PLEASE HELP QUICK simplify (4x^2+12x-16/2x+10)/(6x+24/x^2+9x+20)

Answer:

The first year Sam invested $2,000. The third year sally invested $1,900.

Step-by-step explanation:

Let $x be the amount of money Sam invested the first year. The second year, he invested $2,000 less than 5/2 times the amount he invested the first year, then the second year he invested

[tex]\$\left(\dfrac{5}{2}x-2,000\right).[/tex]

The third year, he invested $1,000 more than 1/5 of the amount he invested the first year, then the third year he invested

[tex]\$\left(\dfrac{1}{5}x+1,000\right).[/tex]

During three years Sam invested

[tex]\$\left(x+\dfrac{5}{2}x-2,000+\dfrac{1}{5}x+1,000\right)=\$\left(\dfrac{37}{10}x-1,000\right).[/tex]

The first year, Sally invested $1,000 less than 3/2 times the amount Sam invested the first year, then the first year she invested

[tex]\$\left(\dfrac{3}{2}x-1,000\right).[/tex]

The second year, she invested $1,500 less than 2 times the amount Sam invested the first year, then the second year she invested

[tex]\$(2x-1,500).[/tex]

The third year, she invested $1,400 more than 1/4 of the amount Sam invested the first year, then the third year she invested

[tex]\$\left(\dfrac{1}{4}x+1,400\right).[/tex]

During three years Sally invested

[tex]\$\left(\dfrac{3}{2}x-1,000+2x-1,500+\dfrac{1}{4}x+1,400\right)=\$\left(\dfrac{15}{4}x-1,100\right).[/tex]

If Sam and Sally invested the same total amount at the end of three years, then

[tex]\dfrac{37}{10}x-1,000=\dfrac{15}{4}x-1,100,\\ \\\dfrac{37}{10}x-\dfrac{15}{4}x=1,000-1,100,\\ \\-\dfrac{1}{20}x=-100,\\ \\x=\$2,000.[/tex]

Thus,

[tex]\$\left(\dfrac{1}{4}\cdot 2,000+1,400\right)=\$1,900.[/tex]

Answer: Remainder: 206

Quotient: 3x³+7x²+21x+70 + [tex]\frac{206}{x-6}[/tex]

Step-by-step explanation: You can either use long division or synthetic division. I will use synthetic division: 3 | 3 -2 0 7 -4... the remainder is 206 and the quotient is 3x³+7x²+21x+70  + 206/x-6

The remainder is 206 and the quotient is ([tex]3x^{4} - 2x^{3} + 7x -4[/tex] -206) /(x - 3)

A result obtained by dividing one quantity by another is called a quotient.

Remainder is the value left after the division.

∴ Here the remainder will be putting x = 3 in the dividend.

So, remainder = [tex]3(3)^{4} - 2(3)^{3} + 7(3) - 4[/tex] = 206

in a division, dividend is equal to divisor multiplied by quotient plus remainder.

Let the quotient be Q(x)

Here,  we can write,

[tex]3x^{4} - 2x^{3} + 7x -4[/tex]  = (x - 3)Q(x) + 206

⇒ Q(x) = ([tex]3x^{4} - 2x^{3} + 7x -4[/tex] -206) / (x - 3)

So, the required quotient is  ([tex]3x^{4} - 2x^{3} + 7x -4[/tex] -206) / (x - 3)

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Answer:

RM  ≈ 6.08 ( to 2 dec. places )

Step-by-step explanation:

to calculate the distance use the distance formula

• d = √(x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = R(- 2, 3) and (x₂, y₂ ) = M(4, 2)

d = [tex]\sqrt{(4+2)^2+(2-3)^2}[/tex] = [tex]\sqrt{36+1}[/tex] = [tex]\sqrt{37}[/tex] ≈ 6.08

Answer:

Box-1:

Neither

Box-2:

[tex]8(t+8)[/tex]

Box-3:

[tex]8(t+8)[/tex]

Box-4:

[tex]8t+8[/tex]

Box-5:

Neither

Box-6:

[tex]8t+8[/tex]

Step-by-step explanation:

We can verify each box

Box-1:

[tex](8+t)+(8+8)[/tex]

we can simplify it by combining like terms

[tex]=8+t+8+8[/tex]

[tex]=8+t+16[/tex]

[tex]=t+24[/tex]

none of them matches

so, Neither

Box-2:

[tex]8t+64[/tex]

we can write as

[tex]8\times t+8\times 8[/tex]

now, we can factor out 8

[tex]8(t+8)[/tex]

Box-3:

[tex]8\cdot t+8\cdot 8[/tex]

we can factor out 8

[tex]8(t+8)[/tex]

Box-4:

[tex]4t+8+4t[/tex]

we can combine like terms

[tex]4t+4t+8[/tex]

[tex]8t+8[/tex]

Box-5:

[tex]8t+16[/tex]

we can factor common term

[tex]8\times t+8\times 2[/tex]

now, we can factor out 8

[tex]8(t+2)[/tex]

so, we can see that none are matching

so, Neither

Box-6:

[tex]4(2t+2)[/tex]

we can distribute 4

[tex]4\times 2t+4\times 2[/tex]

we can simplify it

[tex]8t+8[/tex]

simple answer

8(t+8):

(8 • t) + (8 • 8)

8t + 64.

8t + 8:

4t + 8 + 4t

4(2t + 2)

Neither:

(8 + t) + (8 + 8)

8t + 16

pls mark brainlist

Answer: 13

Step-by-step explanation:

f(x) = 4x + 1

f(3) = 4(3) + 1

     = 12 + 1

     = 13

Answer:

Step-by-step explanation:

She paid $40 each week, hence the "w" next to 40. She then paid $12.50 so both $40w and $12.50 would equal to $492.50. So she paid $492.50 in all for the class.

Now the w would equal, 12. Multiply 40 x 12 and it'd equal 480. 

Then you add the additional $12.50 she paid for the registration & it'd equal to $492.50.

Hope That Helps!

To solve for w in the equation 40w + 12.50 = 492.50, subtract 12.50 from both sides of the equation and then divide both sides by 40.

To solve for w, we need to isolate it on one side of the equation. We can do this by subtracting 12.50 from both sides of the equation:

40w + 12.50 - 12.50 = 492.50 - 12.50

This simplifies to:

40w = 480

Next, divide both sides of the equation by 40:

w = 480 / 40

w = 12

Therefore, the equation represents a situation where w is equal to 12.

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Answer:

4 x (3+7) = (4 x 5) + (4 x 5) => 40= 20+20

Step-by-step explanation:

12+28=>40=(4 x 5) + (4 x 5)

Answer:

A jagged curve

Step-by-step explanation:

Your always going to burn calories but the rate will always change and how many based on what you do will always change so it is never a constant slope.

Answer:

a jagged curve

Step-by-step explanation:

The number of calories you burn varies throughout the day, increasing and decreasing. A jagged curve represents increases and decreases over time.

Answer:25%

Step-by-step explanation:

(10 x 100) - 800= 200

200/800 x 100

percantage profit= 25%

Answer:

80%

Step-by-step explanation:

800 ÷ 100 = 8$ → purchased each

8$ to 10$ = 80%

Answer: The first vendor AKA the 8 ears for $2.56

Step-by-step explanation:

You have to take the 8 and figure out how much you are being charged for each 2.56 divided by 8 is .32, so each ear is .32 cents per ear, and the second vendor is 4.32 divided by 12 which is .36, so each ear is .36 cents. so technically the first vendor has cheaper corn.

Answer:

1. C

2. B

3. B

4. C

5. A

Step-by-step explanation:

1. 2/5 times 3/7 equals 6/35 and cannot be simplified

2. 9/10 times 5/7 equals 45/70 or 9/14

3. 1/3 times 1/2 equals 1/6

4. 3/4 times 1/2 equals 3/8

5. 2/3 of 7/8 equals 7/12

Answer:

52.94  miles per unit

Step-by-step explanation:

The unit rate is found by dividing miles per time

90 miles /1.7 unit

52.94117647  miles per unit

We must first open the parenthesis. We get 15*7+15y, or 105+15y. We can now add 12 to 105 which would be 117. Now we have -4-5y+117+15y. With this we can move the -4 to 117 which is 113 and the -5y to 15y which is 10y. So we got 113+10y as our answer.

Hope this helps. <3

Answer:

a(5) = 7

Step-by-step explanation:

Look at 5 on the n line, the horizontal line look up to the dot on that line.  Whats it value on the vertical line a(n)?  7 so a(5) = 7

Answer:

$105.48

Step-by-step explanation:

Multiply 131.85 by 0.2 to get 20% of 131.85.

You will get 26.37.

Since it is 4 people, multiply by 4.

You will get $105.48.

Answer: $105.48

Step-by-step explanation: If the check is $131.85, all you have to do is multiply that by .2 and you get $26.37, but since there are four friends you would have to multiply that by 4 to get the result $105.48.

Because AC lies opposite the angle of the smaller measure than the angle opposite FH. The sides at these angles have the same length.

Answer:

The two angles are each 31 degrees.

Step-by-step explanation:

Find x

3x + 10

5x - 4

By setting 3x+10 equal to 5x-4, we find x=7. Substituting this value back into the expressions for both angles 1 and 2, we find that both angles measure 31 degrees, confirming that our solution is correct.

The question asks you to solve for the degree measure of both angles 1 and 2, which are represented by the expressions (3x+10)° and (5x-4)° respectively. Because these angles are vertical, we know that they are congruent, or equal in measure.

Therefore, we can form an equation by setting the two expressions equal to each other and then solving for x:

(3x+10) = (5x-4)

Subtracting 3x from both sides yields:

10 = 2x - 4

Then, adding 4 to both sides, we get 14 = 2x. Dividing both sides by 2, we find x = 7.

To check our work, we substitute x = 7 into the original equations for both angle 1 and angle 2:

Angle 1: 3(7) + 10 = 31°

Angle 2: 5(7) - 4 = 31°

As you can see, the degree measures are the same, which verifies that we solved for the variable correctly.

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Answer:

[tex]log_n(m)= \frac{4}{3}[/tex]

Step-by-step explanation:

N^4/3=m

[tex]n^{4/3}=m[/tex]

We need to write the equation in logarithmic form

we take log on both sides

[tex]log(n^{4/3})=log(m)[/tex]

We apply log property to remove the exponent 4/3

As per log property we can move exponent before log

log(a^m) = m log (a)

So our equation becomes

[tex]\frac{4}{3}log(n)=log(m)[/tex]

Now we divide both sides by log(n)

[tex]\frac{4}{3} =\frac{log(m)}{log(n)}[/tex]

Now we apply change of base formula

log(a)/ log(b)= log_b(a)

[tex]\frac{4}{3} =log_n(m)[/tex]

So log form is

[tex]log_n(m)= \frac{4}{3}[/tex]

To convert [tex]N^{4/3}[/tex] = m to logarithmic form, identify the base (N), the exponent (4/3), and the result (m). The logarithmic form is [tex]log_N(m)[/tex] = 4/3.

To convert the given equation [tex]N^{4/3}[/tex] = m into logarithmic form, we'll follow these steps:

The general logarithmic form of the equation aᵇ = c is [tex]log_a(c)[/tex] = b.

Applying this to our equation:

Hence, the logarithmic form of the equation [tex]N^{4/3}[/tex] = m is:

Answer:

x=2, y=2

(2,2)

Step-by-step explanation:

To solve by elimination, we need to have on variable an its coefficient be the opposite of the other

I will multiply the second equation by 2 to make 2x  become 4x to eliminate the x variable

2(2x+4y) = 12*2

4x+8y = 24

Now add the first equation with the modified second equation

-4x - 2y = -12

4x   +8y =24

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

       6y   = 12

Divide each side by 6

6y/6 = 12/6

y =2

Now we need to find x

2x+4y = 12

Substitute in y=2

2*x + 4*2 = 12

2x+8 = 12

Subtract 8 from each side

2x +8-8 = 12-8

2x=4

Divide each side by 2

2x/2 =4/2

x=2

one may note that 1 CC, Cubic Centimeter, or 1 cm³, is actually equivalent to 1 mL, milliliter.

so 2 cc = 2 mL.

Answer:

2 mL

Step-by-step explanation:

Here cm³ and  mL are units of volume i.e., the three dimensional space enclosed by plane surfaces. m³ is the SI unit of volume. Liter (L) is also an accepted unit where

1 L = 0.001 m³

So 1 ml = 0.001 × 10⁻³ m³

1 mL³ = 10⁻⁶ m³             (1)

1 m³ = 10⁶ cm³

1 cm³ = 10⁻⁶ m³             (2)

From equation 1 and 2

1 mL = 1 cm³

1 mL = 1 cc

2 cc = 2 Cubic centimeter = 2 cm³

1 cc = 1 mL

So,

2 cc = 2 mL

Answer:

       = 1099  cm^2

Step-by-step explanation:

The surface area of a cylinder is found by using the formula

SA=2πrh+2πr^2

We know the diameter.  To find the radius, we take the diameter and divide by 2.

r =d/2

r =14 cm/2 = 7 cm

h = 18 cm

Substituting what we know

SA = 2 * pi * 18 * 7 + 2 * pi * (7)^2

    = 252 *pi + 2* pi *49

   = 252 pi + 98 pi

  = 350 * pi

Let pi be approximated by 3.14

 SA = 350 * 3.14

       = 1099  cm^2

Answer:

64

Step-by-step explanation:

20 x 3.2=64

16/5=3.2

replacing the 3 1/5 with 3.2 making it easier to do the math

Answer:

The answer is 64

Step-by-step explanation:

What to do is this.

Turn 3 1/5 into a improper fraction and it will look like this 16/5

Now do 20/1 times 16/5 and you will get 64

Answer: 8

Step-by-step explanation:

Answer:

The correct answer is A) slope: -13 Intercept: 1

Step-by-step explanation:

When you have something in slope-intercept form, the slope is always the coefficient of x, which in this case is -13.

The intercept is always the constant at the end of the equation, which in this case is 1.

Answer:

a)

Step-by-step explanation:

Answer:

B.$941.11

Hope this helped

Step-by-step explanation:

Answer:

5/8=0.625

Step-by-step explanation:

Answer:

m ≥ 1016

Step-by-step explanation:

13+0.06M≥73.96

0.06M ≥ 60.96

m ≥ 1016

Answer:

8(2p-1)

Step-by-step explanation:

To factor the expression, we need to factor the terms

16p = 8*2*p

8 = 8*1

We can factor out an 8,  leaving what remains inside the parentheses

16p-8

8(2p-1)

Final answer:

(m-p)(x) represents the subtraction of function p(x) from m(x). Assuming p(x) is -4x + 2, (m-p)(x) simplifies to 7x - 4.

Explanation:

To calculate (m-p)(x), we need to subtract the function p(x) from the function m(x).

Given m(x) = 3x - 2 and noting there seems to be an error in p(x), as it should likely be a function of x, let's assume the student meant p(x) = -4x + 2 based on the pattern of the provided information.

The subtraction of these two functions is performed as follows:

m(x) - p(x) = (3x - 2) - (-4x + 2)

Simplify by distributing the negative sign through the second polynomial:

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

Combine like terms:

7x - 4

So, (m-p)(x) = 7x - 4.