-2x + 3 < 5

solve and show steps please

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:

3x + 9

Step-by-step explanation:

An equilateral triangle has all sides equal

Perimeter = 3 × (x + 3)

3x + 9

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

Answer:

Tom can cut 12 (15 inch pieces) from the two boards.

Step-by-step explanation:

We're first given foot measurements and we're asked to find the answer in inches. That means we must convert 8 feet to inches, which is a 1:12 inches conversion. 8 times 12 will give you 96, so now you will multiply that value by 2 because Tom has 2 8-foot long boards. That will give you 192 inches. Since the question is asking for 'how many 15 inch pieces he can cut from the two boards?', you will need to divide 192 inches by 15 to find the answer. This will give you 12.8 boards. Because you can't have parts of an object, the answer will be 12 whole boards.

Answer:

12.67 years

Step-by-step explanation:

Follow below steps;

To find out how long it takes for the value of the account to reach $6,730:

Calculate the formula for compound interest: A = P(1 + r/n)^(nt)

Plug in the values: $6,730 = $4,300(1 + 0.036/4)^(4t)

Solve for time(t): approximately t = 10.35 years, which rounded to the nearest year is 10 years

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:

"Domain of set B: {2, 4,-4, 0}"

Step-by-step explanation:

When it the set A,B,C (and others) are given in this form it means that the coordinate pairs are the domain and range of each set, respectively.

The first coordinate is part of the domain (x) and the second coordinate is part of the range (y).

For example, the domain of A is all the numbers that are the first in each coordinate pair, so domain of A would be 1, -1, and 6.

Likewise, the domain of B would be 2, 4, -4, and 0.

Hence,

Domain of set B: {2, 4,-4, 0}  --  is the correct answer.

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

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.

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:

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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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:

Step-by-step explanation:

[tex]n-number\ of\ hours\\\\\text{The equation of the function:}\\\\f(n)=0.25(n-1)+0.50\\\\\text{for n = 8:}\\\\f(8)=0.25(8-1)+0.50=0.25(7)+0.50=1.75+0.50=2.25[/tex]

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.

Let x = angle we must find

tan x = 14/30

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

x = 25.0168934781

Answer: 25 degrees

Answer:

8 to 53;45

Step-by-step explanation:

This is because 8 is the smallest and 53 is the biggest and the difference of 53-8 = 45

(please give brainliest)

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]

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

Step-by-step explanation:

1.List your assets (what you own), estimate the value of each, and add up the total.

2.List your liabilities (what you owe) and add up the outstanding balances.

3.Subtract your liabilities from your assets to determine your personal net worth.

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:  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:

c

Step-by-step explanation:

Answer:

C.) 3/2

Explanation:

PLATO

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:

x>-2

Step-by-step explanation:

I can't read or understand your choices... But you can only take log of positive numbers....

That is you need x+2 is to be positive.

That is as an inequality you need x+2>0

Solving x+2>0 gives you x>-2

Answer:

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

Step-by-step explanation:

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:

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:

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:

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.

Answer:

7740° / 45

Step-by-step explanation:

The sum of the interior angles is given by this formula: (n - 2) * 180°. So a regular 45-gon would have interior angles that add up to: (45 - 2) * 180°. = 43 * 180°. = 7740°. Now divide that by the 45 angles to find the measure of one interior angle

hope that helped :(

The measure of each exterior angle of a regular 45-gon is calculated using the formula: Exterior Angle = 360° / Number of Sides. Hence, each exterior angle of a 45-gon measures 8°.

In mathematics, the measure of each exterior angle of a regular polygon can be found using the formula: Exterior Angle = 360° / Number of Sides. So, to find the measure of an exterior angle in a 45-sided shape, or 45-gon, you would perform the calculation: 360° / 45 = 8°.

This indicates that each exterior angle of a regular 45-gon measures 8 degrees. This is a key concept to remember when working with regular polygons, as it can be used to determine other characteristics of the shape such as the sum of the exterior angles, which in any polygon is always 360°.

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