need ASAP! please help with this. ​

Factorization is a mathematical process of breaking down a number or an expression into smaller numbers or simpler expressions that can be multiplied together to get the original number or expression.

Expressions, which are essentially mathematical statements containing numbers and letters, can be factorized in algebra. For illustration, consider the phrase 2x + 4. Finding the expressions or numbers that are common to each term allows us to factorize the expression. Since 2 appears in both terms, we can remove it by factoring to get 2(x + 2).

Given equation =  [tex]2x^{2} + 7x + 6[/tex]
                         ⇒   [tex]2x^{2} + 4x + 3x + 6[/tex]

                         ⇒ [tex]2x ( x+2) +3(x+2)[/tex]

                         ⇒[tex](2x + 3) (x+2)[/tex]

Therefore the factors of the expression [tex]2x^{2} + 7x + 6[/tex] are [tex](2x + 3) (x+2)[/tex].

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Answer:

6600 is the answer

Step-by-step explanation:

The prism is a right hexagonal prism.

The lateral area of the right hexagonal prism is 1008 square centimeters.

The sum of the area of a regular hexagon is 187.06 cm².

The surface area of the prism is 1196.06 cm².

We have,

7)

The prism is a right hexagonal prism.

8)

Perimeter = 6 x side length = 6 x 12 cm = 72 cm

Each rectangular face of the prism has a height of 14 cm and a width equal to one of the sides of the hexagon, which is 12 cm.

The area of each face.

= height x width

= 14 cm x 12 cm

= 168 cm²

And,

Lateral Area

= 6 x Area

= 6 x 168 cm²

= 1008 cm^2

9)

The formula for the area of a regular hexagon is given by:

Area = (3 x sqrt(3) / 2) x side length^2

Side length = 12 cm

Area = (3 x √(3) / 2) x 12²

Area = (3 x √(3) / 2) x 144

Area = 54 x √(3)

Area ≈ 93.53 cm² (rounded to two decimal places)

Now,

The sum of the area of a regular hexagon.

= 2 x 93.53

= 187.06 cm²

10)

There are 6 surfaces.

Each surface is in rectangular shape.

So,

Surface area

= 6 x (12 x 14)

= 1008 cm²

And,

The surface area of the prism.

= 1008 + 187.06

= 1196.06 cm²

Therefore,

The prism is a right hexagonal prism.

The lateral area of the right hexagonal prism is 1008 square centimeters.

The sum of the area of a regular hexagon is 187.06 cm².

The surface area of the prism is 1196.06 cm².

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The equation to calculate an object's speed is Speed = Distance ÷ Time.

Option A is the correct answer.

We have,

Speed is the ratio of distance and time.

Mathematically,

It can be written as,

Speed = Distance / Time

Speed = Distance ÷ Time

Thus,

The equation to calculate an object's speed is Speed = Distance ÷ Time.

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Writing the correct number relies on what our number system calls the place value system. The 9, the 3, and the 1 are all located in different spots in the larger number, and each of them is called a digit.

Putting the digits in the wrong locations could result in disaster when dealing with money and in many other situations.

The probability that a randomly selected carton has a puncture or a smashed corner is 17.5%.

Given that, a company has 8% puncture, 10% have a smashed corner, and 0.5% have both a puncture and a smashed corner cartons,

We need to find the probability that a randomly selected carton has a puncture or a smashed corner,

So,

P(A or B) = P(A) + P(B) - P(A and B)

= 0.08 + 0.10 - 0.005

= 0.175

= 17.5%

Hence, the probability that a randomly selected carton has a puncture or a smashed corner is 17.5%.

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The edge length of one cube-shaped box used to store canned goods is 2 feet.

The surface area of a cube-shaped box is given as 24 square feet. Let's assume that the length of each edge of the cube is 'a'.

The surface area of the cube is given as 6a² since a cube has 6 faces, each with an area of 'a²'.

We are given that the surface area of one box is 24 square feet. Therefore,

6a² = 24

Dividing both sides by 6, we get

a² = 4

Taking the square root of both sides, we get:

a = 2

Therefore, the edge length of one box is 2 feet.

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Answer:

Ryan: (100/13)(1/1,609.34)(3,600) =

17.21 miles per hour

Ryan is faster than Juan, by about 2.21 miles per hour

Answer:20

Step-by-step explanation:

40/2=20

20 days of giving away 2 tickets

The volumes of the image for each given value of k are computed below

From the question, we have the following parameters that can be used in our computation:

Volume = 8

Scale factor = k

The volume of the image  is calculated as

Volume = 8k^3

Using the values of k, we have

Volume = 8(1/2)^3 = 1

Volume = 8(0.6)^3 = 1.728

Volume = 8(1)^3 = 8

Volume = 8(1.5)^3 = 27

Hence, the volumes are calculaed above

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The exact value for the trigonometric function of numbers is derived to be √3/2.

Trigonometric identities are equations that involve the trigonometric functions (such as sine, cosine, tangent, cosecant, secant and cotangent) and are true for all possible values of the variables involved. These identities can be used to simplify trigonometric expressions, solve equations, and prove other mathematical statements.

Then sum and difference identities states that:

sin(A ± B) = sinAcosB ± cosAsinB

cos(A ± B) = cosAcosB ∓ sinAsinB

so;

sin(11°) cos(49°) + cos(11°) sin(49°) = sin(11 + 49)

sin(11°) cos(49°) + cos(11°) sin(49°) = sin(60°)

sin(11°) cos(49°) + cos(11°) sin(49°) = √3/2.

Therefore, the exact value for the trigonometric function of numbers is derived to be √3/2.

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Answer:

a) y = -2x + 3

b) y = -3x + 7

c) y = -1/2x + 4

d) y = 2

Step-by-step explanation:

Gradient is also known as slope

a) y = mx + b

3 = (-2)0 + b

b = 3

y = -2x + 3

b) y = mx + b

1 = (-3)(2) + b

1 = -6 + b

b = 7

y = -3x + 7

c) Slope m = (y2 - y1)/(x2 - x1)

m = (2 - 3)/(4 - 2) = -1/2

y = mx + b

3 = -1/2(2) + b

3 = -1 + b

b = 4

y = -1/2x + 4

d) The x‐axis or any line parallel to the x‐axis has a slope of 0.

y = mx + b

2 = -3(0) + b

b = 2

y = 2

Answer:

a) The equation of this line is y = -2x + 3

b) The equation of this line is y = -3x + 7

c) The equation of this line is y = -1/2x + 4 or y = -0.5x + 4

d) The equation of this line is y = 2

Step-by-step explanation:

The equation of a line can be written in the form y = mx + c, where m is the gradient and c is the y-intercept.

a) The equation of the line with a gradient of -2 and cutting the y-axis at 3 can be found using the point-slope form of a linear equation. The point-slope form is given by y - y1 = m(x - x1), where m is the gradient and (x1, y1) is a point on the line. Substituting m = -2 and (x1, y1) = (0, 3), we get:

y - 3 = -2(x - 0)

Simplifying the right-hand side gives:

y - 3 = -2x

Adding 3 to both sides gives the final equation:

y = -2x + 3

b) The equation of the line with a gradient of -3 and passing through the point (2, 1) can be found using the point-slope form again. Substituting m = -3 and (x1, y1) = (2, 1), we get:

y - 1 = -3(x - 2)

Simplifying the right-hand side gives:

y - 1 = -3x + 6

Adding 1 to both sides gives the final equation:

y = -3x + 7

c) To find the equation of the line passing through the points (2, 3) and (4, 2), we first need to find its gradient. The gradient is given by:

m = (y2 - y1)/(x2 - x1)

Substituting the coordinates of the two points, we get:

m = (2 - 3)/(4 - 2) = -1/2 or -0.5

Now, we can use the point-slope form again, this time with (x1, y1) = (2, 3) and m = -1/2:

y - 3 = (-1/2)(x - 2)

Simplifying the right-hand side gives:

y - 3 = (-1/2)x + 1

Adding 3 to both sides gives the final equation:

y = (-1/2)x + 4 or y = -0.5x + 4

d)The line is parallel to the x-axis and passes through the point (-3 ; 2). A line parallel to the x-axis has a gradient of 0. The general equation of a line is y = mx + c, where m is the gradient and c is the y-intercept. Since the gradient is 0, the equation becomes y = c. Since the line passes through the point (-3 ; 2), we can substitute y = 2 into the equation to find that c = 2. Therefore, the equation of this line is y = 2.

Ask a dif site if this one dont have it

Answer:

Step-by-step explanation:

We can start by drawing a diagram of the situation:

markdown

Copy code

                     *

                    / \

                   /   \

                  /     \

                 /       \

         _______/_________\_______

              4ft         4ft

               |          |

              1ft        h ft

We can see that the distance from the center of the wheel to the white plank is also 4 feet (since the radius of the wheel is 4 feet).

Next, we need to find the height of the white plank after the wheel is rolled forward through an angle of π/3 radians.

To do this, we can use trigonometry. Let's call the height of the white plank after the motion "h". We can use the sine function to relate the angle through which the wheel is rolled and the height of the plank:

sin(π/3) = h/4

Simplifying this equation, we get:

h = 4sin(π/3)

h = 4(√3/2)

h = 2√3

Therefore, the height of the white plank after the motion is 2√3 feet from the ground.

Being a student and preferring logo A are dependent events.

We have,

Being a student and preferring logo A are not independent events because they are related to each other.

If a student prefers logo A, then they belong to the group of students who prefer logo A.

On the other hand, if a student belongs to a different group, such as the group of students who prefer logo B or are undecided, then they cannot be said to prefer logo A.

In general, two events are considered independent if the occurrence of one event does not affect the probability of the other event occurring.

However,

In this case, knowing whether someone is a student does affect the probability of them preferring logo A.

Thus,

Being a student and preferring logo A are dependent events.

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The probability of a random point which is located on  AK  will be present on BE is equal to 0.3.

From the attached figure we have,

On the number line point A is located at -10.

And on the same number line point K is at 10.

Distance between AK = ( 10 ) - ( -10 )

⇒ Distance between AK = 10 + 10

⇒ Distance between AK = 20

Now, on the same number line location of point B is -8.

And location of point E is -2.

Length of BE = ( -2 ) - ( -8 )

⇒ Length of BE = -2 + 8

⇒ Length of BE = 6

Probability of random point on AK will be on BE

= Favorable outcomes / total number of outcomes

= Length of BE / Length of AK

= 6 / 20

= 3 / 10

= 0.3

Therefore, the probability of a random point located on AK will be on BE is equal to 0.3.

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The above question is incomplete , the complete question is:

What is the probability that a random point on AK will be on BE?

Attached figure.

The solution to the system of inequalities 2x − y < 4 and x + y < −1 is the intersection of the shaded regions below the lines 2x - y = 4 and x + y = -1, labeled AB on the graph. Regions A and B represent the solutions to each individual inequality.

To solve the system of inequalities 2x − y < 4 and x + y < −1, we can use the following steps

Solve each inequality for y in terms of x

2x - 4 < y

-x - 1 < y

Plot the boundary lines for each inequality as dotted lines. To do this, we can use the equality signs instead of the inequality signs.

2x - 4 = y

-x - 1 = y

Shade the region that satisfies each inequality. To do this, we can test a point that is not on the boundary line in each inequality. For example, we can test (0,0) in the first inequality

2(0) - 0 < 4

0 < 4

Since (0,0) satisfies the first inequality, we shade the region below the line 2x - y = 4. Similarly, we can test (0,-2) in the second inequality

(0) + (-2) < -1

-2 < -1

Since (0,-2) satisfies the second inequality, we shade the region below the line x + y = -1.

The solution to the system of inequalities is the intersection of the shaded regions, which is labeled AB in the graph. The shaded region labeled AB is the region that satisfies both inequalities, which is the region below both lines.

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Answer:

C is most likely

Step-by-step explanation:

Answer:

d. The number of white marbles in the bag was equal to the number of blue marbles.

The surafce area of the cone with a slant height of 14 in and a diameter of 6 in is 160.2 in².

A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.

The surface area of a cone can be expressed as;

SA = πrl + πr²

Where r is radius of the base, l is the slant height of the cone and π is constant pi.

Given that:

Slant height l = 14 in

Diameter d = 6 in

Radius r = diameter/2 = 6/2 = 3in

S.A = ?

Plug the given values into the above formula and solve for the surface area.

SA = πrl + πr²

SA = ( π × 3in × 14in ) + ( π × (3in)² )

SA = 160.2 in²

Therefore, the surface area is 160.2 in².

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The correct options are:

[tex]8(x^2 + 2x) = -3\\\\8(x^2 + 2x + 1) = -3 + 8[/tex]

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

Now, We have the quadratic equation is:

[tex]8x^2 + 16x + 3 = 0[/tex]

We separate variables from constants

[tex]8x^2+16x = -3[/tex]

Taking the common factor  8

[tex]8(x^2+2x)=-3[/tex]

Completing squares in the brackets and balancing the equation in the right side

[tex]8(x^2+2x+1)=-3+8[/tex]

Factoring the perfect square

[tex]8(x+1)^2=5[/tex]

[tex](x+1)^2=\frac{5}{8}[/tex]

[tex](x+1)=[/tex] ± [tex]\sqrt{\frac{5}{8} }[/tex]

x = -1 ± [tex]\sqrt{\frac{5}{8} }[/tex]

The correct options are:

[tex]8(x^2 + 2x) = -3\\\\8(x^2 + 2x + 1) = -3 + 8[/tex]

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

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The given question is incomplete, complete question is:

Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options.

8(x2 + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot

8(x2 + 2x + 1) = 3 + 1

8(x2 + 2x) = –3

The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.

We have,

We can use trigonometry to solve this problem.

          C

        /   \

       /     \

      /θ     \

     /         \

    /           \

   A-------------B

          50 ft

In this diagram, A represents the launch pad, B represents the maximum altitude of the rocket, C represents the position of the photographer, and θ represents the angle at which the tripod should be set.

We want to find θ.

First, we can find the height of the triangle ABC using the Pythagorean theorem:

AB² = AC² + BC²

200² = AC² + 50²

AC² = 200² - 50²

AC = √(200² - 50²)

AC = 190.526 ft

Next, we can use the tangent function to find θ:

tan(θ) = opposite/adjacent = AB/BC = 200/50 = 4

Taking the arctangent of both sides, we get:

θ = [tex]tan^{-1}(4)[/tex]

θ = 75.96 degrees

Therefore,

The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.

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One pound of spice mix will have 1 1/9 cups of cinnamon.

Given that in 3/4 pound of a spice mix there are 5/6 cups of cinnamon,

we need to find the amount of cinnamon in a pound,

Since, 3/4 pound = 5/6 cinnamon

So,

1 pound = 5/6 x 4/3

= 20/18 = 10/9

= 1 1/9 cups

Hence, one pound of spice mix will have 1 1/9 cups of cinnamon.

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The result of the multiplication of the complex numbers z₁ and z₂ expressed in their polar form is -0.866 + 0.5i.

To multiply complex numbers expressed in polar form, we need to multiply their magnitudes and add their angles.

Let z₁ = r₁(cosθ₁ + isinθ₁) and z₂ = r₂(cosθ₂ + isinθ₂) be two complex numbers in polar form. Then their product is given by:

z₁*z₂ = r₁r₂(cosθ₁cosθ₂ - sinθ₁sinθ₂ + i(cosθ₁sinθ₂ + sinθ₁cosθ₂))

In this case, we have z₁ = 230° and z₂ = 540°. So, we need to convert these angles to radians and then find the cosine and sine values:

z₁ = 230° = 230/180 * π radians = 1.27 radians

z₂ = 540° = 540/180 * π radians = 3π radians

Now we can substitute these values in the formula above:

z₁z₂ = r₁r₂(cosθ₁cosθ₂ - sinθ₁sinθ₂ + i(cosθ₁sinθ₂ + sinθ₁cosθ₂))

= 1 * 1(cos1.27cos3π - sin1.27sin3π + i(cos1.27sin3π + sin1.27*cos3π))

= -0.866 + 0.5i

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Applying the right triangle altitude theorem, the value of x in the given right triangle is: x = 4.

According to the right triangle altitude theorem, we have the following from the theorem as:

h = √(xy), where h is the altitude of the triangle and x and y are the segments divided on the hypotenuse.

Therefore, we have:

2√6 = √(x*3)

(2√6)² = x*3

12 = 3x

x = 12/3

x = 4

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Answer: 46

Step-by-step explanation:

368/8 = 46

36/8 = 4R4

48/8 = 6

46

The resistance of 1800 feet of the same sort of wire with a 0.45in diameter is roughly 15037.45 ohms.

Let R be the resistance of the wire,

L be the length of the wire,

d be the diameter of the wire, and

k be a constant of variation.

Then we have the equation:

R = k * L / d^2

Solving for k to find the resistance of a wire of varying length and diameter.

We can create an equation using the information provided:

15611 = k * 700 / 0.2^2

Solving for k, we get:

k = 15611 * 0.2^2 / 700

k ≈ 0.1799

Using k to calculate the resistance of a wire with a length of 1800 feet and a diameter of 0.45 inches:

15037.45 ohms = 0.1799 * 1800 / 0.452 R

As a result, the resistance of 1800 feet of the same sort of wire with a 0.45in diameter is roughly 15037.45 ohms.

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The solution is given below.

The result of the mixed digits given when expressed as improper fractions are as follows;

3 1/2 = ((2×3)+1)/2 = 7/2

7 4/5 = ((5×7)+4)/5 = 39/5

5 3/4 = ((4×5)+3)/4 = 23/4

4 1/3 = ((3×4)+1)/3 = 13/3

4 2/3 = ((3×4)+2)/3 = 14/3

5 1/5 = ((5×5)+1)/5 = 26/5

8 2/3 = ((3×8)+2)/3 = 26/3

2 3/5 = ((5×2)+3)/5 = 13/5

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complete question:

3 1/2 as a improper fraction7 and 4/5 as an improper fraction5 3/4 as an improper fraction4 1/3 as an improper fraction4 + 2/3 as an improper fraction5 1/5 as an improper fraction8 2/3 as an improper fraction 2 3/5 as an improper fraction

The value of z with a p-value of 0.262 is given as follows:

z = -0.64.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, we want the z-score with a p-value of 0.262, hence, looking at the z-table, we have that it is:

z = -0.64.

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