What is the product of all constants $k$ such that the quadratic $x^2 + kx +15$ can be factored in the form $(x+a)(x+b)$, where $a$ and $b$ are integers?

Answer:

[tex]3\%[/tex] p.a.

Step-by-step explanation:

The formula for simple interest is [tex]I=PRT[/tex] ([tex]I =[/tex] interest, [tex]P =[/tex] principal, [tex]R =[/tex] rate)

First, let's express the interest earned in one and three years:

[tex]I_{1} = PRT_{1}[/tex] (finding the interest earnt in one year)

[tex]I_{1} = \$ 500\times R \times 1[/tex]

[tex]=\$ 500R[/tex]

[tex]I_{2} = PRT_{2}[/tex] (finding the interest earnt in three years)

[tex]I_2 = \$ 500 \times R \times 3[/tex]

[tex]=\$ 1500R[/tex]

From the information "The difference between the total interest earned after 3 years and the total interest earned after 1 year is $30", we can write:

[tex]I_{2}-I_{1} = \$ 30[/tex]

[tex]\$ 1500R - \$500 R = \$ 30[/tex]

[tex]\$ 1000R = \$ 30[/tex]

[tex]R = 0.03[/tex]

[tex]=3\%[/tex] p.a.

∴ The annual interest rate is [tex]3\%[/tex]

Hope this helps :)

The annual interest rate if You deposit $500 in an account that earns simple interest. The difference between the total interest earned after 3 years and the total interest earned after 1 year is $30 is 3%.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

The principal amount, P = $500,

Time, t = 1 year and T = 3 year,

Calculate the interest by the formula given below,

[tex]SI = P\times R\times T / 100[/tex]

Here, SI is the simple interest.

So for 1 year time,

Substitute the values,

SI = 500 × R × 1 / 100

SI = 5R

Now for 3 year

SI = 15R

But 15R - 5R = 30 (Given in question)

R = 3%

Therefore, the annual interest rate if You deposit $500 in an account that earns simple interest. The difference between the total interest earned after 3 years and the total interest earned after 1 year is $30 is 3%.

To know more about interest:

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Answer:

2 hours

Step-by-step explanation:

First, we notice that the time taken to paint a fence is inversely proportional to the number people used because as the number of people increase, the time taken to paint the fence decreases.

5 people can paint a fence in 4 hours.

1 person can paint a fence in = 5 x 4

                                                = 20 hours

10 people can paint the fence in = 20/10

                                                      = 2 hours

plz mark as brainliest

Answer:

Step-by-step explanation:

x = 5

Answer:

x=5

Step-by-step explanation:

Answer:

The total cost of making the tank equals $2,082.48

Step-by-step explanation:

Giving the following information:

The tank requires 208 sq ft of material at $9.29 per square foot.

It also requires 4.5 hours of labor at $26.40 per hour plus 1.6 hours of labor at $19.60 per hour.

To calculate the total cost, we need to multiply the unitary variable cost by the total amounts:

Direct material= 9.29*208= $1,932.32

Direct labor= 4.5*26.4 + 1.6*19.6= $150.16

The total cost of making the tank equals $2,082.48

Answer:

x = 3

y= 12

Step-by-step explanation:

2x + 2y = 30

y - 4x = 0  /*2

2x + 2y = 30

2y - 8x = 0

-----------------

10x = 30

x = 3

y= 12

Answer:

( 3 , 12 )

Step-by-step explanation:

2x + 2y = 30 and y - 4x = 0 are two given equation

Name The equation

2x + 2y = 30 ...(1)

y - 4x = 0

y = 4x ...(2)

Now, Put the value of y in equation 1

2x + 2y = 30

2x + 2(4x) = 30

2x + 8x = 30

10x = 30

x = 30/10

x = 3

Now,

Put the value of x in equation 2

y = 4x

y = 4(3)

y = 12

Thus, The value of x is 3 and the value of y is 12

2x + 2y = 30 ...(1)

2(3) + 2(12) = 30

6 + 24 = 30

30 = 30

y = 4x ...(2)

12 = 4(3)

12 = 12

Hence, L.H.S = R.H.S

-TheUnknownScientist

Answer:

it just died because of natural causes haha

Step-by-step explanation:

Answer:

uhhh maybe because it got old or lack of care for they sheep or it got hunted ;-;

Step-by-step explanation:

Answer:can I see the answer for the drop down box..

Step-by-step explanation:

Answer: The answer is they left about 24% of the tip

Step-by-step explanation: Find 15% of the total number, add 20 to it, then divide by the total bill

Answer:

I don't know nothing about this lol...

Step-by-step explanation:

Answer: The above Table 1 will calculate the population size (N) after a certain length of time (t). All you need to do is plug in the initial population number (No), the growth rate (r) and the length of time (t). The constant (e) is already entered into the equation. It stands for the base of the natural logarithms (approximately 2.71828). Growth rate (r) and time (t) must be expressed in the same unit of time, such as years, days, hours or minutes. For humans, population growth rate is based on one year. If a population of people grew from 1000 to 1040 in one year, then the percent increase or annual growth rate is 40/1000 x 100 = 4 percent. Another way to show this natural growth rate is to subtract the death rate from the birth rate during one year and convert this into a percentage. If the birth rate during one year is 52 per 1000 and the death rate is 12 per 1000, then the annual growth of this population is 52 - 12 = 40 per 1000. The natural growth rate for this population is 40/1000 x 100 = 4%. It is called natural growth rate because it is based on birth rate and death rate only, not on immigration or emigration. The growth rate for bacterial colonies is expressed in minutes, because bacteria can divide asexually and double their total number every 20 minutes. In the case of wolffia (the world's smallest flowering plant and Mr. Wolffia's favorite organism), population growth is expressed in days or hours.

Each wolffia plant is shaped like a microscopic green football with a flat top. An average individual plant of the Asian species W. globosa, or the equally minute Australian species W. angusta, is small enough to pass through the eye of an ordinary sewing needle, and 5,000 plants could easily fit into thimble.

See Straight Pin & Sewing Needle Used In Wayne's Word Articles

There are more than 230,000 species of described flowering plants in the world, and they range in size from diminutive alpine daisies only a few inches tall to massive eucalyptus trees in Australia over 300 feet (100 m) tall. But the undisputed world's smallest flowering plants belong to the genus Wolffia, minute rootless plants that float at the surface of quiet streams and ponds. Two of the smallest species are the Asian W. globosa and the Australian W. angusta. An average individual plant is 0.6 mm long (1/42 of an inch) and 0.3 mm wide (1/85th of an inch). It weighs about 150 micrograms (1/190,000 of an ounce), or the approximate weight of 2-3 grains of table salt. One plant is 165,000 times shorter than the tallest Australian eucalyptus (Eucalyptus regnans) and seven trillion times lighter than the most massive giant sequoia (Sequoiadendron giganteum).

See Photo Of Massive Giant Sequoia Tree

See Photo Of The Australian Wolffia angusta

See Photo Of The Indian Wolffia microscopica

See Additional Color Images Of Wolffia Species

The growth rate for Wolffia microscopica may be calculated from its doubling time of 30 hours = 1.25 days. In the above population growth equation (N = Noe rt), when rt = .695 the original starting population (No) will double. Therefore a simple equation (rt = .695) can be used to solve for r and t. The growth rate (r) can be determined by simply dividing .695 by t (r = .695 /t). Since the doubling time (t) for Wolffia microscopica is 1.25 days, the growth rate (r) is .695/1.25 x 100 = 56 percent. Try plugging in the following numbers into the above table: No = 1, r = 56 and t = 16. Note: When using a calculator, the value for r should always be expressed as a decimal rather than a percent. The total number of wolffia plants after 16 days is 7,785. This exponential growth is shown in the following graph where population size (Y-axis) is compared with time in days (X-axis). Exponential growth produces a characteristic J-shaped curve because the population keeps on doubling until it gradually curves upward into a very steep incline. If the graph were plotted logarithmically rather than exponentially, it would assume a straight line extending upward from left to right.

Sixteen days of exponential growth in Wolffia microscopica.

Wolffia plants have the fastest population growth rate of any member of the kingdom Plantae. Under optimal conditions, a single plant of the Indian species Wolffia microscopica may reproduce vegetatively by budding every 30 hours. One minute plant could mathematically give rise to one nonillion plants or 1 x 1030 (one followed by 30 zeros) in about four months, with a spherical volume roughly equivalent to the size of the planet earth! Note: This is purely a mathematical projection and in reality could never happen!

Step-by-step explanation:

Answer:

x= -1/5

hope this helps you

Answer:

x = - [tex]\frac{1}{5}[/tex], x = 5

Step-by-step explanation:

Given

[tex]\frac{x+1}{x-1}[/tex] - [tex]\frac{x-1}{x+1}[/tex] = [tex]\frac{5}{6}[/tex]

Multiply through by 6(x - 1)(x + 1) [ the LCM of the denominators ]

6(x + 1)² - 6(x - 1)² = 5(x - 1)(x + 1) ← expand factors and simplify

6(x² + 2x + 1) - 6(x² - 2x + 1) = 5(x² - 1)

6x² + 12x + 6 - 6x² + 12x - 6 = 5x² - 5

24x = 5x² - 5 ( subtract 24x from both sides )

0 = 5x² - 24x - 5 ← in standard form

0 = (x - 5)(5x + 1) ← in factored form

Equate each factor to zero and solve for x

5x + 1 = 0 ⇒ 5x = - 1 ⇒ x = - [tex]\frac{1}{5}[/tex]

x - 5 = 0 ⇒ x = 5

Step-by-step explanation:

$9.99 + $0.35t <= $12

$0.35t <= $2.01

t <= 5.74

The most number of toppings would be 5.

Answer:

9.99 + 0.35t ≤ 12

5 toppings

Step-by-step explanation:

First part of question:

9.99 + 0.35t ≤ 12

"At most" means you use ≤.

Second part of question:

Take the inequality and solve for t:

9.99 + 0.35t ≤ 12

0.35t ≤ 2.01

t ≤ 5.74

So, the most number of toppings that a pizza can have and still be at most $12 is 5 toppings. You have to round down 5.74 to 5 otherwise the cost will exceed $12.

Answer:

I think option D.

Step-by-step explanation:

lmk if it's wrong

Answer:

149 in sq

Step-by-step explanation:

split in to the 3 rectengles

top right 6x(9-6)=18

middle rec 6×(10+6)=96

bottom rec. 5x7=35

total 149

Answer:

area = 149 in.²

Answer:

he's getting the ps5

Step-by-step explanation:

In conclusion if the store has the ps5 he's getting it and if not he wont

Answer:

Step-by-step explanation:

1 yard = 0.000568 miles

49280 yards = 28 miles

1 mile = 1,760 yards

Divide total feet by 1760

49,280 / 1760 = 28 miles.

Answer:

Both of the arrowed ones are the sides

Answer:

In technical terms, the slope of the line is the change in y over the change in x. But I just like to think of it as rise over run. To find the slope of the line, pick two points on the line.

Answer:

(3,0)

Step-by-step explanation:

Hope this helps

Answer:

y = 12

Step-by-step explanation:

Answer:

63 dm (aproximadamente)

Explicación paso a paso:

Dada a medida dos dous lados do triángulo: 54 dm e 32,4 dm.

Dado que se afirma que o terceiro lado é o hipoteno, que é o lado máis longo dun triángulo rectángulo, o hipoteno (h) pódese obter así:

h = sqrt (54 ^ 2 + 32,4 ^ 2)

h = sqrt (2916 + 1049,76)

h = sqrt (3965,76)

h = 62,974280

h = 63 dm (aproximadamente)

Answer:

5n + 300 ≥ 1000

Step-by-step explanation:

Answer: thousandths

9,000

Step-by-step explanation:

Answer: thousandths

Step-by-step explanation:

9,000

Answer:

3. f' ( x) = 5

4. d= 69.21

I hope i helped

Answer:

w=−12

Step-by-step explanation:

1

6

w+

5

8

=

−11

8

Step 2: Subtract 5/8 from both sides.

1

6

w+

5

8

−

5

8

=

−11

8

−

5

8

1

6

w=−2

Step 3: Multiply both sides by 6.

6*(

1

6

w)=(6)*(−2)

w=−12

Step-by-step explanation:

3 supervisors = 60 employees

=> 264 supervisors = 60 * (264/3) = 5,280 employees. (C)