Simplify 12 × 10 ^8/ 4 × 10^5 and leave in ordinary form

Final answer:

To solve the quadratic equation 2x² + 9x - 5 = 0, the quadratic formula is used, and after calculating the discriminant and applying the formula, one of the roots is found to be 1/2, which is option C.

Explanation:

To solve the quadratic equation 2x2 + 9x - 5 = 0, we can use the quadratic formula which is x = (-b ± √(b2 - 4ac)) / (2a). In this equation, a equals 2, b equals 9, and c equals -5.

Firstly, we need to calculate the discriminant: b2 - 4ac which is 92 - 4 * 2 * (-5) = 81 + 40 = 121.

Since the discriminant is a perfect square, we can proceed with the formula: x = (-9 ± √(121)) / (2*2). The square root of 121 is 11, so we have:

Thus, one of the roots of the equation is 1/2, which corresponds to option C.

Answer:

[tex](-\infty,+\infty)[/tex]

Step-by-step explanation:

The given inequality is 3x-2>4 or [tex]5x-3\leq 7[/tex]

We group similar terms to obtain: 3x>4+2 or [tex]5x\le7+3[/tex]

Simplify to get:

3x>6 or [tex]5x\le10[/tex]

x>2 or [tex]x\le 2[/tex]

This implies that the solution set is all real numbers.

The solution in interval notation is [tex](-\infty,+\infty)[/tex]

Answer:

k(x)=x^3+9x+5x^2+45

Step-by-step explanation:

k(x)=x^3+5x^2+9x+45

k(x)=x^2(x+5)+9(x+5)

K(x)=(x+5)(x^2+9)

k(x)=x^3+9x+5x^2+45

Answer:

it's B

Step-by-step explanation:

a triangle cannot two obtuse angles

A traingle does not contain two obtuse angles. Option B is correct.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.

Here,
A triangle cannot contain two obtuse angles.

A triangle cannot have the two obtuse angle, becaue for a triangle sum of the iternal angle must not exceeds 180°

Thus, A traingle does not contain two obtuse angles. Option B is correct.

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Answer:

2(x+4)=6+x

Step-by-step explanation:

Let x be our variable.

We want to write about equation using x that gives us -2 as solution.

We can write many of such equation.

An example is:

[tex]2( x + 4) = 6 + x[/tex]We cross check.

Let us expand:

[tex]2x + 8 = 6 + x[/tex]

Group similar terms:

[tex]2x - x = 6 - 8[/tex]

Combine similar terms:

[tex]x = - 2[/tex]

Answer:

60 hours

Step-by-step explanation:

you multiply 5×12 and then you get 60

Answer:

13.1mi

Step-by-step explanation:

Length(l) = 4.1mi

Breadth(b) = 2.5 mi

Perimeter of a rectangle = addition of all sides that is = l + l + b + b as a rectangle has 2 opposite equal length and also breadth.

Therefore perimeter = 4.1 + 4.1 + 2.5 + 2.5

= 8.1 + 5

=13.1 mi

I hope this was helpful, Please mark as brainliest

Answer:

13.2 mi

Step-by-step explanation:

Perimeter of a rectangle

= 2 (L + W)

From the question

L = 4.1

W = 2.5

Using the above formula , we have P = 2 (4.1 + 2.5)

Using the distributive property

2x4.1 + 2x2.5

8.2 + 5

13.2mi

Answer:

x = 10/3

Step-by-step explanation:

(x - 1)/5*35 = (4x + 3)/35*35

7(x - 1) = 4x + 3

7x - 7 - 4x + 7 = 4x + 3 - 4x + 7

3x/3 = 10/3

x = 10/3

Answer:L F and K G

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The answer is not A because:

lines gk and kg are the same line

The answer is not B because:

lines il and gk are perpendicular if they were to touch

The answer is not C because:

line fl and il are perpendicular

The answer IS D because:

lines fl and gk are parallel because they will never touch

Answer:

The dimensions of the wall are 100 ft x 100 ft

Step-by-step explanation:

we know that

The perimeter of a rectangular wall is

[tex]P=2(x+y)[/tex]

where

x is the length

y is the width

we have

[tex]P=400\ ft[/tex]

so

[tex]400=2(x+y)[/tex]

simplify

[tex]200=x+y[/tex]

[tex]y=200-x[/tex] ----> equation A

The area of a rectangular wall is equal to

[tex]A=xy[/tex] ----> equation B

substitute equation A in equation B

[tex]A=x(200-x)\\A=-x^2+200x[/tex]

This is the equation of a vertical parabola open downward (because the leading coefficient is negative)

The vertex represent a maximum

Convert the quadratic equation in vertex form

[tex]A=-x^2+200x[/tex]

Factor -1

[tex]A=-(x^2-200x)[/tex]

Complete the square

[tex]A=-(x^2-200x+100^2)+100^2[/tex]

[tex]A=-(x^2-200x+10,000)+10,000[/tex]

Rewrite as perfect squares

[tex]A=-(x-100)^2+10,000[/tex] ----> equation in vertex form

The vertex is the point (100,10,000)

The x-coordinate of the vertex represent the length of the wall for a maximum area

so

[tex]x=100\ ft[/tex]

Find the value of y

equation A

[tex]y=200-(100)=100\ ft[/tex]

therefore

The dimensions of the wall are 100 ft x 100 ft

To find the dimensions of a rectangular wall that maximizes the area enclosed by 400 feet of brick, you can use the formula for the area of a rectangle and find where the derivative of the area equation equals zero. By solving the resulting equations, you can determine the dimensions of the wall that will maximize the enclosed area.

To find the dimensions of a rectangular wall that maximizes the enclosed area with 400 feet of brick, we need to use the formula for the area of a rectangle, which is length times width. So, let's represent the width of the wall as x and the length as y. Since we have 400 feet of brick, we can write the equation 2x + 2y = 400. We can rearrange this equation to solve for y: y = (400 - 2x)/2. Now we have the area equation A = x * y,

which becomes A = x * ((400 - 2x)/2). To find the maximum area, we can take the derivative of A with respect to x and set it equal to zero: (400 - 4x)/2 = 0. Solving for x, we get x = 100. Substituting this back into the y equation, we find y = 100 as well. Therefore, the dimensions of the rectangular wall that maximize the area enclosed by the brick are 100 feet by 100 feet.

Answer:

55 square feet

Step-by-step explanation:

We can represent the area as a sum of two rectangles.

A = 8 * 5 + 5 * 3 = 40 + 15 = 55 square feet

Answer:

Step-by-step explanation:

Area of rectangle at top

length =5ft; breadth = 3 ft

Area = 5*3 = 15 sq.ft

Area of rectangle at bottom

length = 8ft ; breadth =8-3 = 5 feet

Area = 8*5 = 40 sq.ft

Area of the figure = 15 + 40 = 55 sq.ft

Answer:

look at shown picture.

Answer:

The answer is 4

Step-by-step explanation:

Why?...Because this is a site where everything is fake and incorrect.

Conviction of DUI results in increased fines and jail time if aggravating factors such as high alcohol levels or prior offenses are present.

If you are convicted of DUI (driving under the influence), your fine and jail time will typically be increased if certain aggravating factors are present. These can include having a high blood alcohol content, previous DUI convictions, causing an accident while DUI, especially if injury or death occurred, having minors in the vehicle, and others. The penalties are enhanced due to the increased risk and harm these factors represent.

Answer:

A

Step-by-step explanation:

-3×5+4×3+10×2

=-15+12+20

=17

Answer:

A: 3x5 + 4x3 +10x2

Step-by-step explanation:

Answer:

x>7

Step-by-step explanation:

2x+6>20

2x>20-6

2x>14

x>14/2

x>7

8.2is the answer

Step-by-step explanation:

|CB|+8

Answer:

d

step-by-step explanation:

Do you do Accelus Online School?

I do that too!

Sorry i'd totally answer this question but i'm struggling toooo

Hello there n ÷ 5 - 9  = 2!

Here's how i solved it:

The quotient of a number and -5, decreased by 9, is 2

"is 2" means the result is 2, so we can have one side of the equation set up to look like this: = 2.

The quotient of a number and -5, decreased by 9, is 2

This looks like: n ÷ 5

The quotient of a number and -5, decreased by 9, is 2

We are taking 9 away from the previous expression, so n ÷ 5 - 9

Putting it all together, we have: n ÷ 5 - 9  = 2

The algebraic mathematical problem is to solve the equation x/-5 - 9 = 2. Simplifying this equation through a series of algebraic steps gives the result x=-55.

The subject of your question is algebra, a branch of mathematics. You are looking for a number which, when divided by -5 and then decreased by 9, equals 2. The equation that represents this problem is x/-5 - 9 = 2.

To solve for x, we would first get rid of the -9 from the left side of the equation. We do this by adding 9 to both sides of the equation. We then have x/-5 = 2 + 9, which simplifies to x/-5 = 11.

Next, we isolate x by multiplying both sides of the equation by -5. We now get x= -5*11, which gives x = -55. Thus, the number x that satisfies this equation is -55.

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Answer:

Step-by-step explanation:

i think its b or c

The confidence interval of the mean weight of all the coins is 8.0518g. The correct option is B.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used.

Given that a sample of 20 silver dollar coins is weighed. The mean of the sample is 8.0710 g and the standard deviation of the sample is 0.0411 g.

The confidence interval is calculated by the formula:-

CI = X ± z (S / √n)

CI = 8.0710 ± [ (1.96 x 0.0411) / √20 ]

CI = 8.0710 - 0.018

CI = 8.053 g

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Answer:

Position 12.

Step-by-step explanation:

It will be n the center of the bottom 23 numbers ( when the data is arranged in ascending order).

That is in position 12.

Answer:17

Step-by-step explanation:trust me use mathaway;)  mathaway dot com

Answer:

x=-41/3, y=6 (-41/3, 6).

Step-by-step explanation:

3x+4y=-17

y=-6*-1

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

3x+4y=-17

y=6

3x+4(6)=-17

3x+24=-17

3x=-17-24

3x=-41

x=-41/3

Answer:

x=-y/2

Step-by-step explanation:

1. The value of a variable that makes an equation true.

2. In chemistry, a solution is a homogeneous mixture composed of only one phase

The value of x in the equation  2.14x - 12.18 = 5.76 is  8.38.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, we have to solve for x or find the value of x in the equation

2.14x - 12.18 = 5.76.

2,14x = 5.76 + 12.18.

2.14x = 17.94.

x = (17.94/2.14).

x = 8.38.

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Final answer:

The sum of 8/15 and 2/5 is 14/15, which is closer to 1 than to 0 or 1/2 after finding a common denominator and adding the fractions.

Explanation:

To determine whether 8/15 + 2/5 is closer to 0, 1/2, or 1, you need to first find a common denominator for the fractions. The least common denominator for 15 and 5 is 15. You can then rewrite the second fraction, 2/5, with 15 as the denominator by multiplying both the numerator and denominator by 3, which gives you 6/15.

Now add the two fractions:

8/15 + 6/15 = 14/15

This sum is very close to 1, but still less than 1. Therefore, 14/15 is closest to 1.

To conceptualize this, you can think about the fractions in terms of division: 8 divided by 15 is a bit more than half, and 2 divided by 5 is exactly 0.4, which is also slightly less than half. Their sum is thus nearly a whole but not quite there, clearly indicating it's closer to 1 than to 0 or 1/2.

Answer:

The distance between the cruise ship and the sail boat is 517 feet.

Step-by-step explanation:

The cruise ship is 236 feet tall, and the sailboat is 236 tall; this means the distance between the top of the cruise ship and the top of the sail boat is

236 feet - 27 feet = 209 feet.

We also know that the angel of depression from the top of the cruise ship to the bottom of the cruise ship is 22°. This forms a right triangle as shown in the figure attached.

Now from trigonometry we get:

[tex]tan \: \theta = \dfrac{209}{d}[/tex]

[tex]d= \dfrac{209}{tan\:\theta }[/tex]

[tex]\boxed{d=517ft}[/tex]

The distance between the cruise ship and the sailboat is 517 feet.

Final answer:

To calculate the horizontal distance between the cruise ship and the sailboat, we subtract the sailboat's height from the cruise ship's height to get 209 feet, use the angle of depression and tangent function, and find that the distance between them is approximately 517.57 feet.

Explanation:

To find the distance between the cruise ship and the sailboat, we need to apply trigonometry. First, we determine the difference in height between the two, which is the cruise ship's height above the water subtracted by the sailboat's height. This will be 236 feet - 27 feet = 209 feet. Since the angle of depression from the cruise ship to the sailboat is 22 degrees, we can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side to the adjacent side.

The opposite side, in this case, is the difference in height (209 feet), and the adjacent side is the horizontal distance between the ships, which we're trying to find. Thus:

tangent(22 degrees) = opposite/adjacent

adjacent = opposite/tangent(22 degrees)

= 209 feet / tangent(22 degrees)

Now we calculate the tangent of 22 degrees and then divide 209 feet by this amount to find the distance between the two vessels.

Using a calculator, tangent(22 degrees) ≈ 0.4040, so:

adjacent ≈ 209 feet / 0.4040 ≈ 517.57 feet

Therefore, the horizontal distance between the cruise ship and the sailboat is approximately 517.57 feet.

Answer:

An example of a situation that you might not be able to use an equation with a single unknown is

[tex]x = \ln{e^x}[/tex]

Step-by-step explanation:

An example of a situation that you might not be able to use an equation with a single unknown is

[tex]x = \ln{e^x}[/tex]

The identity on both sides which results in 1 = 1 and thus the equation is not usable.

A situation where an equation with a single unknown cannot be effectively used is when you need to explore or solve multiple variables or dimensions, like best represented by physics-related problems. The number of unknowns should not exceed the number of equations for correct problem-solving. Equations with a single unknown may not always suffice, especially for problems involving various dimensions or variables.

An example of a situation where you may not be able to use an equation with a single unknown to understand is a problem that involves multiple elements or dimensions needing exploration. For instance, in physics, if you're calculating an object's motion, you may need to take into account various forces acting on it, its initial velocity, its acceleration, and the time. No single equation with just one unknown can solve this problem; you would need multiple equations to represent each of these dimensions.

Remember that the number of unknowns should not be larger than the number of equations. Otherwise, the problem can't be solved. Therefore, the complexity of your problem can sometimes make it impossible to use an equation with a single unknown. Physics is often an area where this is true, due largely to the dimensional consistency of equations.

Nevertheless, equations with a single unknown can often be combined together or manipulated to solve specific problem-solving strategies. Overall, while an equation with a single unknown is a powerful tool, it may not always be sufficient to understand every situation, especially those involving multiple dimensions or variables.

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