The square of the sum of six and a number

Answer: 197

Step-by-step explanation: I took the test :)))

Since this is an arithmetic sequence, you can conclude that the addition to the number is constant.

Let x = the number asked

       k = constant number added to the sequence

7 + k = x

x + k = 17

Solve the system of equation:

7 + k + k = 17

7 + 2k = 17

2k = 10

k = 5

Therefore, the missing number is 12 (7 + 5).

The amount that goes into the principal when friend pays you $200.00 at the end of the first month is $296.56.

The first interest will be:

= 1137.45 × (0.036/12)

= 3.41

The amount owed at the month end will be:

= 1137.45 + 3.41

= 1140.86

The new balance after 200 payment will be:

= 1140.86 - 200

= 940.86

Therefore, the reduction in principal will be:

= 1137.45 - 940.86

= 196.59

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Answer: is b. log57 + 5log5a

Susan and Joseph can fix 17 broken cars together in 12 hours.

To calculate the time it takes for Susan and Joseph to fix 17 broken cars together, we can calculate their individual rates of work.

Susan takes 3 hours to fix 2 cars, so her rate is 2/3 cars per hour.

Joseph takes 4 hours to fix 3 cars, so his rate is 3/4 cars per hour.

When they work together, their rates are additive. So their combined rate is (2/3 + 3/4) cars per hour. This is equal to (8/12 + 9/12) cars per hour, which simplifies to 17/12 cars per hour.

To find the time it takes to fix 17 cars, we can divide the number of cars by the combined rate: 17 cars / (17/12 cars per hour) = 12 hours.

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After 19 years, the final amount is $29,936.93, to the nearest dollar.

The formula for exponential growth:

[tex]final amount = initial amount * (rate)^(number of time periods)[/tex]

In this case, the initial amount is $7,200, the rate is 2 (since the money doubles every 8 years), and the number of time periods is 19/8=2.375 (since 19 years is 2.375 times the 8-year doubling period). Plugging these values into the formula, we get:

final amount = $7,200 * 2^2.375

The final amount is $29,936.93, to the nearest dollar.

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The exponential equation for this situation is y = 110(0.9) ^x. This is because 110 is the principal or the initial number of horses and y is the resultant population after a certain number of years X with a rate of 0.9.  Note that the rate is less than 1 which means that the population is decreasing as time goes by.

Answer:

The person is right.

Step-by-step explanation:

Look at his profile.

To solve this word problem, set up the equation (1/5) x + (1/10) x = 42 and solve for x. The team scored 140 points.

To solve this word problem, we can start by letting the total number of points scored by the team be represented by 'x'. Since Michaela scored one-fifth of the team's points, her score can be represented as (1/5)x. Similarly, Aleah's score can be represented as (1/10)x. Together, their scores add up to 42 points, so we can set up the equation:

(1/5)x + (1/10)x = 42

To simplify the equation, we can find a common denominator of 10:

(2/10) x + (1/10) x = 42

Combining like terms, we get:

(3/10) x = 42

To isolate x, we can multiply both sides of the equation by 10/3:

x = 42 * (10/3)

Simplifying further, we get:

x = 140

Therefore, the team scored 140 points.

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Question

Answer

EF = 32

1. B

2. D

3. C

4. A

5. B

ESKETIT

Answer:

Step-by-step explanation:

We will make a substitution to make our work easier (when we get there).  We also need to know that

[tex]i^2=-1[/tex]

We will use that as another substitution.  First, let's make the job of factoring a bit easier.  Here's the first substitution.  We will let

[tex]x^4=u^2[/tex]

Therefore,

[tex]x^2=u[/tex]

Now we will write the polynomial in terms of u instead of x:

[tex]f(x)=u^2+21u-100[/tex]

Solve for the values of u by setting the polynomial equal to 0 and factoring.  When you factor, you will get:

[tex](u+25)(u-4)[/tex]

But don't forget that

[tex]x^2=u[/tex]

so we have to put those back in now:

[tex](x^2+25)(x^2-4)=0[/tex]

By the Zero Product Property, either

[tex]x^2+25=0[/tex] or

[tex]x^2-4=0[/tex]

We will factor the first term.  Solving for x-squared gives us:

[tex]x^2=-25[/tex] and

x = ±√-25

which simplifies down to

x = ±√-1 × 25

we can sub in an i-squared for the -1:

x = ±√[tex]i^2*25[/tex]

The square root of i-squared is "i" and the square root of 25 is 5, so

x = ±5i

The next one is a bit easier.  If

[tex]x^2=4[/tex], then

x = ±2

You can see you have 4 solutions.  But you knew that already, since this is a 4th degree polynomial.  The types of solutions are:  2 real, 2 imaginary

Answer:

A. [tex]y=2x[/tex]

Step-by-step explanation:

We are asked to find the equation that represents a direct variation.

We know that a direct variation is in form [tex]y=kx[/tex], where y is directly proportional to x and k is constant of variation.

Upon looking at our given choices, we can see that equation [tex]y=2x[/tex] represents direct variation, where [tex]k=2[/tex].

Therefore, option A is the correct choice.

C. 4.59

Significant digits are digits expressing precision of a measurement. Non-zero digits are always significant but zeroes can be either included or ignored. For instance, zeroes that comes before other digits aren't significant. For example 0.058 has two significant digits. In this exercise, we have two numbers:

12.0875

7.50

The number 12.0875 has five significant digits while 7.50 has three significant digits. If we add or subtract two numbers, the least number of decimal places (that isn't the same as significant digits) in any of the two numbers must be the same as the number of decimal places in the result. Hence, for 12.0875 we have four decimal places and for 7.50 we have two decimal places. Therefore, the result must have two decimal places:

12.0875 - 7.50 = 4.59