Solve this quadratic equation by completing the square.

Answer:

c

Step-by-step explanation:

Answer:

C.) 3/2

Explanation:

PLATO

Answer:

$2,830.09

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 5.8/100

r = 0.058 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 2,000.00(1 + 0.058/12)(12)(6)

A = 2,000.00(1 + 0.004833333)(72)

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $2,000.00 at a rate of 5.8% per year compounded 12 times per year over 6 years is $2,830.09.

The question asks about the amount of money Haley would have after 6 years, saving $2000 in an account earning 5.8% interest compounded monthly. Using the compound interest formula, she would have approximately $2780.73.

This question deals with a financial concept known as compound interest. The formula for compound interest is A = P(1+r/n)^(nt), where A is the amount that the principal P has grown to after n number of times compounded over t periods at an interest rate of r. To calculate how much money Haley has, plug in the values: P=$2000, r=5.8/100=0.058, n=12 (since interest is compounded monthly), and t=6 years.

Therefore, the money Haley has is A=$2000 (1+0.058/12)^(12×6) ≈ $2780.73. Thus, after 6 years, Haley has approximately $2780.73, due to the monthly compounded interest of her savings.

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Answer:

The slope is 2

Step-by-step explanation:

To find the slope given two points, we use the formula

m = (y2-y1)/(x2-x1)

   = (-4--2)/(2-3)

   = (-4+2)/(2-3)

   = -2/-1

   = 2

Answer:  7.2

Step-by-step explanation:

Use pythag. here: a(a)+b(b)=c(c)

4(4)=16

6(6)=36

16+36= 52

The square root of 52 is your answer: 7.21110255093. You can round this to 7.2

Answer:ANS.B

Step-by-step explanation:1/3*3/4=3/12=.25 THE BETTER DEAL

3/12-2/10=30/120-24/120=6/120=1/20 ANS.B

Answer: 10

Step-by-step explanation:

We know that in the binomial expansion of [tex](a+b)^n[/tex], the total number of terms = n+1

For the binomial expansion of [tex](3x + 5)^9[/tex] , n= 9

Then, the  total number of terms in binomial expansion of [tex](3x + 5)^9[/tex] will be :-

[tex]n+1=9+1=10[/tex]

Hence, there are 10  terms are in the binomial expansion of [tex](3x +5)^9[/tex].

Answer:

The answer is x^2-4x+1

Step-by-step explanation:

For this case, we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend, until reaching the remainder.

It must be fulfilled that:

Dividend = Quotient * Divider + Remainder

Answer:

Option C

See attached image

Answer:

x = 3

Step-by-step explanation:

5x−7=8

Add 7 to each side

5x-7+7 = 8+7

5x = 15

Divide by 5

5x/5 = 15/5

x=3

Answer:

1 2/3 pages per minute

Step-by-step explanation:

1) 10/6 = 1.6666666666666 = 1 2/3

Final answer:

To calculate the printing time per page for a color printer, divide the total printing time by the number of pages. In this case, it takes 0.6 minutes to print one page.

Explanation:

To find out how many minutes it takes to print one page on a color printer that prints 10 pages in 6 minutes, we can use time quantification. We divide the total time taken to print the pages by the number of pages printed. So, performing the calculation:

Identify the total time taken for a known number of pages: 6 minutes for 10 pages.

Divide the total time by the number of pages to find the time per page: 6 minutes \/ 10 pages = 0.6 minutes per page.

Hence, the printer takes 0.6 minutes to print one page.

The solution to the inequality is [tex]\(x > -9\)[/tex]. Therefore, the option b is correct.

To solve the inequality [tex]\(-3x - 7 < 20\)[/tex], we'll isolate the variable [tex]\(x\)[/tex] step by step.

Given inequality:

[tex]\[ -3x - 7 < 20 \][/tex]

Add 7 to both sides of the inequality:

[tex]\[ -3x < 20 + 7 \ \\\\\\[ -3x < 27 \][/tex]

Now, divide both sides by [tex]\(-3\)[/tex]. Remember, when dividing or multiplying by a negative number, we need to reverse the inequality sign:

[tex]\[ x > \frac{27}{-3} \ \\\\\\[ x > -9 \][/tex]

The solution to the inequality is [tex]\(x > -9\)[/tex]. This means that any value of [tex]\(x\)[/tex] that is greater than -9 satisfies the inequality [tex]\(-3x - 7 < 20\)[/tex].

Answer:

b less than or equal to -2.

Step-by-step explanation:

- 2/3 (9+12b) ≥ 10

-6 - 8b ≥ 10

-8b ≥ 16

b ≤ -2.    ( Note the inequality sign flips as we are dividing by a negative).

In order to add the numbers 9.73 and 21.6 correctly, follow the steps below:

Step 1: Write the numbers so that the decimal points are aligned. If the numbers have a different number of decimal places, you can add zeros to the end of one of the numbers so that they both have the same number of decimal places. This doesn't change the value of the number, but it makes them easier to add.

```
 9.73
+21.60
```

Step 2: You begin adding from the rightmost digit and move to the left, regrouping (carrying over) as necessary.

Starting with the rightmost decimal digits, you have:

```
 3 (from 9.73)
+ 0 (from 21.60 because we added a zero to match the number of decimal places)
```

Adding these together, you simply get 3 since 3 + 0 = 3.

Step 3: Now add the second rightmost decimal digits:

```
 7 (from 9.73)
+ 6 (from 21.60)
```

Adding these together, 7 + 6 = 13, so you write down the 3 and carry over the 1 to the next higher place value.

Step 4: Add the digits to the left of the decimal point next, remembering to add any carried over value:

```
 1 (carried over from the previous step)
+ 9 (from 9.73)
+ 1 (from 21.60, there's no decimal here but we align based on the decimal point)
```

This gives us 1 + 9 + 1 = 11. So we place the 1 right to the left of the decimal point and carry over the other 1.

Step 5: Continue to the next highest place value:

Since there is no other digit in 9.73 at this place value, we can simply add what we have:

```
 1 (carried over from the previous step)
+ 0 (since there is no other digit in 9.73)
+ 2 (from 21.60)
```

This gives us 1 + 0 + 2 = 3.

Now, combine all of the numbers we've placed:

```
 31.33
```

So, the correct way to add 9.73 and 21.6 is to align the digits on the decimal point and add from right to left, regrouping as necessary. This corresponds to answer choice D.

Answer:

31 / 12

Step-by-step explanation:

To get the perimeter, just add up all the sides of the parallelogram, so 5/8 + 5/8 + 2/3 + 2/3 = 31/12

Answer:

Hello everyone, the answer is 2, edge 2022. Hoped I helped :)

Step-by-step explanation:

Final answer:

There are 4 cups in 1 quart of milk.

Explanation:

In 1 half quart of milk, there are 2 cups. To find out how many cups are in 1 quart of milk, we can set up a proportion:

2 cups / 1 half quart = x cups / 1 quart

Cross multiplying, we get:

2 * 1 quart = 1 half quart * x cups

2 quarts = 0.5 quarts * x cups

Dividing both sides by 0.5 quart, we find that:

x = 2 * 2 = 4

Therefore, there are 4 cups in 1 quart of milk.

Answer:  The correct option is (B) [tex]a_n=3n+9.[/tex]

Step-by-step explanation:  We are given to select the equation that represents the nth term of the following sequence :

12,   15,   18,   21,  .    .   .

We see that

the given sequence is an arithmetic one with first term a = 12  and common difference d given by

d = 15 - 12 = 18 - 15 = 21 - 18 =  .   .   .   =3.

We know that

the nth term of an arithmetic sequence with first term a and common difference d is given by

[tex]a_n=a+(n-1)d.[/tex]

Therefore, the nth term of the given sequence is

[tex]a_n=a+(n-1)d=12+(n-1)\times3=12+3n-3=3n+9.[/tex]

Thus, the required nth term of the given sequence is [tex]a_n=3n+9.[/tex]

Option (B) is CORRECT.

Answer:

Area= 206.202 cm squared

Step-by-step explanation:

Formula for area of Circle=

[tex]\pi r ^{2} [/tex]

Now we will input the value:

[tex]\pi (8.1)^{2} [/tex]

And, calculate the answer

[tex]3.14 \: \times 65.61[/tex]

[tex] = 206.0154[/tex]

Answer:

[tex]area = 206.0154[/tex]

I'm not sure if you need the rounded up answer or not, so I kept the answer in exact form.

Answer:  The required simplified answer in standard form is [tex]8y^6-88y^5-6y^3+61y^2+55y.[/tex]

Step-by-step explanation:  We are given to multiply the following polynomials and write the answer is standard form :

[tex]M=(-6y+8y^4-5)(y^2-11y)~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To multiply the given polynomials, we need to multiply each term of one polynomial to each term of the other polynomial.

From (i), we have

[tex]M\\\\=(-6y+8y^4-5)(y^2-11y)\\\\=y^2(-6y+8y^4-5)-11y(-6y+8y^4-5)\\\\=-6y^3+8y^6-5y^2+66y^2-88y^5+55y\\\\=8y^6-88y^5-6y^3+61y^2+55y.[/tex]

Thus, the required simplified answer in standard form is [tex]8y^6-88y^5-6y^3+61y^2+55y.[/tex]

Answer: 8y^6- 88y^5- 6y^3 +61y^2 +55y

Answer:

(g°f)x =16 when x = 5

Step-by-step explanation:

It might be easier to understand if you wrote this the other acceptable way.

g(x) = x^4

f(x) = 2x - 8

g(f(x))  means that in g(x) wherever you see and x you put f(x)

g(f(x)) = (f(x) ) ^ 4 Now put in the general value for f(x)

g(2x - 8) = (2x - 8)^4

You really don't want to expand this (although it would give you the right answer eventually).

g(2*5 - 8) = (2 * 5 - 8)^4

g(2*5 - 8) = (10 - 8)^4

g(2*5 - 8) = 2^4

Answer 16

Answer:

c=25

Step-by-step explanation:

x^2 + 10x+c

To find the value of c, take the coefficient of the x term, divide it by 2, then square it

10/2 =5

Then square it

5^2 =25

c=25

Answer:

B and D

Step-by-step explanation:

Given a line with slope m = - [tex]\frac{3}{5}[/tex]

Since the lines are parallel we require the points with the same slope

Using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = 8, 8) and (x₂, y₂ ) = (2, 2)

m = [tex]\frac{2-8}{2-8}[/tex] = 1 ← not parallel

Repeat with (x₁, y₁ ) = (5, - 1) and (x₂, y₂ ) = (0, 2)

m = [tex]\frac{2+1}{0-5}[/tex] = - [tex]\frac{3}{5}[/tex] ← Parallel

with (x₁, y₁ ) = (- 3, 6) and (x₂, y₂ ) = (6, - 9)

m = [tex]\frac{-9-6}{6+3}[/tex] = - [tex]\frac{5}{3}[/tex] ← not parallel

with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (3, - 2)

m = [tex]\frac{-2-1}{3+2}[/tex] = - [tex]\frac{3}{5}[/tex] ← Parallel

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (5, 5)

m = [tex]\frac{5-2}{5-0}[/tex] = [tex]\frac{3}{5}[/tex] ← not parallel

The ordered pairs (-5, -1) and (0, 2); (0,2) and (5,5) could be points on a parallel line because they have the same slope according to the slope formula.

In Mathematics, to find whether two points could be on a parallel line, we first need to understand the concept of slope. The slope of a line is determined by the ratio of the vertical change (delta y) to the horizontal change (delta x) between any two points on a line. It is often expressed as 'rise over run'.

If two lines are parallel, they have the same slope. Now, let's check the given ordered pairs. Using the slope formula (slope = (y₂-y₁) / (x₂-x₁)), you find the slope between each set of points:

From the calculation, (-5, -1) and (0, 2) have the same slope with (0,2) and (5,5). Therefore, the lines passing through these pairs of points are parallel to each other.

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Answer:

2

4

8

increases

Step-by-step explanation:

The average rate of change between x-values can be calculated by using the formula [tex](f(x2) - f(x1))/(x2 - x1).[/tex]. For x = 1 and x = 2, the rate is 2; for x = 2 and x = 3, the rate is -4; and for x = 3 and x = 4, the rate is 8.

The question asks about the average rate of change between certain points on an x-axis. In mathematics, the average rate of change is calculated by dividing the change in the output by the change in the input. In other words, it reflects how much the function's value (y-coordinate) changes when the input (x-coordinate) moves 1 unit.

To find the average rate of change, use the formula [tex](f(x2) - f(x1))/(x2 - x1).[/tex] In this case:

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Answer:

g = 8.  (Answer C)

Step-by-step explanation:

We are given 8/3 = g/3.

If we multiply both sides by 3, this will eliminate the fractions, and we will be left with g = 8.  (Answer C).

The solution to the proportion 8/3 = g/3 is g = 8, corresponding to option C.

In this proportion, the value of g can be found by solving the equation 8/3 = g/3. Because both sides of the equation are divided by 3, the 3's essentially cancel each other out, leaving you with g = 8.

Therefore, the solution to the proportion 8/3 = g/3 is g = 8. So, the correct answer is C. 8.

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Answer:

40(1.25-t)

Step-by-step explanation:

There are 3 components to consider; time, speed and distance

Time and Speed are given.

The distance has to be calculated.

Distance for trip to home

Speed = Distance/Time

40 = Total Distance/1.25-t

Total Distance = 40(1.25-t)

Therefore, 40(1.25-t) is the correct answer.

!!

Answer:

Option C. 40(1.25 - t)

Step-by-step explanation:

Eduardo's average speed on his commute to work = 55 miles per hour

On the way home his average speed was = 40 miles per hour

Round trip took him 1.25 hours.

Let t be the total time taken by Eduardo for the trip to work.

Then time taken on the way home = Total time for round trip - Time taken from work to home

                                                          = (1.25 - t) hours

Average speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]

40 = [tex]\frac{\text{Distance}}{(1.25-t)}[/tex]

Now the distance for his trip home can be represented by

Distance = 40(1.25 - t)

Option C. 40(1.25 - t) will be he answer.

Answer:

x^3 - x^2 - 17x + 12

Step-by-step explanation:

To multiply two polynomials together, first multiply each term of one polynomial by each term of the other polynomial. Then, collect like terms.

(x + 4)(x^2 - 5x + 3) =

Multiply x by each term of x^2 - 5x + 3. Multiply 4 by each term of x^2 - 5x + 3.

= x^3 - 5x^2 + 3x + 4x^2 - 20x + 12

Now collect like terms and write them in descending order of degree.

= x^3 - x^2 - 17x + 12

Answer:

x^3-x^2-17x+12

Step-by-step explanation:

Answer:

[tex]\displaystyle 3w+9-6r[/tex]

Step-by-step explanation:

Distributive property: A(B+C)=AB+AC

Group like terms.

[tex]\displaystyle-5r-r+3w+7+2[/tex]

Add the numbers from left to right.

[tex]\displaystyle-5r-r=-6r[/tex]

[tex]\displaystyle -6r+3w+7+2[/tex]

Finally, add the numbers from left to right, to find the answer.

[tex]2+7=9[/tex]

[tex]\displaystyle 3w+9-6r[/tex], is the correct answer.

Hope this helps!

Answer:

3w - 6r +9

Step-by-step explanation:

3w+7-5r+2-r​

Combine like terms

3w   -5r-r  +7+2

3w - 6r +9

Let x = angle we must find

tan x = 14/30

arctan(tan x) = arctan(14/30)

x = 25.0168934781

Answer: 25 degrees

Answer:

See explanation

Step-by-step explanation:

Let x be the number of spade shovels, y -the number of flat shovels and z - the number of square showels sold that day.

The store keeps an inventory of 80 shovels, then

x+y+z=80

The store always buy twice as many spade shovels as square, so

x=2z

The total cost of all shovels is

16x+9.60y+12.80z=1,072

a) The system of three equations is

[tex]\left\{\begin{array}{l}x+y+z=80\\ \\x=2z\\ \\16x+9.60y+12.80z=1,072\end{array}\right.[/tex]

b) In matrix form this is

[tex]\left(\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 16&9.60&12.80\end{array}\right)\cdot \left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}80\\0\\1,072\end{array}\right)[/tex]

c) The determinant is

[tex]\left\|\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 16&9.60&12.80\end{array}\right\|=0-32+9.60-0+19.20-12.80=-16[/tex]

d) Find three determinants:

[tex]\left\|\begin{array}{ccc}80&1&1\\ 0&0&-2\\ 1,072&9.60&12.80\end{array}\right\|=0-2,144+0-0+1,536-0=-608[/tex]

[tex]\left\|\begin{array}{ccc}1&80&1\\ 1&0&-2\\ 16&1,072&12.80\end{array}\right\|=0-2,560+1,072-0+2,144-1,024=-368[/tex]

[tex]\left\|\begin{array}{ccc}1&1&80\\ 1&0&0\\ 16&9.60&1,072\end{array}\right\|=0+0+768-0-0-1,072=-304[/tex]

So,

[tex]x=\dfrac{-608}{-16}=38\\ \\y=\dfrac{-368}{-16}=23\\ \\z=\dfrac{-304}{-16}=19[/tex]

e) If the store doubled all prices and inventory, then the new matrix is

[tex]\left(\begin{array}{ccc}1&1&1\\ 1&0&-2\\ 32&19.20&25.60\end{array}\right)\cdot \left(\begin{array}{c}x\\y\\z\end{array}\right)=\left(\begin{array}{c}160\\0\\2,144\end{array}\right)[/tex]