What is the difference ? X/x^2-2x-15-4/x^2+2x-35

multiply both sides of the equation by 3.

2x+3y=9

move variable to the right side and change its sign

2x=9-3y

divide both sides of the equation by 2

x=9/2-3/2y

To find the 8th term of the pattern 1, 2, 5, 10, 17, analyze the differences between consecutive terms and find the common difference. Add that common difference to the 7th term to find the 8th term.

To analyze the pattern, we can observe that the difference between consecutive terms is increasing by 1 each time. Let's find the common difference:

From these differences, we can see that the common difference is increasing by 2 each time. So the difference between the 7th term and the 6th term would be 7 + 2 = 9. Using this pattern, we can find the 8th term:

Answer:

log(bsae(3))27=c

Step-by-step explanation:

a p e x

The logarithm equation is equivalent to the exponential equation is c = log₃27

A logarithm is the power to which a number must be raised in order to get some other number.

Given that, exponential equation, [tex]3^{c}[/tex]=27

By the exponential form of logarithm:

[tex]x^{a} =m[/tex] then logarithm form is a = logₓ m

Therefore,

[tex]3^{c}[/tex]=27

Taking logarithm both sides,

[tex]3^{c}[/tex]=27

c = log₃27

Hence, the logarithm equation is equivalent to the exponential equation is c = log₃27

Learn more about logarithm, click;

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He washes 7 cars and gets $4.00 for each one :

So it's the number of cars times the money he gets for each one - 7 times 4 = 28

He fills 10 bags of leaves and gets $1.00 for each bag:

So it's the number of bags times the money he gets for each one - 10 times 1 = 10

Than you add the money from the cars to the money of bags : $10 + $28 =

$38 total

Answer: $38.00

why; live

N x 7 +3 = 45

N = 6    Hope this helps.

Hi GueenSilia,

Answer: (n x 7) + 3

45 - 3 = 42

42 / 7 = n

n x 7 + 3 = 45

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

42 / 7 = 6

6 x 7 = 42

42 + 3 = 45

n = 6

To find f(2), look and see where the line crosses the Y axis, when The line is on X 2.

The line is on Y = -2, so the answer would be -2.

Answer:

[tex]y=3[/tex]

Step-by-step explanation:

Given figure is a rectangle.

In a rectangle , opposite sides are equal

to find out y we equate the opposite sides 10 and 2y+4

[tex]10=2y+4[/tex]

Subtract 4 from both sides

[tex]10-4=2y+4-4[/tex]

[tex]6= 2y[/tex]

Divide both sides by 2

[tex]y=3[/tex]

Final answer:

The equation of a vertical line passing through the point (5,2) is x = 5. This type of line has an undefined slope and is defined by its x-coordinate, not dependent on the y-coordinate.

Explanation:

The equation of a vertical line that passes through the point (5,2) can be determined by understanding that a vertical line has an undefined slope and does not depend on the y-coordinate for its location on a coordinate plane. Instead, a vertical line's location is solely determined by its x-coordinate. Therefore, the equation of a vertical line that passes through (5,2) will have the same x-coordinate for all its points. This means that the equation for the vertical line through (5,2) is simply x = 5.

This equation is different from the conventional y = mx + b, which defines a straight line with a slope m and y-intercept b. In the case of a vertical line, the slope is undefined, and therefore, the standard linear equation cannot be applied. Instead, the equation is independent of y and is expressed only in terms of the constant x-value of the vertical line.

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it will be 14 more minuted because she has completed 5/19 minutes it takes to reach the beach.. we can get this answer by taking the total number of minuted to get to the beach (19) and subtract the number of minutes she has already walked (5)..... our answer is that she has 14 minutes left till she reaches the beach.

Answer

It is Going To Take 14 Minutes

The elevation of Smallville is calculated by multiplying the elevation of Longfield by 4. Longfield's elevation is -144 1/2 feet, which is equivalent to -289/2 as an improper fraction. Multiplying this by 4 gives the elevation of Smallville as -578 feet.

To find Smallville's elevation, we first take the elevation of Longfield, which is -144 1/2 feet below sea level. Since Smallville is 4 times farther below sea level than Longfield, we have to multiply the elevation of Longfield by 4.

First, convert -144 1/2 to an improper fraction: -144 1/2 = -289/2.

Now, multiply by 4:

(-289/2) × 4 = -289 × 2 = -578 feet

So the elevation of Smallville is -578 feet below sea level.

9) [tex]3 + 5n = 1 + 8n + 2[/tex]  | subtract 5 on both sides, and solve 8n and -5n

[tex]3 = 1 + 3n + 2[/tex]  | combine like terms, add 2 and 1

[tex]3 = 3n + 3[/tex]  | subtract 3 on both sides, and solve 3 and -3

[tex]0 = 3n[/tex]  | divide by 3n

[tex]0 = n[/tex]  | final answer

10)  [tex]5x + 12 = 4x + 6[/tex]  | subtract 4x on both sides, solve -4x and 5x

[tex]x + 12 = 6[/tex]  | subtract 12 on both sides, solve -12 and 6

[tex]x = -6[/tex]  | final answer

11)   [tex]-8x - 4 = 7 (-2 - 4x) + 4x[/tex]  | distribute 7 into the parentheses

[tex]-8x - 4 = -14 - 28x + 4x[/tex]  | combine like terms

[tex]-8x - 4 = -14 - 24x[/tex]  | add 8x on both sides, and solve 8x and -24x

[tex]-4 = -14 - 16x[/tex]  | add -14 on both sides, and solve 14 and -4

[tex]10 = -16x[/tex]  | divide by -16 on both sides, and solve

[tex]-0.625 = x[/tex]  | final answer

12)   [tex]16 - 2n = - 8 + 4 (n - 3)[/tex]  | distribute 4 into the parentheses

[tex]16 - 2n = -8 + 4n - 12[/tex]  | combine like terms

[tex]16 - 2n = 4n - 4[/tex]  | add 2n on both sides, and solve 2n and 4n

[tex]16 = 6n - 4[/tex]  | add 4 on both sides, and solve 4 and 16

[tex]20 = 6n[/tex]  | divide by 6 on both sides, and solve

[tex]3.33333 = n[/tex] | final answer (repeated)

13)  [tex]-6 (3 - 6r) = -18 + 4r[/tex]  | distribute -6 into the parentheses

[tex]-18 + 36r = -18 + 4r[/tex]  | subtract 4r on both sides, solve 36r and -4r

[tex]-18 + 32r = -18[/tex]  | add -18 on both sides, solve -18 and 18

[tex]32r = 0[/tex]  | divide by 32 on both sides, and solve.

[tex]r = 0[/tex]  | final answer

14)   [tex]4 (3b - 1) = 9 - b[/tex]  | distribute 4 into the parentheses

[tex]12b - 4 = 9 - b[/tex]  | add -b on both sides, solbe 12 and b

[tex]13b - 4 = 9[/tex]  | add -4 on both sides, solve 9 and 4

[tex]13b = 13[/tex]  | divide 13 on both sides, solve

[tex]b = 1[/tex]  | final answer

15)   [tex]-6x + 7 (1 - x) = -4 (x - 4)[/tex]  | distribute 7 into parentheses

[tex]-6x + 7 - x = -4 (x - 4)[/tex]  | distribute -4 into the parentheses

[tex]-6x + 7 - x = -4x + 16[/tex]  | combine like terms

[tex]-5x + 7 = -4x + 16[/tex]  | add -4x on both sides, solve -5x and 4x

[tex]-x + 7 = 16[/tex]  | subtract 7 on both sides, solve 16 and -7

[tex]-x = 9[/tex]  | divide by -1 on both sides, solve

[tex]x = -9[/tex]  | final answer

16)   [tex]5 - (8v + 5) = -4 (1 + 3v)[/tex]  | distribute the - and -4 into the parentheses

[tex]5 - 8v - 5 = -4 - 12v[/tex]  | combine like terms

[tex]10 + 8v = -4 - 12v[/tex]  | add 12v on both sides, solve 12v and 8v

[tex]10 + 20v = -4[/tex]  | subtract 10 on both sides, solve -4 and -10

[tex]20v = - 14[/tex]  | divide 20 on both sides, and solve

[tex]v = -0.7[/tex]  | final answer

17)   [tex]-8 (4 + 4n) = 8 (n + 6)[/tex]  | distribute -8 and 8 into the parentheses

[tex]-32 - 32n = 8n + 48[/tex]  | add -32n to both sides, solve 32n and 8n

[tex]-32 = 40n + 48[/tex]  | subtract 48 on both sides, solve -32 and -48

[tex]-80 = 40n[/tex]  | divide -80 on both sides, and solve

[tex]-2 = n[/tex]  | final answer

UNDER CONSTRUCTION (I WILL EDIT WHILE YOU RECIEVE THE ANSWERS)

How to Get Answer for Number 9:

3+5n = 1+8n+2

5n+3=(8n)+(1+2)(Combine Like Terms)

5n+3=8n+3

Step 2: Subtract 8n from both sides.

5n+3−8n= 8n+3−8n

−3n+3=3

−3n+3−3=3−3

−3n=0

Answer: n = 0

[tex]\frac{-3n}{-3} =\frac{0}{-3}[/tex]

10.

5x + 12 − 4x = 4x + 6 − 4x

x + 12 = 6

x + 12 − 12 = 6 − 12

Answer: x = −6

11. Answer is also x = 0

(More answers will come as edited)

On Saturday Nikki and Tyler walked to the local farmers market Nikki bought 8 apples for $6 dollars and Tyler brought 3 fewer apples than Nikki. How much did Tyler spend on apples?​

Tyler brought 8 apples - 3 apples = 5 apples.​

​To calculate the price of 5 apples we have to establish a proportion :

If 8 apples cost $6​

Then 5 apples will cost $X​

​X = 5apples * $6/8apples = $3.75

​Answer : Tyler spent on apples $3.75

​Hope this helps!​​​​

[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​​

She rode her bike 10.2 mile the final week.

You simply just add all of the numbers together & subtract from 62.9 then get 10.2.

Hopefully this helps! :-)

Answer:

B is your best Bet

Step-by-step explanation:

for this problem, you would have to do B because thats the best bet compared to the other answers

Combine like terms:

4x, 7x, -10x

-10, 14, 2

4x + 7x - 10x = x

-10 + 14 + 2 = 6

6 + x should be the correct answer.

1st and 5th are true.

First, subtract 44 from the 96. You get 52. Then, divide 52 by 7 to figure out what each shirt costs. The answer is 52/7, or $7.43. She spent 7 dollars and 43 cents on each shirt.

19% turns into 20%

20%*41=8.2

Have a nice day.

[tex]3x\sqrt[3]{648x^4y^8}\\\\=3x\sqrt[3]{216\cdot3x^{3+1}y^{3+3+2}\\\\=3x\sqrt[3]{216}\cdot3x^3x^2y^3y^2y^2}\qquad|\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\3x\sqrt[3]{216}\cdot\sqrt[3]{x^3}\cdot\sqrt[3]{y^3}\cdot\sqrt[3]{y^3}\cdot\sqrt[3]3xy^2}\quuad|\text{use}\ \sqrt[3]{a^3}=a\\\\=3x(6)(x)(y)(y)\sqrt[3]{3xy^2}\\\\=18x^2y^2\sqrt[3]{3xy^2}\to\boxed{B.}[/tex]

Answer:

The medium-sized can is the cheaper by the oz, and is $0.005 per oz. cheaper.

Step-by-step explanation:

Medium can:  $0.92/(46 oz) = $0.020/oz

Large can:   $3.60 / (144 oz) = $0.025/oz

Surprisingly, the medium can price per oz. is lower than that of the large can.  The difference is $0.005 per oz.

The medium can of tomato juice has the lower unit price at $0.02 per ounce, which is $0.005 lower per ounce than the large can's unit price of $0.025 per ounce.

To determine which can of tomato juice has the lower unit price, we need to calculate the cost per ounce for each can. For the medium can, we divide the cost by the number of ounces:

Medium can unit price = $0.92 / 46 ounces = $0.02 per ounce

For the large can, we perform a similar calculation:

Large can unit price = $3.60 / 144 ounces = $0.025 per ounce

The medium can has a lower unit price of $0.02 per ounce compared to the large can's unit price of $0.025 per ounce. The difference in unit price is $0.025 - $0.02 = $0.005, or half a cent per ounce.

you have to divide 64 and 8

then you get the answer: 8 ounces per cup

1. expand using place value.

337,060 = 300,000 + 30,000 + 7,000 + 000 + 60 + 0

Next, we will use exponents:

300,000 = 3 * 10^5

30,000 = 3 * 10^4

7,000 = 7 * 10^3

000 = 0 * 10^2

60 = 6 * 10

0 = 0 * 10^0

then after combing these exponents, we can write the number as:

337,060 = 3 * 10^5 + 3 * 10^4 + 7 * 10^3 + 0 * 10^2 + 6 * 10 + 0 * 10^0

Finally, removing the meaningless zeroes, we would end up with:

337,060 = 3 * 10^5 + 3 * 10^4 + 7 * 10^3 + 6 * 10

5x-5=30

Add 5 to both of the sides

5x=35

Divide 5 to both of the sides

X=7

Answer: D. About [tex]\frac{1}{2}[/tex] inches per hour.

Step-by-step explanation:

1. The city received [tex]12^{\frac{1}{4}}[/tex] inches of rain in [tex]25^{\frac{1}{2}}[/tex] hours.

2. Let's write the mixed number as decimal numbers:

[tex]12^{\frac{1}{4}}in=12.25in[/tex]

[tex]25^{\frac{1}{2}}h=25.5h[/tex]

3. To find the approximate rainfall rate in inches per hour, you must divide 12.25 inches by  25.5 hours, as following:

[tex]\frac{12.25in}{25.5h}=0.48\frac{in}{h}[/tex]

4. If you round the result to the nearest tenth, you obtain:

[tex]0.5\frac{in}{h}=\frac{1}{2}\frac{in}{h}[/tex]

5. Therefore, the answer is the option D.

The approximate rainfall rate is closest to 0.5 inches per hour therefore the correct answer is Option D.

To determine the approximate rainfall rate in inches per hour, we need to divide the total amount of rainfall by the duration over which it fell.

Using the formula for intensity:

The approximate rainfall rate is closest to 0.5 inches per hour, so the correct answer is Option D: about 1/2 inch per hour.

The equation is [tex]\sqrt{x-2 \\ \\[/tex] -[tex]\sqrt{2x}[/tex] = [tex]\sqrt{x +2}[/tex]

Solution

Step 1:

Take square on both sides, we get

3x - 2[tex]\sqrt{x-2}[/tex][tex]\sqrt2{x}[/tex] -2 = x +2

Step 2:

Subtract 3x - 2 from both sides, we get

-2[tex]\sqrt{x-2} \sqrt{2x} = -2x + 4[/tex]

Step 3:

Again, square on both sides in order to get rid of the square root from the above equation, we get

[tex]8x^{2}-16x = 4x^{2} -16x +16[/tex]

Now we have to simplify it,

[tex]4x^{2} -16 = 0[/tex]

Step 4:

Now we have to solve this quadratic equation, in order to get the solution.

We get x = 2 and x = -2, When we verifying solution in the original given equation, the solution does not satisfy the equation.

Reason: We get negative number in the square root.

Therefore, it has no Roots.

Answer: b) No roots

Denise needs to buy 25/3 gallons of 85% ethanol and 35/3 gallons of 25% ethanol to have 20 gallons of 50% ethanol.

x | y | 20 gal

use x and y because you don't know how much she needs.

0.85x | 0.25y | 20(0.5)

85% is 85/100 or 0.85, and you need that much of x, same goes for the 25% and 50% mixtures

so now you can make up 2 equations

1) x + y = 20

2) 0.85x + 0.25y= 10 (you get 10 when you multiply 20 by 0.5)

now you can solve for x or y using substitution. first rewrite 1) in terms of x or y:

x+ y= 20 ----> y= 20 - x

now you can substitute 20- x for y in the second equation..

0.85x + 0.25y= 10

0.85x + 0.25(20-x)= 10 distribute here..(0.25 * 20 and 0.25 * (-x) )

0.85x + 5 - 0.25x = 10 combine like terms

0.6x +5 = 10 move the 5 over to the other side

0.6x= 10 -5

0.6x = 5 divide both sides by 0.6

x= 25/3 or 8.3 now you know the amount of x so you can substitue this back into the first equation to find y.

0.85x + 0.25y= 10

0.85(25/3) +0.25y= 10

85/12 + 0.25y= 10

0.25y = 10- 85/12

0.25y= 35/12

y= 35/3 or 11.6

you can check by putting these values into the euations:

1) x+ y= 20

25/3 + 35/3 =20

20= 20 good so far

2) 0.85x + 0.25y= 10

0.85(25/3) + 0.25(35/3)=10

10 = 10 so our values for x and y work