Which set of values could be from a direct proportion?

Answer:

The integers are -13 and -12

Step-by-step explanation:

Let

x ----> the first consecutive negative integer

x+1 ----> the second consecutive negative integer

we know that

[tex]x(x+1)=156[/tex]

Apply the distributive property

[tex]x^2+x=156\\x^2+x-156=0[/tex]

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

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

in this problem we have

[tex]x^2+x-156=0[/tex]  

so

[tex]a=1\\b=1\\c=-156[/tex]

substitute in the formula

[tex]x=\frac{-1(+/-)\sqrt{1^{2}-4(1)(-156)}} {2(1)}[/tex]

[tex]x=\frac{-1(+/-)\sqrt{625}} {2}[/tex]

[tex]x=\frac{-1(+/-)25} {2}[/tex]

[tex]x_1=\frac{-1(+)25} {2}=12[/tex]  ----> the solution cannot be a positive number

[tex]x_1=\frac{-1(-)25} {2}=-13[/tex]

therefore

[tex]x=-13\\x+1=-12[/tex]

Answer:

32 chairs in each row

The drawing will help.

To find out how many chairs are in each row, divide the total number of chairs by the number of rows. In this case, there are 16 rows and 512 chairs in total, so there are 32 chairs in each row.

To find out how many chairs are in each row, you need to divide the total number of chairs by the number of rows. In this case, there are 16 rows and 512 chairs in total. So, you can divide 512 by 16 to find out how many chairs are in each row. The result is 32. Therefore, there are 32 chairs in each row of the auditorium.

https://brainly.com/question/1396063

#SPJ2

Answer:

x=-3

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

A

A.K.A – 3.

Step-by-step explanation:

The dimensions of the tennis court are:

Length = 14 m

Length = 14 mWidth = 10 m

Let the width be y.

From the question given above,

The length is 6 meters less than twice it’s width. This can be obtained written as:

Area = 140 m²

Dimension = Area = Length × width

140 = (2y – 6)y

140 = 2y² – 6y

Rearrange

2y² – 6y – 140 = 0

Divide through by 2

y² – 3y – 70 = 0

y² – 3y – 70 = 0

y² – 10y + 7y – 70 = 0

Factorize

y(y – 10) + 7(y – 10) = 0

(y – 10)(y + 7) = 0

y – 10 = 0 or y + 7 = 0

y = 10 or –7

Since measurement can not be negative,

Width = y = 10 m

Length = 2y – 6

y = 10

Length = 2(10) – 6 = 20 – 6

Therefore, the dimensions of the tennis court are

Length = 14 m

Length = 14 mWidth = 10 m

Learn more: https://brainly.com/question/20605232

Answer: C

Step-by-step explanation:

y<x-1

so you looking at the region below the line but not including it so graph c is good

Answer:

If you need proof here it is

Answer:

20/69=0.2898550724637...

Step-by-step explanation:

a calculator

The result of 7 divided by 24.15 is approximately 0.29 when rounded to two decimal places.

The student has inquired about the result of the mathematical operation, division, specifically what is 7 divided by 24.15. To solve this question, you simply divide 7 by 24.15 on a calculator or by manual long division. The answer is approximately 0.29 when rounded to two decimal places. It should be noted that the exact quotient might vary depending on the number of decimal places you consider.

https://brainly.com/question/2273245

#SPJ2

Answer:

The scale factor is 1/3

Step-by-step explanation:

we know that

The scale factor is equal to divide the length side of the image (square A'B'C'D') by the length side of the pre-image (square ABCD)

Let

z ---> the scale factor

x----> the length side of the image (square AB'C'D')

y----> the length side of the pre-image (square ABCD)

[tex]z=\frac{x}{y}[/tex]

we have

[tex]x=2\ units\\y=6\ units[/tex]

substitute

[tex]z=\frac{2}{6}[/tex]

simplify

[tex]z=\frac{1}{3}[/tex]

The scale factor is less than 1, so the dilation is a reduction

therefore

The scale factor is 1/3

Answer:

[tex]k=\pm9,p=-23[/tex]

Step-by-step explanation:

Given:

The equation is:

[tex]81y - 17 = k^2y + 6+p[/tex]

Here, the left hand side of the equation will be equal to that of the right hand side only if the coefficients of 'y' are same on both sides and the constant terms are also equal to each other.

Therefore,

[tex]81=k^2\ and\ -17=6+p[/tex]

Solving each for 'k' and 'p'.

[tex]k^2=81\\\textrm{Taking square root on both the sides}\\\sqrt{k^2}=\pm\sqrt{81}\\k=\pm9.......(\sqrt{81}=9)[/tex]

[tex]-17=6+p\\\textrm{Adding -6 on both the sides}\\-17-6=p+6-6\\p=-23[/tex]

Therefore, the values of 'k' are -9 and 9. Value of 'p' is -23.

Answer:

So each interior angle measurement of the regular triangle is 60 degrees.

Step-by-step explanation:

If the triangle is regular, this means all the side measurements are congruent to each other and that all the angle measurements are congruent to each other.

If the sum of the angles in a triangle is 180 degrees and you know they are each the same then you could either solve x+x+x=180 or know we are just dealings with an equiangular triangle in which all angles have measurement 60 degrees.

If need more convincing, let's actually solve:

x+x+x=180

3x=180

x=180/3

x=60

So each interior angle measurement of the regular triangle is 60 degrees.

Answer:

Step-by-step explanation:

The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .

Answer:

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

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (3, 1) ← 2 points on the line

m = [tex]\frac{1-3}{3-0}[/tex] = - [tex]\frac{2}{3}[/tex]

Answer:

Both the zoo-keepers are correct.

Step-by-step explanation:

The first zoo keeper uses the equation:

x - 41.5 = 13.5

⇒ x = 13.5 + 14. 5 = 55

Now, the second zoo- keeper uses the equation:

41.5 + 13.5 = x

⇒ x = 55

Both use x = 55.

Answer:

Both zookeepers are correct because they have equivalent equations. Both of the equations will give a healthy speed of 55 km/hr

Step-by-step explanation:

examples response

Answer:

the last one

(-15)x12

hope this helps!

Answer:4000 deposit times 0.5 interest is 2,000. 2,000 x4 = 8,000 for 4 years.

Step-by-step explanation:

Answer:

6y^3+17y^2+22y+15

Step-by-step explanation:

(2y+3)(3y^2+4y+5)

6y^3+8y^2+10y+9y^2+12y+15

6y^3+17y^2+22y+15

Answer:

B. 6y^3+17y^2+22y+15

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

The whole circumference (i.e complete circle) is an arc which measures 360°

in our case, it is given that our arc measures only 30°

the fraction of our arc of 30° to the complete circle of 360° is

30/360

= 3/36

= 1/12

Answer:

x=5

Step-by-step explanation:

so to isolate the x you dived the -3 to both sides

so it will now be

x=5 because a negative times or divided by a negative equals a positive so to prove that x=5

-3(5)=-15

which is true

Step-by-step explanation:

Let the mass of the person be [tex]m[/tex].

Let the spring constant be [tex]k[/tex].

Let the displacement in spring be [tex]x[/tex]

Let the acceleration due to gravity be [tex]g[/tex]

As it is given that the person just stands,the forces are balanced.

So,[tex]mg=kx[/tex]

Given,

[tex]m=60Kg\\k=2500Nm^{-1}\\g=9.8ms^{-2}[/tex]

[tex]60\times 9.8=2500\times x\\x=\frac{588}{2500}=0.2352m[/tex]

According to the map, each line is 10 feet.

A is 4 lines from the one marked 30 ft.

4 x 10 = 40 feet.

30 +40 = 70 feet.

The answer is 70 feet.

Answer:

B

Step-by-step explanation:

Square root of 72=

8.485281474

A. 6

B. 6 square root 2=

8.485281474

C. 36

D. square root of 6=

2.449489743

Answer:42000

Step-by-step explanation:

There is no number higher than 5 after the thousands so you would keep it the same

Solving the inequality [tex]-x+8>6[/tex] we get [tex]x<2[/tex]

Step-by-step explanation:

We need to find the value of x from the inequality [tex]-x+8>6[/tex]

Solving:

[tex]-x+8>6[/tex]

Subtract 8 on both sides:

[tex]-x+8-8>6-8[/tex]

[tex]-x>-2[/tex]

Divide both sides by (-1). For doing this the sign of inequality is reversed i.e, > is changed into <

[tex]x<2[/tex]

So, Solving the inequality [tex]-x+8>6[/tex] we get [tex]x<2[/tex]

Keywords: Solving inequalities

Learn more about Solving inequalities at:

#learnwithBrainly

Answer:

x(x-5) = 14

x^2-5x-14 = 0

x^2 -7x+2x-14=0

x(x-7)+2(x-7)=0

(x+2)(x-7)=0

x = -2, 7

Hope this helps!

The most you will pay for renting the bicycle for at most 5 hours is $40.

The total cost of renting a bicycle for h hours is given by the function c = 8h, where c represents the total cost and h represents the number of hours rented. In this case, you figure you can rent a bicycle for at most 5 hours. To find the most that you will pay, substitute h = 5 into the function c = 8h:

c = 8(5) = 40

Therefore, the most you will pay for renting the bicycle for at most 5 hours is $40.

https://brainly.com/question/33617658?referrer=searchResults

#SPJ2

Vi walks 2 miles on first day, 2 miles on second day, 8 miles on third and fourth day and 1 mile on fifth day.

Step-by-step explanation:

Let,

x be the distance walked by Vi.

Therefore,

On first day = x

Second day = x

On days three and four,Vi walks twice as long as on the first two days

Third and fourth day = 2(x+x) = 2(2x) = 4x

On fifth day = half of first day = [tex]\frac{1}{2}x[/tex] = 0.5x

Total distance = 13 miles

Therefore,

[tex]x+x+4x+0.5x =13\\6.5x=13[/tex]

Dividing both sides by 6.5

[tex]\frac{6.5x}{6.5}=\frac{13}{6.5}\\x=2[/tex]

Distance on first day = x = 2 miles

second day = x = 2 miles

third and fourth day = 4x = 4(2) = 8 miles

fifth day = 0.5x = 0.5(2) = 1 miles

Vi walks 2 miles on first day, 2 miles on second day, 8 miles on third and fourth day and 1 mile on fifth day.

Keywords: distance, addition

Learn more about distance at:

#LearnwithBrainly

Answer:

Greater than the original value because it increases is more than the decrease

Step-by-step explanation:

Answer:

Overall, a 200% increase.

Step-by-step explanation:

Quantity after a 50% increase would be 1.50x, where x is the starting value.

if a 33.33% increase were to follow, then the final quantity would be

1.3333(1.50x), or just barely under 2x (representing an increase of 200% in x).

Answer:

1 1/8 cup of brown sugar.

Step-by-step explanation:

Here is the correct question: A recipe calls for 3/4 cup brown sugar for  each 2/3 cup white sugar. How many cups of  brown sugar per cup of white sugar is this?    

Given: 3/4 cup of brown sugar for each 2/3 cup of white sugar.

Finding requirement of brown sugar for 1 cup of white sugar.

∴ Each 2/3 cup of white sugar require 3/4 cup of brown sugar.    

Now, 1 cup of white sugar require brown sugar = [tex]\frac{\frac{3}{4} }{\frac{2}{3} } cups[/tex]

 = [tex]\frac{3}{4} \times \frac{3}{2} = \frac{9}{8} \ cup[/tex]

Thus, we can say [tex]\frac{9}{8}[/tex] = 1 1/8 cup of brown sugar is required per cup of white sugar.

Answer:

[tex]\frac{1}{48}[/tex]th

Step-by-step explanation:

Let X cookies are sold at the local bake sale.

So,

[tex]\frac{X}{4}[/tex] cookies will be made by Kim.

Now,

Given is One-third of her cookies are chocolate chip.

So, One-third of [tex]\frac{X}{4}[/tex]  will be chocolate chip

Which is [tex]\frac{X}{12}[/tex].

Out of whixh one-fourth have nuts.

So,[tex]\frac{X}{48}[/tex] cookies will be having nuts.

So, [tex]\frac{1}{48}[/tex]th of the Total cookies at the bake (X) will be having nuts.

Answer:

A. is False

B. is True

C. is False

D. is False

Step-by-step explanation:

Its absolute value so that means all numbers are now positive only with the ones that are with the double lines

Answer:

Subtract equation 1 from equation 2

Step-by-step explanation:

Solve the following system:

{3 x + 4 y = 12 | (equation 1)

3 x = 2 y - 8 | (equation 2)

Express the system in standard form:

{3 x + 4 y = 12 | (equation 1)

3 x - 2 y = -8 | (equation 2)

Subtract equation 1 from equation 2:

{3 x + 4 y = 12 | (equation 1)

0 x - 6 y = -20 | (equation 2)

Divide equation 2 by -2:

{3 x + 4 y = 12 | (equation 1)

0 x+3 y = 10 | (equation 2)

Divide equation 2 by 3:

{3 x + 4 y = 12 | (equation 1)

0 x+y = 10/3 | (equation 2)

Subtract 4 × (equation 2) from equation 1:

{3 x+0 y = (-4)/3 | (equation 1)

0 x+y = 10/3 | (equation 2)

Divide equation 1 by 3:

{x+0 y = (-4)/9 | (equation 1)

0 x+y = 10/3 | (equation 2)

Collect results:

Answer:  {x = -4/9 , y = 10/3