Milton spilled some ink on his homework paper. He can't read the coefficient of $x$, but he knows that the equation has two distinct negative, integer solutions. What is the sum of all of the distinct possible integers that could be under the ink stain

Answers

Answer 1

Answer:

[tex]Sum = -81[/tex]

Step-by-step explanation:

See the comment for complete question.

Given

[tex]c = 36[/tex] ----- Constant

No coefficient of x^2

Required:

Determine the sum of all distinct positive integers of the coefficient of x

Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

[tex]x^2 + ax + 36 = 0[/tex]

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

[tex]x = -\alpha[/tex] and [tex]x = -\beta[/tex]

Using the above roots, the equation can be represented as:

[tex](x + \alpha)(x + \beta) = 0[/tex]

Open brackets

[tex]x^2 + (\alpha + \beta)x + \alpha \beta = 0[/tex]

To compare the above equation to [tex]x^2 + ax + 36 = 0[/tex], we have:

[tex]a = \alpha + \beta[/tex]

[tex]\alpha \beta = 36[/tex]

Where: [tex]\alpha, \beta <0[/tex] and [tex]\alpha \ne \beta[/tex]

The values of [tex]\alpha[/tex] and [tex]\beta[/tex] that satisfy [tex]\alpha \beta = 36[/tex] are:

[tex]\alpha = -1[/tex] and [tex]\beta = -36[/tex]

[tex]\alpha = -2[/tex] and [tex]\beta = -18[/tex]

[tex]\alpha = -3[/tex] and [tex]\beta = -12[/tex]

[tex]\alpha = -4[/tex] and [tex]\beta = -9[/tex]

So, the possible values of a are:

[tex]a = \alpha + \beta[/tex]

When [tex]\alpha = -1[/tex] and [tex]\beta = -36[/tex]

[tex]a = -1 - 36 = -37[/tex]

When [tex]\alpha = -2[/tex] and [tex]\beta = -18[/tex]

[tex]a = -2 - 18 = -20[/tex]

When [tex]\alpha = -3[/tex] and [tex]\beta = -12[/tex]

[tex]a = -3 - 12 = -15[/tex]

When [tex]\alpha = -4[/tex] and [tex]\beta = -9[/tex]

[tex]a = -4 - 9 = -13[/tex]

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is:

[tex]Sum = -37 -20 -15 - 9[/tex]

[tex]Sum = -81[/tex]


Related Questions

4 (k - 6) = 6 (-4 - 5k)
a) 10
b) 0
c) -2
d) 8

Answers

Step-by-step explanation:

step 1. what is the question? solve for k? okay.

step 2. 4(k - 6) = 6(-4 - 5k)

step 3. 4k - 24 = -24 - 30k

step 4. 34k = 0

step 5. k = 0.

1 ÷ 8, or 1/8, is 0.125

Answers

Answer:

both

Step-by-step explanation:

Answer:

true! :)

Step-by-step explanation:

Where could point E be located on the coordinate plane? I’ll mark you as brainliest! Quadrant one, or Quadrant two, or Quadrant three or , Quadrant four , or Y axis, or X axis?

Answers

Answer:

Quadrant II and III

Step-by-step explanation:

Given

Point E

[tex]x < 0[/tex] i.e. negative x

and

[tex]y \ne 0[/tex]

Required: Determine the possible quadrant(s) of E

[tex]y \ne 0[/tex]. means that point E belongs to at least 1 quadrant. So, x-axis and y-axis are ruled out

Solving further:

[tex]x < 0[/tex]

The two quadrants where the x coordinates is negative are II and III.

Hence, point E belongs to quadrants II or quadrants III

A hot air balloon is at an altitude of

100 1/5 yards. The balloon's altitude decreases

by 10 4/5 yards every minute. Determine the

number of minutes it will take the balloon to reach an altitude of 57 yards.

Answers

Answer:

It will take 4 minutes for the balloon to reach an altitude of 57 yards.

Step-by-step explanation:

Initial altitude:

100 1/5 yards = 100 + 0.2 = 100.2 yards.

Decrease per minute:

10 4/5 yards = 10 + 0.8 = 10.8 yards.

So, after t minutes, the height of the ballon is given by:

[tex]h(t) = 100.2 - 10.8t[/tex]

Number of minutes it will take the balloon to reach an altitude of 57 yards.

This is t for which [tex]h(t) = 57[/tex]. So

[tex]h(t) = 100.2 - 10.8t[/tex]

[tex]57 = 100.2 - 10.8t[/tex]

[tex]10.8t = 43.2[/tex]

[tex]t = \frac{43.2}{10.8}[/tex]

[tex]t = 4[/tex]

It will take 4 minutes for the balloon to reach an altitude of 57 yards.

A sum amount
to rupees 34476 in two and a half years at 4% CI. the sum is ​

Answers

Given:

Amount = Rs. 34476

Rate of compound interest = 4%

Time = [tex]2\dfrac{1}{2}=2.5[/tex] years

To find:

The principal value.

Solution:

Formula for amount is

[tex]A=P\left(1+\dfrac{r}{100}\right)^t[/tex]

Where, P is principal value, r is rate of interest and t is time in years.

Putting the given values, we  get

[tex]34476=P\left(1+\dfrac{4}{100}\right)^{2.5}[/tex]

[tex]34476=P\left(1+0.04\right)^{2.5}[/tex]

[tex]34476=P\left(1.04\right)^{2.5}[/tex]

[tex]\dfrac{34476}{\left(1.04\right)^{2.5}}=P[/tex]

Now,

[tex]P=31256.0090[/tex]

[tex]P\approx 31256[/tex]

Therefore, the value of sum or principal value is Rs.31256.

Given f(x) = -3x + 1 and g(x) = 4*, find the following combinations:
g(x)-f(x)
g(x) •f(x)
f(x)
8(x)

Answers

Step-by-step explanation:

Please refer to the attachment

2/5× = ?


I don't understand how to answer this​

Answers

Answer:

10

Step-by-step explanation:

2x5 is basically 1x5= 5x2=10

i need the answer asap

Answers

Step-by-step explanation:

A (-3 , 4) and C ( 2 , -6 ) and ratio of AB : AC is 4:5

now , let AB be 4x and AC be 5x such that

AC = AB + BC

AC - AB = BC

5x - 4x = BC

x = BC

ratio of AB : BC = 4:1

by using section formula

( mx2 + nx1 / m+n , my2 + ny1 / m+n )

where m = 4 and n = 1

B = ( 4×2 + 1×-3 / 4+1. ,. 4× -6. + 1× 4 / 4+1 )

B = ( 8 -3 / 5. ,. -24 + 4 / 5)

B = ( 5/5. ,. -20/5 )

B = ( 1. , -4 )

A rectangle is inside a circle with a 5 cm radius.

What is the area of the shaded region?

Use 3.14 for ​π​.

Enter your answer as a decimal

Answers

Answer:

Do it your self

Step-by-step explanation:

Gross

Answer:

30.5

Step-by-step explanation:

can you all please help me with a and b ​

Answers

Answer:

Step-by-step explanation:

a.

area of one face=3²=9 units²

b.

whole surface area=6×3²=6×9=54 units²

Cam walked 4 units down and 8 units left to reach the origin. What is the ordered pair of his starting point?

Answers

answer is (4,8) or (-8,4)

Use the Normal model N(1156,59) for the weights of steers.
a) What weight represents the 39th percentile?
b) What weight represents the 99th percentile?
c) What's the IQR of the weights of these steers?

Answers

What weight represents 39th percentile

Tony has a bucket filled with 10 green, 3 blue, 1 red, and 7 yellow tennis balls. He removes 4 tennis balls from the bucket without replacing them.

Which of the following outcomes could represent the tennis balls Tony selected?

(A) All of the tennis balls are blue.

(B) There is 1 tennis ball of each color.

(C) There are exactly 3 green tennis balls.

(D) There are more red tennis balls removed than other colors.

(E) The number of red tennis balls is the same as the number of blue tennis balls.

Answers

B is the right answer

Answer:

b

Step-by-step explanation:

Write the expression
a2b3c2d in expanded
form.

Answers

Answer:

a*2+b*2+c*2+d

Step-by-step explanation:

If i's meant to be Pythagorean theorem, a*a+b*b=c*c

In AHIJ, the measure of ZJ=90°, HI = 65 feet, and IJ = 31 feet. Find the measure of
H to the nearest tenth of a degree.
I
65
31
J
H

Answers

Answer:

14

Step-by-step explanation:

Dz

Answer:

H=28.4846≈28.5  

Step-by-step explanation:

SOH-CAH-TOA

sinH= opposite/hypotenuse=31/65

sinH=31/65

H=28.4846≈28.5      Type into calculator and round to the nearest tenth of a degree.

28.5

(10 − 343) − 2 × 6 simplify the operation using the order of operations

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{\bf{{(10-343)-2\times6}}}\\\bold{Do\ PEMDAS}\\\bold{PEMDAS\ is....}\\\bold{Parentheses}\\\bold{Exponents}\\\bold{Multiplication}\\\bold{Division}\\\bold{Addition}\\\bold{Subtraction}}[/tex][tex]\\\bold{Do\ PEMDAS}\\\\\bold{PEMDAS\ is....\downarrow}\\\\\bold{Parentheses}\\\bold{Exponents}\\\bold{Multiplication}\\\bold{Division}\\\bold{Addition}\\\bold{Subtraction}}[/tex]

[tex]\large\text{\bf{(10 - 343) - 2 * 6}}\\\large\text{\bf{10 - 343 = -333}}\\\large\text{\bf{(-333) - 2 * 6}}\\\large\text{\bf{2 * 6 = 12}}\\\large\text{\bf{(-333) - 12 = -345}}\\\boxed{\boxed{\large\text{\bf{Answer: -345}}}}\huge\checkmark[/tex]

[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Identify the diameter of circle A

AB
AS
BT
TS

Answers

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Circles.

Since we know that, diameter is always twice of radius, and also one important point that,

A diameter is the longest chord of the circle passing from the centre of the circle, hence here,

BT is the diameter of the circle,

option c.) BT

Answer:

BT

Step-by-step explanation:

This is because a line which passes through the centre of a circle and falls on the circumference is called the diameter.

Melanie's fruit punch recipe calls for 6 cups of apple juice for every 3 cups of carrot juice. How many cups of carrot juice are used for each cup of apple juice?​

Answers

Answer:

1/2 cup carrot juice for every cup of apple juice

Step-by-step explanation:

Answer:

1/2 cup carrot juice for every cup of apple juice

Step-by-step explanation:

6:3 6 dived by 6 is 1 and 3 dived by 6 is 0.5 also known as 1/2

what’s four times a number (algebra wise)

Answers

Answer:

4x

Step-by-step explanation:

In Mr. Richard's class, 5/8 of the students like
to bake. Of those students, one-half prefer to
bake cookies. What fraction of the students
prefer to bake cookies?

Answers

Do you have answer choices?

Please do all of the attachments, quick. It is due please
First one with the right answer gets brainlest, and I will give extra points please.

Answers

First attachment = 3
Second attachment = -7
Third attachment = 25

Que es una ecuación cuadrática

Answers

Step-by-step explanation:

En álgebra, una ecuación cuadrática es cualquier ecuación que se puede reorganizar en forma estándar como ax ^ {2} + bx + c = 0 donde x representa una incógnita, y a, byc representan números conocidos, donde a ≠ 0. Si a = 0, entonces la ecuación es lineal, no cuadrática, ya que no hay término ax ^ 2.

Find the slope.

Bonus: Write the equation of the line.

Answers

Answer:

1 so y=1+b

Step-by-step explanation:

9514 1404 393

Answer:

slope: -1equation: y = -x +3

Step-by-step explanation:

The slope is the ratio of "rise" to "run". The "rise" is the vertical distance between two points; the "run" is the corresponding horizontal distance.

Here, we see point A is (0, 3) and point B is (1, 2). Then the "rise" is 2 -3 = -1, while the "run" is 1 - 0 = 1. The slope is the ratio ...

  m = rise/run = -1/1 = -1

The slope of the line is -1.

__

The point A is the y-intercept, where the line crosses the y-axis. It tells us the value of y is 3 when x=0. So, we can write the equation in slope-intercept form as ...

  y = mx + b . . . . . where m is the slope (-1) and b is the y-intercept (+3)

  y = -x +3

Is 4x-10y=2 equal to 4x-3y=0?

Answers

Answer:

No it is not

Step-by-step explanation:

What is y if x is 0?

Answers

Answer: is there a picture or something i can see to help you?

No pictures ? I don’t know

Write the equation in standard form using integers.

Answers

Answer:

it would be:

3x-4y=-8

Step-by-step explanation:

Jessica earned $14 by baby sitting 4 hours
What's Jessica rate and Jessica's Unit Rate?

Answers

Answer:

$3.50

Step-by-step explanation:

14 ÷ 4 = 3.5

good luck, i hope this helps :)

Solve the inequality.
-3.25y <-61.75

Answers

Step-by-step explanation:

-3.25y < -61.75

-3.25y < -61.75

-3.25. -3.25

whenever an inequality is divided by a negative number the sign changes, so if the sign of the inequality is greater than( > ) it becomes less than( < ) or the other way around. In this case the less than will be greater than.

y > 19 , S.S= [ 20,21,22,23.....]

Lily and Matthew are walking from home to school. Matthew has to return a library book on the way and follows the sidewalk. Lily walks directly to school. Assume the path they take forms a right triangle. Use the lengths in the diagram to determine how far Lily walks. Round your answer to the nearest tenth of a mile. Show your work and explain how you determined your answer. 20 points btw

Answers

I think it’s 0.1875 ❤️

How did the Great Depression impact European nations?

Answers

It impacted the nations by America not making trades
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