The solutions to the equation 2x^2+x-1=2 are x=-3/2 or x= __?__

Answer:

[tex]1\frac{7}{18}[/tex]  or one seven eighteenths

Step-by-step explanation:

we know that

12 one half times one nine is the same that multiply 12 one half by one nine

so

[tex](12\frac{1}{2})(\frac{1}{9})[/tex]

Convert mixed number to an improper fraction

[tex]12\frac{1}{2}=12+\frac{1}{2}=\frac{12*2+1}{2}=\frac{25}{2}[/tex]

substitute

[tex](\frac{25}{2})(\frac{1}{9})=\frac{25}{18}[/tex]

Convert to mixed number

[tex]\frac{25}{18}=\frac{18}{18}+\frac{7}{18}=1\frac{7}{18}[/tex]

therefore

12 one half times one nine is one seven eighteenths

By using the tangent function tan(31°) = opposite/adjacent, and knowing the rock's height of 555 meters, we can find the distance from the rock that Archimedes should sleep to wake up with direct sunlight. The distance is calculated as the height of the rock divided by the tangent of the angle of the sun, which will give the desired result.

To find out how far from the rock Archimedes went to sleep, we can use the concept of trigonometry. Specifically, we will use the tangent function, which relates the angle of the sun to the height of the rock and the distance of the shadow on the ground.

Given that the sunshine angle is 31 degrees and the rock is 555 meters tall, we can set up our equation using the tangent function: tan(31°) = opposite/adjacent, where the opposite side is the height of the rock, and the adjacent side is the distance from the rock where Archimedes slept.

The equation would look like this:

tan(31°) = 555 / distance

To solve for the distance, we rearrange the equation:

distance = 555 / tan(31°)

By calculating this, we would get the distance where Archimedes should sleep to be woken by the direct sunlight.

Answer:

24 hours

24 hours is the solution to 300=10(2)^t/15

After 24 hours the scientist expect to have 300 bacteria cells.

Given :

the number of cells to be given by the formula, where t is the number of hours since the experiment started.

[tex]C=100(2)^{\frac{t}{15} }[/tex]

't' represents the time taken for the cells to grow.

we need to find out the time taken to have 300 bacteria cells.

So, we replace C with 300 and solve for t

[tex]C=100(2)^{\frac{t}{15} }\\300=100(2)^{\frac{t}{15} }\\\frac{100\cdot \:2^{\frac{t}{15}}}{100}=\frac{300}{100}\\2^{\frac{t}{15}}=3\\\frac{t}{15}\ln \left(2\right)=\ln \left(3\right)\\t=\frac{15\ln \left(3\right)}{\ln \left(2\right)}\\t=23.77443[/tex]

So, it takes 24 hours to have 300 bacteria cells.

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Answer:

1

Step-by-step explanation:

Simplify the following:

(1/6)^0

Hint: | Any nonzero number to the zero power is one.

(1/6)^0 = 1:

Answer:  1

Answer:

The scale factor of the smaller rectangle to the larger rectangle is 3/2

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

To find out the scale factor of the smaller rectangle to the larger rectangle. set up a proportion

[tex]\frac{9}{6}=\frac{3}{2}[/tex] ----> ratio of corresponding heights

or

[tex]\frac{12}{8}=\frac{3}{2}[/tex] ----> ratio of corresponding bases

therefore

The scale factor of the smaller rectangle to the larger rectangle is 3/2

Answer:

i) angle 3 is 120°

ii) angle 3 + angle 4  = 180°  as both angles make up a staright line

    ∴  angle 4  = 180° - angle 3  = 180° - 120° = 60°

iii) angle 6 = angle 3  = 120°   as they are opposite interior angles

iv) angle 6 + angle 8  = 180°  as both angles make up a straight line  

   ∴  angle 8  = 180° - angle 6  = 180° - 120° = 60°

Step-by-step explanation:

i) angle 3 is 120°

ii) angle 3 + angle 4  = 180°  as both angles make up a staright line

    ∴  angle 4  = 180° - angle 3  = 180° - 120° = 60°

iii) angle 6 = angle 3  = 120°   as they are opposite interior angles

iv) angle 6 + angle 8  = 180°  as both angles make up a straight line  

   ∴  angle 8  = 180° - angle 6  = 180° - 120° = 60°

Lee sold 60 magazine

Step-by-step explanation:

Terrence and Lee were selling magazines for a charity

We need to find how many magazines Lee sold

Assume that Lee sold x magazines

∵ Terrance sold 30% more than Lee in the first week

∵ Lee sold x magazines in the first week

- Find 30% of x and add it to x to find how many magazines

  Terrance sold

∵ Terrance sold = 30% × x + x

∴ Terrance sold = [tex]\frac{30}{100}[/tex] × x + x = 0.3 x + x

∴ Terrance sold = 1.3 x magazines in the first week

∵ Terrance sold 12 magazines in the second week

- Add 1.3 x to 12 to find the number of magazines that Terrence

  sold in the two weeks

∴ Terrence sold 1.3 x + 12 magazines in the two weeks

∵ Lee did not sell any in the next week

∴ Lee sold x magazines in the two weeks

∵ Terrance sold 50% more than Lee by the end of the 2nd week

- Equate 1.3 x + 12 by the sum of x and 50% of x

∴ 1.3 x + 12 = 50% × x + x

∵ 50% × x = [tex]\frac{50}{100}[/tex] × x = 0.5 x

∴ 1.3 x + 12 = 0.5 x + x

- Add the like terms in the right hand side

∴ 1.3 x + 12 = 1.5 x

- Subtract 1.3 x from both sides

∴ 12 = 0.2 x

- Divide both sides by 0.2

∴ 60 = x

Lee sold 60 magazine

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Answer:

1/6y + 1/6(y + 12) - 2

Answer:

C

Step-by-step explanation:

Edge 2020

Allen and Beverly both thought of the number 18. When Allen doubled the number and added 15, he got 51. Beverly, in reverse order, subtracted 15 from the number and then doubled it to get 6.

Let the number that Allen and Beverly thought of be represented by 'x'.

Allen doubled the number and added 15 to the result, which gives us the equation:2x + 15 = 51

Now, we need to solve for 'x' to find the original number.

Subtract 15 from both sides of the equation: 2x = 51 - 15

2x = 36

Now, divide both sides by 2 to isolate 'x': x = 36 / 2

x = 18

So, Allen and Beverly both thought of the number 18.

Now, Beverly performs the same operations but in reverse order: 1. She starts with the number 18.

2. She subtracts 15 from it:18 - 15 = 3

3. Then, she doubles the result:2 * 3 = 6

So, Beverly gets the result of 6 by performing the same operations in reverse order.

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Answer:

12 + 2g ?

Step-by-step explanation:

6 + 6 = 12. g + g = 2g. So together you get 12 + 2g. I am not 100% sure.

Answer:

x= 1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

3(1)+3(-x/3)=3(5x/3)

3-x=5x

3=x+5x

3=6x

x=3/6

simplify

x=1/2

The number of Douglas fir pine trees is 350, and the number of Ponderosa pine trees is 500

From the question, we are to determine the number of each kind of pine trees.

Let x represent Douglas fir pine trees

and y represent Ponderosa pine trees

From the first statement - There are 850 Douglas fir and Ponderosa pine trees

We can write that

x + y = 850 ------------- (1)

Also,

The company paid an average of $300 for each Douglas fir and $225 for each Ponderosa pine; and the company paid $217,500 for the trees.

From this statement, we can write that

300x + 225y = 217500  ---------------- (2)

Now, we will solve the equations simultaneously

From equation (1)

x + y = 850

Then,

x = 850 - y ------------ (3)

Substitute this into equation (2)

300x + 225y = 217500

300(850-y) + 225y = 217500

255000 -300y + 225y = 217500

255000 - 75y = 217500

255000 - 217500 = 75y

37500 = 75y

∴ y = 37500/75

y = 500

Substitute the value of y into equation (3)

x = 850 - y

x = 850 - 500

x = 350

∴ x = 350 and y = 500

Hence, the number of Douglas fir pine trees is 350, and the number of Ponderosa pine trees is 500

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Answer:

23.5

Step-by-step explanation:

[tex]\text{Hey there!}[/tex]

[tex]\text{In order for you to solve for you solve for the equation, you have to do}\\\text{PEMDAS}[/tex]

[tex]\text{PEMDAS means}\downarrow\\\text{Parentheses}\\\text{Exponents}\\\text{Multiplication}\\\text{Division}\\\text{Addition}\\\text{Subtraction}[/tex]

[tex]\text{In this equation we have}\downarrow\\\bullet\text{Multiplication}\\\bullet\text{Division}\\\bullet\text{Addition}[/tex]

[tex]\bf{15\times18+\dfrac{12}{3} +9}\\\\\\\bf{15\times18=270}\\\\\\\bf{\dfrac{12}{3} = 4}\\\\\\\bf{270+4+9}\\\\\\\bf{270+4=270}\\\\\\\bf{274+9=answer}\\\\\\\boxed{\bf{Answer}:283}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

you multiply the second equation by -2.

Step-by-step explanation:

to get rid of y and find x. Then you plug x into one of the equations to find y

Answer:

[tex]Any\ two\ equations\ x,\ 54.57-x\\\\For\ example\ 23.37+31.20=54.57[/tex]

Step-by-step explanation:

[tex]Let\ first\ decimal=x\\\\Second\ decimal=y\\\\x+y=54.57\\\\y=54.57-x\\\\so\ any\ two\ decimal\ x\ and\ 54.57-x\ will\ give\ 54.57\\\\If\ we\ take\ first\ decimal(x)=23.37\\\\second\ decimal=54.57-23.37\\\\second\ decimal=31.20\\\\\Rightarrow 23.37+31.20=54.57[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\mathsf{The\ slope\ formula\ is: \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\mathsf{y_2=2}\\\mathsf{y_1=6}[/tex]

[tex]\mathsf{x_2=5}\\\mathsf{x_1=3}[/tex]

[tex]\mathsf{Equation: \dfrac{2-6}{5-3}}\\\\\bullet\mathsf{2-6=-4\leftarrow your\ \bf{y}\mathsf{\ value}}\\\\\bullet{\mathsf{5-3=2\leftarrow your\ \bf{x}\ \mathsf{value}}}\\\\\mathsf{New\ equation/answer:\ \dfrac{-4}{2}}\\\\\boxed{\bf{Answer:\mathsf{-2\ or\ \dfrac{-4}{2}}}}[/tex]

[tex]\text{Good luck on your assignment enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

x = −10

Step-by-step explanation:

1. Add 12.11x to both sides.

−10.5 = 75.6 − 3.5x + 12.11x

2. Simplify 75.6 - 3.5x + 12.11x to 75.6 + 8.61x.

−10.5 = 75.6 + 8.61x

3. Subtract 75.6 from both sides.

−10.5 − 75.6 = 8.61x

4. Simplify −10.5 −75.6  to −86.1.

−86.1 = 8.61x

5. Divide both sides by 8.61.

​​[tex]-\frac{8.61}{86.1}[/tex] = x

6. Simply [tex]-\frac{8.61}{86.1}[/tex] to 10

−10 = x

7. Flip it.

x = −10

Answer:

20

Step-by-step explanation:

Yellow, Green, Red, Green, Blue

Yellow, Red, Green, Red, Blue

Yellow, Blue, Red, Blue, Green

Yellow, Blue, Green, Blue, Red

5x4 = 20 because those are all the possible ways with yellow as the first building color, so there are 4 possible ways with yellow being in front, meaning all five of the colors have 4 possible ways of being in front. so 5x4=20

Answer:

84

Step-by-step explanation:

84 cause there will be 108 ways - 24 ways

Answer:5-y=a

Step-by-step explanation:

Answer:

the correct answer is B

Answer: b

i just wrote it down on paper and used a calculator to reassure.

Answer:

Tina makes per hours [tex]=\$11.925[/tex]

Step-by-step explanation:

Tina makes [tex]8[/tex] hours [tex]=\$10.40[/tex]

and additional tips [tex]=\$85[/tex]

total amount makes for [tex]8[/tex] hours [tex]= \$10.40+\$85[/tex]

total amount makes for [tex]8[/tex] hours [tex]=\$95.40[/tex]

total amount makes for [tex]1[/tex] hours [tex]=\frac{total\ amount}{total\ time}\\\\=\frac{\$95.40}{8}\\\\=\$11.925[/tex]

The distance between the two sailboats is approximately 2,197 feet.

1. Find Distances to Boats:

  - Use the tangent function for each angle of depression to find the distances from the observation deck to each sailboat. For boat 1 (42 degrees), use [tex]\(\tan(42^\circ) = \frac{\text{height}}{\text{distance}}\)[/tex], and for boat 2 (29 degrees), use [tex]\(\tan(29^\circ) = \frac{\text{height}}{\text{distance}}\)[/tex].

2. **Calculate Individual Distances:**

  - For Boat 1: [tex]\( \text{Distance}_{\text{Boat 1}} = \frac{\text{height}}{\tan(42^\circ)} \)[/tex]

  - For Boat 2: [tex]\( \text{Distance}_{\text{Boat 2}} = \frac{\text{height}}{\tan(29^\circ)} \)[/tex]

3. Determine Distance Between Boats:

  - The distance between the two boats is [tex]\( \text{Distance}_{\text{Boat 1}} - \text{Distance}_{\text{Boat 2}} \)[/tex].

4. Final Answer:

  - The final answer is the distance between the two sailboats, which is approximately 2,197 feet.

Answer:

[tex](x^2)^2=x^4[/tex]

Step-by-step explanation:

Because of the power of a power property states that [tex]((x^n)^m)=x^{n\times{m}}[/tex], where n and m are real numbers, then, the expression you have just posted can be simplified by applying this property to [tex](x^2)^2=x^{2\times2}=x^4[/tex].

Answer: yes

Step-by-step explanation:Can you brainless me

Answer:

b 25

Step-by-step explanation:

Answer: its c: 30

Step-by-step explanation:

i just got this wrong so haha

Answer:

Hello, Subtract 4x 4 x from both sides of the equation. Divide each term by 3 3 and simplify. Divide each term in 3y=−4x+15 3 y = - 4 x + 15 by 3 3 . Use the slope-intercept form to find the slope and y-intercept.

Hope This Helps!

Answer:

You just divide the numbers to get the hourly pay.

98÷5÷2

$9.80/hr

Answer:

b

Step-by-step explanation: i just know

Answer:

bb

Step-by-step explanation:

Many of the colors in them were "home dyed," as commercial dyes were unknown is the correct answer because "As" correctly begins the subordinate clause and shows the relationship to the main clause