Delta=(-18)^2-4\cdot9\cdot7=324-252=72\\\\\sqrt\Delta=\sqrt{72}=\sqrt{36\cdot2}=\sqrt{36}\cdot\sqrt2=6\sqrt2\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a};\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\x_1=\dfrac{18-6\sqrt2}{2\cdot9}=\dfrac{9-3\sqrt2}{9}=\dfrac{3-\sqrt2}{3}\\\\x_2=\dfrac{3+\sqrt2}{3}[/tex]

Related Questions

I need help with the first three please!!!

Answers

Number 1is nine days for the rest do you have formulas

what equation results from completing the square and then factoring.

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The answer is D (x+11)^2=152

a number is chosen at random from 1 to 50. find the probability of selecting divisors of 12

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Hi! 

First of all, we need to know how many divisors 12 has. 

12: 1, 2, 3, 4, 6, 12

Since there are 6 divisors of 12, this means the probability is 6/50. 

You could just stick with 6/50 as your answer, but most probability is measured in percents so we'll convert 6/50 into a percent. 

Percents are measured out of 100, so to make 6/50 into a percent we need to do some cross-multiplying. 

[tex] \frac{6}{50} = \frac{x}{100} [/tex]

First, multiply 6 by 100

6 × 100 = 600

Next, divide the product by 50.

600 ÷ 50 = 12

So, your final answer is:

As a ratio:

[tex] \frac{6}{50} = \frac{12}{100} [/tex] 

As a fraction:

12/100 or 6/50

As a percent:

12%

Hope this helps!

Help with question 12 please

Answers

I really don’t know I’m so sorry hope someone will help
Daniel's Train: 1:45 + 12 min = 1:57
Teri's Train: 2:35 - 20 min = 2:15
Time between 1:57 and 2:15 is 13 minutes

the following scatter plot demonstrates that there is a positive correlation between the two quantities.

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I think the answer is true.
 

what's the answer to this?

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The measure of the side length of the right triangle is 20.

What is the measure of the missing side length?

A tangent makes an angle of 90 degrees with the radius of a circle.

Therefore, the triangle formed is a right triangle.

From the diagram:

Leg 1 = 12

Leg 2 = 16

Hypotenuse =?

To find the hypotenuse, we use the Pythagoras theorem:

(Hypotenuse)² = ( Leg 1 )² + ( Leg 2 )²

(Hypotenuse)² = ( 12 )² + ( 16 )²

(Hypotenuse)² = 144 + 256

(Hypotenuse)² = 400

Take the square roots of both sides:

Hypotenuse = √400

Hypotenuse = 20

Therefore, the side length measures 20 units.

Option C) 20 is the correct answer.

The complete question is:

Find the missing line segment in the diagram.

Learn more about Pythagorean theorem here: brainly.com/question/343682

#SPJ1

four times the sum of a number and 2/3 is 16/3. find the number. express your answer as a fraction in simplest form

Answers

times= multiply
sum= addition
is= equal sign

x= a number

4 times x plus 2/3 equals 16/3.


4x + 2/3= 16/3
subtract 2/3 from both sides

4x= 14/3
divide both sides by 4

x= 14/3 ÷ 4
to divide fractions, multiply by reciprocal/inverse of 4

x= 14/3 * 1/4
multiply numerators (top); multiply denominators (bottom)

x= (14*1)/(3*4)
x= 14/12
simplify by 2

x= 7/6


ANSWER: The number in simplest form is 7/6.

Hope this helps! :)

which values are outliers ?

5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9

select all correct answers

Answers

5.8 0.8 5.9 6.1 and 10.9 are all correct answers.

Hope this Helped!

;D
:D
:)
;)
XD
:'D

Answer:

0.8 and 1.1 are outliers of the given data set.

Step-by-step explanation:

The given data set is

5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9

Arrange the data set in ascending order

0.8, 1.1, 4.9, 5.2, 5.8, 5.9, 6.1, 6.1, 7.4, 10.2, 10.9

Divide the data in four equal parts.

(0.8, 1.1), 4.9,( 5.2, 5.8), 5.9,( 6.1, 6.1), 7.4, (10.2, 10.9)

From the above division we get,

[tex]Q_1=4.9[/tex]

[tex]Median=5.9[/tex]

[tex]Q_3=7.4[/tex]

The interquartile range of the data is

[tex]IQR=Q_3-Q_1[/tex]

[tex]IQR=7.4-4.9=2.5[/tex]

If all the data elements lies in the interval [Q₁-1.5(IQR),Q_3+1.5(IQR)], then the data set has no outliers.

[tex][Q_1-1.5(IQR),Q_3-1.5(IQR)]=[4.9-1.5(2.5),7.4-1.5(2.5)]=[1.15,11.15][/tex]

Since all the elements lie in the interval [1.15,11.15] except 0.8 and 1.1, therefore 0.8 and 1.1 are outliers.

Using polar coordinates to find area inside a rectangle.
The vertices are (0,0), (0,4), (2,4), (2,0).
This is a calculus level question, please help :(

Answers

Use the vertices to find the length and width of the rectangle:

Length = (0,0) (0,4) = 0-0 = 0, 4-0 = 4

Length = 4

Width = (0,0) (2,0) = 2-0 = 2, 0-0 = 0 = 2

Width = 0

Area = 4 x 2 = 8 square units

What is the output value for the following function if the input value is 3.2?

y = 2x - 1

1
2
4.2
5.4

Answers

the answer to this is 5.4

The given function is y = 2x -1 which is of the form of a straight line with the form y = mx + c

now, we have been given that the value of x is 3.2 as it says input value is 3.2

we plug in x =3.2 in the equation

y = 2x -1

y = 2*3.2 -1

y = 6.4 -1

y = 5.4

So the value of y we get is 5.4

Answer = 5.4 (option D)

I need help ASAP

The figure of a rocket launched for space exploration is shown below.
Find the volume of the rocket to the nearest hundredth.

A) 90.36 cubic meters

B) 98.91 cubic meters

C) 80.07 cubic meters

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It would be B.) 98.91 cubic meters

35x^7+15x^5-10x^3/5x^3

Answers

So if i did all the math correct, the answer would be 514,720,226
35x⁷ + 15x⁵ - 10x³/5x³
35x⁷ + 15x⁵ - 10/5
35x⁷ + 15x⁵ - 2

Eli, Freda and Geoff were given £800 to share in the ratio of their ages.
Eli is 9 years old,Feda is 13 years old and Geoff is 18 years old.
How much should they each get?
Eli-
Freda-
Geoff-

Answers

First, we are going to find the sum of their age. To do that we are going to add the age of Eli, the age Freda, and the age of Geoff:
[tex]9+13+18=40[/tex]
The combined age of Eli, Freda, and Geoff is 40, so the denominator of each ratio will be 40.

Next, we are going to multiply the ratio between the age of the person and their combined age by £800:
For Eli: [tex] \frac{9}{40} *800=180[/tex]
For Freda: [tex] \frac{13}{40} *800=260[/tex]
For Geoff: [tex]\frac{18}{40} *800=360[/tex]

We can conclude that Eli will get £180, Freda will get £260, and Geoff will get £360.

Final answer:

Calculate how £800 should be divided among Eli, Freda, and Geoff based on their ages.

Explanation:

Ratio of ages: 9:13:18 = 9/40 : 13/40 : 18/40

Total amount: £800

Eli: £200

Freda: £290

Geoff: £410

Part 1: Solve the system by graphing. Draw the graphs on paper and indicate their intersection point. Type the ordered pair solution here as your answer to Part 1.
Part 2: Solve the system using the substitution method. Show all work here and indicate the solution for the system as an ordered pair.
Part 3: Solve the system using the addition method. Show all work here and indicate the solution for the system as an ordered pair.

2x+3y=6

x-2y=10

Answers

Part (1):
The graph is shown in the attached image.
As we can note from the graph, the solution of the system of equations is indicated by the point of intersection between the two lines which is (6,-2)

Part (2):
The equations given are as follows:
2x + 3y = 6 ...........> equation I
x - 2y = 10
which can be rewritten as:
x = 2y + 10 ...........> equation II

Substitute with equation II in equation I and solve for y as follows:
2x + 3y = 6
2(2y+10) + 3y = 6
4y + 20 + 3y = 6
7y = 6 - 20
7y = -14
y = -2

Substitute with y in equation II to get x as follows:
x = 10 + 2y 
x = 10 + 2(-2)
x = 10 - 4
x = 6

The solution is (6,-2)

Part (3):
The equations given are:
2x + 3y = 6 .............> equation I
x - 2y = 10 ...........> equation II

Multiply equation II by -2, this will give:
-2x + 4y = -20 ............> equation III

Add equation I and equation III as follows:
                                       2x + 3y = 6
                                +    -2x + 4y = -20
                           .........................................
                                       0x + 7y = -14
7y = -14
y = -2

Substitute with y in equation II to get x as follows:
x - 2y = 10
x - 2(-2) = 10
x + 4 = 10
x = 10 - 4
x = 6

The solution is (6,-2)

Hope this helps :)


What is the coefficient of y in the expression 3 ⋅ 6 + 4y?

Answers

4 is the answer
Hope this helps:)

Answer:

Sorry I'm late, but I think the answer is D.

Step-by-step explanation:

a store sign reads take 90% off the original price when you take an additional 15% off the sale price which is 75% of the original price. Is the store sign correct

Answers

If you did 75%+15% you would get 90%, so yes the sign is correct.
Hope This Helps!
~Cupkake

PLEASE HELP AND FAST, 15 POINTS! In the coordinate plane shown, how far apart are points B and D? Explain how you can use the Pythagorean theorem to determine this.

Answers

5 to the power of 2 = 25
9 to the power of 2 = 81
25 + 81 = 106
Square root of 106 = 10.29563
If you round it to the nearest hundredth, it will become 10.30
If you round it to the nearest tenth, it will become 10.3

helppppppppppppppppppppppppp

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Set the two expressions equal to each other.

7x + 3 = 9x

Simplify, isolate the x, subtract 7x from both sides

7x (-7x) + 3 = 9x (-7x)
3 = 2x

Set the equation = 0, subtract 3 from both sides

3 (-3) = 2x (-3)

0 = 2x - 3

2x - 3, or D, should be your answer

hope this helps

can somebody help me please this is my last question i need to submit this!! help!!

Answers

Both the vertical and horizontal cross-section would be a square.  The cross-sections are the same because all of a cube's dimensions are the same.  A cube is made up of 6 congruent square faces.

I need help on these problems

Answers

Hope this helps and hope you can read it, if not let me know :)

Which characteristics best describe an obtuse isosceles triangle? I. One angle is greater than 90°. II. All side lengths are equal. III. Two sides meet at a 90° angle. IV. Two sides are equal in length. A. I and IV B. II and III C. I and II D. III and IV

Answers

An obtuse triangle is a triangle that has an angle greater than 90 degrees, so 1. One angle is greater than 90 degrees is correct.

An obtuse isosceles triangle is defined as a three-sides triangle shape that has one angle (out of three angles) more than 90 degrees and whose two sides are always congruent that includes obtuse angle in between. So it will follow :-

⇒ Obtuse means "one angle is greater than 90 degrees".

⇒ Isosceles means "Two sides are equal in length".

So, option A is correct, i.e. statements I and IV.

What is the solution of x+8/5x-1>0 ?

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x + [tex] \frac{8}{5} [/tex]x - 1 > 0

First combine like-terms (x + [tex] \frac{8}{5} [/tex]x).
2.6x - 1 > 0

Add 1 to both sides.
2.6x > 1

Divide both sides by 2.6 to isolate x.
x > 0.38

Answer:

Step-by-step explanation:

Which graph represents the given inequality?
y > 4x - 2

Answers

In each graph, take a any point on either side and substitute in  the inequality. Then check if it satisfies the inequality. 
For graph 1, take a point (0,0).
substituting it we get,

y>4x-2   ⇒ 0>-2. This is true yet the region where (0,0) is, is shaded. So, wrong graph.

For graph 2, take point (0,0).
y>4x-2   ⇒ 0>-2. This is true but againt the region is shaded. so, wrong graph.

For graph 3, take point (0,0)
y>4x-2   ⇒ 0>-2. This is true. Since the point (0,0) is in this region, which is not shaded, it means that this is the required region. The correct graph is graph 3.


Find the difference. express your answer in simplest form. (2s/s^2-4s+4) - (4/s^2-4s+4)

Answers

To find the difference, we are going to destroy the parenthesis first, and then, we are going to perform the operations. Remember that to destroy a parenthesis preceded by a negative sign (-), you should change the signs of the factors inside the parenthesis:
[tex] \frac{2s}{s^2-4s+4} -( \frac{4}{s^2-4s+4} )[/tex]
[tex]\frac{2s}{s^2-4s+4} -\frac{4}{s^2-4s+4}= \frac{2s-4}{s^2-4s+4} [/tex]

Now we can factor both numerator and denominator and simplify:
[tex]\frac{2s-4}{s^2-4s+4} = \frac{2(s-2)}{(s-2)^2} = \frac{2}{s-2} [/tex]

We can conclude that the difference in simplest form is: [tex] \frac{2}{s-2} [/tex]
To get started, combine -4s+4 with 4s - 4.  Result:  0.  That leaves

 2s        4          2(s+2)
------ - ------- = ------------
s^2      s^2           s^2

the initial number of bacteria in a culture is 12,000. the xulture doubles each day write an exponential functin to model the population Y of bacteria after X days

Answers

The equation would be y=12000(2)ˣ.

This equation is of the form y=a*bˣ, where a is the initial population and b is the rate that it increases by.  In this problem, a = 12000 and b=2, since it doubles each time.

Answer:

[tex]Y = 12,000 \cdot (2)^X[/tex]

Step-by-step explanation:

The exponential function is given by:

[tex]y =a \cdot b^x[/tex]

where,

a is the initial values and b is the growth factor.

As per the statement:

The initial number of bacteria in a culture is 12,000.

⇒Number of bacteria initially(a) = 12,000

It is also given that the culture doubles each day.

⇒ growth factor [tex]b= 2[/tex]

We have to find the exponential function to model the population Y of bacteria after X days.

By definition of exponential function:

[tex]Y = 12,000 \cdot (2)^X[/tex]

where, x represents the days and Y is the population after X days.

Therefore,  an exponential function to model the population is,

[tex]Y = 12,000 \cdot (2)^X[/tex]

help me? Answers por favor ?

Answers

6. complementary is they add to 90 degrees, a right angle.
4x+50=90.
90-50=4x
40=4x
x=10

7. theyre suplementary, they add to 180 degress, a straight line.
 42+6x=180
6x=180-42
6x=138
x=23

8-10, Do i state them all or just some. (Im going to name just 1 or 2)

8. angle AKB and BKG, angle CGD and CGJ
9.CGK and KGJ
10. DGE and KGJ

Darnell rented a moving truck.The weight of the empty truck was 7,860 pounds.When Darnell filled the truck with his items,it weighed 6 tons.what was the weight in pounds of the items was Darnell placed in the truck? show the work

Answers

1 ton = 2000 lb
Multiply by 6.
6 ton = 12,000 lb

The problem statement tells you 
  (truck weight) + (Darnell's items) = 12,000 lb
  7,860 lb + (Darnell's items) = 12,000 lb

Subtracting the weight of the truck gives
   (Darnell's items) = (12,000 -7,860) lb = 4,140 lb

The weight of items Darnell placed in the truck was 4,140 lb.

In 1980 the population in Detroit, Michigan was approximately 1, 200, 000. If the population decreased at an annual rate of 14.6% over the next decade What was the population of Detroit in 1990, 10 years later

Answers

1,200,000X.164=175,200
1,200,000-175,200=1,024,800

Cindy's job is to check computer printers for defects. Out of 420 printers she has to check, only 3 of the first 84 have been defective. What is the best prediction of the total numbers of printers in this group that will be defective?

Answers

46% printers are defective = 106 printers defective

watts,volts and amps are used to measure electricity. there is a formula that shows the relationship between watts,volts and amps. volts times amps = watts . if the volts are 120 and the amps are 5 how many watts are there?

Answers

VA=W
120(5)=W
600=W
600 Watts
Final answer:

The number of watts for a circuit with 120 volts and 5 amps is 600 watts.

Explanation:

The formula for calculating the power in an electrical circuit is: Power (P) = Voltage (V) × Current (I).

To calculate the number of watts, we can substitute the given values into the formula:
Volts (V) = 120
Amps (I) = 5

Therefore, the number of watts (P) = 120 V × 5 A = 600 W.

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