The product of two consecutive positive odd numbers is 195.By constructing a quadratic equation and solving it, find the two numbers
Please help

Answers

Answer 1

Step-by-step explanation:

x = one odd number

the second odd number is (x+2), as both are consecutive.

so,

x × (x + 2) = 195

x² + 2x = 195

x² + 2x - 195 = 0

the formula to solve this is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 2

c = -195

x = (-2 ± sqrt(4 - 4×1×-195))/(2×1) =

= (-2 ± sqrt(4 + 4×195))/2 = (-2 ± sqrt(784))/2 =

= (-2 ± 28)/2 = -1 ± 14

x1 = -1 + 14 = 13

x2 = -1 - 14 = -15 which is invalid as the numbers are positive.

so, the two numbers are 13 and 15.


Related Questions

Is w = 4 a solution to the inequality below? w < 11 5 yes no ​

Answers

Answer:

yes

Step-by-step explanation:

just sub in the 4 for the w and see if the equation can be solved. if it can, then w=4 is a solution.

since 4 IS less than 11 5, w=4 can be a solution.

Brainliest please!!! Have a good day!!!!

The residents of a city voted on whether to raise property taxes. The ratio of yes to no votes was 8 to 5. if there were 7332 total votes, how many no were there?

Answers

Answer:

  2820 no votes

Step-by-step explanation:

The fraction of votes that were 'no' is ...

  no/total = (5)/(8+5) = 5/13

The number of votes that were 'no' is ...

  (5/13)(7332) = 2820 . . . no votes

The arithmetic mean of the heights of five pupils in a class is 164cm if another pupil whose height is 168cm joins the class, calculate the arithmetic mean of the heights of the 6 pupils​

Answers

Answer:

164.67 cm

Step-by-step explanation:

The arithmetic mean of height of 5 pupils is 164cm . Let the sum of heights of 5 pupils be x . Then , according to the question ,

[tex]\sf\longrightarrow \dfrac{x}{5}= 164cm [/tex]

On solving ,

[tex]\sf\longrightarrow x = 5*164cm =\bf{820cm}[/tex]

When a student of height 168cm is added ,

[tex]\sf\longrightarrow Mean = \dfrac{820cm+168cm}{6}\\[/tex]

[tex]\sf\longrightarrow Mean = \dfrac{988}{6}\\ [/tex]

[tex]\sf\longrightarrow \boxed{\pink{\sf Mean = 164.66 \approx 164.67 cm }}[/tex]

"15 is always equal to the product of a number and 5" translates to a mathematical equation.
O True
O False

Answers

Answer:

This is True

Step-by-step explanation:

I know this because it is like dividing you just divide 15 by 5 and the it will be equal

Choose yes or no to tell if the digit in the tens place is 1/10 of the value of the digit in the hundreds place 54,450

Answers

Answer:

No

Step-by-step explanation:

54,450

Digit in tens place = 5

value = 50

54,450

Digit in hundreds place = 4

value = 400

1/10 value = 40

No  the digit in the tens place is more than 1/10 the value of the digit in the hundreds place

50 is greater than 40

A train has an odd number of cars. The number of cars Is greater than 1 and less than 9

Answers

I think the correct answer is 3


BRAINLIEST PLEASE

6) The 4,000 students at Tech High were surveyed about their use of text
messaging. How many students said they text 50-100 times a day? *
1 point
How many text messages do you send
a day?
0-50
10%
50-100
75%
100-150
10%
More than 150
5%
Your answer

Answers

Answer: 3,000

Step-by-step explanation:

4,000 divided by 4 is 1,000. This means that 25% of 4,000 is equal to 1,000. 75 divided by 3 is 25. Multiply 1,000 times 3 to get your answer, 3,000, which is 75% of 4,000.

What is the equation of this line *

Answers

Answer:

I would have to see the line to answer the question.

Solve the equation
9 + 13 = 31

Answers

False

9 + 13 = 31

22 ≠ 31

Answer:

22

Step-by-step explanation:

po ang tamang sagon po

What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box
Quick please!!!! 50 points!!

Answers

Answer:

2,1

Step-by-step explanation:

2,1 Correct 37$44634636444+64/+7$;+8$’codk odnicurn jfncurncjeuc

The area of the surface of a ball is equal to the area of the curved surface of a right circular cylinder. If both the height and diameter of the cylinder are 12cm , find the diameter of the ball

Answers

Answer:

D=12 cm

Step-by-step explanation:

please check the image for the answer. Thank you .

2. What is the average rate of change of the function f(x)=3x2 - 12 over the interval [1, 3]?

Answers

Answer:

5.2. Explanation: The average rate of change of the function f(x) on the interval [a,b] is: average rate of change=f(b)−f(a)b−a.

Step-by-step explanation:

Please help! I also don’t understand a). My friend did it for me when I wasn’t looking so if you could explain that too, that’s be great

Answers

Answer:

a) 45

b) No. AD and BC arent parallel.

Step-by-step explanation:

a)

3x + 2x + x + 90 = 360

6x = 270

x = 45

Hope you could understand.

If you have any query, feel free to ask.

if a:b=3:4 and b:c=2:5 find i)a:c and II) a:b:c​

Answers

Answer:

a:c= 3/5 = 0.6

a:b:c= 3/4/5=0.15

Convert 232 fluid ounces to gallons (1 gallon = 128 fluid ounces)

Answers

232 fluid ounces is equal to 1.8125 gallons.

Answer:

Exact: 1.8125

Rounded Answers:

Nearest Thousandth: 1.813

Nearest Hundredth: 1.81

Nearest Tenth: 1.8

I need help!!
If any boady could tell me the awnswer that would be great

Answers

Answer:

1/4 and 3/8  = 2/8 and 3/8

1/4 and 1/2 = 1/4 and 2/4

2/16 ad 3/8 = 2/16 and 6/16

1/4 and 2/16 = 4/16 and 2/16

1/2 and 3/8 = 4/8 and 3/8

Step-by-step explanation:

Answer:

The first box goes with the third bottom box. The second box goes with the 5th bottom box. The third box goes with the first bottom box. The fourth box goes with the fourth bottom box. Lastly the 5th box goes with the second bottom box.

Hope this helps

Please help me I don’t know how to solve this

|-4-r|=4

Answers

Answer:

r = 0 and r = -8

Step-by-step explanation:

|-4-r|=4

-4 = -4-r = 4

0 = - r = 8

0 = r = -8

When you have absolute value signs, to get rid of the absolute value signs and find the value of the term, you simply add another eqaul sign (=), and add a negative in front (- =). If it is already set to equal a negative, there isn't any solution.

|x| = 4

-4 = x = 4

So x would equal 4 and -4 for this example.

Another example:

|x|=-5

Because it's equal to a negative, the solution is automatically no solution.

The actual answer is r = 0 and r = -8

Lesson 6 Practice Problems
1. A pink paint mixture uses 4 cups of white paint for every 3 cups of red paint.
The table shows different quantities of red
and white paint for the same shade of pink.
Complete the table.
white paint
(cups)
red paint
(cups)
4
3
1
1
4
5

Answers

Answer:

                               WHITE PAINT                                    PINK PAINT

                                       (CUPS)                                              (CUPS)

                                             4                                                         3        

                                            4/3                                                       1

                                            1                                                         3/4

                                            16/3                                                     4

                                             5                                                         15/4

-Lexi

I need help with my Geometry. Can you help?
Thanks.​

Answers

Answer:

  1.  32 units

  2.  C(-15, -4) and D(17, -4)

Step-by-step explanation:

1.

The midpoint divides CD into two segments that are the same length:

  CM = MD

  8(x -2) = 4(5x -16)

  8x -16 = 20x -64 . . . eliminate parentheses

  48 = 12x . . . . . . . . . add 64 -8x

  x = 4 . . . . . . . . . . . divide by 12

Then the length of CD is ...

  CD = 2·CM = 2(8(x -2)) = 2(8(4-2))

  CD = 32

__

2.

If we put C and D on the same horizontal line as M, their coordinates are ...

  C = M -(16, 0) = (1,-4) -(16, 0) = (-15, -4)

  D = M +(16, 0) = (1, -4) +(16, 0) = (17, -4)

Coordinates C and D that have M(1, -4) as a midpoint are ...

  C(-15, -4) and D(17, -4).

You earn
$10 per hour working as a manager at a grocery store.
You are required to work at the grocery store at least
8 hours per week. You also teach music lessons for
$15 per hour. You need to earn at least $120 per week,
$
do not want to work more than 20 hours
but you
per week.
a. Write and graph a system of linear inequalities
that represents the situation.
b. Identify and interpret a solution of the system.
c. Use the graph to determine whether you can work
8 hours at the grocery store and teach 1 hour of
music lessons.

Answers

We want to get a system of inequalities that models the given situation.

The solutions are:

a) The system is:

x ≥ 8x*$10 + y*$15 ≥ $120x + y ≤ 20.y ≥ 0

And the graph can be seen at the end.

b) A solution can be x = 12 and y = 2

c) x = 8 and y = 1 is not a solution.

First, we need to define two variables:

x = number of hours working as a manager.y = number of hours teaching lessons.

a) First, we know that you must at least 8 hours per week in the grocery store, then:

x ≥ 8

We know that you need to earn at least $120 per week, then we have the inequality:

x*$10 + y*$15 ≥ $120

And you don't want to work more than 20 hours per week, this gives:

x + y ≤ 20.

We also add the trivial restriction:

y ≥ 0

Then the system is:

x ≥ 8x*$10 + y*$15 ≥ $120x + y ≤ 20.y ≥ 0

The graph can be seen at the end.

b) The solution region is the interception of the four shaded regions (is the dark blue part).

A solution in that region can be:

x = 12

y = 2

c) The point x = 8, y = 1 is graphed, you can see that it is outside the solution region, thus, this is not a solution.

If you want to learn more about inequalities, you can read:

https://brainly.com/question/2065712

Which term of the arithmetic sequence 1, 3, 5, 7, ... is 99?
It is the
th term.

Answers

Answer:

it is the 50th tearm

Step-by-step explanation:

I just added '2' to '1' 50 times in a sense and got 99


If m<8= x°, which angles have a measure of 180º – xº? Select all that apply.
<3
<4
<6
<10

Answers

Answer:

  ∠6, ∠10

Step-by-step explanation:

Apparently, we are to assume that the avenues are parallel.

The angles that form a linear pair with ∠8 will be supplementary: ∠6 and ∠7. The angles that correspond to those will also be supplementary to angle 8: ∠10 and ∠11.

Among the answer choices ∠3, ∠4, ∠6, ∠10, only ∠6 and ∠10 are equal to 180° -x.

_____

Additional comment

It appears we are to assume that 1st Ave is parallel to 2nd Ave. If that is the case, then we might also assume that D Street is perpendicular to those avenues. In that case, all of angles 5, 6, 7, 9, 10, 11, 12 are equal to 180° -x, because x and all of those are all 90°.

During lunch, Mr. Lee eats a piece of chicken that contains 9 1/9 grams of protein, and Mr. Scott eats a piece of salmon that contains 7 1/7 grams of protein. How much more protein did Mr. Lee eat at lunch?

Answers

Answer:

Mr. Lee ate [tex]1\frac{61}{63}[/tex] more protein than Mr. Scott

Step-by-step explanation:

Find the least common denominator for both fractions.

9: 9, 18, 27, 36, 45, 54, 63

7: 7, 14, 21, 28, 35, 42, 49, 56, 63

Multiply 1/9 by 7/7:

[tex]9 \frac{1}{9} = 9 \frac{7}{56} \\[/tex]

Multiply 1/7 by 9/9:

[tex]7\frac{1}{7} = 7\frac{9}{63}[/tex]

Subtract the two fractions:

[tex]9\frac{7}{63} - 7\frac{9}{63} = 1\frac{61}{63}[/tex]

what is the first step in solving problem using GMDAS?

Answers

Answer:

D

Step-by-step explanation:

Gemdas-this means grouping

exponent, multiplication, Division,addition,

and subtraction order of operations

Sana tama HAHAHAHA

Use the following function rule to find f(0).

f(x)= 12(9)^x


f(0) =

Answers

Answer:

12

Step-by-step explanation:

f(0)=12(9)^0

(9)^0=1

f(0)=12(1)=12

[tex]f(x) = 12 \cdot 9^x\\\\f(0) = 12 \cdot 9^0 = 12 \cdot 1 =12[/tex]


Can sides with lengths of 8, 3, 8 form a triangle

Answers

no the sume of the lengths of any two sides of a triangle must be greater than the lenght of the third side

Answer:

Yes, sides with lengths of 8, 3, 8 can form a triangle. The type of triangle sides with these lengths would form is called an isosceles triangle. Isosceles triangles have three sides, two of which are equal.

i need help...Which table represents a function?

A 2-column table with 4 rows. The first column is labeled x with entries negative 3, 0, negative 2, 8. The second column is labeled y with entries negative 1, 0, negative 1, 1.

A 2-column table with 4 rows. The first column is labeled x with entries negative 5, 0, negative 5, 6. The second column is labeled y with entries negative 5, 0, 5, negative 6.

A 2-column table with 4 rows. The first column is labeled x with entries negative 4, negative 2, negative 2, 0. The second column is labeled y with entries 8, 2, 4, 2.

A 2-column table with 4 rows. The first column is labeled x with entries negative 4, 3, 1, negative 4. The second column is labeled y with entries 2, 5, 3, 0.

Answers

Answer: Choice A

Explanation:

A function has each x value map to exactly one y value. Choice A demonstrates this, which is why it's a function. Note how none of the x values are repeated in this table.

Choices B, C and D have repeated x values, which in turn means that we have an x input lead to multiple y outputs. For instance, choice B says that the input x = -5 has the two outputs y = -5 and y = 5; this is sufficient to show that table B is not a function. Choices C and D are a similar story.

A cloth bag contains a mix of black, white and red balls. Selecting one ball at random, the probability of getting a black ball is 0.2 , while the probability of getting a white ball is 0.5 . (a) Selecting one ball at random, what is the probability of getting a red ball ? (b) If in total there are 5 white balls in the bag, how many black balls are there ? (c) If there are in total 3 red balls in the bag, how many balls are there altogether ?
pls give the way​

Answers

Answer:

a) 0.3

Step-by-step explanation:

The probability of getting a red ball, the number of black balls and total balls are 0.3, 2 and 10 respectively.

What is probability?

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

The probability of getting a black ball is 0.2.

The probability of getting a white ball is 0.5.

(a) As the bag contains only black, white and red balls, the probability of getting a red ball is,

1 - (0.2 + 0.5)

= 0.3

(a) The probability of getting white balls can be written as,

P (white ball) = Number of white balls ÷ Total number of balls

Substitute all the given values to get,

Total number of balls = 5 ÷ 0.5

                                   = 10

Similarly, for black balls it can be written that,

P (black ball) = Number of black balls ÷ Total number of balls

Substitute all the given values to get,

Number of black balls = 10 × 0.2

                                    = 2

(c) When number of red balls are three then,

P (red ball) = Number of red balls ÷ Total number of balls

Substitute all the given values to get,

Total number of balls = 3 ÷ 0.3

                                    = 10.        

Hence, the answers for all the parts are 0.3, 2 and 10 respectively.

To know more about probability click on,

https://brainly.com/question/11234923

#SPJ2

                 

10 Jim was thinking of a number. Jim subtracts 14 from it and gets an answer of 43.9. What was the original number?

Answers

57.9 add 14 to the answer and you get your number

Which of the following fractions has a repeating decimal expansion (other than repeating zero)
A 17/20
B 17/25
C 17/3
D 17/22​

Answers

Answer:

C

Step-by-step explanation:

→ Immediately remove option A and B from the list as they convert to non recurring decimals

Option C or D are both recurring

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