can you rearrange it so T is the subject

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:

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:

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:

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:

Step-by-step explanation:

A function is a relation between sets that associates to every element of a first set exactly one element of the second set.

Each element from the first set is assigned exactly one element from the second set.

It's not a function, because for 0 are assigned two elements 1 and 3.

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

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:

the last one

(-15)x12

hope this helps!

Final answer:

The amount of each semi-annual interest payment that Mr. Davis receives for his fifty $1,000 bonds at an 8.5% annual interest rate is $2,125.

Explanation:

Mr. Davis purchased fifty $1,000 bonds at 96.50, and the annual interest rate is 8.5%.

To calculate the semi-annual interest payment on a bond, you first need to determine the annual interest amount per bond, and then divide it by two, because interest is paid semi-annually.

First, find the annual interest for a single bond: $1,000 x 0.085 = $85.

Since Mr. Davis owns 50 bonds, the total annual interest for all bonds is 50 x $85 = $4,250.

Now, to find the semi-annual interest payment, divide the total annual interest by 2:

$4,250 / 2 = $2,125.

Therefore, the amount of each semi-annual interest payment that Mr. Davis receives is $2,125.

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!

Answer:

the guy wire is 7.211 ft long

Step-by-step explanation:

Notice that we are in the presence of a right angle triangle formed by: the height (the standing 6 ft pole), the base (the distance from the pole to the anchoring point on the ground), and the actual guy wire. See attached image for reference.

Notice that since pole and ground are perpendicular to each other (at 90 degrees) , the guy wire forms what is called the "hypotenuse" (longest side) of the right angle triangle. We can therefore use the Pythagorean Theorem to solve this problem with the formula for the hypotenuse:

[tex]Hypotenuse=\sqrt{side1^2 +side2^2} \\Hypotenuse= \sqrt{6^2+4^2}\\Hypotenuse=\sqrt{36+16} \\Hypotenuse=\sqrt{52} \\Hypotenuse=7.2111\, ft[/tex]

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.

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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

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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

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Answer:

4/2=2

Step-by-step explanation:

Step-by-step explanation:

4/4 + 4/4

1 + 1

2

Amount owed at the end of 1 year is 3640

Given that yoko borrows $3500.

Rate of interest charged is 4% compounded each year

Need to determine amount owed at the end of 1 year.

In our case :

Borrowed Amount that is principal P = $3500

Rate of interest r = 4%

Duration = 1 year and as it is compounded yearly, number of times interest calculated in 1 year n = 1

Formula for Amount of compounded yearly is as follows:

[tex]A=p\left(1+\frac{r}{100}\right)^{n}[/tex]

Where "p" is the principal

"r" is the rate of interest

"n" is the number of years

Substituting the values in above formula we get

[tex]\mathrm{A}=3500\left(1+\frac{4}{100}\right)^{1}[/tex]

[tex]\begin{array}{l}{A=\frac{3500 \times 104}{100}} \\\\ {A=35 \times 104} \\\\ {A=3640}\end{array}[/tex]

Hence amount owed at the end of 1 year is 3640

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 stock is now worth  of $30.024.

Step-by-step explanation:

Here, the price of the stock last year =$36

The percentage down in the price of stock in a year  = 16.6 %

Now, 16.6% of the value of stock  $36  = [tex]\frac{16.6}{100}  \times 36= 5.976[/tex]

⇒16.6% of $36 =  $ 5.976

Now, the Current Worth of Stock = Stock Value last year - Decrease in the stock price

                                                         =  $36 - $ 5.976  = $30.024

Hence, the stock is now worth  of $30.024.

Answer:

6x^2-12x+6

Step-by-step explanation:

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

6x^2-6x-6x+6

6x^2-12x+6

The product of (2x - 2) and (3x - 3) using the FOIL method is 6x^2 - 12x + 6.

The expression (2x − 2)(3x – 3) can be considered as a product of two binomials and can be solved by applying the distributive property or the FOIL method - First, Outer, Inner, Last. We first distribute the 2x from the first binomial to each term in the second binomial (6x2 - 6x) and do the same with -2 (-6x + 6). Adding these together leads to 6x2 - 12x + 6, which is none of the options provided.

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Answer:

The side length of the square is 7 inches².

Step-by-step explanation:

Given:

The dimensions of the tiles are 2 x 3, 3 x 5, 1 x 4, and 4 x 6 to form a single square.

Now, to get the length of the square formed by the tiles. We need to get the area of the square.

Area of the square formed by the four tiles = [tex]2\times 3+3\times 5+1\times 4+4\times 6[/tex]

                                                                        = [tex]6+15+4+24[/tex]

                                                                        = [tex]49[/tex]

So, the area of the square is 49 inches².

Putting the formula of square for getting the side length:

Area of the square = side²

[tex]49=side^{2}[/tex]

using square root on both sides:

[tex]7=side[/tex]

Therefore, the side length of the square is 7 inches².

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.

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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:

[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:42000

Step-by-step explanation:

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

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:

B. There is one boy for every 6 girls in class.

Step-by-step explanation:

When you have a ratio, it compares two numbers. When you have a ratio 1:6 the colon (:) there can be read as "is to" or "for every".

That means that ratio can be read as 1 is to 6 or "there is 1 for every 6."

In this case 1:6 represents the number of boys to the number of girls to class. This means that there is 1 boy for every 6 girls in class.

Answer:

choose b or d

Step-by-step explanation:

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 pound of apples cost $3.69,

1 gallon of gasoline for $3.68,

1 magazine for $3.65,

1 sandwich for $3.62.

Step-by-step explanation:

40.59/11=3.69

44.16/12=3.68

54.75/15=3.65

50.68/14=3.62

11 pounds of apples for $40.59 Equation: t = $3.69n. 12 gallons of gasoline for $44.16 Equation: t = $3.68n. 15 magazines for $54.75 Equation: t = $3.65n. 14 sandwiches for $50.68 Equation: t = $3.62n with arrowBoth.

To match the proportional relationships to their corresponding equations:

1. 11 pounds of apples for $40.59

  - The cost per pound is [tex]\( \frac{40.59}{11} \approx 3.69 \).[/tex]

  - Equation: t = $3.69n

2. 12 gallons of gasoline for $44.16

  - The cost per gallon is [tex]\( \frac{44.16}{12} \approx 3.68 \).[/tex]

  - Equation: t = $3.68n

3. 15 magazines for $54.75

  - The cost per magazine is [tex]\( \frac{54.75}{15} \approx 3.65 \).[/tex]

  - Equation: t = $3.65n

4. 14 sandwiches for $50.68

  - The cost per sandwich is [tex]\( \frac{50.68}{14} \approx 3.62 \).[/tex]

  - Equation: t = $3.62n

In each case, the equation t = kn represents the proportional relationship, where k is the constant unit rate of cost per item. The arrowBoth indicates the direction of the proportional relationship.